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Transcript

LARGE TRANSFORMERS FOR POWER ELECTRONIC LOADS O.W. Andersen, Senior Member IEEE Norwegian Inst. of Technology, N-7034 Trondheim, Norway Abstract - The transformers described here are in the multimegawatt range. They are rapidly becoming more important and have characteristics and features that are different in many ways from those of normal power transformers. Information about them has been incomplete, scattered and hard to find in the literature. Harmonics are of prime importance in these transformers. Their appearance and suppression are explained with an emphasis on making it easy to understand. Different winding arrangements are presented and their characteristics explained. Cores with gaps to limit inrush currents are also discussed. I. INTRODUCTION Starting with six pulse loads, the line currents are analyzed for their harmonic content. It is explained how transformers can be used to increase the number of pulses and how this eliminates certain harmonics and reduces others. The relative merits of different winding arrangements are discussed. It is also explained how filter windings can be arranged for optimum filter performance, with further reduction of the harmonic content. Results of theoretical analysis of harmonics are confirmed, using numerical circuit analysis. The theory assumes that the three phase primary voltages are sinusoidal and balanced and that firing angles are precisely the same in all the phases. In practice, there will always be deviations from these assumptions, and measured harmonic content can be significantly different from that predicted by the theory. II. SIX PULSE POWER ELECTRONIC LOADS Two types of six pulse loads are investigated here, a three phase rectifier bridge as shown in Fig. 1, and a triac or back to back thyristor controlled three phase reactor, as shown in Fig. 2. The rectifier can have either diodes or thyristors, with very similar behavior with respect to harmonic currents. In the reactor, the harmonic content is increased as the firing angle is increased beyond 90 degrees, where the currents are sinusoidal and the reactive power maximum. In the rectifier, the harmonic content is less when the commutation angle is large, but it is always substantial. Even harmonics are absent due to the symmetry between negative and positive half cycles. Triple harmonic line currents, if present, would have the same instantaneous values in all three phases. Since they don't have any return paths, they also become zero. In general, all the other harmonics are present, and the 5th and the 7th harmonics will usually have the largest amplitudes. Typical six pulse line currents are shown in figures 3 and 4, together with their harmonic spectra. They have been calculated with program PECAN (Power Electronic Circuit Analysis), which is described in [1]. In the harmonic spectra, lengths of vertical bars are proportional to harmonic content. The term six pulse refers to the number of times per cycle conduction starts in a switching element. They are 60 degrees apart. III. TWELVE PULSE CONNECTIONS To get twelve pulse connections with lower harmonic content, two six pulse loads are usually supplied through a transformer with two secondary windings, one Y-connected and one D-connected. The loads have the same rated voltage and current, and rectifier loads can be connected in series or in parallel. The 30 degree phase shift of line currents from the two windings gives the twelve pulses. A possible winding arrangement is shown in Fig. 5. The two parts of the often Y-connected primary winding, H1 and H2, are in parallel. Reactances between the high voltage winding and each of the two low voltage windings will be equal, and forces are reasonably under control for a short circuit in either LY or LD. Fig.1. Rectifier. Fig. 3. Line current with harmonic spectrum. Fig. 5. Twelve pulse transformer. Fig. 2. Reactor. Fig. 4. Line current with harmonic spectrum. Firing angle 113.5. Fig. 6. Line currents. The phase angles of the currents in LY and LD can be explained with reference to Fig. 6. A line current from the LD winding is here displaced +30 with respect to the corresponding line current from LY. However, the corresponding phase currents line up, and add directly into the primary high voltage winding. Therefore, 30 must be subtracted from the angle of the line current in LD to get the angle of the phase current. This applies regardless of frequency, therefore not only for the fundamental, but also for the higher frequency harmonics. Between phases 1 and 2 there is a 120 displacement for the fundamental, and 5x120=600 for the 5th harmonic. Between phases 1 and 3 the displacement is 5x240=1200. Subtracting multiples of 360 from 600 and 1200 gives anglesFi 240 and 120 for the 5th harmonic, and the phase sequence is negative. With +30 displacement of fundamental line current in LD, the displacement is -5x30=-150 for the 5th harmonic line current, and for the phase current, the displacement is -15030=-180. Consequently, 5th harmonic phase currents are in direct phase opposition between LY and LD, and induce opposing circulating currents in H1 and H2. Theoretically, the 5th harmonic line current in the high voltage winding will be zero. A similar investigation of the 7th harmonic reveals that the phase sequence is positive, the line current in LD is displaced +210, and the phase current 210-30=180. Again, phase opposition prevents the harmonic from being transferred as primary line current. The lowest order harmonics that will appear in the high voltage line currents are the 11th and the 13th. Analyzed in a similar way, they are found to add directly from LY and LD. Of the harmonic currents that appear in a six pulse connection, those that are eliminated in a twelve pulse connection are of orders 5-7-17-19-29-31 and so on, and those that remain unchanged are of orders 11-13-23-25-35-37. The fairly large gap between the windings at the radial centerline in Fig. 5 is there to avoid excessive eddy current losses due to radial magnetic leakage fields set up by harmonic currents, which are in phase opposition between LY and LD. IV. FILTER WINDINGS AND TRANSFORMER REACTANCES The transformer can be supplied with an additional winding connected to filters, to reduce the harmonics further. The winding arrangement can be as shown in Fig. 7. Like the high voltage winding, also the filter winding has two permanently parallel connected parts, F1 and F2. Yoke LY F1 H1 LD F2 H2 Core leg Yoke Fig. 7. Transformer with filter winding The transformer now has an equivalent circuit for the reactances, as shown in Fig. 8. Since XY = XD due to the symmetry, there are four reactances that must be determined from four short circuit calculations, H-F, H-LY, F-LY and LY-LD. Fig. 8. Equivalent circuit For the efficiency and the design of the filters, it is highly desirable that XF comes out as zero. It is remarkable that with the winding arrangement in Fig. 7, that seems to follow automatically within very narrow tolerances, as evidenced from the analysis of several transformers of this type, in sizes up to 137 MVA. In five 54 MVA rectifier transformers that were built and tested in Norway, the reactance XF was calculated and tested as zero within a tenth of a percent. V. REACTANCE CALCULATIONS The calculations of reactances are complicated by the fact that circulating currents and current distribution between parallel connected windings are not known at the outset. A flux plot from a finite element reactance calculation HLY is shown in Fig. 9. The winding arrangement is the same as that of Fig. 7. The LY winding is short circuited, while LD is open. The filter winding is also open, but a circulating current flows between the two parts F1 and F2. Power is supplied to the primary winding, with H1 and H2 connected in parallel. VI. 24 AND 48 PULSE CONNECTIONS The normal 24 pulse connection has two transformers in parallel, each with an LY and LD secondary winding, and with primary phase shift windings with voltages displaced 7.5 and +7.5. Between the four secondary windings, voltages are displaced 15 degrees. The two transformers have twelve pulse connections by themselves, with the same harmonics eliminated as described earlier. The 15 degree displacement betwen them reduces substantially also harmonics of orders 11-13-35-37, and only those of orders 23-25 (and 47-49) remain essentially unchanged. The 11th harmonic has negative phase sequence, and 11x15=-165 displacement of a line current in LD. With 30 subtracted to get the angle of the phase current, it becomes 195. Current vectors of unit length adding under this angle give a vectorial sum equal to 2 x sin 7.5, whereas the algebraic sum is 2. The reduction in per unit is therefore sin 7.5 = 0.131. Harmonics of orders 13-35-37 are found to have the same reduction factor 0.131. Fig. 9. Flux plot for transformer reactance H-LY It is known that for +100% current in LY, the sum of the currents in H1 and H2 must be -100%, and the currents in F1 and F2 must be equal with opposite signs. Because of the parallel connections, flux linkages must be equal in H1 and H2, and also in F1 and F2. A first initial calculation has -100% current in H1 and zero in H2 and F1. A second calculation has -90% current in H1, 10% in H2 and zero in F1. A third calculation has -100% current in H1, zero in H2 and -10% in F1. Correct currents in H2 and F1 can now be determined from the linear relationships between currents and flux linkages based on the three initial calculations, with the flux linkages equalized. Current distributions and circulating currents will always adjust themselves to give minimum magnetic field energy. The accuracy of the calculated currents can therefore be checked by observing how the magnetic energy changes with small deviations from the calculated currents. The changes should always be positive. When the calculations are right, it never fails. With this winding arrangement and +100% current in LY, approximately -50% flows in H1, H2 and F1, and +50% in F2. Also the reactance calculations F-LY and LY-LD require three initial calculations, in order to find unknown currents. Only the calculation H-F is straightforward, with all the currents known in advance. Fig. 10. 12 and 24 pulse rectifier line currents Fig. 11. 12 and 24 pulse reactor line currents. Firing angle 113.5 12 and 24 pulse line currents for rectifiers and reactors are shown in figures 10 and 11, as analyzed with PECAN. Fourier analysis can be performed very easily with this program, and the reduction of 11th and 13th harmonics to 13.1% is confirmed with great accuracy. The reduction of harmonics of orders 35-37 is also confirmed, but the accuracy is not quite as good, due to numerical errors. 12 pulse currents are shown as dashed lines in the figures, and their 24 pulse sums are shown as solid lines. For the reactor, the 113.5 firing angle corresponds to half rated reactive power. The 24 pulse line current remains reasonably sinusoidal down to about 15% power. 48 pulse connections are also used occasionally, and have an additional reduction factor of sin 3.75 = 0.0654 for the 23rd and 25th harmonics. With the highest pulse connections, rated voltages are often very low, and LY and LD can have as few as 4 and 7 turns. In such cases, the currents are so large that LY and LD must be on the outside of the primary phase shift winding. VII. PHASE SHIFT WINDINGS Three possible phase shift windings are shown schematically in Fig. 12. There is no good reason for using the polygon or hexagon connection for this purpose, so it is only mentioned here as a possibility. In Fig. 13, the connections are shown differently. The two parts of each phase winding which are concentric on the same core leg are shown above each other. A possible winding arrangement is shown in Fig. 14. H1,S1 and H2,S2 are connected in parallel at the terminals. In the zig-zag or Z-connection, the currents in the two concentric windings on one core leg are 60 displaced in phase. In the extended delta connection, the displacement is only 30. With the small displacements of line voltages, as required by 24 and 48 pulse connections, extended delta has significant advantages. For 7.5 displacement, the phase shift only adds 2.6% to the sum of the kVAs for the H and S windings, compared with 6.7% for the zig-zag connection. The smaller phase displacement of currents also gives better conditions for the magnetic leakage field, with a tendency of lower eddy current losses and short circuit forces. In addition, the smaller windings S1 and S2 will get proportionally more copper in them, and be better capable of withstanding the short circuit forces. The Z-connection is used occasionally, where tap connections are required at the neutral. However, when the voltage is regulated, the phase shift also changes, and will not always be ideal for harmonic suppression. Fig. 12. Phase shift connections Fig. 13. Phase shift connections Fig. 14. Winding arrangement VIII. HARMONIC CURRENT FLOW In transformers for twelve pulse loads, 5th and 7th harmonics flow in phase opposition in the LY and LD windings. Their magnetic leakage fields are essentially radial, and set up circulating currents between the parallel connected parts of both the primary winding and a possible filter winding. The calculation of harmonic losses involves finding these circulating currents, which can be done following a similar procedure as explained for the reactances. Primary line currents are theoretically zero. The 11th and the 13th harmonics are in phase in LY and LD. Their magnetic leakage fields are essentially axial, as for the fundamental. No circulating currents flow due to these harmonics. If a filter winding is present, they will ideally be balanced by opposing currents in this winding due to low impedance filter loads, and then also here primary line currents will be close to zero. In wire windings, eddy current losses are proportional to (fdB)2, where d is conductor dimension perpendicular to the flux density B, and f is the frequency. Even though flux density may be low for the harmonics, frequency is high, and harmonic eddy current losses are often higher than for the fundamental. There is no practical way to find these losses from factory tests, and a designer has to rely almost entirely on numerical calculations. Harmonic currents have been found here in two very simple circuits in Fig. 1 and 2, in order to explain the basic concepts. Practical applications will always be more complicated and warrant a more detailed analysis. An interesting feature of this arrangement is that a short circuit test no longer gives reliable information about load losses under normal operating conditions. During the short circuit test the core flux is only large enough to balance the leakage flux. In per unit, for rated currents the flux equals the short circuit impedance. Ampereturns in the two windings are essentially balanced, and the leakage flux follows paths largely unaffected by the core gaps. Under normal operating conditions, however, the magnetizing current is significant, and the much higher core flux fringes out into the inner winding and produces eddy current losses which can be much higher than those tested at short circuit. This is especially important when the inner winding L1-L2 is a sheet winding. The losses will be highest at zero powerfactor, when the magnetizing current is in phase with the load current. This adverse effect of core gaps is counteracted to some extent by having gaps also in the windings, as shown in Fig. 15. X. CONCLUSIONS High pulse harmonic suppression is very effective, and has been analyzed here both analytically and numerically. For additional suppression of harmonics, transformers can be equipped with windings connected to filters, where the filter winding reactance in the equivalent circuit is close to zero. XI. REFERENCES IX. TRANSFORMERS WITH CORE GAPS Transformers for power electronic loads sometimes have cores with gaps in the middle of each core leg, as shown in Fig. 15. A core gap can be quite large, typically of about 10 mm length. The purpose of this is to limit remanent flux and keep magnetizing reactance reasonably constant. This in turn limits inrush currents and thereby protects the power electronic devices. Yoke Leg L1 H1 Leg L2 H2 Yoke Fig. 15. Transformer with core gaps [1] O.W. Andersen, "Time Domain Circuit Analysis", IEEE Computer Applications in Power, April 1992, pp. 34-38. [2] O.W. Andersen, "Magnetic Leakage Fields in Rectifier Transformers", Conference Proceedings ICEM, Paris September 1994, pp. 738-740. Odd W. Andersen has been Professor of Electric Power Engineering at the Norwegian Institute of Technology since 1964. Before that time, he was a synchronous machine designer with Canadian General Electric. He has been on sabbatical leave three times in the United States, where he has worked for the General Electric Company in the Turbine Generator Department in Schenectady and in the Transformer Department in Pittsfield, and has been a visiting professor at Rensselaer Polytechnic Institute in Troy and at the University of Minnesota. He made his first computer program in 1957, and it has been an ongoing activity ever since. Most of the programs are for optimized design of rotating machines and transformers, finite element field calculations and circuit analysis. More in http://www.elkraft.unit.no/~andersen