Space Charge Accumulation in Polymeric. High Voltage DC Cable Systems

Transcription

1 Space Chage ccumulation in Polymeic High Voltage DC Cable Systems

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3 Space Chage ccumulation in Polymeic High Voltage DC Cable Systems Poefschift te vekijging van de gaad van docto aan de Technische Univesiteit Delft op gezag van de Recto Magnificus pof. d. i. J. T. Fokkema voozitte van het College voo Pomoties, in het openbaa te vededigen, op dinsdag 28 novembe 2006 om 15:00 uu doo Riccado ODEG dottoe in ingegneia elettica, Politecnico di Milano geboen te Lecco (Italië)

4 Dit poefschift is goedgekeud doo de pomoto: Pof. d. J. J. Smit Samenstelling pomotiecommissie: Recto Magnificus, Pof. d. J. J. Smit, Pof. d. eng. J.. Feeia, Pof. i. W. L. Kling, Pof. d. i. E. F. Steennis, Pof. d. J. C. Fothegill, D. i. P. H. F. Moshuis, D. i. M. D. Veweij, Voozitte Technische Univesiteit Delft, pomoto Technische Univesiteit Delft Technische Univesiteit Delft/Eindhoven Technische Univesiteit Eindhoven Univesity of Leiceste, United Kingdom Technische Univesiteit Delft Technische Univesiteit Delft This eseach was funded by the Euopean Commission in the famewok of the Euopean poject enefits of HVDC Links in the Euopean Powe Electical System and Impoved HVDC Technology (contact ENK6-CT ). ISN Copyight 2006 by R. odega Cove: photogaph by uno van den Elshout copyight PhotologiX.nl Pinting: Optima Gafische Communicatie Rottedam, The Nethelands

5 He who loves pactice without theoy is like the sailo who boads ship without a udde and compass and neve knows whee he may cast. Leonado da Vinci i miei genitoi, i miglioi maesti che abbia mai avuto [To my paents, the best teaches I ve eve had] lla mia compagna, Yvonne, pe avemi insegnato a conoscee meglio me stesso [To my gilfiend Yvonne, who taught me moe about who I am]

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7 Peface This Ph.D. thesis was completed within the famewok of the poject HVDC ( enefits of HVDC Links in the Euopean Powe Electical System and Impoved HVDC Technology ) funded by the Euopean Commission. The HVDC poject was launched in Januay 2003 to povide a methodology and associated softwae and hadwae tools to assess the potential technical, economical and envionmental benefits and impacts of high-voltage diect cuent inteconnections embedded in the actual electical powe tansmission and distibution systems of the Euopean netwok. The poject investigated also the potential benefits of using envionmentally moe acceptable high-voltage diect cuent powe cable systems. Delft Univesity of Technology contibuted to the HVDC poject togethe with the following Euopean Patnes: Univesity of Leiceste (UK) Univesity of Suey (UK) Univesity of ologna (IT) Univesity Paul Sabatie, Toulouse III (FR) IECOS (UK) CESI (IT) Pysmian Cavi e Sistemi Enegia S..l. (IT) oealis (SW) TenneT (NL) Tena (IT) RTE (FR) Some of the data pesented in this thesis wee poduced by the poject Patnes in the famewok of the HVDC poject. When so, this is explicitly indicated in the thesis. vii

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9 Table of contents Peface vii Table of contents ix 1. Intoduction Geneal HVDC cable systems HVDC cable insulation Polymeic HVDC cable systems and space chages Histoical development of HVDC cables Space chage and space chage field Reseach and development tend fo space chage phenomena in HVDC polymeic cable insulation Objective of the pesent study Scientific contibution of the thesis to the field of polymeic HVDC cable systems Outline of the thesis Expeimental methods Test specimens Conduction cuent measuements Space chage measuements Geneal Pulsed electoacoustic method (PE) PE method fo multi-dielectic test objects PE method fo cable geomety test objects Space chage paametes ccuacy of the measuements Test conditions Tempeatue conditions Electical conditions Expeimental obsevation of space chage and electic field dynamics Conduction cuent measuements on XLPE and EPR flat specimens Intoduction Results Discussion Summay and conclusions Space chage measuements on XLPE-EPR flat intefaces Intoduction Results Discussion ix

10 Summay and conclusions Space chage measuements on MV-size XLPE cables Intoduction Results Discussion Summay and conclusions Space chage measuements on dual-dielectic mini-cables Intoduction Results Discussion Summay and conclusions Space chage measuements on MV-size models of cable joints Intoduction Results Discussion Summay and conclusions Conclusions Calculation of space chage and electic field in DC cable systems Intoduction Physical model Theoetical backgound Model of the insulation Numeical implementation of the physical model Results of the calculation Calculation vs. measuements Effect of the conductivity function on the calculated pattens Electic field in cable systems fo paticula situations Conclusions Space chage at intefaces in HVDC cable systems Intefaces in HVDC cable systems Space chage accumulation at the semicon-insulation inteface Chage accumulation mechanisms at the semicon-xlpe inteface ccumulation of chage at the semicon-xlpe inteface in the studied specimens Space chage accumulation at the dielectic inteface Mawxell-Wagne theoy fo the intefacial polaization Deviation fom the Maxwell-Wagne theoy: liteatue Deviation fom the Maxwell-Wagne theoy: expeimental esults Thee-laye model fo the dielectic inteface Suggestions on how to impove the macoscopic model fo space chage accumulation x

11 6. Feasibility study fo on-line on-site PE measuements Intoduction Implementation Conclusions Conclusions Space chage at dielectic discontinuities Space chage in cable systems that expeience a tempeatue dop acoss the insulation Recommendations and suggestions fo futhe studies Recommendations Recommendations fo PE testing on HVDC cable system insulation Recommendations fo the design of polymeic HVDC cable systems Recommendations fo the opeation on HVDC cable systems Suggestions fo futhe study ppendix Space chage measuements on multi-dielectics by means of the PE method Geneation of acoustic waves Calculation of electically-induced pessue waves DC voltage applied in absence of space chage and intefacial chage Space chage in the absence of DC voltage and intefacial chage Pesence of intefacial chage in absence of DC voltage and space chage DC voltage applied in pesence of space chage and intefacial chage coustic wave taveling and eflection coustic wave popagation coustic wave eflection Intepetation of detected acoustic signals Test specimens and test pocedues Measuement esults Intepetation of measuement esults Conclusions PE method fo cylindical test objects Diffeent type of PE set-ups Shape of the eath electode pplication of the pulsed voltage pplication of the pulse to the cables Effect of cylindical geomety on the amplitude of acoustic waves xi

12 C. ttenuation and dispesion of acoustic waves in the PE method C.1. Poblem identification C.2. Theoetical backgound C.3. Pocedue fo ecoveing the oiginal acoustic wavefom fom the attenuated and distoted wavefom D. Calibation D.1. Flat homogeneous test object D.2. Flat multi-dielectic test object D.3. Cylindical homogeneous test object D.4. Cylindical multi-dielectic test object E. Equations adopted in the numeical pocedue E.1. Poisson s equation fo the electic field E.2. Calculation of the chage-induced field E.2.1. Field induced by space chage in coaxial intefaces E.2.2. Field induced by intefacial chage in coaxial intefaces E.2.3. Geneal expession of the field E.3. Fouie s heat diffusion equation fo cables and cable joints Refeences List of abbeviations List of symbols Summay Samenvatting Sommaio cknowledgement Cuiculum Vitae xii

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15 Chapte 1 - Intoduction 1. Intoduction 1.1 Geneal HVDC cable systems Since the nineteen fifties, high voltage (HV) diect cuent (DC) cable systems have been used woldwide fo the tanspot of electical enegy. cable system consists of a cable and its accessoies, i.e. joints and teminations. Teminations ae needed at the ends of the cable cicuit, to gade the electic field and to connect the cable to the powe line. Joints ae equied when the cable becomes too long to be poduced in one length. Taditionally, HVDC cable systems have been used only when altenate cuent (C) technology could not be applied. The main eason fo this is that DC links need two convesion stations at the ends of the tansmission link. In the past, the convesion stations often inceased the costs of the poject too much. typical example of HVDC cable application is the sea-cossing enegy tanspot. In this case, C ovehead lines cannot be employed. Moeove, if the length of the sea cossing exceeds km, the use of C cables becomes unfeasible because of the high value of the capacitive eactive powe. Theefoe, HVDC cable systems ae the only technically applicable solution fo long distance undegound o submaine connections. The taditional estictions on the use of HVDC technology ae apidly changing, especially within Euope, giving a potential oppotunity fo application of HVDC cable systems. The actual Euopean tansmission netwok consists in fact of lage HVC synchonous zones, athe scacely inteconnected by HVDC links. New HVDC links ae a means fo einfocing the actual HVC Euopean tansmission netwok. The main dives fo HVC netwok einfocement by means of HVDC links ae [73, 154]: - The libealization of the electical enegy maket and the consequent incease of taded enegy ae leading to lage vaiations of the powe flows. This asks fo additional coss-bode tansmission capacity. - Decentalized powe geneation plants, in paticula wind enegy, ae inceasingly being intoduced in the netwoks. Decentalized geneation plants essentially opeate at vaiable conditions that may have an impact on the powe quality of the netwok, e.g. [136]. - Nowadays, moe difficulties ae encounteed in getting the necessay pemits to build additional ovehead tansmission lines. - The effect of magnetic fields on human health and the visual/noise impact ae ongoing contovesial debates because of which the public efains to accept new ovehead tansmission lines. 1

16 Chapte 1 - Intoduction In this famewok HVDC cable links can povide: - inteconnection between independent netwoks, inceasing the tansmission capacity and inceasing the possibilities fo enegy exchange; - the contol of eactive powe, which suppots the netwok stability and the powe quality (when voltage souce convetes VSC ae used); - elatively shot time fo deliveing a new link. s impotant as the pevious aspects, HVDC cable systems ae consideed envionmental fiendly, because of thei vey low visual impact and noise impact. Futhemoe, when using HVDC cables in a bipola configuation, pactically no magnetic field is poduced HVDC cable insulation The main concen about the employment of new HVDC cable links is the athe high cost of the connection. The cost of the connection could be significantly educed by using polyme-insulated HVDC cable systems (also called extuded HVDC cable systems) instead of mass-impegnated o oil-filled HVDC cable systems (also called lapped o oil-pape HVDC cable systems). The extusion poduction pocess is, in fact, simple and cheape than the pocess fo manufactuing lapped insulation. In addition, extuded cable systems pesent the following advantages if compaed to lapped cable systems: - no use of any impegnants o oil; - moe mechanical igidity, allowing the use of a thinne cable amo; - highe maximal woking tempeatue; - easie cable maintenance and easie component eplacement; - easie pepaation and mounting of cable joints. On the othe hand, HVDC mass-impegnated cables have been poven to be eliable ove many decades, while HVDC polymeic cables have been only ecently employed. The eason fo this will be explained in the next paagaph. 2

17 Chapte 1 - Intoduction 1.2. Polymeic HVDC cable systems and space chages Histoical development of polymeic HVDC cables The fist HVDC cable went into sevice in 1954, fo connecting the Gotland Island in the altic Sea to the Swedish mainland. This was a mass-impegnated cable. Since then, many HVDC cables have been employed all ove the wold. Most of these cables ae mass-impegnated o oil-filled insulated. Though the yeas, the powe tanspoted by the DC links and thei ated voltages have inceased, the cable systems have become longe, the C/DC convesion technology has changed, but massimpegnated and oil-filled insulation have been, in pactice, the only type of insulation to be used up to In that yea, the fist commecial HVDC polymeic cable system was put into sevice. This tend is in contast to what happened in the C cable technology, whee polymeic insulation has been successfully used since many decades. Now it is the dominating C cable technology. The main issue, which needed to be esolved fo the development of the HVDC polymeic cables, is the contol of the space chage phenomena, which affect the eliability of the connection. Nowadays, this concen has been addessed, but only patially solved. s a consequence, mass-impegnated pape is still the dominating technology fo HVDC cable insulation. Recently, some innovative HVDC cable pojects making use of polymeic cable insulation have been completed [52, 130], up to a ated voltage of 150 kv and fo a maximal powe capacity of about 500 MW 1. Howeve, in these pojects, the polaity of the DC voltage must be kept fixed and then the invesion of the powe flow has to be done by inveting the cuent diection. This limits the application of the polymeic cable system to HVDC links using IGT-based convetes (VSC). In the futue, as it has aleady happened fo C cables, polymeic HVDC cables ae expected to eplace the taditional lapped HVDC cables. Howeve, in ode to make this step feasible, moe undestanding about the fundamental space chage pocesses occuing in polymeic DC cable insulation is needed. 1 ccoding to [77], the HVDC polymeic cable technology will be soon upgaded up to 300 kv and 1000 MW. 3

18 Chapte 1 - Intoduction Space chage and space chage field One of the intinsic popeties of the DC cable insulation is the accumulation of chages. Insulating mateials allow a weak electical conduction. This weak flow of chage within the insulation may not be unifom, because of a local non-homogeneity of the mateial. ccoding to the cuent density continuity equation, when an inequality occus between the flow of chages into a egion and the flow of chages out of that egion, chage accumulates in that egion, see equation (1.1): ρ j + = 0 (1.1) t In equation (1.1), j is the cuent density, ρ is the chage pe unit volume (also called space chage density o simply space chage) and t the time. ccoding to Gauss law, a space chage field E ρ is associated to a chage distibution: ρ = E (1.2) ( ) 0 ρ whee 0 is the vacuum pemittivity and the elative pemittivity of the insulation. Theefoe, the electic field E within the insulation in the pesence of space chage is given by the sum of two contibutions: the space chage field and the extenal field E 0 (also called Laplacian field), which is induced by the applied voltage, see equation (1.3). E = E 0 + (1.3) E ρ In the C situation, the flow of chages invets its diection too quickly to allow a significant gowth of space chage at the insulation inhomogeneities, at least fo conventional insulating mateials. This means that the space chage field can be neglected. On the othe hand, unde DC stessing condition, the flow of chage maintains the same diection. This allows a build-up of chage, which, in geneal, significantly affects the electic field distibution inside the insulation. ccumulated chages can be eleased by the insulation when the extenal field is emoved and the insulation shot-cicuited. Howeve, this pocess can last quite a long time, depending on the type of insulation and on the tempeatue. In geneal, chage depletion is much longe fo polymeic insulation than fo lapped insulation. consequence of this phenomenon is that the accumulated chages will be kept within the insulation also when the extenal DC voltage is emoved o when the value of the extenal DC voltage changes. The invesion of the voltage polaity in HVDC cables is a pactical example of such a situation. In this paticula case, the insulation expeiences the sum of the space chage field and the field induced by the DC voltage, which diection has been inveted. This geneally leads to a maximum field nea the inne conducto of the cable. In the wost case, the maximum field can be as high as twice the maximum value of the Laplacian field. 4

19 Chapte 1 - Intoduction Reseach and development tend fo space chage phenomena in HVDC polymeic cable insulation Duing the last thee decades, space chage phenomena in HVDC insulation have been investigated woldwide. Many techniques have been developed fo the expeimental obsevation of space chage. This, combined with a bette theoetical undestanding of the physical pocesses and an impovement of the extusion cable technology, has been instumental to the development of polymeic HVDC cables [30]. Table 1.1 epots an oveview of the most adopted non-destuctive 2 methods fo the measuement of space chage in solid insulation. Nowadays, the scientific community agees that space chage measuing techniques have eached matuity. Howeve, thee ae still two main diections of advancement egading the use of space chage measuements fo the development of polymeic HVDC cable insulation. The fist one consides the impovement of the space chage measuing systems and the enlagement of the applicability field fo space chage measuing techniques, e.g. [54]. Often, combinations of moe insulating mateials o semiconducting and insulating mateials ae used in cable systems. Fo instance, new (nano)composite mateials ae potential candidate fo the cable insulation technology. Consequently, the objects of space chage measuements as well as the measuing conditions ae becoming moe complex. This means that the measuing systems and thei opeational limits have to be upgaded. The second field of advancement fo space chage methods egads the exploitation of the infomation deived fom the measuement esults, e.g. [116]. In addition to the indication of space chage and electic field magnitude and location, futhe quantities can be deived fom the esults of the measuements. If popely analyzed, these quantities can suppot the identification of the chage caies, the natue of the conduction mechanism and even the aging state of the insulation. 2 Destuctive methods fo the measuement of space chage, such as the dust figue method [8] and the pobe technique method [82, 83], wee also used until the beginning of nineteen eighty. The pinciples of those techniques consist of cutting the test object into small slices and detecting the chage pesent at the suface of the cut slice. 5

20 Chapte 1 - Intoduction Table 1.1. Some of the most common non-destuctive methods fo measuing space chage in solid insulations. NON-DESTRUCTIVE METHODS METHOD Themal pulse method [43] Themal step method [36] Lase intensity modulation method [88] Optical methods [142] Pessue wave popagation methods PIPP [51, 143] LIPP [7, 135] Non-stuctued acoustic pulse [106] Pulsed electoacoustic method [6, 13, 60, 61, 94, 99, 100, 143] DESCRIPTION One side of a flat test object is exposed to a tempeatue pulse. s a consequence, a themal wave tavels though the test object. This displaces the space chage, poviding an electic signal at the extenal electodes. y means of deconvolution techniques, the space chage distibution can be obtained fom the electic signal measued at the electodes. This method is simila to the themal pulse method, but instead of a themal pulse a themal step is applied to the test object. sinusoidal-modulated lase-induced heating is poduced at both sides of a flat test object. In this way, tempeatue waves popagate though the mateial, inteacting with the space chage. The esult is a pyoelectic cuent to be measued at the extenal electodes. polaized light passes though the test object, which must be tanspaent. The electic stess distibution and/o the mechanical stess distibution acoss the test object may modify the optical popeties of the mateial. If this happens, the light passing though the test object has a phase delay. y measuing the phase delay of the light, and by knowing how the stess applied to the mateial affect its optical popeties, infomation about the electic/mechanic stess is povided. pessue pulse/step is applied to the test object. pessue wave is geneated and it tavels though the mateial. The acoustic wave displaces the space chage, poviding an electical signal measuable at the extenal electodes. Depending on the way in which the pessue pulse/step is geneated, the method has diffeent names: - PIPP (piezoelectically-induced pessue pulse); the pulse is piezoelectically geneated; - LIPP (lase-induced pessue pulse); the pulse is lase-geneated; - Non-stuctued acoustic pulse; the pulse is geneated by an HV spak between a conducto and a diaphagm. n electic pulse is applied to the test object, esulting in a petubation foce at the space chage location. Consequently, an acoustic wave is geneated. The acoustic wave is detected by a piezoelectic senso afte having taveled though the mateial and though the eath electode. The piezoelectic senso povides a voltage signal which caies the space chage infomation. 6

21 Chapte 1 - Intoduction 1.3. Objective of the pesent study The geneal objective of the pesent study is to obtain a bette undestanding of the majo factos that contol the space chage pocesses in polymeic HVDC cable systems. Electic field pediction methods, which include space chage phenomena, have to be developed to povide tools and pinciples to suppot the design and the opeation of HVDC polymeic cable systems. In ode to achieve this goal, two main factos of influence have been investigated: 1. Cable accessoies ae consideed to be the weakest pat of a cable system, because of the pesence of a dielectic inteface between the cable insulation and that of the accessoy. This thesis aims at a bette knowledge of the polaization phenomena occuing at dielectic intefaces. To that pupose, we developed an accuate methodology fo the expeimental study of the space chage behavio at the dielectic inteface. 2. When opeating, HVDC cable systems expeience a tempeatue dop acoss thei insulation. This thesis aims to povide a bette undestanding about the mechanisms esponsible fo space chage accumulation when a tempeatue dop is pesent acoss the insulation of the cable system. To that pupose, we developed a physical model fo the pediction of space chage dynamics and electic field in loaded HVDC cable systems. The physical model is validated by means of laboatoy investigation Scientific contibution of the thesis to the field of polymeic HVDC cable systems This thesis contibutes to the scientific development in the field of polymeic HVDC cable systems by: - eviewing the pulsed electoacoustic method fo the measuement of space chages at dielectic discontinuities, such as those encounteed in cable accessoies; - developing measuing systems which ae able to detect chages in test objects esembling the eal HVDC cables and cable accessoies; - identifying the main mechanisms esponsible fo the accumulation of chages at dielectic discontinuities and ecognizing the main paametes affecting the accumulation of chage; - expeimentally investigating the effect of a tempeatue gadient on chage accumulation in the insulation of HVDC polymeic cables and cable accessoies; - expeimentally investigating the effect of the voltage polaity evesal on loaded HVDC cables and cable accessoies; - developing a model fo the pediction of chage accumulation in HVDC cable systems and implementing it by means of a numeical pocedue; - developing opeational ecommendations fo the optimization of the electic stess in paticula woking conditions of the cable system. 7

22 Chapte 1 - Intoduction 1.5. Outline of the thesis In Chapte 2, the expeimental methods adopted in this wok ae descibed. They ae: - conduction cuent measuements, - space chage measuements. In paticula, space chage measuements wee pefomed on test specimens of complex geomety. This was done in ode to epoduce the insulation chaacteistics of eal HVDC cables and HVDC cable accessoies as accuately as possible. Special test set-ups had to be designed and constucted, along with the elated pocedues and softwae tools fo the intepetation of the esults and the coection of the output data. This is discussed in detail in ppendixes -D. In Chapte 3, the expeimental esults ae pesented and discussed. Expeimental investigation was caied out on the test specimens unde themal and electical conditions that esemble the woking conditions of HVDC cable systems. In fact, space chage measuements wee pefomed when: - a tempeatue dop is pesent acoss the insulation of the test specimens; - the polaity of the DC voltage, which is applied at the studied test specimen, is inveted. physical model fo the calculation of space chage and electic field in HVDC cable systems is pesented in Chapte 4 as well as its numeical implementation. The esults of conduction cuent measuements wee used as input fo the model, while the esults of space chage measuements wee adopted fo the model validation. The equations adopted fo the calculation of space chage and electic field ae deived in ppendix E. The most citical spots of HVDC cable systems ae the intefaces between diffeent mateials. oth the semicon-dielectic intefaces and the dielectic-dielectic intefaces ae studied in Chapte 5. The expeimental esults of Chapte 3 wee compaed with the esult of the theoetical modeling and the infomation available in the liteatue. Chapte 6 discusses the feasibility of pefoming on-line space chage measuements on actual HVDC cable system on-site. The oveall conclusions of the thesis ae dawn in Chapte 7. Finally, a numbe of ecommendations ae given in Chapte 8, along with some suggestions fo futhe study. 8

23 2. Expeimental methods Chapte 2 Expeimental methods In this chapte, the expeimental investigations pefomed in this wok ae intoduced. In section 2.1, the diffeent test specimens used fo the laboatoy eseaches ae descibed. Section 2.2 deals with the test set-up and the test potocol that wee adopted fo measuing the conduction cuent in insulating mateials. The technique, the test set-ups and the test potocols used fo space chage measuements on diffeent test objects ae discussed in section 2.3. In section 2.4, the expeimental conditions, at which the measuements wee pefomed, ae given. In the thesis, the chaging phenomena occuing in extuded DC cables and accessoies ae investigated. This is the main eason fo choosing the expeimental methods pesented in this chapte. In fact, space chage measuements diectly povide infomation about the chage that may be pesent within the insulation and the consequent field distotion. On the othe hand, the outcomes of conduction cuent measuements ae the basic input fo the model poposed in Chapte 4, which descibes the studied chaging phenomena Test specimens Expeimental investigations wee pefomed on diffeent types of test specimens of inceasing complexity: i.e. flat specimens, dual-dielectic mini-cables, MV-size cables and MV-size models of cable joint. The two main dielectic mateials composing the insulation of the test specimens ae HVDC cable-quality coss-linked polyethylene (XLPE) and ethylene-popylene ubbe (EPR). In addition, semicon electodes wee used. In Table 2.1, some electical popeties of the mateials ae shown. Table 2.1. Electical popeties of the specimen mateials. R [-] σ 20 C [Ω -1 m -1 ] σ 60 C [Ω -1 m -1 ] XLPE EPR semicon - >1 >1 Tape-type semicon - >1 >1 9

24 Chapte 2 Expeimental methods Flat specimens XLPE and EPR flat specimens consist of 30 cm x 30 cm plates in which a semicon electode is coss-linked at one side. Combinations of flat specimens ae obtained by putting two diffeent plates one onto each othe. Unless stated othewise, no lubicants o specific teatments wee applied at the inteface between the two plates. In Figue 2.1.a and in Figue 2.1.b, flat specimens ae epesented. In ode to expel coss-linking by-poducts 1, all flat specimens wee themally teated at 80 C fo 5 days befoe any testing. In Table 2.2, the amount of by-poducts befoe and afte the themal teatment is epoted [122]. This infomation was povided by the manufactue of the studied mateials in the famewok of the HVDC poject. a b Figue 2.1. Flat specimens. a) Dimensions of a flat specimen. b)coss section of a combination of flat specimens. Table 2.2. Coss-linking by-poducts in the studied flat specimens [122]. y-poduct efoe themal teatment fte themal teatment (80 C fo 5 days) Dicumyl peoxide [ppm] < 10 < 10 cetophenon [ppm] 4929 < 10 lpha methyl styene [ppm] < 10 < 10 Cumene [ppm] < 10 - Cumyl alcohol [ppm] 9100 < 10 Dual dielectic mini-cables Dual-dielectic mini-cables, as used in this wok, ae laboatoy models of a coaxial XLPE-EPR inteface. Dual dielectic mini-cables consist of a tiple-extuded constuction made of an innemost laye of semicon, a middle laye of EPR (o XLPE) and an outemost laye of XLPE (o EPR). The total insulation thickness is 2.1 mm (1.5 mm 1 The amount of by-poducts pesent within the insulation affects the electical popeties of the insulation and in paticula its space chage behavio [102, 111, 138]. In time, the insulation eleases the volatile by-poducts. Consequently, the electical popeties of the insulation may change in time, when the amount by-poducts in the insulation diminishes. In ode to neglect this phenomenon and making measuements compaable, the by-poducts wee expelled befoe any testing. 10

25 Chapte 2 Expeimental methods middle insulation mm oute insulation). Taped-type semicon was mechanically pessed against the oute insulation and, ultimately, a conductive eath sceen was applied. In Figue 2.2, the dimensions of a dual-dielectic mini-cable ae shown. efoe any testing, all the dual-dielectic mini-cables wee themally teated at 80 C fo 5 days. In Table 2.3, the amount of by-poducts befoe and afte the themal teatment is epoted. Table 2.3. Coss-linking by-poducts in the studied dual-dielectic cables [122]. y-poduct efoe themal teatment fte themal teatment (80 C fo 5 days) Dicumyl peoxide [ppm] < 100 < 100 cetophenon [ppm] 2927 < 100 lpha methyl styene [ppm] < 100 < 100 Cumene [ppm] < 100 <100 Cumyl alcohol [ppm] Figue 2.3. Dimensions of a MV-size cable Figue 2.2. Dimensions of a dual-dielectic mini-cable. 11

26 Chapte 2 Expeimental methods MV-size cables MV-size cables consist of 4.5-mm thick extuded XLPE cables with a conducto of 50mm 2. In Figue 2.3, the dimensions of a MV-size cable ae shown. efoe any testing, all the MV-size cables wee themally teated at 80 C fo 20 days. In Table 2.4, the amount of by-poducts befoe and afte the themal teatment is epoted. Table 2.4. Coss-linking by-poducts in the studied MV-size cables [122]. y-poduct efoe themal teatment fte themal teatment (80 C fo 20 days) Dicumyl peoxide [ppm] 17 < 10 cetophenon [ppm] 1169 < 10 lpha methyl styene [ppm] 15 < 10 Cumene [ppm] < 10 <10 Cumyl alcohol [ppm] MV-size models of cable joints MV-size models of cable joints ae constucted in the following way. Fistly, the eath sceen and the oute semicon of an XLPE-insulated cable (aea of the inne conducto = 50 mm 2 ; insulation thickness = 4.5 mm) is scaped off fo a length of 80 mm. Then, pat of the exposed insulation is emoved by means of a glass blade and the insulation suface is smoothed by using successive gades of abasive cloth. fte these opeations, the thickness of the emaining XLPE in the cental pat of the opening is 2 mm. t this point, a 100-mm long elastic tube made of EPR (thickness = 2 mm) can be applied on the XLPE by means of a special tool. fte fitting the EPR tube onto a hollow mandel placed ove the exposed XLPE, the tool pulls back the mandel. In this way, the EPR tube stetches ove the XLPE. To make easy this opeation, silicon oil has to be applied at the inne suface of the EPR tube. Finally, an oute semicon is taped on the EPR. In Figue 2.4, a coss section of a joint model is epesented. efoe any testing, all the MV-size models of cable joints wee themally teated at 80 C fo 20 days. Conditioning of used specimens fte a measuement, the specimen used fo the test was conditioned in an oven at 80 C fo at least 24 hous. This was done in ode to eset the space chage histoy of the specimen, allowing to use the same specimen fo diffeent measuements. 12

27 Chapte 2 Expeimental methods a b Figue 2.4. a) Coss-section of a MV-size model of a cable joint. b) Detail of the dielectic inteface Conduction cuent measuements Measuements of DC conduction cuent on flat specimens wee pefomed fo two main puposes. Fistly, fom the measued cuent values, the DC conductivity of the insulation can be infeed. This was done at diffeent electic fields and at diffeent tempeatue conditions. Secondly, esults of cuent measuements can povide infomation on the conduction mechanisms. If the set of data collected fom the measuements at diffeent conditions ae plotted in a voltage-cuent chaacteistic (o in a cuent density-field (J-E) chaacteistic), the electic field above which the conduction mechanism changes can be detected. This paticula value of the electic field is usually called electic theshold. (Seveal woks, e.g. [15, 48, 113, 133, 134], on HVDC polymeic insulation have shown that significant space chage build-up stats when the applied field is above the electic theshold. Recently, this paamete has also been associated with the statup of electical aging [46, 47]. Fo these easons, the electic theshold can be consideed a paamete of utmost inteest not only fo insulation design, but also fo mateial chaacteization and mateial compaison [3, 15, 113, 114]). Test set-up Conduction cuent measuements wee pefomed in a thee-teminal cell by means of a Keithley 617 electomete. In ode to potect the electomete fom ove cuents, the instument was connected to the measuing electode via a seies esisto. The DC voltage was supplied to the test specimen via a Rogowski-pofiled electode made of aluminum. In all tests, a 1-mm semicon laye was applied to the aluminum measuing and guading electodes. In this way, the insulation of the test specimen was always in contact with the semicon. pesonal compute equipped with a GPI inteface was used fo displaying and stoing the acquied data. In Figue 2.5, the test set-up is epesented, wheeas in Table 2.5 some specifications of the set-up ae given. 13

28 Chapte 2 Expeimental methods Figue 2.5. Expeimental set-up used fo measuements of conduction cuent. Table 2.5. Specifications of the set-up used in this wok fo conduction cuent measuements. Conduction cuent set-up Measuing electode: diamete = 28 mm HV electode diamete = 35 mm Guading electode: diamete = 40 mm-350 mm Sensitivity: /m 2 Max tempeatue: 80 C Max voltage: +/- 30 kv Seies esisto: 10 MΩ Test pocedue In Figue 2.6., the typical behavio of the detected cuent density j(t) is epesented. The cuent density is obtained by means of the following equation: j () t () t i = (2.1) m, el whee i(t) is the cuent measued by the electomete and m,el is the aea of the measuing electode. Defining the steady-state value of the cuent density J ss as: J = j t (2.2) ss () t the conductivity σ of the insulation can be infeed fom: 14

29 Chapte 2 Expeimental methods J ss σ = (2.3) E 0 whee E 0 is the extenal field which is applied acoss the insulation unde test. In pactice, in ode to each a quasi steady-state egime, the applied field has to be pesent acoss the insulation fo a sufficiently long polaization time. Fo the test condition adopted in this study, the polaization time vaies fom a few hous, in case of measuements pefomed at a elatively high applied field and tempeatue, to a few days, in case of measuements pefomed at elatively low applied field and tempeatue. In some of the tests, the measued cuent did not stabilize on a constant value even afte a few days. In these cases, a gaphical fitting was used to estimate the steady-state value of the measued cuent. Figue 2.6. Example of detected cuent density. EPR flat specimen at 20 kv/mm and 40 C. 15

30 Chapte 2 Expeimental methods 2.3. Space chage measuements In this section, the following topics ae discussed: some geneal consideations about space chage measuements and an oveview of the most used space chage measuing techniques; the method used in this investigation (pulsed electoacoustic method) and the test set-ups adopted fo measuing space chage; the pulsed electoacoustic method when the test object is a multi-dielectic; the pulsed electoacoustic method when the test object has cylindical geomety; the paametes used fo evaluating the esults of space measuements Geneal Space chage measuements can povide two main infomations: the actual electic field distibution and an indication of the aging state of the insulation. Electic field distibution The pesence of space chage in insulating mateials distots the initial Laplacian electic field distibution. This leads to a local field enhancement within the mateial that may cause insulation degadation and, ultimately, electical beakdown. If the space chage distibution ρ is known, then the electic field E can be calculated by combining equations (2.4) and (2.5) 2 ρ U = (2.4) 0 E = U (2.5) Whee U is the voltage distibution acoss the insulation, 0 the vacuum pemittivity and the elative pemittivity, which is assumed to have no jump vaiations within the dielectic. Figue 2.7 shows the electic field deduced fom the space chage distibution in an XLPE flat specimen. In the figue, it is vey evident that when space chage is pesent, the field is locally enhanced. Space-chage elated aging Up to now, the scientific community does not have a univocal opinion about space chage being a cause of aging of the insulation, a symptom of it o both of them. Howeve, what is unde discussion is whethe thee is a connection o not between tapping of space chage and electical aging has often been mentioned. ccodingly, fom the space chage distibution, an indication of the aging state of the mateial could be infeed. This has been the topic of many publications. In efeence [90], an up-to-date and compehensive discussion about the subject can be found. 16

31 Chapte 2 Expeimental methods a b Figue 2.7. Examples of space chage (figue a) and electic field (figue b) distibutions in a 1.5-mm thick XLPE insulation. pplied voltage= 17 kv. In the pesent thesis, the main goal of space chage measuements is the detemination of the electic field distibution. Fo this pupose, the polaity, the location and the magnitude of the accumulated space chage has to be known. This infomation was obtained by means of the space chage measuing technique descibed in the following section Pulsed electoacoustic method (PE) Pinciple In this wok, the PE method was used fo measuing the dynamic space chage distibution in both flat and cylindical solid insulations. In Figue 2.8, the PE pinciple is schematically epesented. Figue 2.8. Schematic epesentation of the specimen configuation and test set-up fo space chage measuements by means of the PE method. 17

32 Chapte 2 Expeimental methods In the PE method, a pulsed voltage u p (t) is applied acoss a test object (e.g. a flat o cylindical specimen). The pulsed voltage can be supeimposed on a DC voltage U 0. In this case, a decoupling capacito C and a esisto R have to be placed in seies to the pulse souce and DC souce espectively. Depending on the thickness of the specimen, typical values fo the amplitude of the pulse ae kv wheeas the pulse width vaies in the ange ns. Refeence [39] discusses in detail how to choose the pope pulse paametes given a specific size of the test object. If space chage is embedded within the test object, the application of the pulse induces a petubation foce on the space chage distibution. The petubation foce makes the chage to move slightly and, as a esult, stain (acoustic) waves ae initiated at the space chage location. Those waves ae detected by a piezoelectic senso afte having taveled though the test object and though the eath electode. Usually, polyvinylidenefluoide (PVDF) o lithium niobate (LiNbO 3 ) ae used as sensos. In ode to avoid eflections of acoustic waves, a pope acoustic temination is equied at the senso. Fo this pupose, a mateial with the same acoustic popeties of the senso is used in combination with a mateial which is able to absob the acoustic waves. The electic signal povided at the senso is amplified and fed into a scope, whee it is displayed and stoed. Coection of the detected signal Geneally, the electical signal detected at the scope does not diectly epesent the acoustic signal at the senso. This is mainly due to the fact that the senso-amplifie system acts as a high-pass filte [118]. In ode to coect the detected signal, deconvolution techniques [78, 100] have been adopted in this wok. Moeove, acoustic waves ae attenuated and dispesed, while taveling though lossy media. So, the acoustic signal detected at the senso does not diectly coespond to the space chage distibution within the test specimen. In this study, the oiginal acoustic signal is ecoveed fom the attenuated one by means of the pocedue descibed in ppendix C. The pocedue is mainly based on the ideas poposed by Li [97]. Voltage-off and voltage-on measuements Thee ae two main conditions at which measuements can be pefomed. - Voltage-off condition. Space chage is measued while the DC voltage is absent and while the test object is shot-cicuited. The space chage pesent in the bulk of the insulation is detected. In addition, chages, which ae induced by the space chage, ae also detected at both electodes. - Voltage-on condition. Space chage within the test specimen is measued while the DC voltage is applied. The space chage pesent in the bulk of the insulation is detected as well as the chages at the electodes. In this case, electode chages ae induced by both the space chage and by the applied voltage. Calibation of the measuing system must be pefomed in ode to convet the detected signal at the scope in [mv] into a space chage signal in [C/m 3 ]. This is done on the basis of a known chage distibution at the eath electode. In ppendix D, the calibation pocedue is discussed in detail fo diffeent types of test objects. 18

33 Chapte 2 Expeimental methods Test set-ups In table 2.6, the main chaacteistics of the thee diffeent PE set-ups used in this wok ae shown. In all the set-ups, a scope stoed and displayed the output signal (scope type WaveRunne 6050, 500 MHz, 5-Gs/s LeCoy). Table 2.6. Some specifications of the PE set-ups used in this wok. PE set-up fo thin flat specimens (d<1mm) mplifie: gain = 60 d; input impedance = 50 Ω bandwidth = MHz Senso: PVDF, 9 µm Pulse geneato: amplitude = 0-1 kv pulse width = 7 ns pulse ise time = 3 ns Max. tempeatue: 70 C PE set-up fo thick flat specimens (d>0.5mm) mplifie: gain = 50 d; input impedance = 1.5 kω bandwidth = MHz Senso: PVDF, 40 µm Pulse geneato: amplitude = 0-2 kv pulse width = 50 ns pulse ise time = 5 ns Max. tempeatue: 70 C PE set-up fo cable-geomety test objects mplifie: gain = 70 d; input impedance = 1.5 kω bandwidth = MHz Senso: PVDF, 25 µm Pulse geneato: amplitude = 0-4 kv pulse width = 80 ns pulse ise time = 10 ns Max. tempeatue: 70 C 19

34 Chapte 2 Expeimental methods PE method fo multi-dielectic test objects Recently, the PE method has been applied also to lamina test objects composed of two o moe layes of diffeent dielectics (multi-dielectics). Hitheto, seveal kinds of multi-dielectics have been tested by means of the PE method, e.g. [16, 17, 20, 21, 35, 79, 95, 101, 107, 139, 140, 145, 147]. Nevetheless, only little attention has been paid to the fact that, geneally, the PE method does not diectly povide the space chage distibution within the test specimen if the test specimen is composed of diffeent insulation layes [17, 22, 25, 108, 148, 149]. Thee ae two main easons why the output signal of a PE measuement does not diectly coespond to the space chage distibution within a multi-dielectic. 1. In the PE method, a pulsed voltage is applied acoss the insulation to be tested. The pulse induces a tansient mechanical stess within the multi-dielectic which initiates the acoustic signal to be detected. ssuming each laye of a multidielectic is electically homogeneous, the electically-induced tansient mechanical stess is detemined not only by the space chage distibution, but also by the diffeent pemittivities of each laye of the multi-dielectic. The main consequences of this fact ae: - the shape of the space chage distibution within the test specimen is diffeent fom the shape of the mechanical stess distibution induced by the pulsed voltage; - a diffeent calibation facto must be chosen fo each laye of the multidielectic. 2. The PE method is based on geneation and popagation of acoustic waves. In the case of diffeent acoustic popeties of the mateials in contact (acoustical mismatching), waves expeience diffeent geneation, tansmission and eflection coefficients. The main consequences of this fact ae: - the shape of the detected acoustic signal is diffeent fom the shape of the stess distibution within the multi-dielectic; - eflections can occu at the intefaces between two diffeent mateials, leading to possible misjudgment of measuement esults. Theefoe, in ode to coectly evaluate the space chage distibution in a multidielectic by means of PE measuements, the elation between the detected acoustic signal and both location and magnitude of space chage must be known. To contibute to this discussion, the autho studied the electo-acoustic phenomena occuing in a multi-dielectic tested by means of the PE method. This is detailed explained in ppendix, whee the pinciple of the PE technique is eviewed in case the test object is a multi-dielectic. Repesentation of space chage pofiles fo multi-dielectics test objects In this thesis, the pesented space chage pattens fo multi-dielectics do not epesent the actual space chage distibutions within the multi-dielectic. Instead, they epesent the electically-induced mechanical stess distibutions calibated in [C/m 3 ]. If a pope 20

35 Chapte 2 Expeimental methods calibation pocedue is accomplished (see ppendix D), the space-chage-calibated stess distibution povides a coect estimation of the space chage accumulated in the insulation bulk. t the electode-dielectic intefaces and at the dielectic inteface, the patten povides a signal which is diffeent fom the actual space chage distibution, but moe meaningful. In fact, the space-chage-calibated patten indicates the inteface location and it suggests how the electic field is distibuted acoss the multidielectic 2. The EPR, the XLPE and the semicon used in this wok have quite simila acoustic impedances (see Table.1. in ppendix ). So, if not stated othewise, eflection phenomena ae neglected in the space chage pattens pesented in this thesis. In fact, no clea eflected peaks could be identified in the pattens elated to XLPE-EPR multidielectics PE method fo cable geomety test objects typical coaxial cable suitable fo PE measuements consists of inne conducto, inne semicon, insulation and oute semicon. The conductive eath sceen is emoved at the measuing location. In fact, at the measuing location, the oute semicon must be in contact to the measuing electode of the PE cell. The acoustic impedance of the semicon is usually vey simila to that of the cable insulation. So, no eflections of acoustic waves occu at the semicon-insulation inteface. The DC voltage is applied between the cable conducto and eath via a esisto. s detailed explained in ppendix, thee ae seveal ways of injecting the pulsed voltage acoss the cable insulation at the measuing section. In this wok, the pulsed voltage is injected acoss the measuing section via the oute sceen of the cable, as shown in Figue 2.9. In this way, the cable itself acts as a decoupling capacito. The cable is fixed to the PE cell by means of a cable holde. This guaantees a good acoustic contact between oute semicon and measuing electode (see Figue 2.10). The measuing electode can be eithe flat o cuved. The PE system adopted in this investigation is povided with a flat measuing electode, which allows pefoming measuements on cables of diffeent sizes. s in the PE method fo flat specimens, the acoustic signal is collected by a piezoelectic senso, amplified and displayed by a scope. 2 In the space-chage-calibated stess distibution, a signal peak is pesent at the dielectic inteface, also in the absence of space chage at that location. The vaiation of the intefacial peak magnitude fom its initial value epesents the accumulated chage at the inteface. If the intefacial peak has the same polaity as that of the applied voltage, then the laye connected to eath is the most electically-stessed laye. On the othe hand, if the intefacial peak has polaity opposite to that of the applied voltage, then the laye connected to HV is the most electically-stessed laye. 21

36 Chapte 2 Expeimental methods Figue 2.9. Schematic epesentation of the cable configuation and test set-up fo PE measuements on cable-geomety test objects. Dawing not on scale. Figue Coss section of the cable and of the PE cell at the measuing point. Coection of the detected signal s in the case in which a flat object is tested, the signal detected on a cable geomety object esults diffeent fom the space chage distibution. This is again due to the esponse of the measuing system, which is fequency dependent, and because the acoustic waves ae attenuated and dispesed. In addition, because of the cylindical geomety of the test object, the acoustic waves and the pulsed field ae divegent. This has to be taken into account in ode to obtain a coect space chage pofile. Fo this eason, the geometical facto K g (), which is deived in ppendix, was applied to the unpocessed space chage wavefoms. 22

37 Chapte 2 Expeimental methods Space chage paametes Dynamic space chage distibution The basic outcome of a space chage measuement is the dynamic space chage distibution. The dynamic space chage distibution, ρ(x,t), epesents the amount of chage pe unit volume pesent within a test object as a function of position x and time t, see Figue Fom this basic quantity, a numbe of deived quantities can be deduced. They can be used to evaluate and compae measuement esults. Dynamic electic field distibution Figue 2.12 shows the dynamic electic field distibution, E(x,t), which epesents the magnitude of the electic field pesent within a test object as a function of position and time. E(x,t) can be deived by solving equation (2.4), in which the dynamic space chage distibution has been intoduced. (Equation (2.5) must be used to satisfy the bounday conditions). Figue D plot of the dynamic space chage distibution ρ(x,t) deduced fom a space chage measuement on a 4.5-mm thick cable. pplied voltage: +90 kv. Figue D plot of the dynamic electic field distibution E(x,t) deduced fom a space chage measuement on a 4.5-mm thick cable. pplied voltage: +90kV. 23

38 Chapte 2 Expeimental methods Field enhancement facto The field enhancement caused by the space chage can be descibed by means of the field enhancement facto F E%. F E% epesents the pecentage with which the field stength is maximally inceased by the space chage [78]. Fo a flat specimen, F E% is defined as: U 0 E max F d E % = 100 (2.6) U 0 d whee E max is the maximum electic field pesent within a test object of thickness d and U 0 is the applied voltage. In this thesis, the field enhancement facto fo cylindical test objects is used as a function of the adius, F E% (): U 0 E() F % ( ) d E = 100 (2.7) U 0 d This is done because of in a cable the Laplacian field distibution is invesely popotional to the adius. So, fo cylindical test objects, F E% () epesents the pecentage with which the electic field diffes fom the aveage field U 0 /d, because of the geomety and because of the pesence of space chage. s a consequence, when no space chage is pesent, F E% () is diffeent fom zeo and becomes: U 0 E0 () F %,0 ( ) d E = 100 (2.8) U 0 d whee E 0 () indicates a Laplacian distibution of the electic field. Figue Field enhancement factos fo an XLPE-insulated cable. a) space chage is absent; b) a elatively small amount of space chage is pesent in XLPE bulk; c) a elatively big amount of space chage is pesent in XLPE bulk. 24

39 Chapte 2 Expeimental methods In Figue 2.13, the field enhancement facto is plotted fo a cable in which: (a) space chage is absent (Laplacian field); (b) a elatively small amount of space chage is pesent within the insulation bulk; (c) a elatively big amount of space chage is pesent within the insulation bulk. The figue shows that a situation in which space chage is pesent within a cable is not necessaily the wost situation with egad to the maximum field (case b ). Space chage location and aveage chage Space chage can build up in seveal locations of the insulation. - Nea the electodes. Chage with the same polaity as that of the chage induced by the applied voltage at the adjacent electode is called homo-chage. The effect of homo-chage is to incease the electic field in the insulation bulk and to decease the electic field nea the electodes. On the othe hand, heteo-chage is space chage with polaity opposite to that of the chage induced by the applied voltage at the adjacent electode. The effect of heteo-chage is to incease the electic field nea the electodes and to decease the electic field in the insulation bulk. - In the insulation bulk. Space chage can accumulate all ove the insulation bulk. Fo instance, this happens when a tempeatue dop is pesent acoss the insulation. The polaity of the space chage in the bulk can be eithe the same as that of the applied voltage o opposite to that of the applied voltage. In the fist case, the chage inceases the electic field nea the eath electode and deceases the electic field nea the HV electode. In the second case, the chage inceases the electic field nea the HV electode and deceases the electic field nea the eath electode. - t dielectic intefaces. Geneally, dielectic intefaces ae favoite locations fo space chage accumulation. Intefacial chage with the same polaity as that of the applied voltage inceases the field in the insulation between the inteface and the eath electode and deceases the field in the insulation between the inteface and the HV electode. On the othe hand, intefacial chage with the polaity opposite to that of the applied voltage inceases the field in the insulation between the inteface and the HV electode and deceases the field in the insulation between the inteface and the eath electode. - t the electode-insulation inteface. When a DC voltage is applied acoss the insulation, chages ae pesent at both electode-insulation intefaces. In addition, if space chage is pesent within the insulation, chages ae induced at the electodeinsulation intefaces (those chages ae often called mio chages). So, the total chage at the electode-dielectic inteface is given by both the chages due to the applied voltage and the mio chages. The aveage chage density pesent in the insulation is defined as: d 1 ρ avg = ( x) dx d ρ (2.9) 0 Induced chages at the electodes ae not included in (2.9). The aveage chage is mostly used fo compaing diffeent mateials with egad to the accumulation of space chage, e.g. [115]. 25

40 Chapte 2 Expeimental methods Functions fo the evolution in time of space chage The evolution in time of space chage in a specific location of the insulation is geneally descibed by means of one o moe exponential functions. Theefoe, moe time constants ae geneally necessay fo descibing the space chage gowth and decay, e.g. [14, 144]. Figue shows an example of functions descibing the evolution in time of space chage in diffeent locations of an XLPE-insulated cable that expeiences a tempeatue dop acoss the insulation. Figue Evolution in time of space chage in diffeent location of an XLPEinsulated cable acoss which a tempeatue dop is pesent. a) space chage nea the inne semicon; b) space chage in the middle of the cable insulation; c) space chage nea the oute semicon ccuacy of the measuements Results of PE measuements ae subjected to uncetainty. In this section the accuacy of the PE measuements is evaluated. The most elevant factos affecting the accuacy of PE measuements ae the systematic eo of the calibation pocedue and the statistical eo due to the pesence of noise in the detected signal. The systematic eo in the calibation depends on the accuacy of the following noncoelated quantities: dimensions of the test object, speed of sound of compession waves in the mateial, DC voltage, aea of the signal peak at the eath electode. Following the eo analysis poposed in [78], the systematic eo of the calibation pocedue used in this thesis esults about 12%. In addition to this, the calibation pocedue is based on the hypothesis that no space chage builds-up duing the calibation measuement. This was checked fo all the measuements pesented in the thesis, by compaing the signals detected just befoe and just afte the application of the DC voltage used fo the calibation. If the diffeence between the two signals is lowe than twice the noise level, then the calibation was accomplished coectly. If not, a new calibation measuement was epeated at a lowe DC voltage. 26

41 Chapte 2 Expeimental methods The pesence of noise in the signal is the oigin of a statistical eo. Noise is intoduced in the measuing system at the following locations: at the senso, at the senso-amplifie connection, in the amplifies and in the cables binging the signal into the scope. To educe the noise level, the signal saved at the scope was the aveage of 1000 sweeps, i.e. the noise level was deceased appoximately of a facto 32. This ensued a noise/signal atio of a few pecent. esides the noise, electo-magnetic distubances, which ae geneated by the fiing of the pulse, ae also pesent in the measued signal. Howeve, since those distubances ae constant in time, they can be detected befoe stating a measuement and then they can be subtacted fom the measued signal. In conclusion, due to both systematic eo and statistical eo, the uncetainty of ou measuement esults is about 15% Test conditions Tempeatue conditions Electical behavio of polymeic mateials stongly depends on tempeatue. In paticula, in case of polymeic-type cable systems, the adial electic stess pofile can be citically affected by the tempeatue distibution acoss the insulation. Fo these easons, the adial tempeatue distibution is discussed in the following fo the insulation of a cable system. Steady state ecause of joule losses in its inne conducto, a loaded cable system is heated 3. This geneates a tempeatue dop between the inne conducto and the oute shield. The steady-state tempeatue distibution acoss the cable insulation can be obtained by means of equation (2.10): T () = T a ln ln in ( T T ) in out in out (2.10) In the cable accessoies the insulation is composed of two diffeent dielectics aanged in a coaxial lay out. Then, the tempeatue will be distibuted not only accoding to the specific geomety of the insulation, but also accoding to the themal conductivity k of each mateial. So, the tempeatue distibution is: 3 Insulation losses, which ae due to leakage cuents though the insulation bulk, ae also a souce of heat. Howeve, in case of polyme-insulated cables, the insulation losses ae usually negligible if compaed to the joule losses in the cable conducto. 27

42 Chapte 2 Expeimental methods T T () () = T = T in out ln int ln in in in + ln out ln + int k ln in k ( T T ) out int out k k in out ( T T ) out in in out + ln out int in < < (2.11) int int < < out (2.12) The symbols adopted in (2.10), (2.11) and (2.12) have the following meaning: = geneic adius in = inne conducto adius out = oute sceen adius int = inteface adius T() = tempeatue at the geneic adius T in = tempeatue at the inne conducto T out = tempeatue at the oute sceen k in = themal conductivity innemost dielectic k out = themal conductivity outemost dielectic Equations (2.11) and (2.12) assume that the intefacial contact between the two dielectics does not affect the tempeatue distibution. This may be consideed tue if the dielectic inteface is chemically bonded (e.g. in case of coss-linked inteface). Howeve, in case of a not-bonded inteface, a contact themal esistance pe unit of length (R th,c, expessed in K m W -1 ) needs to be taken into account. The paamete R th,c is mainly affected by the oughness of the sufaces in contact, by the contact pessue and by the pesence of lubicants at the inteface [131]. ecause of the contact themal esistance, the two diffeent media in contact expeience diffeent tempeatues at the inteface. The value of the intefacial tempeatues, T int,in and T int,out in Figue 2.15, can be deduced fom the following equations: T T () () ln ( T T ) in out in = Tin in < int int out k in ln + ln + 2π k in Rth, c in int k out in in out ( T T ) out in out = Tout + < < out ln int k k ln + ln out int + 2π k out R th, c < (2.13) int (2.14) 28

43 Chapte 2 Expeimental methods a b Figue a) Radial tempeatue distibution in the insulation of a loaded cable. b) Radial tempeatue distibution in the insulation of a loaded cable accessoy. Themal tansient When a load is applied to a cable system, which was in a unifom tempeatue condition, a themal tansient stats. The tempeatue distibution acoss the insulation as function of time can be calculated by means of Fouie s heat diffusion equation: T k Q = T t c δ + c δ (2.15) whee c and δ ae espectively the specific heat and the density of the mateials being studied, wheeas Q epesents the heat losses pe unit of volume. In Chapte 4, equation (2.15) is used fo the numeical calculation of the dynamic adial distibution of the tempeatue in cable systems. The duation of the themal tansient, expeienced by the cable insulation, can be estimated by means of the themal time constant τ th. The themal tansient can be consideed finished afte a time equal to 5τ th. The themal time constant is given by: τ = R C (2.16) th th th whee R th and C th ae espectively the themal esistance pe unit of length and the heat capacitance fo unit of length of the themal system composed by the cable and the envionment suounding the cable. Fo the cable insulation only, R th and C th ae: R C th, cable 1 = ln 2π k out in 2 2 ( ) th, cable out in (2.17) = π c δ (2.18) 29

44 Chapte 2 Expeimental methods wheeas fo the insulation of the cable accessoy: R C th, accessoy ln 1 = 2π kin int in ln + k out int out [ c δ ( ) + c ( )] 2 th, accessoy = in in int in out δ out out int (2.19) π (2.20) It is to be noted that the themal time constant of the insulation depends on the mateial popeties, on the geomety and on the cable dimensions (the thicke the cable insulation, the longe the themal tansient). In Table 2.7, the themal time constant is calculated fo diffeent types of cables. In pactice, the themal tansient fo the whole themal system will depend the cable insulation, on the layes of mateial suounding the insulation and on the themal popeties of the envionment in which the cable is deployed [62]. Theefoe, the themal tansient of a cable system in sevice is geneally (much) longe than that of the cable insulation epoted in Table 2.7. Table 2.7. Estimation of the themal time constant of the cable insulation. in [mm] out [mm] k [W m -1 K -1 ] c [J K -1 kg] δ [kg m -3 ] τ th [s] XLPE mini-cable XLPE MV-size cable XLPE HV-size cable Mass-impegnated HV-size cable Induced-cuent heating technique In ode to obtain the same tempeatue conditions a cable insulation expeiences in pactice, the induced-cuent heating technique was used in this study. schematic diagam of the induced-cuent heating technique is epesented in Figue y means of a cuent tansfome, an C cuent is induced in the conducto of the cable object of the measuement, which is connected in a loop. In this way conducto losses ae poduced and a tempeatue dop is pesent between inne conducto and oute shield of the cable. The tempeatue and the cuent in the cable wee continuously monitoed duing the tests. This was done on a dummy loop with the same chaacteistics as the cable object of the measuement. Two tempeatue sensos wee placed on the dummy loop, the fist at the conducto and the second at the oute semicon. 30

45 Chapte 2 Expeimental methods Figue Schematic epesentation of the induced-cuent heating technique. Dawing not on scale. Tempeatue values adopted in the pesent wok In the pesent wok, the laboatoy investigations wee pefomed at seveal tempeatue conditions. Flat specimens wee tested at seveal unifom and constant tempeatues, between 20 C and 60 C. Measuements on dual-dielectic cables, MV-size cables and MV-size models of cable joints wee pefomed at oom tempeatue and when a tempeatue dop was pesent within the insulation. The tempeatue at the inne conducto was kept between 20 C and 65 C, wheeas the tempeatue at the oute semicon was kept between 20 C and 45 C. In all tests, the measuements wee stated only afte the tempeatue sensos indicated that a stable tempeatue distibution was eached Electical conditions Duing its opeation, the insulation of an HVDC cable system expeiences seveal distibutions of the electic stess. Fo instance, the electic field distibution acoss the dielectic is diffeent if the voltage has just been applied o the voltage has been pesent fo seveal hous. In the pesent wok, the laboatoy investigations wee pefomed at seveal electical conditions. They wee chosen in ode to test the insulation unde stesses as close as possible to those an HVDC polymeic-type cable expeiences in the field. DC voltages only wee used: neithe impulse no C voltages wee taken into account in this wok. Fo this eason, the following conditions wee adopted. - Electic field. The specimens wee stessed at an aveage electic field U 0 /d between 5 kv/mm and 30 kv/mm. 31

46 Chapte 2 Expeimental methods - Voltage polaity. oth positive and negative voltages wee applied at the test specimens. Moeove, in some of the tests, the polaity evesal condition was included. - Polaization time. Geneally, a depolaization time of s (5.6 h) was used. Howeve, in some of the tests, the voltage was applied fo a much longe time, up to s (2 weeks). - Depolaization time. Geneally, a polaization time of 3600 s (1 h) was used. Howeve, some of the tests lasted fo a much longe time afte the emoval of the voltage and the shot-cicuiting of the specimen, up to s (2 weeks). 32

47 Chapte 3 Expeimental obsevation of space chage and electic field dynamics 3. Expeimental obsevation of space chage and electic field dynamics This chapte summaizes the main esults of the expeimental wok pefomed in the famewok of this thesis. In Section 3.1 the esults of conduction cuent measuements ae pesented and discussed. Conduction cuent measuements wee pefomed in ode to feed the numeical calculation pesented in Chapte 4. In fact, the input paametes of the calculation wee chosen to match the values of the insulation conductivity deduced fom the conduction cuent measuements. In this way, the conduction mechanisms expeimentally identified ae taken into account in the numeical calculation. Space chage measuements can give infomation about chaging phenomena occuing in actual HVDC polymeic cables. Howeve, measuements should be pefomed on test specimens esembling as much as possible the actual cables, in ode to povide esults that ae epesentative fo the actual situation. Moeove, the test conditions adopted fo the measuements should be vey simila to the conditions a cable expeiences when opeating in pactice. In the liteatue a vast amount of publications is available about expeimental space chage investigations on thin flat specimens. Howeve, only a limited numbe of publications discusses esults obtained fom measuements on full-size models of DC cables. To fill this lack of empiical knowledge and to povide a bette undestanding about space chage phenomena on actual DC cables, we pefomed space chage measuements on MV-size DC cables. The condition in which a tempeatue dop is pesent acoss the cable insulation is consideed along with the situation in which the polaity of the applied DC voltage is inveted. This is discussed in Section 3.3. Dielectic intefaces encounteed in cable joints and teminations ae geneally egaded as the weakest pats of a DC cable system. Howeve, little attention only has been given in the liteatue to the polaization phenomena occuing at dielectic intefaces. Theefoe, we pefomed space chage measuements on XLPE-EPR intefaces of inceasing complexity, i.e. flat specimens, dual-dielectic mini-cables and MV-size models of cable joints. The esults of space chage measuements pefomed on those thee diffeent types of dielectic intefaces ae espectively analyzed in Section 3.2, 3.4 and 3.5. Finally, some conclusions ae dawn in Section

48 Chapte 3 Expeimental obsevation of space chage and electic field dynamics 3.1. Conduction cuent measuements on XLPE and EPR flat specimens Intoduction Measuements of conduction cuent wee pefomed on XLPE and EPR flat specimens at diffeent values of the applied field and tempeatue. The way in which the expeiments wee caied out is descibed in Section 2.2. The following infomation is deduced fom the expeimental esults: - the conductivity of the two insulating mateials, as function of field and tempeatue; - an indication of the main mechanisms diving the DC conduction in the studied specimens; - an estimation of how the electic field is expected to be distibuted acoss a flat XLPE-EPR intefaces when a DC voltage is applied Results In Figues 3.1 and 3.2, the J-E chaacteistics (see Section 2.2) of XLPE flat specimens and EPR flat specimens ae espectively shown fo diffeent tempeatue values. The fitting lines ae also epesented in the figues. The intesection of two fitting lines defines the electic theshold, i.e. the value of the electic field above which the conduction mechanism changes. J-E chaacteistics fo the XLPE specimens show quite clealy a theshold-type behavio, see Figue 3.1. Regading the EPR specimens, only the J-E chaacteistic elative to measuements pefomed at oom tempeatue shows a theshold-type behavio. t 60 C, no theshold can be detected fo values of the applied field between 1.3 kv/mm and 20 kv/mm, see Figue 3.2. This actually means that the theshold fo the EPR at 60 C is to be expected below 1.3 kv/mm. Figue 3.1. Steady state cuent densityelectic field chaacteistics of XLPE flat specimens. Expeimental points and fitting lines. The slope of the fitting lines is included in backets, wheeas the aows indicate the electic thesholds. 34

49 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Figue 3.2. Steady state cuent densityelectic field chaacteistics of EPR flat specimens. Expeimental points and fitting lines. The slope of the fitting lines is included in backets, wheeas the aow indicates the electic theshold Discussion Conductivity as function of field and tempeatue Fom the J-E chaacteistics the value of the insulation conductivity can be infeed as a function of the electic field and tempeatue. Figues 3.3 and 3.4 show espectively the effect of the applied field and tempeatue on the DC conductivity of the studied XLPE and EPR flat specimens. It is to be noted (see Figue 3.4) that the conductivity of both mateials, at a given field of 20 kv/mm and within the ange 20 C - 60 C, fits well with an henius-type elationship: σ ( T ) = exp (3.1) T whee and ae constants. In Table 3.1, the values of the constants and, which ae deduced fom Figue 3.4, ae shown. This infomation is used in the numeical calculation pesented in Chapte 4, whee a model fo the tempeatue dependency of the conductivity is employed. The physical implications of such a dependency ae discussed in the following. Figue 3.3. Conductivity of XLPE specimens and EPR specimens as a function of the applied electic field fo a tempeatue of 22 C [27]. Expeimental points. 35

50 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Figue 3.4. Conductivity of XLPE specimens and EPR specimens vs. ecipocal absolute tempeatue, fo an applied field of 20 kv/mm [27]. Expeimental points and fitting lines. Table 3.1. and coefficients as defined in Equation (3.1) fo the conductivity of the studied XLPE and EPR specimens. MTERIL [Ω -1 m -1 ] [K] XLPE EPR Conduction mechanisms ccoding to the theoy of electic conduction in solid dielectics (e.g. [45, 124]), a log-log plot of the steady-state J-E chaacteistic can show the tansition between diffeent conduction mechanisms. In fact, if the slope of the chaacteistic is 1, ohmic conduction is believed to be the dominant mechanism. On the othe hand, a slope > 1 indicates that a conduction mechanism is active in which the cuent density is moe than popotional to the applied field. In the fist case, the conductivity of the insulation is independent fom the applied field. In the latte, the conductivity is field dependent. tansition between two diffeent types of conduction mechanisms was obseved fo XLPE specimens and fo the EPR specimens at oom tempeatue. Similaly to what is epoted in the liteatue [114], the values of electic theshold expeimentally detemined fo XLPE fit well with an henius-type elationship within the ange 20 C - 60 C, as shown in Figue 3.5. EPR specimens at 60 C have shown only a conduction mechanism in which the cuent density is moe than popotional to the applied field fo fields between 1.3 kv/mm and 20 kv/mm. oth types of specimens show an henius-type tempeatue dependency of the conductivity. tap-limited mobility intepets this phenomenon. ecause of the pesence of tap states within the band gap of dielectics, not all the chage caies contibute to the conduction. Howeve, accoding to the tap-limited model [45], the numbe of effective chage caies, which is popotional to the mobility and then to the 36

51 Chapte 3 Expeimental obsevation of space chage and electic field dynamics conductivity, is a function of tempeatue and an henius-type model descibes the physical phenomenon. So, the tap-limited mobility is believed to be the eason fo the obseved dependency of the conductivity on tempeatue. Figue 3.5. Electic theshold fo XLPE flat specimens vs. ecipocal absolute tempeatue. Expeimental points (as deived fom J-E plots) and fitting line. henius coefficients: = V m -1 ; = K. Effect of conductivity on intefacial chage and electic field in flat XLPE-EPR intefaces ased on the esults of conduction cuent measuements pefomed on single flat specimens, the electical behavio of a flat XLPE-EPR intefaces is discussed in the following. ccoding to the Maxwell-Wagne (MW) theoy fo the intefacial polaization [84, 150], chage accumulates at the inteface between two dielectics and if a discontinuity in the atio between conductivity and pemittivity exists (i.e. if (σ/) 0). The exponential gowth of the MW intefacial chage, which is elated to the tansition between capacitively-distibuted field to esistively-distibuted field, is descibed by a time constant τ: τ d + d MW = (3.2) d σ + d σ whee d, d ae the thickness of the two dielectics, σ, σ the conductivities and, the pemittivities. Equation (3.2) can be used fo the calculation of the MW time constant of the specimen combinations studied in this wok, as shown in Figue 3.6. Since the conductivity of the XLPE and EPR specimens is much moe affected by the tempeatue athe than by the applied field, the time constant is estimated assuming that a constant field of 20 kv/mm is pesent in each laye of the combination. (The effect of the field dependency of the conductivity on accumulation of intefacial chage will be consideed in Chapte 4). The MW time constant shows an heniustype dependency with the tempeatue. This is due to the fact that the MW tansition is pactically diven by the conductivity of the most conductive laye of the combination (EPR in the studied case), which follows also an henius-type behavio. In fact, compaing the chats in Figues 3.4 and 3.6, the slope of the MW constant is 37

52 Chapte 3 Expeimental obsevation of space chage and electic field dynamics compaable with the slope of the EPR conductivity ( τ,mw = K; σ,epr = K). Duing the tansition time (tansition time 5τ MW ), the electic field distibution in the two mateials can dastically change, even if we assume that no space chage accumulates in the insulation bulk. Fo instance, fom Figue 3.4, we can see that the lowe the tempeatue, the lage the elative diffeence between the conductivity of EPR and that of XLPE. This means that the esistively-distibuted field acoss an XLPE/EPR combination is almost entiely applied on the XLPE laye at oom tempeatue. Howeve, in ode to each this situation a DC voltage must be applied fo a elatively long time (5τ MW 400 h). On the othe hand, at highe tempeatues (T > 70 C), the conductivity of XLPE is expected to be lage than that of EPR. In this case, the electic field will be mostly distibuted acoss the EPR laye. In this situation, a elatively shot tansition time is expected (5τ MW 2.5 h). Figue 3.6. Maxwell-Wagne time constant of a combination of XLPE/EPR flat specimens vs. ecipocal absolute tempeatue, when an extenal field of 20 kv/mm is applied [27]. Calculated points and fitting line. henius coefficients: = s; = K Summay and conclusions Fom the conduction cuent measuements pefomed on XLPE and EPR flat specimens, the following can be concluded. - oth the conductivities of XLPE and EPR specimens stongly depend on applied field and tempeatue. In paticula, an henius-type dependency of conductivity on tempeatue is found. This let us assume that a tap-limited mobility model is valid fo the studied specimens (when the field is aound 20 kv/mm). - J-E chaacteistics of XLPE specimens show the pesence of an electic theshold. The tempeatue dependency of the electic theshold fo the XLPE (within a tempeatue ange 20 C - 60 C) can be descibed by using an henius-type elationship. 38

53 Chapte 3 Expeimental obsevation of space chage and electic field dynamics - t oom tempeatue, the J-E chaacteistic of EPR specimens shows the pesence of an electic theshold. t 60 C, no theshold can be infeed fo fields between 1.3 kv/mm and 20 kv/mm and the only conduction mechanism active is chaacteized by a cuent density which is moe than popotional to the applied field. - On the basis of the Maxwell-Wagne theoy, esults obtained fom conduction cuent measuements on single flat specimens can be used fo descibing the electical behavio of a combination of flat specimens. The MW time constant can be estimated fo XLPE-EPR combination. Fo the studied specimens, a stong tempeatue dependency of the MW time constant is found (also in this case of the henius type) Space chage measuements on XLPE-EPR flat intefaces Intoduction Space chage and electic field distibutions wee investigated in combinations of XLPE-EPR flat specimens. Neithe lubicants no specific chemical teatments wee applied at the dielectic inteface of the flat specimens. The DC voltage was applied acoss the specimens as shown in Figue 3.7. typical voltage-on space chage pofile, measued immediately afte the application of the DC voltage on an XLPE-EPR specimen combination, is depicted in Figue 3.8.a. In Figue 3.8.b, the coesponding electic field distibution is epesented. In addition to the peaks at both the electodes, a peak is pesent at the dielectic inteface in the space chage pofile. This peak is due to the discontinuity of the pemittivity at the dielectic inteface. vaiation of the peak magnitude fom its initial value indicates that intefacial chage has been accumulated. detailed explanation fo this phenomenon is given in ppendix. Figue 3.7. XLPE-EPR flat specimens as tested in the PE set-up. 39

54 Chapte 3 Expeimental obsevation of space chage and electic field dynamics a b Figue 3.8. a) Typical voltage-on space chage pofile measued immediately afte the application of the DC voltage. b) Electic field distibution deduced fom the space chage pofile. pplied voltage U 0 = + 30 kv Results The main esults of voltage-on space chage measuements pefomed on XLPE-EPR laminates ae summaized Figue 3.9. Figue 3.9 shows the space chage accumulation in time fo diffeent tempeatue conditions. Duing the chaging peiod ( s 5.6 h), space chage accumulated at specific locations of the specimen. - t the dielectic inteface. In all tests, space chage with the same polaity as that of the applied voltage accumulated at the dielectic inteface. The magnitude of the chage at the inteface inceases with the tempeatue. - In the bulk of XLPE. t 40 C, taces of space chage wee measued. The polaity of the space chage is the same as that of the applied voltage. t 60 C, the accumulated chage is vey evident. maximum value of about 0.4 C/m 3 is pesent at a distance of 0.95 mm fom the eath electode. - Next to the inteface in the XLPE. t 40 C and 60 C, a peak of chage with polaity opposite to that of the chage at the inteface was measued. - In the EPR, nea the HV electode. t 60 C, taces of heteo-chage wee measued in the EPR. Measuements of space chage wee pefomed at both positive and negative polaity of the test voltage. lthough quite simila space chage pattens wee detected at diffeent voltage polaities, at positive voltage moe chage accumulates at the inteface. This is shown in Figue ecause of the pesence of chage within the insulation, the electic field is distoted. Duing the polaization time, the electic field in the XLPE inceases while the field in the EPR deceases. The most stessed pat of the insulation is in the XLPE, nea the eath electode. Nea the eath electode, at 40 C, the field modification facto is about 15%, wheeas at 60 C the field modification facto inceases up to 75%. 40

55 Chapte 3 Expeimental obsevation of space chage and electic field dynamics In Figue 3.11, the electic field pofiles deived fom the space chage distibutions at 60 C ae shown. Voltage-on space chage distibutions. U 0 = +30 kv, T = 20 C. No significant chage accumulation can be obseved duing the polaization time. Only taces of positive chage at the inteface ae measued. Voltage-on space chage distibutions. U 0 = +30 kv, T = 40 C. Space chage accumulates at the dielectic inteface, in the bulk of the XLPE and in the EPR nea the HV electode. Voltage-on space chage distibutions. U 0 = +30 kv, T = 60 C. Space chage accumulates at the dielectic inteface, in the bulk of the XLPE, in the EPR nea the HV electode and in the XLPE next to the inteface. Figue 3.9. Voltage-on space chage pofiles of XLPE-EPR flat specimens. 41

56 Chapte 3 Expeimental obsevation of space chage and electic field dynamics a b Figue Voltage-off space chage pofiles in XLPE-EPR flat specimens [21]. a) pplied voltage: +30 kv fo s. b) pplied voltage: -30 kv fo s. Figue Electic field distibutions in XLPE-EPR laminates. U 0 = +30 kv, T = 60 C Discussion Intefacial chage The expeimental esults indicate that the tempeatue plays a majo ole in the accumulation of chage at the inteface in the studied combinations of flat specimens. Figue 3.12 shows the amount of intefacial chage, which is deduced fom the voltage-on space chage pofiles measued at diffeent tempeatues. The intefacial chage κ epesented in Figue 3.12 is deived fom the expeimental pattens accoding to equation (3.3): xi, EPR t= 0 xi, XLPE () t = ( ρ() t ρ ) κ dx (3.3) 42

57 Chapte 3 Expeimental obsevation of space chage and electic field dynamics whee x i,xlpe and x i,epr ae espectively the stating point and the end point of the intefacial peak, ρ(t) is the voltage-on space chage distibution and ρ t=0 is the voltageon space chage distibution immediately afte the application of the DC voltage. The pictue clealy shows that at 60 C, the intefacial chage has almost eached a constant value afte the polaization time of s. On the othe hand, at 20 C and 40 C, the polaization phenomenon has not yet aived at a steady state. This validates the esults of conduction cuent measuements pesented in Section 3.1. In that section, a longe time is pedicted fo the intefacial polaization at lowe tempeatues, see Figue 3.6. Moeove, accoding to Figue 3.4, the diffeence between the conductivity of the XLPE and that of the EPR is lage at lowe tempeatues. Theefoe, the highest amount of chage is expected to accumulate at the inteface at lowe tempeatues if the polaization time is sufficiently long. Figue Intefacial chage measued in EPR-XLPE flat specimens. U 0 = +30 kv fo s. Space chage in the XLPE and in the EPR t 40 C and at 60 C, chage within the XLPE bulk was measued. The amount of chage inceases with the tempeatue. ccoding to the esults of conduction cuent measuements fo the XLPE, the electic theshold fo non-linea conduction deceases if the tempeatue inceases. Moeove, at 40 C and at 60 C, the field in the XLPE laye of a combination of flat specimens is inceased by the pesence of intefacial chage. So, the combination of a lowe theshold value with a highe electic field may explain why space chage could be measued in the bulk of XLPE only fo tempeatue values above 40 C. In Figue 3.13, the evolution in time of the measued space chage is shown at diffeent locations of the specimen fo the tempeatue of 60 C. The space chage in the bulk of the XLPE (x = 1 mm) follows appoximately the behavio of the space chage at the inteface (x = 1.5 mm). This suppots the hypothesis that the field enhancement induced by the intefacial chage may be a cause of chage build-up in the bulk of the XLPE. 43

58 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Fig Evolution in time of space chage in specific locations of the insulation: x = 1.5 mm at the dielectic inteface; x = 1 mm in the XLPE bulk; x = 1.3 mm in the XLPE next to the inteface. U 0 = +30 kv; T = 60 C. Howeve, the fact that the chage accumulates at a specific location of the specimen may also indicate a macoscopic non-homogeneity of the insulation at that location. The flat specimens wee obtained by a means of a pess-molding opeation, pefomed at 180 C followed by a cooling of 15 K pe minute. It is possible that one o moe amalgamation zones wee fomed duing the poduction of the specimens. It has been epoted [18, 33] that space chage accumulates at amalgamation zones in polyethylene. In [18], it was found that a chaacteistic of the amalgamation zone in polyethylene is the pesence of ionic dissociable species, which wee identified to be the main cause fo the obseved space chage. Figue 3.13 shows also the dynamics of the chage in the XLPE nea the inteface (x = 1.3 mm) at 60 C. The gowth of this heteo-chage is faste than that of the chage at the inteface. Theefoe, the heteo-chage in the XLPE nea the inteface should not have a diect elation to the field enhancement induced by the chage at the inteface. t 60 C heteo-chage was also measued in the EPR nea the HV electode. This means that not all the chages that move towad the electodes and towad the dielectic inteface can be tansfeed. In othe wods, both the semicon-insulation inteface and the dielectic-dielectic inteface pesent blocking popeties. In the liteatue, e.g. [96, 102, 111, 138], it has been epoted that heteo-chage accumulates in coss-linked mateials. The heteo-chage has been often associated to the pesence of coss-linking by-poducts, that once ionized move towad the electodes leading to a heteo-chage egime. Howeve, the studied specimens wee themally teated befoe any testing. Theefoe, a vey tiny amount of esidual coss-linking by-poducts can be pesent in the specimens afte the themal teatment (see tables in Section 2.1). Consequently, it is quite unlikely that the esidual by-poducts ae the cause fo the obseved heteochage. This opinion is validated by the chemical/physical 1 analysis pefomed on ou specimens in the famewok of the HVDC poject [103]. oth fesh and used 1 The following chemical/physical analysis wee pefomed on the studied specimens at the Polyme Reseach Cente - Univesity of Suey in the famewok of the HVDC poject [103]: FTIR-TR; optical micoscopy; NSEM/EDX; Raman spectoscopy; IR spectoscopy. 44

59 Chapte 3 Expeimental obsevation of space chage and electic field dynamics specimens wee analyzed. No evidence of migating species that coelate with ionic conduction wee found. diffeent explanation, which consides chages of electonic natue can be speculated fo the obseved chaging phenomena. Depending on the tempeatue, some shallow taps may be pesent in the tap distibution. s a consequence, chage caies with a elatively high mobility would contibute to the conduction. They would move quickly to the electodes and to the dielectic inteface, being blocked. This could explain why the heteo-chage accumulation is faste than the accumulation of intefacial chage and why it is obseved at the highe tempeatues only Summay and conclusions Space chage measuements on XLPE-EPR flat intefaces showed the following main esults. - Space chage with the same polaity as that of the applied voltage accumulates at the inteface between XLPE and EPR. Since the measuements did not last long enough fo the chaging pocess at lowe tempeatues to finish, the highest amount of intefacial chage was measued at the highe tempeatue, situation in which a faste chage build-up occus. Howeve, it is believed that if the measuing time is inceased, the highe amount of chage will be seen at the lowe tempeatue, as pedicted by the esults of conduction cuent measuements. - The intefacial chage modifies the field distibution: the field inceases in the XLPE and deceases in the EPR. - t the tempeatues of 40 C and 60 C, space chage accumulates in the XLPE bulk. Two hypotheses wee fomulated fo explaining the obseved phenomenon. Fistly, the space chage accumulation may have been tiggeed by the combined effect of the lowe value that the electic theshold assumes at highe tempeatues and the incease of the field in the XLPE when intefacial chage is pesent. Secondly, amalgamation zones could have been pesent within the specimens because of thei poduction pocess, leading to favouite egions fo space chage accumulation. - t 60 C, heteo-chage accumulates in both XLPE and EPR. The blocking popeties of the semicon-dielectic inteface and of the dielectic-dielectic inteface ae assumed to be the cause fo the obseved heteo-chage. - Measuements pefomed at diffeent voltage polaity do not show pefectly symmetic pattens. In fact, moe intefacial chage was measued at positive voltage polaity. 45

60 Chapte 3 Expeimental obsevation of space chage and electic field dynamics 3.3. Space chage measuements on MV-size XLPE cables Intoduction Space chage and electic field distibutions wee investigated in MV XLPE-insulated cables. In all the measuements pesented in this section, the DC voltage is applied at the inne conducto, wheeas the oute conducto is connected to eath. typical voltage-on space chage pofile, measued immediately afte the application of the DC voltage, is depicted in Figue 3.14.a. In Figue 3.14.b, the coesponding electic field distibution is epesented. Space chage measuements wee pefomed at diffeent tempeatue conditions and at diffeent values and polaities of the applied voltage. In the following tables, the test conditions ae summaized. 4.5 mm 4.5 mm a b Figue a) Typical voltage-on space chage pofile measued immediately afte the application of the DC voltage. b) Electic field distibution deduced fom the space chage pofile. pplied voltage at the conducto: U 0 = + 90 kv. Tab.3.2.a. Test conditions adopted fo the space chage measuements on MV cables: tempeatue conditions. Cable load [] T out [ C] T in [ C] T [K] T [K/mm] T out =tempeatue oute semicon; T in =tempeatue inne semicon; T =tempeatue dop; T=aveage tempeatue gadient. 46

61 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Tab.3.2.b. Test conditions adopted fo the space chage measuements on MV cables: polaization conditions. Voltage [kv] Voltage polaity +/- +/- +/- and polaity evesal Electic field (aveage) [kv/mm] Polaization time [s] Results The main outcomes of space chage measuements pefomed on MV XLPE cables ae shown in Figues 3.15 and Fom the measued space chage pattens, the following chaacteistics have been obseved. - t oom tempeatue, no significant chage build-up was obseved duing the polaization time fo voltages up to 90 kv. Theefoe, the elative pattens ae not epesented in Figues Space chage with the same polaity as that of the applied voltage accumulated in the insulation bulk when a tempeatue dop was pesent acoss the cable insulation (T in > T out ). The amount of chage inceases with the tempeatue dop fo a given applied voltage (see Figues 3.15.c and 3.15.d). The amount of chage inceases with the applied field fo a given tempeatue distibution (see Figues 3.15.a and 3.15.b). - Heteo-chage nea the inne semicon was measued in some of the measuements, pefomed when a tempeatue dop was pesent (see Figues 3.15.c and 3.15.d). Measuements of space chage wee pefomed at both positive and negative polaities. Diffeently fom what obseved fo flat XLPE-EPR specimens, Figue 3.16 shows that space chage pattens detected at diffeent voltage polaities ae pactically symmetic fo MV size cables. The space chage accumulated within the cable insulation modifies the electic field fom its initial Laplacian distibution. Duing the polaization time, the electic field inceased in the insulation nea the oute semicon while the field deceased nea the inne semicon. In Figue 3.17, examples of the electic field pofiles deived fom the space chage distibutions ae shown. 47

62 Chapte 3 Expeimental obsevation of space chage and electic field dynamics a Voltage-on space chage distibutions. U 0 = kv T in = 65 C T out = 45 C T = 20 K T = 4.4 K/mm b Voltage-on space chage distibutions. U 0 = +45 kv T in = 65 C T out = 45 C T = 20 K T = 4.4 K/mm c Voltage-on space chage distibutions. U 0 = +90 kv T in = 40 C T out = 30 C T = 10 K T = 2.2 K/mm d Voltage-on space chage distibutions. U 0 = +90 kv T in = 65 C T out = 45 C T = 20 C T = 4.4 K/mm Figue Voltage-on space chage pofiles of MV cables. 48

63 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Figue Voltage-off space chage pofiles in MV XLPE cables. U 0 = +/-90 kv fo s T in = 65 C T out = 45 C T = 20 K T = 4.4 K/mm Figue Electic field distibutions in MV XLPE cables. U 0 = +90 kv T in = 65 C; T out = 45 C T = 20 K T = 4.4 K/mm Discussion In this section, the effect, which the tempeatue distibution and the extenal applied field have on space chage behavio, is discussed fo the studied MV cables. t the end of the section, the esults of a measuement, in which the polaity of the applied voltage is inveted, ae pesented and analyzed. Effect of tempeatue distibution on space chage accumulation ecause of the tempeatue dependency of the insulation conductivity, the conductivity distibution is a deceasing function of the adius if the cable is loaded. ecause of this fact, chage with the same polaity as that of the applied voltage is expected to accumulate. ( model fo this phenomenon will be pesented in Chapte 4). This chage is esponsible fo the so-called field invesion phenomenon occuing in DC cables, i.e. the electic field is highe nea the oute shield athe than nea the inne conducto [49, 80]. Figue 3.18 shows the field enhancement factos deived fom measuements pefomed at +90 kv DC voltage and at thee diffeent tempeatue conditions. In Figue 3.18, the thick full line epesents the field enhancement facto when no 49

64 Chapte 3 Expeimental obsevation of space chage and electic field dynamics tempeatue dop is pesent (i.e. T in = T out = 20 C), the dashed line epesents the field enhancement facto when a tempeatue dop of 10 K is pesent (T in = 40 C; T out = 30 C) and the dotted line when the tempeatue dop is 20 K (T in = 65 C; T out = 45 C). In the last situation (dotted line), the field invesion phenomenon is clealy evident. Figue Field enhancement factos fo MV XLPE cables. U 0 = +90 kv fo s. Expeimental esults show that both the amount of space chage and its accumulation time depend on the tempeatue distibution. These facts ae diect consequence of the tempeatue dependency of the insulation conductivity. In the studied situations, the insulation of the cable is not in a macoscopically homogeneous condition. This is mainly because of the fact that the tempeatue distibution induces a non-homogeneous conductivity. The highe the tempeatue dop acoss the insulation, the lage the non-homogeneity of the conductivity and theefoe the highe the value of the accumulated space chage. This is shown in Figue 3.19, whee esults of measuements pefomed at diffeent tempeatue dops ae compaed. On the othe hand, space chage takes a cetain time to accumulate within the insulation. The moe conductive the insulation, the faste the space chage accumulation. Since the insulation conductivity stongly inceases with the tempeatue, the highe the absolute value of the tempeatue, the faste the space chage accumulation. In Figue 3.20, the space chage evolution in time at specific locations of a loaded cable is epesented. The figue shows that the faste space chage accumulation is pesent in the cable insulation nea the inne semicon, whee a highe tempeatue is pesent. 50

65 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Figue Maximum value of the accumulated space chage in MV XLPE cables afte a polaization time of s. Fo evey value of the applied voltage, the amount of accumulated chage inceases with the tempeatue dop. Figue Evolution in time of accumulated space chage in specific locations of a MV XLPE cable. U 0 = +90 kv, T = 20 K. a nea the inne semicon; adius = 5 mm; T = 62 C. b in the middle of the insulation; adius=6.75 mm; T = 53 C. c nea the inne semicon; adius=8.5 mm; T = 47 C. Space chage shows a faste dynamics at highe tempeatues. Effect of the applied field The applied field contibutes in two diffeent ways to the build-up of space chage. Fistly, the initial Laplacian field is not unifom, but invesely-popotional to the adius. The conductivity of the insulation inceases with the electic field. Theefoe, the electic field contibutes to the non-homogeneity of the insulation conductivity and to the consequent space chage fomation 2. Moeove, a faste space chage accumulation is expected at highe fields, when the conductivity is highe. 2 In geneal, the field dependency of the conductivity is moe than linea (at least fo values of the electic field above the electic theshold). ecause of this fact, the field is gaded at stess enhancements. Theefoe, a stongly field-dependent conductivity is usually consideed a positive popety fo a mateial to be used as insulation fo DC cables [28, 44]. 51

66 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Secondly, fo a given non-homogeneous distibution of the insulation conductivity the amount of space chage inceases with the field. The effect of the applied field on the enhancement facto is epesented in Figue In the figue, thee field enhancement factos ae deived fom measuements pefomed at thee diffeent values of the extenal field. The following conditions wee adopted fo the thee measuements: tempeatue dop 20 K, tempeatue at the inne semicon 65 C, tempeatue at the oute semicon 45 C, polaization time s. In the figue, the full line epesents the field enhancement facto when a voltage of kv is applied (aveage field = 5 kv/mm), the dashed line epesents the field enhancement facto when a voltage of +45 kv is applied (aveage field =10 kv/mm) and the dotted line when a voltage of +90 kv is applied (aveage field = 20 kv/mm). Figue 3.21 indicates that a highe extenal field poduces a highe field enhancement facto fo the specific studied conditions. Howeve, the time the DC voltage is applied acoss the cable insulation is (much) shote than the time it takes fo the electic field to change fom capacitively distibuted to esistively distibuted 3. Consequently, a stable space chage egime is not yet eached in the pefomed measuements. In ode to undestand how the field enhancement facto changes if the measuing time is inceased, a plot of the evolution in time of the chage nea the inne conducto is epesented in Figue The figue epesents the measued space chage in p.u., i.e. the measued chage divided by the value of the space chage at the eath electode at time t = 0 s. This is done in ode to diectly compae space chage dynamics obtained fom measuements pefomed at diffeent applied voltages. Figue 3.22 shows that fo a given tempeatue distibution, moe space chage accumulates in the cable insulation when a highe extenal field is pesent (see dotted line). Howeve, it is evident that at the lowe fields the space chage functions have not yet eached thei maximum value. This indicates that moe space chage than what measued accumulates if a (much) longe measuing time is chosen fo the measuements pefomed at 22.5 kv and 45 kv. Theefoe, the field enhancement facto would incease also at low fields if the extenal voltage is applied fo a sufficiently long time. This will be theoetically explained in the next chapte. Space chage measued in the insulation bulk of MV cables has been associated to a gadient of the insulation conductivity, which is induced by a tempeatue dop acoss the insulation and/o by a divegent electic field. Howeve, heteo-chage was also obseved nea the inne semicon at the tempeatue dops of 10 K and 20 K, fo diffeent values of the applied field. oth the polaity and the dynamic of the heteochage cannot be connected to a tempeatue/field-induced gadient of the insulation conductivity. 3 n estimation of the time it takes fo the electic field to change fom capacitively distibuted to esistively distibuted can be obtained by consideing the electical time constant τ el : τ el = 0 / σ out. σ out epesents the conductivity of the coldest pat of the insulation at the aveage field expeienced by the cable. The tansition time can be assumed about five times τ el. Fo the situation depicted in Figue 3.21, the tansition time is of the ode of seveal hundeds of hous at the voltage of 22.5 kv, hunded hous at 45 kv and a few tens of hous at 90 kv. 52

67 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Similaly to what was said in Section 3.3.3, the heteo-chage can be attibuted to the blocking popeties of the semicon-dielectic inteface. This phenomenon will be futhemoe investigated in Chapte 5. Figue Field enhancement factos fo MV XLPE cables. T=20 K (T in = 65 C, T out = 45 C); voltage applied fo s. Figue Evolution in time of accumulated space chage nea the inne semicon of a MV XLPE cable fo thee diffeent extenal fields when a tempeatue dop T=20 K is pesent. Radius = 5 mm; T = 62 C. Space chage shows a faste dynamics at the highe applied field. Polaity evesal The situation in which the polaity of the applied voltage is inveted is consideed one of the most sevee condition fo the cable insulation, if the DC cable is loaded [37, 38]. Fo this eason, space chage measuements wee also pefomed duing a polaity evesal test. In Figue 3.23, space chage pofiles detected duing a polaity evesal test ae epesented. Duing the test, a load was applied at the cable and a tempeatue dop of 20 K was pesent acoss the cable insulation. The test was pefomed accoding to the following pocedue. Fistly, a voltage of +90 kv is applied fo s (5.6 hous). Then, the voltage is emoved and the cable conducto eathened. t this point, a few voltage-off measuements of space chage ae done. fte emoving the eath 53

68 Chapte 3 Expeimental obsevation of space chage and electic field dynamics connection, a voltage of 90 kv is applied. The opeations necessay fo inveting the voltage polaity and pefoming the voltage-off measuements take two minutes. Figue shows the electic field distibutions coesponding to the space chage pofiles of Figue It is inteesting to see that the highest electic stess the cable expeiences duing the test is pesent at the inne conducto immediately afte the evesal of the voltage polaity. The eason fo this behavio is that immediately afte the invesion of the voltage polaity, the distibution of space chage is almost unchanged. In fact, the time equied fo the change of the voltage polaity (120 s) is much shote than the time the accumulated space chage needs to decay (tens of minutes hous). So, also the space chage field associated to the intenal chages emains pactically the same. s a consequence, the sum of the unchanged space-chage field and the applied field with diection is evesed, esults in a maximum field inside the cable of about 60% highe than the Laplace field, as shown in Figue Such a field is appoximately two times the aveage field within the cable (i.e. the field enhancement facto is 100%). Figue Space chage pofiles measued on a MV XLPE cable duing a polaity evesal test. T =20 K. Figue Electic field distibutions in a MV XLPE cable duing a polaity evesal test. T = 20 K. 54

69 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Summay and conclusions Fom space chage measuements pefomed on MV XLPE cables the following conclusions can be dawn. - Space chage with the same polaity as that of the applied voltage accumulates within the insulation of the studied cables when a tempeatue dop is pesent. Fo a given applied field, this chage inceases with the tempeatue dop, wheeas, fo a given tempeatue distibution, the amount of chage inceases with the applied field. The accumulated chage modifies the initial field distibution. The field inceases nea the oute semicon and deceases nea the inne semicon. It is to be noted that measuements pefomed at the lowe tempeatues and/o fields have lasted not long enough fo the chaging pocess to be completely finished. Fo claifying the effect of a (much) longe polaization time, esults of space chage calculations in DC cables will be pesented and discussed in the next chapte. - The absolute value of the tempeatue and the magnitude of the applied field affect the space chage dynamics. faste space chage accumulation is obseved at highe tempeatues and at highe fields. This is attibuted to the fact that the space chage accumulation is faste when the conductivity of the insulation is highe (the conductivity of the insulation is an inceasing function of tempeatue and field). - Heteo-chage nea the inne semicon was measued fo tempeatue dops acoss the insulation of 10 K and 20 K. The blocking popeties of the semicon-dielectic inteface ae assumed to be the cause fo the obseved heteo-chage. This topic will be futhemoe discussed in Chapte 5. - polaity evesal test was pefomed on a loaded cable. Space chage measuements wee pefomed befoe and afte the invesion of the voltage polaity. The expeimental esults show that this condition is paticulaly citical fo the cable insulation. In fact, afte the invesion of the voltage polaity, a maximum field, 60% highe than the Laplace field, was measued nea the inne conducto, leading to a field enhancement facto of almost 100%. The space chage field, which is induced by the space chage accumulated within the cable duing the polaization time (about 6 hous), is the oigin of such a high field enhancement. 55

70 Chapte 3 Expeimental obsevation of space chage and electic field dynamics 3.4. Space chage measuements on dual-dielectic mini-cables Intoduction In ode to investigate the space chage and electic field distibutions at coaxial intefaces, space chage measuements wee pefomed on dual-dielectic mini-cables. Two types of dual-dielectic mini-cables wee studied: EPR-XLPE mini-cables, in which the EPR is the innemost insulation and the XLPE is the outemost insulation, and XLPE-EPR mini-cables in which the XLPE is the innemost insulation and the EPR is the outemost insulation. In all the measuements, a DC voltage was applied at the inne conducto, wheeas the oute semicon was connected to eath. Typical voltage-on space chage pofiles, which wee measued immediately afte the application of the DC voltage, ae epesented in Figue 3.25 fo both types of mini-cables. In the figue, the coesponding electic field distibutions ae also depicted. Similaly to what is obseved in flat intefaces, a peak is pesent in the space chage pattens at the dielectic inteface also in the absence of intefacial chage. gain, the discontinuity of the pemittivity at the dielectic inteface is the cause of this peak. Space chage measuements wee pefomed at diffeent tempeatue conditions and at diffeent values and polaities of the applied voltage. The polaization conditions ae summaized In Table 3.3.a. In Table 3.3.b the tempeatue conditions ae summaized. In Table 3.3.b, the tempeatue distibutions acoss a EPR-XLPE dual-dielectic minicable ae also epesented fo the diffeent studied conditions. (The tempeatue distibutions in XLPE-EPR mini-cables ae vey simila to those epesented in the table). The data in the table ae obtained using the measued tempeatue values and assuming a themal conductivity of 0.3 W/mK fo both XLPE and EPR. Tab.3.3.a. Test conditions adopted fo the space chage measuements on dualdielectic mini-cables: polaization conditions. Dual-dielectic EPR-XLPE Dual-dielectic XLPE-EPR Voltage [kv] Voltage polaity +/- and pol. ev. +/- Electic field (aveage) [kv/mm] Polaization time [s]

71 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Tab.3.3.b. Test conditions adopted fo the space chage measuements on dualdielectic mini-cables: tempeatue conditions. EPR-XLPE XLPE-EPR Cable load [] T out [ C] T in [ C] T inteface T [K] T [K/mm] T XLPE [K/mm] T EPR [K/mm] a c b d Figue 3.25.a,b. a) Typical voltage-on space chage pofile measued immediately afte the application of the DC voltage acoss an EPR-XLPE dual-dielectic mini-cable. b) Electic field distibution deduced fom the space chage pofile. pplied voltage: U 0 = + 30 kv. Figue 3.25.c,d. c) Typical voltage-on space chage pofile measued immediately afte the application of the DC voltage acoss an XLPE-EPR dual-dielectic mini-cable. d) Electic field distibution deduced fom the space chage pofile. pplied voltage: U 0 = + 30 kv. 57

72 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Results Figue 3.26 shows the main esults of space chage measuements pefomed on dualdielectic mini-cables, which ae summaized in the following. - Chage with the same polaity as that of the applied voltage accumulates at the dielectic inteface of EPR-XLPE dual-dielectic mini-cables. - Chage with polaity opposite to that of the applied voltage accumulates at the dielectic inteface of XLPE-EPR dual-dielectic mini-cables. - Fo both types of mini-cables, the magnitude of the intefacial chage inceases with the tempeatue dop. Howeve, moe intefacial chage accumulates in EPR-XLPE mini-cables athe than in XLPE-EPR mini-cables (compae Figues 3.26.c and 3.26.f). - Fo both types of mini-cables, space chage with the same polaity as that of the applied voltage accumulates in the innemost dielectic when a tempeatue dop is applied. The magnitude of this chage inceases with the tempeatue dop. Howeve, moe space chage in innemost dielectic accumulates in XLPE-EPR mini-cables athe than in EPR-XLPE mini-cables (compae Figues 3.26.c and 3.26.f). - Chage with polaity opposite to that of the intefacial chage accumulates in the XLPE adjacent to the inteface of XLPE-EPR mini-cables when the load is 75. (see Figue 3.26.f). Measuements of space chage wee pefomed at both positive and negative polaities. Figue 3.27 shows that voltage-off space chage pattens measued at diffeent voltage polaities ae not identical. t negative voltage moe chage accumulates at the inteface of EPR-XLPE dual-dielectic mini-cables. On the othe hand, at positive voltage moe chage accumulates at the inteface of XLPE-EPR dual-dielectic minicables (see aows in the figue). In Figue 3.28, examples of the electic field pofiles deived fom the space chage distibutions ae shown. Duing the polaization time, the electic field inceases in the XLPE and deceases in the EPR fo EPR-XLPE dual-dielectic mini-cables. On the othe hand, fo XLPE-EPR mini-cables, a local enhancement of the electic field in the XLPE nea the inteface is obseved. 58

73 Chapte 3 Expeimental obsevation of space chage and electic field dynamics a d b e c f Figue 3.26.a,b,c. Voltage-on space chage pofiles of EPR-XLPE dual-dielectic mini-cables. pplied voltage U 0 = + 30 kv. a) I = 0 ; T = 0 K; T = 0 K/mm b) I= 50; T= 9K; T= 4.3 K/mm c) I=75; T=22 K; T=10.5 K/mm Figue 3.26.d,e,f. Voltage-on space chage pofiles of XLPE-EPR dual-dielectic mini-cables. pplied voltage U 0 = + 30 kv. d) I = 0 ; T = 0 K; T = 0 K/mm e) I= 50; T= 10K; T= 4.7 K/mm f) I=75; T=23 K; T=10.9 K/mm 59

74 Chapte 3 Expeimental obsevation of space chage and electic field dynamics a b Figue Voltage-off space chage pofiles of dual-dielectic mini-cables. a) EPR-XLPE; U 0 = +/-90 kv fo s; I =75 ; T = 22 K; T = 10.5 K/mm. b) XLPE-EPR; U 0 = +/-90 kv fo s; I =75 ; T = 23 K; T = 10.9 K/mm. a b Figue Electic field distibutions in dual dielectic mini-cables. a) EPR-XLPE; U o = +30 kv; I = 75 ; T = 22 K; T = 10.5 K/mm. b) XLPE-EPR; U 0 = +30 kv; I = 75 ; T = 23 K; T = 10.9K/mm Discussion Fom a macoscopic point of view, two main mechanisms ae esponsible fo the accumulation of space chage in coaxial intefaces. 1. ccoding to the MW theoy fo the intefacial polaization, chage is expected to accumulate at the dielectic inteface. This happens when the atio of the conductivities of the mateials in contact is diffeent fom the atio of the pemittivities. 2. nalogously to what occus in loaded cables, the tempeatue dop acoss the coaxial inteface leads to a conductivity gadient in the insulation. Unde this condition, space chage with the same polaity as that of the applied voltage accumulates in the insulation bulk when an electic field is applied. 60

75 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Intefacial chage Chage with the same polaity as that of the applied voltage builds-up at the dielectic inteface of EPR-XLPE dual dielectic mini-cables. On the othe hand, chage with polaity opposite to that of the applied voltage accumulates at the dielectic inteface of XLPE-EPR dual dielectic mini-cables. oth behavios ae in ageement with the MW theoy. The conductivity of XLPE is much lowe than the conductivity of EPR in the studied conditions. Consequently, the theoy pedicts intefacial chage to accumulate with such a polaity to enhance the electic field in the less conductive mateial (i.e. XLPE, fo the studied conditions) and to decease the field in the moe conductive mateial (i.e. EPR, fo the studied conditions). In both types of dual-dielectic mini-cable, moe chage was measued at the highe tempeatues. This may seem in contast to the fact that the lagest amount of intefacial chage is expected at the lowe tempeatues, when the conductivities of XLPE and EPR diffe by odes of magnitude. Howeve, similaly to what explained fo flat intefaces in Section 3.2.3, the DC voltage was not applied fo a time long enough to let the chaging phenomenon each a steady state. This is evident in Figue 3.29, whee the evolution in time of intefacial chage is shown fo both types of dual dielectic mini-cables at diffeent tempeatues. So it is believed that moe intefacial chage accumulates at lowe tempeatues, as expected by the MW theoy, if the voltage is applied fo a sufficiently long time (time >> s). In ode to check whethe this assumption is coect, a 2-week long measuement was pefomed on a EPR-XLPE dual-dielectic mini-cable at oom tempeatue. The esults of the test ae epesented in Figues 3.30 and The pictues show that indeed a chage of almost 200 µc/m 2 accumulates at the inteface afte two weeks of polaization. a b Figue Evolution in time of intefacial chage in dual-dielectic mini-cables. a) EPR-XLPE mini- cables. b) XLPE-EPR mini-cables. pplied voltage U 0 =+30 kv fo both mini-cables. 61

76 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Figue Voltage-on space chage pofiles of XLPE-EPR dual-dielectic minicables. U 0 = 30 kv, T = 20 C, polaization time = 2 weeks. The aows indicate the diection in which the space chage patten evolves in time. Figue Evolution in time of intefacial chage in XLPE-EPR dualdielectic mini-cables. U 0 =+30 kv, T = 20 C. ulk space chage Chage with the same polaity as that of the applied voltage builds-up in all the studied coaxial intefaces when a tempeatue dop is pesent acoss the insulation. This phenomenon is attibuted to the fact that a gadient in the insulation conductivity exists when a tempeatue dop is applied. The effect of bulk chage is to incease the field nea the oute semicon and to decease the field nea the inne semicon. Mutual evolution in time of space chage, intefacial chage and electic field Expeimental esults show an inteesting chaacteistic of coaxial intefaces. ccumulation of intefacial chage affects the behavio of bulk space chage due to the tempeatue dop and vice-vesa. In fact: - the magnitude of both space chage due to the tempeatue dop and intefacial chage inceases with the electic field at the space/inteface chage location; - the electic field at the space/inteface chage location depends on the chage distibution within the entie insulation; - theefoe, thee is a mutual evolution in time of intefacial chage, space chage and electic field in loaded coaxial intefaces. 62

77 Chapte 3 Expeimental obsevation of space chage and electic field dynamics This phenomenon can be obseved in the expeimental esults pesented in this section. Fo instance, compaing space chage chaacteistics of the two diffeent types of dualdielectic mini-cables, it is evident that moe intefacial chage accumulates in EPR- XLPE mini-cables athe than in XLPE-EPR mini-cables. The opposite can be said fo the space chage in the bulk of the innemost insulation (see Figues 3.26 and 3.27). The eason fo this is that in XLPE-EPR cables the intefacial chage inceases the field in the innemost laye of the cable, wheeas in EPR-XLPE cables the intefacial chage deceases the field in the innemost laye of the cable. Since the magnitude of bulk space chage in the innemost laye inceases with the field, moe space chage is expected when a highe field is pesent. The mutual evolution in time of chages and electic field depends on seveal factos. pplied voltage, geomety, tempeatue distibution, pemittivity and conductivity have indeed a ole in the pocess. Using these macoscopic paametes of the insulation as input, the model pesented in Chapte 4 will be used fo the estimation of the time-dependent field distibution and chage accumulation in coaxial intefaces. Chage adjacent to the inteface and polaity effects In addition to the macoscopic chaging behavio descibed above, the studied coaxial intefaces show othe two diffeent accumulation phenomena, which cannot be coelated to a tempeatue-dop-induced gadient of the insulation conductivity. - Chage with polaity opposite to that of the chage at the inteface can be obseved nea to the inteface in the XLPE laye of XLPE-EPR dual-dielectic mini-cables. This is simila to what has been obseved at flat intefaces (see Section 3.2.3). - Space chage pattens measued at diffeent voltage polaities ae not exactly symmetic. Pefectly symmetic pattens ae expected fom the MW theoy fo the intefacial polaization. Those phenomena will be dealt in details in Chapte 5. Polaity evesal Space chage measuements wee also pefomed duing polaity evesal tests fo EPR-XLPE mini-cables [24]. The following pocedue was employed fo the measuements. Fistly, a voltage of -30 kv is applied fo 10 4 s (2.8 hous). Then, the voltage is emoved and the cable conducto connected to eath. fte emoving the eath connection, a voltage of +30 kv is applied fo anothe 10 4 s. The opeations necessay fo inveting the voltage polaity takes about 60 s. In Figue 3.32, space chage pofiles detected duing a polaity evesal test ae epesented, wheeas in Figue 3.33, the coesponding electic field distibutions ae shown. The highest electic stess the mini-cable expeiences duing the test is pesent at the inne conducto immediately afte the evesal of the voltage polaity. The maximum field inside the mini-cable is about 25% highe than the Laplace field (i.e. a field enhancement facto of about 75%). On the othe hand, the absolute value of the field at the inteface afte polaity evesal is lowe than the initial intefacial field (see solid and dashed lines in Figue 3.33). 63

78 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Figue Space chage pofiles measued on a EPR-XLPE mini-cable duing a polaity evesal test [24]. I = 75 ; T 22 K; T 10.5 K/mm. Figue Electic field pofiles measued on a EPR-XLPE mini-cable duing a polaity evesal test [24]. I = 75; T = 22 K; T = 10.5 K/mm Summay and conclusions Fom the esults of space chage measuements on dual-dielectic mini-cables, the following conclusions can be dawn. - Chage accumulates at the dielectic inteface of the studied coaxial specimens following appoximately the behavio expected by the MW theoy. This means that the conductivity of the insulation has a majo ole in the polaization pocess of the inteface of the studied mini-cables. Howeve, measuements showed that polaization phenomena depends also on factos which ae not included in the MW model, fo instance the polaity of the applied voltage. This will be futhemoe studied in Chapte 5. - Measuement esults show that in coaxial specimens thee is a mutual evolution in time of space chage, intefacial chage and electic field. This fact should be taken into account in the calculation of the electic field distibution. 64

79 Chapte 3 Expeimental obsevation of space chage and electic field dynamics When a DC voltage is applied acoss a coaxial inteface, in addition to the initial Laplace field and the final esistive field, the field at intemediate stages need to be calculated. In fact, duing the tansition between capacitive and esistive field, a local maximum of the field distibution can be pesent in an unusual location of the insulation Space chage measuements on MV-size models of cable joints Intoduction Space chage and electic field distibutions wee investigated in MV-size models of cable joints. In all the measuements pesented in this section, the DC voltage was applied at the inne conducto, wheeas the oute semicon was connected to eath. typical voltage-on space chage pofile, which is measued immediately afte the application of the DC voltage acoss a joint model, is epesented in Figue In the figue, the coesponding electic field distibution is also depicted. a b Figue 3.34.a,b. a) Typical voltage-on space chage pofile measued immediately afte the application of the DC voltage acoss a MV-size model of a cable joint. b) Electic field distibution deduced fom the space chage pofile. pplied voltage U 0 = + 80 kv. Space chage measuements wee pefomed at diffeent tempeatue conditions and at diffeent values and polaities of the applied voltage. In Table 3.4.a, the tempeatue conditions ae summaized. The figue in the table points out the effect that a nonbonded inteface has on the tempeatue distibution. In fact, in the studied MV-size models of joints, the tempeatue changes with a step at the inteface. The data in the table ae obtained by using the tempeatue values in Table 3.4.a and consideing a 65

80 Chapte 3 Expeimental obsevation of space chage and electic field dynamics themal conductivity of 0.3 W m -1 K -1 fo both XLPE and EPR. In addition, a contact themal esistance pe length unit of 0.2 K m W -1 is taken into account, because of the fact that the contact between XLPE and EPR at the inteface is not ideal, see Section 2.4. The polaization conditions ae summaized In Table 3.4.b. Tab.3.4.a. Test conditions adopted fo the space chage measuements on coaxial intefaces: tempeatue conditions. Cable load [] T out [ C] T in [ C] T inteface [ C] * 58 * 32.5 ** 50 ** T [K] T [K/mm] T XLPE [K/mm] T EPR [K/mm] (*) tempeatue at the XLPE-side of the inteface (**) tempeatue at the EPR-side of the inteface Tab.3.4.b. Test conditions adopted fo the space chage measuements on MV-size models of joints: polaization conditions. Voltage [kv] Voltage polaity +/- +/- and polaity evesal Electic field (aveage) [kv/mm] Polaization time [s] Results The main outcomes of space chage measuements pefomed on MV-size models of cable joints ae epesented in Figue Expeimental esults show the following main chaacteistics. - t the constant tempeatue of 20 C and at applied voltage of +40 kv, no space chage can be obseved (theefoe, the elative pattens ae not epesented in Figue 3.35). t +80 kv, only a little chage with polaity opposite to that of the applied voltage accumulates at the XLPE-EPR inteface (see Figue 3.35.b). - Chage with the same polaity as that of the applied voltage accumulates in the XLPE and at the inteface when a tempeatue dop is pesent acoss the insulation of the joint model. The magnitude of the space chage inceases with the tempeatue dop 66

81 Chapte 3 Expeimental obsevation of space chage and electic field dynamics (compae Figues 3.35.b, 3.35.c and 3.35.d) and with the applied voltage (compae Figues 3.35.a and 3.35.d). - t the tempeatue dop of 20 K, chage with the same polaity as that of the applied voltage accumulates in the EPR (see Figues 3.35.a and 3.35.d). - Heteo-chage builds-up in the XLPE nea the inne electode at the tempeatue dop of 10 K and 20 K (see Figues 3.35.a, 3.35.c and 3.35.d). The effect of the accumulated chages is to move the location of the maximal electic stess fom the XLPE to the EPR. This is pointed out in Figue fte applying +80 kv to a joint model fo s when a 20 K tempeatue dop is pesent, the maximum field is located in the EPR, nea the dielectic inteface. In this situation, the field at the inne semicon is appoximately 50% lowe of its initial value. On the othe hand, at the inteface and the at the oute semicon, the field became about 50% highe than the initial field. Measuements of space chage wee pefomed at both positive and negative polaities. Figue 3.37 shows that slightly dissimila space chage pattens ae detected at diffeent voltage polaities. XLPE EPR Figue Electic field distibutions in a MV-size model of a cable joint. U 0 = +80 kv; T in = 65 C; T out = 45 C; T = 20 K; T = 5 K/mm. inteface Figue Voltage-off space chage pofiles in MV-size models of joints. U 0 = +/-80 kv fo s; T in = 65 C; T out = 45 C; T = 20 K; T = 5 K/mm. 67

82 Chapte 3 Expeimental obsevation of space chage and electic field dynamics a Voltage-on space chage distibutions. U 0 = +40 kv T in = 65 C T out = 45 C T = 20 K T = 5 K/mm b Voltage-on space chage distibutions. U 0 = +80 kv T in = 20 C T out = 20 C T = 0 K T = 0 K/mm c Voltage-on space chage distibutions. U 0 = +80 kv T in = 40 C T out = 30 C T = 10 K T = 2.5 K/mm d Voltage-on space chage distibutions. U 0 = +80 kv T in = 65 C T out = 45 C T = 20 K T = 5 K/mm Figue Voltage-on space chage pofiles in MV-size models of joints. 68

83 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Discussion Similaly to what said fo dual-dielectic cables, also in MV-size models of joints chage is expected to accumulate at the dielectic inteface and, when a tempeatue dop is pesent, in the insulation bulk. Howeve, diffeently to what obseved in dual-dielectic cables, in MV-size models of joints the intefacial chage accumulates with such a polaity to incease the electic field in the EPR and to decease the field in the XLPE. ccoding to the MW theoy, this behavio implies that the conductivity of XLPE is highe than that of EPR fo the studied conditions. To veify whethe the conductivity of XLPE is highe than that of EPR in the studied joint models, the adial distibution of the insulation conductivity σ() is calculated accoding to the following elation [26]: () = σ [ α ( T () )] σ exp T (3.4) 0 0 The value of the conductivity σ 0 at the efeence tempeatue T 0 and the value of the paamete α ae epoted in Table 3.5. They ae chosen in ode to match the expeimental data pesented in Section 3.1. Figue 3.38 shows that indeed the conductivity of the XLPE is highe than that of EPR, fo the tempeatue conditions T=10 K and T= 20 K. Theefoe, the paticula tempeatue distibution pesent acoss the joint model is the main cause of the obseved space chage and field behavios. It is to be noted that the contact between XLPE and EPR stongly affects the tempeatue distibution (and then the field distibution) by means of the paamete contact themal esistance. Figue Radial distibution of the insulation conductivity calculated fo the studied MV-size models of joint models at diffeent tempeatue when a DC voltage of 80 kv is applied. Table 3.5. Paametes used fo the calculation of the conductivity distibution in MV-size models of cable joints. T 0 [ C] σ 0 [Ω -1 m -1 ] α [1/K] XLPE kv/mm 0.2 EPR kv/mm

84 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Polaity evesal Space chage measuements wee pefomed also duing a polaity evesal test. test pocedue simila to that used fo MV-size cables was adopted. Fistly, a voltage of +80 kv is applied fo s (5.6 hous). Then, the voltage is emoved and the cable conducto eathened. t this point, a few voltage-off measuements of space chage ae done. fte emoving the eath connection, a voltage of 80 kv is applied. The opeations necessay fo inveting the voltage polaity and pefoming the voltageoff measuements take about two minutes. In Figue 3.39, space chage pofiles detected duing the polaity evesal test ae epesented, wheeas Figue 3.40 shows the coesponding electic field distibutions. Similaly to what obseved fo MV-size cables, the joint model expeiences the highest electic stess at the inne conducto immediately afte the evesal of the voltage polaity. The maximum field is about 50% highe than the Laplacian field, as shown in Figue Such a field is moe than two times the aveage field within the cable (i.e. the field enhancement facto is 125%). Figue Space chage pofiles measued on a MV-size model of cable joint duing a polaity evesal test. U 0 = +/-80 kv; T in = 65 C; T out = 45 C ; T = 20 K ; T = 5 K/mm. Figue Electic field distibutions in a MV-size model of cable joint duing a polaity evesal test. U 0 = +/-80 kv; T in = 65 C; T out = 45 C ; T = 20 K ; T = 5 K/mm. 70

85 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Summay and conclusions Fom the space chage measuements pefomed on MV-size models of cable joints, the following conclusions can be dawn. - Chage with the same polaity as that of the applied voltage accumulates at the XLPE-EPR inteface. The effect of the intefacial chage is to incease the electic field in the EPR and to decease the field in the XLPE. - Space chage with the same polaity as that of the applied voltage accumulates within the insulation of the joint models when a tempeatue dop is applied. The chage builds-up mainly in the XLPE. The amount of accumulated chage inceases with the tempeatue dop fo a given applied field and with the applied field fo a given tempeatue condition. The effect of this chage is to incease the electic field nea the oute semicon and decease the field nea the inne semicon. - The detected space chage is mainly attibuted to the non-unifom conductivity distibution of the insulation. - Some heteo-chage was also measued in the XLPE, mainly at the highe tempeatues. - polaity evesal test showed that this condition is paticulaly citical fo the studied joint models. In fact, afte invesion of the voltage polaity, a maximum field 50% highe than the Laplacian field was measued nea the inne conducto, leading to a field enhancement facto of about 125%. 71

86 Chapte 3 Expeimental obsevation of space chage and electic field dynamics 3.6. Conclusions Space chage measuements pefomed on diffeent types of XLPE-EPR specimens showed that diffeent accumulation mechanisms ae esponsible fo space chage build-up in the insulation of the studied specimens. Conductivity-gadient accumulation If a gadient is pesent in the spatial distibution of the conductivity, space chage accumulates in time with such a polaity to incease the field in the pat of the insulation whee the conductivity is lowe and to decease the field in the pat of the insulation whee the conductivity is highe. Since the insulation conductivity depends on electic field and tempeatue, this mechanism is active when a tempeatue dop and/o a field gadient ae pesent acoss the insulation. In paticula, this mechanism is evident in all the esults of tests pefomed while a tempeatue dop is applied acoss the insulation. The amount of accumulated chage inceases with the tempeatue dop fo a given applied field, wheeas fo a given tempeatue dop the amount of chage inceases with the applied field. The accumulation in time of the chage is faste at highe tempeatues and at highe applied fields. Theefoe, if a tempeatue dop is applied, space chage accumulates faste in the wamest pat of the insulation. In the coldest pat of the insulation, slowe space chage build-ups ae pesent. Consequently, this kind of accumulation pocess can be consideed stabilized only when the space chage in the coldest pat of the insulation has eached a steady state. Intefacial polaization t dielectic intefaces, the Maxwell-Wagne polaization mechanism is esponsible fo the accumulation of chage. The MW polaization can be consideed a paticula case of the accumulation mechanism descibed above. If the insulation is composed of two diffeent mateials, then the distibution of conductivity and that of the pemittivity have a discontinuity at the inteface between the two mateials. In pactice, this leads to a discontinuity of the atio between pemittivity and conductivity at the dielectic inteface. Fo this eason, intefacial chage is expected to accumulate. Intefacial chage was measued in all specimens in which a dielectic inteface is pesent. oth magnitude and accumulation time ae in a quite good ageement to what expected by the MW theoy. s fo the pevious mechanism, chage takes moe time to accumulate at lowe tempeatue. (s an example, at oom tempeatue, the accumulation of intefacial chage in a XLPE-EPR inteface takes moe than two weeks befoe eaching the steady state, when an aveage field of about 14 kv/mm is applied). Heteo-chage and polaity effects Measuement esults showed also accumulation of chage which could not be coelated neithe to the conductivity-gadient mechanism no to the intefacial polaization mechanism. 72

87 Chapte 3 Expeimental obsevation of space chage and electic field dynamics Fo tempeatues above 40 C, heteo-chage accumulates in the XLPE of diffeent types of specimens. The heteo-chage has been attibuted to the blocking popeties of the semicon-dielectic inteface and dielectic-dielectic inteface encounteed in the studied specimens. The MW theoy pedicts symmetic behavio of the intefacial chage at diffeent polaities of the applied voltage. Howeve, measuements showed clea diffeences between intefacial chage pattens detected at diffeent voltage polaities. Those chaging phenomena will be futhemoe investigated in Chapte 5. physical model of the insulation descibing the space chage accumulation in cable systems will be pesented in the next chapte. Fo the studied specimens, the extent of chage that has been attibuted to the conductivity-gadient accumulation mechanism and to the intefacial polaization mechanism ae moe significant than the extent of chage attibuted to chage injection/blocking. This means that the conductivity of the insulation and its dependency on field and tempeatue have a majo ole in the chaging behavio of the studied XLPE-EPR specimens. Fo this eason, the model pesented in Chapte 4 will conside the space chage build-up due to only the conductivity-gadient accumulation mechanism and the intefacial polaization mechanism. The chage dynamics will be calculated fo the studied specimens and compaed to the expeimental esults. In this way, the model pesented in the next chapte will be validated. 73

88 Chapte 3 Expeimental obsevation of space chage and electic field dynamics 74

89 Chapte 4 Calculation of space chage and electic field in DC cable systems 4. Calculation of space chage and electic field in DC cable systems In this chapte, a physical model and a numeical pocedue ae pesented fo the calculation of the space chage dynamics and the electic field distibutions in DC cable systems. In Section 4.1, some geneal consideations about the models and the pocedues fo the calculation of the space chage and the electic field in DC insulation ae given. In paticula, an oveview is shown of the pocedues available in the liteatue fo the calculation of the DC field in cables. The physical model and the coesponding calculation pocedue developed in this thesis ae intoduced in Section 4.2. Moeove, the limits of the chosen model ae assessed and the hypotheses, on which the model is based, ae discussed. Section 4.3 shows the esults of the calculation in the fom of space chage pattens. The expeimental pattens pesented in Chapte 3 ae compaed to the pattens deived by means of the numeical pocedue. In Section 4.4, the space chage and the electic field ae deived fo seveal situations of pactical inteest. Finally, some conclusions ae dawn in Section Intoduction Though the yeas, seveal models have been pesented in the liteatue fo the calculation of space chage and electic field in DC insulation when a conductivity gadient and an extenal field ae pesent at the same time. In geneal, the models (see Table 4.1) conside the insulation as a weakly conductive continuum in which a non-homogeneity can be induced by a non-unifom applied stess. This is the case of loaded DC cables and of the majoity of HVDC devices. In fact, in those components a conductivity gadient is induced by the non-unifom electic field and/o by the tempeatue dop acoss the insulation. The main advantage of this type of model is that only a few macoscopic paametes of the insulation ae equied fo the chaacteization of the model (e.g. conductivity and pemittivity as a function of field and tempeatue). This makes the model applicable to a numbe of diffeent situations without the need fo modifying its stuctue. Moeove, fo a given mateial, the model can be applied to seveal geometies and seveal extenal conditions without changing the paametes of the insulation. Othe advantages ae that the implementation of a macoscopic modeling of the insulation is elatively staightfowad and the application of the model to pactical cases is faily simple. On the othe hand, no infomation is povided fo instance about chage caie injection, blocking o space chage tapping. Those space chage pocesses can be 75

90 Chapte 4 Calculation of space chage and electic field in DC cable systems descibed by a diffeent type of model, which consides the micoscopic popeties of the insulation, e.g. [31, 32, 91, 129]. Howeve, a lage numbe of paametes have to be popely set in ode to achieve good esults. Hitheto, seveal authos studied the space chage phenomena in DC cables caused by a tempeatue-dop-induced conductivity gadient. fte the pioneeing wok of Lau [89], in which the evolution of chage in time was consideed fo the fist time, a numbe of publications have appeaed. Table 4.1 gives an oveview of some of the macoscopic models and elative pocedues available in the liteatue fo the calculation of space chage in DC cables. The pocedue developed in this thesis diffes fom the pocedues listed in Table 4.1 on the fact that it can be applied fo the study of an insulation system consisting of two diffeent mateials. This is done by consideing both the conductivity-gadient mechanism and the intefacial polaization mechanism fo the chage accumulation. In this way, we ae able to calculate space chage dynamics and electic field not only in loaded cables, but also in loaded cable joints. 76

91 Chapte 4 Calculation of space chage and electic field in DC cable systems Table 4.1. Liteatue suvey of some of the models and pocedues developed though the yeas fo the calculation of the space chage and field in DC cables. UTHOR YER(S) REFERENCE Lau 1970 [89] Mclliste et al. Coelho et al. Jeoense et al.. ambey et al. oggs et al. Hanley et al. Ildstad et al [104, 105] [2, 41, 42] [78, 80] [9-11, 66] [28, 29, 65] 2003 [63] [74, 75] NOTES Fist wok consideing the time-dependent accumulation of space chage in DC cables due to a conductivity gadient. The field dependency of the conductivity is not consideed. n expession, which allows the calculation of the steady-state space chage distibution in DC cables, is deived in a closed mathematical fom. oth tempeatue and field dependencies of conductivity ae consideed. The accumulation in time of the space chage is not consideed, but only the final steady-state distibution is calculated. The papes analyze and extend the wok pesented in [89]. The field dependency of the insulation conductivity is included in the calculation. numeical pocedue is poposed fo the calculation of time-dependent space chage and electic field in DC pape-insulated cables. The themal and the electical tansient ae coupled. The effect of themal cycles on chage and field is included in the pocedue. The insulation losses can be included in the pocedue. The steady-state space chage distibution is calculated fo flat geomety. Results of calculations ae compaed with measuements done by means of the LIPP method. Measuement ae also pefomed unde isothemal conditions, in ode to distinguish space chage induced by the tempeatue gadient and space chage due to diffeent accumulation mechanisms. The time-dependent field distibution is numeically calculated. The adopted pocedue is optimized fo polymeic DC cables. space-dependent conductivity nea the semicon sceens can be used fo modeling suface effects at the polyme-semicon inteface. geneal eview is given of polymeic insulation fo the use in HVDC cables. In paticula, some pactical examples ae given fo the expected field distibutions and space induced by a conductivity gadient in polymeic DC cables. The pocedues developed in [104, 105] ae used fo the calculation of the field in dc polymeic cables unde seveal woking conditions. The input paametes fo the calculation ae deived fom space chage and conduction cuent measuements. 77

92 Chapte 4 Calculation of space chage and electic field in DC cable systems 4.2. Physical model Theoetical backgound The following thee equations descibe the electical behavio of a non- homogeneous weakly conductive mateial: j = σ E Ohm s law (4.1) = E Gauss law (4.2) ρ 0 ( ) ρ j = Cuent continuity equation (4.3) t y combining these thee equations 1, the space chage is given by: ρ = σ ρ 0 + j t σ 0 (4.4) Equation (4.4) shows that when the cuent density is diffeent fom zeo, space chage ρ accumulates if the atio between elative pemittivity and conductivity σ is not unifom acoss the insulation, see the second tem on the ight-hand side of equation (4.4). The pemittivity of the insulation can be consideed constant within the ange of tempeatues and fields adopted in this wok [45]. On the othe hand, the conductivity is to be consideed a function of both tempeatue and field. In the liteatue, e.g. [28, 104] the following two equations ae often used fo taking into account the field and tempeatue dependency of conductivity: ν E σ ( T, E) = σ ef exp[ α ( T Tef )] (4.5) E ef E ( E ) ( T, sinh a E) exp k T σ = (4.6) E In equation (4.5), σ ef is the conductivity at the tempeatue T ef and at the field E ef, wheeas ν and α ae constants. In equation (4.6), E a is the themal activation enegy, k oltzmann s constant, and ae constants. Equation (4.5) is an empiical fomula. On the othe hand, equation (4.6) is deived fom the hopping theoy model of conduction in amophous dielectics [45, 87]. Theefoe, Equation (4.6) assumes that the hopping mechanism is active. This gives a physical explanation to the specific tempeatue dependency and field dependency of the conductivity. Howeve, thee paametes, and E a ae needed fo the chaacteization of the conductivity function. 1 If φ is a scala function and f is a vecto function, the following elation is valid: v φ f = φ f + φ ( ) ( ) f 78

93 Chapte 4 Calculation of space chage and electic field in DC cable systems Field calculations wee pefomed using both conductivity equations. The effect of the two diffeent conductivity equations on the calculation esults is discussed in Section 4.3. s discussed in Section 2.4.1, eithe a steady-state tempeatue distibution o a dynamic tempeatue distibution can be applied acoss the cable insulation. oth conditions ae consideed in the developed pocedue. In ode to solve equation (4.4), the following initial conditions and bounday conditions ae used. Initial conditions The electic field immediately afte the application of the DC voltage is capacitively distibuted. This implies that at time t = 0 s, no space chage is pesent within the insulation: ( t = 0 ) = 0 ρ (4.7) ounday conditions The extenal DC voltage applied acoss the insulation must be known and the electic field distibution must fulfil the following equation: E = U (4.8) In ppendix E, the equations pesented in this section ae chaacteized fo the specific studied configuation (i.e. two diffeent insulating mateials aanged in a coaxial lay out) Model of the insulation The system to be studied consists of the cable insulation in non-ohmic 2 contact with the electodes [45]. This is modelled by consideing an equivalent insulation in ohmic contact with the electodes. The conductivity of the equivalent insulation is deived by fitting the conductivity function with the expeimental esults of conduction cuent measuements. The measuements have been pefomed on the system to be modelled, i.e. the cable insulation in non-ohmic contact with the electodes. In this way, the equivalent insulation includes the effect that the electodes have on the conduction pocess. In Figue 4.1, this concept is schematised. Limits of the model y consideing ohmic contact between insulation and electodes, injection and blocking popeties of the dielectic/electode inteface cannot be included in the model. The same is valid fo the dielectic inteface between two insulations, if a cable joint is modelled. 2 Ohmic contact between electodes and insulation occus if the cuent injected by the electodes equalizes the cuent tanspoted by the insulation. If this condition is not fulfilled, the contact is non-homic. 79

94 Chapte 4 Calculation of space chage and electic field in DC cable systems The equivalent insulation is consideed to have a conductivity function which paametes do not depend on the position. Nevetheless, in the insulation nea the electode/insulation intefaces and nea the dielectic inteface, the conductivity may diffe fom the conductivity of the insulation bulk, because of the so called suface effects [29, 65]. The model uses the steady-state values fo the paametes conductivity and pemittivity. Howeve, since the time step used in the calculation is elatively shot (see next section), dynamic values would be moe appopiate fo the model. Seveal types of chage caies (e.g. electons, holes, ions) contibute to the conduction pocess in insulating mateials. The paamete conductivity takes into account the oveall contibution that each type of chage caie has on the conduction pocess. Howeve, each type of chage caie behaves diffeently, fo instance, with egad to chage tapping in the insulation and chage blocking at the intefaces. ecause of this fact, the macoscopic model cannot pedict phenomena such chage blocking nea to intefaces o the fact that the amount of space chage accumulated at a dielectic inteface may depend on voltage polaity [21, 24, 146]. In Chapte 5, these points will be consideed and suggestions on how to adapt the model will be given. Figue 4.1. Schematic epesentation of the macoscopic model adopted in this wok. 80

95 Chapte 4 Calculation of space chage and electic field in DC cable systems Numeical implementation of the physical model The model is implemented by means of a numeical pocedue. Fo the pocedue it is assumed that the adial space chage distibution within the cable / cable joint is the same along the whole cable, independently on the axial position and on the angula position. Theefoe, a one dimensional configuation, which is epesented in Figue 4.2, is used. Figue 4.2. Model of the insulation as used in this wok. The insulation is divided into a numbe of patitions of thickness. = inne adius = oute adius C =inteface adius The insulation is divided into 201 annulus-shaped patitions of thickness (see Figue 4.2). Each patition is chaacteized by the following quantities, which ae in geneal function of time t and adius : -Tempeatue T(t,) -Electic field E(t,) -Cuent density J(t,) -Space chage ρ(t,) -Conductivity σ(t(t,),e(t,)) -Pemittivity () In case of cable joints, the intefacial chage κ(t), which accumulates at the intefacial adius c, is to be consideed as well. The quantities above specified ae assumed to be constant within each patition and within a time inteval t. fte calculating all quantities fo the initial conditions, the time is inceased by a time step t and the quantities ae ecalculated. This is epeated until the time has eached a pedefined value o the calculation has conveged towad a solution. n exponentially inceasing time step is used in ode to educe the numbe of iteations. The calculation can be consideed conveged if the divegence of the 81

96 Chapte 4 Calculation of space chage and electic field in DC cable systems cuent density is smalle than a pedefined eo. In fact, when the divegence of the cuent density is zeo, the actual electic field is a puely esistively-distibuted field. If a dynamic tempeatue distibution is consideed, fistly the time dependent tempeatue distibution is calculated. fte this, the electical equations ae solved consideing the time-dependent tempeatue distibution peviously deived. In fact, solving simultaneously the themal and electical tansients can lead to convegence poblems o to a long calculation time. This is due to the fact that the time necessay to each a steady state is geneally diffeent fo the themal and electical tansients. In Figue 4.3 the flow-chat of the pocedue is epesented. Figue 4.3. Flow-chat of the pocedue fo the calculation of space chage and electic field in DC cables and DC cable joints. 82

97 Chapte 4 Calculation of space chage and electic field in DC cable systems 4.3. Results of the calculation Calculation vs. measuements In this section the esults of the calculation ae pesented and compaed with the expeimental esults. gaussian filte is applied to the simulated data, in ode to epoduce pattens of the same type as the measued pattens. ll the calculated pattens ae obtained by consideing the same polaization and tempeatue conditions as adopted fo the measuements. Fo each studied situation, the insulation is always chaacteized with the following paametes: el. pemittivity XLPE = 2.3 el. pemittivity EPR = 2.9 Conductivity XLPE as in equation (4.5): σ ef = Ω -1 m -1 ; T ef = 20 C; E ef = 13 kv/mm; α = 0.16 K -1 ; ν = 1.8 Conductivity EPR as in equation (4.5): σ ef = Ω -1 m -1 ; T ef = 20 C; E ef = 13 kv/mm; α = 0.1 K -1 ; ν = 1.6 MV-size XLPE cable The development in time of space chage and electic field is calculated fo a studied MV-size XLPE cable unde the following conditions: pplied voltage : U 0 = + 90 kv Tempeatue : T in = 65 C ; T out = 45 C ; T = 20 K; T = 4.4 K/mm In Figue 4.4, the esults of the calculation ae compaed to the esults of the measuements. Figue 4.4 shows that accumulation of positive space chage is pedicted in the insulation bulk due to the pesence of the tempeatue dop. The maximum of the calculated space chage distibution is slightly undeestimated and no heteo-chage nea the inne semicon is simulated (compae Figues 4.4.a and 4.4.b). On the othe hand, the fact that most of the chage accumulates in the fist 10 4 s of polaization is acceptably estimated by the model. This is shown in Figues 4.4.e and 4.4.f, whee the chage evolution in time is shown at specific locations in the cable insulation. The calculated field pattens and the measued electic field pattens ae quite simila: the field invesion phenomenon is in fact pedicted by the model. Howeve, the field at the oute semicon is slightly undeestimated. In addition, the minimum of the field distibution nea the inne semicon (compae Figues 4.4.c and 4.4.d) is not epoduced. 83

98 Chapte 4 Calculation of space chage and electic field in DC cable systems a b Figue 4.4.a. Calculated space chage pattens. Figue 4.4.b. Measued space chage pattens. c d Figue 4.4.c. Calculated electic field pattens. Figue 4.4.d. Measued electic field pattens. e f Figue 4.4.e,f. Evolution in time of space chage in specific locations of a MV XLPE cable. e) Expeimental pattens. f)calculated pattens. a) nea the inne semicon; = 5 mm; b) in the middle of the insulation; = 6.75 mm; c) nea the oute semicon; = 8.5 mm. 84

99 Chapte 4 Calculation of space chage and electic field in DC cable systems EPR-XLPE dual-dielectic mini-cables The development in time of space chage and electic field is calculated fo a studied EPR-XLPE dual-dielectic mini-cable unde the following conditions: pplied voltage : U 0 = + 30 kv Tempeatue : T in = 68 C ; T out = 46 C ; T = 22 K; T = 10.5 K/mm In Figue 4.5, the esults of the calculation ae compaed to the esults of the measuements. The macoscopic model pedicts accumulation of chage at the inteface between EPR and XLPE because of the jump in pemittivity and conductivity. In addition, space chage is pedicted in the bulk of the EPR due to the pesence of the tempeatue gadient. The magnitude of both the intefacial chage and the chage in the bulk of the EPR ae well epoduced by the model. lso in this case, the fact the most of the chage accumulates in the fist 10 4 s of polaization is coectly pedicted. The pesence of chages within the insulation leads to a significant distotion of the electic field distibution, compae Figue 4.5.c and 4.5.d. This is well pedicted by the model. a EPR -XLPE b EPR -XLPE Figue 4.5.a. Calculated space chage pattens. Figue 4.5.b. Measued space chage pattens c d EPR -XLPE Figue 4.5.c. Calculated electic field pattens. EPR -XLPE Figue 4.5.d. Measued electic field patten. 85

100 Chapte 4 Calculation of space chage and electic field in DC cable systems XLPE-EPR dual-dielectic mini-cables The development in time of space chage and electic field is calculated fo a studied XLPE-EPR dual-dielectic mini-cable unde the following conditions: pplied voltage : U 0 = + 30 kv Tempeatue : T in = 64 C ; T out = 41 C ; T = 23 K; T = 10.9 K/mm In Figue 4.6, the esults of the calculation ae compaed to the esults of the measuements. Similaly to what has been obseved fo EPR-XLPE dual-dielectic mini-cables, the macoscopic model pedicts accumulation of chage at the inteface between EPR and XLPE and in the bulk of the XLPE. The intefacial chage is slightly undeestimated wheeas the chage in the XLPE nea the inne semicon is slightly oveestimated. Nevetheless, the electic field distibution is well pedicted by the model. a XLPE - EPR b XLPE - EPR Figue 4.6.a. Calculated space chage pattens. c Figue 4.6.b. Measued space chage pattens. d XLPE - EPR Figue 4.6.c. Calculated electic field pattens. XLPE - EPR Figue 4.6.d. Measued electic field pattens. 86

101 Chapte 4 Calculation of space chage and electic field in DC cable systems MV-size models of XLPE-EPR cable joints The development in time of chage and electic field is calculated fo a studied MVsize model of XLPE-EPR cable joint unde the following conditions: pplied voltage : U 0 = + 80 kv Tempeatue : T in = 65 C ; T out = 45 C ; T = 20 K; T = 5 K/mm In Figue 4.7, the esults of the calculation ae compaed to the esults of the measuements. gain, fom a macoscopic point of view, it can be deived that positive chage will accumulate at the inteface of the cable joint unde the studied tempeatue conditions (see Figues 4.7.a and 4.7.b). Howeve, the amount of intefacial chage is slightly undeestimated by the model. In addition, thee is some diffeences between the chage pofiles in the XLPE bulk. Nea the inne semicon the model pedicts positive chage, wheeas no chage was measued at that location. s pointed out in Chapte 3, thee is expeimental evidence of accumulation of negative heteo-chage nea the inne conducto. The heteo-chage compensates to a lage extent the positive chage due to the tempeatue dop. Despite those facts, the electic field distibution is athe well pedicted by the model. In fact, the calculation indicates that the field inceases in the EPR and deceases in the XLPE. Howeve, because of the diffeences obseved in the space chage pattens, the maximum value of the field in the EPR nea the inteface is slightly undeestimated by the model (see Figues 4.7.c and 4.7.d). XLPE - EPR XLPE - EPR Figue 4.7.a. Calculated space chage pattens. Figue 4.7.b. Measued space chage pattens. XLPE - EPR Figue 4.7.c. Calculated electic field pattens. XLPE - EPR Figue 4.7.d. Measued electic field pattens. 87

102 Chapte 4 Calculation of space chage and electic field in DC cable systems Effect of the conductivity function on calculated pattens In Figue 4.8, the conductivity of the XLPE flat specimens with semicon electodes is epesented as function of the electic field fo thee diffeent tempeatues: 20 C, 40 C and 60 C. The expeimental points and the points calculated by means of equations (4.5) and (4.6) ae epesented in the figue. In Table 4.2, the values of the paametes adopted in the two equations ae epoted. oth equations fit quite well the expeimental points, fo values of the electic field which ae above the theshold field identified in Section 3.1. Figue 4.8. Conductivity of XLPE specimens with semicon electodes as a function of the electic field fo thee tempeatue values. Expeimental points and points calculated by means of equations (4.5) and (4.6). Table 4.2. Paametes adopted to fit the conductivity functions (4.5) and (4.6) with the expeimental esults of conduction cuent measuements. Equation paamete value unit eq. (4.5) * α 0.15 K -1 ν V -1 Ω -1 eq. (4.6) V -1 m E a 1.48 ev * The conductivity at 13kV/mm and 20 C, σ ef = Ω -1 m -1, has been used as efeence value. It is to be noted that the activation enegy adopted in Equation (4.6) coesponds to the value of the henius coefficient deived fom conduction cuent measuements ( see coefficient in Table 3.1). The activation enegy adopted in this wok is faily high in compaison with the values usually found in the liteatue fo XLPE [9, 28]. Howeve, in this wok, the adopted activation enegy does not chaacteize the XLPE insulation alone, but it includes the effect that the semicon electodes have on the conduction in the XLPE. Calculated space chage and electic field pattens, which 88

103 Chapte 4 Calculation of space chage and electic field in DC cable systems wee obtained by inseting into the model the two diffeent conductivity equations, did not show significant diffeences Electic field in cable systems fo paticula situations In this section, the model will be applied to an HVDC cable system woking at seveal situations of pactical inteest. The studied cable has the following chaacteistics: Voltage = 150 kv (bipola) Powe = 300 MW Cuent = 1 k Inne adius = 19 mm Oute adius = 31 mm Insulation = XLPE, with the same popeties as in Section Losses = 35 W/m Themal popeties of the equivalent laye (as defined in appendix E): Themal conductivity of the equivalent laye = 0.2 W m -1 K -1 Density of the equivalent laye = 1800 kg m -3 Specific heat of the equivalent laye (see ppendix E) = 1500 J kg -1 K -1 Radius of the equivalent laye (see ppendix E) = 100 mm Envionment tempeatue = 20 C Polaity evesal Let us assume that the voltage polaity will be inveted afte the cable has woked fo 8 h at nominal conditions. In this situation the tempeatue at the inne conducto is about 60 C, wheeas the tempeatue at the oute semicon is 50 C. In Figue 4.9, the calculated space chage pattens and the electic field distibutions ae epesented. a b Figue 4.9. Space chage (a) and electic field (b) pattes calculated befoe and afte the invesion of the voltage polaity. 89

104 Chapte 4 Calculation of space chage and electic field in DC cable systems Results of calculations show that because of the pesence of space chage, the field pofile afte 8 h of polaization deceases nea the inne semicon and inceases nea the oute semicon. ecause of this, the maximum field deceases (compae full line with dotted line in Figue 4.9.b). Howeve, the pesence of space chage stongly affect the field afte the invesion of the voltage polaity, as pointed out in Figue 4.9.b. Immediately afte the polaity evesal, the absolute value of the maximum field at the inne semicon inceases with about 25% (compae full line with dashed-dotted line in Figue 4.9.b). Inceasing of the tanspoted powe Let us assume that the powe tanspoted by the cable is inceased by 10% (i.e fom 300 MW to 330 MW). The space chage and the electic field distibutions is calculated fo the following two situations. - The cuent is inceased by 10% and the voltage is kept at its nominal value. Since the cuent inceases, the cable losses incease, and a new tempeatue distibution is established acoss the cable insulation. The tempeatue at the inne conducto becomes 69 C, wheeas the tempeatue at the oute semicon becomes 57 C. - The voltage is inceased by 10% and the cuent is kept at its nominal value. Since the nominal cuent flows into the cable, the tempeatue distibution acoss the insulation emains the same as in the pevious example. The space chage and electic field pattens coesponding to the two studied situations ae shown in Figue The figue shows that fo both cases moe space chage accumulates if compaed to amount of chage accumulated at the nominal conditions (compae Figues 4.9.a, 4.10.a and 4.10.c). In paticula, in the situation in which the cuent is inceased by 10%, the highest total amount of chage is accumulated in the cable insulation. This will have consequences on the field distibution in case of the voltage polaity is evesed, accoding to what concluded fo the pevious example. Compaing the electic field distibutions in Figues 4.10.b and 4.10.d, it can be noted that the capacitive field at time = 0 s is highe fo the case in which the voltage is inceased by 10% (full lines in the figues). On the othe hand, afte 4 h of polaization, the cable expeiences the highest electic field in the case in which the cuent is inceased by 10% (compae dashed lines in Figue 4.10.b and 4.10.d). This is due to the field distotion induced by the accumulated space chage, which is highe when the cuent, athe than the voltage, is inceased by 10% (compae dashed lines in Figues 4.10.a and 4.10.c). Finally, afte 8 h of polaization, the maximal field in the cable insulation is pactically the same fo both situations (see dotted lines in Figue 4.10.b and 4.10.d). In fact, afte 8 hous of polaization, the space chage becomes elatively high also when the voltage is inceased by 10% (but still smalle than the chage accumulated when the cuent is inceased by 10%, see dotted lines in Figues 4.10.a and 4.10.c). 90

105 Chapte 4 Calculation of space chage and electic field in DC cable systems a b c d Figue Space chage and electic field pattes calculated fo a situation in which the tanspoted powe is inceased by 10%. Space chage (a) and electic field (b) pattes calculated fo a situation in which the cuent is inceased by 10%. Space chage (c) and electic field (d) pattes calculated fo a situation in which the voltage is inceased by 10%. Dynamic tempeatue distibution In Figue 4.11, the tempeatue distibution acoss the cable insulation is epesented as a function of time and adius, when the cable woks at nominal conditions. It can be obseved that the tempeatue distibution has not yet eached a steady state afte 8 h. (The tempeatue calculation indicated that a steady state is eached afte about 24 h). The tempeatue acoss the cable insulation inceases with the time, fom 20 C at time = 0 s to the steady state tempeatue distibution of C at time=24h. This affects the of space chage dynamics and electic field distibutions, as shown in Figue Figue D plot of the dynamic tempeatue distibution acoss the cable insulation when the nominal cuent flows into the cable conducto. 91

106 Chapte 4 Calculation of space chage and electic field in DC cable systems a b Figue Space chage (a) and electic field (b) pattes calculated consideing a dynamic tempeatue distibution acoss the cable insulation. The amount of space chage in the pattens in Figue is much lowe, if compaed to the chage obseved in the pattens calculated at the same conditions, but consideing a steady state tempeatue distibution (see Figue 4.9.a). This is due to two main effects. Fistly, the cable expeiences the maximal tempeatue dop at the steady state condition. Theefoe, duing the themal tansient the tempeatue gadient is lowe and then less chage accumulates. Secondly, the time equied fo the chage accumulation depends on the absolute value of the tempeatue. Duing the themal tansient the tempeatue distibution is lowe then the steady state tempeatue distibution. This implies a slowe chage build-up than that occuing in the steady state situation. s a consequence, the chage accumulation pocess does not finish duing the polaization time. This contibutes to the fact that less chage is calculated when a dynamic tempeatue distibution is consideed. The elatively low amount of chage accumulated in the cable poduces only a slight distotion of the field distibutions, which ae all quite close to the capacitive field pofile. Effect of the intefacial contact in cable joints Electic field and space chage ae calculated fo a cable joint with the following specifications: Voltage = 150 kv (bipola) Powe = 300 MW Cuent = 1 k Inne adius = 19 mm Oute adius = 31 mm Inteface adius = 25.5 mm Innemost insulation = XLPE, with the same popeties as in Section Outemost insulation = EPR, with the same popeties as in Section Thee situations ae studied, which ae chaacteized by thee diffeent qualities of the themal contact at the inteface between XLPE-EPR: - R th,c = 0 K m W -1 ideal themal contact between XLPE and EPR; - R th,c = 0.15 K m W -1 athe good themal contact between XLPE and EPR; 92

107 Chapte 4 Calculation of space chage and electic field in DC cable systems - R th,c = 0.3 K m W -1 faily bad themal contact between XLPE and EPR. R th,c is the contact themal esistance pe unit of length, intoduced in Chapte 2. In Figue 4.13, the tempeatue distibution acoss the insulation of the joint is epesented fo the thee studied cases, wheeas in Figue 4.14 the electic field distibutions ae epesented. Figue 4.14 shows that the quality of the themal contact at the XLPE-EPR inteface stongly affects the electic field distibution within the joint insulation. In case of ideal contact, the field is highe in the XLPE and lowe in the EPR. If the quality of the contact becomes wose (i.e. the contact themal esistance inceases), the field in the XLPE deceases and the field in the EPR inceases. In the case in which the contact is bad (see Figue 4.14.c), the field in the EPR esults highe than the field in the XLPE. The polaization at the inteface depends on the conductivity of XLPE and EPR. The conductivity is tempeatue dependent and the tempeatue distibution is diffeent accoding to the type of contact (see Figue 4.13). Then, the polaization at the inteface is affected by the quality of themal contact. Figue 4.15 shows the accumulation in time of chage at the XLPE-EPR inteface. In the figue, it is evident how diffeent the polaization of the inteface is accoding to the qulity of the themal contact at the inteface (see fo instance full and dotted lines in Figue 4.14). Figue Tempeatue distibution acoss the insulation of a cable joint calculated fo diffeent qualities of the intefacial contact. Figue Evolution in time of intefacial chage calculated fo an XLPE- EPR cable joint. 93

108 Chapte 4 Calculation of space chage and electic field in DC cable systems Calculated electic field distibutions: a ideal contact (R th,c = 0 K m W -1 ) T in = 60 C T out = 50 C Calculated electic field distibutions: b good contact (R th,c = 0.15 K m W -1 ) T in = 65 C T out = 50 C Calculated electic field distibutions: c bad contact (R th,c = 0.3 K m W -1 ) T in = 71 C T out = 50 C Figue Electic field pofiles calculated fo an XLPE-EPR cable joint. 94

109 Chapte 4 Calculation of space chage and electic field in DC cable systems 4.5. Conclusions In this chapte a physical model, which descibes the dynamic space chage behavio in cables and cable joints, was pesented. The model was implemented by means of a numeical pocedue, allowing the calculation of the space chage distibution and the time dependent electic field. Despite the fact that the model is based only on macoscopic popeties of the insulation, the expeimental data pesented in Chapte 3 wee quite well epoduced by the poposed model. This validates the theoy that the macoscopic popeties of the insulation have a majo effect on space chage and electic field behavio of the studied test specimens within the adopted tempeatue/voltage conditions. Howeve, in some cases, some diffeences ae obseved between calculated and expeimental pattens. In paticula at the highe tempeatues, the measued heteochage distibution nea the electode-insulation inteface could not be pedicted by the model. Futhemoe, at the dielectic inteface of MV-size models of cable joints, moe chage accumulated than what estimated by the physical model. Those findings point out that at intefaces the space chage accumulation mechanism is geneally moe complex than the mechanism expected fom a puely macoscopic appoach. The poposed model can give a quantitative indication of the time-dependent electic field in full-size DC cable systems. Results of calculation eveal that the cable load can stongly affect the space chage distibution and consequently the electic field. This was vey evident in the following conditions. - Polaity evesal. If the voltage polaity is inveted on a loaded cable, the electic field esults enhanced nea the inne conducto, because of the accumulated space chage. This agees with the expeimental esults of Chapte 3. - Oveloading of the cable. Unde this condition, the model pedicts the highest amount of accumulated space chage. Theefoe, inceasing the cuent above its nominal value not only leads to an incease of the themal stess, but also to an enhancement of the electic stess expeienced by the cable insulation. - ad themal contact at intefaces in cable joints. If the themal contact esistance between the cable insulation and the estoed insulation of the joint is elatively high, the tempeatue dop acoss the dielectic inteface esults quite lage. This affects the polaization of the inteface and leads to an enhancement of the electic field in the insulation of the accessoy nea the inteface. 95

110 Chapte 4 Calculation of space chage and electic field in DC cable systems 96

111 Chapte 5 Space chage at intefaces in HVDC cable systems 5. Space chage at intefaces in HVDC cable systems oth the expeimental data and the esults of the theoetical modelling have shown that intefaces in HVDC cable systems ae paticulaly citical with egad to the accumulation of space chage. Fo this eason, this chapte focuses on intefaces pesent in HVDC cable systems and on thei polaization mechanisms. In Section 5.1, the diffeent types of intefaces encounteed in HVDC polymeic cable systems ae intoduced and compaed to the intefaces of the studied test specimens. The concept of width of an inteface is also discussed. In section 5.2, the effect of the semicon-insulation inteface on space chage accumulation is discussed on the basis of the liteatue and on the expeimental esults pesented in this thesis. Section 5.3 discusses the effect of a dielectic inteface on space chage accumulation. The theoy of intefacial polaization is eviewed and an impoved model is given. Finally, in Section 5.4 some suggestions ae given on how to impove the model pesented in Chapte Intefaces in HVDC cable systems Two main types of intefaces ae encounteed in extuded-type HVDC cable systems: semicon-dielectic intefaces and dielectic-dielectic intefaces, also simply called dielectic intefaces. In Figue 5.1, both intefaces ae epesented. a b Figue 5.1. Intefaces in extudedtype HVDC cable systems. a)semicon-dielectic inteface. b)dielectic-dielectic inteface (o simply dielectic inteface). 97

112 Chapte 5 Space chage at intefaces in HVDC cable systems Semicon-dielectic inteface In a cable system, the semicon shields seve two puposes. - The conducto suface and the eath sceen suface ae elatively ough, showing potusions and shap points. y application of a semicon laye, a unifom electic stess distibution is obtained ove the ough metal sufaces. - The inne semicon ensues a tight contact between the insulation and cable conducto, avoiding cavities that may lead to patial dischages (PD s) [84, 85]. Similaly, the oute semicon ensues a tight contact between the insulation and the eath sceen. oth semicon layes ae chemically bonded with the cable insulation. This is obtained by the tiple extusion poduction pocess and the following coss-linking pocess [64]. The smoothness of the semicon-dielectic inteface is vey citical with egad to the pefomance of the cable. In fact, potusions of the semicon into the insulation can lead to local field enhancements. In this context, concentation, shape and size of the potusions ae all of impotance [76]. The semicon-xlpe inteface of the test specimens used in this thesis, was optically analyzed in the famewok of the HVDC poject [103]. In Figue 5.2, a detail of the inteface is shown fo a flat specimen and fo a mini-cable. Optical micoscopy indicated that in both specimens the inteface is athe shap. µm µm XLPE semicon semicon XLPE flat specimen mini-cable Figue 5.2. Optical micoscopy image of the semicon-xlpe inteface in flat specimens and mini-cables [103]. (Coutesy of the Polyme Reseach Cente - Univesity of Suey). 98

113 Chapte 5 Space chage at intefaces in HVDC cable systems Dielectic inteface Dielectic intefaces ae pesent in cable accessoies, between the insulation of the cable and that of the accessoy. Diffeently fom the semicon-insulation inteface, whee a chemical bond exists, in dielectic intefaces the bond between the two dielectics is geneally physical 1 [64]. In othe wods, a mechanical pessue keeps togethe the cable insulation and the accessoy insulation. Two ideal had bodies put into contact cannot touch in moe than thee points. In these contact points the pessue would be infinite. In eality, the mateial yields and theeby defines contact aeas. In between those aeas, micoscopic cavities ae inevitable [40]. Thei size is in the ode of a few micons o moe, accoding to the suface oughness and the applied pessue. Cavities can be ai-filled, in case of pue contact between the two bodies, o lubicant-filled, in case of a lubicant used at the inteface 2. nothe chaacteistic of dielectic intefaces in cable accessoies is that a component of the electic field is pesent tangential to the inteface. In Table 5.1 the main chaacteistics of the dielectic intefaces of the studied specimens ae summaized. It can be noted that the dielectic inteface of a MV-size model of a cable joint shows the same chaacteistics as the inteface of a full-size actual component. In Figue 5.3, a detail of the XLPE-EPR inteface is shown fo a dual-dielectic minicable [103]. Optical micoscopy pefomed on such inteface indicated that the inteface is athe shap, but less shap than the semicon-xlpe intefaces shown in Figue 5.3. µm Figue 5.3. Optical micoscopy image of the XLPE-EPR inteface in dualdielectic mini-cables [103]. (Coutesy of the Polyme Reseach Cente - Univesity of Suey). XLPE EPR 1 In pemolded joints a one-piece ubbe accessoy poduces an elastic compessive foce onto the cable insulation. In this case the bond between the ubbe and the cable insulation is puely mechanical. Howeve, extusion-molded joints exist, whee the same type of esin as used fo the cable insulation is on-site extuded and coss-linked ove the cable insulation. In this case, the accessoy and the cable fom a single block and the dielectic inteface is chemically bonded. 2 In paticula cases, field gading mateials, with highly non-linea conductivity, ae also applied at the dielectic inteface in cable accessoies [52]. 99

114 Chapte 5 Space chage at intefaces in HVDC cable systems Table 5.1. Main chaacteistics of the dielectic intefaces of the studied specimens. Chaacteistic Flat specimens MV-size model of Dual-dielectic cable joints mini-cables Simple contact. Pefect contact. t the inteface, the suface of XLPE and that of t the inteface, the Inteface EPR touch defining contact aeas. Howeve, molecula chains of the because of the finite intefacial pessue and the EPR and those of the finite suface oughness of both mateials, XLPE ae linked micoscopic cavities ae likely to be pesent in togethe. between the contact aeas. Type of contact at the dielectic inteface Suface popeties Lubicants Physical (no bond). Thanks to the sping system mounted on the PE measuing cell, a pessue * of a few hundeds of kpa is applied at the inteface. Neithe XLPE no EPR expeienced a specific suface teatment. No lubicants wee applied. Physical (no bond). ecause of its elasticity, the EPR exets a adial compessive foce on the XLPE. The EPR has not eceived specific suface teatment. The suface of the XLPE was polished by means of abasive cloth. tiny amount of silicon oil was applied at the inteface duing the mounting of the joint. Chemical bond. The inteface is cosslinked. (See Figue 5.3 fo a detail of the XLPE-EPR inteface). N.. N.. Tangential No Yes No field * In addition to the extenal pessue/foce that keeps togethe the two layes of a specimen, an electically-induced pessue is also pesent when a voltage is applied acoss a test specimen (this pessue is often called Maxwell stess). Definition of the width of an inteface In this thesis, the following definition of intefacial width is used. Let us assume that we ae able to measue a physical quantity ψ along a combination of two mateials and, fom the bulk of the mateial to the bulk of the mateial, see Figue 5.4. The quantity ψ is expect to vay gadually acoss the inteface, fom the value ψ in the bulk of the insulation to the value ψ in the bulk of the insulation. We can now define the thickness of the inteface as it is shown in Figue

115 Chapte 5 Space chage at intefaces in HVDC cable systems Figue 5.4. Definition of the intefacial thickness Space chage accumulation at the semiconinsulation inteface In Chapte 4, a mechanism esponsible fo the accumulation of space chage within the insulation bulk is descibed. Section is dedicated to the most common mechanisms fo the accumulation of space chage at the semicon-insulation intefaces. Section discusses the expeimental esults on the basis of the accumulation mechanisms active at the semicon-insulation inteface Chage accumulation mechanisms at the semicon-xlpe inteface Ionization of species within the dielectic Unde the influence of the electic field, ionic species may be poduced within the cable insulation by dissociation of neutal impuity molecules, such as coss-linking by-poducts. Molecula ions with a cetain polaity dift towads the electode which has opposite polaity. Howeve, electodes allow chage tansfe, but not mass tansfe. Consequently, ions ae blocked leading to a heteo-chage egime unless they ae compensated by chages of opposite polaity injected at the electodes [92]. lthough this phenomenon eveals itself at the semicon-insulation inteface, ionic species ae geneally fomed in the whole insulation and not only nea the electodes. Suface effects The base polyme fo cabon-filled semicon compounds is geneally pola to facilitate the dispesion of the cabon black into the polyme. So, the chemical composition of semicon compounds diffes substantially fom that of the non-pola compounds used as dielectics [65]. ccoding to [29, 65], diffusion of components fom the semicon into the dielectic inceases the insulation conductivity nea the semicon. ecause of this fact, homo-chage is expected to accumulate. 101

116 Chapte 5 Space chage at intefaces in HVDC cable systems Injection/extaction ccoding to [45], if the flow of chages injected at the electodes is lage than the flow of chages though the dielectic, a homo-chage egime is established. ecause of the pesence of homo-chage, the electic field nea the injecting electode deceases. This will eventually stop the chage accumulation. In this case the flow of chage though the dielectic equalizes the injected flow of chages at the electode. Such a chage accumulation mechanism is often called high-field injection. On the othe hand, if the flow of chages though the dielectic is lage than the flow of chage injected at the electodes, a heteo-chage egime is established. This accumulation mechanism is often called chage blocking. The theoy of chage tansfe pocesses at the metal-polyme inteface has been the subject of seveal studies, e.g. [45, 92, 93, 109, 110, 152]. The vaious chage tansfe pocesses ae based on the concept that an electon must ovecome a potential baie in ode to leave/ente the electode and ente/leave the insulation. Nevetheless, no specific theoy has been developed fo the chage injection at the semicon-polyme inteface. The main eason fo this is that the semicon polyme inteface is athe complex and difficult to chaacteize. On the othe hand, obsevation of accumulated chage at the semicon-polyme inteface is nowadays accuate and eliable, thanks to the impovement of the space chage measuing techniques developed in the past decade. Howeve, as pointed out by Lewis [92, 93], chage tansfe at electodes is a highly localized phenomenon. Since neithe the dielectic no the electode have unifom suface conditions, injection, extaction and blocking can simultaneously occu at the same inteface. Theefoe, only the oveall effect of the localized tansfe phenomena can be obseved expeimentally. Polaization at localized insulation defects, such as wate tees t the location of an insulation defect, such as a wate tee, space chage accumulates [125, 141]. Unde specific conditions, vented wate tees can be initiated at the semicon-insulation inteface. Chages with the same polaity as that of the teeinception electode ae pesent at the tee tip. Howeve, this phenomenon is not studied in this eseach, since no wate tees wee pesent in ou test specimens ccumulation of chage at the semicon-xlpe inteface in the studied specimens Optical micoscopy shows that the semicon-xlpe inteface of the studied specimens is faily shap (see Figue 5.2). This is confimed by the Raman spectoscopy pefomed in the famewok of the HVDC poject [103]. The scan of the cabon band at 1609 cm -1 was used to map the cabon signal on the studied specimens and to plot the intefacial width. In this way, the diffusion of the semicon into the XLPE has been detected. Fo both flat specimens and mini-cables the intefacial width defined by the cabon band at 1609 cm -1 is about 5 µm. This is shown in Figue 5.5. This esult indicates that the diffusion of semicon into the XLPE occus only in the diect vicinity of the semicon. Theefoe the suface effects mentioned in Section and the consequent homo-chage distibution ae likely to be mino fo the studied 102

117 Chapte 5 Space chage at intefaces in HVDC cable systems specimens. In fact, in most of the measuements heteo-chage has been clealy obseved (especially nea the HV electode) and none of the specimens has shown homo-chage. µm optical image line scan XLPE semicon intensity of the cabon signal µm Raman scan of the cabon intensity at 1609 cm -1 Figue 5.5. Optical micoscopy image and Raman micoscopy scan of the semicon- XLPE inteface in a flat specimen [103]. (Coutesy of the Polyme Reseach Cente - Univesity of Suey). It is then evident that at the semicon-xlpe inteface the mechanisms fo heteo-chage accumulation ae dominant in the studied specimens fo the studied test conditions. s aleady stated in Chapte 3, ionic species ae quite unlikely to be the cause fo the obseved heteo-chage. Specimens ae made of high puity XLPE and they wee themally teated in ode to expel coss-linking by-poducts. Moeove, chemical analyses, which wee pefomed on the specimens in the famewok of the HVDC poject, have not evealed pesence of migating species that can be coelated with ionic conduction [103]. Theefoe, we conclude that heteo-chage is to be attibuted to blocking popeties of the semicon electodes. In addition to the heteo-chage at the semicon-xlpe inteface, space chage with the same polaity as that of the applied voltage was measued within the whole insulation bulk of the studied specimens. This occued when a tempeatue dop is applied acoss the insulation, see Chapte 3. The bulk chage was attibuted to the tempeatue dop in the insulation, as explained in Chapte 4. Howeve, in the liteatue it has been shown that high-field injection mechanisms may oveule the accumulation of chage in specimens in which a tempeatue gadient exists [10, 53, 67]. Theefoe, a 103

118 Chapte 5 Space chage at intefaces in HVDC cable systems discimination is necessay between the extent of space chage accumulation due to the tempeatue dop and that due to high-field chage injection fom the electodes. Fo this pupose, space chage measuements wee caied out on MV-size cables also unde isothemal conditions. Unde this paticula condition, no tempeatue gadient mechanism is active and only chage due to the high-field injection mechanism should be detected. In Figue 5.6, the space chage pattens measued unde steady tempeatue dop conditions ae compaed to the pattens measued unde steady isothemal conditions. Figue 5.6 shows that unde isothemal conditions less chage accumulates in the insulation bulk in compaison with the situation in which the tempeatue dop is applied. This validates the theoy that, fo the studied specimens, the dominant accumulation mechanism is due to the conductivity gadient induced by the tempeatue dop. In the space chage pattens measued unde isothemal condition, negative homo-chage is pesent at the oute eath electode, wheeas negative heteochage is pesent at the inne HV electode (see Figue 5.6.b). These esults confim that in the studied specimens the heteo-chage is caused by the blocking popeties of the semicon electode. Negative chage is injected at the eath electode and, afte having migated though the insulation, is blocked in font of the HV electode. In the space chage patten measued unde tempeatue dop conditions, this phenomenon is much less evident, since high-field injection has now a mino ole. a HV tempeatue dop eath Voltage-on space chage distibutions of MV-size XLPE cables. U 0 = +90 kv T in = 65 C T out = 45 C T = 20 K T = 4.4 K/mm b HV isothemal eath heteo-chage homo-chage Voltage-on space chage distibutions of MV-size XLPE cables. U 0 = +90 kv T in = 65 C T out = 65 C T = 0 K T = 0 K/mm Figue 5.6. Voltage-on space chage pofiles in MV-size cables. a) tempeatue dop is applied; b) isothemal condition. 104

119 Chapte 5 Space chage at intefaces in HVDC cable systems 5.3. Space chage accumulation at the dielectic inteface In this section, the space chage accumulation at dielectic intefaces is analyzed on the basis of expeimental findings pesented in the liteatue and on the esults of space chage measuements shown ealie in this thesis. In paticula, the validity of the Maxwell-Wagne (MW) theoy fo the intefacial polaization is discussed and the main paametes, which affect the intefacial polaization but which ae not included in the MW model, ae identified. Finally, a thee-laye model of the inteface, which includes the suface effects, is given Maxwell-Wagne theoy fo the intefacial polaization Maxwell capacito The most common appoach fo modeling the accumulation of chage at dielectic intefaces is the Maxwell-Wagne theoy fo the intefacial polaization [84, 150], aleady intoduced in Section 3.1. The MW theoy consides the so called Maxwell capacito, an hypothetical configuation in which two plan paallel electodes ae sepaated by two isotopic dielectics, see Figue 5.7. In such a system, the popeties of the insulation vay with a step function at the inteface and the electical contact between the two dielectic is supposed to be ohmic. Figue 5.7. Maxwell capacito consideed in the Maxwell-Wagne theoy fo the intefacial polaization. The MW theoy gives an expession in a closed mathematical fom fo the calculation of the time dependent suface chage κ(t) at the inteface. When a DC voltage U 0 is applied acoss the Maxwell capacito, the suface chage becomes: () σ σ t κ t = U 0 1 exp (5.1) σ d + σ d τ MW whee d, d ae the thickness of the two dielectics, σ, σ the conductivities and, the pemittivities. The time constant τ MW is given by Equation (5.2): 105

120 Chapte 5 Space chage at intefaces in HVDC cable systems τ d + + d MW = (5.2) d σ d σ The main advantage of the MW appoach is that the intefacial chage can be diectly calculated fom the knowledge of a few insulation popeties and the value of the insulation thickness. To be noted that once the intefacial chage is known, the electic field in both dielectics can be found: E ( ) () t () t κ d U ( ) ( ) = (5.3) ( ) d ( ) + d ( ) ( ) Modified MW appoach Equation (5.3) shows that in a combination of two dielectics the electic field distibution changes in time, because of the accumulation of intefacial chage. The conductivity of insulating mateials stongly depends on the electic field the mateial expeiences. Thus, also the conductivity changes in time while chages accumulate at the inteface. If the field dependency of the conductivity is taken into account, the conventional MW appoach discussed above is no longe valid [21]. Intefacial chage and electic field have to be calculated numeically. Fo this pupose, the numeical pocedue pesented in Chapte 4 is used, afte being adapted to the flat geomety. In Figue 5.8, electic field and intefacial chage calculated numeically ae compaed to the esults of the conventional MW calculation. two-laye insulation composed of XLPE and EPR flat specimens is consideed fo both calculations. It can be noted that when the field dependency of the insulation conductivity is taken into account, a smalle amount of accumulated chage is pedicted along with a weake field distotion. Figue 5.8. Calculated intefacial chage and electic field in XLPE-EPR flat specimens, when a DC voltage is applied [21]. Input data: U 0 =+30 kv; d XLPE = 1.5 mm; d EPR =1.5 mm;,xlpe = 2.3;,EPR =2.9; conductivity as deived fom conduction cuent measuements at the tempeatue of 40 C (see Section 3.1). 106

121 Chapte 5 Space chage at intefaces in HVDC cable systems Deviations fom the Maxwell-Wagne theoy: liteatue Diffeences between bulk and suface popeties The MW appoach does not include the fact that the suface of insulating mateials pesents electical popeties diffeent fom those shown by the insulation bulk. The suface of insulatos may exhibit ohmic conduction, e.g. due to the pesence of a film of condensed wate o because a specific chemical teatment has been applied [127]. Moeove, in most cases, it can be expected that the oute pat of the mateial is oxidized to a lage degee than the inne pat [116]. The way in which a test specimen is poduced influences the popeties of the insulation bulk. Howeve, the poduction pocess may have an even lage effect on the suface popeties. Fo instance, if the specimen has been cut, the molecula chains esult abuptly teminated nea to the suface. This will have consequences on the distibution of taps nea the suface. consequence of the diffeence between bulk and suface popeties is that chage geneally accumulates at intefaces between two identical dielectics [20, 35, 79]. This is not pedicted by the MW theoy, whee the dielectics ae assumed to be isotopous. Seveal woks, e.g. [16, 144, 145], have shown that the polaity of the chage measued at the dielectic inteface agees with the MW theoy. Howeve, the amount of chage accumulated at the inteface is often quite diffeent fom what is expected by the MW theoy. Effect of intefacial contact ccoding to the MW theoy, the inteface is a shap discontinuity. In the eality, the dielectic inteface has a finite thickness. This can vay fom a few micons, fo chemically bonded intefaces o extemely smooth sufaces in contact, to seveal tens of micons, when faily ough sufaces ae placed into contact. The fact that the inteface is not shap allows accumulation of chages at both sides of the inteface. In fact, seveal expeimental esults have shown a bipola chage distibution at the inteface fo vaious mateials, e.g. [20, 35, 79, 95, 139]. The mechanical pessue applied at the inteface has a ole in defining the inteface thickness fo intefaces in simple contact. Howeve, while the contact pessue is a cucial facto with egad to the PD activity at the inteface [120], the amount of chage that accumulates at dielectic intefaces has been found to be quite insensible to the applied mechanical pessue [20]. Effect of lubicants Lubicants such as oil o gease ae often applied at dielectic intefaces of HV components. Lubicants have geneally a (much) highe conductivity in compaison with the conductivity of solid insulating mateials. Theefoe, the conductivity of the intefacial aea is expected to incease when lubicants ae used. This explains why a faste space chage accumulation has been obseved in lubicated intefaces if compaed to dy intefaces. [20]. Effect of ai pockets i pockets ae pesent within the intefaces in simple contact (physical intefaces) when no lubicant is pesent o when the lubicant has died out. i pockets may 107

122 Chapte 5 Space chage at intefaces in HVDC cable systems affect the build up of intefacial chage. i is in fact an electonegative gas, which will attact electons. nothe effect due to the pesence of ai within the inteface is the alteation of the space chage signal. Since the PE method is based on the geneation and on the popagation acoustic waves, eflection and efaction of phenomena could occu at the inteface, leading to a modification of the oiginal space chage signal. desciption of this phenomenon is given in ppendix. Effect of the voltage polaity In the liteatue, dissimilaities have been found between space chage pofiles measued at diffeent voltage polaities [21, 24, 146]. ccoding to the MW appoach, no polaity effects ae expected and intefacial chage pattens measued at diffeent polaities should be pefectly symmetic. In [116, 146], the idea that the inteface is to be egaded as a semi-blocking contact has been poposed in ode to explain the polaity effects. Howeve, such a model is still fa fom being implemented Deviations fom the Maxwell-Wagne theoy: expeimental esults In Chapte 3, seveal esults of space chage measuements pefomed on vaious types of dielectic intefaces wee shown. Geneally, a quite good ageement was found between the amount of measued chage and the chage expected by means of the MW theoy. Nevetheless, some of the chaging phenomena expeimentally obseved could not be explained by means of the MW theoy. In this section, these paticula phenomena ae descibed and discussed. Chage accumulation next to the inteface In all types of specimens, space chage accumulated next to the dielectic inteface. This phenomenon was paticulaly evident within the XLPE laye of the specimens. In Figue 5.9 thee examples ae given (see dotted cicles in the figues). Such a space chage patten may indicate that in the XLPE next to the inteface the density of deep taps is highe than in the bulk of the XLPE. Deep taps decease the mobility of chage caies (electons and/o holes) in the dielectic. ccodingly, in the XLPE adjacent to the inteface, whee a highe density of taps is assumed, a mismatch will occu between the cuent density into this egion and the cuent density out of this egion. Consequently, chages will accumulate next to the inteface. In Figue 5.10, this mechanism is schematically epesented. 108

123 Chapte 5 Space chage at intefaces in HVDC cable systems a eath HV Voltage-on space chage distibutions of XLPE-EPR flat specimens U 0 = +30 kv ; T=60 C (isothemal condition). b HV XLPE eath EPR Voltage-on space chage pofiles of XLPE-EPR dual-dielectic mini-cables. U 0 = + 30 kv. T in = 64 C T out = 41 C; T = 23K; T = 10.9 K/mm. c HV XLPE EPR eath Voltage-on space chage distibutions of MV-size models of cable joints. V = + 40 kv T in = 65 C T out = 45 C T = 20 K T = 5 K/mm Figue 5.9. Space chage pattens of XLPE-EPR intefaces in which space chage is notable in the XLPE next to the inteface (see dotted cicle). Figue If the XLPE bulk can tanspot chages faste than the dielectic inteface can supply them, chages accumulate next to the inteface. 109

124 Chapte 5 Space chage at intefaces in HVDC cable systems Polaity effects Expeimental esults show that space chage pofiles measued at diffeent voltage polaities ae not symmetic. In paticula, fo the diffeent types of specimens, the following behavio has been obseved at the inteface. - Flat specimens: moe positive chage accumulates than negative chage. - Dual-dielectic XLPE-EPR mini-cables: moe negative chage accumulates than positive chage. - Dual-dielectic EPR-XLPE mini-cables: moe negative chage accumulates than positive chage. - MV-size models of cable joints: moe positive chage accumulates than negative chage. The esults indicate that if the XLPE-EPR inteface is coss-linked (dual-dielectic mini-cables) moe negative chage accumulates. On the othe hand, if the XLPE-EPR inteface is in simple contact (i.e. flat specimens and MV-size models of cable joints), moe positive chage accumulates. The eason fo this specific behavio is still unknown. Howeve, it is evident that the studied dielectic intefaces behave diffeently fo diffeent types of chage caies, which valoises the speculation that the inteface behaves as semi-blocking contact Thee-laye model fo the dielectic inteface 3 The electic bounday, which divides the bulk electic popeties of the two dielectics in contact, is not shap and it is composed of the suface laye of the two dielectics and the intefacial mateial (o ai in case no lubicants ae used). In Figue 5.11, a eal inteface between two dielectics and is modeled as fictitious dielectic C in between two intefaces which behave accoding to the MW theoy. The dielectic C accounts fo the impefect contact between sufaces, fo the possible pesence of lubicants and fo the highe conductivity of the suface of dielectics. Figue eal inteface is modelled as a fictitious dielectic in between two intefaces which behave accoding to the MW theoy [20]. 3 This section is based on the wok pesented by the autho at the Int. Conf. Elect. Insul. Diel. Phen., lbuqueque, 2003 [20]. 110

125 Chapte 5 Space chage at intefaces in HVDC cable systems The fictitious dielectic C can be chaacteized by a thickness d C, a conductivity σ C and a pemittivity C. The suface oughness ξ and ξ of the dielectics and detemine the thickness of the dielectic C : dc ξ + ξ (5.4) Equation (5.4) is valid if the defomation of the micoscopic suface peaks is elatively small. Howeve, inceasing the mechanical pessue oigin of the contact, a eduction of d C is expected. The pemittivity C is mainly given by the pemittivity L of the lubicant that can be pesent at the inteface and by the pemittivity and of the dielectics and. If L is smalle than and, the following elation is valid: ξ + ξ L < C < (5.5) ξ + ξ If no lubicants ae pesent at the inteface, the vacuum pemittivity 0 can eplace L in eq. (5.5). Regading the conductivity σ C, a distinction can be made between two situations. If a lubicant is pesent within the inteface, the conductivity of the dielectic C will be mainly given by the conductivity of the suface laye of dielectics and, and by the conductivity σ L of the lubicant. ssuming that the conductivity of the suface of dielectics and is highe than that of the bulk of the insulatos (σ and σ ), and assuming that lubicants such as oil o gease ae nomally much moe conductive than solid insulatos, σ C esults: σ, σ << σ < σ (5.6) C L In case no lubicant is pesent between mateials and, σ C is expected to be lowe than that peviously estimated, but always highe than the bulk conductivity σ and σ. Intefacial chage estimation In an inteface behaving accoding to the MW theoy, the intefacial chage is given accoding to Equation (5.1) and (5.2). If now we apply those equations to the inteface model in Figue 5.11, at the -C inteface we obtain: κ C τ σ C σ = U σ + σ d 1 exp τ C C d C C MW, C d + d t (5.7) C C MW = (5.8) C d σ C + dc σ ssuming that the applied DC voltage is capacitively divided acoss the two layes and, the voltage U -C becomes: U d C U = U 0 (5.9) d + d 111

126 Chapte 5 Space chage at intefaces in HVDC cable systems Inseting (5.9) into (5.7) and consideing: σ d << σ d (5.10) and C C C C σ >> σ (5.11) one obtains: κ C d + d U 0 1 exp τ t MW, C (5.12) Moeove, taking into account that: d << d (5.13) C C the MW time constant τ MW,-C can be expessed as: C τ MW C (5.14) σ C Similaly, fo the C- inteface the intefacial chage and the time constant esults: κ τ C d + d U 0 1 exp τ t MW, C (5.15) C MW C (5.16) σ C ccoding to the pesented model, a bipola chage distibution builds-up at both sides of an inteface. The magnitude of this chage depends on the bulk popeties of the two dielectics in contact, wheeas the time equied fo the bipola chage to accumulate depends on the popeties of the intefacial laye. The accumulation of the bipola chage distibution occus in the intefacial laye in the vey beginning of the tansition fom capacitive to esistive field. This is due to the fact that the time constant fo the bipola chage accumulation (τ MW,-C o τ MW,C- ) is much smalle than the time constant fo the conventional MW accumulation (τ MW,- ). ecause of the accumulation of bipola chage, the electic field acoss the intefacial laye stongly deceases. Since the thickness of the intefacial laye is geneally vey small if compaed to the total thickness of the specimen, the electic field in the insulation bulk emains pactically unchanged. Of couse, if time inceases, additional chage of one polaity only will accumulate at the inteface, modifying the electic field in the whole specimen and leading to a esistive distibution of the electic field. Validity of the assumptions The validity of the assumptions adopted in the model pesented above can be checked by calculating the exact field and the exact intefacial chage in a thee-laye dielectic. The following equations ule the chage accumulation pocess in a thee-laye dielectic: 112

127 Chapte 5 Space chage at intefaces in HVDC cable systems Chage continuity equation at the dielectic discontinuities: κ C jc j = t κ C j jc = t κ j j = t (5.17) (5.18) (5.19) Gauss law at the dielectic discontinuities: κ C = E C EC (5.20) κ C = C EC E (5.21) κ = E E (5.22) Ohm s law in the insulation bulk: j = σ (5.23) i E i i y combining equations (5.17) (5.23), the following elation can be obtained: E E EC + σ E = + σ E = C +σ C E t t t C (5.24) y integating (5.24) and using (5.25) as bounday condition, the electic field can be calculated fo each laye of the dielectic. s initial condition, we assume that no chage is pesent at time t = 0 s, see (5.26): E d + E d + EC d C = U 0 (5.25) κ t = 0 = (5.26) i ( ) 0 Figue 5.12 epesents the electic fields and the intefacial chages calculated fo a model of a eal inteface, i.e. a thee-laye dielectic in which the layes, and C have the following chaacteistics: σ, C >> σ σ and C << d d d, Figue Electic fields () and inteface chages () in a thee-laye model of a eal inteface. Laye : =2.3; σ = Ω -1 m -1 ; d=1.5 mm. Laye : =2.8; σ = Ω -1 m -1 ; d=0.05 mm. Laye C : =2.9; σ = Ω -1 m -1 ; d=1.5 mm. 113

128 Chapte 5 Space chage at intefaces in HVDC cable systems Figue 5.12 points out that fo a thee-laye model of a eal inteface, indeed the elation κ -C -κ C- is valid when the time is much shote than the time constant τ MW,-. y using the values in the caption of Figue 2, one obtains τ MW,- = 10 6 s. esides, the figue shows that the accumulation of intefacial chage fo t << τ MW,- follows appoximately the time constant τ MW,-C (o τ MW,C- ). y using the values in the caption of Figue 5.12, τ MW,-C = τ MW,C- = 250 s Suggestions on how to impove the macoscopic model fo space chage accumulation In Chapte 4 a cable system was modelled as an equivalent insulation in between ohmic electodes. In this way, the high-field injection and/o the blocking mechanisms fo space chage accumulation ae included in the bulk popeties of the equivalent insulation. Howeve, as shown in this chapte, it would be moe coect to localize these effects nea the intefaces. In ode to implement this idea without changing the stuctue of the model, the following actions can be pefomed: - consideing the equivalent insulation inhomogeneous, by means of a positiondependent conductivity; - consideing the paametes, which descibe the field and tempeatue dependency of the conductivity, position-dependent. This means that Equation (4.5), which is hee epeated fo claity, could be modified as in Equation (5.17): σ, ef ef (4.5) E ef E ( T E) = σ exp[ α ( T T )] ν ν ( x) E σ ( T, E, x) = σ ef ( x) exp[ α( x)( T Tef )] (5.27) E ef 114

129 Chapte 6 Feasibility study fo on-line on-site PE measuements 6. Feasibility study fo on-line on-site PE measuements The feasibility of pefoming on-line and on-site PE measuements on HVDC polymeic type cable systems is studied in this chapte. In Section 6.1, the concept of on-line on site PE measuements is intoduced and the benefits of such measuements ae discussed. schematic desciption of how to implement on-line on site PE measuements on HVDC cables is given in Section 6.2. Finally some conclusions ae dawn in Section Intoduction On-line on-site space chage measuements ae defined as space chage measuements pefomed on HVDC cable systems in opeation. Up to now, no measuement of this kind has been epoted in the liteatue. Space chage measuements ae a means fo poviding the actual field distibution within the insulation of an HVDC cable system. This infomation is of utmost impotance, because the electic field influences the life time of the cable system, e.g. [45]. Unfotunately, space chage measuements povide the electic field distibution fo a vey tiny potion of the cable system. In case of PE measuements, this potion is defined by the length of the piezoelectic senso, which is at most a few centimetes. Theefoe, it is athe unlikely that a PE measuement could identify a weak spot of the insulation, whee an anomalous electic field distibution is pesent. This would occu only if the weak spot coesponds to the potion of the cable whee the measuement is done. Moeove, on an HVDC cable the adial electic field distibution changes along the length of the cable, since diffeent cable locations expeience diffeent tempeatue conditions. Despite of those facts, the electic field distibution infeed by an on-line on site space chage measuement is a significant infomation fo monitoing the oveall condition of the cable insulation. Fistly, the measuement can be pefomed on a potion of the cable whee the most citical woking conditions ae expected. Fo instance this could be a joint of the cable system in which the tempeatue is expected to be highe than in the est of the cable. y measuing the space chage in that specific section, the maximum electic field would be chaacteistic fo the whole insulation system and theefoe it could be of use fo contolling and optimising the opeation. Secondly, we need to make a diffeence between two ievesible electical phenomena occuing in insulating mateial: aging and degadation. ccoding to [55], mateial 115

130 Chapte 6 Feasibility study fo on-line on-site PE measuements aging is a global phenomenon, i.e. it is pesent on the whole insulation subjected to electic stess. Fo the insulation of HVDC cables unde typical stess conditions, electical aging is chaacteized by a elatively long duation (tens of yeas). Following the definition given in [55], degadation is a local phenomenon, i.e. it is pesent at a specific location of the insulation. Fo the insulation of HVDC cables unde typical stess conditions, degadation phenomena ae chaacteized by a elatively shot duation (fom a few days to a few yeas, accoding to the type of degadation mechanism). Geneally, aging pecedes degadation and degadation pecedes the electical beakdown. It is theefoe vey useful to undestand the aging state of the insulation in ode to get an idea of the isk fo electical beakdown occuence. y compaing the space chage and the electic field distibutions measued in the couse of the yeas, changes in the measued pattens could be identified. These can be coelated to the aging state of the insulation, e.g. [4, 5], and then to an indication of the isk of beakdown. nothe application of on-line on-site space chage measuements is povided by keeping a ecod of the electic field expeienced by the cable though the yeas in a data-base. The infomation contained in the data-base could be used to assist cable management. Fo instance, decisions egading the planning of the maintenance o the analysis of the emaining cable life could be suppoted by the data-base infomation Implementation In ppendix, thee PE configuations fo measuing space chage on cables ae descibed. mong those configuations, the most suitable fo pefoming PE measuements on HVDC cables in the field is that in which the pulsed voltage is applied between the PE cell and eath, see Section.1.2 and Fig..3 in ppendix. In fact, because of the length of the cable, the configuation in which the pulse is applied at the conducto is not optimal, since it would esult in eflections of the pulsed voltage. Moeove, the configuation in which the pulse is applied at the eath sceen is not applicable, since the eath sceen must be kept at eath potential. Two majo technical poblems have to be consideed in ode to put into pactice online on-site space chage measuements. 1. The oute semicon of the cable must be exposed at the measuing point. This implies that the PE system needs to be mounted inside a special compatment. This compatment has to be pefectly sealed, in ode to potect the cable and to pevent the intoduction of any moist. 2. The measuing system can affect the tempeatue distibution within the insulation of the measuing potion of the cable. In ode to minimize this phenomenon, the themal popeties of the measuing system need to be consideed in its design. Figue 6.1 shows a schematic epesentation of a PE system fo measuing space chage on HVDC cables in the field. The entie system is contained within an amoed compatment (3) which is sealed togethe with the amo of the cable (1). t the measuing section the eath sceen of 116

131 Chapte 6 Feasibility study fo on-line on-site PE measuements the cable (2) is emoved and the oute semicon (7) is exposed. The continuity of the eath cicuit is guaanteed by a by-pass eath connection (4). The acoustic signal caying the space chage infomation is tansmitted fom the cable insulation to the PE cell (8) via an aluminum block (6). The aluminum block acts as a delay line fo the acoustic signal and as injecting electode fo the pulsed voltage (10). In ode to obtain a pope shape of the pulse, the load of the tansmission line (10), which supplies the pulse voltage, has to match the chaacteistic impedance of the line. Fo this pupose, temination esistos (5) ae connected between the aluminum block (6) and eath (2). The PE cell (8) has the function of detecting the acoustic signal and conveting it into an optical signal, which is tansmitted to a save & display equipment by means of an optic fibe link (9). In Figue 6.2, a detail of the PE cell is epesented. piezoelectic senso is placed at one side of the aluminum block which suounds the cable. The senso convets the acoustic signal into an electical signal which is fed into an amplifie. Since the PE cell expeiences the pulsed voltage, the output signal of the amplifie cannot be diectly supplied to an eathed equipment fo displaying and saving the space chage infomation. Fo this eason, the output signal of the amplifie is conveted into an optical signal by means of an electo-optical convete. This guaantees the electical sepaation between the PE cell and eath. Finally, the conveted optical signal is bought to a save & display equipment via an optic fibe link. The amplifie and the electo-optical convete ae poweed by an electically-sepaated DC supply. Figue 6.1. Schematic epesentation of a PE system fo on-line on-site measuements of space chage on HVDC cable systems. 117

132 Chapte 6 Feasibility study fo on-line on-site PE measuements In ode to obtain a good-quality output signal, a coodination between the width of the input pulsed voltage, the senso thickness and the input impedance of the amplifie is equied [39]. Moeove, the noise level has to be minimized, by shielding the PE cell and by adopting a low-noise amplifie configuation [137]. Figue 6.2. Detail of the PE cell of a space chage measuing system fo on-line on-site measuements on cables Conclusions Space chage measuements on HVDC cables in opeation epesent a potential tool fo monitoing the electic field distibution within the cable insulation. This can be used fo vaious puposes: - the contol of the electic field in weak spots of the cable system; - the assessment of the aging state of the cable insulation and then the evaluation of the isk of electical beakdown; - the suppot of cable management decisions by means of a data-base containing the electic field histoy of the cable. In this chapte we showed that pefoming on-line on-site PE measuements on HVDC cables is theoetically feasible. To pove this, a schematic design of a PE system, which is adapted fo measuing space chage on HVDC cables in opeation, was given. 118

133 Chapte 7 - Conclusions 7. Conclusions In this thesis, we investigated space chage phenomena occuing in DC polymeic cable systems. We showed that the following two phenomena have majo influence on the technical pefomance of the insulation of HVDC polymeic cable systems: 7.1 Space chage fomation at dielectic discontinuity, such as the intefaces of cable accessoies. 7.2 Space chage accumulation pocess due to a tempeatue dop acoss the insulation of the cable system Space chage at dielectic discontinuities Fist of all, we eviewed the PE method to make it suitable fo the study of polaization and chaging phenomena at dielectic intefaces. In fact, if a discontinuity of the dielectic and/o acoustic popeties occus at the inteface, the signal povided by the PE method does not diectly coespond to the space chage distibution. In ode to coectly evaluate the esults of the PE measuements, we intoduced: 1. methodology fo the intepetation of the detected space chage pattens which takes into account the eflection and the popagation of acoustic waves within the test specimen. 2. pocedue fo the calibation of the measuing system that makes use of a diffeent calibation facto fo each laye of the test specimen. We expeimentally obseved space chage accumulation at the dielectic intefaces of the studied test specimens. oth magnitude and dynamics of the chage could be faily well descibed by the Maxwell-Wagne theoy fo the intefacial polaization. This means that the conductivity has a lage influence on the polaization at the inteface. 1. The lage the elative diffeence between the conductivities of the two dielectics foming the inteface, the lage the accumulated chage at the inteface. 2. The highe the conductivity of one of the two dielectics, the faste the chage accumulation at the inteface. Since the conductivity inceases with tempeatue and field, the highe the tempeatue (and/o the field), the faste the chage accumulation at the inteface. We obseved two main deviations fom the behavio pedicted by the Maxwell- Wagne theoy. 1. We measued diffeent absolute values of intefacial chage magnitude at diffeent voltage polaities. Fom the latte, we conclude that a semi-blocking contact is likely to occu at dielectic intefaces. 2. We found that heteo-chage geneally accumulates adjacent to the inteface of the studied test specimens. We could attibute this phenomenon to the mophological diffeences between the bulk and the suface laye of polymeic insulation. 119

134 Chapte 7 - Conclusions Fo MV-size models of cable joints, we confimed expeimentally that the tempeatue distibution acoss the joint has indeed a majo effect on the distibution of the electic field. In paticula, the lage the tempeatue jump at the dielectic inteface, the highe the field in the ubbe pat of the joint. This is an unfavoable condition fom a design point of view. 7.2 Space chage in cable systems that expeience a tempeatue dop acoss the insulation In the thesis, we analyzed space chage accumulation when a tempeatue dop and an electic field ae simultaneously pesent acoss the insulation of the studied test specimens. We found that the conductivity gadient induced by the tempeatue dop is esponsible fo the accumulation of chage within the insulation bulk. y using a macoscopic modeling of the insulation, we could quite well epoduce the magnitude and the dynamics of the space chage measued on the studied test specimens. This confims that the conductivity and its dependencies on tempeatue and field stongly affect the accumulation of space chage in the insulation bulk. In fact, both measuements and calculations of space chage point out that: 1. Fo a given applied field, the amount of space chage in the insulation bulk inceases with the tempeatue dop. 2. Fo a given tempeatue dop the amount of space chage in the insulation bulk inceases with the applied field. 3. The accumulation of space chage in the insulation bulk becomes faste when the tempeatue inceases. 4. The accumulation of space chage in the insulation bulk becomes faste when the applied field inceases. 5. The chage distibution takes a cetain time to each a quasi-steady state. This time depends on the value of the insulation conductivity and, fo the studied XLPE insulation, it can be as long as seveal weeks fo tests done at oom tempeatue and at modeate fields. In addition to the chage in the insulation bulk, attibuted to the pesence of the tempeatue dop, we measued heteo-chage, mainly in the XLPE nea the inne semicon of the studied specimens. This is not pedicted by the developed macoscopic model. Howeve, ou intepetation is that this phenomenon is due to high-field chage injection and blocking mechanisms. We pefomed space chage measuements on loaded MV-size models of cable systems unde polaity evesal condition. The esults of ou measuements show that the maximum electic field immediately afte this evesal opeation is pesent at the inne conducto and its value can be highe than the maximum Laplacian field. We concluded that this field enhancement is caused by the space chage due to the tempeatue dop. 120

135 Chapte 8 Recommendations and suggestions fo futhe study 8. Recommendations and suggestions fo futhe study On the basis of the esults achieved in this thesis wok, a numbe of ecommendations will be pesented in Section 8.1. Ou findings have possible implications on: - the testing of cable insulation by means of the PE method (Section 8.1.1); - the design of HVDC extuded-type cable systems (Section 8.1.2); - the opeation of HVDC extuded-type cable systems (Section 8.1.3). Finally, some suggestions fo futhe eseach ae given in section Recommendations Recommendations fo PE testing of HVDC cable system insulation Space chage measuements on multi-dielectics We ecommend to use specific pocedues (such as those pesented in ppendix ) fo the intepetation and fo the calibation of measuement esults povided by PE measuements on multi-dielectic test objects. Space chage measuements on cables when a tempeatue dop is applied Fo a coect PE measuement of the space chage induced by a tempeatue dop acoss the insulation of a DC cable, the following thee popeties of the space chage patten need to be consideed. 1. The amount of chage is athe small: its magnitude is of the ode of a few hundeds of mc/m 3 fo MV-size XLPE-insulated cables and of the ode of a few tens of mc/m 3 fo HV-size XLPE-insulated cables unde typical stess conditions [42, 63]. Theefoe, we ecommend to check that the PE system adopted fo the measuement is sufficiently sensitive. The sensitivity of the PE system used in this thesis fo the measuements on MV cables is 50 mc/m The chage is distibuted in the whole insulation bulk: a wide distibution of chage is detected by the measuing system only if the fequency ange of the measuing system is sufficiently boad [39, 118]. Fo instance, fo a 1-mm thick XLPE cable, the lowe cut-off fequency of the measuing system should not be highe than 300 khz. Conventional PE systems, which ae equipped with a 50-Ω input esistance amplifie and a piezoelectic senso with a capacitance of about 1 nf, have a lowe cut-off fequency of about 3 MHz. Theefoe, a conventional PE system is not suitable fo measuing wide distibutions of chage such as those induced by a tempeatue gadient in (MV)HVDC cables. So, we ecommend to check that the fequency ange of the PE system adopted fo the measuements is sufficiently 121

136 Chapte 8 Recommendations and suggestions fo futhe study wide. The fequency ange of the PE system used in this thesis fo the measuements on MV cables is MHz. 3. The chage distibution takes a cetain time to each a quasi-steady state: this time depends on the value of the insulation conductivity and can be as long as seveal weeks fo tests done at oom tempeatue and at modeate fields. Fo the measuement of the quasi steady-state space chage it is equied to adopt a polaization time sufficiently long, accoding to the type of insulation, the tempeatue conditions and the applied field Recommendations fo the design of polymeic HVDC cable systems Cable insulation The macoscopic modeling of the insulation pesented in this thesis povides a quite good estimation of the electic field within the cable. This implies that the tempeatue dependency and the field dependency of the conductivity need to be consideed fo the calculation of the dynamic field distibution within the cable. The conductivity as a function of field and tempeatue can be obtained fom conduction cuent measuements. Howeve, conduction cuent measuements should be pefomed on specimens of the cable insulation that have the same type of electodes as the cable is equipped with (i.e. semicon electodes in case of extuded cables). This is necessay because the measued conduction cuent depends on the electode mateial. We ecommend to check the extent of space chage accumulation due to high-field injection and/o blocking mechanisms and to conside the enhancement of field amplitude caused by injected/blocked chages in the cable design. This effect can be quantified by compaing measued space chage pattens to space chage pattens pedicted ou macoscopic model. nothe way to detemine the space chage accumulation due to high-field injection and/o blocking mechanisms is to pefom space chage measuements unde isothemal conditions. Joint insulation In ode to educe the maximum field in the ubbe pat of the joint, we ecommend to design the joint and to mount it in such a way that it minimizes the contact themal esistance at the dielectic inteface. Results of space chage measuements on models of cable joints indicate that chage tends to be blocked in the XLPE next to the inteface. We ecommend to take into account the field enhancement induced by the chage blocked next to the inteface in the design of the cable joint. Cable system The tempeatue conditions expeienced by a cable system ae geneally diffeent accoding to the location whee the cable system is deployed. Fo instance, in case of submaine cables, the pat of the cable laying in shallow wate expeiences highe tempeatues than the pat of the cable laying in deep wate. 122

137 Chapte 8 Recommendations and suggestions fo futhe study We showed that, fo a given applied field, the highest field enhancement facto is geneally pesent at the highe tempeatue at which the cable has to opeate. This let us believe that, fo a submaine cable, the insulation of the cable laying in deep wate will expeience a maximum electic field which is smalle than the maximum electic field expeienced by the insulation of the cable length laying in shallow wate. Theefoe, the insulation of the deep-wate pat of the cable might allow a moe compact design in compaison with the insulation of the shallow-wate pat of the cable. This means that the insulation thickness of the deep-wate length of cable might be educed. moe compact design of a potion of the cable system pesents the following advantages: - less insulating mateial is used; - the volume of the cable is smalle; - the minimal banding adius is smalle; - moe length of cable can be shipped on the cable laying vessel, theefoe: - less field joints may be equied; - a shote time fo the deployment of the cable is needed. On the othe hand, the following disadvantages aises if a pat of the cable system has a moe compact design: - two diffeent cable systems have to be designed and poduced; - two tansition joints need to be designed and mounted fo joining togethe the shallow-wate cable and the deep-wate cable. We ecommend to investigate the advantages and disadvantages of using a moe compact cable design fo a potion of the cable system. This could shoten the deployment time, especially when less field joints ae equied if compaed to the situation in which the entie cable pesents the same design Recommendations fo the opeation of HVDC cable systems In Chapte 4 we showed that the dynamic electic field distibution can be pedicted (up to a cetain degee) fo a DC cable system consideing the tempeatue dependency and field dependency of the insulation conductivity. This knowledge can be used to define opeational pocedues that minimize the electic stess within the cable system fo a numbe of woking conditions. Fo instance, citical woking conditions can be pedicted and suggestions can be obtained on how to minimize the electic stess in the cable system fo a given enegy tanspot. In the following, two pactical examples ae given. Polaity evesal It is well known that the invesion of the voltage polaity on a loaded DC cable leads to a field enhancement in the insulation nea the inne conducto. This is the eason 123

138 Chapte 8 Recommendations and suggestions fo futhe study why nowadays the voltage polaity cannot be inveted fo extuded-type DC cable systems. On such cable systems, the invesion of the powe flow is done by inveting the cuent diection athe than the voltage polaity. Howeve, a pocedue could be followed to minimize the maximal electic field afte polaity evesal and to shoten the time this elatively high field is pesent within the cable. In this way, the polaity evesal becomes a feasible option also fo polymeic HVDC cable systems. s an example of the pocedue, we make use of the fact that the amount of space chage, which accumulates in the cable befoe the invesion of the voltage polaity, is elatively small, then the space chage field also emains elatively low and the maximal field afte polaity evesal is contained. This condition can be obtained by deceasing the tempeatue dop expeienced by the cable (i.e. by deceasing the cuent) a few hous befoe pefoming the polaity evesal opeation. (Eventually, the applied voltage can be inceased, fo maintaining constant the tanspoted powe). To shoten the time duing which a elatively high field is pesent afte the polaity evesal, the cuent can be inceased afte the polaity evesal. n incease of the cuent induces a highe tempeatue dop acoss the insulation. This favos the depletion of space chages, since the polaity of the voltage is now opposite to that of the accumulated chages. (Eventually, the applied voltage can be deceased, poviding an additional decease of the maximum electic field while the tanspoted powe is maintained constant). Incease of the enegy tanspot In Chapte 4, the electic field distibution was deived by means of a physical model fo an initially space-chage-fee DC cable, in which the tanspoted powe was equied to be 10% highe than its nominal value. Two diffeent situations wee investigated: 1) the voltage is inceased by 10%; 2) the cuent is inceased by 10% (see Section 4.4). The esult was that just afte the application of the DC voltage the maximum field was highe in the situation 1 - the voltage is inceased by 10% -, nea the inne conducto. On the othe hand, afte a few hous fom the application of the DC voltage, the maximum field was highe in the situation 2 - the cuent is inceased by 10% -, nea the oute conducto. The eason fo this behavio is that moe space chage accumulates when the cuent, athe than the voltage, is inceased by 10%. Moeove, in this situation the space chage accumulation is faste if compaed to the accumulation of chage occuing when the voltage is inceased by 10%. (See Figue 4.10 fo the plots of electic field distibutions and space chage distibutions fo the diffeent situations). This example shows that an opeational pocedue can be identified fo oveloading the cable and at the same time containing the maximal electic field. Initially, the field nea the inne conducto needs to be contained. Theefoe, the cuent has to be inceased while the voltage is kept elatively low. fte a cetain time, the maximal field is pesent nea the oute conducto. To contain it, the cuent has to be deceased while the voltage can be inceased. We ecommend to investigate the dynamic electic field distibution by means of a model (such as that pesented in this thesis) fo seveal woking conditions of the cable 124

139 Chapte 8 Recommendations and suggestions fo futhe study system. In this way, opeational pocedues, which minimize the electic stess within the cable system, could be defined fo diffeent situations. This could enhance the pefomance of the cable (e.g. incease the tanspoted capacity o decease the losses in the conducto) without exceeding the maximal design field Suggestions fo futhe study Macoscopic modeling of the insulation The macoscopic modeling of the insulation adopted in this thesis consides the tempeatue and field dependencies of the conductivity position-independent. Howeve, mophological diffeences exist between the insulation bulk and the egions of the insulation adjacent to the semicon-dielectic intefaces and to the dielecticdielectic intefaces. In ode to include this into the macoscopic modeling, futhe wok need to be done. fist step could be consideing the field and tempeatue dependencies of the conductivity as functions of the position. ging In the eseach pesented in this thesis, space chage phenomena have been investigated in non-aged cable insulation. Futhe investigation is equied to undestand whethe the diffeent chage accumulation mechanisms ecognized in this wok change with the aging state of the insulation. On-line on-site space chage measuements chapte of this thesis is dedicated to explain how to implement on-line on-site space chage measuements on HVDC cable systems. Howeve, futhe wok need to be done befoe such a measuement could be pefomed on actual HVDC cable systems. 125

140 Chapte 8 Recommendations and suggestions fo futhe study 126

141 ppendix

142

143 ppendix Space chage measuements on multi-dielectics by means of the PE method. Space chage measuements on multidielectics by means of the PE method 1 In this appendix, the pinciple of the PE technique is eviewed in case the test object is a multi-dielectic. The geneation of electically-induced acoustic waves is descibed in Section.1. Section.2. deals with the tansmission and eflection of acoustic waves. In section.3., two examples of how to intepet esults of PE measuements ae given. Finally, some conclusions ae dawn in Section Geneation of acoustic waves Calculation of electically-induced suface foces The electically-induced suface foces (pessues) wee calculated fo the situation depicted in Figue.1. In the figue, the two flat insulating mateials in contact, and, ae placed in between electode-1, which is connected to high voltage, and electode-2, which is connected to eath. Figue.1. Electically-induced suface foces in a multi-dielectic tested by means of the PE method geneal expession of the foce f fo a unit volume, which acts on a dielectic when it is stessed with an electic field E, may be deived themodynamically, e.g. [126]: 2 ( E a) + Π E f = ρ E E (.1) This appendix is based on the wok of the autho et al., published on Tans. Diel. Elect. Insul., Vol.13, No.2, 2006 [25]. 129

144 ppendix Space chage measuements on multi-dielectics by means of the PE method In (.1), ρ is a distibution of fee space chages, 0 the vacuum pemittivity, the elative pemittivity of the dielectic, a the electostictive coefficient and Π the pemanent dipole density. The foce fo a unit volume is the sum of fou contibutions. - The fist tem epesents the foce acting on a distibution of fee space chages ρ embedded in the dielectic. nalogously, a foce pe unit aea acts on a distibution of suface chages κ pesent within the mateial. - The second tem of (.1) will contibute to the foce whee the dielectic is not homogeneous. s a consequence, a foce pe unit volume is oiginated at the inteface between two diffeent dielectics if an extenal field is applied. ecause of this fact, the PE method geneally povides a signal at the dielectic inteface of a multi-dielectic, whee a discontinuity of the pemittivity exists. This phenomenon occus even in the situation in which neithe space chage no intefacial chage is pesent within the multi-dielectic. - The thid tem epesents the so-called electostiction tem. This takes into account the volume foce the dielectic expeiences in an non-unifom electic field, due to the vaiation of the elative pemittivity with stain, epesented in (.1) by the electostictive coefficient a. - The last tem must be taken into account only if pemanent dipoles ae pesent into the dielectic (e.g. in case of piezoelectic mateials). So, in geneal, electic foces due to space chages ae not the only souces of the signal povided by elastic methods fo space chage measuements [34, 68, 69]. Consideing the mateials and of the multi-dielectic in Figue.1. do not show any pemanent dipoles, and assuming that the extenal field is homogeneous because of the paticula electode-specimen geomety, only the fist two tems of (.1) contibute to the foce density in the studied configuation. y integation of (.1) along the x-diection, as defined in Figue.1., the electostatic suface foce p(x,t) is given. The esult is a spatial distibution of the electostatic suface foce which is diffeent fom zeo only in specific locations of the multi-dielectic: - p e () t - p e2 ( t) - p () t 1 at the inteface between electode-1 and mateial-; at the inteface between mateial- and electode-2; at the inteface between mateial- and mateial- (because of both the discontinuity of the pemittivity and the possible pesence of intefacial chage κ); ρ t (o ρ () t ) at the space chage ρ (o ρ ) location. - () p p The acoustic signal detected by the senso is the tansient component ~ p ( x, t) of the total electostatic pessue p(x,t). The tansient component of the electostatic pessue will be calculated in the next subsections, with the following assumptions: 130

145 ppendix Space chage measuements on multi-dielectics by means of the PE method - the pulsed field in both and layes can be expessed as: e e p, p, = p (.2) d + d, () t u () t,,, () t u () t = p (.3) d + d,, whee d and d ae the thickness of layes and wheeas, and, elative pemittivities of and ; ae the - the electic field E, which is due to the applied voltage, the space chage and the intefacial chage, is assumed to be constant and is deived fom equations (.4) and (.5): U 0 = E (.4) ( E ) ρ 0 = (.5) - the constant field E is much bigge than the pulsed field; - the mobility of the space chage ρ is sufficiently low to make this chage detectable by means of the PE method. In the following sections, the tansient pessue distibutions ae deduced fo a numbe of simple cases. Moe complicated cases can then be handled as a supeimposition of seveal simple cases DC voltage applied in absence of space chage and intefacial chage Figue.2 epesents the pessue distibution when a DC voltage is applied to the multi-dielectic in the absence of space chage and intefacial chage. In pactice, this situation occus duing the fist instants afte the application of the DC voltage, when the electic field can be consideed capacitively distibuted. fte a cetain time, depending on the insulation popeties and on the test conditions, chages accumulate within the insulation, leading to a esistive distibution of the field. The electic field E E,, 0, U 0, d +, d 0 in the -laye due to the DC voltage U 0 can be witten as: = (.6) simila expession can be found fo the field E 0, in the -laye. y consideing the total field acting on the multi-dielectic as the sum of the DC field E and the pulsed field e 0 p (t), the pessue at the electode-1/mateial- inteface becomes: p ( ) 2 0, 1 (.7) 2 () t = E e () 0, e 1 0, + p, t 131

146 ppendix Space chage measuements on multi-dielectics by means of the PE method 132 Combining (.2), (.6) and (.7) and consideing 0 E >> e p, the tansient component () t p e 1 0, ~ of the pessue () t p e 1, 0 becomes: () () t u U d d t p p e 0 2,, 2,, 0 0, ) ( ~ 1 + = (.8) nalogously, at the inteface between mateial- and electode-2, the tansient pessue () t p e 0, 2 ~ is given by: () () t u U d d t p p e 0 2,,, 2, 0 0, ) ( ~ 2 + = (.9) t the inteface between mateial- and mateial-, the electostatic pessue is given by integating the second tem of (.1): d E p =,, 2 0 0, 2 (.10) Intoducing the electic flux density D, whee: E D 0 = (.11) the pessue can be expessed as: = = D d D p,, , ,, (.12) Equation (12) can be ewitten in tems of time-dependent electic field: () () ( ) + = p t e E t p,, 2, 0, 2, 0 0, (.13) The tansient component () t p 0, ~ esults: () () t u U d d t p p 0,, 2,, 2, 2, 0 0, 1 1 ) ( ~ + = (.14) Figue.2. Electically-induced pessue distibution in a multi-dielectic tested by means of the PE method (U 0 0, ρ=0, κ=0).

147 ppendix Space chage measuements on multi-dielectics by means of the PE method.1.3. Space chage in the absence of DC voltage and intefacial chage In Figue.3, the pessue distibution in the multi-dielectic is epesented when space chage is pesent within mateial- wheeas intefacial chage and extenal DC voltage ae absent. The pesence of a slab of low-mobility positive space chage of density ρ and width b, whee b <<d, which is embedded in the -laye of the specimen, affects the electostatic pessue distibution within the specimen. Fistly, a suface foce is geneated at the space chage location, () t b e () t x ρ in Figue.3. Its amplitude is given by: p ρ, = ρ p (.15) xρ, y inseting (.2) in (.15) the tansient component ~ p ( t) of the pessue ρ, p ( t ) x ρ ρ, x ρ becomes: ~, ρ b pρ x () t u p () t, = (.16) ρ ( d + d ),, second consequence is that the multi-dielectic expeiences an electic field E ρ associated with the space chage ρ. y using (.4) and (.5), the field in the - laye is given by: E ρ, E ρ, ρ b d = 0 [( xρ ) d ], +, ( d + d ),,, if 0 < x< x (.17) ρ b, xρ = if xρ x d d + d ) < < (.18) 0, (,, wheeas in the -laye the field is: E ρ b x ρ ρ, = (.19) 0 ( d, + d, ) When the pulsed field e p (t) is supeimposed on the field E ρ, the pessue distibution is diffeent fom zeo not only at the space chage location but also at the electode/dielectic intefaces ( pρ e ( t), 1 and pρ e ( t), ) and at the inteface between the 2 two diffeent dielectics ( pρ, ( t) ): p p ( ) 2 ρ, p, () t = E e () ρ, e1 0, + t 1 (.20) 2 ( ) 2, p, 1 (.21) 2 () t = E e () ρ, e2 0, + t ρ 1 2 pρ () t = E, + e () t, 0, ρ (.22) 2 2 ( ) 1 1 p,,, The tansient component of the pessues defined in ( ) can be found by ρ 133

148 ppendix Space chage measuements on multi-dielectics by means of the PE method combining (.2), (.3), ( ) and consideing E ρ >> e p : ρ b [( d x ) d ] ~ p ρ e () t =, 1 (, ρ, +, 2 d + d ) ~ p () t,, ρ, e (,, ρ ) 2 2 d, + d, () t u p () t (.23) ρ b x = u (.24) ~ ρ p () ( ) b,,, t ρ, 2 ( d + d ) p xρ = u (.25),, p () t Simila expessions can be found in case of a slab of positive space chage ρ of width b embedded in the -laye of the multi-dielectic at a distance x ρ. Figue.3. Electically-induced pessue distibution in a multi-dielectic tested by means of the PE method (U 0 =0, ρ 0, κ=0) Pesence of intefacial chage in absence of DC voltage and space chage The pessue distibution in the multi-dielectic shown in Figue.4 is epesentative of the situation in which only intefacial chage is pesent in the multi-dielectic and no DC extenal voltage is applied. If a positive suface chage κ is pesent at the dielectic inteface, a suface foce pκ, () t is geneated at the chage location: 1 pκ, () t = κ [ e p, () t + e p, ()] t (.26) 2 In (.26), the suface chage κ is assumed to expeience the aveage pulsed field at the dielectic inteface. Combining (.2), (.3) and (.26), the tansient component ~ p () t of the pessue p () t κ κ, is obtained:, 134

149 ppendix Space chage measuements on multi-dielectics by means of the PE method ~ p κ,, +, () t = κ u p () t (.27) 2 ( d + d ),, The electic field Eκ associated with the suface chage can be calculated by means of (4) and (5). In the -laye the field is given by: E κ, = (.28) 0 ( d + d ) κ d, wheeas in the -laye: E, κ, = (.29) 0 ( d + d ) κ d,, t the electode/dielectic intefaces the pessues pκ ( t) and pκ () t ae pesent: p p ( ) 2 κ, p, () t = E e () κ, e 1 0, + t, e 1, e 2 1 (.30) ( ) 2 κ, p, () t = E e () (.31) κ, e2 0, + t y means of (.2), (.3), ( ) and consideing E κ >> e p, the tansient components ~ p, e () t and ~ p ( t ) κ κ e become: 1 κ d, 2 ~ p,e 1 ()= t κ (,, ) u p () t (.32) 2 d + d ~ p, e 2, κ d,,, () t = u () t (.33) κ ( d + d ), 2, p Figue.4. Electically-induced pessue distibution in a multi-dielectic tested by means of the PE method (U 0 =0, ρ=0, κ 0). 135

150 ppendix Space chage measuements on multi-dielectics by means of the PE method.1.5. DC voltage applied in pesence of space chage and intefacial chage In geneal, the total tansient pessue distibution within the test object can be expessed as the supeimposition of the tansient pessue distibutions obtained in the thee paticula situations studied befoe: ~ p ( x, t) ~ p ( x, t) + ~ p ( x, t) ~ p ( x t) = (.34) 0 ρ +, i κ i It is to be noted that fo evey consideed case, the total pessue distibution, p TOT, acoss the multi-dielectic is zeo: d + d 0 ( x) dx = 0 ptot = f (.35).2. coustic wave taveling and eflection Fom the suface foces calculated in the pevious section the acoustic waves detected at the senso can be obtained. Fistly, acoustic waves taveling though an elastic medium ae attenuated and dispesed. Fo situations whee these effects ae not negligible, pocedues fo ecoveing the oiginal wavefom fom the attenuated/distoted signal have been developed [97]. Secondly, waves geneated at diffeent locations of the dielectic expeience diffeent geneation, tansmission and eflection coefficients. These phenomena will be studied fo a multi-dielectic coustic wave popagation fte thei geneation, pessue waves tavel both in the diection of electode-1 and electode-2. Howeve, only those waves that tavel towads electode-2 ae detected by the senso. Waves taveling towad electode-1 do not each the senso, unless they ae eflected at the inteface between two diffeent media. This will be discussed late. The popagation of compessional pessue waves oiginated duing the testing of the multi-dielectic shown in Figue.5. is descibed in the following. The acoustic impedance of a mateial that is elevant in ou case is defined as: Z ac i = δ i v (.36), i whee δ i is the mass density of the medium and v i the speed of compessional waves in the medium. Consideing the waves taveling though the multi-dielectic as plana waves, the geneation coefficient G, the tansmission coefficient T and eflection coefficient R can be calculated as [19]: 136

151 ppendix Space chage measuements on multi-dielectics by means of the PE method Figue.5. Popagation of acoustic waves in a multi-dielectic tested by means of the PE method. G T Z ac, j i j = (.37) Z ac, i + Z ac, j 2 Z ac, j i j = (.38) Z ac, i + Z ac, j R Z Z ac, j ac, i i j = (.39) Z ac, i + Z ac, j whee the foote i identifies the medium fom which the wave comes fom, while the foote j identifies the medium towad which the wave is taveling. If an acoustic wave is oiginated at the inteface between two media, i and j, the geneation coefficient indicates the faction of this wave taveling into medium j. On the othe hand, if an acoustic wave tavels fom medium i towads medium j, the tansmission and eflection coefficients indicate the factions of this wave which ae espectively tansmitted into medium j and eflected back into medium i. In the situation depicted in Figue.5., the pessue wave ~ p e2 () t, which is the faction of ~ p () t taveling into the senso, can be calculated as follows: ~ p () t G e 2 e = 2 e2 T ~ p ( t τ ) e2 S (.40) e2 e2 t the senso location, the wave aives afte a time τ e2 fom the fiing of the pulse. τ e2 is the time the acoustic waves take fo taveling though electode-2 and is given by: 137

152 ppendix Space chage measuements on multi-dielectics by means of the PE method τ = d v (.41) e2 e2 e2 Expessions simila to (.40) can be detemined fo p ( t) espectively the faction of ~ p ( t). and ~ p () t taveling into the senso: e1 ~ p () t = G T e T ~ 2 e2 S p ( t τ τ e ) 2 ~ p t G T T T ~ p ( t τ τ τ ) () e e e S e = 1 whee: ~, and ~ p () t which ae e 1 (.42) e1 e (.43) 2 τ = d v (.44) τ = d v (.45) With egad to the acoustic waves due to the space chage ρ within the bulk of the - laye, the pessue wave ~ pρ () t, taveling fom the space chage location x ρ into the senso is: ~ p τ 1 () t = T T T ~ p ( t τ τ ) ρ e2 e2 S ρ τ ρ e (.46) 2 2 ( d x ) v = (.47) ρ ρ The coefficient ½ in (.46) is a diect consequence of (.37). The acoustic coefficients peviously intoduced ae defined in case of two pefectly bonded media. Howeve, mateials adopted fo PE measuements pesent a finite suface oughness. So a non-ideal contact is pesent at the inteface. The main consequence of this fact is that when an ultasonic wave is nomally incident to the inteface, the acoustic coefficients will be fequency dependent [50]. In ode to neglect this phenomenon, the suface oughness of the sufaces in contact must be much smalle then the wavelength of the acoustic waves taveling though the inteface. In pactice, to obtain this condition, sufaces in contact must be sufficiently smooth and/o a tiny amount of silicon oil can be used in ode to impove the acoustic contact. Howeve, if oil is used at the dielectic/dielectic inteface, the multi-dielectic may exhibit a quite diffeent space chage behavio fom the situation in which the inteface is dy [20, 139, 140] coustic wave eflections ccoding to [78], if the eath electode (electode-2) is sufficiently thick, eflections of acoustic waves at the inteface between electode-2 and senso do not affect the signal coming fom the specimen. Moeove, waves popagate without eflections afte passing the senso if an appopiate acoustic temination is used. In case of multi-dielectics, anothe inteface exists whee eflections could occu. If Z ac, and Z ac, ae the acoustic impedances of the mateials and in Figue 7, thee is acoustic mismatching if Z ac, Z ac,. In this case, the eflection coefficient defined in 138

153 ppendix Space chage measuements on multi-dielectics by means of the PE method (.39) takes a value diffeent fom zeo fo all the waves passing the / inteface. Then, eflected waves, which could ovelap the waves epesentative fo the pessue distibution inside the specimen, ae expected. In the case analyzed in Figue.6., the stess wave ~ p e2 ( t), which is the faction of ~ p e2 () t eaching the senso afte taveling though the -laye and afte being eflected back at the / inteface, is given by: ~ p () ~ e t = Ge R T e Te S p e ( t τ τe ) (.48) Similaly, ~ p ρ () t, which is the eflection at the / inteface of the wave geneated at the space chage ρ location, becomes: 1 () t = R T T ~ p ( t τ + τ τ ) ~ p ρ 2 e2 e2 S ρ ρ e (.49) 2 2 τ = d + d x v (.50) ρ ( ) ρ / Howeve, these acoustic waves do not influence a measuement if they ae detected by the senso afte the aival of ~ p e ( t) (wave geneated at electode-1/dielectic- 1 inteface). In othe wods, the time a eflected wave takes fo eaching the senso must be longe than that needed by the wave oiginated at the electode-1/dielectic- inteface fo aiving at the senso. Then, no ovelapping occus if the following condition is fulfilled: ( xρ d ) v > d v (.51) Figue.6. Reflection of acoustic waves in a multi-dielectic tested by means of the PE method. 139

154 ppendix Space chage measuements on multi-dielectics by means of the PE method.3. Intepetation of detected acoustic signals In this paagaph examples of detected acoustic signals in two diffeent types of multidielectics ae shown and discussed Test specimens and test pocedues multi-dielectic of the fist type consists of a 175-µm thick sheet of polycabonate (PC) in contact with a 100-µm thick sheet of low-density polyethylene (LDPE). multi-dielectic of the second type is made of a 1.5-mm thick plate of coss-linked polyethylene (XLPE) in contact with a 0.8-mm thick plate of epoxy esin (aldit esin CW1483D, filled with 47% Gwt Micodol). Neithe lubicants no teatments of any kind wee applied at the dielectic inteface. The paticula mateials chosen fo this wok wee selected because of the fact that thei acoustic and electic popeties ae quite dissimila, as shown in Table.1. In this way, the detected acoustic signal is expected to be quite diffeent fom the space chage distibution. Measuements on PC-LDPE multi-dielectics wee pefomed by means of the PE system fo thin flat specimens descibed in Table 2.4. The pulsed voltage was set to 300 V. The multi-dielectic was placed in between a semicon HV electode and an aluminum eath electode. The LDPE side of the specimen was connected to HV, wheeas the PC side was connected to eath potential. positive DC voltage of 2.75 kv was applied to the multi-dielectic fo a polaization time of 20 s, duing which voltage-on measuements wee pefomed. fte emoving the DC extenal voltage and shot-cicuiting the specimen (these opeations equied a few seconds), voltage-off measuements wee pefomed. Table.1. Some electic and acoustic popeties of mateials used fo PE measuements in this investigation. Mateial Speed of sound Density coustic Relative [m s -1 ] [Kg m -3 impedance pemittivity ] [Kg m -2 s -1 ] [-] XLPE Epoxy PC LDPE EPR PVDF l Semicon Semicon The density and the speed of sound stongly depend tape on how stetched the semicon tape is

155 ppendix Space chage measuements on multi-dielectics by means of the PE method XLPE-epoxy multi-dielectics wee tested in the PE set-up fo thick flat specimens (see Table 2.4). pulse with amplitude of 2 kv was used. positive DC voltage of 23 kv was applied to the multi-dielectic. Semicon electodes wee used. The XLPE side of the multi-dielectic was connected to HV and the epoxy side to eath. s in the pevious case, the polaization time was 20 s, duing which voltage-on measuements wee pefomed. The thickness of the semicon eath electode was chosen in such a way that eflected acoustic waves at the inteface between semicon eath electode and aluminum PE table did not ovelap the waves epesentative of the pessue distibution inside the multi-dielectic. ll the measuements wee done at oom tempeatue. The shot polaization time and the elatively low electic stess (the aveage electic field inside a tested multidielectic was 10 kv/mm) guaanteed that neithe space chage no intefacial chage could build up duing the voltage-on measuements. Since the fequency esponse of the tansduce amplifie system was not flat, deconvolution techniques [100] wee applied to the detected signal. In ode to convet the deconvolved wavefoms into space chage signals, the calibation pocedues descibed in ppendix D, Section D.2, wee used Measuement esults In Figue.7.a, an example of a voltage-on signal detected on a space-chage fee PC- LDPE multi dielectic is epesented. The signal clealy shows the pesence of thee peaks, which coespond to the electostatic pessue at the electodes and at the dielectic inteface. It is to be noted that neithe space chage no intefacial chage was pesent within the multi-dielectic. Figue.7.b. epesents the voltage-off signal measued on a PC-LDPE multi dielectic composed of a space chage-fee LDPE sheet in contact with a PC sheet in which positive space chage is pesent. The PC sheet was in fact pe-stessed fo 860 hous at 17.5 kv. fte this electical teatment, positive space chage was stably tapped within the PC. (In Figue.7.d., the voltage-off signal measued on the single PC-laye is shown). In Figue.7.b., not only peaks at the electodes and at the dielectic inteface ae visible, but also at the space chage location and within the LDPE-laye. It is to be noted that the LDPE is space chage fee and neithe extenal DC voltage is applied no intefacial chage is pesent. In Figue.7.c., the voltage-on signal detected on a space-chage fee XLPE-epoxy multi-dielectic is shown. Seveal peaks ae pesent in the signal. In addition to the peaks at both the electodes and at the dielectic inteface, two peaks within the XLPElaye ae notable. s in the case epesented in Figue.7.a, neithe space chage no intefacial chage is pesent within the specimen. 141

156 ppendix Space chage measuements on multi-dielectics by means of the PE method a b c d Figue.7.a. coustic signal in a space-chage fee PC-LDPE multi-dielectic. Voltage-on measuement Figue.7.b. coustic signal in a PC-LDPE multi-dielectic, in which space chage is pesent within the PC. Voltage-off measuement; wavefom not deconvolved. Figue.7.c. coustic signal in a space-chage fee XLPE-epoxy multi-dielectic. Voltage-on measuement. Figue.7.d. coustic signal in a single PC-laye, in which space chage is pesent. Voltage-off measuement; wavefom not deconvolved Intepetation of measuement esults In ode to intepet the acoustic signals epesented in Figues.7.,.9. and.10., the expected acoustic signal at the senso was calculated. Fo this pupose, each laye of the multi-dielectic, the electodes and the senso wee modeled as loss-fee acoustic lines. Evey acoustic line was chaacteized by its acoustic impedance and delay time, calculated as descibed in section.2.1. The electically-induced pessue waves wee modeled as pulsed pessue geneatos placed in the acoustic netwok as shown in Figue.11. The amplitude of the pulses was given accoding to (.8), (.9) and (.14). In this way, the detected pessue signal in the space-chage fee situation 142

157 ppendix Space chage measuements on multi-dielectics by means of the PE method was deived. Compaing the expeimental pattens shown in Figues.7.a. and.7.c. to the esult of calculations epesented in Figues.12. and.13., the following can be said. The location and sign of the peaks in the measued signal coespond to those calculated. The magnitude of the measued peaks is also in good ageement with the calculation. Only the peak measued at the HV electode showed amplitude smalle than that pedicted by the calculation. The main eason fo this is believed to be the attenuation and dispesion the acoustic waves geneated at the HV electode expeience taveling though the mateial and though the dielectic inteface. The oigin of the peak detected at the LDPE location in the signal shown in Figue.7.b. is to be attibuted to eflection of acoustic waves at the PC-LDPE inteface. So the signal within the LDPE does not epesent any space chage. In fact, as shown in Figue.14, the pessue waves, which ae geneated at the space chage location and which tavel towad the HV electode, ae eflected at the PC-LDPE inteface and then detected at the senso afte taveling though the PC and the eath electode. The two peaks, which ae detected between the dielectic inteface and the HV electode in the measued signal shown in Figue.7.c., ae also due to eflection of acoustic waves and do not epesent any space chage, as explained in Figue.15. Peak 1 is the eflection at the epoxy-xlpe inteface of the faction of the acoustic wave geneated at the semicon-epoxy inteface which tavels towad the HV electode. Peak 2 is the double eflection, fist at semicon-epoxy inteface and then at the epoxy- XLPE inteface, of the faction of the acoustic wave geneated at the epoxy-xlpe inteface and taveling towad the eath electode. Figue.11. coustic netwok as used fo the calculation of the signal expected at the senso. The acoustic impedance Z ac =Z acs, elates to the acoustic temination. Figue.12. Expected acoustic signal at the senso calculated fo a PC-LDPE multidielectic. The multidielectic is assumed to be space-chage fee. 143

158 ppendix Space chage measuements on multi-dielectics by means of the PE method Figue.13. Expected acoustic signal at the senso calculated fo an XLPE-epoxy multidielectic. The multidielectic is assumed to be space-chage fee. Figue.14. coustic wave tavelling and eflection in a PC- LDPE multi-dielectic in which space chage is pesent within the PC. Voltage-off measuement; wavefom not deconvolved. Figue.15. coustic wave taveling and eflection in a spacechage fee XLPE-epoxy multi-dielectic. Voltageon measuement. 144

159 ppendix Space chage measuements on multi-dielectics by means of the PE method.4. Conclusions Geneation, taveling and eflection of electically-induced acoustic waves in a multidielectic tested by means of the PE method wee descibed in this appendix. ased on a theoetical appoach, pocedues wee developed fo elating the space chage magnitude and location to the acoustic output signal given by a PE system. Expeimental investigations validated the poposed analytical methods. Geneally, when a multi-dielectic is tested, the detected acoustic signal does not coespond to the space chage distibution. Thee ae two main easons. 1. The electically-induced pessue distibution is diffeent fom the chage distibution if the pemittivities of the layes composing the multi-dielectic ae not the same. This leads to the pesence of a pessue signal at the dielectic inteface even in the absence of intefacial chage. Moeove, the diffeent pemittivity values should be consideed in the calibation pocedue fo conveting the output signal into a calibated space chage pofile. 2. The detected acoustic signal does not coespond to the pessue distibution if the layes of the multi-dielectic have diffeent acoustic popeties. In fact, the magnitude of the acoustic waves is affected by the acoustic impedance of the mateials. esides, in case of acoustic mismatching, eflected waves may ovelap the waves epesenting the pessue distibution inside the multi-dielectic. Theefoe, when the PE method is applied to multi-dielectic test objects, paticula attention should be paid to the intepetation of the detected signal. If the multidielectic is electically and acoustically inhomogeneous, pocedues should be used in ode to collect a meaningful space chage patten. 145

160 ppendix Space chage measuements on multi-dielectics by means of the PE method 146

161 ppendix PE method fo cylindical test objects. PE method fo cylindical test objects In this appendix, the PE method fo measuing the dynamic space chage distibution in cable-geomety test objects is descibed. In section.1, a compaative desciption of diffeent PE set-ups is given. Section.2 deals with the application of the pulse voltage to the cable object of a test. Finally, the use of a coection facto, that takes into account the specific geomety of the test object, is explained in section Diffeent types of PE set-ups In the last decades, seveal types of PE systems have been developed fo measuing space chage in cable-geomety test objects. They diffe fo the shape of the eath electode and fo the way in which the pulsed voltage is applied. Table.1. lists some liteatue discussing PE set-ups fo measuing space chage in cable-geomety test objects. Table.1. Some liteatue dealing with PE systems fo space chage measuements in cable-geomety test objects. UTHOR YER(S) REFERENCE(S) TYPE OF PE SET-UP Yasuda et al.. 91 [153], 1 Liu et al. 93 [98], 1 Hozumi et al. 92, 94, 98 [70-72], 2 Wang et al. 95 [151], 1 Muonaka et al. 96 [119],, 1, 3 Nagashima et al.. 98 [121], 1 Kanno et al. 98 [81] 3 Fu et al. 00, 00, 01, 03 [56-59], 1 Montanai et al [112, 128], 3 odega et al. 05 [23, 24], 3 = cuved eath electode = flat eath electode 1= pulse applied at the cable conducto 2= pulse applied at the PE cell 3= pulse applied at the oute sceen 147

162 ppendix PE method fo cylindical test objects.1.1. Shape of the eath electode Two diffeent configuations fo the eath electode of the PE system exist. In the fist configuation, the PE eath electode has a cuved suface, which fits with oute semicon of the cable (see Figue.1.a). The senso and its acoustic temination have cuved geomety as well. In the second configuation, the PE eath electode, the senso and its acoustic temination ae flat (see Figue.1.b). Compaing the two PE aangements, the cuved-electode configuation pesents two main disadvantages. Fistly, the mounting of the senso is athe complicate. ecause of the cuved shape of the electode, it is not easy to obtain a good acoustic contact at the electode-senso inteface. Secondly, diffeent eath electodes ae equied fo diffeent cable diametes. Those dawbacks ae absent in the flat-electode configuation. On the othe hand, in the flat-electode configuation, the piezoelectic senso is elatively naow. Then, the capacitance of the senso is smalle than that of the senso used in the cuved electode configuation. low senso capacitance may lead to a distoted signal if the input impedance of the amplifie is low [118], e.g. 50Ω. a b Figue.1. Diffeent shapes of the PE eath electode. a) Cuved eath electode. b) Flat eath electode pplication of the pulsed voltage Thee ae thee main ways fo applying the pulsed voltage acoss the cable insulation: - the pulse is applied via the cable conducto; - the pulse is applied via the PE cell; - the pulse is applied via the oute sceen of the cable. Pulse applied via the cable conducto In the aangement depicted in Figue.2, the pulse voltage is applied between the cable conducto and eath. decoupling capacito is equied to apply the pulse voltage simultaneously with the poling voltage. 148

163 ppendix PE method fo cylindical test objects This aangement pesents two main limits. Fistly, the decoupling capacito, which capacitance must be much bigge than that of the cable, must withstand the poling DC voltage. This may equie a lage-size component. Secondly, if the cable is longe than the wavelength of the pulse, the cable cannot be seen as a lumped capacitance anymoe. The injected pulsed voltage may be distoted duing popagation though the cable and eflected at the teminations. Pulse applied via the PE cell The disadvantages of the aangement in Figue.2 ae ovecome by using the set-up shown in Figue.3. Pat of the oute sceen is emoved, in ode to expose the oute semicon at the measuing point. The pulse voltage is applied between the PE cell and eath. In this way, at the measuing point, the pulse will not be distoted/eflected. Moeove, a decoupling capacito is not needed, because of the cable itself is used fo this pupose. Howeve, the equipments fo measuing the output signal (e.g. oscilloscope) cannot be diectly connected to the PE cell, since the PE cell expeiences the pulse potential. Theefoe, electo-optical convesion of the signal is necessay in ode to guaantee a pope electical isolation between the PE cell and the measuing equipments. In addition, an electically sepaated souce must be used fo supplying the amplifies and the electo/optical convete inside the PE cell. Pulse applied via the oute sceen In Figue.4, a PE set-up in which the pulse is applied between the oute sceen and eath is epesented. s in the pevious case, the oute semicon at the measuing point is exposed by emoving pat of the oute sceen. The pulse is applied between the two sepaated sceens and eath. Theefoe, the cable itself acts as decoupling capacito. In this aangement, the PE cell is at eath potential. So, the measuing equipments can be diectly connected to the PE cell. Figue.2. PE set-up in which the pulse is applied via the cable conducto. 149

164 ppendix PE method fo cylindical test objects Figue.3. PE set-up in which the pulse is applied via the PE cell. Figue.4. PE set-up in which the pulse is applied via the oute sceen. 150

165 ppendix PE method fo cylindical test objects.2. pplication of the pulse to the cable In this wok, a PE system with a flat eath electode was adopted (Figue.1.b). In evey test, the pulse was applied to the cable via the oute sceen, as shown in Figue.4. The equivalent cicuit fo the pulse voltage is epesented in Figue.5. Figue.5. Equivalent cicuit fo the pulse voltage. The two halves of the cable ae epesented by tansmission lines with impedance Z cable, wheeas the measuing point is epesented by a lumped capacito C m. tansmission line, Z line, connects the pulse geneato to the cable object of the test. The tansmission line is popely teminated by means of the esisto R pulse (R pulse = Z line ). Table.2 shows the paametes of the pulse cicuit adopted in the pesent wok. The pulse has a vey shot ise time and a naow width (typical values ae 2-20 ns and ns fo pulse ise time and pulse width espectively, wheeas the pulse amplitude is 0.5-5kV). So, when stay inductances L s ae pesent in the pulse cicuit, fly-back voltages may be geneated. This will distot the pulse shape. (Fo example, the inductance of a simple 1-mm 2 wie is about 10nH/cm. Consideing a 5-kV pulse with a ise time of 10 ns and consideing a 50-Ω tansmission line, a 1-kV fly-back voltage will be geneated when a 10-cm long wie is used). Moeove, the oute semicon pesents a finite esistance R sem, which connects the oute sceen to eath. This deceases the total pulse load that may become too small fo matching the tansmission line Z line. In ode to avoid the negative effects poduced by both the stay inductances and the finite semicon esistance, a low-inductance damping esisto, R d, is connected in seies to the cable object of the test, as shown in Figue.5. In Figues.6, the calculated shape of the pulse voltage at the oute sceen is shown. The figue shows that when no damping esisto is used, fly-back voltages ae pesent in the pulse wavefom. 151

166 ppendix PE method fo cylindical test objects Table.2. Some paametes of the pulse cicuit adopted in this wok. SYMOL QUNTITY VLUE UNIT u p Pulse amplitude 0-4 kv T pulse Pulse width 80 ns R line Temination esisto 50 Ω Z Chaacteistic impedance of line the pulse line 50 Ω * Z Chaacteistic impedance of cable the cable object of the test Ω ** C Cable capacitance at the m measuing point 5-10 pf R d Damping esisto 180 Ω R dc DC esisto 30 MΩ 1 µ out 2π lm * Z cable = ln ** Cm = 2π in out ln in - µ = pemeability of the insulation (µ=µ 0 = 4π 10-7 H/m) - l m = length of the cable at the measuing section (l m = 5 cm) Figue.5. Calculated pulsed voltage at the oute sceen of a cable. pplied pulse: 4 kv, 80 ns. 152

167 ppendix PE method fo cylindical test objects.3. Effect of the cylindical geomety on the amplitude of acoustic waves When a cylindical-geomety object is tested by means of the PE method, the acoustic signal detected at the senso does not coespond to the chage distibution in the test object. Theefoe, the detected signal must be coected. Divegence of the pulsed field The electic field distibution e pulse (), which is due to the applied pulse u p, is: e pulse () u p = ln out in (.1) The magnitude of the pessue wave geneated at the space chage location is popotional to the pulsed field at the space chage location. ecause of the pulsed field distibution is not homogeneous, the space chage distibution will be position dependent. In ode to coect the detected signal fom the divegence of the pulsed field, a facto K g,pulse is defined as: g pulse ( out ) p() ( ) p e K, = = = (.2) pulse out e pulse () out Whee p( out ) is the magnitude of a pessue wave associated to a given amount of chage at the oute adius out, wheeas p() is the magnitude of a pessue wave associated to the same amount of chage at the geneic adius. Divegence of acoustic waves The magnitude of an acoustic wave deceases while taveling fom the inne pat of the cable towad the senso. This is diect consequence of the wave equation: p v p = 0 (.3) 2 t In cylindical coodinates and esticting the analysis to the adial dimension only, (.3) becomes: v 2 2 p p 2 t The solution of (.4), fo high ω, is [1, 12]: p ( t) = exp ( v t) (.4) iω, (.5) v whee i is the imaginay unit, ω is the angula fequency of the acoustic wave and is a constant established by the bounday conditions. 153

168 ppendix PE method fo cylindical test objects Equation (.5) shows that the amplitude of a cylindical acoustic wave, which tavels in the adial diection, deceases with the squaed oot of the adius. Theefoe, the amplitude of the acoustic waves detected at the senso is smalle than the amplitude of the wave at the space chage location. In ode to coect the detected signal fom the divegence of the acoustic waves, a facto K g,wave is defined as: K p(, t) (, t τ ) p p(, t) (, t) g, wave = = = p out out out (.6) Whee p() is the magnitude of a geneic pessue wave geneated at the adius, wheeas p( out,t-τ) is the magnitude of the same pessue wave afte having taveled fo a time τ fom the adius to the oute adius out. Geometical coection facto The combined effect of the divegence of both pulsed field and acoustic waves is coected by using a geometical facto K g defined as: () v K = sig, coected g = = K g, pulse K g, wave vsig,det ected () out (.7) wee v sig,coected and v sig,detected ae espectively the coected signal and detected signal. 154

169 ppendix C ttenuation and dispesion of acoustic waves in the PE method C. ttenuation and dispesion of acoustic waves in the PE method This appendix is devoted to the attenuation and dispesion phenomena expeienced by the acoustic waves taveling in non-ideally elastic insulations tested by means of the PE method. In Section C.1., an intoduction to the poblem is given. Some theoy about the popagation of acoustic waves in lossy and dispesive media is pesented in Section C.2. Finally, Section C.3. descibes the pocedue used in this thesis fo ecoveing the oiginal acoustic wavefom fom the detected PE signal. C.1. Poblem identification Geneally, insulating mateials suitable fo PE measuements (e.g. polymes) ae acoustically lossy and dispesive media. In a lossy medium, the amplitude of a pessue wave due to space chage deceases while the wave tavels though the test object. ecause of this phenomenon is fequency dependent, the chage peak in the detected signal esults not only smalle, but also boade if compaed to the peak that would be detected if the medium was ideal (oiginal peak). (The high fequency components of the acoustic waves expeience stonge attenuation than the lowe fequencies). In a dispesive medium, the shape of a pessue wave due to space chage changes while the wave tavels though the test object. This is due to the fact that the speed of sound in the medium is fequency dependent. The longe the distance that waves have to tavel within the medium, the moe attenuated and distoted the coesponding signals. Theefoe, the attenuation and dispesion phenomena ae fequency and position dependent. In Figue C.1., the effect of attenuation and dispesion is shown fo acoustic signals oiginated at diffeent location of a test object. Figue C.1. ttenuation and dispesion of acoustic waves in the PE method. 155

170 ppendix C ttenuation and dispesion of acoustic waves in the PE method C.2. Theoetical backgound geneal expession fo a tansient plana acoustic wave p(x,t) taveling though an ideal medium is obtained though its Fouie integal epesentation: p 1, = 2π (C.1) ( x t) pˆ ( x, ω) exp( iω t) dω in which: ( x, ω) = P ( ω ) exp( i β ω ) pˆ 0 (C.2) is the expession of the acoustic wave in the Fouie domain. In (C.2), P 0 (ω) epesents the magnitude of the pessue wave component with angula fequency ω at the location x=0. This waves popagates without attenuation and has a velocity v that is elated to the phase coefficient β accoding to: v β = (C.3) ω In case of a lossy and dispesive medium, (C.2) can be ewitten as [97, 132]: pˆ x, t = P0 ω exp α ω x exp i β ω x (C.4) ( ) ( ) ( ( ) ) ( ( ) ) whee α(ω) and β(ω) ae espectively the fequency-dependent attenuation facto and phase facto, espectively. The facto α(ω) takes into account that the wave magnitude deceases while the wave tavels though the medium (attenuation). The facto β(ω) takes into account that the speed of sound in the medium is fequency dependent (dispesion). Next, a function G(x,ω) can be defined as: pˆ ( ) ( x, ω ) G x, ω = = exp( α( ω ) x) exp( i β ( ω ) x) (C.5) pˆ 0, ω ( ) In ode to calculate the coefficients α(ω) and β(ω), the acoustic wavefom at two diffeent locations of the sample ae sufficient. Geneally, the acoustic wave geneated at the HV electode p(d,t)) (whee d is the sample thickness) and the coesponding detected wave at the senso p(0,t) ae used [97]. In this paticula case, G becomes: F ( ) ( p( d, ω )) G d, ω = = exp( α( ω ) d ) exp( i β ( ω ) d ) (C.6) F p 0, ω ( ( )) whee F is the Fouie tansfom. Then, α(ω) and β(ω) can be deived fom the following elations: 1 exp( α ( ω) d ) = G( d, ω) α( ω) = ln G( d, ω ) (C.7) d 1 β ( ω ) d = angle( G( d, ω )) β ( ω ) = angle( G( d, ω )) (C.8) d 156

171 ppendix C ttenuation and dispesion of acoustic waves in the PE method C.3. Pocedue fo ecoveing the oiginal acoustic wavefom fom the attenuated and distoted wavefom Once the function G(x,ω) is detemined by means of the coefficients α(ω) and β(ω), the pessue distibution p(x,t) inside the sample can be deived as: p 1 ( x, t) F [ P( 0,ω ) G( x,ω )] = (C.9) wee F -1 epesents the invese Fouie tansfom. The pessue distibution p(x,t) fo t=0 epesents the acoustic wave befoe it has taveled though the medium (i.e. befoe attenuation and dispesion phenomena have occued). On the othe hand, the pessue distibution p(x,t) fo x=0 epesents the acoustic wave afte it has taveled though the medium (i.e. afte attenuation and dispesion phenomena have occued), see Figue C.1. Theefoe, the detected voltage signal coesponds to pessue p(0,t), wheeas the ecoveed voltage signal coesponds to the pessue p(x,0)= p(v t,0). In ode to implement the pocedue descibed in this chapte, the oiginal signal at the HV electode location is equied. If the sample is space-chage fee, the ecoveed signal at the HV electode location is known. In fact, in this situation, the signal epesents the electode chage only, which can be detemined if a known voltage is applied acoss the sample. In Figue C.2., the detected signal v detected, the ecoveed signal v ecoveed and the oiginal signal expected fom the electode chage distibution v oiginal ae given fo a flat 4.5-mm thick XLPE cable in which no space chage is pesent. In the figue, the ecoveed signal does not exactly coespond to the oiginal signal. s explained in [58], this is due to the fact that some of the highe fequencies of the oiginal signal may be totally attenuated, so they ae not pesent in the detected signal. Theefoe, it is not possible to ecove completely the oiginal wavefom. Howeve, the aea of the peak at the HV electode coesponds to the coect chage value. Hence, the ecoveed signal can be used fo the detemination of the electic field. When the computation of the paametes α(ω) and β(ω) is pefomed based on the function G(d,ω), some poblems may occu. Fistly, G(d,ω) is given as atio of two functions. If the denominato contains zeos, the division becomes impossible. Secondly, the mathematical pocedue will poduce a highe amplification fo the high fequencies of the signal, athe then fo the low fequencies. So, if noise is pesent in the detected signal, it will be amplified as well. To avoid these complications, two specific functions wee assumed fo α(ω) and β(ω) in this wok: α( ω) ω β 2 = + a (C.10) ( ω ) b ω = (C.11) 157

172 ppendix C ttenuation and dispesion of acoustic waves in the PE method Equations (C.10) and (C.11) epesents α(ω) and β(ω) when the oiginal wavefom and the attenuated/distoted one ae Gaussian functions 1. Satisfactoy esults wee obtained. In ode to check whethe the ecoveed signal is coect, a double integation of the calibated signal can be done. s detailed explained in ppendix D, the double integation of the detected signal must povide the voltage distibution acoss the sample. In Figue C.3, the functions α and β, used fo ecoveing the wavefom epesented in Figue C.2, ae epesented as function of the fequency. Figue C.2. Detected signal v detected, ecoveed signal v ecoveed and oiginal signal expected fom the electode chage distibution v oiginal. The signals ae elative to a 4.5-mm thick XLPE cable. No space chage is pesent. Figue C.3. ttenuation coefficient α and dispesion coefficient β as function of the fequency, fo the XLPE insulation used in this wok. 1 Let s name y 1 (t) and y 2 (t) the two Gaussian functions descibing espectively the oiginal wavefom and the attenuated one, whee: 2 2 y 1() t = 1 exp( a1 ( t τ1) ) and y 2 ( t) = 2 exp( a2 ( t τ 21) ) The Fouie tansfoms of y 1 and y 2 ae: 2 2 π ω π ω Y1 ( ω ) = 1 exp i τ1 ω and Y2 ( ω ) = 2 exp iτ 2 ω a1 4a1 a2 4a2 Consequently, the function G(ω) becomes: 2 a ω G( ω) = Y Y = i ω ( τ τ ) = ( d ( + aω ) ( i bω d) a a a 1 2 exp 1 2 exp exp a2 = ln d 2 a a = b = ( τ ) 4 d a1 a2 1 τ 2 d 2 Theefoe: α( ω) = + a ω and β ( ω ) = b ω 158

173 ppendix D - Calibation D. Calibation This appendix deals with the calibation of the measued space chage signals. The calibation pocedue is given fo fou diffeent types of test object: D.1. flat homogeneous test object; D.2. flat multi-dielectic test object; D.3. cylindical homogeneous test object; D.4. cylindical multi-dielectic test object. Calibation of the measued signals should be pefeably pefomed on deconvolved wavefoms which have been also coected taking into account the attenuation and dispesion phenomena descibed in ppendix C. D.1. Flat homogeneous test object To convet a pocessed wavefom v signal (t) into a calibated space chage pofile ρ(t), a calibation facto K cal (e.g. [78]) is defined: K = v t ρ t (D.1) cal signal () () The calibation facto is usually calculated based on the knowledge of the chage at the eath electode. In ode to check whethe the calibation is coectly done, the electic field distibution E(x) acoss the sample can be povided by means of the following equation: E 1 ( x) = ρ( x) 0 d 0 dx (D.2) If the calibation is coect, the voltage distibution acoss the sample, V(x), must esult fom: V d = ( x) E( x) 0 dx (D.3) whee: x = v t (v is the speed of sound in the sample) and d is the sample thickness. In Figue D.1, an example of calibated space chage distibution is given along with the deived electic field distibution and voltage distibution acoss a flat homogeneous sample. 159

174 ppendix D - Calibation D.2. Flat multi-dielectic test object When a multi-dielectic is tested, the same amount of chage pesent in both layes will geneate a pessue wave with highe amplitude in the laye with lowe pemittivity. This is a diect consequence of equation (.15) in ppendix. Then, the calibation facto cannot be the same fo both layes of the multi-dielectic. ssuming the mateial is connected to the eath electode, the calibation facto K,cal deduced fom the chage at the eath electode is to be used fo the calibation of the signal in the laye of the multi-dielectic. K,cal is given by equation (D.1). On the othe hand, the signal oiginated in the mateial, which is connected to the HV electode, is to be evaluated accoding to the calibation facto K,cal defined as: = K (D.4) K, cal, cal,, The calibation pocedue descibed above is based on the value of electode chages, which ae known if the voltage U 0 applied to the multi-dielectic is capacitively distibuted. Howeve, if U 0 is a DC voltage, tansition fom a capacitively-gaded to a esistively-gaded field occus in time. This leads to a build-up of intefacial chage at the dielectic inteface and to a consequent modification of the chages at the electodes. Then, as suggested in [14], the calibation measuements must be accomplished long befoe this tansition becomes effective. The electic field distibution acoss the multi-dielectic can be povided by means of equation (D.2), in which the elative pemittivity has to be consideed function of the distance. Equation (D.3) can be used fo detemine the voltage distibution acoss the multi-dielectic. In Figue D.2, an example of calibated space chage distibution is given along with the deived electic field distibution and voltage distibution acoss a multi-dielectic. D.3. Cylindical homogeneous test object fte being coected accoding to the geometical facto deived in ppendix, the signals measued on a cylindical geomety test object can be calibated. known chage at the eath electode can be used fo calculating the calibation facto defined in equation (D.1), to convet the non-calibated signal into a calibated space chage pofile. Once the adial space chage distibution ρ() is known, the electic field distibution can be deived accoding to: E out () = ρ() 1 0 in d whee in and out ae espectively the inne and oute adius. Then, the voltage distibution is given by: (D.5) 160

175 ppendix D - Calibation out () E() V = d (D.6) in In Figue D.3, an example of calibated space chage distibution is given along with the deived electic field distibution and voltage distibution acoss a MV-size cable. D.4. Cylindical multi-dielectic test object s in the case dealt in the pevious section, also fo a cylindical multi-dielectic the detected signals must be coected accoding to the geometical facto deived in ppendix, befoe the calibation is pefomed. The calibation facto in (D.1) can be deived fom a known chage at the oute electode. This calibation facto can be used fo conveting into space chage unit the signal oiginated within the dielectic connected to the oute electode. On the othe hand, the calibation facto in (D.4) is to be used fo conveting into space chage unit the signal oiginated within the dielectic connected to the inne electode. Fo the same easons explained in Section D.2, also in case of a cylindical multidielectic the calibation should be accomplished long befoe the tansition fom capacitive field to esistive field becomes effective. fte obtaining the adial space chage distibution within the cylindical multidielectic, the electic field distibution can be deived by means of (D.5), in which the elative pemittivity is to be conside a function of the adius. Finally, equation (D.6) can be used fo the detemination of the voltage distibution acoss the coaxial multi-dielectic. In Figue D.4, an example of calibated space chage distibution is given along with the deived electic field distibution and voltage distibution acoss a MV-size model of a cable joint. 161

176 ppendix D - Calibation a d b e c f Figue D.1. Calibated space chage distibution (a), electic field distibution (b) and voltage distibution (c) in a homogeneous flat sample. Sample thickness:1.5mm; applied voltage: +15 kv. Sample space chage fee. Figue D.2. Calibated space chage distibution (d), electic field distibution (e) and voltage distibution (f) in a flat XLPE- EPR multi-dielectic. Total thickness:3 mm; applied voltage: +30 kv. Multi-dielectic space chage fee. 162

177 ppendix D - Calibation a d b e c f Figue D.3. Calibated space chage distibution (a), electic field distibution (b) and voltage distibution (c) in a MVsize XLPE cable. Insulation thickness:4.5mm; applied voltage: +90kV. Cable space chage fee. Figue D.4. Calibated space chage distibution (d), electic field distibution (e) and voltage distibution (f) in a XLPE- EPR MV-size model of a joint. Total insulation thickness:4 mm; applied voltage: +80 kv. Joint model space chage fee. 163

178 ppendix D - Calibation 164

179 ppendix E Equations adopted in the numeical pocedue E. Equations adopted in the numeical pocedue In this appendix the equations used Chapte 4 ae deived fo the paticula configuation encounteed in cables and cable joints. In paticula the following topics ae discussed: E.1. solution of the Poisson s equation fo the electic field in cylindical coodinates; E.2. calculation of the intenal-chage-induced electic field in coaxial intefaces; E.3. Fouie s heat diffusion equation fo cables and cable joints. E.1. Poisson s equation fo the electic field Equation (E.1) is the Poisson s equation fo the electic field: ρ 2 U = (E.1) In cylindical coodinates and assuming that the space chage ρ, the electic field E and the potential U ae function only of the adius, equation (E.1) becomes: 2 () U () ρ() 1 U + = 2 The electic field is elated to the potential by means of: E = U (E.2) (E.3) Unde the pevious assumptions equation (E.3) can be ewitten as: U () () E = (E.4) Inseting (E.4) into (E.2), one has: () ρ() 1 E E() + = (E.5) epesents a diffeential equation which solution is 1 : 1 1 ρ () () E = C + d (E.5) (E.6) 1 E + 1 Using: E = E(), equation (E.6) can be ewitten as: () = E() solution is: () 1 E exp d C1 + whee C and C 1 ae constants. ρ () ρ ( ) exp = d d = C + d ρ(), which 165

180 ppendix E Equations adopted in the numeical pocedue whee C is a constant which value can be deduced fom the specific bounday condition. E.2. Calculation of the chage-induced field E.2.1. Field induced by space chages in coaxial intefaces Let s conside the situation depicted in Figue E.1. Two diffeent insulating mateials, and, ae aanged in a coaxial layout. Each mateial is chaacteized by its pemittivity and. The space chage distibutions ρ () and ρ () ae pesent within the insulations. Neithe extenal voltage is applied no chage κ is pesent at the dielectic inteface. Consequently, no extenal field E 0 is applied and no intefacialchage-induced field is pesent. Only the space-chage-induced field E ρ contibutes to the electic field distibution E() within the mateial. Figue E.1. Coaxial inteface in which space chage is pesent within the insulation. Neithe extenal voltage is applied no intefacial chage is pesent. The field distibution can be calculated by integating the following equations: C no extenal voltage is applied () d + E () = E 0 (E.7) no intefacial chage is pesent E ( ) E ( ) = 0 Inseting (E.6) into (E.7) and (E.8), one obtains: C C (E.8) c 166

181 ppendix E Equations adopted in the numeical pocedue 167 () () () + = = C d C E E ρ ρ 1 if c < < (E.9) () () () + = = C d C E E ρ ρ 1 if C < < (E.10) whee: () () () = C C C d d d d d C C C C C C ln ln ln 1 1 ρ ρ ρ (E.11) () () () + + = C C C d d d d d C C C C C C ln ln ln 1 1 ρ ρ ρ (E.12) E.2.2. Field induced by intefacial chage in coaxial intefaces Let s now conside the situation depicted in Figue E.2. s in the pevious situation, two diffeent insulating mateials, and, ae aanged in a coaxial layout and each mateial is chaacteized by its pemittivity and. Howeve, intefacial chage κ is pesent at the bounday between the two diffeent insulating mateials. Neithe extenal voltage is applied no space chage is pesent within the insulation. Consequently, no extenal field E 0 is applied and no space-chage-induced field is pesent. Only the inteface-chage-induced field E κ contibutes to the electic field distibution E() within the mateial. In this case, the following two equations have to be combined fo calculating the electic field distibution: no extenal voltage is applied () () = + C C E d E 0 (E.7) intefacial chage is pesent ( ) ( ) κ = c C E E (E.13) Inseting (E.6) into (E.7) and (E.13) and consideing ρ() = 0, one obtains:

182 ppendix E Equations adopted in the numeical pocedue E () = E () 1 κ C κ = if < < c (E.14) ln C + ln C E () = E () κ 1 = κ C ln C + ln C if < < (E.15) C Figue E.2. Coaxial inteface in which intefacial chage is pesent. Neithe extenal voltage is applied no space chage is pesent. E.2.3. Geneal expession fo the field in coaxial intefaces Geneally, a DC voltage U 0 is applied acoss the dielectic inteface while space chage and intefacial chage ae pesent. In this situation, the following equation is to be used fo the calculation of the electic field: E = E 0 + E E (E.16) () () () () ρ + κ whee E 0 is the Laplacian field [85]. Theefoe, the electic field becomes: E if () () 1 U = + + C 0 1 ρ 1 κ C C d C + ln ln ln C C + ln C < < (E.17) c 168

183 ppendix E Equations adopted in the numeical pocedue and E if () () 1 U = ρ 1 κ C C d C + C ln ln ln C C + ln C < < (E.18) C E.3. Fouie s heat diffusion equation fo cables and cable joints In ode to obtain the tempeatue distibution within the insulation of a cable/cable joint, it is necessay to solve the heat diffusion equation: T k Q = T t c δ + c δ (E.19) whee c and δ ae espectively the specific heat and the density of the mateials being studied, and Q the heat losses pe unit of volume. In the studied cases, the only consideed loss is the powe pe unit of length P c dissipated in the cable conducto, which is assumed to be constant. The cable jacket, the shield, the sheath and the envionment suounding the cable ae modeled with an equivalent outemost laye made of a fictitious mateial E. n isothemal tempeatue distibution is assumed at the inne conducto, because of its high themal conductivity. Using cylindical coodinates and assuming that the tempeatue distibution is a function only of adius and time, equation (E.19) becomes. T t (, t) T k 1 1 = c δ (, t) (E.20) The tem consideing the heat dissipation does not appea diectly in equation (E.20). This is because the heat dissipation is taken into account in the bounday conditions. In Figue E.3, the model used fo the calculation of the dynamic adial tempeatue distibution in cables and cable joints is epesented. Equation (E.20) is subject to the following initial and bounday conditions. Initial condition The tempeatue at time zeo is isothemal and equal to the envionment tempeatue T amb : T, t = 0 = T (E.21) ( ) amb 169

184 ppendix E Equations adopted in the numeical pocedue ounday conditions The tempeatue at the outemost adius E is constant and equal to the envionment tempeatue T amb : T =, t = T (E.22) ( E ) amb The caloific flux at inne conducto is constant: k T ( =, t) Pc = 2π (E.23) t the sepaation between the diffeent mateials of the system, the caloific flux continuity must be fulfilled: T ( =, t) T ( =, t) C C k = k (E.24) T ( =, t) T ( =, t) k = ke (E.25) The contact between two mateials is assumed to be pefect, i.e. no contact themal esistances ae pesent in the dynamic model. Theefoe the tempeatue in two adjacent mateials at the bode points is consideed identical. Figue E.3. Model used fo the calculation of the dynamic tempeatue distibution in cables and cable joints. 170

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196 Refeences 182

197 Lists List of symbols Symbol Vaiable Unit [IS] Fist henius coefficient m,el ea of the measuing electode m 2 a Electostictive coefficient - Tempeatue henius coefficient K C Electic capacitance F C th Themal capacitance pe unit of length J K -1 m -1 c Specific heat J K -1 kg -1 D Electic flux density C m -2 d Thickness m E Electic field V m -1 E a ctivation enegy J E max Maximum value of the electic field V m -1 E ef Refeence electic field V m -1 E 0 pplied extenal field V m -1 E Constant field V m -1 E ρ Space chage field V m -1 e p Pulsed electic field V m -1 exp Exponential function - F Fouie tansfom - F -1 Invese Fouie tansfom - F E% Field enhancement facto - G i-j Geneation coefficient of acoustic waves - i Cuent i Imaginay unit - f Foce pe unit volume N m -3 The unit of the fist henius coefficient is equal to the unit of the quantity descibed by the henius law. 183

198 Lists Symbol Vaiable Unit j Cuent density m -2 J ss Steady state value of the cuent density m -2 K cal Calibation facto K g Geometical coection facto - k Themal conductivity W m -1 K -1 k oltzmann s constant J K -1 k in k out Themal conductivity of the innemost insulation Themal conductivity of the outemost insulation W m K -1 W m K -1 i Cuent L Inductance H P c Conducto losses pe unit of length W m -1 p Pessue Pa p TOT Total pessue distibution Pa p 0 p κ p ρ Electostatic pessue induced by the applied field Electostatic pessue induced by the intefacial chage field Electostatic pessue induced by the space chage field p~ Tansient pat of the electostatic pessue Pa ~ Tansmitted component of the tansient pat of p ' the electostatic pessue ~ Reflected component of the tansient pat of the p " electostatic pessue Q Heat losses pe unit of volume J m -3 R Electic esistance Ω R i-j Reflection coefficient of acoustic waves - R th Themal esistance fo unit of length K m W -1 R th,c Contact themal esistance pe unit of length K m W -1 Radius m Pa Pa Pa Pa Pa 184

199 Lists Symbol Vaiable Unit in Cable adius at the inne semicon m int Cable adius at the dielectic inteface m out Cable adius at the oute semicon m T Tempeatue K T i-j Tansmission coefficient of acoustic waves - T in Tempeatue at the inne semicon K T int Tempeatue at the dielectic inteface K T out Tempeatue at the oute semicon K T ef Refeence tempeatue K t Time s U Voltage V U 0 pplied extenal voltage V u p Pulsed voltage V v Speed of sound m s -1 v ignal Detected signal V x Distance m Z Electic impedance Ω Z ac coustic impedance Kg m -2 s -1 α Paamete indicating the tempeatue dependency of the insulation conductivity Thickness of an annulus-shaped patition m T Tempeatue dop K t Time step s 1/K δ Density kg m -3 Pemittivity F m -1 Relative pemittivity - 0 Vacuum pemittivity κ Suface chage C m -2 ν Paamete indicating the tempeatue dependency of the insulation conductivity Π Pemanent dipole density C m

200 Lists Symbol Vaiable Unit ρ Space chage density C m -3 ρ avg veage value of the accumulated space chage C m -3 σ Electic vonductivity Ω -1 m -1 τ Delay time s τ th Electic time constant s τ MW Maxwell-Wagne time constant s τ th Themal time constant s ω ngula fequency s -1 ξ Suface oughness m ψ Geneic quantity a.u. Nabla opeato - T Tempeatue gadient K m

201 Lists List of abbeviations bbeviation C l TR a.u. DC EDX e.g. EPR et al. FTIR GPI HV i.e. IGT IR J-E LDPE LIPP MV MW NSEM PC PD PE PIPP PVDF vs. VSC XLPE Meaning ltenate cuent luminum ttenuated total eflectance bitay unit Diect cuent Enegy dispesive analysis by X-ays Exempli gatia fo example Ethylene popylene ubbe Et alii and othes Fouie tansfom infaed Geneal pupose inteface bus High voltage Id est that means Insulated gate bipola tansisto Infaed Cuent density - electic field Low density polyethylene Lase-induced pessue pulse Medium voltage Maxwell-Wagne Natual scanning electo micoscopy Polycabonate Patial dischage Pulsed electoacoustic Piezoelectically-induced pessue pulsed Polyvinylidenefluoide Vesus Voltage souce convete Coss-linked polyethylene 187

202 Lists 188

203 Summay Summay Since the 1950s, high voltage (HV) diect cuent (DC) cable systems have been used woldwide fo the tanspot of electical enegy. Taditionally, HVDC cable systems have been employed only when altenate cuent (C) technology could not be applied. In fact, the main concen about the use of new HVDC cable links is the athe high cost of the connection. This could be significantly educed by using polyme-insulated HVDC cable systems (also called extuded HVDC cable systems) instead of mass-impegnated o oil-pape filled HVDC cable systems (also called lapped HVDC cable systems). The extusion poduction pocess is, in fact, simple and cheape than the pocess fo manufactuing lapped insulation. In addition, extuded cable systems pesent some envionmental advantages if compaed to lapped cable systems. On the othe hand, HVDC mass/oil-impegnated cables have been poven to be eliable ove many decades, while HVDC polymeic cables have been only ecently employed. The main issue, which needed to be esolved fo the development of the HVDC polymeic cables, is the contol of the space chage phenomena, which affect the eliability of the connection. Nowadays, this concen has been addessed, but only patially solved. s a consequence, mass-impegnated pape is still the dominating technology fo HVDC cable insulation. In fact, one of the intinsic popeties of the polymeic DC cable insulation is the accumulation of chages. ccumulated chages distot the initial Laplacian field distibution, leading to a local field enhancement that may cause insulation degadation and pematue beakdown of the system. The geneal objective of the pesent study is to obtain a bette undestanding of the majo factos that contol the space chage pocesses in polymeic HVDC cable systems. In ode to achieve this goal, two main factos of influence ae investigated. 1. Space chage at dielectic discontinuities Cable accessoies ae consideed to be the weakest pat of a cable system, because of the pesence of a dielectic inteface between the cable insulation and that of the accessoy. This thesis aims at a bette knowledge of the polaization phenomena occuing at dielectic intefaces. Fistly, we developed an accuate methodology fo the expeimental study of the space chage behavio at the dielectic inteface. We eviewed the pulsed electoacoustic (PE) method fo the measuement of space chage in case of dielectic intefaces. Secondly, we expeimentally obseved space chage accumulation at the dielectic intefaces of diffeent test specimens. oth magnitude and dynamics of the chage could be faily well descibed by the Maxwell-Wagne theoy fo the intefacial polaization. This means that the conductivity of the insulation has a lage influence on the polaization at the inteface. Howeve, we also obseved deviations fom the behavio pedicted by the Maxwell-Wagne theoy. We could 189

204 Summay attibute this to the mophological diffeences between the bulk and the suface laye of polymeic insulation. 2. Space chage in cable systems that expeience a tempeatue dop acoss the insulation coss the insulation of HVDC cable systems a tempeatue dop is pesent when the cable caies a cuent. This thesis aims to povide a bette undestanding about the mechanisms esponsible fo space chage accumulation when a tempeatue dop is pesent acoss the insulation of the cable system. To that pupose, we developed a physical model fo the pediction of space chage dynamics and electic field in loaded HVDC cable systems. The physical model has been validated by means of laboatoy investigation. Ou study indicates that space chage accumulates in the insulation bulk when a tempeatue dop and an electic field ae simultaneously applied to the cable system. We attibuted this phenomenon to the tempeatue dependency of the insulation conductivity. In addition to the chage in the insulation bulk, we measued so-called heteo-chage, mainly nea the inne semicon of the studied test specimens. This was not pedicted by the developed physical model. Howeve, ou intepetation is that this phenomenon is due to high-field chage injection and blocking mechanisms. Ou findings have possible implications on: 1. The measuements of space chage in cable system insulation by means of the PE method: we identified the main equiements the PE measuing system needs to meet in ode to coectly measue the space chage distibutions, accoding to the type of the test object and the test conditions. 2. The design of HVDC extuded-type cable systems: by poviding the electic field distibution in HVDC cable systems, the physical model pesented in the thesis can be used as a suppot tool fo the design of cable system insulation. 3. The opeation of HVDC extuded-type cable systems: we showed how diffeent opeational conditions affect the electic field distibution in the cable system; on the basis of this infomation, we poposed pocedues to optimize the electic stess on cable systems in paticula opeation conditions. 190

205 Samenvatting Samenvatting Sinds de vijftige jaen woden hoogspanning (HV) gelijkstoom (DC) kabelsystemen ove de hele weeld gebuikt voo het tanspot van elektische enegie. Vanwege de hoge kosten, weden HVDC kabelsystemen alleen toegepast als de wisselspanning (C) technologie niet gebuikt kon woden. Een significante vemindeing van de kosten is mogelijk als voo de HVDC kabelisolatie kunststof wodt gebuikt (geïsoleede kunststof kabels woden ook geëxtudeede kabels genoemd) in plaats van de klassieke met olie geïmpegneede papieen kabelisolatie (ook geïmpegneede of olie-papie kabels genoemd). Het poduceen van geëxtudeede kabels is namelijk simpele en goedkope dan het poduceen van olie-papie kabels. Daanaast zijn geëxtudeede kabels milieuviendelijke in vegelijking met olie-papie kabels. Geïmpegneede kabels hebben echte ove meedee decennia bewezen eg betouwbaa te zijn tewijl geëxtudeede kabels pas ecentelijk woden toegepast. Het belangijkste met betekking tot de ontwikkeling van HVDC kabels van kunststof, is de accumulatie van uimtelading, die de betouwbaaheid van de vebinding beïnvloed. Tegenwoodig wodt dit pobleem ekend, maa het is slechts ten dele opgelost. Daadoo is geïmpegneed papie nog steeds de belangijkste technologie bij HVDC kabelisolatie. In feite is de opbouw van lading één van de intinsieke eigenschappen van de kunststof kabelisolatie. Opgebouwde lading vetekent de initiële distibutie van het elektische veld, waadoo concentaties kunnen ontstaan die de isolatie aantasten en kunnen leiden tot vootijdig uitvallen van het kabelsysteem. De algemene doelstelling van ondehavig ondezoek is om de belangijkste mechanismen te begijpen die de uimtelading in kunststof HVDC kabelsystemen eguleen. Om dit doel te beeiken zijn twee factoen die van gote invloed zijn, ondezocht. 1. Ruimtelading in diëlektische discontinuïteiten Kabelganituen woden als het zwakste deel van een kabelsysteem beschouwd omdat e een diëlektisch gensvlak tussen de kabelisolatie en het ganituu bestaat. Ondehavig poefschift beoogt mee begip te vekijgen ove de polaisatiefenomenen op diëlektische gensvlakken. Ten eeste hebben we een nauwkeuige methodologie ontwikkeld voo de expeimentele bestudeing van het gedag van uimtelading op diëlektische gensvlakken. We hebben de gepulseede elektoakoestische methode (PE) hezien om uimtelading op diëlektische gensvlakken te kunnen meten. Ten tweede hebben we de accumulatie van uimtelading bestudeed op de diëlektische gensvlakken van veschillende monstes. Zowel de gootte als de dynamiek van de lading kon voldoende woden bescheven doo de Maxwell-Wagne theoie voo gensvlakpolaisatie. Dit betekent dat de geleidbaaheid van de isolatie een gote invloed heeft op de gensvlak polaisatie. We vonden echte ook afwijkingen van het gedag voospeld doo de Maxwell-Wagne theoie. We konden deze afwijkingen toeschijven aan de mofologische veschillen tussen de bulk en het oppevlak van kunststof isolatie. 191

206 Samenvatting 2. Ruimtelading in kabelsystemen met tempeatuuveschil. Ove de isolatie van HVDC kabelsystemen staat een tempeatuugadiënt als ze stoom voeen. Dit poefschift heeft tot doel om mee begip te vekijgen ove de mechanismen die veantwoodelijk zijn voo uimteladingsopbouw als e spake is van een tempeatuugadiënt in de isolatie van het kabelsysteem. Om die eden hebben we een natuukundig model ontwikkeld om de dynamiek van uimtelading en het elektische veld in geladen HVDC kabelsystemen te kunnen voospellen. Het model wodt ondesteund doo ondezoek in het laboatoium. Ons ondezoek duidt aan dat uimtelading zich in de bulk van de isolatie ophoopt als een tempeatuugadiënt en een elektisch veld tegelijketijd in de kabel aanwezig zijn. We scheven dit fenomeen toe aan de tempeatuuafhankelijkheid van de geleidbaaheid van de isolatie. Naast de lading in de bulk van de isolatie, hebben we ook de aanwezigheid van zogenaamde heteo-lading vastgesteld naast de binnenste halfgeleidende laag van de bestudeede monstes. Dit wed niet doo het ontwikkelde natuukundige model voospeld. Onze intepetatie is echte dat dit fenomeen het gevolg is van high-field chage injection en blocking mechanismen. Onze esultaten hebben mogelijke implicaties voo: 1- Het meten van uimtelading in kabelisolatie doo middel van de PE-methode: we hebben de belangijkste veeisten geïdentificeed waaaan PE-meetsystemen moeten voldoen om de distibutie van uimtelading goed te kunnen meten, afhankelijk van het type testobject en de testomstandigheden. 2- Het ontwep van HVDC kabelsystemen van het geëxtudeede type: doo de mogelijkheid van het voospellen van het elektische veld in HVDC kabelsystemen, kan het natuukundige model gepesenteed in dit poefschift gebuikt woden bij het ontwepen van kabelisolatie. 3- Het gebuik van HVDC kabelsystemen van het geëxtudeede type: we hebben laten zien hoe veschillende opeationele condities de distibutie van het elektische veld beïnvloeden. Op basis van deze infomatie stelden we pocedues voo om de elektische belasting op kabelsystemen in bepaalde opeationele omstandigheden te optimaliseen. 192

207 Sommaio Sommaio I sistemi in cavo in coente continua (CC) pe il taspoto dell enegia elettica in alta tensione (T) fanno la loo compasa negli anni cinquanta e sono oggi pesenti su scala mondiale. I sistemi in cavo TCC sono stati tadizionalmente utilizzati quando la tecnologia in coente altenata (C) non poteva essee applicata, questo a causa dei costi piuttosto elevati. Una significativa iduzione dei costi si potebbe ottenee utilizzando sistemi in cavo TCC di mateiale polimeico (tale tipologia di cavo é anche chiamata cavo estuso ) invece dei classici sistemi TCC in cavo in cata impegnata (anche semplicemente chiamato cavo in cata ). La poduzione di cavi estusi é infatti piú semplice ed economica di quella dei cavi in cata. Inolte, se paagonati ai cavi in cata, i cavi estusi pesentano un mino impatto ambientale, non necessitando di alcuna sostanza impegnante. D alta pate, l utilizzo di cavi impegnati TCC può contae su un altissimo livello di affidabilità confemato da olte mezzo secolo di espeienza nel settoe elettico; tale caatteistica, invece, non può essee ancoa attibuita ai cavi polimeici TCC, visto che la loo intoduzione nel settoe è ancoa toppo ecente e quindi non è stata ancoa possibile una eale e duatua pova sul campo. Il itado nello sviluppo dei cavi polimeici TCC é stato causato dal fatto che, nell isolamento di tali cavi, il fenomeno dell accumulo di caica isulta di difficile contollo, pegiudicando, così, l affidabilitá dell inteo sistema in cavo. Questo poblema é stato identificato e studiato, ma non é ancoa stato completamente isolto. Pe questo motivo i sistemi in cavo in cata impegnata appesentano ancoa tutt oggi la tecnologia dominante nel settoe dei cavi TCC. L accumulo di caica é una caatteistica intinseca dell isolante polimeico pe cavi CC. La caica accumulata modifica la distibuzione iniziale del campo elettico, geneando concentazioni che possono degadae l isolante e quindi povocane un pematuo cedimento e compomettee la funzionalitá dell inteo sistema in cavo. Questa tesi si popone di miglioae la conoscenza dei fattoi pincipali che contollano il pocesso di accumulo di caica nei sistemi in cavo polimeico TCC. tal fine sono stati studiati i seguenti aspetti: 1. Le pati piú vulneabili dell inteo sistema in cavo sono gli accessoi, in quanto in essi é pesente un intefaccia ta dielettici, fomata dall isolante del cavo e da quello dell accessoio. La tesi sviluppa una metodologia pe lo studio speimentale dell accumulo di caica nelle intefacce ta dielettici. Tale metodologia consiste nella evisione del metodo dell impulso elettoacustico (PE), pe endelo applicabile alla misua di caica intefacciale ta dielettici. Le misue di laboatoio hanno dimostato che l accumulo di caica segue appossimativamente il compotamento pevisto dalla teoia Maxwell-Wagne pe la polaizzazione intefacciale. Ció implica che la polaizzazione dell intefaccia dipende fotemente dalla conducibilitá dell isolante. I isultati speimentali mostano inolte compotamenti della caica non pevisti dalla teoia Maxwell-Wagne. Quest ultimi 193

208 Sommaio sono stati attibuiti alla paticolae mofologia dello stato supeficiale del mateiale isolante, in possimitá dell intefaccia. 2. Quando un sistema in cavo TCC é in funzione, il suo isolamento é sottoposto ad un gadiente temico. Questa tesi analizza i meccanismi di accumulo di caica nell isolante in pesenza di un gadiente temico. La tesi popone un modello fisico dell isolamento dei sistemi in cavo TCC, in gado di calcolae il compotamento dinamico della caica accumulata, e, quindi, del campo elettico, in funzione del gadiente temico. La validitá del modello é stata veificata tamite misue speimentali di caica. I isultati pesentati nella tesi indicano che, quando un gadiente temico é applicato al cavo in pesenza di un campo elettico, vi é accumulo di caica nell isolante. Tale fenomeno é stato attibuito al fatto che la conducibilitá dell isolante vaia fotemente con la tempeatua. Diffeentemente da quanto calcolato dal modello, una ceta caica é stata inolte misuata vicino al semiconduttoe inteno del sistema in cavo. La tesi dá un intepetazione a tale fenomeno in temini di meccanismi di iniezione e di blocco della caica. I isultati della iceca effettuata possono tovae appllicazione nei seguenti campi: 1. La caatteizzazione dei mateiali isolanti tamite misue di caica (metodo PE): la tesi individua i equisiti che un sistema pe misue PE deve possedee pe una coetta valutazione della distibuzione della caica, a seconda delle diffeenti tipologie di povini e condizioni di misua. 2. La pogettazione dei sistemi in cavo polimeico TCC: il modello fisico poposto in questa tesi puó essee utilizzato come stumento di suppoto pe la pogettazione dei sistemi in cavo TCC, essendo in gado di fonie la distibuzione dinamica del campo elettico. 3. Il modo d utilizzo dei sistemi in cavo polimeico TCC: la tesi mosta come la distibuzione del campo elettico sia influenzata dalle condizioni di lavoo del sistema in cavo; tale infomazione può essee utilizzata pe ceae pocedue opeative atte a ottimizzae il campo elettico gestendo il sistema in cavo in condizioni di lavoo vaiabili. 194

209 cknowledgement & CV cknowledgement When I think about the wok done to complete this thesis, I feel indebted to many people. Fist of all, I would like to expess my gatitude to my pomoto, pof. Smit. mong many things, I am thankful to him fo his tust. I will not foget his esolution fo helping me stay in Delft when the Italian Defence Ministy wanted me back home. Not of less impotance was the spontaneous suppot my supeviso d. Moshuis offeed me duing my stay at Delft Univesity of Technology. I am gateful fo his inspiation, encouagement and guidance. I wamly thank all colleagues, fome colleagues and staff of the HV depatment at the Delft Univesity of Technology, fo poviding a fiendly and stimulating wok envionment. In paticula, I would like to thank my fome colleagues d. eye and d. van den osch fo all the inteesting discussions we had inside and outside ou laboatoy. I m thankful to ing. van Nes, m. van de Gaaf and m. Naagen, fo thei invaluable help in designing and constucting the test set-ups used in this eseach. I enjoyed thei company vey much and thei oiginal Dutch humou too (most of the time). My gatitude goes also to i. Redjosentono and i. Staathof, the fome students who woked with me on this eseach. It was a geat pleasue to have the oppotunity to wok on the Euopean poject HVDC. I m sinceely gateful to all the HVDC Patnes, fo the attention they gave to my eseach. I would like to expess a paticula appeciation to: the coodinato of the HVDC poject, pof. Fothegill, fo putting high value on this wok within the poject; d. Fabiani and pof. Montanai fom the Univesity of ologna, fo many fuitful discussions on the effect of tempeatue dop on DC cable insulation; pof. Dissado fom the Univesity of Leiceste, fo his constuctive citicism about the modelling of space chage dynamics; pof. Stevens and co-wokes of the Univesity of Suey, fo pefoming the physical-chemical analyses of intefaces; d. Le Roy, d. Teyssede and d. Lauent fom the Univesity Paul Sabatie, Toulouse III, fo ou poductive coopeation; Pysmian Cavi e Sistemi Enegia S..l. and oealis.. Wies & Cables.U., fo poviding us with the test specimens used in this eseach. Finally, I would like to acknowledge the fact that this eseach would not have been possible without the funds of the Euopean Commission. 195

210 cknowledgement & CV Cuiculum Vitae Riccado odega on on pil 26 th 1976 in Lecco, Italy. He eceived his MSc in Electical Engineeing at the Politecnico di Milano, Milan, Italy in In the same yea he joined the HV Technology & Management depatment at the Delft Univesity of Technology, Delft, The Nethelands, whee he woked as a eseache in the field of wind-electostatic enegy convesion. In 2003 he stated a Ph.D. pogam on HVDC polymeic-type cable systems, leading to this thesis. Riccado odega and a PE system fo cables. HV laboatoy, Delft Univesity of Technology, Septembe