基于复杂网络拓扑的电网Braess悖论现象研究

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

摘要/Abstract

摘要：

为探究较优的电网结构, 减小Braess悖论现象的发生概率, 采用二阶类Kuramoto相振子模型对电网进行合理建模, 参照IEEE14、IEEE30和IEEE39标准测试网络的拓扑结构, 保留网络节点数和连边数不变, 采用ER随机模型生成同样大小的随机网络。通过在随机网络中增加发电机节点个数, 改变发电机位置等方式, 研究不同结构下电网中新增传输线路导致的Braess悖论发生概率。研究表明: 适当增加电网中发电机节点个数可以减少电网中Braess悖论发生概率, 且以大度节点作为发电机节点有利于提高电网同步能力, 降低Braess悖论发生概率。本研究对电网的拓扑设计和优化具有一定指导意义。

关键词: 复杂网络, 拓扑结构, 同步性能, Braess悖论

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

中图分类号:

TM711

邵贝贝, 邹艳丽, 洪少燕, 梁婵娟. 基于复杂网络拓扑的电网Braess悖论现象研究[J]. 计算物理, 2023, 40(6): 770-778.

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.

图/表 11

表1 IEEE14系统原网络及新增部分传输线路后网络的稳态频偏和临界同步耦合强度

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

表2 三种标准测试系统特性参数

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

表3 14节点的网络中发电机和负载节点个数分配表

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

图1 节点的度分布图, (a)、(b)、(c)对应网络1、2、3

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

图2 大度节点作为发电机的网络拓扑图, (a)、(b)、(c)、(d)对应网络含1个、3个、5个、7个发电机节点

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

图3 小度节点作为发电机的网络拓扑图, (a)、(b)、(c)、(d)对应网络分别含1个、3个、5个、7个发电机节点

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

图4 14节点网络新增一条传输线路后Kc增加、减小或者保持不变时的线路比例随发电机节点个数变化(a)14节点网络中大度节点作为发电机；(b)14节点网络中小度节点作为发电机

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

表4 30节点的网络中发电机和负载节点个数分配表

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

表5 39节点的网络中发电机和负载节点个数分配表

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

图5 30和39节点网络新增一条传输线路后Kc增加、减小或者保持不变的线路比例随发电机节点个数的变化(a)30节点网络中大度节点作为发电机；(b)30节点网络中小度节点作为发电机；(c)39节点网络中大度节点作为发电机；(d)39节点网络中小度节点作为发电机

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

图6 14、30、39节点网络中分别以大度节点和小度节点作为发电机新增一条传输线路后Kc增加和减小的线路比例随发电机个数的变化(a)、(c)、(e)表示Kc增加的线路比例；(b)、(d)、(f)表示Kc减小的线路比例；((a)、(b)为14节点网络；(c)、(d)为30节点网络；(e)、(f)为39节点网络)

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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