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ACTA ELECTROTEHNICA 122 Inrush Current of a Group of Transformers – Effect of the Secondary Load Răzvan Radu, Dan D. Micu, Dan Ovidiu Micu, Andrei Ceclan Technical University, dept. of Electrical Engineering and Measurements, Cluj-Napoca, Romania Abstract—Occurrence of inrush transients, which are mostly comprised of the 3rd and 5th harmonic is influenced by a variety of factors such as the switching angle, the remanent flux of the transformers’ cores but also the load on the secondary side. Keywords— inrush; transient; load; impedance. 1. INTRODUCTION Modern energy distribution grids are moving ahead towards smart grid control and smart metering. But there is a constant need for having adequate protection systems in order to avoid or limit power outages to a minimum. One important disturbance which affects protective relays is the occurrence of inrush currents when reconnecting a group of transformers, which is the typical event following the elimination of a faulty section of the grid. As part of our study which targets using inrush as the key to optimize the operation of protective relays, we constructed an analytical model of the main electrical elements needed to be taken into account for the simulation of inrush transients [1]. One important detail to take into account is the type and ratio of the load of each transformer. Hence, this paper shows how the peak inrush and its decay rate are affected by the load ratio and its power factor. 2. ANALYTICAL MODEL The model we propose for the distribution transformer is a quadripole with the secondary load represented as an impedance Zs. The model is shown in Fig 1 below. Fig. 1. Distribution transformer model with load on secondary Using our previously defined method, determination of the parameters is facilitated so a model can be constructed for each standard rated power [1]. Therefore, being given the catalog data of the transformers, precisely the rated power Sn in VA, primary voltage U1 in V , short-circuit (winding) losses Psc in W, short-circuit impedance(voltage) uk in %, noload (iron) losses P0 in W, and no-load current i0 in %, we just need to multiply uk and i0 by 10-2 to standardize the units. In such way, the no-load parameters can be easily determined [1]: R1 = 1 Psc ⋅ U 12 ⋅ 2 S n2 (1) Z1 = u k ⋅ U 12 Sn (2) X 1 = Z12 − R12 (3) Z1 = Z 2 ' = R1 + j ⋅ X 1 (4) The transversal element (admittance) is then determined : G0 = P0 U 12 (5) B0 = i0 ⋅ S n U 12 (6) Y = G0 − j ⋅ B0 © 2015 – Mediamira Science Publisher. All rights reserved (7) Volume 56, Number 1-2, 2015 Next, the remaining element is the load impedance. In order to obtain the correct values, given that the transformers are operating live and there is no possibility to actually measure the on-site impedance of the load, the simplest method is to determine the secondary current at full-load[2]. Next, the full-load value can be downscaled and facilitates calculation of the equivalent impedance by applying Ohm’s law. The values can then be recalculated for different power factors by determining the resistance and reactance which comprise the load impedance. I 2n Sn = 3 *U 2n (8) With U2n being the rated line voltage on the secondary side, which in our case is 400V. Then, the impedance is obtained at various points by simply dividing the rated phase voltage by I2n*load ratio (0…1). This impedance has to be reported on the primary side, achieved by amplifying the obtained value with the transformer ratio[3]. Z s' = U 2n k _ load * I 2 n 123 This model is based on validated parameters, so the components of the quadripole are easily determined as : Rcable = 0,188 ⋅ lc Lcable = 0,186 *10 −3 ⋅ lc (13) −6 Ccable = 0,65 *10 ⋅ lc , Where lc is the cable length given in kilometers. 1 ⋅ (Rcable + j ⋅ ω ⋅ Lcable ) 2 Y = j ⋅ ω ⋅ Ccable Z1 = Z 2 ' = 3. (14) NUMERICAL SIMULATIONS AND RESULTS The model is based on step-by-step simplification of the string of transformers and cables, usually interconnected as shown in Fig.3. (9) Z s = Z s' * K 2 (10) Fig. 3 General topology of a medium voltage feeder upon reconnection Given the power factor of the load, we can fully characterize the transformer by knowing the active and reactive power consumption through the two components of the load impedance, the resistance and inductive reactance. After modeling each element, the schematic is then reduced to an ideal voltage source, a switch to be closed at a given moment, and an equivalent impedance of the entire feeder, given as: Rs = Z s * PF (11) Z e = Re + j ⋅ X e (12) From here, the permanent regime current is determined as: X s = ω * Ls = Z s − Rs 2 2 In fact, various models can be constructed and through series and paralleling of impedances, each transformer can be simplified to a single equivalent impedance Ze [4],[5]. The model of the underground cable is also a quadripole requiring per-unit length parameters [1]. I perm = U f ⋅ Re Re + X e 2 2 + U f ⋅ Xe Re + X e 2 2 (16) And knowing that the equivalent inductance is given by Le=Xe/ω, with ω=2*π*f, we can determine the time constant of the circuit as: τ= Fig. 2 The quadripole model of the underground cable (15) Le Re (17) Hence, the inrush regime consists mainly of 3 stages: the peak inrush from the switching to 20*τ , the transition from the transient from 20*τ to 30*τ, and the slow decay to the permanent regime load after a duration of 30*τ. In this case, the inrush of a group of transformers can be described by: ACTA ELECTROTEHNICA 124 i (τ ) = 4 ⋅ i p 0 ⋅ e − 1 25τ + 3 ⋅ i p0 ⋅ e i (τ ) = i perm (τ ) + 4 ⋅ i p 0 ⋅ e − 1 125τ − 1 75τ , τ < 20 ⋅ τ , τ > 20 ⋅ τ (18) (19) Where, with γ the phase, i p0 = Uf ⋅ 2 Re + X e 2 2 X ⋅ sin γ + arcτan e , τ > 20 ⋅ τ Re (20) Based on this model, on-site samples of the inrush transient were collected for a case concerning of the reconnection of 7 distribution transformers (total rated power is 2960 kVA), assuming a 50% load degree on each transformer at neutral power factor. The data were analyzed and extrapolated to a range of load ratios in order to demonstrate the effects the load over the inrush transient. The results are purposed to be used for the overcurrent relays, as described below. The safe area to set the protective relays is restricted by the permanent load limit of the underground cables, which, for the existing cables, having a cross-section of 3x150mm2 and Aluminium conductors, is derated to a value of 280 A because of the insulation aging. Hence, we define the safe area as the right-hand side starting from the point where the decaying inrush transient crosses the 280 A mark. It is easy to observe that a larger load ratio leads to an increased peak inrush and shifts the “safe area” towards 0.65 seconds for the worst case scenario of reaching 100% load on all transformers, as shown in Fig. 4. On the other hand, if we consider that the load ratio cannot change dramatically, because the power substations power the same consumers, a more plausible 10% increase in load would mean the safe area shifts from 0.225 to 0.325 seconds, thus a 0.1 seconds increase in the required trip delay. Next, we can easily distinguish the effect of the load type, through a power factor reduced to 0.8, as in Fig.5. In this case, the safe area is shifted from 0.225 to 0.3 seconds, and the corresponding difference of 0.075 seconds shows less impact than the load ratio. Fig. 5. Numerical aproximation of the inrush transient at 0.8 power factor, case 1 The second on-site set of data was collected following the reconnection of a group of 4 transformers (total rated power 1910 kVA), making an assumption of 90% load ratio. In this case, increasing from 90% to 100% load ratio would mean the safe area shifting from 0.23 to 0.28 seconds, thus a 0.05 seconds increase, as shown in Fig. 6. An interesting fact is that the power factor has a bigger impact in this case, altering the safe area to 0.37 seconds (0.14 seconds increase), opposite when compared to the other case. Fig. 6. Numerical aproximation of the inrush transient at 0.92 power factor, case 2 Fig. 7. Numerical aproximation of the inrush transient at 0.8 power factor, case 2 Fig. 4. Numerical aproximation of the inrush transient at 0.92 power factor, case 1 After the analysis of the data, the final conclusions can be drawn out. Before issuing any conclusions and comments, we have to detail that, in the absence of instantaneous measurements on the corresponding transformers, we were compelled to make some assumptions which may affect the coefficients of the inrush transient equation. Volume 56, Number 1-2, 2015 The first assumption made was that the transformers, for the two depicted cases, operate at either 50% load or 90% load, value approximated by existing measurements at different hours, hence different load profiles in the urban area. Even so, the method described here and in [1], [6] allows modeling of any feeder with any combination of usual transformers. The second assumption made was that the corresponding power factor is the neutral 0.92, considering that the transformers provide electricity to a residential area. Having the results at hand, we can conclude that the biggest requirement is to investigate the actual load profiles with digital analyzers, given that both characteristics have different impact on the inrush transient. ACKNOWLEDGMENT This paper is supported by the Human Resources Development Program POSDRU/159/1.5/S/137516 financed by the European Social Fund and by the Romanian Government. REFERENCES 1. 2. 3. 4. 5. 4. CONCLUSIONS This paper is a part of our detailed research on inrush transients in energy distribution grids with the final target of using transients as disturbance and then optimize the operation of relays accordingly. Here we have shown that there is a correlation (direct dependence) between the load ratio of the transformers and the magnitude of the inrush transient generated by the group. It has also been proven that the biggest impact is the load ratio itself, with the load type (described by its power factor) having less impact on the peak inrush and its damping rate. 125 6. R. Radu, D. O. Micu, D. D. Micu, A. Ceclan, “Analytical model for a Medium Voltage distribution grid’s main elements – transformers and cables”, in press. F. de Leon and A. Semlyen, “Complete transformer model for electromagnetic transients,” IEEE Trans. Power Del., vol. 9, no. 1, pp. 231–239, 1994. D. Micu, V. Topa, “Basic electrotechnics and electrical circuits”, Technical University of Cluj-Napoca, 1987. F. de Leon and A. Semlyen, “Efficient calculation of elementary parameters of transformers,” IEEE Trans. Power Del., vol. 7, no. 1, pp. 376–383, Jan. 1992. N. Chiesa, “Doctoral Thesis: Power Transformer Modeling for Inrush Current Calculation”, Norwegian University for Science and Technology, 2010. R. Radu, Dan O. Micu, A. Ceclan, C. Barbulescu, and St. Kilyeni, “Recent advances on the influence of power transformers inrush current over the optimization of medium voltage feeder protection”, Universities Power Engineering Conference, Dublin, 2013. Răzvan Radu Technical University, dept. of Electrical Engineering and Measurements Cluj-Napoca, Romania [email protected]