Comparative analysis of influence of the type line supplying nonlinear load on deformation of voltage and current in the power system

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Computer Applications in Electrical Engineering Comparative analysis of influence of the type line supplying nonlinear load on deformation of voltage and current in the power system Stanisław

1 Computer Applications in Electrical Engineering Comparative analysis of influence of the type line supplying nonlinear load on deformation of voltage and current in the power system Stanisław Bolkowski, Wiesław Brociek Warsaw University of Technology Warszawa, Plac Politechniki 1, iem.pw.edu.pl Robert Wilanowicz Kazimierz Pulaski University of Technology and Humanities Radom, ul. Malczewskiego 29 The results of simulation tests concerning the cooperation of the nonlinear load with the power system are presented. In numerical experiments we have taken data from the real systems, including the cable and overhead lines. In practice the nonlinear load of high power may be supplied by the overhead or cable lines. The paper presents the comparative analysis, how the applied type of the line influences the level of distortion of the voltages and currents in the power system. The values of the higher harmonics of the voltages and currents as well as THD have been determined in the paper. These values have been estimated for the beginning and ending terminals of the overhead and cable lines supplying the nonlinear load of the inductive character concerning the cooperation of the filtering compensating device and the nonlinear load of high power. All experiments have been performed using MicroCap-8 program. In the paper we have included he exemplary results of the numerical calculations. KEYWORDS: deformations of voltage and current, frequency characteristics, passive filters, overhead and cable lines 1. Introduction The main reason of the deteriorating of the quality of the electrical energy in the power system is the increasing number of the nonlinear loads in the system. Even at sinusoidal voltage excitation the current of the nonlinear receiver is distorted (non-sinusoidal). The non-sinusoidal current flowing through the real source of non-zero internal impedance causes the distortion of the terminal voltage as well. In this way both: current and voltage in the system at nonlinear load are distorted and contain higher harmonics. In practice the nonlinear load of high power may be supplied by the overhead or cable lines. The type of supply line has a significant impact on the level of distortion of voltages and currents in the supply system in the event of a harmonic caused by nonlinear loads. In this paper a comparative analysis of the impact of such non-linear receiver to the level of distortion of voltages and currents in the supply system. The values o f harmonic currents and voltages and THD at the

As a result of distortion we can observe the resonance phenomena of different harmonics, that can be observed in the supplying line.

2 S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence beginning and the end of the supply line. It presents also examples of the simulation results on the impact of a passive filter on the level of distortion in the reporting system. As a result of distortion we can observe the resonance phenomena of different harmonics, that can be observed in the supplying line. These phenomena depend not only on the parameters of the line, but also on the value of consumed currents, that is on the power of the nonlinear load. The paper presents the results of numerical experiments performed for the system composed of nonlinear load and the supplying power line. In the experiments we have taken into account the frequency characteristics of the absolute values of the impedances measured at the terminals of the nonlinear load. 2. System description Figure 1a presents the general scheme of supplying the nonlinear load u = f(i). The model presented in Fig. 1, is composed of the following elements: supplying point 110 kv of short-circuit power Szw = 500 MVA, 50 km of overhead line at 110 kv of 240 mm2 cross-section, transformer 110/15 kv, the main supplying point (PCC) 15 kv of short-circuit power Szw = 200 MVA, 10 km supply line of 15 kv (overhead or cable), of 120 mm2 cross-section, transformer 15/3 kv and the nonlinear load u = f(i). The unity parameters of the overhead transmission line 15 kv are as follows : R = 0,245 Q/km, L0 = 1,1 mh/km, C0 = 9,78 nf/km and of the cable transmission line 15 kv Ro = 0,253 Q/km, L0 = 0,39 mh/km, C0 = 0,23 jf/km. The parameters (RS, LS) of the model have been determined using following formulas (for f = SOHz) [1,2] S S ZW 200*106 R S «0,1XS = 0.124Q (2) L S = ^ = 4e "3 H (3) a It is interesting to know that the resonance phenomena may occur in the line (cable or overhead), supplying the nonlinear load. In the case of resonance the exact value of the resonance frequency is of great importance. The input impedance Z WE = f ( a ) seen from terminals 2-2 at representation of the line by the 2-port of lumped parameters (Fig. 1b) and the other part of the system by the impedance Z s = R s+jxs [1] can be described by the following expression [1, 2]: Z (, ) = [(1 + Z 0(kl)Y2(kl) ) Z S + Z 0(kl) ] E ( Y + Y + Y Y Z )Z + (1 + Z Y ) ( 1 1(kl)~ 1 2(kl) 1 l(kl)1 2(kl) 0(kl) / S \ 0(kl) 1(kl) / (1) 12

a) 1 Z 0 = R 0 + J X L0 and Y0 = J k k 0 - ( 5) b) c) Fig. 1. The general scheme of the investigated system (a), the lumped model the supplying line (b), the distributed parameter model of the line

At such frequency the analysis of the phenomena occurring in the system needs to be represented as the long transmission line. In such case the input impedance of the system (Fig.

3 a) 1 Z 0 = R 0 + J X L0 and Y0 = J k k 0 - ( 5) b) c) Fig. 1. The general scheme of the investigated system (a), the lumped model the supplying line (b), the distributed parameter model of the line (c); Izr(k) - the RMS value of the current of kth harmonic At the frequency of higher harmonics (for example the 20th - 1 khz) we can observe the resonance phenomena in the line. At such frequency the analysis of the phenomena occurring in the system needs to be represented as the long transmission line. In such case the input impedance of the system (Fig. 1c) seen from the terminal 2-2 can be presented as following [1, 2, 4]. Z WE (kl) = Z C(k) Zs(k>CkY(k>l + Zc<i'> + Zc(k> Sh^ (6) Z )sh v l + Z c h y l ^S(k)/* n i(k)1 ^ ^C(k)c n i(k)1 where Y(k) - the propagation constant of the line, Z c{k) - the wave (characteristic) impedance of the line for kth harmonic. Figure 2 presents the change of the absolute value of the impedance Zwe = f(w) as a function of the length of 15 kv line l = 10km, 15 km, 20 km for cable line. Figure 3 shows the results of the AC analysis of the live change of the absolute 13

The change of the absolute value of the impedance Zwe = fro) as a function of the length of 15 kv line l = 10 km, 15 km, 20 km for cable line f f i D M V<14)fi(V4) Fig. 3.

4 value of the impedance Z we = fro ) for the model: 10 km of cable line of 15 kv represented by lumped 2-port (Fig. 3b), and 10 km overhead line of 15 kv represented by long transmission line model (Fig. 3a). Micro-Cap 8 Evaluation Version Fig. 2. The change of the absolute value of the impedance Zwe = fro) as a function of the length of 15 kv line l = 10 km, 15 km, 20 km for cable line f f i D M V<14)fi(V4) Fig. 3. The live change of the absolute value of the impedance Zwe = f(ro) for the model: a) 10 km of cable line of 15 kv (Ro = ohm/km, Lo = 0.39 mh/km, Co=0.23 uf/km) represented by lumped 2-port, b) 10 km overhead line of 15 kv (Ro = ohm/km, Lo = 1.1 mh/km, Co = 9.78 nf/km) represented by long transmission line model To find out at what length of the line and at what frequency we may observe the resonance effects in the system of Fig. 1a we should perform multiple calculations of the impedances described by the equations ( 1) and (2) [1]. 14

3. The simulation results of power system of medium voltage at nonlinear load Figure 4 presents the scheme of one phase of the 15 kv line supplying the nonlinear load u = f(i).

We have made the following assumptions: the supply (PCC) is composed of an ideal voltage source of the a value corresponding to one phase of the three-phase 15 kv system with components Rs, Ls, of

5 3. The simulation results of power system of medium voltage at nonlinear load Figure 4 presents the scheme of one phase of the 15 kv line supplying the nonlinear load u = f(i). The calculations have been performed for the overhead and cable lines supplying the nonlinear load. We have made the following assumptions: the supply (PCC) is composed of an ideal voltage source of the a value corresponding to one phase of the three-phase 15 kv system with components Rs, Ls, of the values dependent on the short-circuit power rails 15 kv (Szw = 200MVA) the nonlinear load of R2 = f (t), L2 = f (t) to simulate the load that results in the nonlinear current and inductive reactive power. The unity parameters of transmission line of 15 kv are as follows: overhead line Ro = Q / km, Lo = 1.1 mh / km, Co= 9.78 nf / km. cable line Ro = Q / km, Lo = 0.39 mh / km, Co = 0.23 ^F / km. Fig. 4. The scheme of the simulated system composed of the model PCC-15kV, the transmission line (overhead or cable) at 15 kv of length l = 10 km and cross section S = 120 mm2 at nonlinear load The influence of the type of power line voltage and current distortion in the supply system, can be to examined using the representing modules the equivalent impedance versus frequency seen from the terminals non-linear load[2]. This approach enables the study of changes of impedance for the whole analyzed frequency range. This is particularly important in the case of a parallel connection of passive filters at the beginning or end of the supply line. Based on the waveform of Figure 5, we can conclude that the overhead line has slightly higher impedances for frequencies lower than 1 khz in comparison to the cable line. In order to perform quantitative analysis of the phenomena occurring in the analyzed systems, the calculations of distortion of currents and voltages in the circuit o f Figure 4 will take into account the distorted load current waveforms. 15

000K -12.000K c) v( ' 2 )(V ) 300.000 0.000 20.000m 40.000m 60.000m T (Secs) 20.000m 40.000m 60.000m T (Secs) 80.000m 100.000m 120.000m 80.000m 100.000m 120.000m -300.000 0.000m -i(r5) (A) 20.000m 40.000m 60.000m 80.000m 100.000m 120.000m T (Secs) Fig.

6 Based on the transients value of the load current (Fig. 5), the values of effective individual harmonic currents: I50Hz = 249A, I250Hz = 21.6A, I350Hz = 21.6 A, and the percentage of their share in the fundamental harmonic nonlinear load current: I5%= 8.6% It% = 8.6% K a) Micro-Cap 8 Evaluation Version UFK5H.CIR 0.000K K b) K 0.000K K c) v( ' 2 )(V ) m m m T (Secs) m m m T (Secs) m m m m m m m -i(r5) (A) m m m m m m T (Secs) Fig. 5. Transients of a) voltage at main supply point (PCC of 15 kv, b) load voltage at the end overhead line 15 kv, c) the nonlinear load curent Model of nonlinear load impedance Zob = f(t) assuming the initial phase of the first harmonic receiver voltage 9 = 0 generates a load current of the instantaneous value equal to: iob(t) = 248.4y[2sin(oji o ) + 21.ó42sin(5m i o ) sin (7 o i - 142o ) sin (1 1 o i o) + 1.8^ 2sin(13rni + 122o) + 0.M 42sin(17m i + 123o) ^2sin(19rni o) Figure 5 illustrates these transients used in further analysis. The values of each harmonic of the load current when powered by an overhead and cable lines used in calculations are comparable. The values of each harmonic load current when powered by an overhead line and cable used in calculation are comparable. The limit value of THDV at 15kV and 30kV is [2] TH D V = n U X ( ) 2100% < 8% k=2 Uj (7) Figure 6 and 7 presents spectrum o f the load current and voltage 15 kv in Fig. 4 at overhead line. 16

V alues o f individual voltage and current harm onics, and the coefficients TH D V and TH D I at the beginning o f the overhead line (PCC), and at the end o f the line (the point o f attachm ent o f

5 50 k ' ' * 0. 7 5 0 K " " 1.0 00k " " " 1.2* H A R M (i(r 2 )) F (H z) 12.500 10.000 7.5 0 0 5.0 0 0 2.5 0 0 T i.00l0 ^ " 0.2 50 k " " " 0.500K " " 0. 7 50 k " " 1.0 0 0 k " " ' 1.

7 V alues o f individual voltage and current harm onics, and the coefficients TH D V and TH D I at the beginning o f the overhead line (PCC), and at the end o f the line (the point o f attachm ent o f the load) are shown in Table M icro -C a p 8 E valuation V ersion circuitl.cir CumulativiAmplitede of i(r2) vs Fre4uencyequency ^ 0 0 0K " " K " " * k ' ' * K " " k " " " 1.2* H A R M (i(r 2 )) F (H z) T i.00l0 ^ " k " " " 0.500K " " k " " k " " ' 1.2' IH D (H A R M (i(r 2 )),5 0 ) (% ) F (H z) Fig. 6. Spectrum of the load current ( overhead line) K K 0. K K ^ 0 0 0K " " k " " 0.5 H A R M (V (4 )) F (H z) M ic ro -C a p 8 E valuation V e rs io n circuit1.cir 0 ó 50 k " " 1.0 S 0 ^ ^ " " " 1 2 W H k " k " " 0.5 IH D (H A R M (V (4 )),5 0 ) (% ) F (H z) 0 ó 5 0 k " " 1.0' S 0 K " " " " 1. 2! Fig. 7. Spectrum of the 15 kv load voltage ( overhead line) Table 1. The maximum values and percentage of the higher harmonics of the currents and voltage for powering the nonlinear load overhead line Source current Load Load Harmonic Source voltage current voltage order A % A % V % V % 1 249, , ,9 8,8 21,6 8, , ,8 7 21,9 8,8 21,6 8, , ,7 11 1,96 0,78 1,94 0, , , ,83 0,77 1,9 0, , ,09 THD[%] 12,5 12,44 2,07 8,33 17

Analogous calculations were performed for the cable line. Figure 8 presents transient of voltage, current of the load and the source voltage at 15 kv presented in Fig. 4 at cable line.

8 Analogous calculations were performed for the cable line. Figure 8 presents transient of voltage, current of the load and the source voltage at 15 kv presented in Fig. 4 at cable line. Micro-Cap 8 Evaluation Version T (Secs) Fig. 8.Transients of a) voltage at main supply point (PCC of 15 kv, b) load voltage at the end cable line 15 kv, c) the nonlinear load curent Table 2 presents the values and percentage of the higher harmonics of the voltage and current, and the coefficients THDV and THDI presented in Fig. 4 for powering the nonlinear load cable line. Table 2. The maximum values and percentage of the higher harmonics of the currents and voltage for powering the nonlinear load cable line Source Load Load Source voltage Harmonic current current voltage order A % A % V % V % 1 252, , ,9 7,7 24,0 9, , ,8 7 25,7 10,2 24,0 9, , ,9 11 2,70 1,06 2,24 0, , ,6 13 2,84 1,12 2,19 0, ,4 89 0,78 THD[%] 14,27 13,22 2,42 4,99 Figure 9 and 10 presents spectrum of the load current and voltage 15 kv in Fig. 3 at cable line. 18

S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence 75.0 00 50.0 00 M ic ro -C a p 8 Evaluation V ersio n circuit1.cir Cum ulativeam plitude o f i(r 4) vs Frequencyequency 25.

2 5 0K IH D (H A R M (i(r 4 )),5 0 ) (%) F (H z) P ercent Distortion o f i(r 4) vs Frequency 0.5 0 0K F (H z) 0.7 5 0K 1.000K Fig. 9. Spectrum of the load current (cable line) 1.250K 1.500K 1.200K 0.

9 S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence M ic ro -C a p 8 Evaluation V ersio n circuit1.cir Cum ulativeam plitude o f i(r 4) vs Frequencyequency " i.. I----* « HARM (i(r4 )) « K K IH D (H A R M (i(r 4 )),5 0 ) (%) F (H z) P ercent Distortion o f i(r 4) vs Frequency K F (H z) K 1.000K Fig. 9. Spectrum of the load current (cable line) 1.250K 1.500K 1.200K K K K 0.000K. T M ic ro -C a p 8 Evaluation V ersio n circuitl.cir i V - V i i H A R M (V (9)) P p r r. p n t n i Q t n r t i n n n f X /fc f t \ / q F r p n n p n r. \ / f. T.. i i K K K K 1.000K IH D (H A R M (V (9 )),5 0 ) (%) Fig. 10. Spectrum of the 15 kv load voltage (cable line) 1.250K On the basis of performed simulations we may conclude that the type of the power line may have the important impact on the voltage distortion. 4. The numerical results of simulation of medium voltage line and passive filter Figure 11 present circuit model of one phase of the 15 kv network with a nonlinear load with and attached filter 5th and 7th harmonics (filtering compensating devices - FCD). One way to analyse the negative impact of nonlinear load on the power system is the use of harmonic filters [3]. For this purpose, we used the system of Figure 4, and performed the calculations with attached filters of fifth and seventh harmonics at the end of the line (Fig. 11). Exemplary results of the simulation are shown in Figure

devices (FCD) and nonlinear load (R2, L2) In numerical experiments have been focused on the analysis of the influence of passive filters on the deformation o f voltage in system.

10 S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence Fig. 11. The scheme of one phase of the simulated system composed of model PCC - 15 kv transmission line (overhead or cable) at 15 kv of length l =10 km and cross section S = 120 mm2, filtering compensating devices (FCD) and nonlinear load (R2, L2) In numerical experiments have been focused on the analysis of the influence of passive filters on the deformation o f voltage in system. The passive filter is built as one or more section tuned to the particular frequencies to be eliminated. The quality of resonance section depends on the harmonics to which are tuned. D k = 1 0 k (8) where k - the order o f harmonic. The impedance of the filter (50 Hz) section to 1th harmonic is of the capacitive character, which means, that it can be used as the device for compensation of the reactive device. The parameters of individual branches (cell) of the passive filter tuned for 250 Hz and 350 Hz (in the Fig. 11) are as follows: - the fifth harmonic filter of Q5 = 50, C5 = 40 ^F, L5 = 10,1 mh, R5 = 0,318 Q - the seventh harmonic filter of Q7 = 70: C7 = 10 ^F, L7 = 20,7 mh, R7 = 0,65 Q Figure 12 presents the absolute values o f the impedance o f the overhead and cable lines as a function of the frequency in the circuit of Fig. 11. The values of the current of the nonlinear load in the circuit of Fig. 11 are the same as in the case of circuit of Fig. 4. Hence the harmonic spectrum of Fig. 13 and 14 are typical for both circuits. Application of filter in the analysed system causes the reduction of the network impedance which are characteristic for the load of particular frequencies. At the same time we observe the reduction of the deformation of the current as well as its magnitude. It is well illustrated in Fig. 13 and

S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence Fig. 12. The change of the absolute value of the impedance Zwe=fra) for the scheme in Fig.

0 0 0K 6.0 0 0K 3.0 0 0K 0.0 0 0 K 0.0 0 0K H A R M (v(4)) 1.000 0.800 0.600 0.400 0.200 0.0 0 0 0.0 0 0K 0.2 5 0K IH D (H A R M (v(4 )),5 0 ) (%) M icro -C a p 8 E valuation V ersion F ILT R.

11 S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence Fig. 12. The change of the absolute value of the impedance Zwe=fra) for the scheme in Fig. 11: a) 10 km of cable line of 15 kv (Ro = ohm/km, Lo = 0.39 mh/km, Co = 0.23 if/km), b) 10 km overhead line of 15 kv (Ro = ohm/km, Lo = 1.1 mh/km, Co = 9.78 nf/km) K K K K K K K H A R M (v(4)) K K IH D (H A R M (v(4 )),5 0 ) (%) M icro -C a p 8 E valuation V ersion F ILT R.C IR Am plitude of v(4) vs Frequency K K K 1.000K 1.250K Percent Distortion o f t vs Frequency T 1,.. T. T K K 1.000K 1.250K Fig. 13. Spectrum of the 15 kv load voltage ( overhead line) Table 3 presents the percentage of the THDV and THDI for the system composed of model PCC - 15 kv, transmission line (overhead or cable) at 15 kv of length l = 10 km, the passive filter o f 5th and 7th harmonic and nonlinear load (Fig. 11). Table 3. THD values in the network with the filter of 5th harmonic of Q5 = 50 and 7th harmonic of Q7 = 70 for the overhead and cable line Transmission line Source current Load current Source voltage Load voltage THD [%] overhead THD [%] cable

S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence 0 o0 M ic ro -C a p 8 E valuation V ersion F IL T R.C IR Am plitude o f V (9 ) vs Frequency 1 5.0 0 0 K 1 2.0 0 0 K 9. 6.

n IH D (H A R M (V (9 )),5 0 ) (% ) Fig. 14 Spectrum of the 15 kv load voltage ( cable line) On the basis of simulation results (Table 3 and Fig.

12 S. Bolkowski, W. Brociek, R. Wilanowicz / Comparative analysis o f influence 0 o0 M ic ro -C a p 8 E valuation V ersion F IL T R.C IR Am plitude o f V (9 ) vs Frequency K K K k 0.5 Í0 K 0.7 H A R M (V (9)) * G P ercent Distortion o f V (9 ) vs Frequency... T 1 i f «l i ' ' * G 1!n IH D (H A R M (V (9 )),5 0 ) (% ) Fig. 14 Spectrum of the 15 kv load voltage ( cable line) On the basis of simulation results (Table 3 and Fig. 13 and 14) we may conclude, that of filtering compensating devices (the passive filter) the value of THDV coefficient below 1%. Therefore the deformation coefficient at PCC has been decreased. The presents results prove that application of passive filter causes the significant reduction o f the voltage distortion in the supplying system. 5. Summary On the basis performed calculations we can conclude that the type of the supplying line has significant influence on the level of voltage distortion. We have shown that the distortion depends also on the parameters of the supplying line and the short - circuit power (Szw) at the supply point (PCC). If the supplying system is more complex there is a need to perform the additional analysis of the impedance dependence on the frequency (to identify the resonance frequencies). In comparison to the overhead line the cable line reduces the impedance of the system for characteristic frequencies. Is followed by the higher value of the capacitance Co of the cable. The passive filters cause the voltage resonance at 250 Hz and 350 Hz and current resonance for lower frequencies (Fig. 12). We have observed also significant reduction of the THDV coefficient, which assumed values smaller than 1%. At the same time we observe that for the fundamental harmonic of 50 Hz the system is of capacitive character, which may be applied for compensation o f reactive power. The values of frequency phenomena for each considered case have been evaluated at the experiments performed by using the simulation program MicroCap-8. 22

13 Acknowledgements This work has been supported from National Science Centre. References [1] Bolkowski S., Teoria obwodów elektrycznych, WNT Warszawa [2] Brociek W., Wilanowicz R., Frequency characteristics of the power line with nonlinear load, Przegląd Elektrotechniczny, 2009/4, pp [3] Brociek W., Wilanowicz R., Analysis of the influence of the line supplying the nonlinear load on the deformation of voltages and currents in power system, XXXV IC-SPETO, 2012, pp [4] Pasko M., Sztymelski K., Eliminacja wyższych harmonicznych prądu źródła za pomocą filtrów wzdłużnych, Przegląd Elektrotechniczny, 2001/7-8.

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