Advanced Control of Active Filters. in a Battery Charger Application. Martin Bojrup

Advanced Contol of Active Filtes in a Battey Chage Application Matin Bojup Lund 999

ii Cove pictue Measuement on the dynamic esponse of the MRI hamonic filte contolle: load cuent (top), esulting line cuent (middle), and injected active filte cuent (bottom), see futhe page. Depatment of Industial Electical Engineeing and Automation (IEA) Lund Institute of Technology (LTH) P.O. Box 8 S 22 LUND SWEDEN ISBN 9-88934-3-6 CODEN:LUTEDX/(TEIE-2)/-24/(999) Copyight 999 Matin Bojup Pinted in Sweden by Univesitetstyckeiet, Lund Univesity Lund 999

Abstact In this thesis, a high pefomance battey chage fo electic vehicles (EVs) is investigated. By including active powe line conditioning capabilities in the battey chage, a viable concept fo a fast chaging infastuctue is obtained, beneficial both to the EV uses and the powe distibutos. The thesis contains discussions on modelling aspects and design consideations fo the poposed battey chage, based on a caie wave modulated self commutated 2-level voltage souce convete topology. Futhemoe, model based contolle synthesis is employed, and thoough analysis of the contolle chaacteistics is given. Emphasis is put on the active filteing pefomance of the battey chage. The weaknesses of the model based contol system in active filte applications ae evealed, whee especially the inheent phase deviation of the contol system and the sensitivity to system paametes deteioates the pefomance of the active filte. In ode to ovecome the deteioating popeties of the model based contolle, a contolle stuctue fo active filtes based on seveal integatos in multiple efeence fames is poposed. It is shown, both theoetically and expeimentally, that the poposed contolle exhibits low sensitivity to system paametes and povides fo complete compensation of the inheent phase deviation. The esult is excellent conditioning pefomance of the poposed active filte contolle in steady state.

iv Abstact

Acknowledgements Fist of all, I would like to expess my sincee gatitude to Pe Kalsson fo invaluable discussions duing this poject and a lot of laughs. He has poven to be the pefect fiend, colleague and tavelling companion. I would also like to thank my supeviso Pofesso Mats Alaküla fo his encouagement and suppot duing this wok. I am also gateful to Pofesso Las Getma fo initiating the eseach poject and fo fuitful discussions and comments along the way. The suppot fom the extenal membes of the efeence goup, Andes Lasson (Volvo Technological Development) and Ulf Thoén (Sydkaft AB), has been geatly appeciated. I wish to thank all my colleagues and the staff at IEA fo poviding a ceative and stimulating atmosphee, and in paticula to the lunch paty, to D. Ulf Jeppsson fo maintaining the UNIX system, to Getachew Dage fo maintaining the wokshop and to Bengt Simonsson fo his helping hands in the laboatoy. I would like to thank my immediate family fo thei suppot duing this time. I am also indebted to Kain fo he love and suppot. This wok has been financially suppoted by Elfosk, within the Elekta eseach pogam, which is gatefully acknowledged. Matin Bojup

vi Acknowledgements

Contents Intoduction. Backgound....2 Chaging Fast chaging... 2.3 Influence on the powe gid... 3.4 Desied capabilities of the chage infastuctue... 5.5 Thesis outline... 6 2 Gid conditioning 7 2. Reactive powe compensation Voltage contol... 7 2.2 Load balancing... 2.3 Hamonic eduction in distibution netwoks... 3 3 Design and modelling of the battey chage 9 3. System desciption... 9 3.2 Convetes... 2 3.3 DC-link... 29 3.4 Line filte... 3 3.5 Battey filte... 36 3.6 Taget system specification... 4 4 Contol 43 4. Oveall contol... 43 4.2 Battey cuent contol... 44 4.3 Line cuent contol... 5 4.4 DC-link voltage contol... 57

viii Contents 5 Active filte contol 6 5. Identification based on the load cuent... 62 5.2 Oiginal active filte contolle... 7 5.3 Diect phase compensation of the active filte contolle... 75 5.4 Rotating integatos in active filte contol... 79 6 Expeiments 9 6. Expeimental set-up... 9 6.2 Cuent contol veification Step esponse... 93 6.3 Chaging of battey equivalent... 94 6.4 Load balancing of a two-phase load... 97 6.5 Hamonic filteing of a diode ectifie... 99 6.6 Dynamics of the MRI contolle... 7 Conclusions 3 Refeences 5 A Vecto notation A. Thee phase to two phase tansfomation... A.2 Vecto tansfomation...2 A.3 Instantaneous powe...3 B Nomalisation 5 B. Pe unit definition...5

Intoduction This chapte povides an intoduction to the thesis and points out the main objectives with the wok caied out leading to this thesis.. Backgound The Electic Vehicle (EV) has lately, duing the past yeas, been focus fo thoough eseach whee the majo concen is to find a eplacement fo the Intenal Combustion Engine (ICE) diven vehicle. Envionmental aspects such as the ai pollution due to the emissions of the ICE ae the key diving foces fo the eseach in altenatives to the ICE. Anothe fact is the limited oil esevois, which in the futue inevitable will be depleted. The temendous development in the aea of powe electonics in tems of size, ating and fequency chaacteistics togethe with adapted electical motos make high pefomance EV dives possible. The pefomance chaacteistics, i.e. top speed and acceleation capabilities, of the high pefomance EV dives ae simila o supeio to the ones obtained by an ICE [6]. The majo shot coming of the pesent EV oiginates fom the limited enegy stoage on-boad the vehicle, which educes the obtainable diving ange compaed to an ICE. High powe/enegy density stoage of electic enegy is had to achieve and expensive. But impovement in battey technology fom lead-acid to NiCd o Ni-MH has consideable inceased the stoage capacity. The diving ange of pesent EVs is appoximately 7 km pe one full chage, though dependent on the dive. In ode to incease the diving ange of the EV, on-boad chaging systems such as ICE diven geneatos o fuel cells can be included. This gives highe feedom in the opeation of the ICE. The ICE can be opeated optimally with espect to emissions, efficiency o fuel consumption leading to impoved oveall pefomance [3]. Acceleation and peak powe ae then povided by the electical supply. Fuel cells, on the othe hand, povides electical powe though electo-chemical

2. Intoduction eaction. Fuel cells have high powe/enegy density and the electochemical eaction is almost emission fee, but they ae expensive and still lot of development has to be done [28]. To futhe povide a wide take-up of EVs, a public chaging infastuctue is needed [3]. Such a infastuctue would incease the mobility of the EV dive at least if fast chaging, i.e. chaging with high powe, is an altenative. The diving ange in between chaging instants would be the same, but fast chaging educes the chaging time consideably. Theefoe, an EV dive may accomplish a 2-3 times longe daily diving ange. The topic fo this thesis is to descibe how such a fast chaging station could be implemented in ode to obtain the best use of the investment..2 Chaging Fast chaging Chaging of a battey is accomplished by the supply of a DC cuent to the battey. The DC cuent povides electical chages that ae stoed in the battey though an electo-chemical pocess. Since cuent is defined as the tanspot of electical chages pe time, the enegy deliveed duing the chaging pocess is detemined by the amount of DC cuent supplied and the elapsed time. Electical enegy is tansfeed fom geneato to consume in AC quantities. These AC quantities have to be conveted into DC quantities in a contollable manne suited to the voltage/cuent levels of the battey. This is the task fo the battey chage. Battey chages ae gouped in on-boad and off-boad chages. An onboad chage is individual to the EV and located intenally in the vehicle, while the off-boad chage is of extenal and stand alone type. Off-boad chages ae typically located at a chaging station o at paking aeas. The pinciple of opeation is the same but the on-boad chage pefoms the AC to DC convesion inside the vehicle, thus the vehicle is chaged fom an AC supply. The off-boad chage, on the contay, acts as a DC supply whee the AC to DC convesion is made elsewhee fom the vehicle point of view. Both on-boad and off-boad chages can opeate fom single o thee phase AC supplies. On-boad chages ae mainly of single phase type, since weight and size ae cucial in vehicle applications. Howeve, a theephase chage can povide thee times the chaging powe of a single phase chage, since all thee phases can be loaded as much as the single phase chage loads one phase. Theefoe, the chaging time is educed by

. Intoduction 3 a thid. Table. lists pefomance chaacteistics of diffeent types of chages, when chaging an EV coesponding to a diving distance of km. The enegy consumption of the EV has been estimated to 2 kwh pe km in the compaison. The coesponding efuelling time fo ICE vehicle is also given in Table.. Table. Chaging powe and time coesponding to a diving distance of km. Fuse / Phases Powe Time Type 6 A 3 kw 7 h On-boad 6 A 3 kw 2 h Off-boad 2 A 3 75 kw 5 min Fast chaging station /2 min Gas station Off-boad chages opeate eithe in a conductive o inductive manne. Conductive chages supply the electical enegy though conductos all the way fom the DC output of the chage to the teminals of the battey. Inductive chages, on the othe hand, have a galvanic isolated intemediate stage, i.e. a high fequency tansfome, between the chage DC output and the battey. The pimay winding of the high fequency tansfome is pefeably located in the connecto handle wheeas the seconday winding is located inside the EV [9][29], thus poviding galvanic isolation thoughout the chaging pocess. Howeve, the losses in the high fequency tansfome can educe the enegy efficiency of the chaging pocess. A majo poblem associated with chaging of EV batteies is the lack of standadisation, since almost evey ca manufactue has thei own idea of how it should be done. Due to this, both types of chages ae focus fo development and eseach [5][2]. Heeafte, only thee phase conductive chages ae investigated..3 Influence on the powe gid An intoduction of EVs will have an impact on the powe gid and its opeation. Typically, on-boad chages will be used duing night time when the ca is paked at a esidence. Usually, at night time the load on the powe gid is low esulting in high voltage, which causes the powe gid opeatos to disconnect capacito banks and even inset eactos in ode to maintain the voltage magnitude. In this sense, EV chaging at night can even impove opeation of the powe gid, since the load is smoothened out ove the day. Fast chaging and maintenance chaging at ca paks, on the contay, ae used mainly duing day time in ode to

4. Intoduction incease the opeating ange of the vehicle. At day time the load on the powe gid is high and an incease due to fast chaging can cause oveload situations [2][3]. EV chages will contibute to the incease of powe electonic loads on the powe gid, since powe electonics is necessay in the AC to DC convesion of electical enegy. Powe electonic loads cause, due to thei non-linea chaacteistics, distoted o non-sinusoidal cuents on the powe gid. The distoted cuents cause voltage distosion due to self impedance in cables and tansfomes. Voltage distosion leads to ageing and even to damage and malfunction of sensitive electical equipment, i.e. computes. Othe hamonic cuent geneating electical equipment ae switched mode powe supplies (SMPS) in computes and television sets, adjustable speed dives (ASD) and fluoescent lights. Cuent and voltage distotion ae consideed as a poblem in the opeation of the powe gid, despite difficulties in detemining the eal consequences of thei pesence. Anyway, the poblem with hamonics have been ecognised and standads fo electical equipment, in tems of hamonic emission and immunity, ae being established. As a consequence heeby, fast chages based on line commutated convetes, i.e. diode o thyisto bidge ectifies, though cheap and elatively simple should not be used, since they do not fulfil these standads on hamonic emission into the powe gid. This is concluded fom Figue., whee a typical nonsinusoidal line cuent fom a line commutated chage togethe with its hamonic content ae given. - 2 3.5 5 5 2 25 Figue. t [ms] h h I h /I [%] 5 7 3 7 9 23 25 29 3 35 2.4 2.7 9. 7. 5.7 4.9 4. 3.8 3.3 3. IEC -3-4 I h /I [%] 9.5 6.5 3. 2..2..9.8.7.7.6 Left) Line cuent fom a thyisto based chage and its hamonic content. Right) Compaison of the cuent hamonics against the IEC -3-4 egulation on cuent hamonic emissions.

. Intoduction 5.4 Desied capabilities of the chage infastuctue A fast chage should be capable of chaging EVs with a gid-fiendly cuent, i.e. sinusoidal line cuent with unity powe facto. It should also be flexible enough to handle vaious battey types and sizes, with thei individual voltage levels and cuent ating. In ode to incease the usage of a fast chage infastuctue, additional capabilities in tems of powe gid conditioning can be included. This means that instead of having a negative impact on the powe gid, a chage infastuctue may povide a tool fo powe gid opeatos to maintain, at least locally, a high powe quality. The non-ideal, i.e. eactive, hamonic and asymmetic pats of the load cuent should be geneated locally by the gid conditioning chage. The powe gid supply would then only have to povide the active powe of the load cuent. Figue.2 descibes schematically the opeation pinciple of such a gid conditioning chage. In this way, the load on distibution lines and tansfomes will be loweed and a moe efficient supply of electical enegy obtained. Electical supply P supply P load S load Electical loads P chaging S conditioning Battey chage + Gid conditione Figue.2 Schematic diagam of chage with gid conditioning capabilities. Anothe, moe contovesial capability that can be included in a fast chage infastuctue deals with peak powe geneation, i.e. active powe suppot at high load. EV batteies attached to fast chages may be consideed as a potential enegy eseve. Duing shot peiods of time, enegy could be boowed fom the batteies and supplied to the powe gid. This means that the fast chage opeates as an electonic gas tubine. This last capability has to be applied with geat cae, since the pimay function of a fast chage has to be to chage EV batteies and not the opposite.

6. Intoduction Summaising this discussion leads to a numbe of capabilities desied fo a fast chage infastuctue: Chaging of EVs with sinusoidal line cuent and unity powe facto. Gid conditioning capabilities such as eactive powe compensation, hamonic filteing and load balancing. Possibility to act as an electonic gas tubine, i.e. povide active powe suppot duing shot peiods of time by boowing enegy fom the EV batteies..5 Thesis outline Chapte povides a shot intoduction of the aim of the poject leading to this thesis. In Chapte 2, basic gid conditioning concepts ae investigated and tools to accomplish gid conditioning ae pesented. Chapte 3 descibes implementation, design and modelling consideations fo the poposed fast chage. In Chapte 4, the basic contol stuctues and model based contolles fo a fast chage ae given. In Chapte 5 specific active filte contol stuctues ae thooughly investigated. In Chapte 6 expeimental esults of a chage pototype ae pesented, veifying the poposed concept fo fast chages. Finally in Chapte 7 conclusion emaks ae given. Note that this thesis is one of two, evolved fom the battey chage poject. The accompanying thesis [8], teats hadwae elated aspects of the battey chage, while this thesis focuses on contol and functional aspects.

2 Gid conditioning This chapte descibes the intention of powe gid conditioning, its oigin and how it may be done. The powe gid connects the poduces of electical enegy with the consumes, making it possible to tansfe powe fom the centalised geneatos to the distibuted consumes. Theefoe, it is desied that the voltage magnitude and fequency at the consume end ae close to thei nominal values and that the amount of voltage distotion is low. The powe gid consists of two pats, the tansmission netwok and the distibution netwok. The tansmission netwok consists of a meshed gid connecting diffeent egions, it has high voltage and is theefoe capable of high powe tansfe with low losses. The distibution netwok, on the contay, consists of adial feedes inside a egion whee the powe flows downsteam fom substations to consumes. The adial configuation in combination with the self impedance of the conductos causes load cuent dependent voltage dops and at the end of a feede all upsteam load contibutions to the voltage distosion is seen. Anothe poblem is that esonance between conductos and capacito banks o loads can be enegised by distoted cuents which also causes voltage distotion. Electic enegy tansfe though the powe gid is instantaneous, i.e. thee is no stoage of electical enegy. Theefoe, fequency contol is obtained by matching the active powe poduction in the geneatos with the powe used at the consume end, including the losses in the distibution and tansmission netwoks. If this is not achieved, the excess o the deficit of electical powe poduced will acceleate o deceleate the geneatos esulting in a fequency vaiation. 2. Reactive powe compensation Voltage contol Reactive powe compensation is equivalent to voltage contol, that is by contolling the eactive powe flow in a netwok substantial contol of the voltage magnitude is achieved.

8 2. Gid conditioning Reactive powe Q in contast to the active powe P can not be conveted into mechanical wok, i.e. kinetic enegy o heat etc. Instead, the eactive powe epesents an enegy oscillation between load and geneato. Still eactive powe is a necessay quantity in electical engineeing, since it is used in electical motos to build up the magnetic flux used to convet electical enegy into mechanical wok. Reactive powe is a steady-state popety and defined as the imaginay pat of the complex valued appaent powe S * S = U I = P+ jq (2.) Poblem Losses and lage distance tansfe Conside a loss less single distibution line with eactance X l connecting a stiff (efeence) bus to a load bus as in Figue 2.. E P X l V δ Q Figue 2. Powe flow in a single line with eactance X l. The tansfe of active and eactive powe, fom the stiff bus, ove the line ae stongly coupled and given by P E = V sin δ X l Q = E X E V cosδ l ( ) (2.2) whee E is the voltage at the stiff bus, V is the voltage at the load bus and δ is the load angle, i.e. the angle diffeence between the voltages at the stiff and load bus []. Fom (2.2) it is found that lage amount of eactive powe tansfe esults in a significant voltage dop ove the line. This is due to the dependency between the load angle δ and the active powe tansfe. It is also seen that a weak line, i.e. lage X l, educes the powe tansfe capability. The eactive cuent contibutes to the ms-value of the supply cuent, thus esulting in a highe supply cuent than needed in ode to delive the active powe to the load. This affects the efficiency of the powe gid since in eality lines ae not loss less, thee exist a small esistance in addition to the eactance fo evey conducto. The losses in the conductos ae popotional to the squae of the cuent, theefoe it is

2. Gid conditioning 9 obvious that also active as well as eactive losses incease with a lage amount of eactive powe tansfe. Solution Local poduction Local poduction of eactive powe at a load bus deceases the amount of eactive powe tansfe ove the line. Reducing the ms-value of the supply cuent to only coespond to the active powe demand at the load bus. Theefoe, the losses and the voltage dop acoss the line ae deceased and a moe efficient powe gid is obtained. As a consequence, the voltage at the load bus may be contolled close to the nominal value by contol of the eactive powe input. Shunt capacito banks povide a simple way of eactive powe compensation, see Figue 2.2. In a capacito excited by a AC voltage the cuent leads the voltage by 9 in phaso notation, this phase lead coesponds to a injection of eactive cuent and thus poduction of eactive powe. Shunt capacito banks ae common in distibution netwoks, whee they ae connected and disconnected accoding to the load fluctuation ove the day in ode to maintain a voltage magnitude close to the nominal. X l Q X l Q X l X C Figue 2.2 Reactive powe compensation; shunt (left), TCR (middle) and seies (ight). A moe sophisticated solution includes a thyisto-contolled eacto (TCR) in paallel with the shunt capacitos. Such a device may even absob eactive powe duing light load condition in addition to the poduction of eactive powe. This combination can be teated as a capacito bank with vaiable and even negative capacitance. Synchonous condenses, i.e. synchonous motos with no mechanical load, can also contol thei eactive powe output to povide eactive powe compensation. Anothe fom of eactive powe compensation involves seies capacitos, whee capacito banks ae installed in seies with the line. Thei effect is to educe the total seies impedance of the line seen fom the souce, theeby educing line voltage dops and inceasing the line loadability. Lately, even moe advanced compensato stuctues, whee powe electonics ae included, have been poposed. The unified powe flow

2. Gid conditioning contolle (UPFC) consists of two convetes connected back to back, one in seies with the line and the othe one in paallel [8]. The UPFC ae intended fo use on tansmission systems and is vey flexible. It can pefom shunt eactive compensation as well as voltage magnitude and load angle contol and line impedance compensation. 2.2 Load balancing A balanced powe gid is obtained if the thee phases ae equally loaded, i.e. each phase tansfes one thid of the total powe. This gives the best utilisation of the powe gid, since duing balanced conditions the phases ae affected in the same way. Electical loads can be eithe one, two o thee phase loads but since a line feeds seveal loads, the total load seen fom the souce is balanced if a lage numbe of loads ae distibuted to the diffeent phase conductos. Hence fo the tansmission netwok and the highe voltage distibution netwoks the balanced condition holds tue. But close to the consumes, the load may be imbalanced due to the low numbe of loads to be distibuted. Imbalanced loads o systems may be analysed in steady state by the use of symmetical components []. In accodance with symmetical components, any balanced o imbalanced thee phase quantity ae esolved into thee sequence components, that is positive-, negative- and zeosequence components. The positive-sequence component consists of thee phasos with equal magnitude and 2 phase displacement in positive sequence, i.e. in abc sequence, efe to Equation (A.5). The negativesequence component also consists of thee phasos with equal magnitude and 2 phase displacement howeve in negative sequence, i.e. in acb sequence, while the zeo-sequence component have zeo phase displacement. Figue 2.3 shows an example of an abitay unsymmetical cuent sepaated into sequence components. I pc I pa I nb I na I za I zb I zc I b I c I a I nc I pb a) b) c) d) Figue 2.3 Sequences of an abitaily unsymmetical cuent, a) positive-sequence, b) negative-sequence, c) zeo-sequence and d) total cuent.

2. Gid conditioning In Appendix A., the definition of the thee phase to two phase vecto tansfomation (abc αβ) is given. A balanced system with positivesequence, abc sequence, and ms-value I can be epesented as a vecto in the stationay efeence αβ-fame as αβ jω t i = 3Ie (2.3) p while fo a balanced system with negative-sequence, acb sequence, the vecto is accoding to αβ jω t i = 3Ie (2.4) n Positive- and negative-sequence components can thus be sepaated by the otation diection of the vecto in the stationay efeence αβ-fame, see Figue 2.4. Applying the same tansfomation on a balanced system with zeo-sequence gives iz αβ = (2.5) This means that zeo-sequence components ae not epesented in the stationay efeence αβ-fame. β s β s ω t s β β s ω t s α α s α α Figue 2. 4 Rotation diection of vectos in the stationay αβ-fame, positive-sequence (left) and negative-sequence (ight). In ode to obtain a vecto tansfomation that is valid also fo zeosequence components, the given tansfomation in Appendix A. can be modified accoding to [25] whee an abc αβ vecto tansfomation is used. Poblem Neutal cuents and voltage distosion Imbalanced loads cause a distoted cuent distibution among the phase conductos as well as cuent in the neutal conducto. This leads to highe losses in the phase conductos than fo a balanced load and may cause oveload of a phase conducto. Neutal cuents can esult in ciculating cuents in tansfomes and additional losses in the windings and in the neutal conducto.

2 2. Gid conditioning Anothe aspect of imbalance cuents and especially neutal cuents is the effect on the voltages at the load due to the self impedance in the conductos. The voltage dop in the neutal conducto affects the vitual zeo potential at the load, esulting in an imbalance of the thee phase voltages in tems of magnitude and phase displacement. This may cause ove- and/o undevoltage in some of the phases, which in tun may cause malfunction o destuction of the electical equipment connected to these phases. Solution Rediection of load cuents The most obvious solution to load imbalances is to physically connect simila loads to diffeent phase conductos. Load balancing may also be obtained by ediection of load cuents by a symmetisation unit, see Figue 2.5. The aveage powe used in the load mainly coesponds to the positive-sequence of the load cuent due to the balanced supply voltage of positive-sequence. Theefoe, the negative- and/o zeo-sequence components of the load cuent may be geneated locally and thus eliminating those components fom the supply cuent. The esulting supply cuent would only contain the positive-sequence component of the load cuent and the unsymmetical load is seen as an equivalent symmetical load fom the supply point of view. A B C 2I I -6 I 6 3I N 3I I -6 I 6 I A B C I I -2 I 2 3I 3I N 2I -2 I 2 I 3I 3I Neg. seq. symmetisation Neg. and Zeo seq. symmetisation Figue 2.5 Load balancing pinciple, negative-sequence compensation (left), and negative- and zeo-sequence compensation (ight). In Figue 2.5, the basic opeation pinciples of such symmetisation units ae shown. In the left figue, the negative-sequence cuent of the load is povided by the compensato, thus esulting in only zeo- and positivesequence supply cuents. Total symmetisation is obtained in the ight figue by injection of the negative- and zeo-sequence cuents, esulting in a balanced supply cuent of positive-sequence and no neutal cuent.

2. Gid conditioning 3 2.3 Hamonic eduction in distibution netwoks Electical equipment made of powe electonics connected to the gid causes, due to thei non-linea chaacteistics, non-sinusoidal gid cuents. Accoding to the fouie analysis, evey peiodic wavefom can be teated as the sum of one o seveal sinusoidal wavefoms of diffeent fequencies, i.e. the fundamental fequency and multiples of the fundamental fequency. Since the gid voltage is nealy sinusoidal, the powe used by a hamonic geneating load coesponds to the fundamental fequency component of the load cuent. The cuent hamonics ae a non-desied by-poduct due to the switched opeation of line commutated ectifies, i.e. diode o thyisto contolled ectifies. Cuent hamonics ae in fact a steady-state poblem due to thei peiodic and epetitive behaviou. Howeve, cuent tansients oiginating fom inush cuents at stat up o at distinctive shut downs o disconnection of loads can also be teated, in accodance to the fouie analysis, as cuent hamonics despite thei lack of peiodicity. Still, tansients and thei coesponding cuent hamonics will disappea afte a sufficiently long time. A typical load cuent and the coesponding hamonic spectum of a line commutated thee phase ectifie can be seen in Figue.. The cuent contains the fundamental fequency and hamonics of ode 6k± whee k is any positive intege. The cuent hamonics can futhe be esolved into sequence components, i.e. positive- and negative-sequences, accoding to Table 2.. The absence of zeo-sequence hamonics is due to the balanced configuation of thee phase line commutated ectifies. Howeve, single phase line commutated ectifies have additional zeosequence hamonics of ode 6k+3 whee k = [,,2 ]. Table 2. Hamonic sequences of thee phase line commutated ectifies. Sequence Hamonics Positive, 7, 3, 9, Negative 5,, 7, 23, The load cuent of a line commutated ectifie can be epesented in the stationay efeence αβ-fame as αβ j( ωt+ φ) jh ( ωt+ φh) jh ( ωt+ φh) i = 3I e + 3I e + 3I e (2.6) Load h h= 6k h= 6k+ h

4 2. Gid conditioning whee I and I h ae the ms-values of the fundamental cuent component and the individual cuent hamonics, espectively. Equation (2.6) gives a tue epesentation of the cuent of thee phase line commutated ectifies, wheeas fo single phase ectifies the cuent hamonics of zeo-sequence ae absent. This is due to the vecto tansfomation used, efe to (2.5). Poblem Losses and voltage distotion Cuent hamonics esult in a distoted voltage, which may cause malfunction of sensitive electical equipment, i.e. computes. The voltage distosion is due to the voltage dop acoss the non-zeo impedance of cables and tansfomes. The cuent hamonics can also cause sevee voltage distosion due to esonance oscillations between the self inductance in the distibution netwok and the shunt capacito banks fo eactive powe compensation [3][4]. Cuent hamonics cause additional losses in the distibution netwok. Tansfomes ae exposed to themal stesses due to an incease in ion losses caused by the distoted voltages and cuents. This may lead to deating as well as pematue ageing of the tansfomes. Fo electical motos, the voltage distosion causes themal stesses and toque ipple. Solution Hamonic filteing Cuent hamonics ae often teated as a local poblem at least fo one feede in the distibution netwok. The impedance of the distibution netwok dampens the hamonic popagation [4]. Theefoe, hamonic filteing should be pefomed neaby the souce of the cuent hamonics fo the best esult. If this is done, othe equipment will be unaffected by the hamonic poducing load. Hamonic filteing o compensation is accomplished by the use of passive filtes, shunt active filtes (AF) o seies active filtes. Passive filtes Passive filtes fo hamonic eduction povide low impedance paths fo the cuent hamonics. The cuent hamonics flow into the shunt filtes instead of back to the supply. A typical shunt passive filte and the esulting equivalent impedance seen fom the load ae shown in Figue 2.6. The passive filte consists of seies LC filtes tuned fo specific hamonics in combination with a geneal high pass filte used to eliminate the est of the highe ode cuent hamonics.

2. Gid conditioning 5 Gid C 5 C 7 C hp Load L 5 R 5 L 7 R 7 L hp R hp 5th ham. filte 7th ham. filte High pass filte Impedance Z Figue 2.6 5 5 2 25 3 Hamonic Typical passive filte fo eduction of cuent hamonics and the equivalent impedance seen fom the load. The pefomance of a passive filte is stongly dependent on the system impedance at the hamonic fequencies [27]. The system impedance depends on the distibution netwok configuation and the loads. Theefoe, design of passive filtes involves thoough system analysis in ode to obtain adequate filteing pefomance of the filte. Shunt active filtes A shunt active filte consists of a contollable voltage o cuent souce. The voltage souce convete (VSC) based shunt AF is by fa the most common type used today, due to its well known topology and staight fowad installation pocedue, see Figue 2.7. It consists of a DC-link capacito C dc, powe electonic switches and filte inductos L f. Gid i Line i AF i Load Load Figue 2.7 L f C dc VSC Pinciple configuation of a VSC based shunt active filte. The opeation of shunt AFs is based on injection of cuent hamonics i AF in phase with the load cuent i Load hamonics, thus eliminating the hamonic content of the line (supply) cuent i Line. That is, suppose the load cuent can be witten as the sum of the fundamental cuent component and the cuent hamonics accoding to

6 2. Gid conditioning iload = iload, fund + iload, hamonics (2.7) then the injected cuent by the shunt AF should be i = i, (2.8) AF Load hamonics The esulting line cuent is iline = iload iaf = iload, fund (2.9) which only contains the fundamental component of the load cuent and thus fee fom hamonics. Figue 2.8 shows the ideal phase cuents when the shunt AF pefoms hamonic filteing of a diode ectifie. The injected shunt AF cuent completely cancels the cuent hamonics fom the load, esulting in a hamonic fee line cuent. i Load - i AF - i Line - 2 3 Figue 2.8 t [ms] Shunt AF opeation pinciple when pefoming hamonic filteing. Fom the load cuent point of view, the shunt AF can be egaded as an vaying shunt impedance. The impedance is zeo, o at least small, fo the hamonic fequencies and infinite in tems of the fundamental fequency. Seies active filtes Seies active filtes ae connected in seies with the line though a matching tansfome. VSCs ae appopiate as the contolled souce even fo seies AFs, thus the pinciple configuation of seies AFs ae simila

2. Gid conditioning 7 to shunt AFs. The filte inductos of shunt AFs ae eplaced with the seies tansfome, see Figue 2.9. Gid i Line v AF i Load Load Figue 2.9 VSC C dc Pinciple configuation of a seies AF system. The opeation pinciple of seies AFs is based on isolation of the hamonics in between the load and the supply [4]. This is obtained by the injection of hamonic voltages acoss the tansfome line side. The injected hamonic voltages affect the equivalent line impedance seen fom the load. The equivalent line impedance can be egaded as infinite o lage fo the hamonics wheeas it should ideally be zeo fo the fundamental fequency component. The opeation pinciple of a seies AF is illustated in Figue 2.. i S i Sh Z eq = i Lh Z S v S v AF i L i Sfund Z eq = i Lfund i AF Z AF Z Sfund i AFfund Z AF v Sfund Z Sh v Sh Z AF i AFh a) b) c) Figue 2. Seies AF opeation pinciple; a) single phase equivalent of seies AF, b) fundamental equivalent cicuit, and c) hamonic equivalent cicuit. Hamonic isolation is achieved by means of the infinite impedance fo the cuent hamonics in seies with the line. That is, no cuent hamonics can flow fom load to souce o fom souce to load. Cuent hamonics poduced elsewhee on the souce side of the seies AF can not intefee with loads on the load side, i.e. passive filtes and shunt capacitos. Hybid filtes Hybid filtes consists of combinations of shunt/seies AFs and shunt passive filtes. The main pupose of hybid filtes ae to educe the initial costs and to impove efficiency. The passive filtes educes the bulk hamonic content of the load cuent, wheeas the active filte handles the est of the hamonic content not filteed by the passive filtes. Theefoe, the ating of the active filte can be deceased compaed to a stand alone active filte and thus educing the initial cost. Figue 2. shows two

8 2. Gid conditioning examples of hybid filte configuations, additional configuations have been epoted in the liteatue [3]. Load Load Shunt AF Shunt Passive Filte Seies AF Shunt Passive Filte Figue 2. Hybid filtes; left) combination of shunt AF and shunt passive filte, and ight) combination of seies AF and shunt passive filte. The optimal solution to hamonic eduction in distibution netwoks in tems of pefomance chaacteistics consists of the combination of a shunt and a seies AF with a common DC-link, see Figue 2.2. This combination is efeed to as the unified powe quality conditione (UPQC) and has the same configuation as the UPFC, efe to Section 2. page. Howeve, the UPQC fo distibution netwoks diffe fom the UPFC fo tansmission netwoks in tems of opeation, pupose and contol stategy [3]. The conditioning functions of the UPQC ae shaed by the seies and shunt AFs. The seies AF pefoms hamonic isolation between supply and load, voltage egulation and voltage flicke/imbalance compensation. The shunt AF pefoms hamonic cuent filteing and negative sequence balancing as well as egulation of the DC-link voltage shaed by the AFs. The DC-link voltage egulation is obtained by balancing the active powe fom both the VSCs including all losses in the passive as well as the active components. i Line v AF i AF i Load Load Seies AF Shunt AF Figue 2.2 Configuation of the unified powe quality conditione (UPQC).

3 Design and modelling of the battey chage In this chapte, the hadwae topology of the investigated chage is discussed. Design consideations and modelling aspects of the chage ae given. The topology selection fo the battey chage is based on the desied capabilities fo a fast chage infastuctue deived in Section.4: Conductive chaging of EVs with sinusoidal line cuent. Gid conditioning capabilities such as: Hamonic filteing Load balancing Reactive powe compensation Possibility to act as an electonic gas tubine. These equiements and estictions indicate the type of powe electonics to use. Line commutated convete topologies can not be used, due to thei non-sinusoidal line cuent. The second point hints the usage of an active filte topology as the line side inteface of the battey chage. Finally, the thid capability is accomplished if the battey chage is designed fo bi-diectional powe flow, i.e. the powe can flow in eithe diection between the powe gid and the EV batteies. 3. System desciption The selected battey chage topology able to cay out the listed capabilities is shown in Figue 3., whee the point of common coupling (PCC) towads the powe gid and an EV battey attached to the chage ae also shown. The battey chage consists of a DC-link capacito C dc, a thee phase VSC connected back to back to a half bidge convete, and passive filtes.

2 3. Design and modelling L 2 L V dc C dc L L 2 PCC C C Vbatt Figue 3. The selected battey chage topology. The passive filtes ae, due to the switched opeation of the VSCs, essential components of the battey chage topology. The output voltage pulses of the VSCs ae filteed by the passive filtes, educing the high fequency cuent components. Hence, sinusoidal line cuents as well as a low ipple battey cuent ae obtained. The passive filtes shown in Figue 3. consist of thid ode LCL-filtes instead of odinay fist ode L-filtes. The easons ae discussed in Sections 3.4 and 3.5. At the moment, it is sufficient to say that the high fequency as well as the low fequency chaacteistics of the LCL-filte ae beneficial compaed to the L-filte configuation, i.e. the equivalent impedance is high fo the high fequency cuent components and low fo the active filte cuents. The line side of the battey chage topology foms an equivalent shunt AF. The decoupling of the convetes povided by the DC-link capacito ensues that the functionality of the shunt AF is sepaated fom the battey side opeation. Theefoe, hamonic filteing as well as load balancing and eactive powe compensation may be accomplished by the topology selected. Howeve, the lack of a neutal conducto makes balancing of zeo-sequence cuent components impossible. Thus, only negativesequence cuent balancing is achievable accoding to the discussion in Section 2.2. Finally, the half bidge DC-DC convete enables chaging of EV batteies of diffeent voltage levels. Futhemoe, it allows bi-diectional battey cuent and thus that the battey chage is able to function as an electonic gas tubine. 3.2 Convetes The VSCs of the battey chage consist of fou bidge legs as shown in Figue 3.2. Thee bidge legs fom the line side convete while the fouth bidge leg acts as the DC-DC convete at the battey side. A bidge leg, o a half bidge convete, consists of two tansistos each

3. Design and modelling 2 connected to an anti-paallel diode. The tansistos should pefeably be IGBTs due to thei supeio oveall pefomance chaacteistics, i.e. fowad voltage dop and switching times, in the powe ange consideed. Soft ecovey fee-wheeling diodes should be used in ode to get less snappy tun-off at evese ecovey of the diodes. Dive V dc C dc s Dive Figue 3. 2 The VSCs of the battey chage including dives fo the DC/DC half bidge convete. In Figue 3.2, additional dives needed to convet the logic contol signal s into gate voltages suitable to the IGBTs ae also shown. The logic invete block pio to the lowe IGBT dive ensues that the IGBTs ae not simultaneously conducting. Thus, shot cicuit of the DC-link capacito is pevented. Ideally, thee ae no losses in the VSCs and cuent commutation is instantaneous. Howeve, this is not the case fo pactical VSCs. In pactical convetes the powe electonic devices ae not loss less and the switching times ae finite. When a powe electonic device is conducting cuent, a simultaneous voltage dop of a few volts acoss the device appeas. The finite switching times imply that the cuent and the voltage ae simultaneously high, leading to lage instantaneous powe dissipation duing the switching tansients. These losses, efeed to as conduction losses and switching losses, ae the limiting factos in the cuent loading capability and the switching fequency. Stay inductance futhe stesses the powe electonic devices at the switching instants [27]. Theefoe, snubbes to educe these effects ae often needed. The finite switching times futhe imply that duing commutation both IGBTs may conduct at the same time, since one IGBT is tuning on and the othe one is tuning off. This implies that the DC-link capacito is shot cicuited at the switching instants. This is pevented by additional contol logic in the dives. The tun on of the IGBTs ae delayed in ode to guaantee the completion of the tun off pocess of the othe Insulated Gate Bipola Tansisto

22 3. Design and modelling IGBT. This is efeed to as the intelock o blanking time, since both IGBTs have tempoaily logic low contol signals. The enegy efficiency of the VSCs may be impoved by the use of softswitched topologies instead of the had-switched shown in Figue 3.2 [7]. Extensive analysis of esonant convetes ae pefomed in the paallel thesis [8] and theefoe not consideed in this thesis. Instantaneous modelling In ode to model the VSCs, the simplified equivalent cicuit of Figue 3.3 is used. The equivalent cicuit is deived based on the ideal popeties of the VSCs. Hence, the uppe valve of the half bidge is conducting when the logic contol signal o the half bidge switching state s is high, wheeas the lowe valve conducts when s is low. High and low value of the switching state coesponds to one and zeo, espectively, in the following discussion. u a i a v a s a v link+ u b u c i b i c v b s b v c s c V dc v link s batt i batt u batt Figue 3.3 Simplified ideal model of the VSCs. The instantaneous uni-pola output voltage u batt of the half bidge DC/DC convete is given by u batt = sbattvdc (3.) whee s batt coesponds to the switching state of the DC/DC convete. When s is low, the output voltage is ideally zeo, since the output teminal is shoted by the lowe valve to the DC-link negative supply ail. If, on the othe hand, the switching state s is high then the uppe valve is active. Hence, the output teminal is connected to the positive supply ail of the DC-link and the output voltage ideally equals the value of the DC-link voltage, i.e. V dc. A simila appoach fo the thee phase VSC gives the following expessions fo the output phase voltage potentials with espect to the DClink negative supply ail

3. Design and modelling 23 v v v = s V a a dc = s V b b dc = s V c c dc (3.2) whee s a, s b and s c ae the switching states of the bidge legs fo phases a, b and c, espectively. Fom (3.2) the output phase voltages seen fom the neutal point of the powe gid ae given by u = v + v = s V + v u = v + v = s V + v u = v + v = s V + v a a link a dc link b b link b dc link c c link c dc link (3.3) whee v link is the voltage potential of the DC-link negative supply ail with espect to the powe gid neutal. The voltage potential of the DClink negative supply ail can be detemined fom the balanced condition of a thee phase system, which states that the phase quantities should sum up to zeo accoding to Equation (A.3). That is, since then v link is given by u + u + u = (3.4) a b c sa sb sc v link = + + V dc (3.5) 3 which indicates that the DC-link supply ails of the VSCs ae floating with espect to powe gid neutal. The coesponding voltage vecto of the thee phase VSC in the stationay efeence αβ-fame, obtained by the space vecto tansfomation given in Appendix A., is defined as u u ae j j2π αβ 2 3 = 3 + ube + uce j4π 3 (3.6) Insetion of (3.3) into (3.6) gives the following expession fo the voltage vecto j2π j4π j j2π j4π αβ u 2 3 3 3 3 = 3 savdc + sbvdce + scvdce + v link e + e + e (3.7) 44424443 which can be simplified to =

24 3. Design and modelling j π αβ u 2 23 = V 3 dc sa + sbe + sce j4π 3 (3.8) since the zeo-sequence component v link vanishes in the tansfomation as indicated in (3.7). Fom (3.8) it can be concluded that, since the thee switches can be combined in 2 3 =8 ways, eight discete voltage vectos may be geneated by the thee phase VSC. The voltage vecto space fo the thee phase VSC is displayed in Figue 3.4. Hee, the switching states fo the coesponding voltage vectos ae indicated by the notation u. sss a b c u β u u u u u α u u Figue 3.4 Voltage vecto space fo the thee phase VSC. The length of the voltage vectos ae 2 3 V dc accoding to (3.8), except fo the zeo voltage vectos obtained when all switching states ae equal, i.e. the combinations and. Pulse Width Modulation Pulse width modulation (PWM) methods ae employed in ode to detemine the instantaneous switching states of the VSCs [5][34]. Usually, modulation of the VSCs ae obtained though cuent contol. In closed loop PWM techniques, the cuent contol is included in the switching state geneation, wheeas open loop PWM is based on efeence voltages obtained fom cuent contolles. In the latte case, the efeence voltages ae then used to find the instantaneous switching states of the VSCs eithe by geneal space vecto modulation o, in paticula by caie wave modulation. Closed loop modulation by hysteesis contol Closed loop contol of the VSCs is obtained by hysteesis o toleance band cuent contolles. The pinciple of hysteesis contolles is to keep

3. Design and modelling 25 the cuent within the hysteesis dead band. This is shown in Figue 3.5 togethe with the pinciple scheme of a hysteesis cuent contolle. i a V dc i batt i a * i a s a s b s c s batt i batt i batt * Figue 3.5 Top) Pinciple scheme of a hysteesis cuent contolle. Bottom) Basic cuent wavefom included the contolle dead band (dashed). The basic pinciples of hysteesis cuent contolles causes the cuent to be within the hysteesis dead band. This implies high dynamic pefomance, since the cuent is able to follow almost any efeence cuent tajectoy. Hence, hysteesis cuent contolles ae vey attactive in active filte applications. Howeve, thee ae some inheent dawbacks with this contol method [5] such as lack of intecommunication between the individual hysteesis contolles and theefoe no stategy to geneate zeo voltage vectos. a tendency to lock into limit cycles of high fequency switching. geneation of subhamonic cuent components. the cuent is not stictly limited by the hysteesis dead band as can be seen in Figue 3.5. This can happen wheneve the gid voltage vecto has an component that opposes the active switching state vecto. Anyway, the vaying switching fequency complicates the convete design. Futhemoe, the intended use of LCL-filtes make hysteesis cuent contol less pacticable.

26 3. Design and modelling Open loop modulation by tiangula caie PWM Open loop contol of VSCs is usually obtained by caie based PWM stategies. In Figue 3.6, the pinciple scheme and signal flow diagam fo tiangula caie PWM VSCs with additional symmetisation is shown. Hee, the instantaneous switching states ae geneated fom compaatos, which compae the voltage efeences with the caie signal. At the cossing instants of a voltage efeence and the caie signal, the coesponding switch state changes and commutation of the bidge leg is initiated. i a V dc i batt i a * i u a * s a a s b s c s batt PI u az * u PI batt * PI u z PI i batt * Figue 3.6 Signal flow diagam of caie based PWM. An impotant popety of caie based PWM techniques is detemined by the fequency modulation atio m f defined in [27] as m f = f caie f (3.9) whee f caie and f ae the caie signal fequency and the fundamental gid fequency, espectively. Accuate time aveage output voltages ae obtained, if the amplitude of the caie signal coesponds to the instantaneous DC-link voltage of the VSCs. Hence, the peak value of the caie signal fo the thee phase VSC should be û caie = V 2 dc (3.) wheeas the caie signal used fo the uni-pola half-bidge convete should vay between zeo and V dc. Figue 3.7 shows in detail the logic contol signal geneation of tiangula caie PWM of a thee phase VSC. Since high pefomance is equivalent

3. Design and modelling 27 to a lage m f, which implies that the voltage efeences can be assumed constant duing the caie peiod as shown in the figue. V 2 dc V 2 dc s a u caie u az * u bz * u cz * s b s c Figue 3. 7 Detailed desciption of the logic contol signal geneation fo a thee phase VSC with tiangula caie PWM. Fom Figue 3.7, it can be concluded that the switching fequency f sw of the VSC is given by the caie signal fequency, i.e. f sw = f (3.) caie Symmetisation of the phase voltage efeences, as indicated in Figue 3.6, by the subtaction of a zeo-sequence component u z given by * * * * * * max ( ua, ub, uc)+ min ( ua, ub, uc ) uz = (3.2) 2 impoves the pefomance of the PWM method [5][34]. The utilisation of the DC-link voltage inceases and the cuent ipple deceases. Futhemoe, the phase cuents ae equal to thei aveage values at the tiangula ca ie end-points. Sampling of the phase cuents at these instants educes the need of aveage filtes fo contol puposes in digital contolles. Hence, the sampling ate f s and the coesponding sampling time T s ae given by f T s s = 2 fcaie (3.3) = f s As stated befoe, a lage m f means that the fequency of the caie signal is much highe than the gid fequency. Hence, only small changes in the voltage efeences occu between two peiods of the caie signal. This

28 3. Design and modelling means that the content of the fequency spectum of the output voltages will be dominated by the content at f sw and at multiples of f sw, besides the fundamental gid fequency component. This is illustated in Figue 3.8, whee the nomalised spectum of the output voltage obtained by tiangula caie PWM with m f equal to 99 coesponding to a switching fequency of 495 Hz. Nomalised spectum.75.5.25 Figue 3.8 5 5 2 25 3 35 4 Hamonic Nomalised phase voltage spectum of tiangula caie PWM VSC. The well defined hamonic content of caie based PWM makes the design of pope passive filtes easie. Aveage modelling The fundamental popeties of tiangula caie based PWM with symmetisation imply the use of aveage modelling of the convetes [23]. Duing each sampling inteval, the aveage output voltages equal the efeence voltages. Hence, the aveage output voltage of the half bidge convete is given by { } * batt batt dc batt dc u = s V = u V (3.4) whee the switching state aveage is efeed to as the duty cycle o pulse atio. The ightmost pat of (3.4) indicates the limitation in output voltage due to the DC-link voltage estiction. Simila expessions ae obtained fo the aveage phase voltages of the thee phase VSC, that is { } { } { } u * = 2 V u 2 V u * 2 V u = 2 V u * = 2 V u 2 V a dc az dc b dc bz dc c dc cz dc still unde the balanced constint given by (3.4). (3.5)

3. Design and modelling 29 The aveage models of the VSCs ae used in the pefomance analysis of the contolle stuctues in the battey chage, since they enable time efficient simulation of the pinciple behaviou of the battey chage. Futhemoe, the non-ideal popeties of VSCs such as the semiconducto fowad voltage dop and the blanking time effect may also be contained in the aveage model as descibed in [5]. 3.3 DC-link The DC-link capacito C dc povides an intemediate enegy stoage, which decouples the thee phase VSC fom the half bidge DC/DC convete. Hence, the VSCs can be opeated independently of each othe as long as the aveage powe flow is balanced between the VSCs. The instantaneous diffeence in active powe is stoed in C dc, which causes the DC-link voltage V dc to vay. Hence, the value of C dc is detemined by the constaint on the maximum allowed DC-link voltage ipple V dc. The instantaneous DC-link capacito cuent i Cdc can be deived fom Figue 3.3 and is given by icdc = saia sbib scic sbattibatt (3.6) In [7], a thoough discussion on the limiting factos of the DC-link capacito size is given. It is stated that the DC-link capacito should be lage enough to handle tansients, i.e. load changes and tipping of cicuit beakes, without any sevee effect on the DC-link voltage. The enegy handling capability of the DC-link capacito should coespond to the excess enegy stoed in the passive filtes. Howeve in shunt AF applications, the limiting facto of the DC-link capacito size is detemined by the instantaneous active powe ediected by the shunt AF. This means that the instantaneous active powe contained in the conditioning cuent is tempoaily stoed in the DC-link capacito. The wost case coesponds to long peiods of chaging/dischaging of the DC-link capacito. This implies that load balancing at ated powe of the negative-sequence cuent component gives the limiting design constaint on the DC-link capacito size. A design expession fo the DC-link capacito value is deived, based on simplified analysis of the instantaneous active powe flow in the battey chage when pefoming load balancing at ated powe. The instantaneous active powe flow though the PCC can be expessed, in the synchonously otating efeence -fame oiented to the integal of the gid voltage vecto, fom (A.6) as

3 3. Design and modelling p = e i + e i = { e }= e i (3.7) PCC d d q q d q q whee e q and i q ae the q-axis components of the gid voltage vecto and the injected negative-sequence cuent vecto, espectively. Hence, they ae given by e q = E n i =I m( 3I e )= 3I sin( 2ω t) q n j2ω t n (3.8) whee subscipt n denotes nominal value and ω is the fundamental angula fequency of the gid. If the line filte and the thee phase VSC ae consideed loss less, the instantaneous active powe flow though the PCC should coespond to the powe flow in the DC-link capacito, i.e. pcdc = icdcvdc = ppcc (3.9) Substituting (3.7) into (3.9) and eaanging gives an expession fo the aveage DC-link capacito cuent i Cdc i Cdc eq = V i q (3.2) The diffeential equation fo the DC-link voltage can then be witten d dt V dc dc dc = eq q C V i (3.2) Lineaisation of (3.2) aound the aveage DC-link voltage V dc gives d dt dc dc q Vdc = e q C V i (3.22) whee V dc coesponds to the DC-link voltage ipple. Substituting (3.8) into (3.22) and solving the diffeential equation, a design expession fo the DC-link capacito is found by eaangement of the solution as dc C dc = V dc S n V dc 2ω (3.23) whee S n is the ated powe of the battey chage.

3. Design and modelling 3 3.4 Line filte As stated ealie, the line filte educes the high fequency hamonic content of the battey chage line cuent, caused by the switched opeation of the thee phase VSC. Hence, sinusoidal line cuents can be obtained. Usually, the line filte consists of filte inductos, i.e. L-filte, but by the use of additional capacitos and inductos, othe filte combinations such as LC- o LCL-filtes can be applied. In this section, howeve, only the L-filte and the LCL-filte configuations, shown in Figue 3.9, ae investigated. e i 2 uc i u e i u PCC L 2,R 2 L,R C PCC L,R Figue 3. 9 Line side of the battey chage with LCL-filte (left) and L-filte (ight). LCL-filte Modelling The diffeential equations of the LCL-filte in the stationay efeence αβ-fame ae d dt d dt d dt ( ) R i αβ c L i αβ L u αβ u αβ = + ( ) uc C i i αβ αβ αβ = 2 R i ( ) αβ 2 c L i αβ 2 2 L u αβ e αβ = + 2 2 which ae equivalently epesented by the state space desciption (3.24) d dt αβ i αβ uc αβ i2 R L L = C C R 2 L L2 442443 2 αβ ALCL αβ i αβ uc αβ i2 L u + e L2 2 4 34 αβ B LCL αβ αβ (3.25)

32 3. Design and modelling The fequency esponse of the LCL-filte is shown in Figue 3.. Note the peak at the esonance fequency of the LCL-filte, which implies a pooly damped oscillatoy behaviou. The use of tiangula caie based PWM, howeve, pevents the excitation of this esonance due to its advantageous fequency spectum, efe to Figue 3.8. Anyway, the attenuation at the esonance fequency can be impoved by damping esistos in seies with the filte capacitos at the expense of the high fequency attenuation. Gain [db] -2-4 -6-8 - f [Hz] Figue 3. Fequency esponse fom convete output voltage to output cuent (solid) and with dampe esistos (dashed). Tansfomation of the state space desciption in stationay coodinates into the synchonously otating efeence -fame is obtained by subtaction of the angle diffeence as descibed in Appendix A.2. This opeation is equivalent to a shift in the fequency-domain []. The esulting state space desciption of the LCL-filte in synchonous coodinates is given by d dt i uc i2 R j ω L L = jω C C R 2 jω L L2 4444 42444444 3 2 ALCL i uc i2 L u + (3.26) e L2 2 4 34 B LCL The complex valued state space desciption in synchonous coodinates indicates that the behaviou of the LCL-filte is dependent on the otation diection of the vectos. A eal valued state space desciption of (3.26) is obtained by sepaating the vecto equations in thei eal and imaginay pats, i.e. d- and q-components, espectively. Hence, the LCL-filte is also descibed by the following state space system

3. Design and modelling 33 d dt i i u u i i d q cd cq 2d 2q R ω L L R ω i L L i ω C C u = ω u C C R i 2 ω L2 L2 i R2 ω L2 L2 444442444443 LCL-filte Design ALCL d q cd 2d 2q L L u u + e e L2 L2 442443 cq BLCL d q d q (3.27) The design of the passive filte is dependent on the attenuation needed in ode to educe the high fequency components of the line cuents. Hence, the design inputs fo the passive filte ae the high fequency spectum of the thee phase VSC, shown in Figue 3.8, and the hamonic egulation to be fulfilled, fo example the IEC -3-4 egulation on cuent hamonic emissions into the powe gid. The IEC -3-4 egulation states that cuent hamonics above the 33 d should be less than.6 % of the nominal cuent, i.e. I h.6% of I n fo h 33 (3.28) The design expessions fo the LCL-filte ae deived fom the analysis of an idealised LCL-filte, whee the seies esistance of the inductos ae neglected. The elationship between the convete output voltage and the line cuent in stationay coodinates is given by the tansfe function G αβ (s) deived fom (3.25), with R and R 2 set to zeo, that is ( ) G ()= s [ ] si A B αβ αβ αβ LCL LCL LLC = 2 2 L L s s + + 2 LLC 2 (3.29) whee s denotes the Laplace opeato. The coesponding fouie tansfom G αβ (jω) is obtained fom (3.29) by the substitution of the Laplace opeato s with jω. Hence, the gain function G αβ (jω) of the

34 3. Design and modelling LCL-filte fo each hamonic, i.e. eplacing ω with hω, can thus be expessed by G αβ ( jhω ) = hω LLC 2 2 L L h ω 2 + + 2 LLC 2 (3.3) Fom (3.3) it is clea that seveal combinations of the filte paametes, i.e. L, L 2 and C, can fulfil the hamonic content constaint of the line cuent. Additional equiements, such as the atio between the inne and oute inductos and the idle poduction of eactive powe by the filte, ae needed to deive a design expession. In [23], it is stated that the atio between the inductos is a tade off between low esonance fequency and low cuent ipple in the inne inducto L. Fom [23], a good compomise is obtained if the inne inducto is twice the size of the oute inducto. Futhemoe, an idle eactive cuent of 5 % of the nominal line cuent is consideed easonable. Hence, the additional equiements ae given by L C = 2L 2 = 5. C base (3.3) whee C base is defined in Appendix B.. Substituting (3.3) into (3.3) and solving fo the oute inducto L 2 finally gives a design expession fo the LCL-filte L 2 3 3 U = h Ch 2 + max 4 4Ch 2 2 + h I ω ω ω 2 2 phase, h h max (3.32) whee U phase,h epesents the ms-value of the output phase voltage hamonics given in Figue 3.8. Note that the given design expession is only valid fo hamonics above the esonance fequency of the LCLfilte, efe to Figue 3.. L-filte Modelling and design As descibed peviously, the passive filte usually consists only of filte inductos thus foming a L-filte. The L-filte is descibed by the vecto diffeential equation in stationay coodinates

3. Design and modelling 35 ( ) d dt i R αβ L i αβ L u αβ e αβ = + (3.33) o in synchonous coodinates by the complex valued vecto diffeential equation d dt R i L L u ( ) = + jω i + e (3.34) The complex valued epesentation of the L-filte is tansfomed into a eal valued state space system in synchonous coodinates by sepaating (3.34) into its eal and imaginay pats, that is d dt i i d q R i L d u L d L = ω R i + q u + e q ω e 424L 3 2 4 L34 424 L3 AL BL BL d q (3.35) The pevious discussion on the design of the LCL-filte can be applied also to the L-filte. Hence, a design expession fo the inductance L based on the same equiements as fo the LCL-filte case is given by U phase, h L = max (3.36) h hω I h max Compaing the popeties of L- and LCL-filtes The advantageous chaacteistics of the LCL-filte compaed to the L- filte ae found fom the fequency esponses plotted in Figue 3.. The filte paametes ae obtained fom the design expessions given by (3.3) and (3.32) fo the LCL-filte and (3.36) fo the L-filte. Hence, both filtes fulfil the hamonic cuent constaint. In the high fequency egion (>2.5 khz), the attenuation inceases with 6 db/decade fo the LCL-filte compaed to the 2 db/decade fo the L- filte. Hence, the highe ode cuent hamonics ae bette attenuated by the LCL-filte and thus the total high fequency hamonic distosion is lowe fo the LCL-filte case. In the low fequency egion (< khz), the slope of the fequency esponses ae both 2 db/decade. This implies that the LCL-filte can be egaded as a vitual inducto with an inductance of L +L 2, efe to (3.29). Howeve, the diffeence in the attenuation futhe indicates that

36 3. Design and modelling the sum L +L 2 is smalle than the L-filte inductance L. Consequently, the voltage dop acoss the LCL-filte, caused by the injected cuent hamonics, is lowe compaed to the L-filte case. This is the key advantage of the LCL-filte, which is especially impotant in an active filte application. Futhemoe, the lowe voltage dop acoss the LCLfilte implies that the equied DC-link voltage is lowe. Hence, a geate semiconducto magin can be obtained, i.e. the atio between the opeating and the ated voltage levels of the IGBTs. Gain [db] -2-4 -6-8 - f [Hz] Figue 3. Fequency esponses, LCL-filte (solid) and L-filte (dashed), fom convete output voltage to line cuent. The majo dawbacks of the LCL-filte ae the high cuent ipple in the inne inducto L and the inceased numbe of tansduces needed fo contol puposes. The high cuent ipple in L esults in high amount of ion losses, i.e. hysteesis and eddy cuent losses, which implies the use of thin laminated ion coes o even ion powde coes. Also, the extended complexity inceases the equiements on the signal electonics and the contol system. Futhemoe, the eactive powe equiements of the filte capacitos have to be accommodated by the convete as to pohibit eactive gid cuents when the unit is opeating unde idle conditions. 3.5 Battey filte The battey filte in Figue 3. also consists of a LCL-filte. The intention is to educe the physical size of the filte, since the total inductance of a LCL-filte is smalle than fo a L-filte inductance. Howeve, the lage cuent ipple in the inne inducto L implies high amount of ion losses, and hence lage ion coes ae needed in ode to educe the themal poblems. Anyway, the advantageous high fequency chaacteistics of the LCL-filte, i.e. the 6 db/decade slope, futhe motivates the use of the LCL-filte.

3. Design and modelling 37 Modelling The state space desciption of the single phase LCL-filte is given by d dt i u i c 2 R L L i = u C C R i 2 L L2 44424443 ALCL c 2 L + u V L2 4244 3 BLCL batt (3.37) whee the same quantity notation as fo the line filte ae used, i.e. i and i 2 ae the cuents in the inne and oute inductos L and L 2, espectively. Also, u and u c ae the DC-DC convete output voltage and filte capacito voltage, espectively. In Figue 3.2, the fequency esponses fo the single phase LCL-filte obtained fom (3.37) ae displayed. The coesponding fequency esponse of a L-filte is also shown in the figue. Gain [db] -2-4 -6-8 - f [Hz] Figue 3.2 Fequency esponses fom convete output voltage to cuents i 2 and i, LCL-filte (i 2 solid and i dashed) and L-filte (dash dotted). Design The design pocedue fo the battey side LCL-filte esembles the one used fo the line filte. That is, knowledge of the fequency spectum of the DC-DC convete output voltage and the allowed battey cuent ipple gives the equied oveall attenuation of the LCL-filte. The lack of standadisation implies that no egulation on chaging cuent ipple exist. Howeve, a chaging cuent ipple of % peak to peak of the nominal cuent is consideed easonable and hence the cuent ipple constaint is given by

38 3. Design and modelling ˆ ibatt 5. Ibatt, n (3.38) Conside the pinciple voltage and cuent wavefoms of the LCL filte in Figue 3.3. The half bidge convete output voltage consists of equidistant pulses of constant duation t p. Hence, the convete output voltage u can be expessed analytically by the tigonometic fouie seies 2Vdc sin( hπ D) u() t = D Vdc + cos( hω swt ) (3.39) hπ h= whee D is the duty cycle o pulse atio defined by D t p = (3.4) T Note the diffeence in the i and i 2 cuent wavefoms shown in Figue 3.3, which is due to the high fequency chaacteistics of the LCL-filte shown in Figue 3.2. The almost sinusoidal i 2 cuent is a consequence of the slope of 6 db/decade in the fequency esponse of the LCL-filte and the invese popotionality to fequency of the convete voltage spectum. Theefoe, the design of the LCL-filte should be deived fo the switching fequency and fo a duty cycle D of.5, since this coesponds to the highest amplitude which is concluded fom (3.39). sw V dc T sw t p V batt I batt +2 i I batt I batt -2 i Figue 3.3 Pinciple wavefoms of the battey side. Top) u (solid) and V batt (dashed), and bottom) i 2 (solid) and i (dashed).

3. Design and modelling 39 The tansfe functions fom convete output voltage u to the inne and oute inducto cuents i and i 2 ae obtained fom (3.37) and given by G G i i 2 ()= s ()= s s 2 s s s s + LC L 2 L + L + LLC 2 2 2 LLC 2 L + L + LLC 2 2 2 (3.4) (3.42) whee the seies esistance of the inductos ae neglected. The attenuation at the switching fequency can be obtained fom (3.4) and (3.42) by eplacing s with jω sw, which gives G G i i2 ( jω ) sw ( jω ) sw = = ω ω ω sw sw 2 sw ω ω LC L 2 L + L LLC 2 2 sw 2 LLC 2 L + L LLC 2 2 sw 2 (3.43) (3.44) In the deivation of design expessions fo the LCL-filte, two additional equiements have been applied. Fist, the filte capacito has been chosen equal to the filte capacitos of the line filte. Second, a constaint also on the cuent ipple in the inne inducto implies contol of the stesses applied to the inne inducto and the DC-DC convete. This ease up the manufactuing of these components. Hence, the additional equiements ae given by G ( jω ) = x G ( jω ) i sw i2 sw C = 5. C base (3.45)

4 3. Design and modelling whee the facto x is given by the selected constaint on the cuent ipple of the inne inducto. Fom (3.43) to (3.45) the design expessions fo the inductos can be deived as L 2V dc x + = + xω π ˆ i x ω C 2 sw batt sw L = x + 2 2 ω sw C (3.46) (3.47) In the thesis, the facto x is selected to 3. This should imply that the cuent ipple in the inne inducto is thee times the cuent ipple in the oute inducto. Howeve, as can be seen in Figue 3.3, the actual cuent ipple in i is somewhat highe. This is due to the contibution of the highe ode hamonics, efe to (3.39), which ae moe efficiently attenuated in the oute inducto case. 3.6 Taget system specification The geneal specification of the taget system investigated in the thesis is listed in Table 3.. Hence, the investigated battey chage is the same as the one designed and tested in [5], except fo the ated powe which is kva in this case but 75 kva in [5]. Table 3. Geneal specification of the battey chage. ated powe S n kva gid voltage E n 4 V gid fequency f 5 Hz battey voltage V batt 375 V battey cuent I batt,n 26.67 A Note that the battey cuent is limited eithe by the nominal cuent o by the ated powe listed in Table 3.. In Table 3.2, the paametes of the VSCs and the DC-link ae listed. Futhemoe, as indicated peviously tiangula caie based PWM modulation is used, which implies that the switching fequency and also the contolle sampling time ae fixed. Synchonous sampling at the caie wave end-points, efe to the discussion given in Section 3.2, is employed. Note that the actual DC-link capacito value is not selected accoding to the design expession (3.23). The main eason fo the lage value is to

3. Design and modelling 4 impove the obustness of the physical implementation, descibed in Chapte 6. Anyway, the effect is that the specified peak to peak DC-link voltage ipple is educed to 2.5 % of the nominal DC-link voltage. Table 3.2 Paametes of the voltage souce convetes, including the DC-link. DC-link voltage V dc 75 V DC-link voltage ipple V dc peak-peak % of V dc DC-link capacito C dc design actual 57 µf 2.2 mf switching fequency f sw 4.88 khz sampling time T s 2.4 µs The paametes of the line filte is given in Table 3.3. The design inputs ae the IEC -3-4 egulation on cuent hamonic emissions (3.28) and the convete voltage spectum, efe to Figue 3.8. Note that an additional % magin is applied on the inducto values used in the actual chage. The equivalent seies esistances coespond to the winding esistance of the inductos used in the expeimental set-up, efe to Chapte 6. Table 3.3 Paametes of the line filte. LCL-filte L R C L 2 R 2 design actual design actual design actual 2. mh 2.2 mh 75 mω µf µf. mh.5 mh 66 mω L-filte L design 5.6 mh The coesponding inductance of an equivalent L-filte is also given in Table 3.3. The lage value of this inductance in compaison to the total inductance of the LCL-filte indicates the advantageous low fequency chaacteistics of the LCL-filte, efe to the discussion given in Section 3.4. The paametes of the LCL-filte applied on the battey side is listed in Table 3.4, whee the design is accoding to the discussion given in Section 3.5. In this design, the maximum allowed chaging cuent ipple is given

42 3. Design and modelling by (3.38). Futhemoe, the coesponding inductance of a L-filte is also given in the table. Table 3.4 Paametes of the battey filte. LCL-filte L R C L 2 R 2 design actual design actual design actual 5.6 mh 5.3 mh 57.2 mω µf µf.44 mh.45 mh 9 mω L-filte L design 6.3 mh

4 Contol In this chapte the oveall contol stuctue of the battey chage is pesented. Model based contolle synthesis is applied. Futhemoe, extensive analysis of the pefomance chaacteistics is given with emphasis on stability and fequency domain chaacteistics. 4. Oveall contol The oveall contol stuctue in the battey chage consists of a DC-link voltage contolle, a battey cuent contolle, and a line cuent contolle, efe to Figue 4.. e i 2 uc i u i u c i 2 V dc u V batt Line cuent contolle u * i 2 * i AF * i 2q * DC-link voltage contol u * Battey cuent contolle i * batt Figue 4. Oveall contol stuctue of the battey chage. The DC-link voltage contolle balances the active powe flow in the battey chage. This is obtained by contolling the active cu ent component on the line side. In ode to avoid conflict with the active filte function of the battey chage, the bandwidth of the DC-link voltage contolle has to be low. Howeve, feed fowad of the battey cuent implies faste esponse to changes in the battey cuent, and hence educing the DC-link voltage deviation duing tansients. The battey cuent contolle consists of a model based cascade contolle. The cascade contolle is composed of an oute cuent contol loop fo the battey cuent, i.e. cuent i 2, an intemediate voltage contolle fo the filte capacito voltage, and finally an inne cuent contol loop fo the i cuent. The cascade configuation enables the use

44 4. Contol of basic P- and PI-contolles, whee the gain of the popotional pats ae deived fom the model epesentation of the battey filte, descibed in section 3.5. The line side cuent contolle esembles the cascade contolle stuctue of the battey cuent contolle. Howeve, the line cuent contolle is implemented in the synchonously otating efeence -fame oiented to the integal of the gid voltage vecto as descibed in Appendix A.2. Hence, individual contolles fo the active and eactive cuent components with additional compensation fo the coss-coupling of the d- and q-axis quantities ae obtained. Synchonous coodinates futhe utilise the use of integatos in the contolle stuctue in ode to eliminate the steady state eos of the fundamental cuent components. 4.2 Battey cuent contol A model based discete cascade contolle fo the battey cuent is obtained by applying Eule appoximations to the diffeential equations of the LCL-filte (3.37). By assuming dead beat esponse in each P- contolle, the following discete contolle is deived * L2 u k k T i * c( ) = i2 ( 2( k ) i 2( k ))+ R 2 i 2( k ) + V batt ( k ) s * C i k k T u * uc c k u c k i * ( ) = ( ( ) ( ))+ 2( k ) s * L u k k T i * ( ) = i ( ( k ) i ( k ))+ R i ( k ) + u c ( s k) (4.) whee k indicates the time fo the sampling instants accoding to t k =kt s. The contolle stuctue in (4.) consists of thee cascaded P-contolles with additional feed fowad and feed back tems given by the LCL-filte model. In ode to stabilise the contolle, the gain of the P-pats ae alteed fom the dead beat gain by the constants k i, k uc and k i2. Pope values fo these ae then obtained fom the stability analysis. The contolle in (4.) is futhe modified in thee steps to fit the application. Fist, the discete contolle is implemented in a digital signal pocesso (DSP), which gives a time delay of one sample due to the calculation time. The calculation delay causes additional phase deviation of the system. This deceases the stability magin and hence the bandwidth of the contolled system has to be educed. Howeve, compensation fo the

4. Contol 45 time delay is accomplished by adopting the Otto-Smith contolle [9] fo systems with time delays as descibed in [22]. Second, the feed back of the esistive voltage dops ae eplaced by an integato in the oute cuent contol loop. The integato educes the steady state eo of the DCquantity of the battey cuent as well as compensates fo uncetainties in the model. Thid, if the gain of the inne cuent and capacito voltage P-contolles ae chosen accoding to k i L T s C kuc = (4.2) T then the effect of the capacito voltage dynamics ae cancelled. Hence, no measuement of the capacito voltage is needed fo contol puposes. The final discete cuent contol algoithm employed to the battey chage is theefoe given by s * L2 * uc( k) = ki2 (( i2( k) i2( k)) + i2( k) )+ Vbatt ( k) T * * 2 i ( k) = i ( k) + i ( k) s smith * L u k k T i * i k i k u * ( ) = ( ( ) ( ))+ c ( k ) s (4.3) whee the vaiable i 2 coesponds to the integal pat and is given by i 2 Ts * ( k + ) = ( i2( k) i2( k) )+ i2( k) L R 2 2 (4.4) The delay compensation (Smith pedicto) algoithm employed to the inne cuent contol loop is given by s i p RT s Ts ( k + ) = sp ( k) + L L u ( k ) smith RT s k L s k Ts ( + ) = p ( ) L u ( k ) (4.5) The block diagam epesentation of the discete battey cuent contolle, including the Smith pedicto, is displayed in Figue 4.2.

46 4. Contol S/H S/H V batt (k) i 2 (k) i * batt k L 2 T s i2 T s L 2 /R 2 S/H i * 2 (k) S/H i (k) Figue 4.2 Σ u * c (k) k i L T s S/H i smith (k) -+z- T s /L z-(-r T s /L ) u * (k) Block diagam epesentation of the discete battey cuent contolle. The chaacteistics of the Smith pedicto ae fully utilised if its input coesponds to the output voltage of the half bidge convete. Since the DC-link voltage limits the convete output voltage, efe to (3.4), the same limitation should be applied to the feed back of the voltage efeence. This is obtained by limiting the voltage efeence, which is indicated in the block diagam by the satuation block. Analysis In ode to analyse the battey cuent contolle, the closed loop system of the contolle and the LCL-filte has to be deived. The discete contolle implies that a discete time model of the LCL-filte (3.37) has to be used. The state vecto x and input vecto u of (3.37) ae defined accoding to = [ ] T x i uc i2 (4.6) T u= [ u V batt ] (4.7) The continuous state space system of the LCL-filte (3.37) can be descibed by the discete-time model u V + = LCL + [ LCL LCL ] batt xk ( ) Φ xk ( ) Γ Γ uk ( ) i ( k) = C x( k) 2 LCL whee the system matices ae given accoding to [37] as (4.8) Φ LCL A T e LCL s = (4.9) Ts u Vbatt ALCLh [ ΓLCL ΓLCL ]= e dh B LCL (4.)

4. Contol 47 and the output matix is C LCL = [ ] (4.) The computational delay in the discete contolle implies that the convete output voltage coesponds to the efeence voltage delayed by one sample, that is * u ( k + ) = u ( k) (4.2) The closed loop discete state space system of the contolle and the LCLfilte is deived based on the extended state vecto X and the input vecto U, defined accoding to T = [ c 2 p 2] T = [ batt ] X i u i u s i (4.3) U V i2 * (4.4) Note that the convete output voltage is epesented as a state vaiable in the closed loop system due to the computational delay (4.2). Futhe on, the discete contol algoithm of (4.3) can intepeted as a linea state feed back contolle with feed fowad of the inputs accoding to * u ( k) Lx Lu Ls L i X k LV Li U k p ( ) 2 batt 2* ( ) = [ ] + [ ] (4.5) whee the individual feed back elements of (4.5) ae found fom (4.3), (4.4) and (4.5) L x L L2 = ki ki2 (4.6) Ts Ts L u Ts L = ki ki L = (4.7) T s RT L Ls = s ki ki R p L = (4.8) T s L2 L i = k 2 i2 T (4.9) s L Vbatt = (4.2)

48 4. Contol L L2 L * = ki ki T + T (4.2) i2 2 The closed loop system is then given by the extended discete state space system s s u batt ΦLCL ΓLCL ΓLCL Lx Lu Ls L L L p i Vbatt i * Xk ( + ) = 2 2 Xk ( ) + Uk ( ) Su Ss p I x Ii 2* = [ LCL ] i ( k) C X( k) 2 V (4.22) whee the additional non-zeo elements ae S u Ts = (4.23) L RT Ss = p L s (4.24) I x Ts = L R I i2 2 2 (4.25) Ts * = L R (4.26) 2 2 Stability analysis of the closed loop system finally gives the pope values fo the gain constants k i and k i2 of the P-contolles in the cascaded contolle. Hee, the oot locus method [37] is applied on the closed loop system. The oot locus method is convenient fo sensitivity analysis with espect to the gain of the P-contolles. The stability bounday fo discete time systems is defined by the unit cicle. Hence, if the poles of the closed loop system, i.e. the eigenvalues of the state matix in (4.22), ae inside the unit disc, the discete system is consideed stable. In Figue 4.3 the oot locus of the closed loop system is shown, when both k i and k i2 ae alteed. Since the complex poles appea in conjugated pais, only the uppe half of the unit disc is displayed. Fom the oot locus it can be concluded that a high gain in the inne cuent contol loop, that is close to the dead beat gain, implies an unstable o oscillatoy behaviou.

4. Contol 49 Futhe on, a low value of the gain in the oute cuent contol loop, i.e. k i2 lowe than the dead beat gain, has the same effect. As a conclusion it is stated that the gain of the inne contol loop should be well below dead beat gain, wheeas the gain of the oute loop should be chosen some times highe than the dead beat gain. k i k i2 Imag axis.5 k i k i2 Figue 4.3.5.5 Real axis Root locus fo the closed loop system fo k i =[.5 ] and k i2 =[.5 7]; cicle) k i =.5 and k i2 =, squae) k i =. and k i2 =5. In Figue 4.4, the tansfe functions fom battey cuent efeence i 2 * to battey cuent i 2 ae shown fo two sets of gain constants. The fist set of gain constants ae chosen as k i =.5 and k i2 =, wheeas fo the second set they ae k i =. and k i2 =5. The poles coesponding to these sets of gain constants ae maked in Figue 4.3 with cicles and squaes, espectively. Gain [db] Phase [degees] 2 - -2 - - -2-3 -4-5 f [Hz] Figue 4.4 Fequency esponse fom efeence cuent to battey cuent (i 2 * to i 2 ), solid) k i =.5 and k i2 =, and dashed) k i =. and k i2 =5. The suppession of the esonance peak povided by the second set of gain constants implies a less oscillatoy behaviou, which confims the conclusions dawn fom the oot locus plot. Since the bandwidth of the

5 4. Contol systems ae almost the same, the second set of gain constants, that is k i =. and k i2 =5, ae chosen. Simulation Simulation of the battey side of the chage confims the less oscillatoy behaviou with the second set of gain constants, as shown in Figue 4.5. Howeve, the oscillation does not seem to appea in the inne inducto cuent i. This implies that the oscillation oiginates fom the oute inducto and the filte capacito. Since the gain in the oute cuent contol loop is low fo the fist set of gain constants, the contolle is not able to geneate counte actions to the oscillations. Howeve, the highe gain povided by the second set of gain constants is sufficient in ode to dampen the oscillations. p.u. - p.u. - 2 3 t [ms] * Figue 4.5 Battey side cuents i 2 (dak gey), i 2 (black), and i (light gey). Top: k i =.5 and k i2 =, and bottom: k i =. and k i2 =5. 4.3 Line cuent contol The deivation pocedue of the line cuent contolle esembles the one used fo the battey cuent contolle. The line cuent contolle consists of a model based cascade contol stuctue as was the case fo the battey cuent contolle. Howeve, the line cuent contolle is implemented in the synchonously otating efeence -fame oiented to the integal of the gid voltage vecto as descibed in Appendix A.2. In synchonous coodinates, the eactive and active quantities ae elated to the d- and q-axis components, espectively. Hence, individual contolles fo the active and eactive quantities with additional compensation fo the coss-coupling of the d- and q-axis components ae

4. Contol 5 obtained. Synchonous coodinates futhe utilise the use of integatos in the contolle stuctue in ode to eliminate the steady state eos of the fundamental cuent components. Applying Eule appoximations to the diffeential equations given in (3.26) fo the LCL-filte in synchonous coodinates and by assuming dead beat esponse, the deived discete line cuent contolle in complex vecto notation is given by * L2 * uc( k) = ki2 (( i2 ( k) i2( k) )+ i2( k) )+( R2 + jωl2) i2( k) + e( k) Ts C * i k kuc T u * c k u c k j Cu c k i * ( ) = ( ( ) ( ))+ ω ( ) + 2 ( k ) + i smith ( k) s * L * u ( k) k ( ) ( ) ( ) ( ) ( ) T i k i i k R j L i k u = ( )+ + ω + c k s (4.27) whee integatos in the oute cuent contol loop as well as a Smith pedicto in the inne cuent contol loop in ode to compensate fo the computational delay in the DSP ae included. The integato is given by T s i k L R i * 2 ( + ) = ( 2 ( k ) i 2( k ))+ i 2( k ) 2 2 wheeas the Smith pedicto algoithm is accoding to (4.28) RT s Ts sp ( k + ) = jωts sp( k) + L L u ( k ) RT s Ts ismith ( k + ) = + jωts sp( k) L L u ( k ) (4.29) The block diagam epesentation of the discete line cuent contolle is displayed in Figue 4.6. Note that the feed back of the convete voltage efeence is bounded by the DC-link voltage, in ode to fully utilise the popeties of the Smith pedicto. The esemblance to the battey cuent contolle, displayed in Figue 4.2, is quite obvious. Howeve, the obustness and the fequency domain chaacteistics ae impoved by keeping the intemediate capacito voltage P-contolle in the line cuent contolle. This is especially impotant due to the active filte function of the battey chage.

52 4. Contol S/H i 2 (k) S/H e(k) S/H u c (k) S/H i (k) i * 2 (k) R 2 +jω L 2 k L 2 i2 T s Figue 4. 6 Analysis T s τ Σ u * c (k) jω C R +jω L i * (k) k uc C T s k i L T s u * (k) S/H i smith (k) T s /L -+z- z-(-r T s /L -jω T s ) Block diagam epesentation of the discete line cuent contolle. Analysis of the line cuent contolle is based on the closed loop system of the discete contolle and the line LCL-filte. The closed loop system is deived in the same way as the battey side countepat was in the pevious section. The complex valued discete state space vecto epesentation of the LCL-filte in synchonous coodinates is found fom the continuous model (3.26) and is given by xk ( + ) = ΦLCL xk ( ) + ΓLCLuk ( ) (4.3) i ( k) = C x( k) + D u( k) 2 LCL whee the state vecto x and input vecto u ae defined accoding to The state matix Φ LCL LCL T x i uc i2 (4.3) = [ ] u= [ u e] T (4.32) and the input matix Γ LCL A T Φ LCL e LCL s ae given by = (4.33) T u Γ Γ Γ e s e A LCL = [ ] = h dh B LCL LCL LCL LCL (4.34) and finally, the output matixes ae given by C LCL = [ ] (4.35) D LCL = [ ] (4.36)

4. Contol 53 The extended state vecto X and input vecto U of the closed loop system ae defined accoding to T X i u i u s i (4.37) = [ c 2 p 2] T U e i2 * (4.38) = [ ] The cascade contol algoithm can be intepeted as a state feed back contolle with additional feed fowad of the inputs accoding to * u( k ) u ( k) Lx Lu Ls L i X k Le Li U k p ( ) ( ) 2 2* + = = [ ] + [ ] (4.39) whee L L L L = [ ] x i uc i2 (4.4) The enties ae found fom (4.27), (4.28), and (4.29) and ae given by L k L = T R j L i i + + ω (4.4) s L k L C u = + i kuc j C c T T + ω (4.42) s s L k L T k C L2 i = i uc ki R j L 2 2 + 2 + ω 2 (4.43) T T s L u s s Ts L k L = i = ki (4.44) T s RT L j T k L s = s s i ki R j L p L + ω = ( + ω ) (4.45) T s L k L T k C i = 2 i uc T (4.46) s s L k L T k C e = i uc (4.47) T s s L k L C k T T k L2 i2 * = i + uc i2 (4.48) T s s s

54 4. Contol The complex valued vecto epesentation of the closed loop system in synchonous coodinates can now be expessed as Φ [ Γe Γ ] X i2 * 6444447444448 6 447448 u e ΦLCL ΓLCL ΓLCL L L L L L L x u s i e i * p Xk ( + ) = 2 2 Xk ( ) + Uk ( ) Su Ss p I I I x i2 * i2 ( k) = [ CLCL ] X( k) + [ ] U( k) 4 42444 3 23 [ 2 * ] CX De Di whee the additional non-zeo elements ae given by S u (4.49) Ts = (4.5) L RT Ss = s j T p s L ω (4.5) I x L2 Ts = ki2 Ts L R 2 2 I (4.52) L2 Ts * = ki T L R (4.53) i2 2 s 2 2 The complex valued vecto epesentation of the closed loop system (4.49) is easily tansfomed into a eal valued state space desciption, by sepaation of the complex valued elationships into thei eal and imaginay pats, i.e. the d- and q-components. The gain constants k i, k uc and k i2 ae selected on basis of stability and fequency domain chaacteistics. The selected gain constants ae k k k i uc i2 = 5. = 25. (4.54) = Stability of the system with gain constants accoding to (4.54) is confimed by the pole plot shown in Figue 4.7. The closed loop poles

4. Contol 55 coesponding to the selected gain constants ae shown with lage makes. In the figue, the oot locus of the closed loop system when only one gain constant at the time is alteed while the othes ae fixed is also shown. Imag axis.8.6.4.2 k i.5.5 Real axis Figue 4.7 Root locus plot fo the closed loop system. Selected gain constants ( ), vaying k i ( ), k uc (+) and k i2 (o). Since the closed loop system is epesented in vecto notation, it can be egaded as a single input-single output (SISO) system. Theefoe, odinay gain and phase deviation functions deived fom the fequency esponse ae valid. The vecto notation futhe implies that positive as well as negative fequencies have to consideed. The sign of the fequency coesponds to the otation diection of the vecto, efe to the discussion in Section 2.2 on epesentation of positive- and negative-sequences in vecto notation. Figue 4.8 shows the fequency esponse fo the closed loop system. k i2 k uc k i k uc k i2 Gain [db] Phase [degees] - -5 - -5-2 -25 - - -2-3 -4-5 Figue 4.8 f [Hz] Fequency esponse fom line cuent efeence to line cuent, positivesequence (solid) and negative-sequence (dashed).

56 4. Contol Note the phase deviation of the fequency esponse shown in Figue 4.8. The phase deviation coesponds appoximately to a linea phase lag of thee samples, which is indicated by the gey line in the figue. The effect of the phase deviation will futhe be discussed in Chapte 5. If the eal valued vecto epesentation, i.e. individual epesentation of the d- and q-components, is used, the closed loop system is egaded as a multiple input-multiple output (MIMO) system. In this case, othe fequency domain analysis methods have to be applied [26]. In [], fequency domain analysis based on the minimum and maximum singula values is descibed. It is stated that the gain spead is bounded by the minimum and maximum singula values. The gain may vay between the bounday values fo a specific fequency depending on the diection of the input vecto. In fact, it was found in [] that the complex valued tansfe functions fo the positive- and negative-sequences coespond to these minimum and maximum singula values. Simulation A simulation of the line side cuents of the battey chage, when applied to step changes in the d- and q-cuent efeences, is shown in Figue 4.9. The oveshoot of the step esponses in the oute cuent i 2 of about 3 % is due to the high bandwidth selected fo the line cuent contolle. The high bandwidth in combination with the thid ode LCL-filte imply an oscillatoy behaviou, which is deived fom the peaks in the fequency esponses shown in Figue 4.8. Howeve, due to the active filte option of the battey chage, the high bandwidth is deemed necessay in ode to obtain high filteing pefomance. The coss-coupling of the d- and q-cuents is clealy seen in the simulation. That is, the oscillations in the d- and q-cuents caused by step esponses in the opposite cuent component. Howeve, the steady state influence of the coss-coupling is compensated fo by the line cuent contolle. The slowe esponse in the q-cuent fo a positive step change is due to ovemodulation of the VSC. In Figue 4., a simulation with the aveaged model of the VSC is shown. The dynamic esemblance of the cuent esponses obtained by the aveaged model compaed to the instantaneous model is high. Thei diffeence is meely due to the high fequency cuent ipple, especially in the inne inducto cuent i, caused by the switched opeation of the VSC fo the instantaneous model. Hence, the validity of the aveaged model is confimed. Futhemoe, the time consumption fo the

4. Contol 57 simulation of the aveaged model is deceased by at least one ode of magnitude compaed to the instantaneous model. d-cuents q-cuents p.u..5 p.u..5 Figue 4.9 d-cuents q-cuents p.u..5 p.u..5 5 5 2 t [ms] Line side d- and q-cuents, i 2 * (dak gey), i 2 (black), and i (light gey). 5 5 2 t [ms] Figue 4. Line side d- and q-cuents obtained by simulation of the aveaged model, i 2 * (dak gey), i 2 (black), and i (light gey). 4.4 DC-link voltage contol The pupose of the DC-link voltage contolle is to peseve the DC-link voltage at its efeence value. This is accomplished by balancing the active powe flow in the battey chage. That is, the active cuent component i 2q on the line side is contolled in ode to match the powe consumed by the battey chage. The consumed powe, in this case, coesponds to the chaging (output) powe and the powe dissipated in the battey chage.

58 4. Contol The block diagam epesentation of the DC-link voltage contol loop is shown in Figue 4.. The DC-link voltage contolle consists of a PIcontolle, whee the integal pat educes the steady state eo of the DC-link voltage. The low pass filte intoduced in the feed back loop limits the bandwidth of the DC-link voltage contolle. Hence, geneation of counte actions due to the DC-link voltage vaiation caused by the active filte cuents ae avoided. Futhemoe, the low bandwidth is cicumvented by the feed fowad of the battey cuent. This implies a faste esponse to changes in the battey cuent and theeby eduction of the DC-link voltage deviation duing tansients. i Load V dc * PI-contol G PI (s) * i Cdc e q V dc i 2q * Cuent contol i 2q Vdc i Cdc V dc e q sc dc V dclp Low pass filte G LP (s) Figue 4. Block diagam epesentation of the DC link voltage contolle. The low pass filte futhe implies that the dynamics of the line cuent contolle can be neglected in the DC-link voltage contolle synthesis. Fom Figue 4., the closed loop tansfe function of the DC-link voltage contolle is obtained accoding to G PIc sc G PI () s dc () s = + sc G PI () s G LP () s dc (4.55) The tansfe function of the PI-contolle is given by GPI () s = K( + ) st i (4.56) whee the paametes K and T i ae the gain and integal time constant of the PI-contolle, espectively. The low pass filte consists of a fist ode filte with the cut off fequency selected to f lp =3 Hz. Hence, the tansfe function of the low pass filte is given by G LP ω lp ()= s s + ω lp (4.57)

4. Contol 59 The closed loop tansfe function of the DC-link voltage contolle can then be witten G PIc K ( C T st i + )( s + ω lp ) dc i () s = s s s K ωlp Kω 3 2 lp + ω lp + + C C T dc dc i (4.58) whee the denominato of (4.58) coesponds to the chaacteistic polynomial of the closed loop system. Since the chaacteistic polynomial of the closed loop system is known, and theeby also the chaacteistic equation, the paametes of the PIcontolle can be detemined by pole placement. The poles of the closed loop system ae selected as a tiple pole, in ode to avoid oscillations in the DC-link voltage and also pevent fom a lage voltage oveshoot at system stat up. The chaacteistic polynomial of a tiple pole system is given by 3 3 2 2 3 ( s + x) = s + 3s x + 3 sx + x (4.59) whee x coesponds to the location of the poles on the negative eal axis in the s-plane, i.e. the angula fequency of the closed loop system. By identification of the coefficients of the chaacteistic polynomial given by the denominato of (4.58) with the desied chaacteistic polynomial in (4.59), the following equation system with the coesponding solutions ae obtained 3x = ω lp 2 3x x 3 Kω lp = Cdc Kω lp = C T dc i ω lp x = 3 K C dcω = 3 2 3 Ti = ω lp lp (4.6) Fom (4.6), it can be concluded that the tiple pole placement stategy gives a bandwidth of the closed loop system which is one thid of the low pass filte bandwidth.

6 4. Contol Simulation The pefomance of the DC-link voltage contolle is veified by simulations, whee the aveaged convete models ae used. The simulated DC-link voltage esponse at system stat up is shown in Figue 4.2. In the figue, the effect of the feed fowad of the battey (load) cuent duing a step change is also shown. The feed fowad tem almost eliminates the DC-link voltage dip duing the battey cuent tansient. p.u..875 V dc 2 3 4 t [ms] Figue 4.2 Simulation of the DC-link voltage, in pe unit, at system stat up and a step change in the battey cuent coesponding to ated powe at t=3 ms. PI-contolle with feed fowad of battey cuent (gey) and without (black dashed), and PI-contolle with feed fowad and anti eset windup (black). The oveshoot in the DC-link voltage at system stat up is appoximately 3 %. The oveshoot is due to the zeo povided by the integato in the numeato of the tansfe function (4.58), i.e. the zeo located at /T i on the negative eal axis in the s-plane. Howeve, by limiting the output of the DC-link voltage PI-contolle, the oveshoot at system stat up is educed at the expense of a polonged stat up time. This limitation also educes the esulting line cuents duing stat up, hence smoothe stat up of the system is achieved. Futhemoe, in ode to avoid windup of the integato, an anti eset windup algoithm [37] is employed. The anti eset windup algoithm esets the integato to an appopiate value, if the output of the PIcontolle exceeds the limitation. Hence, the value of the integato is eset so that the output of the PI-contolle is within the bounday. In Figue 4.2, the esult of the PI-contolle output limitation and the anti eset windup stategy is shown. Hee, the output of the PI-contolle is limited within 2 % of the coesponding nominal line cuent.

5 Active filte contol In this chapte specific popeties concening shunt active filte contol ae discussed. The opeation pinciple of a shunt AF fo gid conditioning puposes, such as eactive powe compensation, hamonic filteing and load balancing, is geneally discussed in Chapte 2. It is stated that the basic opeation pinciple of a shunt AF is to inject the undesied components of the load cuent, in ode to cancel thei pesence in the line cuent. This is illustated in Figue 5.. It is clea that the pefomance of the shunt AF is detemined by the amount of eduction of these undesied components in the line cuent. Gid i Line AF iaf i Load Load Cuent contol Identification Figue 5. Shunt active filte opeating pinciple. The function of a shunt AF can be divided into two pats. Fist, the cuents that should be compensated fo have to be identified o detected. This can be pefomed eithe in the fequency domain o in the time domain. Futhemoe, the detection can be based eithe on the load cuent, the supply (line) cuent, o the gid voltage [3]. Detection based on the load cuent, which is used hee, is suitable fo a shunt AF installed in the vicinity of the load to be conditioned. The second pat consists of the active filte cuent contolle, which should ensue good ageement between the injected cuents and the undesied components of the load cuent. Basically, the filteing

62 5. Active filte contol pefomance of a shunt AF is detemined by the cuent contol pat, at least in steady state opeation. Howeve, duing tansient opeation the filteing pefomance is also affected by the identification pat. 5. Identification based on the load cuent Vaious methods fo identification of the undesied load cuent components ae poposed in the liteatue. In this thesis, howeve, only thee methods ae consideed. Fast fouie tansfom The fast fouie tansfom (FFT) method calculates the magnitude and phase of the load cuent fequency components [24]. Then the component coesponding to the fundamental active cuent is emoved. Finally, the active filte cuent efeence is obtained fom the invese FFT of the emaining fequency components. The advantage of the FFT method is that the magnitudes of the fequency components ae known. Hence by manipulation of the magnitudes, oveloading of the shunt AF can be pevented. Futhemoe, selective conditioning is made possible which is useful in some applications, whee the focus is to educe some specific component of the load cuent. Howeve, the calculations involved ae cumbesome and also the lack of infomation egading the sequences, i.e. positive- o negative-sequences, of the conditioning components makes the FFT method less pacticable. Instantaneous eactive powe theoy The instantaneous eactive powe theoy (IRPT) poposed in [][2] is a wide spead concept fo load cuent identification in active filte applications. The idea is to deive the compensating cuent efeences based on the decomposition of the instantaneous active and eactive powe into thei DC and AC components, espectively. The fundamental active and eactive cuents ae then given by the DC component of the instantaneous powe. Consequently, the AC component coesponds to the negative-sequence cuent component as well as the cuent hamonics. Accoding to the IRPT, the coesponding vecto epesentation of the instantaneous powe p in the stationay efeence αβ-fame is defined as αβ αβ p= e i = p+ jq (5.) whee p and q denotes the instantaneous active and eactive powe, espectively. Note, the diffeence fom the nomal definition of

5. Active filte contol 63 instantaneous powe given in Appendix A.3, whee the conjugation is applied on the cuent vecto and not the voltage vecto as in (5.). In ode to illustate the IRPT, conside the case of a load cuent vecto αβ and an ideal gid voltage vecto e αβ given by i Load e αβ E e jωt = ( ) 5 iload = Ie + I e + I 5e + I7e αβ j ωt φ jωt j ωt j7ωt (5.2) Then the instantaneous powe vecto is obtained by inseting (5.2) into (5.), which gives ( ) 2 6 p= E I e + E I e + I e + I e jφ j ωt j ωt j6ωt 5 7 (5.3) The DC component of the instantaneous powe in (5.3) is divided into its coesponding active and eactive component accoding to jφ p = p + jq = E I e = E I (cosφ jsin φ ) (5.4) DC DC DC The AC component of the instantaneous powe is given by 2 6 p = E I e + I e + I e AC j ωt j ωt j6ωt ( 5 7 ) (5.5) Since the compensating cuent should coespond to the instantaneous powe given by all AC components and the eactive DC component, i.e. p = jq + p (5.6) Comp DC AC the compensating cuent is detemined by the invese elationship of (5.), that is αβ pcomp icomp = (5.7) αβ e which in this case coesponds to αβ j( ω t π ) 2 jωt j5ωt j7ωt i = I sinφ e + I e + I e + I e (5.8) Comp 5 The compensating cuent in (5.8) contains all the undesied components of the load cuent in this case. Hence, these components ae cancelled fom the line cuent, which then only consists of the cuent component coesponding to the fundamental active powe, i.e. 7

64 5. Active filte contol αβ jωt i = I cos φ e (5.9) Line As a conclusion, the IRPT enables full identification and decomposition of the compensation cuents that should be injected by the shunt AF. Futhemoe, this is achieved without cumbesome calculations, which is the main eason fo the wide spead use of the method. Instantaneous cuents in synchonous coodinates Anothe appoach fo identifying the undesied components of the load cuent consides the instantaneous cuents epesented in the synchonously otating efeence -fame oiented to the integal of the gid voltage vecto [4][5]. This method esembles the IRPT method and unde ideal conditions they ae equivalent, which will be shown late. Futhemoe, the use of synchonous coodinates is convenient, since the line side cuent contolle of the battey chage, descibed in Section 4.3, aleady utilises the synchonous efeence -fame. As descibed in Appendix A.2, the load cuent vecto in the synchonous efeence -fame is deived fom the stationay efeence αβ-fame by subtaction of the coesponding angle diffeence θ accoding to αβ jθ i = i e (5.) Load Load Conside the case investigated peviously fo the IRPT, whee the gid voltage vecto and load cuent vecto ae given by (5.2). The angle θ used in the vecto tansfomation is given by the agument of the gid voltage integal, that is π θ = ωt (5.) 2 The epesentation of the load cuent vecto of (5.2) in synchonous coodinates is then given by π j 6 2 i I e j φ Load I e j 2ω t = ( + + I e j 6ω t + I e j ω t 5 7 ) e (5.2) The DC component of the load cuent vecto in synchonous coodinates is witten iload, DC = I ( sinφ + jcosφ ) (5.3)

5. Active filte contol 65 whee the eal and imaginay pats coespond to the eactive and active cuent components, espectively. The AC component of the load cuent vecto coesponds to the negative-sequence cuent component and the cuent hamonics, that is j2ωt j6ωt j6ωt i, = j I e + I 5e + I7e (5.4) Load AC ( ) As in the case of the IRPT, the instantaneous cuents epesented in synchonous coodinates povide complete infomation of the diffeent load cuent components. The compensation cuent should coespond to the fundamental eactive cuent, i.e. the eal pat of the DC component, and the AC component i =R e ( i, )+ i, (5.5) Comp Load DC Load AC which is equivalent to the compensation cuent obtained fom the IRPT. The esult of load cuent decomposition by the IRPT and by the epesentation of the instantaneous cuents in synchonous coodinates ae equivalent unde ideal conditions [4]. Howeve, in the pesence of gid voltage distosion, the obtained compensation cuents diffe. The distoted voltage implies that the coesponding cuent hamonics will contibute to the actual powe flow, and hence to the DC component of the instantaneous powe. Accoding to the IRPT, this contibution implies that pat of the load cuent hamonics can not be sepaated fom the fundamental cuent component, and hence can not be detected. Howeve, fo the instantaneous cuents epesented in the synchonous efeence -fame, the effect of the voltage hamonics is educed. This is due to the integation of the gid voltage vecto involved in ode to obtain the tansfomation angle. This means that even if the cuent hamonics contibute to the actual powe flow, they ae still epesented by the AC component of the load cuent vecto. Fom the discussion given above, identification by the instantaneous cuents epesented in the synchonously otating efeence -fame is selected. The choice is motivated by the equivalency to the IRPT method, togethe with the convenient elationship with the line cuent contolle. Table 5. gives the coespondence between the conditioning components and thei epesentation in the synchonous efeence -fame.

66 5. Active filte contol Table 5. Repesentation of the cuent components in the synchonously otating efeence -fame. Component Sequence Fequency Vecto Filtes active positive DC ji q eactive pos. DC i d asymmety negative 2f I e j 2 t 5 th hamonic neg. 6f I e j 6 t 5 7 th hamonic pos. 6f Ie j 6 t 7 th hamonic neg. 2f I e j 2 t 3 th hamonic pos. 2f I e j 2 t In ode to extact and emove the cuent component coesponding to the fundamental active powe, a high pass filte on the q-axis cuent component of the load cuent vecto is sufficient. Howeve, in ode to obtain selective conditioning by the battey chage, filtes extacting the espective conditioning components fom the load cuent ae applied instead. This is illustated in Figue 5.2, whee a low pass filte on the d- axis cuent and a band pass filte at twice the fundamental fequency povides fo the fundamental eactive cuent component and the negative-sequence component, espectively. A high pass filte extacts the coesponding load cuent hamonics, which indicates that thee is no selectivity in the hamonic filteing capability, i.e. eithe all o no cuent hamonics ae filteed. This is not egaded as a sevee estiction of the shunt AF pefomance, but the needed calculation effot is geatly educed. 3 αβ i Load e -jθ i Load LP BP HP i Load,DC i Load,ns i Load,h i AF * Figue 5. 2 Pinciple block diagam of the load cuent identifie. Note that the low pass filte only povides the d-axis DC cuent component. The low pass filte consists of a 4 th ode Buttewoth filte, with cut off fequency f lp equal to 3 Hz. This is a tade off between high attenuation of the cuent hamonics and the negative-sequence cuent component

5. Active filte contol 67 vesus the tansient chaacteistics, i.e. esponse time and oveshoot, of the filte. The coesponding tansfe function of the low pass filte is given by G LP ω lp () s = s + 2. 63ω s + 3. 44ω s + 2. 63ω s + ω 4 4 3 2 2 3 4 lp lp lp lp (5.6) A fist appoach fo designing the band pass filte is to combine a low pass and a high pass filte. Howeve, the band pass filte in fact consists of two identical band pass filtes applied to the d- and q-axis components of the load cuent, espectively. Hence, the calculation effot would be high. Anothe appoach [33] utilises the vecto epesentation of the load cuent and applies a vecto tansfomation into a negative-sequence oiented efeence fame, efeed to as the ns-fame. This implies that the fundamental negative-sequence cuent component is epesented as a DC quantity. Consequently, low pass filtes ae sufficient in ode to extact the negative-sequence component fom the load cuent. The output fom the low pass filtes ae then tansfomed back into the synchonous efeence -fame. The esult of the back tansfomation coesponds to a fequency shift of the low pass filte. The tansfe function of the band pass filte is obtained accoding to [] in complex notation as BP LP ns G () s = G ( s + j2ω ) (5.7) whee the low pass filte consists of a 4 th ode Buttewoth filte, efe to (5.6), with cut off fequency equal to 2 Hz. The fequency esponse of the complex valued band pass filte is shown in Figue 5.3. - Gain [db] -5 - Figue 5.3 Fequency [Hz] Fequency esponse of the band pass filte in the synchonous efeence -fame, positive- (solid) and negative-sequence (dashed). As can be concluded fom the figue, it is only the negative-sequence cuent component of twice the fundamental fequency that passes the filte, which is the intention of the band pass filte.

68 5. Active filte contol Fo the high pass filte, a simila appoach is used. In this case, fist ode high pass filtes ae employed in both the efeence fames coesponding to the positive- and negative-sequences of the fundamental fequency. The complex valued tansfe function of the high pass filte is ns s + j2ω s GHP () s = GHP ( s + j2ω ) GHP () s = s + j2ω + ω s + ω hp hp (5.8) whee the cut off fequency f hp is chosen to Hz. The elatively low cut off fequency of the high pass filtes ensues high phase ageement fo the filteed cuent hamonics. The fequency esponse of the high pass filte is shown in Figue 5.4. The esult is, in some aspect, equivalent to notch filtes at the fundamental fequency in the stationay efeence αβ-fame. - Gain [db] - -2-3 Figue 5.4 Fequency [Hz] Fequency esponse of the high pass filte in the synchonous efeence -fame, positive- (solid) and negative-sequence (dashed). In Figue 5.5, the complete block diagam epesentation of the load cuent identifie is shown. αβ i Load e -jθ i Load e jθ i ns Load ns G LP ns G HP G LP ns i Load,DC e -j2θ e -j2θ G HP i Load,DC i Load,ns i Load,h i AF * Figue 5. 5 Block diagam of the load cuent identifie. Tansient esponses of the filtes Fom the discussion given above, it can be concluded that the steady state pefomance of the filtes, applied in the load cuent identifie, is good. This indicates that the steady state pefomance of the shunt AF is detemined by the cuent contolle. Howeve as mentioned peviously, the tansient pefomance of the shunt AF is affected by the identification

5. Active filte contol 69 filtes. This is illustated in Figue 5.6, whee the filteed outputs ae shown when step changes in each of the conditioning cuent components ae applied. i d,dc i d,ns - i d,h - Figue 5.6 2 3 4 5 6 7 8 t [ms] Ideal (black) and filteed outputs (gey) duing step esponses in the individual d-axis components of the load cuent at ms, 3 ms and 5 ms fo the eactive, hamonic and negative-sequence cuent components, espectively. Note the coupling between the filteed outputs, especially fo the high pass filte output. Fom Figue 5.6, it is concluded that the esponse times fo the low pass and band pass filtes oughly coespond to two fundamental time peiods, i.e. 4 ms. This is due to the low cut off fequencies selected fo the low pass filtes used. The low cut off fequencies futhe povide high eduction of the othe fequency components, which implies low intefeence between the filteed outputs. The high pass filte output, on the contay, is stongly affected by step changes in eithe the fundamental cuent o the negative-sequence cuent component. This is due to the low cut off fequency of the high pass filte, selected in ode to obtain good phase ageement of the hamonic cuent efeence. Initially, all fequency components passes the high pass filte, which implies that the hamonic cuent efeence can be dangeously lage. Futhemoe, the tansient bias in the high pass filte output can cause unintended active o eactive powe flow in the shunt AF.

7 5. Active filte contol 5.2 Oiginal active filte contolle The oiginal and fist appoach to the active filte contolle is obtained by combining the identification filtes with the line side cuent contolle deived in Section 4.3. In Figue 5.7, the block diagam epesentation of this oiginal active filte contolle is shown. i Load LP BP i 2q * i AF * i 2 * i 2 ~PIE u c * u c ~PE i * i ~PE u * HP Figue 5.7 Block diagam epesentation of the oiginal active filte contolle. Note that the fundamental active cuent efeence i 2q * obtained fom the DC-link voltage contolle is added to the active filte cuent efeence. Also note the shote notation applied to the P-contolles (P), with feed back of the d- and q-axis coss-coupling (~) and the additional feed fowad (E). In this section, the pefomance of a shunt AF employing the oiginal active filte contolle is investigated fo one conditioning capability at the time. The same esults ae obtained when all conditioning capabilities ae analysed simultaneously. Howeve, the analysis is simplified since the esults may be hidden unde othe phenomena, when pefoming simultaneous investigation of the conditioning capabilities. Reactive powe compensation Reactive powe compensation is in many aspects the easiest active filte task to be pefomed. Since the synchonously otating efeence fame is employed fo the oiginal active filte contolle, eactive powe compensation is equivalent to contolling the d-axis DC cuent component. Futhemoe, since the active filte contolle contains integatos in the oute cuent contol loop, complete eduction of the eactive cuent component is obtained. The simulated esult, when pefoming eactive powe compensation with the oiginal active filte contolle, is shown in Figue 5.8. In this case the load consists of puely inductive elements, which implies that the load cuent is completely eactive and lags the gid voltage by 9 degees.

5. Active filte contol 7 i Load e a i Line i AF - - - Figue 5.8-2 3 t [ms] Simulated phase cuents when pefoming eactive powe compensation of inductive load. Top) load cuent (black) and gid voltage (gey), middle) esulting line cuent, and bottom) injected AF cuent. The emaining component of the line cuent coesponds to the fundamental active cuent consumed by the active filte itself. This small active cuent component is needed in ode to maintain the DC-link voltage at its nominal value, thus compensating fo the losses in the shunt AF. Load balancing The simulated esult when pefoming load balancing, with the oiginal active filte contolle, is shown in Figue 5.9. In this case, the load consists of a esistive load connected between the phases a and c. Hence, the load cuent consists of equal amount of the positive- and the negativesequence cuent components of fundamental fequency. The two phase load is consideed appopiate, since the load balancing capability is esticted to the negative-sequence component due to the lack of a neutal conducto in the shunt AF, i.e. the battey chage. Unde ideal conditions the esulting line cuent should only contain the fundamental positive-sequence cuent component, since that component coesponds to the aveage powe consumed by the load. Howeve, as can be seen in Figue 5.9, the line cuents ae not totally balanced in this case, despite the injection of the negative-sequence cuent component by the shunt AF. This implies that the injected cuent is not equal to the coesponding negative-sequence cuent component of the two phase load.

72 5. Active filte contol i Load [pu] - i Line i AF - - Figue 5.9-2 3 t [ms] Simulated phase cuents (phase a black, phase b gey, and phase c dashed black) when pefoming load balancing of a esistive two phase load. Top) load cuents, middle) line cuents, and bottom) injected AF cuents. The diffeence between the load cuent and the injected cuent is due to the phase deviation of the line side cuent contolle, see Figue 4.8 on page 55. The phase deviation implies that the injected cuent diffe in phase fom the load cuent. Hence, complete cancellation of the negativesequence cuent component is not accomplished. Nevetheless, the pefomance can be impoved by compensating fo this inheent phase deviation. This is futhe discussed in the next section. Hamonic filteing Since hamonic filteing involves the injection of seveal high fequency cuent components coesponding to the cuent hamonics poduced by the load, it is consideed fom a contol point of view as the hadest task to pefom. In ode to analyse the hamonic filteing popety of the oiginal active filte contolle, the complete model of the high pass filte and the cuent contolle has to be deived. Fom (5.8), the complex valued discete state space epesentation of the high pass filte can be deived and is geneally witten accoding to xhp ( k + ) = Ahp xhp ( k) + BhpiLoad ( k) (5.9) * i ( k) = C x ( k) + D i ( k) AF hp hp hp Load whee x hp is the state vecto of the high pass filte. The complete model is obtained by the seies connection of the state space systems (5.9) and (4.49), which gives

5. Active filte contol 73 Xk ( + ) C Xk X i ( ) * hp e i * Dhp e xhp( k + ) = A x k hp hp( ) + Φ Γ Γ Γ 2 2 Bhp i Xk ( ) e i2 ( k) = [ CX Di * Chp] De Di * Dhp xhp( k) + [ ] 2 2 442443 442443 i [ CX ] [ ] Load Load ( k) ( k) ( k) ( k) (5.2) Neglecting the influence of the gid voltage in the analysis, the closed loop system of the oiginal active filte contolle is witten Xk C Xk ( + ) ( ) X i * hp i * Dhp iload ( k) xhp ( k + ) = A x k hp hp ( ) + Φ Γ Γ 2 2 Bhp (5.2) Xk ( ) iline ( k) = [ C X ] ( ) xhp ( k) + i Load k Basically, both the bandwidth and the phase deviation of the cuent contolle affects the hamonic filteing pefomance. The bandwidth of the cuent contolle, efe to the fequency esponse plot in Figue 4.8, is sufficiently high. The phase deviation, on the othe hand, has a moe deteioating effect on the filteing pefomance. The phase delay, coesponding to thee samples, deceases the hamonic filteing pefomance. This is concluded fom the closed loop fequency esponse displayed in Figue 5. fo the shunt AF investigated, i.e. the fequency esponse fom the load cuent to the esulting line cuent accoding to (5.2). Gain [db] - -2-3 -4-5 Fequency [Hz] Figue 5. Closed loop fequency esponse fo the oiginal hamonic filte contolle in the synchonous efeence -fame, positive-sequence (solid) and negative-sequence (dashed). Note that the low fequency behaviou is due to the high pass filte used in the cuent hamonic identification and not caused by the cuent

74 5. Active filte contol contolle. Anyway, the poo filteing pefomance of the oiginal active filte contolle is clealy seen. In fact, as can be seen in Figue 5., the highe ode load cuent hamonics, i.e. above the 2 th hamonic in synchonous coodinates, ae even amplified instead of educed by the injected hamonic cuents. The poo hamonic filteing pefomance can also be concluded fom the simulated esult shown in Figue 5.. In this case, the load consists of an ideal thee phase diode ectifie with an infinite smoothing choke on the DC side. The DC cuent is completely flat, and hence also the phase cuents when thei coesponding diodes ae conducting the cuent. In this case, the amplitudes of the cuent hamonics decline with the invese of thei coesponding hamonic ode. i Load i Line i AF I h /I fund [pu] - - - [%] 2 5 5-2 3 4 5 Load Line AF 5 7 3 7 9 23 25 29 3 35 37 t [ms] Figue 5. Simulated phase cuents and the coesponding hamonic spectum, when pefoming hamonic filteing with the oiginal active filte contolle. Note the confomity of the esulting line cuent spectum and the closed loop fequency esponse displayed in Figue 5.. Nevetheless, the unacceptable poo filteing esult demands fo modification of the active filte contolle in ode to incease the hamonic filteing pefomance. The inheent phase deviation of the cuent contolle has to be compensated fo, which is the topic of the next section. h

5. Active filte contol 75 5.3 Diect phase compensation of the active filte contolle The main conclusion dawn in the pevious section, is the need fo compensation of the inheent phase delay in the line cuent contolle. This phase delay is the main eason fo the poo hamonic filteing and load balancing esults of the oiginal active filte contolle. In this section, some basic methods that can be used fo the compensation of the phase deviation in the cuent contolle ae descibed. The phase deviation of the line cuent contolle appoximately coesponds to a thee sample delay, see Figue 4.8. Hence, the phase compensation should povide a phase advance coesponding to thee samples in ode to cancel the inheent delay of the cuent contolle. Load balancing In the load balancing case, the phase compensation is obtained in a staight fowad manne, whee the band pass filte output vecto is otated an angle coesponding to the desied phase advance. Hence, the agument of the cuent efeence vecto is modified to povide fo the desied phase advance in the otation diection of the negative-sequence vecto. This phase compensation is descibed, in complex valued vecto notation, by the following expession * j( 2ω 3T i i e s ) = (5.22) AF Load, ns Anothe appoach [5], utilises lead-lag filtes in the d- and q-axis components, espectively, to povide the phase advance of the cuent efeence vecto. The obtained esult is the same, but the simplicity of the staight fowad method is pefeed. The impoved pefomance of the compensated active filte contolle is concluded fom the simulation esult, shown in Figue 5.2, whee the phase compensation given by (5.22) is applied. In this case the line cuent is totally balanced, compae to Figue 5.9 fo the uncompensated esults. The esulting line cuent contains only the positive-sequence component of the load cuent, which coesponds to the ideal case. This esult futhe implies that the injected cuent equals the negative-sequence component of the load cuent.

76 5. Active filte contol i Load [pu] - i Line i AF - - - 2 3 t [ms] Figue 5.2 Simulated phase cuents (phase a black, phase b gey, and phase c dashed black) when pefoming load balancing of a esistive two phase load with the phase compensated active filte contolle. Hamonic filteing The staight fowad method, applied fo the fundamental negativesequence cuent component, is not diectly applicable in the hamonic filteing case. Since in the hamonic filteing case, seveal fequencies ae concened. The staight fowad method would equie simila band pass filtes fo each of the hamonics, in ode to obtain the coect phase advance fo evey hamonic cuent component [2]. Howeve, if the FFT method is employed in the load cuent identification, the coesponding phase of the hamonic cuent efeences can be advanced accoding to the staight fowad method [24]. Since the phase deviation of the cuent contolle coesponds to a thee sample delay, the desied phase compensation is obtained by the pediction of the cuent hamonics thee samples ahead in time. The peiodicity of the cuent hamonics futhe implies that pevious peiods of the hamonic cuent can be used fo the pediction. Hence, the pedicted hamonic cuent is given by the hamonic cuent, one peiod minus thee samples back. Fo each cuent hamonic this can be witten ˆ i ( k + 3) = i ( k T + 3 T ) (5.23) Load, h Load, h whee T h is the time peiod of the coesponding cuent hamonic. The pediction (5.23) is genealised to be valid fo all hamonics by selecting T h accoding to the time peiod of the lowest cuent hamonic, i.e. the sixth hamonic in the synchonous efeence -fame. h s

5. Active filte contol 77 The ealisation of the phase compensation is obtained by a shift egiste, with a length coesponding to the time peiod of the lowest ode cuent hamonic. Hence, the hamonic cuent efeence is given by * i ( k) = i ( k T +3 T ) (5.24) AF Load, h shift egiste The discete state space desciption of (5.24) can geneally be witten xs ( k + ) = As xs ( k) + BsiLoad, h ( k) (5.25) * i ( k) = C x ( k) + D i ( k) AF s s s Load, h The closed loop state space epesentation of the phase compensated hamonic filte contolle is obtained by inseting (5.25) into (5.2), which gives Xk X i Cs i ( + ) Φ Γ * Γ * DsChp Xk () Γ 2 2 i2 * DsDhp xs( k+ ) = As BsChp xs() k + BsDhp iload() k xhp( k+ ) Ahp xhp() k Bhp (5.26) Xk () Line() X i k = [ C ] xs() k + iload() k xhp() k The effect of the applied phase compensating method is visualised by the fequency esponse shown in Figue 5.3. At the fequencies coesponding to the cuent hamonics in the synchonous efeence fame, the attenuation is impoved in compaison to the oiginal active filte contolle. At least 2 db, o ten times, eduction of the hamonic content of the line cuent is achieved. s Gain [db] - -2-3 -4-5 Fequency [Hz] Figue 5.3 Closed loop fequency esponse fo the compensated hamonic filte contolle, positive-sequence (solid) and negative-sequence (dashed).

78 5. Active filte contol The main advantage of this compensation method is the simple ealisation. Howeve, it is seen in Figue 5.3 that the effect of the phase compensation deceases fo the highe ode cuent hamonics. This is due to the fact that fo the highe ode hamonics, the phase deviation of the cuent contolle stats to diffe fom the assumed thee sample phase delay, efe to Figue 4.8. The simulated esult, when pefoming hamonic filteing with the phase compensated active filte contolle, is shown in Figue 5.4. As expected, the hamonic filteing pefomance is geatly impoved in compaison to the esult obtained with the oiginal active filte contolle, efe to Figue 5.. i Load i Line i AF I h /I fund [pu] - - - [%] 2 5 5-2 3 4 5 Load Line AF 5 7 3 7 9 23 25 29 3 35 37 t [ms] Figue 5.4 Simulated phase cuents and the coesponding cuent spectum obtained with the phase compensated active filte contolle. Phase compensated active filte contolle Figue 5.5 shows the block diagam epesentation of the phase compensated active filte contolle. Accoding to the discussion given above, the expected pefomance of this active filte contolle is high. Howeve, in a pactical ealisation of the phase compensated active filte contolle, some degading popeties appea that is not modelled o taken into consideation when pefoming the theoetical analysis. In fact, the expeimental esults, given in Chapte 6, indicate quite poo filteing pefomance of the phase compensated active filte contolle. h

5. Active filte contol 79 i Load LP BP e -j2ω 3T s i 2q * i AF* i 2 * i 2 ~PIE u c * u c ~PE i * i ~PE u * HP z - z - z - z - z - z - Figue 5. 5 Block diagam scheme of the phase compensated active filte contolle. One degading popety is the sensitivity to vaiations in the system paametes. Since the active filte contol is pefomed in open loop, the pefomance is detemined by the accuacy of the estimated paametes used in the cuent contolle. Uncetainties in these paametes cause the actual behaviou to diffe fom the expected. Consequently, the theoetically obtained fequency esponses do not descibe the actual system accuately. Tuning of the active filte contolle paametes based on expeimental esults impoves the pefomance, howeve this pocedue is cumbesome and should be avoided in pactice. Futhemoe, the non-linea popeties of the VSC also have a degading effect on the conditioning pefomance. Fo instance, the blanking time intoduces cuent hamonics which ae not compensated fo, since they do not appea in the load cuent. 5.4 Rotating integatos in active filte contol In ode to ovecome the deteioating popeties of the phase compensated active filte contolle, anothe impoved active filte contolle stuctue is poposed, whee integatos in hamonic oiented efeence fames ae employed [6]. The main focus is to obtain a paamete insensitive active filte contolle with high hamonic filteing pefomance in the steady state [6]. Howeve, as will be shown in this section, additional featues such as hamonic filteing selectivity is also achieved. Futhemoe, the tansient pefomance of the shunt AF is impoved. The idea of the poposed contolle is based on the obsevation of the effect of the integatos applied in the oute cuent loop of the line cuent contolle, descibed in Section 4.3. Due to the infinite gain at zeo fequency of the integato, the steady state eo of the coesponding DC component is eliminated. As a consequence, the uncetainties concening the DC component of the system ae totally compensated fo. In fact, this is equivalent to compensation of both the

8 5. Active filte contol gain and the phase deviation fo the fundamental positive-sequence cuent component in the stationay efeence αβ-fame. Integatos applied in seveal hamonic oiented efeence fames, whee the coesponding cuent hamonics ae epesented as DC quantities, should have the same effect on the steady state eos of the coesponding cuent hamonics [32][35]. This implies that the injected hamonic cuent equals the hamonic content of the load cuent, and hence complete cancellation of the line cuent hamonics ae obtained. Since this is aleady tue in the eactive powe compensation case, efe to Figue 5.8, the oiginal active filte contolle fo eactive powe compensation is kept unchanged. Futhemoe, the same technique is used in a negative-sequence oiented efeence fame, poviding impoved pefomance also of the load balancing popety. Paallel otating integato (PRI) contolle stuctue The block diagam epesentation of the poposed paallel otating integato (PRI) contolle stuctue, whee the additional hamonic oiented integatos ae simply inseted in paallel to the oiginal synchonous efeence -fame integato, is shown in Figue 5.6. Note that in the figue, only the integatos coesponding to the lowe ode cuent hamonics ae shown, i.e. the 5 th and 7 th cuent hamonics. In the thesis, howeve, hamonic oiented integatos fo the 5 th up to the 25 th cuent hamonics ae employed. i Load LP BP HP i 2q * i AF * i 2 * i 2 ~PIE u c * e j6θ I -5 -j6(θ+θ e c ) e -j6θ I 7 e j6(θ+θ c ) u c u RI ~PE i * i ~PE u * Figue 5. 6 Pinciple block diagam epesentation fo the PRI contolle stuctue fo active filtes. Note the additional compensation angle θ c inseted in the tansfomation fom the hamonic oiented efeence fames back to the synchonous efeence -fame. The effect of this additional compensation angle θ c is discussed late on, at the moment it is sufficient to say that it impoves the phase magin, o stability magin, of the PRI contolle. This is especially impotant fo the highe ode cuent hamonics. Howeve, as will be shown late, a suitable value fo θ c is

5. Active filte contol 8 θ c = 5 ω T 2 (5.27) s In ode to include the otating integato loops in the theoetical analysis, the equivalency of the vecto tansfomation fo continuous time and discete time systems have to be given s αβ jω t e s s jω s + jω q q e T s (5.28) which descibes the esult of vecto tansfomation between the stationay and the synchonous efeence fames. Nevetheless, the basic pinciple given in (5.28) is easily extended to abitaily vecto tansfomations. Applying the elationship fo the tansfomation of discete time systems (5.28) on the otating integato loops, the complex valued discete state space system, including the additional compensation angle, is found A RI RI 6447448 64748 I k j Ts e I k j Ts 5( + ) Ke h = 6ω i k I k+ j T + 6 5( ) ω * 6 s e I k j6 T 2 ( s 7( ) ω 7( ) ω ( ) i2 ( k) ) Ke h (5.29) ( ) ( ) =[ ] I k j6θ c j6θ 5 c uri k e e 442 443 I7( k) CRI The integal gain K h is given by B K h = k uc k i2 L T 2 s T τ s h (5.3) whee τ h coesponds to the selected time constant of the hamonic oiented integatos. Note that in ode to coectly intepet the time constant, scaling with espect to the gain constant k uc of the intemediate capacito voltage P-contolle has to be made. Basically, the time constant of the otating integatos can be chosen equal to the time constant of the integato used in the synchonous efeence -fame contolle. Howeve, in ode to impove the tansient behaviou of the shunt AF, the time constants of the hamonic oiented integatos ae selected accoding to τ h = ms (5.3)

82 5. Active filte contol Anyway, the effect of the time constant τ h is discussed moe in detail late on. Extending the line cuent contolle given by (4.49), again neglecting the gid voltage in the analysis, with the state space desciption of the otating integatos (5.29) gives Xk ( + ) C Xk X RI RI ( ) i * * = i ( k) xri( k ) B C A x k RI X + Φ Γ Γ 2 2 + RI RI( ) BRI (5.32) Xk ( ) i ( k) = [ CX ] 2 xri( k) whee Γ RI = [ L i 2 ] T (5.33) links the output of the otating integatos to the convete voltage efeence, efe to Section 4.3. The closed loop discete state space system of the PRI hamonic filte contolle is then obtained by inseting the state space epesentation of the high pass filte (5.9) into (5.32) Xk X RI C ( + ) Φ Γ Γ C Xk RI i * ( ) Γ 2 hp i D 2* hp xri( k+ ) BRICX = ARI BRIChp xri( k) + BRIDhp iload( k) xhp( k+ ) Ahp xhp( k) Bhp (5.34) Xk ( ) Line X i ( k) = [ C ] xri( k) + iload( k) xhp( k) In Figue 5.7, the fequency esponse fo the PRI hamonic filte contolle, with integatos oiented to the 5 th up to the 25 th cuent hamonics, is displayed. The naow notches, at the fequencies coesponding to the hamonics in the synchonous efeence -fame, indicate the elimination of the coesponding cuent hamonics. Hence, the hamonic oiented integatos povide complete compensation of the degading phase deviation in the oiginal active filte contolle. Futhemoe, this is obtained independent of the system paametes.

5. Active filte contol 83 Gain [db] - -2-3 -4-5 Fequency [Hz] Figue 5.7 Closed loop fequency esponse fo the PRI hamonic filte contolle in the synchonous efeence -fame, positive-sequence (solid) and negative-sequence (dashed). Note the similaity between the fequency esponses obtained with the PRI contolle and the oiginal hamonic filte contolle shown in Figue 5.. Except fo the naow notches in the PRI contolle case, they appea to be identical. This implies that the highe ode cuent hamonics, i.e. without coesponding integatos, still ae affected by the phase deviation of the line cuent contolle. Hence, these cuent hamonics ae even amplified instead of educed, which can be concluded fom Figue 5.7. The conclusions dawn fom the fequency esponse, of the PRI hamonic filte contolle, ae confimed by the simulated esults shown in Figue 5.8. The cuent hamonics with coesponding integatos ae pactically eliminated. This implies that the emaining oscillation in the line cuent is completely due to the highe ode cuent hamonics, patly pesent in the load cuent and patly due to the injected filteing cuent. This is concluded fom the plotted hamonic spectum of the cuents. Futhemoe, it can be concluded that the settling time of the integatos coespond to the selected time constant τ h. The still emaining degading popety of the PRI hamonic filte contolle, i.e. the amplification of the highe ode cuent hamonics, is due to the diect path povided by the P-contolles though the cascaded contolle stuctue. The consequence of this is that the contolle puts as much contol effot on these highe ode cuent hamonics, despite the fact that the poduced contol actions only deceases the pefomance of the active filte. Howeve, this is cicumvented by the emoval of the diect path though the active filte contolle. In fact, this is accomplished fo the active filte contolle descibed next, which still has the advantages but lacks the dawbacks of the PRI contolle.

84 5. Active filte contol i Load i Line i AF I h /I fund [pu] - - - [%] 2 5 5-2 3 4 5 Load Line AF 5 7 3 7 9 23 25 29 3 35 37 t [ms] Figue 5.8 Simulated phase cuents and thei hamonic content, when pefoming hamonic filteing with the PRI contolle. Multiple otating integato (MRI) contolle stuctue In ode to ovecome the emaining dawback of the PRI hamonic filte contolle, i.e. the amplification of highe ode cuent hamonics, a futhe impoved otating integato contolle is poposed. Basically, the idea is to emove the diect path though the cascaded contolle stuctue fo the cuent hamonics. This is obtained by emoving the path fom the high pass and the band pass filte outputs to the line cuent contolle. These filte outputs ae instead only input to the multiple otating integato (MRI) loops, see Figue 5.9. As a consequence, hamonic selectivity is obtained since only cuent hamonics with coesponding integatos ae filteed. Hence, in this thesis the 5 th up to the 25 th cuent hamonics ae filteed, while the highe ode cuent hamonics ae left unfilteed. Note the additional anti windup block (AW) inseted in the figue, which is descibed late on. Also note the pinciple diffeence egading the band pass and high pass filte inputs. This implies that the cuent of the battey chage also is filteed. Howeve, the filtes ae not essential fo the function of the hamonic oiented integatos, and hence can be left out in the MRI active filte contolle. Nevetheless, thei pesence educe the ipple in the hamonic oiented integatos caused by the fundamental h

5. Active filte contol 85 cuent component, whose magnitude is seveal times highe than any of the cuent hamonic magnitudes. i Load i 2 AW i Line LP BP HP i 2q * i 2d * i 2 i 2 * ~PIE u c * e j2θ I - e -j2(θ+θ c ) e j6θ I -5 -j6(θ+θ e c ) u RI u c ~PE i * i ~PE u * e -j6θ I 7 e j6(θ+θ c ) Figue 5. 9 Pinciple block diagam epesentation fo the MRI contolle stuctue fo active filtes. The paametes fo the MRI loops, i.e. the compensation angle θ c and the time constant fo the hamonic oiented integatos τ h, ae chosen equal to the PRI hamonic filte contolle. Howeve, the time constant of the negative-sequence oiented integato is selected to τ ns = ms (5.35) which is due to the longe esponse time of the band pass filte, efe to Figue 5.6. Fo the MRI hamonic filte contolle, the complex valued discete state space epesentation is given by Xk ( + ) ΦX ΓRI C RI Xk ( ) xri( k ) BRIDhpCX + = ARI BRIChp xri( k) + BRIDhp iload( k) xhp( k+ ) BhpCX Ahp xhp( k) Bhp (5.36) Xk ( ) iline k CX ( ) = [ ] xri( k) + iload( k) xhp( k) which is simila to the PRI hamonic filte contolle case (5.34). The absence of the diect path, in the MRI hamonic filte contolle, esults in the fact that the highe ode hamonics ae left unfilteed. This is concluded fom the closed loop fequency esponse of the MRI hamonic filte contolle (5.36) displayed in Figue 5.2. The gain is

86 5. Active filte contol appoximately unity fo all fequencies except at the fequencies of the coesponding integatos. Gain [db] - -2-3 -4-5 Fequency [Hz] Figue 5.2 Closed loop fequency esponse fo the MRI contolle with coesponding integatos fo the 5 th up to the 25 th cuent hamonics, positive-sequence (solid) and negative-sequence (dashed). The pole and zeo map of the MRI hamonic filte contolle (5.36) is shown in Figue 5.2. The naow notches in the fequency esponse ae due to the pole and zeo pais located in the vicinity of the unit cicle. In fact, the zeoes ae actually on the unit cicle, which causes the cancellation of the coesponding fequency component, i.e. the depth of the notches in the fequency esponse. In [36], an active filte contolle based on notch filtes in the contolle was poposed esulting in a simila pole and zeo map..5 Imag axis.5 Imag axis.5 Real axis.5 Real axis Figue 5.2 Pole and zeo map fo the closed loop MRI hamonic filte contolle. The ight plot shows a close up of the fist quadant. Note that the location of the poles coesponding to the oiginal line cuent contolle, without the MRI loops, ae popotionately unchanged, efe to the pole map shown in Figue 4.7. The simulated esult, when pefoming hamonic filteing with the MRI contolle, is shown in Figue 5.22. The supeioity of the poposed MRI

5. Active filte contol 87 contolle, compaed to the pevious cases, is clealy seen. The cuent hamonics up to 25 th ae eliminated, wheeas the even highe ode cuent hamonics ae left unfilteed. i Load i Line i AF I h /I fund [pu] - - - [%] 2 5 5-2 3 4 5 Load Line AF 5 7 3 7 9 23 25 29 3 35 37 t [ms] Figue 5.22 Simulated phase cuents and thei hamonic content obtained with the MRI hamonic filte contolle. Note that the esponse time of the MRI contolle coesponds to the selected time constant τ h of the hamonic oiented integatos. This is futhe veified in Figue 5.23, whee the hamonic oiented integato outputs fo the lowest and highest odes of cuent hamonics ae shown. h 5 th 7 th [pu].2 -.2 23 th 25 th.5 -.5-2 3 4 5 6 7 t [ms] Figue 5.23 The integato outputs fo the simulation of the MRI hamonic filte contolle, top) 5 th dak and 7 th light, and bottom) 23 d dak and 25 th light.

88 5. Active filte contol Note that the ipple in the integatos of the lowe figue is due to the emaining highe ode cuent hamonics still pesent in the line cuent. An additional featue of the MRI contolle concens the tansient behaviou of the shunt AF. In the MRI contolle case, the low pass filteing popety of the integatos neutalises the tansient coupling in the high pass filte output shown in Figue 5.6. Hence, the time constant τ h of the hamonic oiented integatos detemines the tansient esponse time of the MRI contolle. Anti windup schemes fo the MRI contolle The MRI contolle povides fo simple counte-measues in ode to pevent fom windup of the hamonic oiented integatos. It is ecognised that integato windup o integato unaway only occus when the VSC, i.e. the actuato, output is limited by the DC-link voltage, efe to the discussion in Section 3.2. Hence, if ovemodulation of the VSC is pevented, then integato windup can not occu. Ovemodulation of the VSC appeas, in steady state, when the voltage dop acoss the LCL-filte becomes lage than the magin between the DC-link voltage and the gid voltage. This voltage dop is dependent both on the magnitude of the injected cuent hamonics and on the equivalent impedance of the filte seen fom the VSC. Howeve, the influence of the latte is educed by the use of a LCL-filte in compaison to an odinay L-filte, efe to the discussion in Section 3.4. Anti windup is achieved in steady state eithe by educing the magnitudes of the injected cuent hamonics o by omitting some of the hamonic oiented integatos. Hence, anti windup is ensued at the expense of a educed filteing pefomance. In the fist case, this can be accomplished by educing the amount of the load cuent pio to the band pass and high pass filtes. This pinciple is shown in Figue 5.9, whee the AW block simply consists of a scaling facto. The value fo the scaling facto AW is then detemined by the following simple algoithm if ovemodulation AW:=MIN(,AW-.) else AW:=MAX(,AW+.) Note that the decement should be consideably lage than the incement in ode to accomplish anti windup in steady state.

5. Active filte contol 89 In the second case, anti windup is povided by continuous eset of the coesponding integatos of the cuent hamonics to be omitted, pefeably applied to the highe ode hamonic oiented integatos. Influence of the MRI paametes The influence of the otating integato paametes, i.e. θ c and τ h, have peviously not been discussed. The value of the compensation angle θ c is, howeve, cucial in ode to obtain stability of the MRI contolle. This is especially impotant fo the highe ode hamonic oiented integatos. The time constants τ h and τ ns, on the othe hand, detemines the tansient chaacteistics of the MRI contolle. In Figue 5.24, the loci of the poles and zeoes of the MRI contolle is shown when the otating integato paametes ae alteed. Note that only the poles and zeoes coesponding to the highest ode hamonic oiented integatos, i.e. fo the 23 d and 25 th cuent hamonics, ae shown. It is concluded that the poposed set of θ c and τ h gives a stable system, since the poles ae inside the unit disc. Imag axis.74.72.7.68 θ c =5/2ω T s τ= ms 3/2 /2 7/2 /2 9/2.68.7.72 Real axis Imag axis.74.72.7.68 τ=2 ms θ c =5/2ω T s τ=5 ms τ=5 ms τ= ms.68.7.72 Real axis Figue 5.24 Pat of loci of pole and zeo map fo the MRI hamonic filte contolle, vaying θ c (left) and vaying τ h (ight). Note that the dotted line coesponds to the fequency of the investigated hamonic in the synchonous efeence -fame. Figue 5.25 shows the effect on the fequency esponse, caused by the paamete vaiations of the MRI contolle. Note the pinciple diffeence in the location of the peaks when the compensation angle θ c is alteed. This is due to the fact that the coesponding fequency, i.e. location, of the poles diffe moe o less fom the fequency of the zeoes involved. The close to the coesponding fequency line, the less distoted fequency esponse.

9 5. Active filte contol Gain [db] 5-5 Gain [db] 5-5 Fequency [Hz] Figue 5.25 Influence of the MRI paametes on the fequency esponse fo the MRI hamonic filte contolle. Top) θ c = 5/2ω T s (black), 7/2ω T s (gey), and 9/2ω T s (dashed black). Bottom) τ h = 5 ms (gey), ms (black), and 5 ms (dashed black). Futhemoe, the width of the notches ae naowed with inceasing time constant, and at the same time the bias in between the notches is loweed. This is due to the moe closely aligned poles and zeoes fo lage time constants. Hence, a tade of between the esponse time and the intemediate bias has to be made. This is especially impotant fo the highest ode hamonic oiented integatos, since a high bias esults in the amplification of the even highe ode cuent hamonics, efe to Figue 5.25. Note that the analysis given eveals that the selected set of MRI paametes ae not the optimal choice. In fact, the compensation angle θ c should pefeably have been selected to 7/2ω T s, since in this case the fequency coespondence of the poles and zeoes ae impoved. Nevetheless, the main objective in tems of high steady state conditioning pefomance is fulfilled with the poposed set of MRI paametes.

6 Expeiments In this chapte, the expeimental esults of the poposed battey chage ae pesented. The basic cuent contolles descibed in Chapte 4 ae veified. Howeve, the emphasis is put on the gid conditioning esults and especially the popeties of the poposed MRI active filte contolle. 6. Expeimental set-up The expeimental set-up is shown in Figue 6.. Note that the powe gid should be connected in the lowe leftmost pat of the figue. The thee phase diode ectifie is applied in ode to geneate the load cuent to be conditioned by the shunt AF pat of the battey chage. The diode ectifie load is puely esistive, i.e. a lamp ballast. Note that the load cuent is not explicitly measued, instead it is estimated fom the measued supply (line) cuent and the battey chage cuent. i 2a i a e ab u cab i i 2 V dc e bc i 2c u cbc i c V batt 4 A 6 A i la i lb i lc A B C Ω i La i Lb i Lc Figue 6. To IGBT dives PWM DSPLINK bus e, i 2, u c, i V dc 8 IEA i line MIMO i, i 2, V batt 3 3 i* batt Schematic layout of the expeimental set-up. 47 Ω 4 A The battey package, shown in the lowe ight of the figue, actually consists of a otating convete, whee the amatue cicuit of a DC machine is used as a battey equivalent. The nominal DC voltage of the

92 6. Expeiments battey equivalent is 24 V, which implies that the maximum chaging powe is lowe than the ated powe of the battey chage. The suge cuents ae limited by the additional esistos in seies with the souce to be connected. Initially at system stat up, the contactos in seies with the cuent limiting esistos ae closed. Afte the initial suge tansient, the main contactos ae closed and thus shot cicuits the cuent limiting esistos. The contactos in seies with the cuent limiting esistos ae at the same time eleased. This is automatically contolled by time elays, which ae not shown in Figue 6.. The VSCs actually consist of six SKM5GB23D half bidge modules, whee the additional two modules ae due to the implementation of the quasi esonant DC link convete descibed in [8]. The modules ae ated 2 V and 4 A at 8 C case tempeatue. The dive SKHI23/2, also manufactued by Semikon, is used. Futhemoe, the blanking time of the IGBTs is selected to 4 µs. The DC link capacito value is given in Chapte 3. The DC link capacito consists of fou electolytic capacitos, two seies connected capacito pais in paallel in ode to sustain the DC link voltage and the DC link cuent. Futhemoe, additional capacitos, i.e. esonant link capacitos [8], distibuted among the half bidges seve as ovevoltage snubbes. The output filte paametes ae accoding to the design expessions given in Chapte 3. The inductos ae wound on ion powde coes manufactued by Micometals, efe to [8]. The filte capacitos consists of polypopylene capacitos manufactued by Ica. The contol algoithms ae implemented in the IEA MIMO contolle [7], which is based on the TMSC32C3 floating point DSP. The main chaacteistics of the IEA MIMO contolle ae, simultaneous sampling of 6 analogue inputs with 2 bits esolution, 8 analogue outputs, and a DSPLINK bus fo expansion boads, i.e. the PWM boad. The PWM boad consists of a tiangula caie wave geneato and compaatos in ode to geneate the instantaneous switching states of the VSCs. The sampling instants of the IEA MIMO ae synchonised to the tiangula caie end-points via the DSPLINK bus. Note that all 6 analogoue inputs ae used fo contol puposes, whee the final input is used fo the battey cuent efeence. The 8 analogue outputs ae used fo debug and contolle analysis. The cuents ae measued with LEM LA5P cuent tansduces, which povides galvanic isolation and high bandwidth. The AC voltages, i.e. gid

6. Expeiments 93 voltage and line filte capacito voltage, ae measued with tansfomes, wheeas the DC voltages, i.e. DC link voltage and the battey voltage, ae measued with LEM LV25P voltage tansduces. Hence, galvanic isolation is obtained also on the voltage measuements. The tansduce outputs ae conveted to suitable electonic voltage levels by opeational amplifies. The measuements shown in this chapte ae obtained with a Tektonix TDS 64A fou channel digitising oscilloscope, whee each channel is stoed by 2 sample points in memoy. The stoed data have then been tansfeed to a compute, whee MATLAB is used in ode to pefom futhe analysis and plotting of data. Howeve, in ode to educe the effect of measuement noise in the esults, the 2 samples ae split into 5 cells each containing fou adjacent samples. The time domain esults given in this chapte ae then povided as the mean values of each fou sample cell. This consideably deceases the noise in the measuement esults shown in this chapte. 6.2 Cuent contol veification Step esponse In ode to confim the tansient behaviou of the cuent contolles used in the battey chage, they have been exposed to step changes in the efeence cuents. In Figue 6.2, the step esponse of the line cuent contolle is shown. Note that epeated changes in both the d- and q-axis cuent components ae made simultaneously. This implies that the line cuent contolle does not ente steady state. Futhemoe, the pulses in the q-cuent component ae cented aound zeo in ode to pevent fom any active powe flow, in aveage, duing the measuement. The eason fo this is that the battey side of the unit is tuned off duing this measuement, in ode not to intefee with the line cuent contolle analysis. Howeve, the instantaneous active powe flow affects the DClink voltage, which esults in DC-link voltage contolle action that is added to the step changes in the q-component of the efeence cuent. This explains the slight deviation duing the pulses in the q-axis efeence cuent component shown in Figue 6.2. The deviation fom the simulated step esponse, shown in Figue 4.9, is appaent. Thee exist no simple explanation fo this deviation in the measuement. Howeve, uncetainties in model paametes, impefect decoupling of the d- and q axis components, the non-linea popeties of the VSC and measuement noise suely contibute to the deviation. Nevetheless, the step esponses shown satisfy the equiements of the application. In any case, the integatos povided in the oute cuent contol loop educe the cuent eo in steady state.

94 6. Expeiments [A] i 2d i 2d * 5 5 i 2q i 2q * -5-2 -5 - -5 5 5 Figue 6.2 t [ms] Step esponse in the d-and q-axis cuent components of the line cuent contolle, efeence cuents (gey) and esulting cuents (black). In Figue 6.3, the step esponse of the battey cuent contolle is shown. In this case, the confomity to the simulated step esponse shown in Figue 4.5 is good, except fo the DC offset in the battey cuent duing the cuent pulses. The DC offset is due to the fact that the integato, in the oute cuent contol loop, does not ente steady state. The selected time constant of the integato is longe than the width of the cuent pulses. [A] 5 i 2 i i 2 * 5-2 -5 - -5 5 5 t [ms] Figue 6.3 Step esponse of the battey cuent contolle, efeence cuent i * 2 (dak gey), oute cuent i 2 (black), and inne cuent i (light gey). 6.3 Chaging of battey equivalent The measued cuents when chaging the battey equivalent ae shown in Figue 6.4. Fom the figue, it is clea that the condition fo sinusoidal line cuent when chaging is met. Futhemoe, the eactive powe equiements of the filte capacitos ae accommodated by the VSC

6. Expeiments 95 esulting in unity powe facto fo the unit, which can be concluded fom the slight phase diffeence in between the oute and inne phase cuents. i 2a i a i 2 i [A] 2 - -2-5 - -5 5 5 Figue 6.4 t [ms] Chaging cuents. Top) battey cuents, oute cuent i 2 (black) and inne cuent i (gey). Bottom) line cuents, oute phase cuent i 2a (black) and inne phase cuent i a (gey). In Figue 6.5, the same cuents ae shown in a shote time scale. Note the high fequency oscillations of 35 khz contained in the cuents. Thei pesence ae unexplainable and attibuted to measuement and/o system noise. Nevetheless, the switching fequency cuent ipple of 5 khz is clealy seen in the inne inducto cuents, i.e. i and i a, shown in gey in the figue. The effective damping povided by the LCL-filtes pactically eliminates this content in the oute inducto cuents shown in black. [A] i 2a i a i 2 i 2 4.5 4.625 4.75 4.875 5 5.25 5.25 5.375 t [ms] Figue 6.5 Chaging cuents in the shot time scale. Top) battey cuents, oute cuent i 2 (black) and inne cuent i (gey). Bottom) line cuents, oute phase cuent i 2a (black) and inne phase cuent i a (gey). When the battey chage is idle unning, the cuent into the battey chage should be zeo in the ideal case. Howeve, losses in the passive filte and in the VSC cause an active cuent component in ode to peseve the DC-link voltage at its nominal value. The intoduced 4 µs dead time, o blanking time, in the IGBT dive cicuits causes low ode cuent hamonics in the phase cuents. Futhemoe, gid voltage

96 6. Expeiments distotion also causes low ode cuent hamonics. In Figue 6.6, the phase cuent when the unit is idle unning is shown. Note the high 5 th hamonic cuent component, which is mainly due to the blanking time of the VSC. The effect of the blanking time, i.e. the low ode cuent hamonics, is geatly educed by the MRI contolle as shown in the middle of Figue 6.6. In this case, the line cuent is pactically sinusoidal with fundamental fequency. This implies that the MRI contolle is capable of educing the intenally geneated cuent hamonics of the battey chage. As a consequence, the MRI contolle can be applied to an electical dive fo eduction of the toque ipple caused by the blanking time o/and the semiconducto fowad voltage dops. i 2a oiginal i 2a MRI i 2a [A].5 -.5.5 -.5 [A ms ].2. -5 - -5 5 5 oiginal MRI t [ms] Figue 6.6 5 5 2 25 3 35 Phase cuent when unit is idle unning. Top) oiginal contolle, middle) with MRI contolle, and bottom) hamonic content of the cuents above. The spectum of the phase cuents is shown in the lowe pat of the figue. The hamonic content of the phase cuent in the MRI contolle case is, in fact, educed down to the noise floo of the expeimental setup. Note that the RMS-values of the fundamental cuent components ae equal in the two cases. Futhemoe, the idle eactive cuent in the filte capacitos coesponding to.73 A ms, i.e. 5 % of the nominal line cuent accoding to the design given in Section 3.4, is accommodated by the VSC. h

6. Expeiments 97 6.4 Load balancing of a two-phase load In ode to confim the load balancing chaacteistics of the investigated battey chage, an asymmetical load is used. The asymmetical load consists of a puely esistive load, i.e. a lamp ballast, connected in between phases a and c. In fact, the thee phase diode ectifie is used also in this case, whee the b phase is disconnected by means of the fuse. Hence, the esulting load cuent contains equal amount of positive- and negative-sequence cuent components of fundamental fequency. The ideal esult of load balancing should theefoe coespond to a esulting line cuent which only contains the positive-sequence cuent component of fundamental fequency. In Figue 6.7, the esult of load balancing with the diect phase compensated active filte contolle is shown. Since the phase ode of the injected AF cuent is acb, it is clea that the injected AF cuent consists of a negative-sequence cuent component. Howeve, the esulting line cuent still contains an asymmety, which implies that the load is not totally compensated fo. This diffe fom the simulated esult shown in Figue 5.2, whee complete compensation of a simila load is obtained with the phase compensated active filte contolle. Fom the expeimental esult, it is clea that the amplitude of the injected negative-sequence cuent component is not sufficient in ode to cancel the asymmety in the line cuents. This is due to the sensitivity to the line cuent contolle paametes, which implies that the gain is not unity fo the negative-sequence cuent component. The sensitivity to the paametes of the line cuent contolle is educed by the MRI contolle, which is due to the integatos intoduced. In Figue 6.8, the esult when pefoming load balancing with the MRI contolle is shown. It is clea that the load is fully compensated fo in this case. The esulting line cuent contains only the positive-sequence cuent component of the two phase load, while the injected cuent by the shunt AF povides the negative-sequence cuent component of the load cuent. Hence, the advantageous chaacteistics of the intoduced negative-sequence oiented integato fo the negative-sequence cuent component ae confimed.

98 6. Expeiments i Load i Line i AF [A] - - - Figue 6.7 i Load i Line i AF [A] - - - Figue 6.8 2 3 4 t [ms] Phase cuents, a (black), b (dak gey), and c (light gey), when pefoming load balancing with the diect phase compensated contolle. Top) estimated load cuents, middle) esulting line cuents, and bottom) AF cuents. 2 3 4 t [ms] Phase cuents, a (black), b (dak gey), and c (light gey), when pefoming load balancing with the MRI contolle fo the negativesequence cuent component. Top) estimated load cuents, middle) esulting line cuents, and bottom) AF cuents. Note that the MRI contolle in this case only contains the negativesequence oiented integato. This implies that the pesence of cuent hamonics ae due to the effect caused by the blanking time and the gid voltage distotion, which is peviously descibed.

6. Expeiments 99 6.5 Hamonic filteing of a diode ectifie The hamonic filteing popety of the investigated battey chage is confimed by the filteing of the cuent hamonics poduced by the thee phase diode ectifie. The thee phase diode ectifie is loaded by an equivalent esisto, which is peviously descibed. Fo the diect phase compensated active filte contolle, the esult of hamonic filteing is shown in Figue 6.9. As can be seen, the measued hamonic filteing esult is quite poo. The hamonic eduction is only 5-7 % in the measued case, which should be compaed to the anticipated eduction of at least 9 % fom the theoetical analysis, efe to Section 5.3. The diffeence is again due to the sensitivity to the paametes in the line cuent contolle. The majo cause fo the emaining line cuent hamonics is given by the diffeence in the amplitudes of the injected cuent hamonics in compaison to the load cuent hamonics. This is concluded fom the spectum of the hamonic content of the cuents displayed in Figue 6.9, which indicates that the gain of the expeimental set-up is lowe than unity fo the cuent hamonics concened. Howeve, the phase compensation, i.e. the phase advance coesponding to thee samples, still impoves the hamonic filteing pefomance. This is concluded fom the fact that the emaining hamonic content of the line cuent is diectly given by the subtaction of the injected cuent hamonics fom the load cuent. This implies that the phase of the injected cuent hamonics coesponds to the load cuent hamonics. Howeve, this is only tue fo the lowe ode cuent hamonics, i.e. up to the 3 th cuent hamonic. Fo the highe ode cuent hamonics the phase coespondence is deteioated, which in fact was anticipated fom the theoetical analysis. In Figue 6., the measued esult obtained with the poposed MRI hamonic filte contolle is shown. The MRI contolle contains hamonic oiented integatos fo the 5 th up to the 25 th hamonic odes. The hamonic filteing esult is excellent and, futhemoe, completely in accodance with the theoetical analysis. The effect of the inseted otating integatos ae twofold. Fist, the gain deviation of the line cuent contolle is completely compensated fo, which implies that the gain is unity fo the coesponding hamonic fequencies. Second, the phase coespondence in between the injected cuent hamonics and the load cuent hamonics ae complete.

6. Expeiments i Load i Line i AF I h [A] - - - [A ms ] 2.5.5 Figue 6.9 i Load i Line i AF I h [A] - - - [A ms ] 2.5.5-2 3 4 5 6 7 t [ms] Load Line AF 5 7 3 7 9 23 25 29 3 35 37 Result of hamonic cuent filteing with the diect phase compensated active filte contolle. Fom top to bottom: estimated load cuent, line cuent, injected AF cuent, and the hamonic content of the cuents. - 2 3 4 5 6 7 t [ms] Load Line AF 5 7 3 7 9 23 25 29 3 35 37 Figue 6. Result of hamonic cuent filteing with the MRI contolle. Fom top to bottom: estimated load cuent, line cuent, injected AF cuent, and the hamonic content of the cuents. h h

6. Expeiments The additional advantageous chaacteistic of the MRI contolle, egading the hamonic selectivity, is also confimed by the measued esults. In this case, this coesponds to the fact that the highe ode cuent hamonics ae left unfilteed. 6.6 Dynamics of the MRI contolle Fom the theoetical analysis on the dynamics of the MRI hamonic filte contolle, it is found that the esponse times of the hamonic oiented integatos ae given by the selected time constants. This is futhe confimed by the simulated esults. Since the same value fo the time constants of the hamonic oiented integatos ae selected fo the expeimental implementation, the anticipated esponse time of the MRI contolle should thus be ms. In Figue 6., the hamonic filteing cuents at tun on of the MRI contolle ae shown. i Load i Line i AF [A] - - - -2-2 3 4 5 6 7 t [ms] Figue 6. Tun on of the MRI hamonic filte contolle, top) estimated load cuent, middle) esulting line cuent, and bottom) injected AF cuent. The hamonic oiented integato outputs fo the lowest and highest odes of the coesponding cuent hamonics ae displayed in Figue 6.2. In this case the esponse time of the integatos ae extended compaed to the simulated case. In fact, the esponse time is appoximately doubled. Also the integatos oiented to the highe ode hamonics have futhe a polonged settling time. The extended esponse time of the hamonic oiented integatos is cetainly due to a numbe of easons. Hee, two easons ae given. Fist, the intepetation of the integato time constant is obtained fom the line

2 6. Expeiments cuent contolle paametes accoding to (5.3). Consequently, vaiations in the system paametes deceases the validity of this intepetation, which causes anothe time constant than the anticipated. Second, the blanking time intoduced in the VSC inceases the settling time of the integatos, since the effect of the blanking time is dependent on the opeating point of the convete. 5 th 7 th [V] 2-2 23 th 25 th 2-2 -2-2 3 4 5 6 7 t [ms] Figue 6.2 Tun on of the MRI hamonic filte contolle. Integato outputs oiented to the cuent hamonics of odes 5 th and 7 th (top), and 23 d and 25 th (bottom). Note that the shown dynamic esponse of the MRI contolle only descibe the tun on of the hamonic oiented integatos. Hence, the tansient behaviou concening load changes is not displayed. Howeve, the tansient behaviou of the MRI contolle is nevetheless impoved. The smooth stat of the integatos neutalises the tansient coupling in the high pass filte output shown in Figue 5.6. In fact, the tansient esponse is vey well descibed by the dynamic esponse shown in this section.

7 Conclusions In this thesis, a high pefomance battey chage fo EVs is pesented. The dawbacks of line-commutated battey chages in tems of the cuent hamonic geneation and the eactive powe equiement, ae ovecome by the use of self commutated chage topologies. By including powe line conditioning capabilities in the battey chage, a viable concept fo a fast chaging infastuctue is obtained. The use of the investment in the fast chaging infastuctue inceases, since both EV uses and powe distibutos can utilise the battey chages fo thei own puposes. The EV use extends the diving ange of the EV wheeas the powe distibuto inceases the powe quality. Futhemoe, the investigated concept is not esticted to battey chages, but can also be applied to othe applications involving the powe gid, such as photo voltaic systems and uninteuptible powe supplies (UPS). The investigated battey chage consists of a thee phase VSC and a half bidge DC-DC convete connected back to back acoss a DC-link capacito. Caie wave based PWM is employed. Futhemoe, the switching fequency hamonics ae attenuated by thid ode LCL-filtes. The advantageous low fequency chaacteistics of the LCL-filte facilitates bette utilisation of the DC-link voltage when pefoming gid conditioning. Modelling aspects and design consideations fo the battey chage ae given in the thesis. The contol system of the battey chage consists of model based discete contolles, whee the synchonous efeence -fame ae applied fo the line cuent contolle. Basically, the deived contol system consists of cascaded P- and PI-contolles. Additional feed fowad ae employed in ode to impove the tansient behaviou of the contol system. Futhemoe, the cascaded cuent contolles ae intepeted as linea state feedback contolles in ode to pefom theoetical analysis and confim stability of the contol system. The use of the synchonous efeence -fame in the line cuent contolle enables diect sepaation between the fundamental, the

4 7. Conclusions negative-sequence and the hamonic cuent components. This is utilised in the load cuent identification pat of the active filte contol stuctue. The model based line cuent contolle suffes fom the inheent phase deviation caused by the PWM technique employed. This is cicumvented by use of the diect phase compensation method. The expeimental esults, howeve, eveal othe weaknesses of this active filte contolle, such as the sensitivity to system paametes and the inability to compensate fo the cuent hamonics caused by the shunt AF itself due to the non-linea popeties of the VSC, such as the blanking time. Instead a contol stuctue fo shunt AFs based on seveal integatos in multiple otating efeence fames is poposed. The main objectives with the poposed MRI contolle ae to educe the sensitivity to system paametes and futhe impove the steady state pefomance of the shunt AF. An additional featue obtained by the poposed MRI contolle is hamonic selectivity. The supeio pefomance of the MRI contolle is veified both theoetically and expeimentally. It is found that the intoduced otating integatos pactically eliminates the coesponding cuent hamonics. Futhemoe, the dynamic pefomance is detemined by the integal time constant selected. Also, the MRI contolle neutalises the coupling duing tansient opeation which is due to the low pass filteing popety of the hamonic oiented integatos.

Refeences [] H. Akagi, Y. Kanazawa and A. Nabae, Instantaneous Reactive Powe Compensatos Compising Switching Devices without Enegy Stoage Components, IEEE Tansactions on Industy Applications, Vol. 2, No. 3, May/June 984, pp. 625-63. [2] H. Akagi, A. Nabae and S. Atoh, Contol Stategy of Active Powe Filtes Using Multiple Voltage-Souce PWM Convetes, IEEE Tansactions on Industy Applications, Vol. 22, No. 3, May/June 986, pp. 46-465. [3] H. Akagi, New Tends in Active Filtes fo Powe Conditioning, IEEE Tansactions on Industy Applications, Vol. 32, No. 6, Novembe/Decembe 996, pp. 32-322. [4] S. Bhattachaya, D.M. Divan and B. Banejee, Synchonous Fame Hamonic Isolato Using Active Seies Filte, EPE 9 Confeence Poceedings, Fienze, Italy, Vol. 3, Septembe 99, pp. 33-335. [5] M. Bojup, P. Kalsson, M. Alaküla and B. Simonsson, A Dual Pupose Battey Chage fo Electic Vehicles, PESC 98 Confeence Poceedings, Fukuoka, Japan, Vol., May 998, pp. 565-57. [6] M. Bojup, P. Kalsson, M. Alaküla and Las Getma, A Multiple Rotating Integato Contolle fo Active Filtes, EPE 99 Confeence Poceedings, Lausanne, Switzeland, Septembe 999. [7] A. Calsson, The back-to-back convete; contol and design, Licentiate s Thesis, Depatment of Industial Electical Engineeing and Automation, Lund Institute of Technology, Lund, Sweden, May 998.

6 Refeences [8] A. Edis, A.S. Mehaban, M. Rahman, L. Gyugyi, S. Aabi and T. Reitman, Contolling the flow of Real and Reactive Powe, IEEE Compute Applications in Powe, No., 998, pp. 2-25. [9] T. Glad and L. Ljung, Regleteknik. Gundläggande teoi, (in Swedish), Studentlitteatu, Lund, Sweden, 989. [] J.D. Glove and M. Sama, Powe System Analysis & Design, PWS Publishing Company, 2nd edition, 994. [] L. Hanefos, On Analysis, Contol and Estimation of Vaiable- Speed Dives, Ph. D. Thesis, Electical Machines and Dives, Depatment of Electic Powe Engineeing, Royal Institute of Technology, Stockholm, Sweden, 997. [2] H.J. Haubich and A.R. Heide, Chaging Stategies fo Electic Vehicles and thei Consequences fo Powe Supply, EPE 97 Confeence Poceedings, Tondheim, Noway, Vol., Septembe 997, pp. 56-565. [3] M. Hemmingsson, A Poweflow Contol Stategy to Minimize Enegy Losses in Hybid Electic Vehicles, Licentiate s Thesis, Depatment of Industial Electical Engineeing and Automation, Lund Institute of Technology, Lund, Sweden, Januay 999. [4] J. Hokfelt and F. Tufvesson, Övetonenas nätpåvekan i låg- och mellanspännings stadsnät, (in Swedish), Maste s Thesis, Depatment of Industial Electical Engineeing and Automation, Lund Institute of Technology, Lund, Sweden, Septembe 993. [5] J. Holtz, Pulsewidth Modulation fo Electonic Powe Convesion, Poc. of the IEEE, Vol. 82, No. 8, August 994, pp. 94-24. [6] H. Kahlen and G. Maggeto, Electic and Hybid Vehicles, EPE 97 Confeence Poceedings, Vol., Septembe 997, pp..3-.54. [7] P. Kalsson, M. Bojup, M. Alaküla and L. Getma, Efficiency of Off-Boad, High Powe, Electic Vehicle Battey Chages with Active Powe Line Conditioning Capabilities, EPE 97 Confeence Poceedings, Tondheim, Noway, Vol. 4, Septembe 997, pp. 4688-4692.

Refeences 7 [8] P. Kalsson, Quasi Resonant DC Link Convetes Analysis and Design fo a Battey Chage Application, Licentiate s Thesis, Depatment of Industial Electical Engineeing and Automation, Lund Institute of Technology, Lund, Sweden, Novembe 999. [9] K.W. Klontz, D.M. Divan and D.W. Novotny, An Actively Cooled 2 kw Coaxial Winding Tansfome fo Fast Chaging Electic Vehicles, IEEE-IAS Conf. Rec., Denve, USA, Octobe 994, pp. 49-54. [2] K. Kubo and K. Sakai, Feedfowad Voltage Compensation fo Digital Active Filte Using Fequency Domain Decomposition, EPE 97 Confeence Poceedings, Tondheim, Noway, Vol. 4, Septembe 997, pp. 4.786-4.79. [2] N.H. Kutkut, D.M. Divan, D.W. Novotny and R.H. Maion, Design Consideations and Topology Selection fo a 2-kW IGBT Convete fo EV Fast Chaging, IEEE Tansactions on Powe Electonics, Vol. 3, No., Januay 998, pp. 69-78. [22] J.W. Lee, An Intelligent Cuent Contolle Using Delay Compensation fo PWM Convetes, EPE 97 Confeence Poceedings, Vol., Septembe 997, pp..342-.347. [23] M. Lindgen, Filteing and Contol of a Gid-connected Voltage Souce Convete, Licentiate s Thesis, Depatment of Electic Powe Engineeing division of Electical Machines and Powe Electonics, Chalmes Univesity of Technology, Gothenbug, Sweden, Septembe 995. [24] M. Lindgen, Modelling and Contol of Voltage Souce Convetes Connected to the Gid, Ph. D. Thesis, Depatment of Electic Powe Engineeing division of Electical Machines and Powe Electonics, Chalmes Univesity of Technology, Gothenbug, Sweden, Novembe 998. [25] P. Lundbeg, Gid-connected NPC Convete in Load Balancing Applications, Licentiate s Thesis, Depatment of Electic Powe Engineeing division of Electical Machines and Powe Electonics, Chalmes Univesity of Technology, Gothenbug, Sweden, Novembe 994. [26] J.M. Maciejowski, Multivaiable Feedback Design, Addison- Wesley, 989.

8 Refeences [27] N. Mohan, T.M. Undeland and W.P. Robbins, Powe Electonics; Convetes, Applications, and Design, Wiley, New Yok, USA, 2nd edition, 995. [28] S. Ogino and Y. Kimua, Fuel Cell Poweed Electic Vehicle, EVS 3 Confeence Poceedings, Osaka, Japan, Vol., Octobe 996, pp. 67-674. [29] D. Ouvekek, Who says you can t pass high powe though a paddle?, EVS 2 Confeence Poceedings, Anaheim, USA, Vol., Decembe 994, pp. 62-68. [3] D. Owen, J. Simpson and J. McGuie, UK Electic Vehicle Chaging Infastuctue Case Study, EVS 2 Confeence Poceedings, Anaheim, USA, Vol., Decembe 994, pp. 36-44. [3] S. Rahman and G.B. Shestha, An investigation into the impact of electic vehicle load on the electic utility distibution system, IEEE Tansactions on Powe Delivey, Vol. 8, No. 2, Apil 993, pp. 59-597. [32] O. Simon, H. Spaeth, K.-P. Juengst and P. Komaek, Expeimental Setup of a Shunt Active Filte Using a Supeconducting Magnetic Enegy Stoage Device, EPE 97 Confeence Poceedings, Tondheim, Noway, Vol., Septembe 997, pp. 447-452. [33] R. Stzelecki, L. Fackowiak and G. Benysek, Hybid Filtation in Conditions of Asymmetic Nonlinea Load Cuent Pulsation, EPE 97 Confeence Poceedings, Tondheim, Noway, Vol., Septembe 997, pp..453-.458. [34] T. Svensson, On Modulation and Contol of Electonic Powe Convetos, Ph. D. Thesis, Depatment of Electical Machines and Powe Electonics, Chalmes Univesity of Technology, Gothenbug, Sweden, Novembe 988. [35] M. Yano, S. Kuamochi and N. Nanaumi, New Contol Method of Hamonic Cuent Compensation Using Individual Rotaing P-Q Fame of Coesponding Fequency, EPE 97 Confeence Poceedings, Tondheim, Noway, Vol. 4, Septembe 997, pp. 4842-4847.

Refeences 9 [36] W. Zhang, On Feedback Contol of Active DC Filtes in HVDC Cable Links with Coastal Lines, Licentiate s Thesis, Division of High Powe Electonics, Depatment of Electic Powe Engineeing, Royal Institute of Technology, Stockholm, Sweden, Decembe 995. [37] K.J. Åstöm and B. Wittenmak, Compute Contolled Systems; Theoy and Design, Pentice-Hall Intenational, Englewoods Cliffs, USA, 2nd edition, 99.

Refeences

A Vecto notation A. Thee phase to two phase tansfomation Thee phase quantities (s a, s b and s c ) ae tansfomed to two phase vecto epesentation by s s js s e j j2π j4π αβ = α + β = 2 a + s b e 3 3 + s c e 3 (A.) o in eal notation ( ) s α = 2 sa 3 2 ( sb + sc ) sβ = 2 ( sb sc ) (A.2) The invese, two phase to thee phase tansfomation fo a balanced system, i.e. is given by sa + sb + sc = (A.3) sa = 2 3 sα sb = s + 6 α 2 s sc = 6 s α 2 s β β (A.4) If the thee phase quantities ae sinusoidally vaying with ms-value S, angula fequency ω and phase shifted 2 in time sa = 2Scos( ωt) 2π sb = 2Scos( ωt 3 ) 4π sc = 2Scos( ωt 3 ) (A.5)

2 A. Vecto notation then the coesponding vecto is s = Se jω 3 t (A.6) Thus, the vecto otates with constant magnitude fequency ω in the stationay efeence αβ-fame. 3S and angula A.2 Vecto tansfomation A vecto in the stationay efeence αβ-fame is tansfomed into the synchonously otating efeence -fame oiented to the integal of gid voltage vecto, see Figue A., by subtacting the angle diffeence θ αβ s = s e jθ (A.7) whee the angle diffeence, tansfomation angle θ, is given by ( ) αβ jω t αβ αβ j ω t π π e = Ene ψ = e dt = Ψ ne 2 θ = ωt 2 The tansfomation can also be expessed in eal notation as sd sq = cosθ sinθ sinθ s cosθ s Hence, a otating vecto in the stationay efeence αβ-fame s Se j = 3 t αβ ( ω ϕ ) α β (A.8) (A.9) (A.) is tansfomed into a vecto in the synchonous efeence -fame ( ) ( ) αβ j ω t π j π ϕ 2 2 s = s e = 3 Se = s + js (A.) whee the eal and imaginay pats ae constants, i.e. DC quantities. d q Figue A. e q s q s β β s s α s d d θ α Ψ = e dt Relationship between the stationay efeence αβ-fame and the synchonously otating efeence -fame.

A. Vecto notation 3 The invese tansfomation, fom the synchonously otating efeence -fame to the stationay efeence αβ-fame is equivalently given by αβ jθ s = s e (A.2) In eal notation the invese tansfomation is given by s s α β cosθ = sinθ A.3 Instantaneous powe sinθ sd cosθ sq (A.3) The thee phase to two phase tansfomation given in (A.) is powe invaiant, i.e. the instantaneous powe can be expessed as p= ua ia + ub ib + uc ic (A.4) o o ( ) = + p=re u αβ αβ i uα iα uβ iβ (A.5) ( ) = + p=re u i u i u i d d q q (A.6)

4 A. Vecto notation

B Nomalisation B. Pe unit definition The base values fo powe, voltage and fequency ae defined accoding to Sbase = Sn Ubase = En (B.) ω = ω base whee S n is the ated powe, E n is the line to line ms-value of the gid voltage and ω is the fundamental gid fequency. The base values fo cuent and impedance ae then obtained accoding to I base Sbase = = 3 In (B.2) U base Z base 2 Ubase U = = S I base base base (B.3) whee I n is the ated line (phase) cuent. Z base can futhe be divided into bases fo inductance and capacitance accoding to C L base base Zbase = (B.4) ω = ω base base Z base (B.5) The nomalised (pe unit) values of the electical paametes ae then given by R pu.. R = Z [ Ω] base (B.6)

6 B. Nomalisation C pu.. L pu.. L H basel X = = ω H = L Z Z [ ] [ ] L,[ Ω] base base C [ F] = = ω basezbasec[ F] = Cbase Z base base Z = X base ω basec[ F] C,[ Ω] (B.7) (B.8)