Three-Phase/Six-Phase Conversion Autotransformers

Transcription

1 1554 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003 Three-Phase/Six-Phase Conversion Autotransformers Xusheng Chen, Member, IEEE Abstract The first commercial demonstration of six-phase transmission, the Goudey-Oakdale three-phase/six-phase project, used two delta wye-grounded three-phase transformers to realize the required phase/voltage conversion. This paper proposes the usage of autotransformers for phase/voltage conversion for the actual three-phase/six-phase systems to be built in the future. The design considerations of the three-phase/six-phase conversion autotransformers are described. Topology-based, nonlinear, core-type conversion autotransformer EMTP models are developed. The behavior of the conversion autotransformers in a practical three-phase/six-phase system is simulated. These include transformer energization, short circuits, voltage regulation, open conductor, and ferroresonance. The simulation results show that the autotransformer is a viable choice for the conversion transformer. Since the cost ratio of the proposed conversion autotransformers with respect to the three-winding conversion transformers is approximately 64%, the new design is superior economically to other transformer designs, and will help push the HPO technology. Index Terms Autotransformer, six-phase, transmission. I. INTRODUCTION CONSIDERATION of the fundamental limits on power transfer in a restricted right-of-way led to the concept of increasing the number of phases in a circuit from three to six or twelve. This is called high phase order power transmission (HPO). At first as an idea, it gained credibility with a feasibility analysis published in the late 1970s [1]. As a laboratory prototype demonstration, an 80-kV phase-to-ground six-phase line and a 138-kV phase-to-ground twelve-phase line were built at the Malta test facility of Power Technologies Inc., Schenectady, NY, with support from the Department of Energy [2]. As the initial application on an operating utility transmission system, the Goudey-Oakdale line near Binghamton, NY, operated as a six-phase, 93-kV phase-to-ground line for two years [3]. Two delta/wye-grounded three-phase transformers were used to realize the required phase/voltage conversion. Possible reuse of the existing three-phase transformers and the isolation of the zero-sequence networks of the three-phase/six-phase systems resulted in the above choice. However, in a panel discussion of the 1994 IEEE Transmission and Distribution Conference, Chicago, IL, Guyker from Allegheny Power Service Corporation pointed out that What is needed today to help push HPO technology is not a cobbling of wye and delta banks, but an autotransformer that provides a balanced set of voltages and currents at a cost comparable to the wye-delta combination currently used. This statement motivated the author to conduct the research reported in this paper. Step-up and step-down three-phase/six-phase conversion autotransformers were conceptually designed. It is well known that the weight and cost of transformers of similar voltage ratings are proportional to the total megavolt ampere (MVA) of parts. The cost ratios of the proposed step-up and step-down autotransformers with respect to three-winding conversion transformers are 64.3% and 64.1%, respectively. Clearly, the autotransformers are superior economically to other transformer designs. Considering that for the same line-to-neutral voltage the six-phase transmission line could double the power flow capability this is why the six-phase transmission system is being actively researched, and that the installation costs of the two delta-wye three-phase transformers used in the Goudey-Oakdale project account for 60% of the total terminal costs [4], the proposed autotransformers will definitely help push the HPO technology. II. CONCEPTUAL DESIGN OF THE STEP-UP CONVERSION AUTOTRANSFORMER AND DETERMINATION OF ITS EMTP MODEL PARAMETERS Fig. 1 shows the three-phase/six-phase transmission system similar to the Goudey-Oakdale system described in [3]. The line-to-neutral voltages for the three-phase and the six-phase lines are kv and 93 kv, respectively. This conversion autotransformer is termed as the step-up autotransformer (the six-phase side has a higher line-to-neutral voltage than that of the three-phase side). Note that the polarities of the dfb three-phase windings (called tertiary windings in this paper) are reversed. The neutrals of the transformer are grounded. The autotransformer is assumed to be 250/125/125-MVA, 66.4/93/93-kV line-to-neutral, 60 Hz, five-legged, and wyegrounded. Its characteristics are summarized in Table I, and its one-phase schematic diagram is shown in Fig. 2. The design of the conversion autotransformer and the preparation of ATP data file proceed as follows: To have the autotransformer provide a balanced set of voltages and currents, it is required that the short-circuit impedances from the three-phase side to the two sets (ace and dfb) of the six phase side be equal. Redefine the autotransformer as a three-winding transformer with series, common, and tertiary windings as I, II, and III windings, respectively (Fig. 2). Assume that cylindrical windings are used and that the layout of one phase of the windings and iron is as shown in Fig. 3. The short-circuit impedances between the three windings I, II, and III are calculated as follows [5]: Manuscript received March 24, The author is with Seattle University, Seattle, WA USA Digital Object Identifier /TPWRD (1) /03$ IEEE

2 CHEN: THREE-PHASE/SIX-PHASE CONVERSION AUTOTRANSFORMERS 1555 TABLE I CHARACTERISTICS OF THE 250-MVA AUTOTRANSFORMER (10) (11) (2) It should be noted that the base current for the six-phase side is twice that of its rated current. The leakage and zero-sequence inductances referred to winding III are calculated as (12) (13) (14) (15) where is the zero sequence leakage inductance through the air and the tank. Usually, transformer winding resistances are calculated from short-circuit test data. Since no conversion autotransformers have yet been built, their values are assumed to be kv kv kv The core loss resistances are connected to the six-phase side for the left side transformer and the three-phase side for the right side transformer (Fig. 1). Their values are k (16) The reason for can be found in [6]. Assuming that the short-circuit reactances are equal to the short-circuit impedances, and noting that inductance is equal to reactance in per unit, the values of the leakage inductances of the model can be determined [6] Choosing 250 MVA, kv and kv as the power and voltage bases, respectively, the base currents, impedances, and inductances for the transformer are calculated as (3) (4) (5) (6) A (7) A (8) (9) k (17) A transformer data file was prepared for ATP supporting routine SPR.FOR [6]. SPR.FOR scales the curve of the transformer to match the specified excitation current, and generates curves for each nonlinear segment of the core. Nine ideal transformers are used to connect the autotransformer model to the system. The turns ratios of the ideal transformers are 0.29:1, 0.71:1, and 1:1, for windings I, II, and III, respectively. ATP input data for the conversion autotransformer are summarized in Table II. The 1.51-mile six-phase transmission line is modeled by ATP branch cards for PI-Equivalents (coupled R-L-C circuits) with the following constants: F F for and The power system external to the three-phase/six-phase system is represented by two three-phase voltage sources,, and, and,, and. The rated voltage of the two sources is 66.4 kv line-to-neutral. III. SIMULATION RESULTS The system of Fig. 1 was simulated comprehensively using ATP. Rated source voltage was assumed for all of the simulation cases if not otherwise specified.

3 1556 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003 Fig. 1. Three-phase/six-phase transmission system. TABLE II ATP INPUT DATA FOR THE 250-MVA AUTOTRANSFORMER Fig. 2. One phase of the step-up conversion autotransformer. Fig. 3. Layout of phase A windings and iron of the step-up conversion autotransformer. A. Energization From the Three-Phase Side (Breaker is Closed, and Breaker is Open) Fig. 4 shows the simulated three-phase side excitation current waveforms,, and, and the six-phase side line-to-neutral voltage waveforms,,,,, and. The rms current is A or p.u., and the core loss is 600 kw or p.u. These should be accurate, because the supporting routine SPR.FOR matches the excitation current and the core loss. The voltages on the six-phase side are balanced.

4 CHEN: THREE-PHASE/SIX-PHASE CONVERSION AUTOTRANSFORMERS 1557 (a) (a) (b) (b) Fig. 4. Simulated excitation current and voltage waveforms. (a) Three-phase side excitation currents. (b) Six-phase side line-to-neutral voltages. B. Short-Circuit Performance Breaker is closed, and the rest breakers are open for all the short-circuit simulations (see Fig. 1) 1) Six-phase short-circuit. Fig. 5(a) shows the six-phase side short-circuit current waveforms. The rms currents for phases,,,,, and are 11.84, 11.91, 11.87, 11.69, 11.74, and ka, respectively. The average short-circuit current for phases ace is ka or p.u., for phases dfb is ka or p.u., and for phases ABC (the three-phase side) is ka, or p.u. The transformer s short-circuit equivalent circuit is shown in Fig. 5(b). The rms short-circuit current can be calculated as p.u. which is seen to be almost the same as the computed value of p.u. The astute readers must have noticed that the conventional star-circuit of a three-winding transformer was used to calculate the six-phase short-circuit currents. A simple reasoning is offered here. If complete balance of the system can be assumed, then and, which suggest that a six-phase short-circuit can be treated as two simultaneous three-phase (ace and dfb) short-circuits. The currents on the three-phase side can be determined by the balance of the magnetomotive forces (mmfs) per phase. The inversion of polarity of one set of the voltages on the six-phase side will not change the short-circuit currents on the three-phase side. 2) Phases and short-circuit. Fig. 5. Six-phase short-circuit (a c e d f b) of the autotransformer. (a) Simulated six-phase side short-circuit current waveforms. (b) Short-circuit equivalent circuit. Fig. 6. Current waveforms for a d short-circuit. Fig. 6 shows the current waveforms for both sides of the transformer. The rms currents are ka or p.u., A, A, and ka or p.u. It is observed that the short-circuit currents of the -ground short-circuit are the same as that of the short-circuit. 3) Phases a and ground short-circuit. Fig. 7 shows the current waveforms for both sides of the transformer. The rms currents are ka or p.u., A, A, and ka or p.u. It is gratifying to note that the results of the short-circuit analysis of the transformer are in excellent agreement with that of the theoretical analysis presented in [7]. C. Voltage Regulation For convenience of simulation, the voltage regulation (VR) is defined as (18)

5 1558 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003 Fig. 7. Current waveforms for a g short-circuit. (a) (b) Fig. 8. Left-side transformer six-phase side voltage waveforms when it carries a rated pure inductive load. where no load voltage rated voltage; full load voltage. Fig. 8 shows the six-phase side voltage waveforms when the left side transformer carries a rated six-phase pure inductive load. The six-phase side voltages are balanced. The voltage regulation is. Knowing p.u. and p.u., the voltage regulation can be easily calculated [see Fig. 5(b)] (c) Since resistances are small comparing to the reactances in the system of Fig. 1, 3.66% is approximately the maximum voltage regulation under rated conditions of the transformer. D. Energization of the Right-Side Transformer after the Left-Side Transformer Has Been Energized Fig. 9 shows the six-phase side inrush and excitation current waveforms. It is observed that the inrush and excitation current waveforms are quite different when the right-side transformer is energized from a six-phase infinite bus. E. Open Conductor Performance The voltage for the two sources is fixed at 106% of the rated voltage. The angles of the source voltages are then adjusted so that the current of the six-phase side of the right-side transformer is at its rated current of 1255 A. In this operating condition, the right side transformer receives 265 MW, with a power (d) Fig. 9. Energization of the right-side transformer after the left-side transformer has been energized. (a) Phases a, c, and e inrush current waveforms. (b) Phases d, f, and b inrush current waveforms. (c) Phases a, c, and e excitation current waveforms. (d) Phases d, f, and b excitation current waveforms. factor of unity. The three-phase/six-phase system is balanced before the line outage.

6 CHEN: THREE-PHASE/SIX-PHASE CONVERSION AUTOTRANSFORMERS 1559 Fig. 11. Three-phase side voltage waveforms. Fig. 10. Simulated voltage and current waveforms of the six-phase transmission line when phase a is disconnected. (a) Voltages on the six-phase transmission line. (b) Currents on the six-phase transmission line. TABLE III VOLTAGE,CURRENT AND POWER ON THE SIX-PHASE LINE (ALL PHASES CONNECTED AND PHASE A DISCONNECTED) Fig. 10 shows the voltage and current waveforms of the sixphase transmission line when phase a is disconnected (breakers and are open). Simulation results for the two operating conditions are summarized in Table III. As shown in Table III, disconnecting phase a drops the current on phase a to zero and voltage on phase a to kv which is a result of both capacitive and inductive coupling from the other phases. The power received by the right-side transformer is MW, a reduction of 18% (compare: ). It is encouraging to observe that the voltages and currents on the reremaining phases are only slightly changed. F. Ferroresonance Transformer ferroresonance is a complicated nonlinear phenomenon. For three-winding, multiphase, multilegged transformers to develop fetroresonance overvoltages, the following four conditions must be met: 1) there is no load on the transformer; 2) one or more phases are disconnected from the source; 3) adequate capacitance to ground is connected to open terminals; 4) no source is connected directly or through small or medium impedances to the other windings on the leg with open terminals. Conditions 1 to 3 are well known for two-winding transformers. Condition 4 is unique to three-winding transformers. The reason is that connection of the source to the windings reduces dramatically the input inductance looking into the open terminals. Since the position of the breakers on both sides of the transformer is under supervision, the chances for ferroresonance are extremely rare. One case study is reported here. Breakers and are switched on to energize the left-side transformer which carries the 1.51-mile six-phase transmission line (breaker is closed and breaker is open). The winding capacitances to the ground of the autotransformer are assumed to be F/phase and F/phase for the three-phase and six-phase sides, respectively. There are no ferroresonance overvoltages when breakers and are closed with rated source voltages of 66.4 kv rms. However, when the length of the transmission line is increased to 10 mi, ferroresonance overvoltages do occur. Fig. 11 shows the three-phase side voltage waveforms when the six-phase line is 15.1 mi long. The aperiodic phase A voltage waveform has a peak value of 146 kv, which is kv kv of the rated peak line-to-neutral voltage. Phase and phase voltages are proportional to phase A voltage. IV. STEP-DOWN CONVERSION AUTOTRANSFORMER Fig. 12 shows the schematic diagram of one phase of the step-down conversion autotransformer. It is found that the layout of the windings and iron of Fig. 3 is unable to make the step-down conversion autotransformer to supply a balanced six-phase voltage at load. Fortunately, a simple change of the layout of the windings and iron such as the one shown in Fig. 13 will solve the problem. The conversion autotransformer is assumed to be 400-MVA, kv line-to-neutral, 60-Hz, five-legged, and

7 1560 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003 Fig. 12. One phase of the step-down conversion autotransformer. Fig. 14. Step-down conversion autotransformer six-phase side voltage waveforms when it carries a rated pure inductive load. of the apparent power ratings of the windings of a given transformer construction. The cost ratios for the conversion autotransformers with respect to the three-winding conversion transformers are determined as follows: 1) Cost ratio for the step-up autotransformer (Fig. 2). (19) Fig. 13. Layout of phase A windings and iron of the step-down conversion autotransformer. wye-grounded. The short circuit impedances are assumed as follows: and Following the same procedure as for the step-up autotransformer discussed in Section II, the following results are obtained: and Note that the constraint of for the layout of windings and iron of Fig. 3 is lifted for that of Fig. 13. The base inductance for winding III, and the leakage and zero-sequence inductances referred to it are The other ATP data are omitted for simplicity. Fig. 14 shows the six-phase side voltage waveforms when the transformer carries a rated pure inductive load. The voltages of the six phases are completely balanced with a voltage regulation of, which can be calculated as. V. ADVANTAGES OF AUTOTRANSFORMERS The weight and cost of transformers of similar voltage ratings are proportional to the total MVA of parts which is the sum full load condition (20) where is the voltage ratio of the primary and second sides;,, and, are rated currents of the common winding, series and tertiary windings, and the three-phase side, respectively. MVA of parts step-up autotransformer MVA of parts step-up three-winding transformer (21) (22) Cost ratio (23) 2) Cost ratio for the step-down autotransformer (Fig. 12). The current rating for the common winding is determined by lines ace open if, and lines dfb open if if if (24a) (24b) Cost ratio if (25a) if (25b) The cost ratios for the 250-MVA step-up and 400-MVA step-down conversion autotransformers with respect to the three-winding conversion transformers are 64.3% and 64.1%, respectively. The savings of cost in using conversion autotransformers are considerable. The autotransformers also have lower per unit losses (higher efficiency) and lower excitation current. The disadvantages include the loss of electrical isolation between the three-phase and the six-phase sides.

8 CHEN: THREE-PHASE/SIX-PHASE CONVERSION AUTOTRANSFORMERS 1561 VI. CONCLUSION Conceptual designs for step-up and step-down threephase/six-phase conversion autotransformers are presented. The proposed autotransformers are placed in a practical three-phase/six-phase system and simulated comprehensively. The conceptual design shows signs of desirable performace and is superior economically to other transformer designs for conversion purposes. Further work is definitely needed to verify other performance measures such as lightning and switching performance, corona behavior, and other important ones. It is suggested that conversion autotransformers be used in the commercial three-phase/six-phase transmission systems to be built in the future. ACKNOWLEDGMENT The author wishes to express his sincere appreciation to Dr. S. S. Venkata of Iowa State University, who initiated this research project and whose advice and experience on HPO technology have been invaluable. REFERENCES [1] S. S. Venkata, W. C. Guyker, and W. H. Booth, 138-kV, six-phase electrical power transmission system, in Proc. Amer. Power Conf., vol. 40, Chicago, IL, Apr. 1978, pp [2] J. R. Stewart and I. S. Grant, High phase order Ready for application, in Proc IEEE Power Eng. Soc. Transmission and Distribution Conf., Minneapolis, Minnesota, Sept , 1981, Paper 81 TD [3] J. R. Stewart et al., Transformer winding selection associated with re-configuration of existing double-circuit line to six-phase operation, IEEE Trans. Power Delivery, vol. 7, pp , Apr [4] T. L. Landis et al., High phase order economics: Constructing a new transmission line, IEEE Trans. Power Delivery, vol. 13, pp , Oct [5] H. W. Dommel, Electromagnetic Transients Programs Reference Manual. Porland, OR: BPA, [6] X. Chen and S. S. Venkata, A three-phase, three-winding core-type transformer model for low-frequency transient studies, IEEE Trans. Power Delivery, vol. 12, pp , Apr [7] S. S. Venkata et al., 138-kV, six-phase transmission system: Fault analysis, IEEE Trans. Power Apparat. Syst., vol. PAS-101, pp , May Xusheng Chen (M 88) was born in Shanghai, China. He received the M.S.E.E. degree in power systems from Jiao Tong University, Shanghai, China, in He received the Ph.D. degree in electrical and computer engineering from Washington State University, Pullman, in Currently, he is a Professor at Seattle University, WA. His areas of interest include power system transients and protection, electrical machine modeling, six-phase nonlinear circuit analysis, power transmission, and wind generation. Dr. Chen is a member of Tau Beta Pi.