Optimization Model for Safeguarding Vulnerable Components in Integrated Energy Systems Based on Weighted Betweenness

doi:10.16183/j.cnki.jsjtu.2023.403

Abstract

Abstract:

Utilizing the complex network theory to mitigate vulnerabilities mitigation in integrated energy systems is significant for enhancing the resilience of sustained energy supply, especially against deliberate physical attacks and natural disasters. To implement more precise preventive measures for vulnerable components in integrated energy systems, this paper proposes a weighted betweenness-based protection optimization model for safeguarding vulnerable segments. The model aims to minimize the weighted betweenness loss incurred post attacks and damages, while simultaneously considering strategies such as establishing backup nodes and backup lines, enhancing physical protection of nodes and lines, and adding new lines. These strategies are subject to constraints such as protection requirements, budget limitations, and constraints on the types and quantities of new lines. The model optimization provides the optimal protection strategies within the allocated budget. To address the complex betweenness computations and non-linear objective functions, the model is formulated as a bilevel structure based on the nature of protection measures first. Then, the lower-level model is solved using a local linearization technique, and a “genetic-mixed integer linear programming” algorithm is proposed for solving the model with high precision and efficiency. The simulation results demonstrate that under conditions of equivalent attack and damage, the system with the optimal protection strategy achieves reduction of 45.37% in weighted betweenness loss compared with that without protection. The optimal strategy outperforms the other five protection strategies considered within the allocated protection budget.

Key words: protection optimization model, weighted betweenness, complex network theory, integrated energy system

CLC Number:

TM743

ZHANG Chenwei, WANG Ying, LI Yaping, ZHANG Kaifeng. Optimization Model for Safeguarding Vulnerable Components in Integrated Energy Systems Based on Weighted Betweenness[J]. Journal of Shanghai Jiao Tong University, 2025, 59(7): 923-937.

Figures/Tables 12

Fig.1

Fig.2

Fig.3

Tab.1

Tab.2

Tab.3

Tab.4

Tab.5

Fig.4

Tab.6

Tab.7

Fig.5

References 31

[1]	ALHARBI R S, NATH S, FAIZAN O M, et al. Assessment of drought vulnerability through an integrated approach using AHP and geoinformatics in the Kangsabati River Basin[J]. Journal of King Saud University-Science, 2022, 34(8): 102332.
[2]	CAO M S, SHAO C Z, HU B, et al. Reliability assessment of integrated energy systems considering emergency dispatch based on dynamic optimal energy flow[J]. IEEE Transactions on Sustainable Energy, 2022, 13(1): 290-301.
[3]	JIANG T, ZHANG R F, LI X, et al. Integrated energy system security region: Concepts, methods, and implementations[J]. Applied Energy, 2021, 283: 116124.
[4]	SUN C H, ZHOU Z Y, ZENG X J, et al. A multi-model-integration-based prediction methodology for the spatiotemporal distribution of vulnerabilities in integrated energy systems under the multi-type, imbalanced, and dependent input data scenarios[J]. Applied Energy, 2022, 320: 119239.
[5]	闫妍, 刘晓, 庄新田. 基于复杂网络理论的供应链级联效应检测方法[J]. 上海交通大学学报, 2010, 44(3): 322-325.
	YAN Yan, LIU Xiao, ZHUANG Xintian. Cascading failure model and method of supply chain based on complex network[J]. Journal of Shanghai Jiao Tong University, 2010, 44(3): 322-325.
[6]	CAO M H, GUO J J, XIAO H, et al. Reliability analysis and optimal generator allocation and protection strategy of a non-repairable power grid system[J]. Reliability Engineering & System Safety, 2022, 222: 108443.
[7]	CHANG L, WU Z G. Performance and reliability of electrical power grids under cascading failures[J]. International Journal of Electrical Power & Energy Systems, 2011, 33(8): 1410-1419.
[8]	CHEN G, DONG Z Y, HILL D J, et al. Attack structural vulnerability of power grids: A hybrid approach based on complex networks[J]. Physica A: Statistical Mechanics & Its Applications, 2010, 389(3): 595-603.
[9]	DU R J, DONG G G, TIAN L X, et al. Targeted attack on networks coupled by connectivity and dependency links[J]. Physica A: Statistical Mechanics & Its Applications, 2016, 450: 687-699.
[10]	刘涤尘, 冀星沛, 王波, 等. 基于复杂网络理论的电力通信网拓扑脆弱性分析及对策[J]. 电网技术, 2015, 39(12): 3615-3621.
	LIU Dichen, JI Xingpei, WANG Bo, et al. Topological vulnerability analysis and countermeasures of electrical communication network based on complex network theory[J]. Power System Technology, 2015, 39(12): 3615-3621.
[11]	SCHNEIDER C M, YAZDANI N, ARAÚJO N A M, et al. Towards designing robust coupled networks[J]. Scientific Reports, 2013, 3: 1969. doi: 10.1038/srep01969 pmid: 23752705
[12]	崔文岩, 孟相如, 康巧燕, 等. 基于复合边权重的加权复杂网络级联抗毁性优化[J]. 系统工程与电子技术, 2017, 39(2): 355-361.
	CUI Wenyan, MENG Xiangru, KANG Qiaoyan, et al. Optimization of cascading invulnerability on weighted complex networks based on composite edge weight model[J]. Systems Engineering & Electronics, 2017, 39(2): 355-361.
[13]	GONG M G, MA L J, CAI Q, et al. Enhancing robustness of coupled networks under targeted recoveries[J]. Scientific Reports, 2015, 5: 8439. doi: 10.1038/srep08439 pmid: 25675980
[14]	郭明健, 高岩. 基于复杂网络理论的电力网络抗毁性分析[J]. 复杂系统与复杂性科学, 2022, 19(4): 1-6.
	GUO Mingjian, GAO Yan. Invulnerability analysis of power network based on complex network[J]. Complex Systems & Complexity Science, 2022, 19(4): 1-6.
[15]	刘涛, 李伟华, 汤熠. 综合智慧能源系统典型构架网络安全防护研究[J]. 综合智慧能源, 2024, 46(5): 81-90. doi: 10.3969/j.issn.2097-0706.2024.05.010
	LIU Tao, LI Weihua, TANG Yi. Research on network security protection of typical architecture of integrated smart energy system[J]. Integrated Intelligent Energy, 2024, 46(5): 81-90. doi: 10.3969/j.issn.2097-0706.2024.05.010
[16]	ZHANG L, SU H, ZIO E, et al. A data-driven approach to anomaly detection and vulnerability dynamic analysis for large-scale integrated energy systems[J]. Energy Conversion & Management, 2021, 234: 113926.
[17]	YANG S H, CHEN W R, ZHANG X X, et al. A graph-based method for vulnerability analysis of renewable energy integrated power systems to cascading failures[J]. Reliability Engineering & System Safety, 2021, 207: 107354.
[18]	XU B Y, HONG L C, GU D Y. Security analysis of integrated energy system under complex network[C]// 2022 IEEE 5th International Electrical and Energy Conference. Nangjing, China: IEEE, 2022: 3325-3329.
[19]	ZHENG T, LIU G, CHENG W, et al. Identification of vulnerable links in integrated energy system based on complex network theory[C]// 2022 4th International Conference on Power and Energy Technology. Beijing, China: IEEE, 2022: 1157-1162.
[20]	戴婷婷, 刘俊勇, 魏震波, 等. 基于复杂网络理论的电力系统脆弱性分析[J]. 现代电力, 2010, 27(1): 56-60.
	DAI Tingting, LIU Junyong, WEI Zhenbo, et al. Analysis of power system vulnerability based on complex network theory[J]. Modern Electric Power, 2010, 27(1): 56-60.
[21]	张国华, 张建华, 杨京燕, 等. 基于有向权重图和复杂网络理论的大型电力系统脆弱性评估[J]. 电力自动化设备, 2009, 29(4): 21-26.
	ZHANG Guohua, ZHANG Jianhua, YANG Jingyan, et al. Vulnerability assessment of bulk power grid based on weighted directional graph and complex network theory[J]. Electric Power Automation Equipment, 2009, 29(4): 21-26.
[22]	丁一, 江艺宝, 宋永华, 等. 能源互联网风险评估研究综述(一): 物理层面[J]. 中国电机工程学报, 2016, 36(14): 3806-3817.
	DING Yi, JIANG Yibao, SONG Yonghua, et al. Review of risk assessment for energy Internet, part Ⅰ: Physical level[J]. Proceedings of the CSEE, 2016, 36(14): 3806-3817.
[23]	潘华, 肖雨涵, 梁作放, 等. 基于复杂网络的电-气-热综合能源系统健壮性分析[J]. 电力自动化设备, 2019, 39(8): 104-112.
	PAN Hua, XIAO Yuhan, LIANG Zuofang, et al. Robustness analysis of electricity-gas-heat integrated energy system based on complex network[J]. Electric Power Automation Equipment, 2019, 39(8): 104-112.
[24]	SHEN Y C, GU C H, ZHAO P F. Structural vulnerability assessment of multi-energy system using a PageRank algorithm[J]. Energy Procedia, 2019, 158: 6466-6471.
[25]	WANG B, WAN S H, ZHANG X J, et al. A novel index for assessing the robustness of integrated electrical network and a natural gas network[J]. IEEE Access, 2018, 6: 40400-40410.
[26]	张殷, 肖先勇, 李长松. 基于攻击者视角的电力信息物理融合系统脆弱性分析[J]. 电力自动化设备, 2018, 38(10): 81-88.
	ZHANG Yin, XIAO Xianyong, LI Changsong. Vulnerability analysis of cyber physical power system from attacker’s perspective[J]. Electric Power Automation Equipment, 2018, 38(10): 81-88.
[27]	汪勋婷, 王波. 考虑信息物理融合的电网脆弱社团评估方法[J]. 电力自动化设备, 2017, 37(12): 43-51.
	WANG Xunting, WANG Bo. Assessment method of vulnerable communities in power grid considering cyber-physical integration[J]. Electric Power Automation Equipment, 2017, 37(12): 43-51.
[28]	王梓行, 姜大立, 漆磊, 等. 基于冗余度的复杂网络抗毁性及节点重要度评估模型[J]. 复杂系统与复杂性科学, 2020, 17(3): 78-85.
	WANG Zihang, JIANG Dali, QI Lei, et al. Complex network invulnerability and node importance evaluation model based on redundancy[J]. Complex Systems & Complexity Science, 2020, 17(3): 78-85.
[29]	VIJAYSHANKAR S, CHANG C Y, UTKARSH K, et al. Assessing the impact of cybersecurity attacks on energy systems[J]. Applied Energy, 2023, 345: 121297.
[30]	邹洋, 王剑晓, 戴璟, 等. 欧洲能源危机成因、影响与应对措施[J]. 电力系统自动化, 2023, 47(17): 1-13.
	ZOU Yang, WANG Jianxiao, DAI Jing, et al. Causes, impacts and mitigation measures of European energy crisis[J]. Automation of Electric Power Systems, 2023, 47(17): 1-13.
[31]	尚学军, 霍现旭, 戚艳, 等. 考虑负荷需求响应的园区综合能源系统运行优化研究[J]. 电力与能源进展, 2020, 8(3): 57-69.
	SHANG Xuejun, HUO Xianxu, QI Yan, et al. Research on operation optimization of integrated energy system for park considering integrated demand response[J]. Advances in Energy & Power Engineering, 2020, 8(3): 57-69.

节点编号	出力/MW	节点编号	出力/MW
30	250	37	540
31	742.24	38	830
32	650	39	1000
33	632	45	303
34	508	53	175
35	650	54	100
36	560	60	100

线路	物理防护程度	是否加备份线路
6-17	0.1886	0
6-11	0	1
7-8	0.0672	0
10-11	0	1
10-56	0.1447	0
16-17	0	1
16-19	0	1
16-21	0.1081	0
17-27	0	1
26-27	0	1
26-28	0.1077	0

节点编号	带权重的节点介数	节点编号	带权重的节点介数
16	189618	19	76904
17	134007	11	72739
6	108201	5	71017
22	103515	27	70214
26	96007	25	67854
2	95548	28	64281
21	86336	14	57780
3	86219	15	57756
10	78354	44	56040
4	78197	56	54930

线路编号	带权重的线路介数	线路编号	带权重的线路介数
16-17	55939	15-16	29458
16-21	44259	28-29	29357
21-22	40725	14-15	27935
16-19	37727	22-62	27570
2-3	36711	6-31	26892
17-27	35681	25-26	26834
4-5	34802	6-11	26281
5-6	34802	1-2	26130
26-28	34645	1-39	26130
26-27	33973	2-25	25051
10-11	32933	17-18	24622

防护策略	损失的带权重介数	损失的带权重介数下降率/%
①	385114
②	276671	28.16
③	258000	33.01
④	210383	45.37