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

Transcription

1 Cmputer Applicatins in Electrical Engineering Cmparative analysis f influence f the type line supplying nnlinear lad n defrmatin f vltage and current in the pwer system tanisław Blkwski, Wiesław Brciek Warsaw University f Technlgy Warszawa, Plac Plitechniki 1, brciek@iem.pw.edu.pl Rbert Wilanwicz Kazimierz Pulaski University f Technlgy and Humanities Radm, ul. Malczewskieg 29 The results f simulatin tests cncerning the cperatin f the nnlinear lad with the pwer system are presented. In numerical experiments we have taken data frm the real systems, including the cable and verhead lines. In practice the nnlinear lad f high pwer may be supplied by the verhead r cable lines. The paper presents the cmparative analysis, hw the applied type f the line influences the level f distrtin f the vltages and currents in the pwer system. The values f the higher harmnics f the vltages and currents as well as THD have been determined in the paper. These values have been estimated fr the beginning and ending terminals f the verhead and cable lines supplying the nnlinear lad f the inductive character cncerning the cperatin f the filtering cmpensating device and the nnlinear lad f high pwer. All experiments have been perfrmed using MicrCap-8 prgram. In the paper we have included he exemplary results f the numerical calculatins. KEYWORD: defrmatins f vltage and current, frequency characteristics, passive filters, verhead and cable lines 1. Intrductin The main reasn f the deterirating f the quality f the electrical energy in the pwer system is the increasing number f the nnlinear lads in the system. Even at sinusidal vltage excitatin the current f the nnlinear receiver is distrted (nn-sinusidal). The nn-sinusidal current flwing thrugh the real surce f nn-zer internal impedance causes the distrtin f the terminal vltage as well. In this way bth: current and vltage in the system at nnlinear lad are distrted and cntain higher harmnics. In practice the nnlinear lad f high pwer may be supplied by the verhead r cable lines. The type f supply line has a significant impact n the level f distrtin f vltages and currents in the supply system in the event f a harmnic caused by nnlinear lads. In this paper a cmparative analysis f the impact f such nn-linear receiver t the level f distrtin f vltages and currents in the supply system. The values f harmnic currents and vltages and THD at the 11

2 beginning and the end f the supply line. It presents als examples f the simulatin results n the impact f a passive filter n the level f distrtin in the reprting system. As a result f distrtin we can bserve the resnance phenmena f different harmnics, that can be bserved in the supplying line. These phenmena depend nt nly n the parameters f the line, but als n the value f cnsumed currents, that is n the pwer f the nnlinear lad. The paper presents the results f numerical experiments perfrmed fr the system cmpsed f nnlinear lad and the supplying pwer line. In the experiments we have taken int accunt the frequency characteristics f the abslute values f the impedances measured at the terminals f the nnlinear lad. 2. ystem descriptin Figure 1a presents the general scheme f supplying the nnlinear lad u = f(i). The mdel presented in Fig. 1, is cmpsed f the fllwing elements: supplying pint 110 kv f shrt-circuit pwer zw = 500 MVA, 50 km f verhead line at 110 kv f 240 mm 2 crss-sectin, transfrmer 110/15 kv, the main supplying pint (PCC) 15 kv f shrt-circuit pwer zw = 200 MVA, 10 km supply line f 15 kv (verhead r cable), f 120 mm 2 crss-sectin, transfrmer 15/3 kv and the nnlinear lad u = f(i). The unity parameters f the verhead transmissin line 15 kv are as fllws : R = 0,245 Ω/km, L 0 = 1,1 mh/km, C 0 = 9,78 nf/km and f the cable transmissin line 15 kv R = 0,253 Ω/km, L 0 = 0,39 mh/km, C 0 = 0,23 µf/km. The parameters (R, L ) f the mdel have been determined using fllwing frmulas (fr ) [1, 2] ,1* U 1,1* (15*10 ) X (1) 6 ZW 200*10 R 0,1 X (2) X L 4e 3 H (3) It is interesting t knw that the resnance phenmena may ccur in the line (cable r verhead), supplying the nnlinear lad. In the case f resnance the exact value f the resnance frequency is f great imprtance. The input impedance Z WE = f( ) seen frm terminals 2-2 at representatin f the line by the 2-prt f lumped parameters (Fig. 1b) and the ther part f the system by the impedance Z s = R s +jx s [1] can be described by the fllwing expressin [1, 2]: [(1 Z0(kl) Y2(kl) )Z Z0(kl) ] Z E(kl) (4) (Y Y Y Y Z )Z (1 Z Y ) 1(kl) 2(kl) 1(kl) 2(kl) 0(kl) 0(kl) 1(kl) 12

3 a) Z 0 R0 jx L0 and 1 Y 0 jkωk 0 2 (5) b) c) Fig. 1. The general scheme f the investigated system (a), the lumped mdel the supplying line (b), the distributed parameter mdel f the line (c); I zr (k) the RM value f the current f kth harmnic At the frequency f higher harmnics (fr example the 20th 1 khz) we can bserve the resnance phenmena in the line. At such frequency the analysis f the phenmena ccurring in the system needs t be represented as the lng transmissin line. In such case the input impedance f the system (Fig. 1c) seen frm the terminal 2 2 can be presented as fllwing [1, 2, 4]. Z WE (kl) Z (k) ch (k) l Z C(k) Z C(k) sh (k) l Z (6) Z )sh l Z ch l C(k) (k) where (k) the prpagatin cnstant f the line, Z c(k) the wave (characteristic) impedance f the line fr kth harmnic. Figure 2 presents the change f the abslute value f the impedance Z we = f( ) as a functin f the length f 15 kv line l = 10km, 15 km, 20 km fr cable line. Figure 3 shws the results f the AC analysis f the live change f the abslute (k) C(k) (k) 13

4 value f the impedance Z we = f( ) fr the mdel: 10 km f cable line f 15 kv represented by lumped 2-prt (Fig. 3b), and 10 km verhead line f 15 kv represented by lng transmissin line mdel (Fig. 3a) K 1.400K 1.300K 1.200K 1.100K 1.000K 0.900K 0.800K 0.700K 0.600K 0.500K 0.400K 0.300K 0.200K 0.100K LINIA.CIR T3.value.len= K K 1.25K V(13)/i(V3) Fig. 2. The change f the abslute value f the impedance Z we = f( ) as a functin f the length f 15 kv line l = 10 km, 15 km, 20 km fr cable line 20 km 15 km Fig. 3. The live change f the abslute value f the impedance Z we = f( ) fr the mdel: a) 10 km f cable line f 15 kv (R = hm/km, L = 0.39 mh/km, C =0.23 uf/km) represented by lumped 2-prt, b) 10 km verhead line f 15 kv (R = hm/km, L = 1.1 mh/km, C = 9.78 nf/km) represented by lng transmissin line mdel T find ut at what length f the line and at what frequency we may bserve the resnance effects in the system f Fig. 1a we shuld perfrm multiple calculatins f the impedances described by the equatins (1) and (2) [1]. 14

5 3. The simulatin results f pwer system f medium vltage at nnlinear lad Figure 4 presents the scheme f ne phase f the 15 kv line supplying the nnlinear lad u = f(i). The calculatins have been perfrmed fr the verhead and cable lines supplying the nnlinear lad. We have made the fllwing assumptins: the supply (PCC) is cmpsed f an ideal vltage surce f the a value crrespnding t ne phase f the three-phase 15 kv system with cmpnents Rs, Ls, f the values dependent n the shrt-circuit pwer rails 15 kv ( zw = 200MVA) the nnlinear lad f R 2 = f (t), L 2 = f (t) t simulate the lad that results in the nnlinear current and inductive reactive pwer. The unity parameters f transmissin line f 15 kv are as fllws: verhead line R = Ω / km, L = 1.1 mh / km, C= 9.78 nf / km. cable line R = Ω / km, L = 0.39 mh / km, C = 0.23 F / km. 15 kv Transmissin line l = 10 km Fig. 4. The scheme f the simulated system cmpsed f the mdel PCC-15kV, the transmissin line (verhead r cable) at 15 kv f length l = 10 km and crss sectin = 120 mm 2 at nnlinear lad The influence f the type f pwer line vltage and current distrtin in the supply system, can be t examined using the representing mdules the equivalent impedance versus frequency seen frm the terminals nn-linear lad[2]. This apprach enables the study f changes f impedance fr the whle analyzed frequency range. This is particularly imprtant in the case f a parallel cnnectin f passive filters at the beginning r end f the supply line. Based n the wavefrm f Figure 5, we can cnclude that the verhead line has slightly higher impedances fr frequencies lwer than 1 khz in cmparisn t the cable line. In rder t perfrm quantitative analysis f the phenmena ccurring in the analyzed systems, the calculatins f distrtin f currents and vltages in the circuit f Figure 4 will take int accunt the distrted lad current wavefrms. 15

6 Based n the transients value f the lad current (Fig. 5), the values f effective individual harmnic currents: I 50Hz = 249A, I 250Hz = 21.6A, I 350Hz = 21.6 A, and the percentage f their share in the fundamental harmnic nnlinear lad current: I 5% = 8.6% I 7% = 8.6% K K K m 2m 4m 6m 8m 10m 12m b) V(8) (V) T (ecs) K K K c) m 2m 4m 6m 8m 10m 12m v(12) (V) T (ecs) 30 UFK5H.CIR -30 m 2m 4m 6m 8m 10m 12m -i(r5) (A) T (ecs) Fig. 5. Transients f a) vltage at main supply pint (PCC f 15 kv, b) lad vltage at the end verhead line 15 kv, c) the nnlinear lad curent Mdel f nnlinear lad impedance Z b = f(t) assuming the initial phase f the first harmnic receiver vltage φ = 0 generates a lad current f the instantaneus value equal t: i (t) sin(ωi 46 ) sin(5ωi 50 ) sin(7ωi 142 ) b 1.89 a) 2sin(11ωi 144 ) sin(13ωi 122 ) sin(17ωi sin(19ωi 24 ) Figure 5 illustrates these transients used in further analysis. The values f each harmnic f the lad current when pwered by an verhead and cable lines used in calculatins are cmparable. The values f each harmnic lad current when pwered by an verhead line and cable used in calculatin are cmparable. The limit value f THDV at 15kV and 30kV is [2] n U k 2 THDV ( ) 100% 8% (7) U k 2 Figure 6 and 7 presents spectrum f the lad current and vltage 15 kv in Fig. 4 at verhead line. 1 ) 16

7 Values f individual vltage and current harmnics, and the cefficients THDV and THDI at the beginning f the verhead line (PCC), and at the end f the line (the pint f attachment f the lad) are shwn in Table circuit1.cir Cumulative Amplitude Percent Distrtin f i(r2) vs f Frequency V(4) vs Frequency HARM(i(R2)) Percent Distrtin f i(r2) vs Frequency IHD(HARM(i(R2)),50) (%) 1.500K 1.200K 0.900K Fig. 6. pectrum f the lad current ( verhead line) circuit1.cir Amplitude f V(4) vs Frequency 0.600K 0.300K K HARM(V(4)) Percent Distrtin f V(4) vs Frequency IHD(HARM(V(4)),50) (%) Fig. 7. pectrum f the 15 kv lad vltage ( verhead line) Table 1. The maximum values and percentage f the higher harmnics f the currents and vltage fr pwering the nnlinear lad verhead line urce current Lad Lad Harmnic urce vltage current vltage rder 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

8 Analgus calculatins were perfrmed fr the cable line. Figure 8 presents transient f vltage, current f the lad and the surce vltage at 15 kv presented in Fig. 4 at cable line K K a) circuit1.cir 6.000K c) K b) K K 8m 10m 12m v(8) (V) v(9) (V) i(r4)*40 T (ecs) Fig. 8.Transients f a) vltage at main supply pint (PCC f 15 kv, b) lad vltage at the end cable line 15 kv, c) the nnlinear lad curent Table 2 presents the values and percentage f the higher harmnics f the vltage and current, and the cefficients THDV and THDI presented in Fig. 4 fr pwering the nnlinear lad cable line. Table 2. The maximum values and percentage f the higher harmnics f the currents and vltage fr pwering the nnlinear lad cable line urce Lad Lad urce vltage Harmnic current current vltage rder 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 f the lad current and vltage 15 kv in Fig. 3 at cable line. 18

9 circuit1.cir Cumulative Amplitude Percent Distrtin f i(r4) vs f Frequency V(4) vs Frequency HARM(i(R4)) Percent Distrtin f i(r4) vs Frequency IHD(HARM(i(R4)),50) (%) Fig. 9. pectrum f the lad current (cable line) 1.500K 1.200K 0.900K circuit1.cir Amplitude f V(9) vs Frequency 0.600K 0.300K K HARM(V(9)) Percent Distrtin f V(9) vs Frequency IHD(HARM(V(9)),50) (%) Fig. 10. pectrum f the 15 kv lad vltage (cable line) On the basis f perfrmed simulatins we may cnclude that the type f the pwer line may have the imprtant impact n the vltage distrtin. 4. The numerical results f simulatin f medium vltage line and passive filter Figure 11 present circuit mdel f ne phase f the 15 kv netwrk with a nnlinear lad with and attached filter 5th and 7th harmnics (filtering cmpensating devices FCD). One way t analyse the negative impact f nnlinear lad n the pwer system is the use f harmnic filters [3]. Fr this purpse, we used the system f Figure 4, and perfrmed the calculatins with attached filters f fifth and seventh harmnics at the end f the line (Fig. 11). Exemplary results f the simulatin are shwn in Figure

10 Fig. 11. The scheme f ne phase f the simulated system cmpsed f mdel PCC 15 kv transmissin line (verhead r cable) at 15 kv f length l =10 km and crss sectin = 120 mm 2, filtering cmpensating devices (FCD) and nnlinear lad (R 2, L 2 ) In numerical experiments have been fcused n the analysis f the influence f passive filters n the defrmatin f vltage in system. The passive filter is built as ne r mre sectin tuned t the particular frequencies t be eliminated. The quality f resnance sectin depends n the harmnics t which are tuned. D k 10k (8) where k the rder f harmnic. The impedance f the filter (50 Hz) sectin t 1th harmnic is f the capacitive character, which means, that it can be used as the device fr cmpensatin f the reactive device. The parameters f individual branches (cell) f the passive filter tuned fr 250 Hz and 350 Hz (in the Fig. 11) are as fllws: the fifth harmnic filter f Q 5 = 50, C 5 = 40 µf, L 5 = 10,1 mh, R 5 = 0,318 Ω the seventh harmnic filter f Q 7 = 70: C 7 = 10 µf, L 7 = 20,7 mh, R 7 = 0,65 Ω Figure 12 presents the abslute values f the impedance f the verhead and cable lines as a functin f the frequency in the circuit f Fig. 11. The values f the current f the nnlinear lad in the circuit f Fig. 11 are the same as in the case f circuit f Fig. 4. Hence the harmnic spectrum f Fig. 13 and 14 are typical fr bth circuits. Applicatin f filter in the analysed system causes the reductin f the netwrk impedance which are characteristic fr the lad f particular frequencies. At the same time we bserve the reductin f the defrmatin f the current as well as its magnitude. It is well illustrated in Fig. 13 and

11 Fig. 12. The change f the abslute value f the impedance Z w e = f( ) fr the scheme in Fig. 11: a) 10 km f cable line f 15 kv (R = hm/km, L = 0.39 mh/km, C = 0.23 F/km), b) 10 km verhead line f 15 kv (R = hm/km, L = 1.1 mh/km, C = 9.78 nf/km) K K 9.000K FILTR.CIR Amplitude f v(4) vs Frequency 6.000K 3.000K K HARM(v(4)) Percent Distrtin f v(4) vs Frequency IHD(HARM(v(4)),50) (%) Fig. 13. pectrum f the 15 kv lad vltage ( verhead line) Table 3 presents the percentage f the THDV and THDI fr the system cmpsed f mdel PCC 15 kv, transmissin line (verhead r cable) at 15 kv f length l = 10 km, the passive filter f 5th and 7th harmnic and nnlinear lad (Fig. 11). Table 3. THD values in the netwrk with the filter f 5th harmnic f Q 5 = 50 and 7th harmnic f Q 7 = 70 fr the verhead and cable line Transmissin line urce current Lad current urce vltage Lad vltage THD [%] verhead THD [%] cable

12 15.000K K 9.000K 6.000K 3.000K K HARM(V(9)) FILTR.CIR Amplitude f V(9) vs Frequency Percent Distrtin f V(9) vs Frequency IHD(HARM(V(9)),50) (%) Fig. 14 pectrum f the 15 kv lad vltage ( cable line) On the basis f simulatin results (Table 3 and Fig. 13 and 14) we may cnclude, that f filtering cmpensating devices (the passive filter) the value f THDV cefficient belw 1%. Therefre the defrmatin cefficient at PCC has been decreased. The presents results prve that applicatin f passive filter causes the significant reductin f the vltage distrtin in the supplying system. 5. ummary On the basis perfrmed calculatins we can cnclude that the type f the supplying line has significant influence n the level f vltage distrtin. We have shwn that the distrtin depends als n the parameters f the supplying line and the shrt - circuit pwer ( zw ) at the supply pint (PCC). If the supplying system is mre cmplex there is a need t perfrm the additinal analysis f the impedance dependence n the frequency (t identify the resnance frequencies). In cmparisn t the verhead line the cable line reduces the impedance f the system fr characteristic frequencies. Is fllwed by the higher value f the capacitance C f the cable. The passive filters cause the vltage resnance at 250 Hz and 350 Hz and current resnance fr lwer frequencies (Fig. 12). We have bserved als significant reductin f the THDV cefficient, which assumed values smaller than 1%. At the same time we bserve that fr the fundamental harmnic f 50 Hz the system is f capacitive character, which may be applied fr cmpensatin f reactive pwer. The values f frequency phenmena fr each cnsidered case have been evaluated at the experiments perfrmed by using the simulatin prgram MicrCap-8. 22

13 Acknwledgements This wrk has been supprted frm Natinal cience Centre. References [1] Blkwski., Teria bwdów elektrycznych, WNT Warszawa [2] Brciek W., Wilanwicz R., Frequency characteristics f the pwer line with nnlinear lad, Przegląd Elektrtechniczny, 2009/4, pp [3] Brciek W., Wilanwicz R., Analysis f the influence f the line supplying the nnlinear lad n the defrmatin f vltages and currents in pwer system, XXXV IC-PETO, 2012, pp [4] Pask M., ztymelski K., Eliminacja wyższych harmnicznych prądu źródła za pmcą filtrów wzdłużnych, Przegląd Elektrtechniczny, 2001/