基于带权重介数的综合能源系统脆弱环节防护优化模型

doi:10.16183/j.cnki.jsjtu.2023.403

上海交通大学学报 ›› 2025, Vol. 59 ›› Issue (7): 923-937.doi: 10.16183/j.cnki.jsjtu.2023.403

• 新型电力系统与综合能源 • 上一篇下一篇

基于带权重介数的综合能源系统脆弱环节防护优化模型

张辰微¹^,², 王颖¹^,²(), 李亚平³, 张凯锋¹^,²

1.东南大学自动化学院,南京 210096
2.东南大学复杂工程系统测量与控制教育部重点实验室,南京 210096
3.中国电力科学研究院有限公司南京分院,南京 210003

收稿日期:2023-08-21 修回日期:2023-09-25 接受日期:2023-10-19 出版日期:2025-07-28 发布日期:2025-07-22
通讯作者: 王颖 E-mail:wyseu@seu.edu.cn
作者简介:张辰微(1999—),博士生,从事综合能源系统保护研究.
基金资助:
国家电网有限公司总部科技项目(SGJSNJ00KHJS2260146)

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

ZHANG Chenwei¹^,², WANG Ying¹^,²(), LI Yaping³, ZHANG Kaifeng¹^,²

1. School of Automation, Southeast University, Nanjing 210096, China
2. Key Laboratory of Measurement and Control of Complex Systems of Engineering of the Ministry of Education, Southeast University, Nanjing 210096, China
3. China Electric Power Research Institute (Nanjing), Nanjing 210003, China

Received:2023-08-21 Revised:2023-09-25 Accepted:2023-10-19 Online:2025-07-28 Published:2025-07-22
Contact: WANG Ying E-mail:wyseu@seu.edu.cn

摘要/Abstract

摘要：

利用复杂网络理论对综合能源系统的脆弱环节进行防护,对提高系统的持续供能能力,特别是在面临蓄意物理攻击和自然破坏时具有重要意义.为了对综合能源系统中的脆弱环节采取针对性预防措施,提出一种基于带权重介数的综合能源系统脆弱环节防护优化模型.该模型以系统受攻击和破坏后损失的带权重介数最小为优化目标,综合考虑建立备份节点、备份线路,以及增加节点物理防护、线路物理防护和新建线路5种防护手段,以满足防护需求、防护预算限制、新建线路类型和数量限制等约束条件,优化得到防护预算内的最优防护策略.为解决模型求解中涉及复杂的介数计算和非线性目标函数求解的问题,首先根据防护手段类型将模型转化为上下双层;其次利用局部线性化技术处理下层模型;最后提出“遗传-混合整数线性规划”算法求解模型,实现模型高精度、高效率求解.仿真结果表明:在相同攻击和破坏条件下,相对于没有任何防护策略的情况,系统在引入最优防护策略后,带权重介数损失减少45.37%;并且该策略在分配的防护预算内优于其他5种防护策略.

关键词: 防护优化模型, 带权重介数, 复杂网络理论, 综合能源系统

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

中图分类号:

TM743

张辰微, 王颖, 李亚平, 张凯锋. 基于带权重介数的综合能源系统脆弱环节防护优化模型[J]. 上海交通大学学报, 2025, 59(7): 923-937.

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.

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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

场景	损失的带权重介数	损失的带权重介下降率/%	成本/万元
场景1	256717	33.33	44999.2982
场景2	248661	35.43	44999.6130
场景3	219995	42.87	45000.5589
场景4	214902	44.19	44872.7364
场景5	245916	36.14	45000.0014
场景6	210383	45.37	45000

基于带权重介数的综合能源系统脆弱环节防护优化模型

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

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摘要/Abstract

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图/表 12

参考文献 31

相关文章 15

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Metrics

本文评价

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

节点	物理防护程度	是否加备用站
6	0.8671	0
7	0.0922	0
10	0	1
11	0	1
16	0.9862	0
17	0.0886	0
19	0.2833	0
21	0.0032	0
22	0.2209	0
26	0	1
27	0	1
28	0.0016	0
56	0.0322	0

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