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
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) 125 16 Additioal with siusoidal 52 1721 curret (W) Additioal with o-siusoidal curret (W) 871 4351.25.2.15.2.175.14 Theoretical Typical.1.5. Figure C7.1.11.91.45.77.29.59.15.53.43.4.1.9 5 7 11 13 17 19 23 25 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.
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 2 1 1 1 966 9227 9227 5 2 4 1921 369 9227 7 14 196 1345 181 8862 11 91 83 874 76 9246 13 77 59 74 55 9246 17 58 34 557 31 8971 19 56 31 538 29 1 446 23 43 18 413 17 925 25 4 16 384 15 9227 Sum = 1 838 8 3476 Total (r.m.s.) = 1 41 K factor = 8 3476 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 2 1 1 1 1 2 4 15 4258 617 14 196 27 3317 5357 91 83 58 9342 488 77 59 78 2895 4642 58 34 123 5274 4155 56 31 149 2386 468 43 18 26 582 3818 4 16 237 9567 387 Sum = 1 838 [a]= 4 7511 Total (r.m.s.) = 1 41 a I 1 /I 2 = 4 3839 e/ e + 1 = 91 I 1 /I 2 = 9227 K 2 = 1 3985 K = 1 18
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 84.75 % (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 = 32 22 3 = 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 = 32 42 3 = 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]. 1 8 6 4 2 2 4 6 8 1 (%) 1 9 8 7 6 5 4 3 2 1 22 % of 3rd harmoic 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 Figure C7.2 Curret waveform ad its spectrum
49 1 1 8 6 4 2 2 4 6 8 1 % 9 8 7 6 5 4 3 2 1 42% of 3rd harmoic 1 2 3 4 5 6 7 8 9 11112131415161718192212223 Figure C7.3 Curret waveform ad its spectrum 15 1 5 5 1 1 9 8 7 6 5 4 3 2 1 15 (%) 1 2 3 4 5 6 7 8 9 111121314151617181922122 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 = 32 1 31 3 = 125 76 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 125 76/1 = 125 67 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.
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 = 1 2 3 ). 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.
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. 2 24 I S L S L S PCC I ONL 1.4 1.2 1. 1 12 R ONL.8 I i Amps U i Volts R OL.6 U S.4 L ONL.2. 1 12 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 L OL 1 9 8 7 6 5 4 3 TYR2 TYR1 2 24 2 1 1 3 4 5 6 7 8 9 1 11 12 13 14 15 2 13 14 15 16 17 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 8. 24. I OL R ONL 1 2 3 4 5 6 7 8 9 11112131415 4. 12. 1..5..5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 1 9 8 7 6 5 4 3 2 1 I i Amps U i Volts R OL. U S L ONL 4. 12. L OL TYR2 TYR1 24. 8. 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 1 13 14 15 16 17 Time (s)
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. 8. 28 IS L S L S PCC.8 1.4 I ONL1 4. 14. 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 I i Amperes. U i Volts R ONL1 R ONL2.4 U S.8 9 8 7 6 5 4 4. 14 3 2 28 8. 1 TYR1 TYR2 TYR3 TYR4 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 1 13 14 15 16 17 Time (s) Load 1 Load 1
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