Voltage and Current Harmonics Case Study

Transcription

1 7 Voltage ad Curret Harmoics Case Study Agelo Baggii ad Zbigiew Hazelka C7.1 SELECTION AND RATING OF TRANSFORMERS FOR A SIX-PULSE CONVERTER [1] Whe the harmoic spectrum is kow, or at least ca be measured with a certai reliability or predicted, the additioal losses ca be easily calculated. The process of calculatio should be made through the followig steps: 1. Determiatio of all the compoets of additioal losses due to the presece of harmoics. 2. Determiatio of the harmoic spectrum, either by measuremet or by estimatio, takig ito accout all harmoic geeratig equipmet, i particular electroic coverters. 3. Calculatio of the cotributio of each harmoic compoet ad determiatio of total additioal losses. I practice, it is importat to use the real harmoic curret magitudes rather tha theoretical values. Table C7.1 shows the calculated additioal losses, for harmoic currets up to order 25, for two trasformers at ormal evirometal temperature, assumig the curret harmoic spectrum illustrated i Figure C7.1. Hadbook of Power Quality Edited by Agelo Baggii 28 Joh Wiley & Sos, Ltd

2 46 Table C7.1 Additioal losses calculated i the presece of o-siusoidal currets Loss type First trasformer Secod trasformer (21 5 C) (22 8 C) Rated power (kva) Additioal with siusoidal curret (W) Additioal with o-siusoidal curret (W) Theoretical Typical.1.5. Figure C Harmoic order.8 Theoretical ad actual values of curret harmoics for a six-pulse coverter (i pu) The results demostrate that the trasformer characteristics play a importat role i determiig the losses with harmoic loads. The trasformers i this example were measured at slightly differet temperatures (21 5 C for the first ad 22 8 C for the secod); this will ot chage the reliability of results. C7.1.1 Calculatio of the K Factor Table C7.2 shows the calculatio of the K factor for the harmoic spectrum of Figure C7.1 o a per uit basis. The first step is the calculatio of the r.m.s. value of total curret I, 1.41 i this case, after which the squares of the proportioate values of each harmoic curret ca be calculated, leadig to the value of K. For such a load, a trasformer with a K ratig of 9 would be appropriate for a six-pulse coverter.

3 Table C7.2 Reductio factors for curret harmoics 47 Harmoic order I h /I 1 I h /I 1 2 I h /I I h /I 2 I h /I 2 h Sum = Total (r.m.s.) = 1 41 K factor = C7.1.2 Calculatio of the Factor K The first step i establishig factor K (Table C7.2) is to discover the value of e, the ratio of eddy curret loss to total load loss at fudametal frequecy. The trasformer maufacturer should be able to provide this, otherwise it is likely to lie i the rage of.5 to.1. The expoet q depeds critically o the costructio of the trasformer ad should also be Table C7.3 Reductio factors for curret harmoics Harmoic order I h /I 1 I h /I 1 2 h I h /I 2 h Sum = [a]= Total (r.m.s.) = 1 41 a I 1 /I 2 = e/ e + 1 = 91 I 1 /I 2 = 9227 K 2 = K = 1 18

4 48 available from the maufacturer. It is likely to lie i the rage 1.5 to 1.7. As before, the calculatios are based o the theoretical values from Figure C7.1. I practice, the trasformer would eed to be derated to % (1/1.18) of omial power ratig whe supplyig a six-pulse coverter. C7.2 DERATING CABLES As described i Sectio 7.6.2, the curret amplitude i the eutral due to the third harmoic could exceed i amplitude the phase curret at the fudametal frequecy. I this case the eutral curret should be cosidered with regard to the sizig of the circuit cables. This example is related to a office buildig where four differet harmoics spectra have bee used to evaluate the cable size to be istalled. The system is a three-phase circuit with a 32 A rated load to be istalled usig a four-core EPR isulated cable laid directly oto the wall. C7.2.1 Scearios These are as follows: 1. Absece of harmoics. For this curret it is commo practice to use a copper coductor cable with a 4 mm 2 cross-sectio with a capacity of 35 A [5]. 2. A value of 22 % of the third-order harmoic (Figure C7.2). For this spectrum the eutral curret will be I N = = 21 1A, I N <I F, so the value is selected o the basis of the lie curret. Applyig a.86 reductio factor (Table 7.12), the equivalet load curret is 32/ 86 = 37 2 A. For this value the cable sectio has a6mm 2 cross-sectio with a capacity of 44 A [5]. For a value of 42 % of the third-order harmoic (Figure C7.3), I N = = 4.3 A, I N >I F, so the value is selected o the basis of the eutral curret. Applyig a.86 reductio factor, the equivalet load curret is 4 3/ 86 = 46 9 A. For this value the cable sectio has a 1 mm 2 cross-sectio with a capacity of 6 A [5] (%) % of 3rd harmoic Figure C7.2 Curret waveform ad its spectrum

5 % % of 3rd harmoic Figure C7.3 Curret waveform ad its spectrum (%) Figure C7.4 Curret waveform ad its spectrum 3. Third-order, harmoic-rich eviromet, as i Figure C7.4. The eutral curret will be I N = = A, I N >I F, so the value is selected o the basis of the eutral curret. Applyig a reductio factor equal to 1, the equivalet load curret is /1 = A. For this value the cable sectio has a 35 mm 2 cross-sectio with a capacity of 128 A [5]. C7.3 HARMONIC SOURCE LOCATION I the evet of sigificat distortio of the supply etwork voltage at the PCC betwee the electricity supplier ad customer, the source of disturbace should be located. This becomes of particular sigificace whe formulatig cotracts for electric power supply or chargig for worseig the quality of supply. I may cases also a quatitative determiatio of the supplier ad customer(s) cotributio to the total voltage distortio at the PCC is required.

6 5 Supply system Load Measurig poit P () = U () I () cos(θ u() Θ i() ) P () P () < Figure C7.5 The priciple of locatig the th harmoic source o the basis of its active power measuremet The most commo practical method for locatig harmoic sources is based o determiig the directio of active power flow for give harmoics, though may authors idicate its limitatios ad propose others methods (ivestigatio of the directio of reactive power flow ad the critical impedace, iterharmoic ijectio, determiig voltage ad curret relative values, etc. [34],[35]). I most cases these methods, apart from their techical complexity, require precise iformatio o values of equivalet parameters of the aalyzed system, which are difficult to access, or ca oly be obtaied as a result of costly measuremets. Accordig to the directio of active power flow method, the domiat source of a give harmoic (of order ) ca be located by determiig the directio of this harmoic active power flow at various poits of the system (Figure C7.5). A o-zero value of P = U I cos ( u i ) is the effect of the iteractio of voltage ad curret with the same frequecy. A liear load supplied with distorted voltage draws active power for each harmoic: P. If o-liear elemets exist at the customer side, the active power for some harmoics ca be supplied to the etwork: P <. The sig of P ca be determied by meas of measurig the phase agles of the voltage ad curret of the same order: u ad i. The priciple of this method is explaied i the example of a sigle-phase circuit, show i Table C7.4 (the supply voltage source is U S, L S, where the oliear load is the thyristor power cotroller (TYR1, TYR2, resistace R ONL, iductace L ONL, which is the source of harmoic currets of order = 2k ± 1 = 3, 5, 7, 9, 11, 13, 15, (for k = ). There cases, distiguished by locatio of the voltage distortio source, are discussed for the power cotroller located: (i) upstream of the PCC, (ii) dowstream of the PCC, ad (iii) harmoic sources at both sides of the PCC.

7 Table C7.4 Example simulatios illustratig the method for harmoic source locatio based o the active power measuremet Waveforms of voltage Active powers of idividual ad curret harmoics Model of the electric power etwork with harmoic source Harmoic source at the supplier s side Active powers of idividual harmoics have a positive sig. The supplier is resposible for the voltage waveform distortio I S L S L S PCC I ONL R ONL.8 I i Amps U i Volts R OL.6 U S.4 L ONL L OL TYR2 TYR Time (s) Harmoic source at customer s side Active powers of give harmoics have a egative sig. The customer is resposible for the voltage waveform distortio. IS L S L S PCC I OL R ONL I i Amps U i Volts R OL. U S L ONL L OL TYR2 TYR Time (s)

8 Table C7.4 (Cotiued) Waveforms of voltage Active powers of idividual ad curret harmoics Model of the electric power etwork with harmoic source Harmoic source at both the customer s ad supplier s side Depedig o the cotrol agle of thyristor switches, oe of the parties, either the supplier or the customer, will be the domiat cotributor to voltage distortio IS L S L S PCC I ONL I i Amperes. U i Volts R ONL1 R ONL2.4 U S TYR1 TYR2 TYR3 TYR Time (s) Load 1 Load 1

9 BIBLIOGRAPHY 53 [1] Arrillaga J., Watso N. R., Che S., Power system quality assessmet, Joh Wiley & Sos, Ltd, Chichester, 2. [2] Arseau R., Filipski P. S., Zelle J., A VA-meter-error aalyzer. IEEE Trasactios o Power Delivery, vol. 6, o. 4, [3] Baggii A., Zaoli F., Progetto di trasformatori per l alimetazioe di azioameti e carichi o lieari. VIII Semiario Iterattivo su Azioameti elettrici iovazioi tecologiche e problematiche emergeti, Bressaoe (BZ), 1 12 marzo [4] CEI 14-4/1983, Trasformatori di poteza. [5] CEI UNEL 3524/1, Cavi elettrici isolati co materiale elastomerico o termoplastico per tesioi omiali o superiori a 1 V i correte alterata e 15 V i correte cotiua. Portate di correte i regime permaete per posa i aria, [6] Chapma D., Harmoics causes ad effects. Leoardo Power Quality Applicatio Guide Part 3.1, 21. [7] Correggiari F., Costruzioe di macchie elettriche, Cisalpio Goliardica, Mila. [8] Datta S. K., Nafsi A., Distributio relay performace uder harmoics coditios. PQA 92, Atlata, Georgia, USA, [9] Desmet J., Baggii A., Harmoics eutral sizig i harmoic rich istallatios. Leoardo Power Quality Applicatio Guide Part 3.5.1, 23. [1] Desmet J., Delaere G., Harmoics selectio ad ratig of trasformers. Leoardo Power Quality Applicatio Guide Part 3.5.2, 25. [11] Elmore W. A., Kramer C. A., Zocholl E., Effect of waveform distortio o protective relays. IEEE Trasactios o Idustry Applicatios, vol. 29, o. 2, [12] EN 516, Voltage characteristics of electricity supplied by public distributio systems. [13] Fassbider S., Harmoics passive filters. Leoardo Power Quality Applicatio Guide Part 3.3.1, 23. [14] Girgis A. A., Nims J. W., Jacomio J., Dalto J. G., Bishop A., Effect of voltage harmoics o the operatio of solid-state relays i idustrial applicatios. IEEE Trasactios o Idustry Applicatios, vol. 28, vol. 5, [15] Gruzs T. M., A survey of eutral currets i three-phase computer power systems. IEEE Trasactio o Idustry Applicatios, vol. 26, o. 4, 199. [16] Hazelka Z., Bie A., Harmoics iterharmoics. Leoardo Power Quality Applicatio Guide Part 3.3.1, 24. [17] IEC , Electrical istallatios of buildigs Part 5-52: Selectio ad electio of electrical equipmet Wirig systems. [18] IEC , Historical ratioale for the limitatio of power-frequecy coducted harmoic curret emissios from equipmet i the frequecy rage up to 9 khz, Techical Report. [19] IEC , Electromagetic compatibility (EMC) Part 2-1: Eviromet Descriptio of the eviromet: Electromagetic eviromet for low-frequecy coducted disturbaces ad sigallig i public power supply systems, 199. [2] IEC , Electromagetic Compatibility (EMC) Part 2-2: Eviromet Compatibility levels for low frequecy coducted disturbaces ad sigallig i public low-voltage power supply systems. [21] IEC , Limits for harmoic curret emissios (equipmet iput curret 16 A per phase). [22] IEC , Electromagetic compatibility (EMC) Part 4: Testig ad measuremet techiques Sectio 7: Geeral guide o harmoics ad iterharmoics measuremets ad istrumetatio for power supply systems ad equipmet coected thereto.

10 54 [23] IEC TC 64 WG 2, Curret-carryig capacity ad related overcurret protectio, Revisio of sectio 523", September [24] IEEE , IEEE Recommeded Practices ad Requiremets for Harmoic Cotrol i Electrical Power Systems, [25] IEEE 1159, Recommeded practice for moitorig electric power quality. [26] Karve S., Harmoics active harmoic coditioers. Leoardo Power Quality Applicatio Guide Part 3.3.3, 21. [27] Norma CEI 64-8/5, Impiati elettrici utilizzatori a tesioe omiale o superiore a 1 V i correte alterata e a 15 V i correte cotiua. Parte 5: Scelta ed istallazioe dei compoeti elettrici, [28] Power System Harmoics, Power Techologies, Ic., [29] Purkayastha I., Savoce P. J., Effect of harmoics o power measuremet. IEEE Trasactios o Idustry Applicatios, vol. 26, o. 5, 199. [3] Shepherd W., Zakikhai P., Eergy flow ad power factor i o-siusoidal circuits, Cambridge Uiversity Press, New York. [31] Stade D., Shau H., Ifluece of voltage harmoics o sigle-phase earth fault currets. PQA 91. [32] Tsukamoto M., Kouda I. N., Miowa Y., Nishimura S., Advaced method to idetify harmoics characteristic betwee utility grid ad harmoic curret sources. 8th Iteratioal Coferece o Harmoics ad Quality of Power, Athes, Greece, October, [33] West K., Harmoics true RMS the oly true measuremet. Leoardo Power Quality Applicatio Guide Part 3.2.2, 21. [34] Xu Wilsu, Liu Yilu, A method for determiig customer ad utility harmoic cotributios at the poit of commo couplig. IEEE Trasactios o Power Delivery, vol.15, o.2, 2. [35] Xu Wilsu, Liu Xia, Liu Yilu, A ivestigatio o the validity of power-directio method for harmoic source determiatio. IEEE Trasactios o Power Delivery, vol. 18, o. 1, 23. [36] Yacamii R., Chag S. C., Noise ad vibratio from iductio machies fed from harmoic sources. Proceedigs of IEEE ICHPS VI, Bologa, September, [37] Żeżeleko I. W., Harmoics i power system supplyig idustrial loads, Elektroatomizdat, Moscow, 1994 (i Russia).