Recent Advances in Energy, Environment and Materials Modeling of grounding systems of power lines under pulse influence Kirill I. Netreba Ph.D. Student at Electrical Engineering Department SPbSPU, Russia [email protected] Nikolay V. Korovkin Head of Electrical Engineering Department SPbSPU, Russia [email protected] m Nikolay V. Silin Head of Electrical Engineering and Electrotechnical Department FEFU, Russia [email protected] Abstract: - The technique of determination of equivalent electromagnetic parameters of grounding systems of power lines is offered and examined. The technique is based on use of the experimental data gained by means of specially developed mobile experimental set. The result of identification is the linear circuit correctly reproducing electromagnetic characteristics of the grounding systems of power lines under arbitrary influences. Key-Words: - grounding system, pulse influence, RLC model, lightning overvoltage account electromagnetic energy in reactive elements, without usage of standard electrical circuit synthesis methods is not substantiated and unpromising. Exception is [9] where oscillogram of transient resistance was obtained as a result of pulse experiment’s data processing. Based on this oscillogram the simplest RL model was fitted. Time constant was also found graphically. In [10] parametric synthesis of the second order passive impedor was done based on pulse experiment data. However, in case of GS not only parameters of equivalent circuit are unknown, but its topology as well. So, resistive model of grounding systems based on “pulse” resistance does not fully reproduce real processes result in GS under pulse influences. 1 Introduction In present time in Russia [1] and in other countries [2] so called resistive model of grounding system (GS) is used. According to this model grounding system is characterized by stationary resistance R on main (low) frequency and by “pulse” resistance Rimp=max(u)/max(i) or r(t)=u(t)/i(t) on pulse influences. It should be noted that in theoretical electrical engineering by pulse resistance it is traditionally understood reaction of the circuit on delta function [3], therefore term “pulse” resistance used in grounding theory is in quotes. Resistive model of GS is simple but theoretically substantiated only for stationary regimes. In [4] absence of correlation between “pulse” resistance obtained under aperiodic and damped vibrational influences is shown. In [5] dependence of “pulse” resistance on frequency (or duration of pulse front) is demonstrated. Therefor when the frequency is changed correction coefficient has to be applied to Rimp. Despite imperfections of usage Rи as main characteristic of GS experimental and theoretical researches are conducted based on “pulse” resistance. To be able to compare “pulse” resistance of different GS without usage of correction coefficient special pulse generator with reference pulse characteristics 0.25/100 and 10/350 mcs is created [6]. In [7, 8] an attempt to synthesize equivalent RLC circuit of GS based on specially defined “local pulse resistance” at time interval till 1mcs was made. Obviously, synthesis of equivalent RLC circuits is the next step in GS model development. However, synthesis of such circuits on “pulse” resistance basis, which doesn’t take into ISBN: 978-1-61804-250-7 2 Synthesis of RLC models of ground grids In this paper methodic of synthesis of GS RLC models is presented. It allows to analyse pulse regimes of GS work in lightning protection systems on strict theoretical basis as opposed to methods based on “pulse” resistance. Transient resistance z(t) is used as primary parameter of grounding system. Numerically it is equal to voltage on the GS under current unit step and it is defined from voltage oscillograms for any current test pulse. Realization of z(t) by methods of electrical circuit synthesis allows to define equal circuit and electromagnetic parameters of GS. 108 Recent Advances in Energy, Environment and Materials of antenna will have frequency about 1 MHz. Wave processes due to wave reflection in grounding ware from power line towers have frequencies (vC/4l, vC/8l) 0.5–1 MHz. Sparking and wave processes in the grounding system itself have higher equal frequencies because of small geometrical size of areas where they occur. So, initial data can be smoothed up to 500 kHz equivalent frequency. With decrease of smoothing frequency complexity of parametric synthesis task reduces and accuracy of initial data approximation increases. Therefor GS models for relatively short frequency range (switching overvoltage) can be obtained quite easily and significantly increase modeling accuracy. 2.1 Initial data processing Experimental data (see Fig.1) i(t) and u(t) obtained under standard lightning pulse influence include information about different physical processes going with process of current flow through GS. Sparking in the soil, wave processes in grounding ware, electromagnetic radiation by tower pole for aerial lines are among these processes. They are quite high-frequency, fast damped and not associated with equivalent circuit of GS though its influence is clearly seen in experimental data. For reduction of this influence experimental data is smoothed and then used for equivalent circuit synthesis. u(t), i(t), o.e. 1 2.1.1 Usage of optimization algorithms for synthesis of RLC models In general parametric synthesis problem can be definitely solved by exhaustive search among all possible values of varying parameters. However, huge amount of possible solutions makes such approach unreasonable concerning time resources. In case of continuous varying parameters which is the case for this work such approach is found to be impossible. Application of different optimization algorithms allows significantly reduce number of estimated solutions. Gradient methods are widely used to solve optimization problems with continuous parameters and with possibility to calculate gradient of functional. However in present work since optimization problem is not unimodal soft compute techniques which allow to find global extremum of the problem are preferable [11, 12]. To do parametric synthesis of equivalent circuit of GS next optimization algorithms were studied and software realized: simulated annealing, genetic algorithm and artificial bee colony algorithm (bee algorithm). These algorithms are able to work with large number of optimized parameters which allows to synthesize circuits of any order to approximate transient processes with high equivalent frequency. Let’s consider application of artificial bee colony algorithms to parametric synthesis problem. Let’s equivalent circuit of the GS has topology as it is shown in Fig.2, a. Voltage source e(t) is experimentally obtained and smoothed voltage oscillogram u(t). The task is to fit values of circuit’s parameters so the error between circuit current icirc(t) and experimental smoothed current iexp(t) was minimized (Fig.2, b): 0.8 0.6 0.4 i(t) 0.2 u(t) 0 -0.2 -0.4 -0.6 -0.8 -1 t, мкc 0 10 20 30 40 50 60 70 80 90 100 Fig.1. Experimental data. Experimental data smoothing process is not formal because smoothing degree influence on topology and parameters of equivalent circuit of GS. Smoothing algorithm used in this work for typical set of experimental data is shown below. Initial data is obtained for rod-shaped GS of overhead line tower. Experimental data (about 104 points) obtained by double-channel oscilloscope in 0-10-4 s time range is interpolated on 215 points and then by Fast Fourier Transform (FFT) converted into frequency domain (214 of complex amplitudes). After this frequency spectrum is cut off up to 211 harmonics. Therefore, frequency of the highest harmonic is 20 MHz which correspond to bandpass of used oscillograph. So, on this stage only high frequency noises appearing due to decimation of analog signal, high frequency noses of measuring complex and electromagnetic environment are removed. For further smoothing equal frequencies of the processes going with process of current flow through GS have to be evaluated. For this purpose let’s use next appropriate estimations. Supposing 25 meter tower pole as quarter-wave oscillator this kind ISBN: 978-1-61804-250-7 t I ( p) = ∫ | iexp (t ) − icirc (t ) |dt , I ( p ) → min, (1) p∈Π 0 109 Recent Advances in Energy, Environment and Materials where I – minimizing function, Π – tolerance range of parameter’s vector p, p=[R1 R2 R3 L C] – vector of equivalent circuit parameters. found for lower frequency oscillograms stay the same for higher frequency oscillograms. 200 i, A u, V/10 8,6 Iэiexp I icirc uexp U/10 4,8e-5 150 38,4 2,8 3,8e-5 100 50 εave=2,7% εmax=25,8% 0 -50 t, mcs 0 10 20 30 40 50 60 70 80 90 100 Fig.3. Voltage and current oscillogram smoothed under 500 kHz equal frequency and equivalent circuit. 140 i, A u, V/10 120 uexp iexp icirc 8,6 4,8e-5 100 Fig.2. a – example equivalent circuit, b – formulation of optimized function. 80 40 Next parameters were applied for bee algorithm: number of scouts s = 20, number of best patches n = 4, number of perspective patches m = 20, number of bees following best patches N = 15, number of bees following perspective patches M = 6. The result is shown in Fig.3. One may see that current i(t) and voltage u(t) smoothed up to 500 kHz are rapidly oscillating functions, however approximation accuracy of obtained equivalent circuit enough high. Thus, average error is εave500=2.7 % and maximum error is εmax500=25.8 %. In Fig.4 equivalent circuit for voltage and current oscillograms smoothed up to 75 kHz is shown. Comparison between Fig.3 and Fig.4 allows to estimate influence of smoothing degree of initial data on topology and parameters of equivalent circuit of GS. As one may see with increase of equivalent frequency of experimental data circuit topology is changed, however not in essence. New physical processes are modeled by appearance of new elements in the circuit. As one may see moving from 75 kHz to 500 kHz one RC chain was added to approximate high frequency processes. At the same time common parameters of the equivalent circuit ISBN: 978-1-61804-250-7 38,4 104 5,8e-11 εave=2,3% εmax=3,8% 60 2,8 3,8e-5 20 0 -20 t, mcs 0 10 20 30 40 50 60 70 80 Fig.4. Voltage and current oscillogram smoothed under 75 kHz equal frequency and equivalent circuit. 3 Calculation of lightning surge Let’s estimate influence of GS model on overvoltage at substation and its protecting surge arrester after lightning stroke at overhead line 150 kV. Fig.5 shows system model to calculate overvoltage for different GS models. Standard lightning impulse 1,2/50 mcs with 350 kV amplitude is appear at voltage maximum in stationary regime. Overvoltage wave goes to protected object PO (substation) and its surge arrester SA through Line1. The length of Line1 enough large so wave processes between PO and SA is damped before arrival of reflected from voltage source wave on Line1. 110 Recent Advances in Energy, Environment and Materials Fig.5. Test model to calculate overvoltage dependence on GS model. Protected object is the transformer working at active-inductive load. Active resistance of the load is equal to wave impedance (R = 300 Ohm). Surge arrester is placed 450 m from PO and connected to grounding system GS. Let’s consider several GS models. The first one (Fig.6, a) neglects active-inductive resistance of the ground system. In this resistive model the value of the R and calculated as stationary resistance of the equivalent circuit. The second one (Fig.6, b) GS is modeled simply as part of full equivalent circuit. The third one (Fig.6, c) is full equivalent circuit obtained by method described above. Calculation results of the overvoltage at surge arrester and protected object are shown in Fig.6. Let’s describe wave processes between SA and PO in general on resistive model sample (curve 1, 5 in Fig.6). As it is seen in the figure protected object voltage may significantly exceed SA voltage. Overvoltage wave is reflected from transformer without sign change which leads to voltage double at protected object comparing to incoming wave (by duration of lightning impulse about a few microseconds transformer is equal to capacitor) Going back to surge arrester reflected from transformer wave goes though protected span almost without distortion at the beginning while total stress of incoming from Line1 wave and reflected from ISBN: 978-1-61804-250-7 transformer wave is less than discharge voltage of surge arrester (Udis). When total voltage of SA is close to Udis reflected from transformer wave stats to reflect from surge arrester with sign change. Therefore after several reflections overvoltage at transformer gradually becomes equal to discharge voltage of surge arrester. According to results shown in Fig.6 GS model has significant influence on maximum overvoltage which occurs at protected object and surge arrester. Usage of RLC circuits as GS models leads to appearance of maximums at each transitional process. For resistive model with surge arrester response its current increase instanter limiting its voltage level. For RLC model current through surge arrester cannot increase immediately because of inductance (see Fig.7) which lead to transitional process and thus higher voltage level. As one can see maximum overvoltage at SA for resistive model is 10,3 % less than for full model which is considerable. For protected object errors for the first maximums are even larger because of voltage doubling (see table in Fig.6). When used resistor as a GS model maximum voltage level at protected object is 13,8 % less comparing to maximum voltage with full circuit as a GS model. 111 Recent Advances in Energy, Environment and Materials 550 U, кB R1 8 500 R1*10 RLсхема model RL полная схема equivalent 7 450 circuit 6 5 400 350 300 4 3 2 1 250 200 150 100 t, мкс 50 860 862 864 866 868 870 Fig.6. Overvoltage at SA (1,2,3,4) and PO (5,6,7,8), table of maximum errors (relative to equivalent circuit), variants of GS models. To compensate active-inductive character of GS it is suggested sometimes to increase simply the value of active resistance. Such an approach as results shows does not give qualitative and quantitative correlation. Increase of active resistance value ten times (from 1,28 Ohm to 12,8 Ohm) remains error between maximum voltage values considerable high (see curves 2, 3 and 6, 7 in Fig. 6). At the same time approximate accounting of GS inductive characteristics leads to wrong results. For concerned case the results are overrated (see curves 4, 8 in Fig. 6). 2.5 I, кA From obtained results one may see that the reason of overvoltage at protected objects depends not only on surge arrester characteristics. Significant error in real overvoltage definition is the error in calculation of grounding system’s transient resistance. 4 Conclusion The technique of determination of equivalent electromagnetic parameters of grounding systems of power lines is offered and examined. The technique is based on use of the experimental data gained by means of specially developed mobile experimental set. Calculations of the overvoltage occurring due to lightning stroke show significant dependence of maximum voltage levels at protected object on GS models. Ω ЗУ: R1=1.28Ohm R1=1,28 полная схема ЗУ full circuit 2 1.5 References: [1] РД 153-34.0-20.525-00. Методические указания по контролю состояния заземляющих устройств электроустановок. М.: СПО ОГРРЭС, 2000. [2] Methods for measuring the earth resistance of transmission towers equipped with earth wires / 1 0.5 0 мкс t,t,mcs 860 862 864 866 868 870 872 874 876 878 Fig.7. Current through surge arrestor. ISBN: 978-1-61804-250-7 112 Recent Advances in Energy, Environment and Materials [3] [4] [5] [6] [7] заземления основного и защитного оборудования на надежность грозозащиты подстанций // Первая Российская конф. по молниезащите: Сб.докл. – Новосибирск: Сибирск.энерг.академия, 2007. – С.383–392. 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