Analysis of the magnetic coupling influence between different feeders on unbalanced distribution networks Code: 12.004 Nélio Alves do Amaral Filho, Mariana Simões Noel da Silva, Leandro Ramos de Araujo, Débora Rosana Ribeiro Penido Araujo Electrical Engineering, Federal University of Juiz de Fora, Minas Gerais - Brazil 12/11/2017 1
Introduction Electrical distribution systems (DS) have attracted the attention of a growing number of researchers Electric power quality Unbalances Increased demand for electricity Operation under harsher conditions Greater need to represent all DS-related characteristics and effects An efficient representation of the system components Tools able to evaluate and analyze the DS more accurately 12/11/2017 2
Introduction Several possible analyses can be performed in distribution systems studies Electromagnetic coupling (mutual coupling) that occurs between two or more feeders when physically arranged in parallel Practice done by the utilities Feeders can be found traveling along the same path and sharing a common pole; the same power corridor on separate poles. The existing mutual coupling can significantly affect the system This coupling is usually neglected in most studies 12/11/2017 3
Objectives Analysis of the electromagnetic coupling influence between different feeders Backward/Forward Sweep (BFS) Method Different constructive characteristics Length of the distribution feeders sections Separation distance between the conductors Phase sequences and geometry of the conductors on the poles 12/11/2017 4
Model of the distribution feeders in parallel Mutual: different feeder A B C A 0,76m Mutual: same feeder B n 1,37m FEEDER 1 FEEDER 2 C 0,6m 0,6m 1 Zii rc rd j0, 07537ln 6, 74580 RMGi 1 Zij rd j0, 07537ln 6, 74580 Dij Z phase Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z aa ab ac aa ' ab ' ac ' ba bb bc ba ' bb ' bc ' ca cb cc ca ' cb ' cc ' a ' a a ' b a ' c a ' a ' a ' b ' a ' c ' b ' a b ' b b ' c b ' a ' b ' b ' b ' c ' c ' a c ' b c ' c c ' a ' c ' b ' c ' c ' (1) (2) (3) Z phase Z Z abc, F1 F1 abc, F1 F 2 abc, F 2 F1 abc, F 2 F 2 12/11/2017 5 Z Z (4)
Backward Forward Sweep Algorithm E1 Variables initialization E3 Identification of sections that share the same pole E2 Layer separation V S =8kV 1 2 3 4 5 6 7 8 12 9 13 10 15 11 14 16 F1 F2 E4 Calculation of Nodal Currents E5 Backward Sweep F1 1 2 4 F2 Layer 1 N End E6.1 Forward Sweep Stop when a coupling section is found E6.2 Mutual coupling: Forward Sweep using eq. (5) N 3 7 5 6 S2 10 9 S1 11 15 13 12 8 14 16 Layer 2 Layer 3 Layer 4 Layer 5 Layer 6 Y E7 Convergence Test ΔV < ε Y E6.3 Have all voltages been updated? V Z Z I V Z Z I abc, F1 abc, F1 F1 abc, F1 F 2 abc, F1 abc, F 2 abc, F 2 F1 abc, F 2 F 2 abc, F 2 (5) 12/11/2017 6
Simulated systems V S =4,16 kv 650 890 810 651 800 802 806 812 814 850. 632 6320 V S =24,9 kv 808 675 671 6710 6750 IEEE 13M IEEE 34M 12/11/2017 7
Simulated systems To investigate the impact of the mutual coupling, 2 cases were analyzed Case 1: ignoring the effect of the mutual impedances between different feeders (without the mutual coupling representation) Case 2: considering the effect of these mutual impedances (mutual coupling) For comparison and results presentation It was calculated the difference between the absolute values obtained from each case, for a same variable (voltage, current or electrical losses) Vk V C2 C1 k V V C1 k k (6) 12/11/2017 8
Maximum voltage difference (%) Maximum voltage difference (%) Experimental results Feeders length 20 18 16 14 12 10 8 6 4 2 0 IEEE 13M 0,1 0,5 1 1,5 2 Factor k 20 18 16 14 12 10 8 6 4 2 0 0,1 0,5 1 1,5 2 2,5 3 3,5 Factor k IEEE 34M 12/11/2017 9
Voltage difference in bus 890 (%) Voltage difference in bus 675 (pu) Experimental results Distance between conductors Dx B A C B A FEEDER 1 FEEDER 2 C Dy 2,5 2 n 0,08 0,07 0,06 1,5 0,05 0,04 1 0,03 0,02 0,5 0,01 0 0,2 0,3 0,6 1 2 4 10 50 Vertical distance between feeders on pole (m) 0 0,15 0,3 0,5 0,75 1 1,25 1,5 1,75 2 Distance between the center conductor and the left conductor (m) IEEE 34M IEEE 13M 12/11/2017 10
Experimental results Different phase sequences or conductor geometry on the pole A B C C B FEEDER 1 FEEDER 2 A A C C A FEEDER 1 FEEDER 2 B 2,13m B 0,6m n n Losses Current - Current - Current - Voltage - Voltage - Voltage - IEEE 13M Eq. Triangle ABC - C'B'A' ABC - A'B'C' BAC - C'A'B' BAC - B'A'C' 0 1 2 3 4 5 6 7 8 9 Current - Voltage - Voltage - 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 12/11/2017 11 Maximum difference (%) Maximum difference (%) Losses Current - Current - Voltage - IEEE 34M Eq. Triangle ABC - C'B'A' ABC - A'B'C' BAC - C'A'B' BAC - B'A'C'
Conclusions The effect of the mutual coupling may become significant in certain conditions System configuration; Long length of feeders sections that are in parallel; Small distances between the phase conductors, both vertically and horizontally; Specific phase sequences. The mutual coupling influence can be considerable not only in the voltage, but also in both current and electrical losses The mutual coupling representation in the power flow analysis algorithms for distribution systems should not be neglected 12/11/2017 12
Acknowledgments The authors thank the Pos-Graduate Program in Electrical Engineering (PPEE) of the Federal University of Juiz de Fora, CNPq, FAPEMIG, and CAPES for the incentive and support. 12/11/2017 13
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