Keywords: Equivalent Instantaneous Inductance, Finite Element, Inrush Current.

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1 Discriination of Inrush fro Fault Currents in Power Transforers Based on Equivalent Instantaneous Inductance Technique Coupled with Finite Eleent Method Downloaded fro ijeee.iust.ac.ir at 5:47 IRST on Wednesday October 3st 208 M. Jaali*, M. Mirzaie* and S. A. Gholaian* Abstract: The phenoenon of agnetizing inrush is a transient condition, which occurs priarily, when a transforer is energized. The agnitude of inrush current ay be as high as ten ties or ore ties of transforer rated current that causes alfunction of protection syste. So, for safe running of a transforer, it is necessary to distinguish inrush current fro fault currents. In this paper, an equivalent instantaneous inductance (EII) technique is used to discriinate inrush current fro fault currents. For this purpose, a three-phase power transforer has been siulated in Maxwell software that is based on finite eleents. This three-phase power transforer has been used to siulate different conditions. Then, the results have been used as inputs in MATLAB progra to ipleent the equivalent instantaneous inductance technique. The results show that in the case of inrush current, the equivalent instantaneous inductance has a drastic variation, while it is alost constant in the cases of fault conditions. Keywords: Equivalent Instantaneous Inductance, Finite Eleent, Inrush Current. Introduction Power transforers are a class of very expensive and vital coponent of electric power systes. The cost associated with unplanned outage of a power transforer is very high. So, it is iportant to iniize the frequency and duration of unwanted outages in this coponent. One of the ain reasons for wrong operation of protective syste for the transforer is inrush current. Inrush current is a transient current that occurs in a transforer due to flux saturation in the core and its agnitude can be as high as fault currents. Because inrush current is not a fault current, it is iportant to develop a technique to distinguish this current fro fault currents. In this regard, soe techniques have been proposed in the literature. Since a agnetizing inrush current generally contains a larger second haronic coponent, [] used second haronic criteria to distinguish inrush current fro fault currents. Also, for iproving the second haronic restraint algorith, in [2] instead of easuring the ratio between the agnitudes of the second and fundaental haronic Iranian Journal of Electrical & Electronic Engineering, 20. Paper first received 23 Nov. 200 and in revised for 30 Apr. 20. * The Authors are with the Departent of Electrical and Coputer Engineering, Babol University of Technology, P. O. Box 484, Babol, Iran. E-ails:.jaali@stu.nit.ac.ir, irzaie@nit.ac.ir and gholaian@nit.ac.ir. coponents, a ratio between the phasors of the has been used. In [3-4], discriination of inrush current fro fault currents have been investigated based on wavelet transfor. In this technique, the wavelet transfor is ipleented on the differential currents and inrush current is distinguished fro fault currents based on different features of their wavelet coponents. Identification of inrush current in transforer using error estiation technique is discussed in [5]. Based on error estiation technique, first, the dead angles are extracted fro the differential current waves. Then, with coparing this wave with two reference waves, inrush current can be discriinated fro fault currents. In [6], inrush current is discriinated fro fault currents by calculating the average of the active power flowing into transforers fro each terinal. In [7], by exaination of the ain flux variation that is constructed by the voltages and currents of transforer windings, inrush current is identified. In [8-9], using S transfor, different features are extracted for inrush current and fault currents. For discriination of inrush current fro fault currents, iproved correlation algorith is used in [0]. In this technique, by exaination of correlation coefficients between two successive half cycles, inrush current can be distinguished fro fault currents. In this paper, an equivalent instantaneous inductance technique (EII) is used for discriination of inrush Iranian Journal of Electrical & Electronic Engineering, Vol. 7, No. 3, Sep

2 Downloaded fro ijeee.iust.ac.ir at 5:47 IRST on Wednesday October 3st 208 current fro fault currents. First, soe forulas based on transforer equivalent circuit have been derived. Then, for verifying these forulas on a typical transforer, a three-phase power transforer has been siulated in Maxwell software together with Siplorer software for investigation of different situations. Finally, a MATLAB progra based on derived forulas has been written to check the validity of the forulas. 2 Equivalent Instantaneous Inductance Technique The differential equation in the priary side of a two-winding transforer can be expressed as follow: d λ(t) = + + () v(t) Ri(t) L where, v (t), L, R and i (t) are the terinal voltage, leakage inductance, resistance and current in the priary winding, respectively. Also, λ(t) and i (t) are the flux linkage and agnetizing current, respectively. It should be noted that the voltage drop of the agnetizing branch of transforer core in equation () has been considered as follow: v (t) d λ(t) d λ(t) = = (2) If L is defined as equation (3), then it represents the instantaneous agnetizing inductance of transforer. L d λ(t) = (3) In the noral and internal fault conditions of transforer, the core is not saturated and the agnetizing current is very little. These situations result in constant instantaneous agnetizing inductance that has very sall variations. However, the inrush current is result of the transforer core saturation. Because in the inrush situation, the transforer core will alternate between the saturation and noral conditions, the instantaneous agnetizing inductance has vast variations. This situation is shown in Fig. where, L nor and L sat represent the agnetizing inductance in the noral and highly saturated conditions, respectively. As it can be concluded, the calculation of the instantaneous agnetizing inductance is very difficult, because it depends on the accurate flux linkage in the transforer core. For overcoing this proble, the EII can be defined as a solution. For this purpose, Fig. 2 that shows the general for of the equivalent circuit for a two-winding transforer can be considered. In this odel the paraeters of the secondary side have been converted to the priary side by the transforation ratio. Also, it should be entioned that L s is the leakage inductance in the short-circuit winding, where L s = corresponds to the noral operation. Fig. Variation of agnetizing inductance during the inrush current. Fig. 2 General equivalent circuit for two-winding transforer. For the equivalent circuit shown in the Fig. 2, the following equation can be written in the priary side: dδi(t) v (t) R i(t) L R i (t) L where Δi(t) and L e are defined as follows: 2 = Δ e 2 (4) Δ i(t) = i (t) i (t) 2 (5) L L s L = L + e L + L s (6) L e is defined as the EII that is a nonlinear function of L with constant L and L s. As it can be concluded, L e will be constant during internal fault and noral conditions, but it will have a drastic variation when an inrush current occurs. Therefore, the EII (L e ) has an equivalent characteristic to the instantaneous agnetizing inductance (L ) and can be used as a criterion for discriination inrush current fro fault currents. The calculation of L e can be done using the paraeters of transforer and easured instantaneous currents and voltages of the priary and secondary sides. Because obtaining the accurate values of the transforer paraeters is difficult, it is necessary to consider an approxiation to siplify the procedure of the calculation of L e. For this purpose, because the voltage drop of the secondary winding load current in L and R is negligible when coparing with that of the differential current in the R and L e, especially for largescale transforers, the third and fourth ter on the right 98 Iranian Journal of Electrical & Electronic Engineering, Vol. 7, No. 3, Sep. 20

3 Downloaded fro ijeee.iust.ac.ir at 5:47 IRST on Wednesday October 3st 208 side of the equation (4) can be eliinated and written as follow: dδi(t) v (t) = R Δ i(t) + L e (7) Equation (7) has been transfored into a discrete difference equation for using trapezoid principle. At kt instant, this equation is as follow: Δ i(k + ) Δi(k ) v(k) = RΔ i(k) + L (8) e 2T where, T is the sapling cycle. For eliinating R in equation (8), equation (7) has been written at (k-)t instant and this equation together with equation (8) have been used for calculation of the equivalent instantaneous inductance at kt instant as follow: L = 2T[v (k) Δi(k ) v (k ) Δ i(k)] e [ Δ i(k + ) Δi(k ) +Δi(k) Δi(k 2) 2 2 Δi(k) Δi(k )] (9) Also, it should be noted that the variation of the EII has been calculated using following equations. Δ L = L (i) L (0) L e N 2 e e e N i = N = L (i) () N i= e where, N is the nuber of saples per power frequency cycle. Δ L e is used to discriinate inrush current fro the fault current based on the following criterion: If Δ L e exceeds a threshold, then there is an inrush current, otherwise fault situation has been occurred. 3 Siulation Results In order to verify the validity of the entioned ethod in the discriination of inrush current fro fault currents, a three-phase power transforer has been siulated in Maxwell software that is based on finite eleent ethod (FEM). The FEM is a rapid and effective way in siulation and odeling of advanced engineering systes that solve a proble by dividing the proble doain into several eleents and then applying physical laws to each sall eleent [-2]. Also, Siplorer software has been used to create transforer connections and different situations including agnetizing inrush and fault conditions. The paraeters of the siulated transforer are given in Table. It should be entioned that the analysis has been investigated on the lower tap that is including HV. Fig. 3 shows this three-phase power transforer in the Maxwell environent. Also, soe geoetry of the eployed transforer with 2D representation is drawn in Fig. 4. The agnetization curve of transforer core is shown in Fig. 5. This curve has been assigned to the aterial that is used for odeling the nonlinear nature of transforer core. It should be noted that a 2 khz sapling frequency has been used to obtain data fro different conditions. Then, the obtained data have been transferred to the MATLAB software. In this software, a progra based on equations (9-) has been written to obtain EII in Table Paraeters of the siulated transforer. Transforer connection Rated apparent power Voltage ratio Rated frequency Δ/Y (LV/HV) 30 MVA 20/63 kv 50 Hz Nuber of LV turn (each lib) 232 Nuber of HV turn (each lib) 352 Nuber of HV2 turn (each lib) 70 Nuber of HV3 turn (each lib) 63 Core steel type M5 Fig. 3 Siulated transforer in Maxwell environent. Fig. 4 Priitive geoetry of the siulated transforer in Table (diensions are in ). Jaali et al: Discriination of Inrush fro Fault Currents in Power Transforers Based on 99

4 Downloaded fro ijeee.iust.ac.ir at 5:47 IRST on Wednesday October 3st 208 Fig. 5 Magnetization curve of the odeled transforer. different cases. The following sections present the results of the above entioned procedure. 3. Magnetizing Inrush Situation In this case, the inrush phenoenon is created through the connection of no load power transforer to the power source in zero tie. The inrush aplitude in this situation for the three-phase power transforer is shown in Fig. 6. As seen fro the figure, all phases have shown inrush current situation that should be analyzed with EII criterion. Figure 7 shows the variation of the EII for three phases of transforer. As seen fro the figure, EII for all phases show a drastic variation with high aplitude, which is the key feature of the inrush current. 3.2 Internal Short Circuit Fault For the siulation of internal fault, two cases have been considered. The first one is the turn-turn short circuit and the second is the turn-ground short circuit Turn-Turn Short Circuit In this case, a short circuit of 30 turns in the phase C for the on load situation of transforer has been considered. Fig. 8 shows the differential currents of all phases in this situation. (a) (b) (c) Fig. 7 Variation of EII in the case of inrush current (a) phase A (b) phase B (c) phase C. Fig. 6 Inrush current for all three phases. Fig. 8 Differential currents when the short circuit of 30 turns occurs in the phase C. 200 Iranian Journal of Electrical & Electronic Engineering, Vol. 7, No. 3, Sep. 20

5 Downloaded fro ijeee.iust.ac.ir at 5:47 IRST on Wednesday October 3st 208 As seen fro Fig. 8, the differential currents of A and B phases are within the range of noinal agnetizing current, but C phase current is larger than the noinal agnetizing current. Therefore, it is necessary to calculate EII for C phase. As seen fro the Fig. 9, the calculated EII for C phase shows a sall variation which corresponds to the entioned criterion Turn-Ground Short Circuit In this case, a turn-ground short circuit in phase B has been considered. Fig. 0 shows the differential currents of all phases in this situation. As seen fro Fig. 0, the differential current of B phase is larger than the noinal agnetizing current, while the differential currents of other phases are in noral range. Therefore, it is necessary to verify B phase with the entioned ethod. Figure shows the calculated EII for B. As it can be concluded fro this figure, a sall variation in EII of B phase corresponds to the entioned criterion for fault situations. So, siilar to previous case, the fault situation can be characterized with sall variation in EII. 3.3 Single Line to Ground Fault In this case, a single line to ground (phase A) occurred on the secondary side with a balanced Y connected of phase connected to the secondary side. Figure 2 shows the three differential currents. In this situation, the differential current of phase A is larger than the noinal. Therefore, the phase A ust be analyzed with EII criterion. Fig. 3 shows the calculated EII for phase A. As seen in this figure, fro the sall variation of EII, it can be concluded that the fault situation has been occurred and the relay ust operate. As it can be concluded fro the EII figures for different situations including inrush and fault conditions, the variation of EII for fault situations are very sall (at ost 0.02), while it is high for inrush situation (at least 50), so a safe threshold between these two nubers can be selected for discriination purpose. Fig. 0 Differential currents in the case of turn-ground short circuit in the phase B. Fig. Variation of EII of phase B in the case of turn-ground short circuit. Fig. 2 Differential currents in the case of single line to ground fault in phase A. Fig. 9 Variation of EII of phase C in the case of turn-turn short circuit. Fig. 3 Variation of EII of phase A in the case of single line to ground fault. Jaali et al: Discriination of Inrush fro Fault Currents in Power Transforers Based on 20

6 Downloaded fro ijeee.iust.ac.ir at 5:47 IRST on Wednesday October 3st Conclusion In this paper, an equivalent instantaneous inductance (EII) technique has been used to discriinate inrush current fro fault currents. This ethod is based on different behaviors of the calculated EII for inrush current and fault currents. The calculated EII during inrush current has a drastic variation, while it is alost constant during fault conditions. For checking the validity of the EII technique in the discriinationn of inrush current fro fault currents, a three phase power transforer has been siulated in Maxwell software that is based on finite eleent ethod. The obtained data of different situations have been ipleented on EII technique. The resultss show a good perforancee of the technique in the discriination of inrush current fro fault currents. References [] Sykes J. A. and Morrison I. F., A proposed ethod of haronic restraint differential protecting of transforers by digital coputer, IEEE Trans. Power Apparatus and Systes, Vol. PAS-9, pp , May 972. [2] Kasztenny B. and Kulidjian A.., An iproved transforer inrush restraint algorith increases security while aintaining fault response perforance, 53rd Annual Conference for Protective Relay Engineers, pp. -27, Apr [3] Faiz J. and Lotfi-Fard S., A novel Wavelet-based algorith for discriination of internal faults fro agnetizing inrush currents in power transforers, IEEEE Trans. Power Del., Vol. 2, No. 4, pp , Oct [4] Youssef O. A. S., A wavelet-based techniquee for discriination between faults and agnetizing inrush currents in transforers, IEEE Trans. Power Del., Vol. 8, No., pp , Jan [5] He B., Zhang X. and Bo Z. Q., A new ethod to identify inrush current based on error estiation, IEEE Trans. Power Del., Vol. 2, No. 3, pp , July [6] Yabe K., Power differential ethod for discriination between fault and agnetizing inrush current in transforers, IEEE Trans. Power Del., Vol. 2, No. 3, pp. 09-8, July 997. [7] Zhao X., Chai J. and Su P., Identificationn of agnetizing inrush currents of power transforers based on features of flux locus, Sixth International Conferencee on Electrical Machines and Systes, Vol., No., pp , Nov [8] Jiao S., Wang S. and Zheng G., A new approach to identify current based on generalized S- transfor, International Conference on Electrical Machines and Systes, pp , Oct [9] Zhang Q.., Jiao S. and Wang S., Identification n inrush current and internal faults of transforerr based on hyperbolic S-transfor, 4th IEEEE Conference on Industrial Electronics and Applications, pp , May [0] Ling X., Liu P. and Malik O. P., Studies for identification of the inrush based on iproved correlation algorith, IEEE Trans. Power Del., Vol. 7, No. 4, pp , Oct [] Liu G. R. and Quek S. S., The finite eleent ethod: A practical course, Elsevier Sciencee Ltd., [2] Faghihi F. and Heydari H., Matheatical proof for the iniized stray fields in transforerss using auxiliary windings based on state equations for evaluation of FEM results, Iranian Journal of Electrical & Electronic Engineering, Vol. 6, No., pp , Mar Morteza Jaali was born in Mahoodabad, Iran, in 984. He received the B.Sc. and M.Sc. degrees in electrical engineering fro University of Tabriz, Tabriz, Iran in 2007 and University of Mazandaran, Mazandaran, Iran in 20, respectively. His research interests include odeling and application of power transforers, finite- eleent odeling, and coputer aided calculation of electroagnetic fields, electric achinery and high voltage engineering. Mohaad Mirzaie was born in GhaeShahr, Iran in 975. He Obtained B.Sc and M.Sc Degrees in Electricall Engineeringg fro University of Shahid Charan, Ahvaz, Iran and Iran University of Science and Technology, Tehran, Iran in 997 and respectively and PhD Degree in Electricall Engineeringg fro Iran University of Science and Technology in His research interestss include high voltage engineering, intelligencee networks for internal faults and studying of insulationn systes in transforers, cables, generators, insulators, electrical otors. Sayyed Asghar Gholaian was born in Babolsar, Iran, in 976. He received B.Sc. degree in electrical engineeringg fro K.N.Toosi University of Technology, Tehran, Iran in 999 and M.Sc. degree in electric power engineering (electrical achines) fro university of Mazandaran, Babol, Iran in 200. He also received the Ph.D degree in electricall engineering fro K.N.Toosi University of Technology, Tehran, Iran in He is currently an assistant professor in the departent of Electrical Engineering at the Babol University of Technology, Iran. His research interests include power electronic and design, siulation, odeling and control of electrical achines. 202 Iranian Journal of Electrical & Electronic Engineering, Vol. 7, No. 3, Sep. 20

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