ANEW, simple and low cost scheme to reduce transformer

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1 950 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 A Sequential Phase Energization Technique for Transformer Inrush Current Reduction Part II: Theoretical Analysis and Design Guide Wilsun Xu, Senior Member, IEEE, Sami G. Abdulsalam, Student Member, IEEE, Yu Cui, and Xian Liu, Member, IEEE Abstract This paper presents a theory to explain the characteristics of a sequential phase energization based inrush current reduction scheme. The scheme connects a resistor at the transformer neutral point and energizes each phase of the transformer in sequence. It was found that the voltage across the breaker to be closed has a significant impact on the inrush current magnitude. By analyzing this voltage using steady-state circuit theory, the simulation and experimental results presented in a companion paper are explained. The results lead to the establishment of a guide to select the optimal value of the neutral resistor. The applicability of the proposed scheme to different transformer configurations has also been investigated in this paper. It is shown that the idea of sequential phase energization leads to a new class of techniques for limiting switching transients. Index Terms Inrush current, power quality, transformer. Fig. 1. Circuit for analyzing transformer energization. I. INTRODUCTION ANEW, simple and low cost scheme to reduce transformer inrush currents has been presented in a companion paper. The scheme uses a resistor connected at the transformer neutral point and energizes each phase of the transformer in sequence. Simulation and experimental results have shown that the scheme is quite effective [1]. The amount of inrush current reduction as a function of neutral resistor value was determined from the results. It was found that there is an optimal value for the resistor. The paper, however, offers no quantitative theory to explain the phenomena. The objective of this paper is to present a theoretical analysis on the proposed scheme. The results lead to the establishment of a design guide for the selection of the optimal resistor value. The theory also makes it possible to analyze the applicability of the proposed scheme to different types of transformer configurations. A rigorous analysis on the proposed scheme needs to study a system of multi-variable nonlinear differential equations. Finding an analytical solution to the problem is probably impossible. Even with many approximations, we still failed to get some meaningful results. The process, however, led us to realize that the steady-state voltage across the breaker to be closed Manuscript received May 20, 2003; revised October 18, This work was supported by the Alberta Energy Research Institute. Paper no. TPWRD W. Xu, Y. Cui, and S. G. Abdulsalam are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada ( wxu@ece.ualberta.ca). X. Liu is with the University of Arkansas, Little Rock, AR USA. Digital Object Identifier /TPWRD has a significant impact on the inrush current magnitude. This voltage can be determined from steady-state circuit analysis. Further investigation of the phenomena reveals that one of the real causes behind the effectiveness of the proposed scheme is the reduction of this voltage through the neutral resistor, which is made possible by sequential phase energization. In the following sections, a steady-state circuit theory is presented to analyze the problem. The theory is then extended to establish a design guide to determine the optimal resistor value. II. STEADY-STATE ANALYSIS OF THE PROPOSED SCHEME The proposed scheme involves the energization of three phases in sequence. The energization of the first phase is very similar to the series resistor insertion scheme. This is a straightforward problem and it will not be considered further in subsequent sections. The challenge here is the analysis of the 2nd and 3rd phase energization. Using the 2nd phase energization as an example, the circuit shown in Fig. 1 can be drawn. The variables shown in the circuit diagram are phasors. This notation will be followed throughout the paper. Without losing generality, the unloaded transformer can be represented as three coupled branches in the figure. In its steadystate form, the equation for the transformer can be written as follows, where and are the self and mutual impedances of the coupled circuit respectively. is shown in Fig. 1. The above /$ IEEE

2 XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II 951 equation assumes that the transformer is balanced among three phases and the resistive component is omitted. The secondary side of the transformer has an impact on the value of the coupling matrix, but it does not change the structure of the circuit. The most important variable of the above circuit is the voltage across the phase B breaker before it is closed. This voltage is labeled as in the figure and is called breaker contact voltage in this paper. Based on circuit theory, the following characteristics regarding to can be stated: If, closing of the phase B breaker would not result in transient currents in the circuit. If the circuit were a linear circuit, the magnitude of the transient currents in the circuit would be in proportion to if the breaker always closes at the same phase angle of. If the circuit is a nonlinear circuit with transformer magnetization characteristics, a larger will generally lead to a larger inrush current if the breaker always closes at the same phase angle of. The relationship between the inrush current and is nonlinear. It becomes clear, therefore, that we can use the magnitude of to investigate indirectly the magnitude of the circuit transients. A larger should be avoided if one wants to reduce the inrush currents. This reasoning is the basis of the quantitative theory presented in this paper. The goal of our analysis is thus transformed into the one of finding the relationship between and. According to Fig. 1, the equation to determine is established as follows: The above set of equations has five known variables. The result for is shown in the following formula: Similarly, we can develop a set of equations for the steadystate circuit condition before the phase C breaker is energized This leads to the solution for the as follows: The impact of on the magnitudes of and can be assessed by plotting formulas (1) and (2). Using the test transformer of [1] ( secondary) as an example, the results are shown (1) (2) Fig. 2. Breaker contact voltages as affected by R. Fig. 3. Comparison of breaker contact voltage curves and the inrush current curves. in Fig. 2. It can be seen that decreases initially when is small. On the other hand, always increases with. The intersection point of the two curves gives a compromised reduction on both voltages. This is the optimal point for the neutral resistor since we don t want either voltage becomes too high. The corresponding voltage is about 80% of the case with solidly grounded transformer, or 66% of the phase to ground voltage of 120 V. Also included in the figure is the measured and results for the experimental transformer. There is a reasonable agreement between the results. The difference is caused by the asymmetry and saturation of the transformer magnetic circuit. Note that the transformer model shown in Fig. 1 is assumed to have the same mutual impedances. Further inspection of the results shows that the curves are very similar to the inrush current versus curves obtained by experiments and simulations [1]. The main difference is on the scale of the Y-axis. This is understandable since the magnitudes of inrush currents are approximately exponential functions of the breaker contact voltages and. Fig. 3 compares the two sets of curves and the similarity can be clearly seen. More importantly, the intersection points of the respective curves are very close. Accordingly, one can find the optimal resistance value using (1) and (2). For the test transformer, the optimal resistance is found to be 1.8 with the steady-state method and 2.4 from the nonlinear simulation results. The corresponding reduction of breaker contact voltage is about 66% in this case.

3 952 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 In summary, (1) and (2) can be combined to establish a single formula for the optimal resistance value as follows: or Fig. 4. Zero sequence test circuit for Y=1 transformer. (3) There is no closed form solution for the above equation. But it can be easily solved numerically. In the next section, approximate analytical expression for the optimal value is established by considering the relationship between and. III. DESIGN GUIDE FOR DIFFERENT TRANSFORMERS Equation (3) shows optimal resistor is a function of and of the transformer. A general method to determine these two parameters is as follows: 1) Ground the transformer neutral for the side where is to be inserted. This is typically the primary side of the transformer. This side is also called the test side. 2) The secondary side of the transformer is left as it is. For example, if the transformer is connected, leave the connection intact. 3) Apply a rated positive sequence voltage to the transformer test side and measure the current injected into the transformer. The ratio of the voltage to the current is the standard open circuit impedance of the transformer. The reactance component of the impedance can be determined accordingly. This value is labeled as. 4) Apply a rated zero sequence voltage to the transformer test side and measure the current injected into the transformer. The ratio of the voltage to the current is a zero sequence impedance of the transformer. Depending on the connection of the secondary side, this impedance is not necessarily the zero sequence open circuit impedance. If the secondary side is -connected, it is actually the short circuit zero sequence impedance of the transformer. The resulting reactance is labeled as. 5) Parameter and can be calculated from the following well known equation [5]: Mathematically speaking, the above procedure is to find and using the following equations: With these understandings, the formulas for the optimal resistance are derived for different types of transformer connections. A. Transformer In this case, the positive sequence test gives the open-circuit reactance or magnetizing reactance of the transformer. The zero sequence test gives the short-circuit zero sequence reactance, as shown in Fig. 4. Since the short-circuit impedance is much smaller than the open circuit impedance Substituting this condition into (3), the equation for the optimal neutral resistor can be established as follows: which gives There is a 32% voltage reduction in this case. If,. The voltage reduction with respect to solidly grounded case is about 20%. B. Y/Y Transformer With 3-Limb In this case, the positive sequence test also gives the standard open circuit reactance or magnetizing reactance of the transformer. For the zero sequence test, the flux has to flow outside of the limb due to the fact that the flux of each phase has the same direction (Fig. 5). The zero sequence impedance is therefore very small. Comparing with, it can be neglected. So the formula for optimal neutral resistor is essentially identical to (4). C. Y/Y Transformer Consisting of Three Single-Phase Units In this case, the positive sequence test also gives the standard open circuit reactance of the transformer. The zero sequence test yields the same flux path as that of the positive sequence test. As a result,. This gives (4) The above condition does not produce an optimal resistance value from (3). It implies that the proposed scheme is not quite workable for this type of transformer. This result can be seen from the breaker contact voltage versus curves shown in Fig. 6. The figure reveals that there is no low voltage intersection point for the two curves. The figure also shows that the problem is caused by the curve, which does not start from zero value in this case. The physical explanation is that the 3rd phase

4 XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II 953 TABLE I NO-LOAD TEST DATA FOR A HYUNDAI TRANSFORMER Fig. 5. Zero sequence flux path for a 3-limb transformer. Applied voltage ; Average no load current ; No load losses. The open circuit impedance is and the open circuit resistance is.itgives Fig. 6. Breaker contact voltages for Y/Y transformer consisting of three single-phase units. is decoupled from the other two phases. A voltage cannot be induced on that phase when the first two phases are energized. D. Y/Y Transformer With 5-Limb This case is very similar to the case of 3 single-phase transformers. The zero sequence flux can return from the iron core, resulting in a zero sequence impedance that is comparable to. Accordingly, the proposed scheme may not work in this case either. E. Summary and Examples In summary, an optimal resistance exists for transformer and for 3-limb Y/Y transformer. These transformers are characterized as having mutual coupling among three phases. The proposed scheme will work for these cases. It can be further inferred that the scheme will also work for 3 winding transformers as long as it has a secondary or tertiary. Since most power transformers have a delta-connected tertiary winding, the proposed scheme can be applied to a wide range of transformers. Furthermore, the same formula for the optimal neutral resistor can be used for all cases. If the open circuit current at rated voltage is expressed in percentage of the transformer rating and the resistance part is ignored, (4) can be further simplified as follows: where is the per-unit transformer excitation current at rated supply voltage. As an example, the experimental transformer used for this project has the following measured values: (5) The corresponding optimal resistance is 1.8. As a second example, a HYUNDAI MVA, 72/13.8 kv, 3-limb, transformer is considered. The manufacturer provided the test data from the 13.8 kv side given in Table I Using a similar procedure and the average current among three phases, the and values are calculated as 283 and 868 respectively. If referred to the primary side where the neutral resistance is to be inserted,. Using formula (4), the optimal neutral resistor is calculated as If formula (5) is used, the resistance is 53 pu or The values agree well with the simulation determined optimal shown in Fig. 8 of the companion paper. IV. NUMERICAL AND SENSITIVITY STUDIES It is a significant claim that the optimal values for inrush current reduction and for breaker contact voltage reduction are very close. The design (4) and (5) are based on such a claim. Although this claim can be understood conceptually from the explanations presented in Section II, there is still a need to verify it further. To this end, two sensitivity studies have been conducted. The studies involve changing the slope of the transformer saturation curve. The first study examines the impact of changing the slope of the unsaturated segment of the curve and the second study examines the impact associated with the slope of the saturated segment. The inrush current results obtained from simulation are shown in Figs. 7 and 8. It can be seen from Fig. 7 that the intersection points of the inrush current curves move horizontally when the slope of the unsaturated curve (i.e. ) changes from 50% to 200% of the measured value. It means that the unsaturated reactance can affect the optimal resistance value. This result agrees well with the conclusion drawn from the breaker contact voltage analysis. The analysis shows that is a function of the unsaturated reactance. Fig. 8 reveals that the intersection points move vertically when the slope of the saturated segment of the saturation curve is changed from 30% to 100%. It implies that the slope has no effect on the value of the optimal. This result further confirms the adequacy of the breaker contact voltage analysis. The analysis does not indicate is affected by the

5 954 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 Fig. 7. Impact of changing the slope of the unsaturated segment of the transformer magnetization curve. Fig. 9. Comparison of simulation and theoretical results for a 3-limb transformer with Y/Y connection. Fig. 8. Impact of changing the slope of the saturated segment of the transformer magnetization curve. Fig. 10. Comparison of simulation and theoretical results for a Yg=1 transformer consisting of three single-phase units. slope of the saturated segment of the transformer magnetization curve. In addition to the above verification studies, the accuracy of the design formula is further evaluated by using a 3 limb Y/Y transformer and a transformer consisting of three single-phase units. The results for the 3 limb Y/Y transformer are shown in Fig. 9. It can be seen that there is a good agreement between the steady-state analysis and the transient simulations. For transformers consisting of three single-phase units, the case of 300 MVA, 13.8/199.2 kv transformer units described in [6] is simulated. Two cases are studied, one with the single-phase units connected in and the other connected in Yg/Y. In both cases the high voltage side is the grounded Y. The results for connection are shown in Fig. 10. This figure confirms the validity of the steady-state analysis method. For the case of the Yg/Y connection, steady state analysis show that the neutral resistor scheme is not as effective since the breaker contact voltage cannot be reduced. The simulation results, however, showed that the proposed scheme has some effects (Fig. 11). The effect could be explained with the following equation: where stands for the Laplace operator and the total circuit impedance seen from the breaker contacts (the 3rd phase closing Fig. 11. Inrush current simulation results for a Yg/Y transformer consisting of three single-phase units. is used as an example). Although this equation applies to a linear circuit only, it is symbolically valid for a saturated transformer. It can be seen that a reduction on will reduce.an increase of could also reduce. It is likely that, in the case of Y/Y transformer bank, the reduction on inrush current is due to the increase of Z(s) by the neutral resistor. We are further investigating this phenomenon. In order to understand the characteristics of the proposed scheme further, additional sensitivity studies have been conducted. Some of the results are presented in the following subsections.

6 XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II 955 A. Impact of Transformer Resistance In the foregone derivations, the transformer resistance was neglected. It would be useful to know what is the effect of this approximation. In this case, the transformer model becomes where is the winding resistance. Using a procedure similar to that described in Section II, the breaker contact voltages are found to be Fig. 12. Breaker voltages as affected by R for switching sequence ACB. Within a certain range of (0 to 20% of ), can be expressed as It can be seen that the impact of is not significant. This conclusion has been validated by the example of the MVA transformer. B. Sequence of Switching The proposed scheme as it stands now requires a switching sequence of phases A, B and C. In this study, we want to know if a switching sequence of A, C and B would bring more inrush current reduction. In this case, the breaker contact voltages are determined as follows Fig. 13. Breaker contact voltages as affected by neutral reactance. switching sequence of ABC, the breaker contact voltages are determined as follows for the transformer case: (6) where subscripts 2 and 3 denote switching order. The resulting breaker contact voltage curves are shown in Fig. 12. It can be seen that the trend of is different from that of. The voltage is always higher than the case of. Consequently, there is no intersection between the two curves. The conclusion of this analysis is that the proper switching sequence for the proposed scheme is A, B and C. C. Neutral Impedance The possibility of using a neutral impedance to reduce the inrush current is also investigated. Adopting the (7) The case of inserting a neutral reactor is examined first. The corresponding breaker contact voltage curves are shown in Fig. 13 and are compared with those associated with the neutral resistor. The results show that does not have a valley. The intersection point of and is higher than the value of obtained with or equal to zero. As a result, connecting a reactor to the transformer neutral is not a solution option. The case of connecting a neutral impedance is also investigated. The breaker contact voltages for the cases of, and are shown in Fig. 14. The results indicate that the case of yields the lowest voltage. So a pure resistor as the neutral impedance is the best option for the proposed scheme.

7 956 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 Fig. 14. Breaker contact voltages as affected by neutral impedance. V. CONCLUSIONS is much cheaper than the pre-insertion resistor scheme since only one resistor and one by-pass breaker are used. It is more robust than the synchronous closing scheme. The scheme needs to determine the residual flux of transformer cores to work effectively. There is no good solution to find residual flux yet. In view of the fact that a lot of distribution transformers have a neutral resistor for single-phase fault detection, the proposed scheme could be applied with very low cost delayed closing of each phases of the transformer might be just sufficient. We believe that another major contribution of this work is the discovery of a new class of methods to reduce switching transients. The method is to reduce the breaker contact (phasor) voltages through sequential phase energization. The true function of the neutral resistor is to minimize the breaker contact voltages. From this perspective, the potential of the proposed scheme is not limited to transformer energization. In theory, it is also applicable to capacitor energization and possibly motor starting. We are currently investigating these subjects as well. This paper has presented a theory to explain the characteristics of a proposed sequential phase energization based inrush current reduction scheme. A formula to determine the optimal resistor value is established. Main findings of the work can be summarized as follows: The mechanism of the proposed scheme can be understood from the perspective of breaker contact voltage reduction. These voltages can be determined using steadystate circuit analysis. The proposed scheme is most effective for transformers with a delta winding or having three limbs, i.e. three windings of the transformer are coupled electrically or magnetically. The optimal neutral resistance for these cases can be determined from formula, where is the open-circuit positive-sequence reactance of the transformer. Selecting a precise value for the neutral resistor is not necessary. As long as it is in the neighborhood of, the scheme is equally effective. The sequence of switching should be as follows: phase A first, followed by phase B and then by phase C. This switching sequence will lead to 20% to 30% reductions on the breaker contact voltages and 80% to 90% reductions on the inrush currents. Time delay between the switching events is in the range of 5 to 60 cycles. Although neutral impedance can also be used for the proposed scheme, study results show that the most effective option is still the neutral resistor scheme. Although a lot of results have been obtained for the proposed scheme, we feel more work is needed. For example, how to determine the current flowing through RN is still an open subject. This current is important for assessing the transient withstand capability of the resistor and the neutral voltage rise. There is also a need to field test the proposed scheme on large transformers. The proposed method compares favorably to the existing schemes of pre-insertion resistor and synchronous closing. It ACKNOWLEDGMENT The authors wish to thank C. Muskens of ATCO Electric and T. Martinich of BC Hydro for the suggestions and comments throughout the course of this project. The help of A. Terheide, a technician in the University of Alberta Power Lab, with experimental investigations is fully acknowledged. REFERENCES [1] Y. Cui, S. G. Abdulsalam, S. Chen, and W. Xu, A sequential phase energization method for transformer inrush current reduction Part I: Simulation and experimental results, IEEE Trans. Power Del., vol. 20, no. 2, pp , Apr [2] Members of the staff of the Department of Electrical Engineering, Massachusetts Institute of Technology, Magnetic Circuits and Transformer. New York: Wiley, 1943, pp [3] R. L. Bean, N. Chacken, H. R. Moore, and E. C. Wentz, Transformers for Electric Power Industry. New York: McGraw-Hill, 1959, pp [4] M. Elleuch and M. Poloujadoff, A contribution to the modeling of three phase transformers using reluctance, IEEE Trans. Magn., vol. 32, no. 2, pp , Mar [5] H. M. Dommel, EMTP Theory Book, 2nd ed. Vancouver, British Columbia: Microtran Power System Analysis Corporation, [6] X. Chen, Negative inductance and numerical instability of the saturable transformer component in EMTP, IEEE Trans. Power Del., vol. 15, no. 4, pp , Oct Wilsun Xu (M 90 SM 95) received the Ph.D. degree from the University of British Columbia, Vancouver, Canada, in He worked in BC Hydro from 1990 to 1996 as an engineer. Dr. Xu is presently a Professor at the University of Alberta, Edmonton, Canada. His main research interests are power quality and harmonics. Sami G. Abdulsalam (S 03) received the B.Sc. and M.Sc. degrees in electrical engineering from Elmansoura University, Egypt, in 1997 and 2001, respectively. He is currently pursuing his Ph.D. degree in electrical and computer engineering at the University of Alberta, Edmonton, Canada. Since 2001 he has been with Enppi Engineering Company, Cairo, Egypt. His current research interests are in modeling and simulation of power system transients.

8 XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II 957 Yu Cui received the B.Eng. degree from Tsinghua University, Beijing, China; an M.Sc. degree from Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China; and an M.Sc. from University of Saskatchewan (Canada) in 1995, 2000, and 2003 respectively. He is currently working on his Ph.D. degree at University of Alberta. His research areas include power system stability and power quality. Xian Liu (M 95) obtained the Ph.D degree in computer engineering from the University of British Columbia, Canada, in Before joining the University of Arkansas at Little Rock, Little Rock, AR. Dr. Liu worked at NORTEL Networks, Ottawa, ON, Canada, and the University of Alberta, Canada, from 1995 to To date he and his research collaborators have published more than 50 journal and conference papers, mainly in the areas of electrical machines, communication networks, and engineering optimization.