energies Article Effective Simulation Approach for Lightning Impulse Voltage Tests of Reactor and Transformer Windings Piyapon Tuethong, Peerawut Yutthagowith * and Anantawat Kunakorn Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand; [email protected] (P.T.); [email protected] (A.K.) * Correspondence: [email protected]; Tel.: +66-(0)2-329-8330 Received: 31 August 2020; Accepted: 4 October 2020; Published: 16 October 2020 Abstract: In this paper, an effective simulation method for lightning impulse voltage tests of reactor and transformer windings is presented. The method is started from the determination of the realized equivalent circuit of the considered winding in the wide frequency range from 10 Hz to 10 MHz. From the determined equivalent circuit and with the use of the circuit simulator, the circuit parameters in the impulse generator circuit are adjusted to obtain the waveform parameters according to the standard requirement. The realized equivalent circuits of windings for impulse voltage tests have been identified. The identification approach starts from equivalent circuit determination based on a vector fitting algorithm. However, the vector fitting algorithm with the equivalent circuit extraction is not guaranteed to obtain the realized equivalent circuit. From the equivalent circuit, it is possible that there are some negative parameters of resistance, inductance, and capacitance. Using such circuit parameters from the vector fitting approach as the beginning circuit parameters, a genetic algorithm is employed for searching equivalent circuit parameters with the constraints of positive values. The realized equivalent circuits of the windings can be determined. The validity of the combined algorithm is confirmed by comparison of the simulated results by the determined circuit model and the experimental results, and good agreement is observed. The proposed approach is very useful in lightning impulse tests on the reactor and transformer windings. Keywords: lightning impulse voltage test; genetic algorithm; reactor and transformer windings; vector fitting 1. Introduction Transformers and reactors are employed in a high-voltage (HV) system in many applications. The transformers are utilized for adjusting voltage levels in the AC transmission and distribution systems. The reactors are utilized for limitation of over voltage, reactive power compensation, tuned and detuned filters, and so on. During the operation of the transformers and the reactors, there are possibilities in insulation failure due to direct lightning and electromagnetic-induced lightning effects. Therefore, it is necessary to test the transformer and reactors with lightning impulse voltage for being an assessment of the insulation performance of the transformers and reactors before installation. The crucial problem in the lightning impulse voltage tests on the transformer and reactor winding is the adjustment of the test voltage waveform according to the standard requirement. As shown in Figure1, the front time ( T1), time to half (T2), and overshoot rate (βe) will be in the ranges of 1.2 µs 30% (0.84 µs to 1.56 µs), 50 µs 30% (40 µs to 60 µs), and less than 5%, respectively [1–5]. ± ± Energies 2020, 13, 5399; doi:10.3390/en13205399 www.mdpi.com/journal/energies Energies 2020, 13, x FOR PEER REVIEW 2 of 19 1.0 be (Overshoot rate) 0.9 ] B . u Energies 2020, 13. , 5399 Vm 2 of 19 p [ e g 0.5 a t l o 1.0 A e V 0.3 (Overshoot rate) 0.9 B 0 Time O1 T 0.5 T1 =10T/6 A T2 Voltage [p.u.] 0.3 Figure 1. Generated lightning impulse voltage waveform. 0 Time Conventionally,O1 the generatorT circuit named Marx’s circuit, as shown in Figure 2, is applied in the lightning impulse voltage tests.T1 =10 TThe/6 charging capacitance (Cs) will be much higher than load T2 capacitance (Cb), since the efficiency of the circuit is necessary to be controlled at a high level (normally more than 90%).Figure The 1.sparkGenerated gap (G lightning) is used impulse as a high voltage-voltage waveform. switch. It will be sparked or Figure 1. Generated lightning impulse voltage waveform. switched on to connect the charging capacitor to the load for the generation of lightning impulse voltage.Conventionally, For the front time the generatorand time to circuit half, namedaccording Marx’s to the circuit, standard as shown requirement, in Figure the2, front is applied time in the lightning impulse voltage tests. The charging capacitance (Cs) will be much higher than and tail time resistances (Rd and Re) can be calculated by Equations (1) and (2) [6]. load capacitance (Cb), since the efficiency of the circuit is necessary to be controlled at a high level (normally more than 90%). The spark gapT (G)CC is used+ as a high-voltage switch. It will be sparked R = 1 sb d (1) or switched on to connect the charging capacitor2.96 CC tosb the load for the generation of lightning impulse voltage. For the front time and time to half, according to the standard requirement, the front time and T1 1 tail time resistances (R and R ) can beRe calculated= by Equations (1) and (2) [6]. (2) d e + 0.73 CCsb ! T Cs + C Practically, in the low frequency rangeR (below= 1 10 kHz)b the winding can be represented well by(1) d C C an equivalent circuit of an inductor in parallel with2.96 a capacitor.s b It is noticed by Glaninger that, if the inductance of the winding is less than 15 mH, the conve ntional! circuit is quite difficult to apply and T1 1 it is difficult to adjust T2 to longer thanR e 40= μs [7]. Therefore, Glaninger’s generator circuit, as(2) 0.73 Cs + Cb illustrated in Figure 3, is recommended to apply in the lightning impulse voltage test. Low frequency model G Rd of winding load Cs Re Cb LL Figure 2. Conventional generator circuit used in the lightning impulse voltage tests, where Cs is a Figurecharging 2. Conventional capacitor, G isgenerator a spark gap,circuitRe usedis a tail in timethe lightning resistor, Rimpulsed is a front voltage time tests resistor,, whereCb is C as is load a chargingcapacitor, capacitor, and LL is G a is load a spark inductor. gap, Re is a tail time resistor, Rd is a front time resistor, Cb is a load capacitor, and LL is a load inductor. Practically, in the low frequency range (below 10 kHz) the winding can be represented well by an equivalentIn Glaninge circuitr’s circuit of an, as inductor shown inin parallelFigure 3 with, the a parallel capacitor. connection It is noticed of the by additional Glaninger that,inductor if the (Linductanced) with the offront the- windingtime resistor is less (R thand) is used. 15 mH, This the is conventional for the purpose circuit of isextending quite diffi thecult time to apply to half and init theis diimpulsefficultto wave adjustforTm2. toThe longer parallel than connection 40 µs [7]. Therefore,of the additional Glaninger’s parallel generator resistor circuit, (Rp) with as illustrated the test objectin Figure is used3, is recommendedfor controlling tothe apply overshoot in the lightningrate of the impulse generated voltage waveform. test. In 1978, K. Feser [8] proposedIn Glaninger’s the approach circuit, for asthe shown selection in Figure of the3, theappropriate parallel connection circuit parameters of the additional—i.e. the inductor charging ( Ld ) with the front-time resistor (Rd) is used. This is for the purpose of extending the time to half in the impulse waveform. The parallel connection of the additional parallel resistor (Rp) with the test object is used for controlling the overshoot rate of the generated waveform. In 1978, K. Feser [8] proposed the approach for the selection of the appropriate circuit parameters—i.e. the charging capacitance (Cs), Energies 2020, 13, 5399 3 of 19 Energiesthe front-time 2020, 13, x resistance FOR PEER (REVIEWRd), the additional inductance (Ld), and the additional parallel resistance3 of (R p19), as given in Equations (3) to (7). In addition, the appropriate tail-time resistor (Re) has to be selected to capacitanceobtain the undershoot (Cs), the front voltage-time less resi thanstance 50% (R ofd), the the peak additional voltage inductance [7–11]. (Ld), and the additional parallel resistance (Rp), as given in Equations (3) to (7). In addition, the appropriate tail-time resistor 2 Cs T /LL (3) (Re) has to be selected to obtain the undershoot voltage≈ 2 less than 50% of the peak voltage [7–11]. 2 6 R CTL=sL0.42 / 10 − /C (3)(4) d × b −6 RC=0.4 10 / 6 dbL (= 1.25 )10− R (4)(5) d × d LR=1.25 10−6 (5) ddRp = (RdLL)/Ld (6) = RRLLp( d Lp) / d (6) Re = 1.6 LL/Cs (7) RLCe= 1.6 L / s (7) Ld Low frequency model of winding load G Rd L Cs Re Rp Cb L Figure 3 3.. Glaninger’s generator generator circuit circuit for for the lightning impulse voltage tests on the winding winding.. However, the the distortion distortion in in the the waveform waveform generated generated by by the the circuit circuit with with parameters parameters from from K. Feser’sK. Feser’s suggestion suggestion was wasnoted. noted. A trial A and trial error and errorapproach, approach, then, is then, employed is employed to adjust to the adjust circuit the parameterscircuit parameters to mitigate to mitigate the waveform the waveform distortion distortion and to obtain and tothe obtain waveform the waveformparameters parameters,, according toaccording the standard to the requirement. standard requirement. An alternative An method alternative was method proposed was based proposed on a neural based network on a neural for thenetwork selection for theof appropriate selection of appropriateGlaninger’s Glaninger’scircuit parameters circuit [11].