如何避免互联电网中的Braess悖论现象

doi:10.19596/j.cnki.1001-246x.8762

摘要/Abstract

摘要：

为了探究如何在互联电网中增加传输线路时避免发生Braess悖论现象, 本文采用二阶类Kuramoto相振子模型对电网进行动力学建模。分别考虑在互联电网子网内和子网间增加传输线路, 探究互联电网发生Braess悖论现象的概率并分析其原因。研究表明: 互联电网发生Braess悖论现象的概率与网间传输功率有关, 当网间的功率传输达到某一临界值时, 在互联电网的受电子网内及子网间增加传输线路, 互联电网发生Braess悖论现象的概率降低到接近于零, 从而避免发生Braess悖论现象。

关键词: 互联电网, Braess悖论, 同步性能, 动力学

Abstract:

In order to explore how to avoid Braess paradox when adding transmission lines in interconnected power grid, this study uses the second order Kuramoto-like model to model the dynamics of the power grid, and connects the subnets through the largest nodes to construct interconnected power grid. When there is power transmission between the two subnets, consider adding transmission lines inside and between subnets to explore the probability of Braess paradox in interconnected power grid and analyze its reasons. The results show that the probability of Braess paradox is related to the transmission power between the subnets. When the power between subnets reaches a critical value, adding transmission lines in the power receiving subnet or between two subnets, the probability of Braess paradox in interconnected power grid will be reduced to nearly zero. Therefore, the Braess paradox phenomenon should be avoided. The reasons for this phenomenon are analyzed in this paper.

Key words: interconnected power grid, Braess paradox, synchronization performance, dynamics

中图分类号:

TM711

张少泽, 邹艳丽. 如何避免互联电网中的Braess悖论现象[J]. 计算物理, 2024, 41(5): 680-688.

Shaoze ZHANG, Yanli ZOU. How to Avoid Braess Paradox in Interconnected Power Grid[J]. Chinese Journal of Computational Physics, 2024, 41(5): 680-688.

图/表 5

图1 子网内新增线路发生Braess悖论的概率随传输功率变化(a)IE14-14子网A; (b)IE14-14子网B; (c)IE14-30子网A; (d)IE14-30子网B

Fig.1 Variation of probability of Braess paradox occurring on new lines of subnets with transmission power (a) IE14-14 subnet A; (b) IE14-14 subnet B; (c) IE14-30 subnet A; (d) IE14-30 subnet B

图2 互联电网拓扑(a)IE14-14;(b)IE14-30

Fig.2 Topology of interconnected power grid (a) IE14-14; (b) IE14-30

图3 子网间新增线路发生Braess悖论的概率随传输功率变化(a)IE14-14;(b)IE30-30;(c)IE14-30;(d)IE30-57

Fig.3 Variation of probability of Braess paradox occurring on new lines of subnets with transmission power (a) IE14-14; (b) IE30-30; (c) IE14-30; (d) IE30-57

图4 IE14-14稳态局部序参数随耦合强度的变化(红色粗线表示发电机节点，蓝色粗线表示与发电机节点相邻的枢纽节点，黑色粗线表示网间传输线的两个端点，其他颜色折线表示网络中除上述节点外的剩余节点。) (a)σ=0.01;(b)σ=0.05;(c)σ=0.4;(d)σ=0.5

Fig.4 Variation of steady-state local order parameter of IE14-14 with coupling strength (Red thick lines represent generator nodes, blue thick lines represent hub nodes adjacent to generator nodes, black thick lines represent two endpoints of transmission line between networks, and the other colored broken lines represent remaining nodes in the network except the above nodes.) (a) σ=0.01; (b) σ=0.05; (c)σ=0.4; (d) σ=0.5

图5 IE14-30稳态局部序参数随耦合强度的变化(红色粗线表示IEEE30子网中发电机节点，蓝色粗线表示IEEE30子网中与发电机节点相邻的枢纽节点，黑色粗线表示网间传输线的两个端点，其他颜色折线表示网络中除上述节点外的剩余节点。)(a)P=1 pu; (b)P=2 pu; (c)P=5 pu; (d)P=6 pu

Fig.5 Variation of steady-state local order parameter of IE14-30 with coupling strength (Red thick lines represent generator nodes in the IEEE30 subnet, blue thick lines represent hub nodes adjacent to generator nodes in IEEE30 subnet, black thick lines represent two endpoints of the transmission line between networks, and the other colored broken lines represent remaining nodes in the network except the above nodes.) (a) P=1 pu; (b) P=2 pu; (c)P=5 pu; (d) P=6 pu

参考文献 26

1	BRAESS D . Vber ein paradoxon aus der verkehrsplanung[J]. Mathematical Methods of Operational Research, 1968, 12 (1): 258- 268. DOI
2	BRAESS D , NAGURNEY A , WAKOLBINGER T . On a paradox of traffic planning[J]. Transportation Science, 2005, 39 (4): 446- 456. DOI
3	XUE J, GEHLOT H, UKKUSURI S V. Braess's paradox in scale-free networks[C]. The 8th International Symposium on Dynamic Traffic Assignment. Seattle, WA. June 29 to July 1, 2020.
4	MA Chunyao , CAI Qing , ALAM S , et al. Airway network management using Braess's Paradox[J]. Transportation Research. Part C Emerging Technologies, 2019, 105, 565- 579. DOI
5	鲁丛林, 蔡宁. Braess's Paradox的博弈论分析[J]. 长沙交通学院学报, 2003, 19 (3): 69- 72. DOI
6	COLOMBO R M , HOLDEN H . On the braess paradox with nonlinear dynamics and control theory[J]. Journal of Optimization Theory and Applications, 2016, 168 (1): 216- 230. DOI
7	辛绍平. 论西电东送的心要性和可行性[J]. 中国电力, 2001, 34 (2): 1- 3.
8	张国宝. "西电东送" 工程: 中国电力史上的重要篇章[J]. 中国经济周刊, 2019, (12): 48- 52.
9	李飏, 周永章. 珠江流域"西电东送" 能源空间配置的综合效益分析[J]. 中国人口·资源与环境, 2008, 18 (3): 147- 151.
10	朱法华, 王圣, 刘思湄. 中国电力规划环评的发展与建议[J]. 电力环境保护, 2007, 23 (5): 9- 13. DOI
11	WANG Dayong , JIA Guozhu , ZONG Hengshan , et al. Abnormal dynamics induced by congestion effect in cascading failures[J]. Modern Physics Letters B, 2019, 33 (2): 1950001. DOI
12	WITTHAUT D , TIMME M . Braess's paradox in oscillator networks, desynchronization and power outage[J]. New Journal of Physics, 2012, 14, 083036. DOI
13	李浩乾, 邹艳丽, 张少泽, 等. 基于复杂网络的电网结构健壮性及Braess悖论现象研究[J]. 计算物理, 2021, 38 (4): 470- 478.
14	WANG Xiangrong, KOC Y, KOOIJ R E, et al. A network approach for power grid robustness against cascading failures[C]//2015 7th International Workshop on Reliable Networks Design and Modeling (RNDM). Munich: IEEE, 2015: 15589535.
15	BAILLIEUL J, ZHANG Bowen, WANG Shuai. The Kirchhoff-Braess paradox and its implications for smart microgrids[C]//2015 54th IEEE Conference on Decision and Control (CDC). Osaka: IEEE, 2015: 6556-6563.
16	张少泽, 邹艳丽, 谭秫毅, 等. 基于复杂网络理论的互联电网Braess悖论现象分析[J]. 计算物理, 2022, 39 (2): 233- 243.
17	WU Zhihao , MENICHETTI G , RAHMEDE C , et al. Emergent complex network geometry[J]. Scientific Reports, 2015, 5, 10073. DOI
18	ZHOU Jin , YU Xinghuo , LU Junan . Node importance in controlled complex networks[J]. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, 2019, 66 (3): 437- 441.
19	STROGATZ S H . Exploring complex networks[J]. Nature, 2001, 410 (6825): 268- 276.
20	BOCCALETTI S , LATORA V , MORENO Y , et al. Complex networks: Structure and dynamics[J]. Physics Reports, 2006, 424 (4/5): 175- 308.
21	汪小帆, 李翔, 陈关荣. 复杂网络理论及其应用[M]. 北京: 清华大学出版社, 2006.
22	蔡泽祥, 王星华, 任晓娜. 复杂网络理论及其在电力系统中的应用研究综述[J]. 电网技术, 2012, 36 (11): 114- 121.
23	FILATRELLA G , NIELSEN A H , PEDERSEN N F . Analysis of a power grid using a Kuramoto-like model[J]. The European Physical Journal B, 2008, 61, 485- 491.
24	NISHIKAWA T , MOTTER A E . Comparative analysis of existing models for power-grid synchronization[J]. New Journal of Physics, 2015, 17, 015012.
25	王意. 复杂电力网络的动力学行为及关键节点识别研究[D]. 桂林: 广西师范大学, 2017.
26	邹艳丽, 王瑞瑞, 吴凌杰, 等. 基于局部序参数的电网同步性能优化[J]. 计算物理, 2019, 36 (4): 498- 504.

[1]	祁青华, 文大东, 陈贝, 高明, 易洲, 邓永和, 邓科, 彭平. 冷速对快凝Ni₅₀Zr₅₀合金团簇结构遗传与演化特性的影响[J]. 计算物理, 2024, 41(4): 494-502.
[2]	许铋立, 景昭, 刘骁, 代波, 姬广富, 张魁宝, 葛妮娜. 硅改性酚醛树脂物理性能的分子动力学模拟[J]. 计算物理, 2024, 41(3): 345-356.
[3]	许晓阳, 赵雨婷. 非等温eXtended Pom-Pom泊肃叶流动的光滑粒子流体动力学方法模拟[J]. 计算物理, 2024, 41(2): 161-171.
[4]	温伯尧, 高根英, 路熙, 关松涛, 骆政园, 白博峰. 球状胶束中表面活性剂脱附的离子调控机制[J]. 计算物理, 2024, 41(2): 193-202.
[5]	高旭东, 孙淑义, 魏雯静, 李公平. 金红石TiO₂辐照损伤模拟研究[J]. 计算物理, 2024, 41(2): 214-221.
[6]	朱璋元, 王秋玲. 考虑级联失效与恢复接续性的复杂网络恢复动力学[J]. 计算物理, 2024, 41(2): 258-267.
[7]	赵双, 陈湘军, 张云贞. 忆阻Lorenz混沌系统的动力学分析与电路实现[J]. 计算物理, 2024, 41(2): 268-276.
[8]	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.
[9]	李禹, 刘慧卿, 冯亚斌, 东晓虎, 王庆, 张波. 典型表活剂与稠油在蒙脱石表面吸附行为的分子动力学模拟[J]. 计算物理, 2023, 40(5): 583-596.
[10]	马文婧, 王进, 郭慧, 吕美妮, 张宏泽, 李冬德. 晶体相场法研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制机理[J]. 计算物理, 2023, 40(4): 416-424.
[11]	韦昭召, 刘凯, 李会军. NiAl合金纳米线弯曲形变行为的分子动力学模拟[J]. 计算物理, 2023, 40(4): 425-435.
[12]	陈莘莘, 祝显毅, 李庆华. 基于时域自适应精细算法的插值型无单元Galerkin法及其在弹性动力学中的应用[J]. 计算物理, 2023, 40(3): 353-358.
[13]	房立庆, 张浩, 师素双, 王明川, 陈东亮, 师占群. 油气混合润滑状态下滑动轴承润滑特性的数值模拟[J]. 计算物理, 2023, 40(1): 47-56.
[14]	余登亮, 南国防, 姜珊, 宋传冲. 滚动轴承支撑下转子系统的耦合故障动力学[J]. 计算物理, 2022, 39(6): 733-743.
[15]	张浏斌, 单彦广, 戎志成. 基于LBM的均匀电场池沸腾单气泡动力学模拟[J]. 计算物理, 2022, 39(5): 537-548.