Computation Method to Improve Three-phase Voltage Imbalance by Exchange of Single-phase Load Connection

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1 Computation Method to Improve Three-phase Voltage Imbalance by Exchange of Single-phase Load Connection Yasuhiro Hayashi, Member, Junya Matsuki, Member, Masayoshi Ohashi, Student Member, Yasuyuki Tada,Member Three-phase voltage imbalance occurs by variety of connecting points of single-phase loads. In order to improve three-phase voltage imbalance, connecting points of single-phases loads are exchanged. System planner has to decide how to exchange connection of single-phase loads with the minimum planning cost in order to improve three-phase voltage imbalance. However, since there are many patterns of connection for single-phase loads, it is not easy to determine the optimal connection pattern for single-phase loads with the minimum planning cost under the constraint for improving voltage imbalance. In this paper, authors propose a computational method to support the planner s decision of single-phase loads connection systematically. The proposed method, which is based on effective enumeration algorithm, can obtain the optimal single-phase loads connection pattern, which satisfies with constraint of voltage balance and has the minimum total number of single-phase loads exchanged from previous single-phase loads connection. In the proposed method, three-phase iterative load flow calculation is applied to calculate rate of three-phase voltage imbalance. Three-phase iterative load flow calculation has two simple procedures: (Procedure1) addition of load currents from terminal node of feeder to root one, and (Procedure2) subtraction of voltage drop from root node of feeder to terminal one. In order to check the validity of the proposed method, numerical results are shown for a distribution system model with DG. Keywords: voltage imbalance, dispersed generator, single-phase load, three-phase load flow calculation, distribution system planning 1. (1) (3) Dept. of Electrical and Electronics engineering, Fukui University 3-9-1, Bunkyo, Fukui R&D center, Tokyo Electric Power Company 4-1, Egasaki-cho, Tsurumi-ku, Yokohama (4) 1 2 SVC 15 B

2 LDC SVR (5) LDC SVR 24 Newton-Raphson (6) Count = i M 3 ij x ij (1) X (OLD) j=1 3 x ij = 1 (i M) (2) j=1 Maximum (U kt ) ε (k N) t T (3) U kt = V 2kt / V 1kt 100 (k N, t T) (4) V 2kt = (V akt + µ 2 V bkt + µv ckt )/3 (k N, t T) (5) V 1kt = (V akt + µv bkt + µ 2 V ckt )/3 (k N, t T) (6) µ = 1/2 + j 3/2 (7) Count t T i M X (OLD) ij i j 1 0 x ij i j U kt t k [%] ε [%] N V 1kt V 2kt V akt V ckt t k µ (1) (2) (3) ε [%] r 366 IEEJ Trans. PE, Vol.125, No.4, 2005

3 3 r 2 3 r ε% 3 r 1 Count = 1 ε% ε% 1 Count = Count + 1 Count ε% ε% (7) (8) (11) 0 1 Fig. 1. General flowchart of the proposed method. LC ak LC bk LC ck V ak V bk V ck = = Z k h U k I ah h U k I bh h U k I ch LC ak LC bk LC ck Z aak Z abk Z ack Z k = Z bak Z bbk Z bck Z cak Z cbk Z cck V ak V bk V ck = V a0 V b0 V c0 V b j j W k V c j j W k (k = 1, 2, 3,, N) (8) j W k V a j (k = 1, 2, 3,, N) (9) (k = 1, 2, 3,, N) (10) (k = 1, 2, 3,, N) (11) B

4 V a0 V b0 V c0 V ak V bk V ck k Z k k LC ak LC bk LC ck k I ak I bk I ck k W k k 0 U k k k N k PQ PQ 2 1 r = 0 2 V (r) ak V (r) (r) bk V ck k = 1 N V a0 = V b0 = V c0 = 1pu V a0 = V b0 = V c0 = 0 3 k I (r+1) k (12) 2 Fig. 2. Concept of three-phase iterative load flow calculation. I ak (r+1) I bk (r+1) I ck (r+1) = P Sak + jq Sak V ak (r) P Sbk + jq Sbk V bk (r) P Sck + jq Sck V ck (r) (k = 1, 2, 3,, N) (12) P Sak + jq Sak P Sbk + jq Sbk P Sck + jq Sck k PQ 4 LC h (r+1) (8) 5 (9) (10) (r+1) V k (11) 6 V (r+1) (r+1) k I k PQ P k + jq k η η = 10 3 V (r+1) k r = r PQ Q 2 Fortran (8) IM- PACT Python Matlab m PC 368 IEEJ Trans. PE, Vol.125, No.4, 2005

5 % LDC 4 5 ε NEMA MG % (13) (12) 2 24 Z k [Ω] j j j = j j j j j j (k = 1, 2, 3,, 19) (13) 1 Table 1. Peak load data. 3 Fig. 3. Initial distribution system model. 2 Table 2. Coefficients of load change. 4 Fig. 4. Profile of voltage at root node. 5 Fig. 5. Profile of DG s output. B

6 6 Fig. 6. Maximum rate of voltage imbalance for each candidate. 8 Fig. 8. Voltage imbalance before exchange of single-phase loads. 7 Fig. 7. The optimal connection sate of single-phase load. 9 Fig. 9. Voltage imbalance after exchange of single-phase loads % 2 1% % % Fig Voltage before exchange of single-phase loads (10 hour) % A B A B 370 IEEJ Trans. PE, Vol.125, No.4, 2005

7 14 Fig. 14. Convergence characteristics of proposed method Fig. 11. Voltage after exchange of single-phase loads (10 hour). Newton-Raphson PQ Fig Fig. 13. Voltage imbalance in disconnecting DG. 10 Line voltage in disconnecting DG kv kv kv Newton-Raphson (6) Newton-Raphson 0.2% 5% 20 Newton-Raphson B

1 H. Taniguchi: Dispersed Generation and Power System Control, T. IEE Japan, Vol.121-B, No.9, pp.

Motohashi, M. Myoga, S. Azuma, and S. Kyomoto: A Protection Scheme and A Method for Keeping a Balance of Voltage for an 11.

4 kv, B, 122, 6, pp.755 760 (2002-6) 5, (1991) 6, (1975) 7, (1980) 8 A. Kurita, T. Yamada, Y. Tada, A. Ono, T. Takazawa, K. Koyanagi, Y.

6 Dynamic Simulation Function, The Papers of Technical Meeting on Power Systems Engineering, IEE Japan, PE-03-88, PSE-03-99, pp.

8 1 H. Taniguchi: Dispersed Generation and Power System Control, T. IEE Japan, Vol.121-B, No.9, pp (2001-9) (in Japanese), B, 121, 9, pp (2001-9) 2, IAE-C0239 (2003) 3 21, OHM, No.10 ( ) 4 K. Oka, J. Motohashi, M. Myoga, S. Azuma, and S. Kyomoto: A Protection Scheme and A Method for Keeping a Balance of Voltage for an kv Three-Phase Four-Wire Distribution System, T. IEE Japan, Vol.122-B, No.6, pp (2002-6) (in Japanese) kv, B, 122, 6, pp (2002-6) 5, (1991) 6, (1975) 7, (1980) 8 A. Kurita, T. Yamada, Y. Tada, A. Ono, T. Takazawa, K. Koyanagi, Y. Takahara, Y. Shishido, A. Taguchi, and H. Okura: Development of IM- PACT Ver.2.6 Dynamic Simulation Function, The Papers of Technical Meeting on Power Systems Engineering, IEE Japan, PE-03-88, PSE-03-99, pp (2003-9) (in Japanese) IMPACT Ver.2.6 VTS,, PE-03-88, PSE-03-99, pp (2003-9) OR IEEE IEEE IEEE 372 IEEJ Trans. PE, Vol.125, No.4, 2005

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