208 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 A Sequential Phase Energization Method for Transformer Inrush Current Reduction—Transient Performance and Practical Considerations Sami G. Abdulsalam, Student Member, IEEE, and Wilsun Xu, Fellow, IEEE Abstract—This paper presents an improved design method for a novel transformer inrush current reduction scheme. The scheme energizes each phase of a transformer in sequence and uses a neutral resistor to limit the inrush current. Although experimental and simulation results have demonstrated the effectiveness of the scheme, the problem of how to select the neutral resistor for optimal performance has not been fully solved. In this paper, an analytical method that is based on nonlinear circuit transient analysis is developed to solve this problem. The method models transformer nonlinearity using two linear circuits and derives a set of analytical equations for the waveform of the inrush current. In addition to establishing a set of formulas for optimal resistor determination, the results also reveal useful information regarding the inrush behavior of a transformer and the characteristics of the sequential energization scheme. This paper also proposed a method, the use of surge arrester, to solve the main limitation of the sequential phase energization scheme—the rise of neutral voltage. Performance of the improved scheme is presented. Index Terms—Inrush current, power quality, transformer. I. INTRODUCTION A sequential phase energization-based scheme to reduce transformer inrush currents has been proposed by the authors in  and  (Fig. 1). The method uses an optimally-sized grounding resistor. By energizing each phase of the transformer in sequence, the neutral resistor behaves as a series-inserted resistor and thereby significantly reduces the energization inrush currents. It was found that a neutral resistor that is 8.5% of the unsaturated magnetizing reactance would lead 80% to 90% inrush currents reduction. However, the resistor sizing issue was not investigated from the transient performance perspective due to difficulties in conducing transient analysis of nonlinear circuits. Our further study of the scheme revealed that a much lower resistor size is equally effective. The steady-state theory developed for neutral resistor sizing  is unable to explain this phenomenon. Extensive investigation showed that the phenomenon must be understood using transient analysis. If we select the neutral resistor to minimize the peak of the actual inrush current Manuscript received September 6, 2005; revised March 6, 2006. This work was supported by the Alberta Energy Research Institute. Paper no. TPWRD00521-2005. The authors are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4 Canada (e-mail: [email protected] ualberta.ca; [email protected]). Color versions of Figs. 2, 4–7, and 9–16 are available online at http://ieeexplore.org. Digital Object Identifier 10.1109/TPWRD.2006.881450 Fig. 1. Sequential phase energization technique for inrush current reduction. directly, we can obtain a much lower resistor value. It was also found that the first phase energization leads to the highest inrush current among the three phases and, as a result, the resistor can be sized according to its effect on the first phase energization. With the help of nonlinear circuit theory , we managed to derive an analytical relationship between the peak of the inrush current and the size of the resistor, which results in a transient-analysis based theory for the resistor selection. One of the objectives of this paper is to present the analytical work and the resultant design guide for the scheme. The developed analytical method is an improvement over the one published in the classic Westinghouse T&D Reference Book  and can be used to analyze general inrush current phenomenon of transformers and reactors. In addition, this paper also addresses the main limitation of the proposed scheme—the rise of neutral voltage. The use of surge arrester is proposed to overcome the limitation. Performance of the improved scheme is presented. The significance of this work is that it is a rigorous analytical study of the transformer energization phenomenon. The results reveal a good deal of information on inrush behavior of transformers and the characteristics of the sequential energization scheme. In addition, the developed analytical method made it possible to accurately estimate energy requirements for the grounding resistor and the voltage limiting surge arrester. II. PERFORMANCE OF THE SEQUENTIAL PHASE ENERGIZATION INRUSH MITIGATION SCHEME Since the scheme adopts sequential switching, each switching stage can be discussed separately. For first phase switching, the scheme performance is straightforward. The neutral resistor is in series with the energized phase and its effect will be similar to a pre-insertion resistor. When the third phase is energized, the voltage across the breaker contacts to be closed is essentially close to zero due to the existence of delta secondary or three- 0885-8977/$20.00 © 2006 IEEE ABDULSALAM AND XU: A SEQUENTIAL PHASE ENERGIZATION METHOD 209 Fig. 3. (a) Transformer electrical equivalent circuit (per-phase) referred to the primary side. (b) Simplified, two slope saturation curve. Fig. 2. Maximum inrush current as affected by the neutral resistor for a 30 , 3 limb transformer, . (Top: experimental, bottom: kVA, 208/208, simulation). Y 01 legged core. So there will be minimal switching transients for when the 3rd phase is energized , . The 2nd phase energization is the one most difficult to analyze. Fortunately, we discovered from numerous experimental and simulation studies that the inrush current due to 2nd phase energization is lower than those due to 1st phase energization (Fig. 2). This is true for the region for the same value of where the inrush current of the 1st phase is decreasing rapidly increases. as As a result, we should focus on analyzing the first phase energization to develop more precise sizing criteria for the neutral resistor. as function of the operating flux linklinear inductance ages is represented as a linear inductor in unsaturated “ ” and saturated “ ” modes of operation respectively, Fig. 3(b). Secondary side resistance and leakage reactance as reand represent the ferred to primary side are also shown. primary and secondary phase to ground terminal voltages, respectively. During first phase energization, the differential equation describing the behavior of the transformer with saturable iron core can be written as follows: (1) In order to represent the highest saturation level without losing generality, switching angle of zero on the applied sinusoidal voltage waveform together with a positive residual flux polarity is assumed throughout the analysis. In this case, saturation takes place at the positive side of the saturation curve. Accordingly, the general inrush current waveform in unsaturated and saturated modes of operation can be given by III. ANALYTICAL STUDY OF FIRST PHASE SWITCHING One of the main focal points of this paper is to develop a solid design methodology for the neutral resistor size. Our approach presented here is based on deriving an analytical expression relating the amount of inrush current reduction directly to the neutral resistor size. Preliminary results have been presented earlier by the authors in . An accurate expression for inrush current will eliminate the requirement of computer simulation on a case-by-case basis. Few investigations in this field have been done and some formulas were given to predict the general wave shape, harmonic content or the maximum peak current –. For the presented application, it was required that the expression can accurately present the inrush current waveform over a wide range of neutral resistance values taking into account system impedance, residual flux value and the neutral resistor itself. (2) where A. Inrush Current Expression The transformer behavior during first phase energization can be modeled through the simplified equivalent electric circuit shown in Fig. 3 together with an approximate two-slope saturation curve, –. In Fig. 3(a), and present the total primary side resistance and leakage reactance. The iron core non- Generally, transformers operate in unsaturated mode immediately after energization since the initial “or residual” flux is below the saturation flux level . For small neutral resistor values, the magnetizing impedance of the switched phase will 210 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 Fig. 4. Analytical and simulation inrush current waveforms (first cycle) for 30 kVA transformer. Yg 0 1 be very high compared to other linear elements in the series circuit and the supply voltage will be mainly distributed across the magnetizing branch until saturation is reached. The saturation time can be calculated as follows: Fig. 5. I 72/13.8 kV (R ) compared to the simulation peak current for 132.8 MVA, Yg 0 1 3 limb transformer. The inrush peak expression (3) can be rewritten as follows: (5) where in (5) is a dimensionless factor which depends on and ) as well as transformer saturation characteristics ( ratio during saturation the total (6) where , , and are the nominal peak flux linkages, supply voltage, and angular frequency, respectively. Fig. 4 shows the first cycle, analytical and simulation waveforms for the 30 kVA transformer with neutral resistor values of 0.1, 0.5, and 1.0 (Ohm), respectively, and a residual flux of 0.75 (p.u.). The inrush waveform will reach its peak during saturation close to when the sinusoidal term peaks. This assumption is valid for two reasons; first, the exponential term coefficient is fractional as compared to the sinusoidal term amplitude since and . Second, the saturation time , is small as increases which will introduce constant, a small shift in the peak current to appear slightly before the sinusoidal peak value. The saturation current “ ” is small as compared to the inrush peak and can be neglected. Accordingly, the can be peak time and the peak inrush current as function of expressed as follows: , the total For the maximum inrush current condition energized phase ratio including system impedance is high and accordingly, the damping of the exponential term in (5) during the first cycle can be neglected (7) Typical saturation and residual flux magnitudes for power transformers are in the range and Accordingly, switching at voltage zero instant with a polarity that matches the maximum possible residual flux, the saturation are within the angle “ ” w.r.t. instant of switching and following ranges, respectively (8) (9) (3) analytical and simulation curves for the 132.8 The MVA transformer described in  during first phase switching are shown in Fig. 5. values leading to considerable inrush reduction will reHigh ratios. It is clear from (6) and (8) that rasult in low tios equal to or less than 1 ensure negative dc component factor ” and hence the exponential term shown in (5) can be “ conservatively neglected. Accordingly, (5) can be rewritten as follows: (10) B. Neutral Resistor Sizing Based on (3), it is now possible to select a neutral resistor size that can achieve a specific inrush current reduction ratio given by (4) Using (7) and (10) to evaluate (4), the neutral resistor size which corresponds to a specific reduction ratio can be given by (11) ABDULSALAM AND XU: A SEQUENTIAL PHASE ENERGIZATION METHOD 211 Equations (9) and (11) reveal that transformers with less severe saturation characteristics “high saturation flux and low maximum residual flux values” require a higher neutral resistor value to achieve the desired inrush current reduction rate. Based on (9) and (11), the inrush current reduction of 90% can be achieved within the range of (12) Based on (12), a small resistor “less than 10 times the saturation series reactance” can achieve more than 90% reduction in inrush current. The amount of reduction in flux during the first cycle can be found from (2) as follows: 2 Fig. 6. Simulation of the 3 300 MVA, Yg-Y transformer , during second phase switching for R = 150:0 (Ohm). where (13) Within the optimum neutral resistor value defined by (12), the total flux reduction during first phase switching is within (14) As the second cycle starts, an initial flux level of will exist. This results in the absence of inrush current after the first cycle since the maximum flux is close to—or below—the saturation flux. IV. SECOND PHASE SWITCHING Transformer behavior during second phase switching was observed through simulation and experiments to vary with respect to connection and core structure type. However, a general behavior trend exists within low neutral resistor values where the scheme can effectively limit inrush current magnitude. For cases with delta winding or multi-limb core structure, the second phase inrush current is lower than that during first phase switching. Single phase units connected in Yg–Y have a different performance as both first and second stage inrush currents has almost the same magnitude until a maximum reduction rate of about 80% is achieved. Generally, based on the well-known saturation characteristics of power transformers, any reduction in inrush current is a result of limiting the maximum flux that can build up in the core. In this section, the performance of the proposed inrush mitigation scheme during second stage switching will be qualitatively analyzed and com. It will pared to the first switching stage for small values of be shown that the transformer saturation level during second phase switching is less than that during first phase switching. A. Three Single Phase Units Connected in Yg–Y For this condition, the transformer can be modeled using two saturable inductor circuits representing each phase. The coupling between both switched phases is introduced only through the neutral resistor. For any energized phase , the flux as function of the primary phase voltage can be given by and the neutral voltage (15) Phase B will start operating in the unsaturated region with its own residual flux. As a result, both phase currents will be . low and the neutral voltage remains close to zero, As soon as Phase B reaches saturation, its current will increase and the neutral voltage will start to build up. The neutral current will be mainly due to the contribution of phase B. Hence, the neutral resistor can be assumed to be in series with phase B and a similar inrush reduction performance, to that of first phase switching, will hold. The process will continue until the neutral voltage integral “amount of reduction” becomes sufficient to drive Phase A into saturation. With phase A originally in steady state, a disturbance in flux equal to the difference between the rated and saturation flux values is required for phase A to reach saturation. Conservatively assuming that the reduction in flux in Phase B results in an increase of the same amount in phase A, to achieve at least 20 to 35% it will be possible to increase reduction in its flux before disturbing phase A, Fig. 6. is increased further, more inrush current reduction can As be achieved in phase B until both phases reach the same satu. As the difference beration level for a specific value of tween saturation and rated flux values increases, more reduction in phase B current can be achieved. The same conditions apply during third switching stage. B. Transformers With Delta Winding and/or 3-Limb Structures The performance during sequential switching for this type , banks will be quite different than for single phase, transformers due to the following reasons: • dynamic flux will exist in un-energized phases; • inrush current can exist in one phase due to external saturation in un-energized phase (return path of the flux). The existence of dynamic flux in un-energized phases will make the initial flux in the switched phase dependent on the instant of switching. In order to maximize the flux of the switched 212 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 Fig. 7. Simulation of the 30 kVA transformer during second phase switching condition showing the phase fluxes and effect of delta winding current for small values of R = 0:1 (Ohm). phase and consequently represent highest saturation condition, the critical switching instant “ ” should be found. The flux in phase B after switching can be calculated as follows: Fig. 8. Modeling the delta winding during the saturation condition of phase C. instant of switching The maximum theoretical flux that can be reached in phase B can accordingly be given by For the maximum flux condition and (16) on phase B voltage waveform The switching angle of corresponds to a zero initial flux value in phase A and, as a result, no initial flux exists when the second phase is energized. This finding is of importance since it proves that the maximum theoretical saturation level during second phase energization will be lower than that during the energization of the first phase which . equals Immediately after 30 of the switching instant, the fluxes in phases A and B are both positive and determined by the terminal voltage integral of both phases. This will lead phase C which represents the return path of both fluxes to saturate first. As shown in Figs. 7 and 8, the saturation of phase C will drive a delta winding current equal to the magnetizing current of phase C under saturation. The induced delta winding current will be reflected as zero sequence current of the same magnitude flowing through phases A and B and a neutral current equal to twice the delta current. For phase B, both integrals of the terminal and the neutral voltages have the same polarity and hence the delta winding will help reducing saturation level further in phase B. For phase A, the supply voltage waveform will have opposite polarity to the neutral voltage, however, due to the difference between the saturation and rated flux values, the disturbance in phase A will be less than that observed in switched phase B. In case of multi limb transformers with no delta winding, the second and third switching stages behavior depends on the number of core limbs. For 3-Limb transformers, the flux in the two energized limbs will add up into the third limb. As the third limb saturates, the return flux path of phase A and B will experience saturation and as a result a neutral current equals twice the phase current will flow. This will result in a similar effect to that from a delta winding. On the other hand, for transformers with 4 or 5 limbs, and shell form cores, the return path of the flux from phases A and B will be unsaturated to some degree and the performance of the scheme will be similar to that of three single phase units connected in Yg–Y. V. NEUTRAL VOLTAGE RISE: STANDARD REQUIREMENTS AND MITIGATION TECHNIQUES From simulation studies carried out on various transformer types and connections, it was found that the peak neutral voltage will reach values up to 1 (p.u.) rapidly as the neutral resistor value is increased. Typical neutral voltage peak profile against neutral resistor size is shown in Fig. 9 for the 132.8 MVA transformer during 1st and 2nd phase switching. The scheme performance during the complete switching sequence is shown in Fig. 10 with optimum neutral resistor of 50 . A delay of one second between each switching stage is ABDULSALAM AND XU: A SEQUENTIAL PHASE ENERGIZATION METHOD 213 Fig. 9. Neutral voltage peak as a function of R during the first and second switching stages for the 132.8 MVA transformer. Fig. 11. I (R )=I (0) percentage inrush current peak for different arrester saturation voltages R = 50 ( ). Fig. 10. Phase currents, neutral current and neutral voltage during complete switching sequence for the 132.8, 72/13.8 kV, Yg-D transformer R = 50 ( ). quency insulation level at neutral for liquid immersed transformers at system voltages of 25 kV or below is 10 kV but not less than the nominal line voltage. In this case, the proposed scheme can be applied without modification for this type at interconnection levels of 25 kV or below. For voltages higher than 25 kV and up to 69 kV, the neutral voltage rise need to be limited to 50% of the nominal line voltage in order to comply with the insulation requirement at neutral, . In case of dry type transformers, the minimum insulation level at neutral should be at least 4 kV at system voltages of 1.2 kV and extends to 10 kV at higher voltage levels. If the transformer is designed for ungrounded Y connection, the neutral insulation level should be the same as the line terminal level . B. Neutral Resistor With Neutral Voltage Limiting Arrester required to allow phase fluxes to lose most of the dc component. The neutral voltage during the first cycle will reach 85% of the rated phase voltage. Quickly after the first cycle, the transformer is unsaturated and the neutral voltage is negligible since . The unsaturated magnetizing reactance is about 900 times the saturation reactance of a transformer, . Accordingly, with the transformer operating in unsaturated mode, the neutral resistor voltage is negligible. Within the optimum resistor value, the neutral voltage peak is less than 0.5 (p.u.) during second phase energization. As soon as the third phase is switched in, the neutral voltage will remain close to zero. It is a common industry practice to grade the insulation over the Yg winding for solidly grounded transformers –. This can introduce limitations to the applicability of the proposed scheme at high voltage levels. The following section addresses the standard requirements and limitations for the application of the proposed scheme to both dry-type and liquid immersed transformers. A. IEEE Standards Requirements A review of the IEEE/ANSI standards – has been carried out in order to evaluate the acceptable neutral voltage rise limit on different power transformer types. The main application of the proposed scheme is the generator’s step up transformers for IPP “Independent Power Producer” which are interconnected to the system at the distribution or sub transmission levels. The interconnection transformer is preferably Wyegrounded on the system side and Delta connected on the generator side , . According to , the minimum low fre- Arrester(s) connected in parallel with the neutral resistor could limit the neutral voltage rise to the standard level. Actually, the resistor-arrester arrangement presents a nonlinear resistor saturating at the arrester’s saturation voltage. According to (15), limiting the neutral voltage rise will reduce the neutral voltage integral and hence, reduce the technique’s efficiency. Limiting the neutral voltage rise to 0.5 (p.u.) will have effect only during first phase switching, Figs. 9 and 10 which is more desirable in order to limit the energy dissipated through the curves of the arrester-neutral resistor arrester. The arrangement is shown in Fig. 11 for the 132.8 MVA transformer. A similar deduction procedure to the one presented in section III leads to the following inrush expression: (17) Accordingly, the peak inrush current during arrester operation can be expressed as (18) From (18), the amount of reduction in current will depend . However, on how fast the arrester will become saturated, since the neutral voltage will start rising after the transformer 214 Fig. 12. Phase currents, neutral current, and neutral voltage during complete switching sequence R = 50 ( ). Arrester saturation voltage is 0.5 (p.u.). IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 Fig. 14. Accumulated energy during different switching stages. Results for the 132.8 MVA transformer with infinite system. sorbed by the neutral resistor during the complete switching sequence for the 132.8 MVA transformer for the case shown in Fig. 10. It is clear from Figs. 14 and 10 that negligible neutral voltage will exist after the first cycle of the 1st phase energization and the energy dissipated through the resistor can accordingly be calculated as follows: Fig. 13. Phase currents, fluxes, neutral current and neutral voltage during complete switching sequence for the 132.8 MVA with 1000 MVAsc system. saturates at , the neutral voltage integral will have a maximum approaches . This limit as the arrester saturation time clarifies the “almost” steady profile of the inrush current as increases shown in Fig. 11. The resistor-arrester arrangement performance during complete switching sequence is shown in Fig. 12. The results shown in Figs. 10 and 12 were obtained assuming an infinite system bus. The scheme performance with 1000 MVA short circuit impedance, assuming 10% of this impedance to be resistive is shown in Fig. 13. It is shown that inrush current reduction to less than 3 times the nominal current can be achieved considering a relatively small source impedance and at the same time limiting the neutral voltage to 0.5 (p.u.). In addition, the scheme will have much better performance with regards to the settling time of inrush currents. C. Energy Requirements Simulation studies can provide an accurate calculation of energy requirement level for the scheme. In this section, approximate formulas will be given for a quick—but accurate—estimate of the energy withstand capability for both the resistor and the resistor-arrester arrangements. As mentioned earlier, there will be negligible neutral voltage across the resistor after the third phase switching. Accordingly, our focus will be on the assessment of energy requirements during first and second phase switching stages. Fig. 14 shows the accumulated energy ab- (19) For the second phase, as can be seen from Figs. 6 and 7, the neutral current can be presented using two sinusoidal half-waves of twice the frequency. Since the neutral voltage rise during second phase is around 0.5 (p.u.) with the same neutral resistor, the energy during 60-cycle period of the second phase switching can be calculated as follows: (20) As can be seen from (20), most of the energy absorbed by the grounding resistor will be during second phase switching. After the third phase is switched in, the neutral current will be very close to zero and energy dissipation through the resistor can be neglected. For the resistor-arrester arrangement, the arrester will be active only during the first cycle of the first switching stage. As shown in (17) the total current through the switched phase will be composed of a dc component through the resistor and an ac component through the arrester. Accordingly, the energy dissipated through the resistor and the arrestor can be calculated, respectively, as follows: (21) ABDULSALAM AND XU: A SEQUENTIAL PHASE ENERGIZATION METHOD 215 Fig. 15. Accumulated energy during different switching stages (J). Arrester set at 0.5 (p.u.) saturation voltage with the 1000 MVAsc system. Fig. 16. Voltage at the primary side of a 22/0.48, 160 kVa, Y-D transformer due to energizing Phase A. Top: isolated neutral. Bottom: neutral grounding. VII. CONCLUSIONS (22) The arrester will not be active for saturation voltages of 0.5 (p.u.) or higher within the optimal neutral resistor value. The neutral resistor energy is the same as that of the original scheme during second switching stage for the same . As shown in Fig. 15, the total energy absorbed by the resistor during all switching stages is about 1.30 MJ, and 250 kJ for the surge arrester(s). Neutral grounding resistors capable of handling 1000–1500 A root mean square (rms) continuous current for 10 s at voltage levels of 33 kV or more are commercially available today. Arresters can handle less energy dissipation (absorption) than resistors. This is due to the fact that they are originally designed for short period operation duration. However, a way of stacking a number of arresters in parallel in order to handle a higher energy rating has been suggested in . Typical energy capability for arrester class up to 48 kV is 4 to 4.9 kJ/kV  and –. VI. CONSIDERATIONS ON FERRORESONANCE The proposed sequential energization scheme could expose a transformer to ferroresonance. Fortunately, the neutral resistor is in series of the resonant circuit and will provide sufficient damping to prevent ferroresonance from happening. In fact,  proposed the idea of using a neutral resistor to mitigate ferroresonance. Based on numerous TNA studies,  found that a neuis sufficient to prevent the occurtral resistor less than 0.05 rence of ferroresonance in Yg–D transformer banks. Based on the finding, we can conclude that the proposed scheme will not experience ferroresonance problem. Our simulation studies on 22/0.48 kV, 4.5%, 160 kVA, Y–D transformer, also confirmed this conclusion. Fig. 16 shows the voltage waveforms at the energizing side of the transformer due to energizing phase A. It is clear that using the optimal resistor successfully damped the overvoltage at un-energized phases B and C within one cycle. This paper presented an improved and more complete design criterion for a novel transformer inrush current reduction scheme. It was shown that a small neutral resistor size of less than ten times the transformer series saturation reactance can achieve 80–90% reduction in inrush currents among the three phases. The transient performance of the scheme was presented and it was demonstrated through detailed analysis that the first phase switching leads to the highest inrush current level. The paper has also addressed the main practical limitation of the scheme as the permissible rise of neutral voltage. A feasible application range for both dry type and liquid immersed transformer has been proposed and the use of surge arresters to extend the application range of the scheme has also been presented. Formulas were also given to estimate the required energy withstand capability for both the neutral resistor and the arrestor if applicable. REFERENCES  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, pt. 1, pp. 943–949, Apr. 2005.  W. Xu, S. G. Abdulsalam, Y. Cui, S. Liu, and X. Liu, “A sequential phase energization method for transformer inrush current reduction—part II: Theoretical analysis and design guide,” IEEE Trans. Power Del., vol. 20, no. 2, pt. 1, pp. 950–957, Apr. 2005.  A. Boyajian, “Mathematical analysis of nonlinear circuits,” General Electric Rev., pp. 531–537, 745–751, Sep. and Dec. 1931.  Westinghouse Electric Corporation, Electric Transmission and Distribution Reference Book, 4th ed. East Pittsburgh, PA, 1964.  S. G. Abdulsalam and W. Xu, “Analytical study of transformer inrush currents and its applications,” in Proc. Int. Conf. Power System Transients, Montreal, QC, Canada, 2005.  B. Holmgrem, R. S. Jenkins, and J. Riubrugent, Transformer inrush current CIGRE paper 12-03, CIGRE. Paris, France, pp. 1-13, 1968.  H. A. Peterson, Transients in Power Systems. New York: General Publishing Co., General Electric, 1951.  L. F. Blume, G. Camilli, S. B. Farnham, and H. A. Peterson, “Transformer magnetizing inrush currents and influence on system operation,” AIEE Trans. Power App. Syst., vol. 63, pp. 366–375, Jan. 1944.  P. C. Y. Ling and A. Basak, “Investigation of magnetizing inrush current in a single-phase transformer,” IEEE Trans. Magn., vol. 24, no. 6, pp. 3217–3222, Nov. 1988. 216 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007  X. Chen, “Negative inductance and numerical instability of the saturable transformer component in EMTP,” IEEE Trans. Power Del., vol. 15, no. 4, pp. 1199–1204, Oct. 2000.  A. Greenwood, Electrical Transients in Power Systems, 2nd ed. New York: Wiley, 1991.  IEEE Standard General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers, IEEE Std. C57.12.00-2000, 2000, pp. 1-53.  IEEE Standard General Requirements for Dry-Type Distribution and Power Transformers Including Those With Solid Cast and/or ResinEncapsulated Windings, IEEE Std. C57.12.01-1998, Dec. 31, 1998.  IEEE standard requirements, terminology, and test procedure for neutral grounding devices, ANSI/IEEE Std. 32-1972, 1972.  British Columbia Transmission Corporation, 69 kV to 500 kV interconnection requirements for power generators, May 2004.  BC Hydro, 35 kV and below interconnection requirements for power generators, Jun. 2004.  J. J. Lee and M. S. Cooper, “High-energy solid-state electrical surge arrestor,” IEEE Trans. Parts, Hybrids Packag., vol. PHP-13, no. 4, pp. 413–419, Dec. 1977.  M. L. B. Martinez and L. C. Zanetta, Jr., “A proposal to evaluate the energy withstand capacity of metal oxide resistors,” in Proc. 11th Int. Symp. High Voltage Engineering, Aug. 23–27, 1999, vol. 2, pp. 309–312.  M. Martinez and L. Zanetta, “On modeling and testing metal oxide resistors to evaluate the arrester withstanding energy,” presented at the IEEE Dielectr. Mater., Meas. Appl. Conf., 2000, Publ. No. 473.  R. H. Hopkinson, “Ferroresonant overvoltage control based on TNA tests on three-phase wye-delta transformer banks,” IEEE Trans. Power App. Syst., vol. PAS-87, no. 2, pp. 353–361, Feb. 1968. Sami G. Abdulsalam (S’03) received the B.Sc. and M.Sc. degrees in electrical engineering from El-Mansoura University, El-Mansoura, Egypt, in 1997 and 2001, respectively. He is currently pursuing the Ph.D. degree in electrical and computer engineering from the University of Alberta, Edmonton, AB, Canada. Currently, he is with the Enppi Engineering Company, Cairo, Egypt. His research interests are in electromagnetic transients in power systems and power quality. Wilsun Xu (M’90–SM’95–F’05) received the Ph.D. degree from the University of British Columbia, Vancouver, BC, Canada, in 1989. He was an Engineer with BC Hydro, Burnaby, BC, Canada, from 1990 to 1996. Currently, he is a Professor with the University of Alberta, Edmonton, AB, Canada, and a Changjiang Professor of Shangdong University, Shangdong, China. His research interests are power quality and harmonics.