Study on Braess Paradox of Power Grid Based on Complex Network Topology

doi:10.19596/j.cnki.1001-246x.8653

Abstract

Abstract:

To explore a better power grid structure and reduce the probability of Braess paradox. In this paper, the second order Kuramoto-like phase oscillator model is used to reasonably model the power grid, and several networks are generated by ER random model in which the number of network nodes and links is the same as IEEE14, IEEE30, and IEEE39, respectively. By increasing the number of generator nodes and changing the position of generators in the random network, the occurrence probability of Braess paradox caused by a new adding transmission lines in the different power grid is studied. Study shows that appropriately increasing the number of generator nodes in the power grid can reduce the probability of the Braess paradox in the power grid, and taking large-degree nodes as generator nodes is beneficial to improve the power grid synchronizability and reduce the probability of Braess paradox. This study has certain guiding significance for the topology design and optimization of the power grid.

Key words: complex network, topological structure, synchronization performance, Braess paradox

CLC Number:

TM711

Beibei SHAO, Yanli ZOU, Shaoyan HONG, Chanjuan LIANG. Study on Braess Paradox of Power Grid Based on Complex Network Topology[J]. Chinese Journal of Computational Physics, 2023, 40(6): 770-778.

Figures/Tables 11

Table 1 The steady state frequency offset and the critical synchronous coupling strength of the original network of IEEE14 system and the network after the addition of some transmission lines

新增传输线路编号	稳态频偏	临界同步耦合强度
原网络	0.0	2.3
(1, 3)	0.0	2.3
(1, 4)	0.0	2.2
(2, 7)	2.6	2.4
(3, 10)	2.6	2.5
(3, 14)	0.0	2.2
(5, 8)	0.0	2.3
(5, 11)	2.6	2.5
(6, 8)	0.0	2.0
(8, 14)	0.0	1.9

Table 2 Three kinds of standard test system characteristics parameters

系统	总节点数	连边数	网络节点平均度
IEEE14	14	20	2.857 1
IEEE30	30	41	2.733 3
IEEE39	39	46	2.359 0

Table 3 Allocation of the number of generators and load nodes in a 14-node network

	14节点网络
发电机节点个数	1	3	5	7
负载节点个数	13	11	9	7

Fig.1 Degree distribution of nodes (a), (b), (c) corresponding to network 1, 2 and 3, respectively

Fig.2 Topology of large degree nodes as generators (a), (b), (c) and (d) corresponding to a network with one, three, five and seven generator nodes, respectively

Fig.3 Topology of small degree nodes as generators, (a), (b), (c) and (d) corresponding to a network with one, three, five and seven generator nodes, respectively

Fig.4 The proportion of lines with Kc increasing, decreasing or unchanging after adding a new transmission line to a 14-node network varies with the number of generator nodes (a) large degree nodes as generators in a 14-node network; (b) small degree nodes as generators in a 14-node network

Table 4 Allocation of the number of generators and load nodes in a 30-node network

	30节点网络
发电机节点个数	3	5	7	15
负载节点个数	27	25	23	15

Table 5 Allocation of the number of generators and load nodes in a 39-node network

	39节点网络
发电机节点个数	3	7	12	19
负载节点个数	36	32	27	20

Fig.5 The proportion of lines with Kc increasing, decreasing or unchanging after adding a new transmission line to a 30-node or a 39-node network varies with the number of generator nodes (a)large degree nodes as generators in a 30-node network; (b)small degree nodes as generators in a 30-node network; (c)large degree nodes as generators in a 39-node network; (d)small degree nodes as generators in a 39-node network

Fig.6 The proportion of lines with Kc increasing and decreasing varies with the number of generators after adding a new transmission line in 14, 30, and 39-node networks, where generators are on large degree nodes or small degree nodes, respectively (a), (c) and (e) denote the proportion of lines with Kc increasing; (b), (d) and (f)denote the proportion of lines with Kc deceasing ((a) and (b)14-node network. (c) and (d)30-node network. (e) and (f)39-node network)

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