A Mixed-Integer Linear Programming Method for Fault Section Location in Distribution Networks under Typhoon Disasters
Wang Qiujie1,2, Gan Dewei1,2, Tan Hong1,2, Chen Jinran3, Yan Fei4
1. Hubei Provincial Collaborative Innovation Center for New Energy Microgrid China Three Gorges University Yichang 443002 China; 2. College of Electrical Engineering and New Energy China Three Gorges University Yichang 443002 China; 3. State Grid Hubei Electric Power Co. Ltd Yichang 443002 China; 4. Chang Jiang Survey, Planning, Design and Research Co. Ltd Wuhan 430010 China
Abstract：Typhoon disasters often cause complex multiple faults in distribution networks, including simultaneous faults across multiple lines or regions. These situations pose significant challenges to power supply reliability and fault diagnosis. Most fault section location methods are developed under the assumptions of a single power source and a single fault, typically relying on fixed fault current direction. However, with the integration of distributed generation (DG), fault currents under multi-source conditions may flow in various or even opposite directions along shared branches. Existing models fail to accurately capture this behavior, leading to location errors and reduced effectiveness in disaster response and post-disaster restoration. To address this problem, a fault section location method was proposed, incorporating multi-source information and formulated as a mixed-integer linear programming problem. The method began with an analysis of the limitations of traditional switching functions. These functions assume a fixed current flow from the main source and cannot accurately represent node states on shared branches with multiple interacting sources. An improved switching function was constructed to address this issue. It redefined current direction by comparing the fault current contributions from the main source and DG, enabling a more realistic representation of current flow under multi-source fault conditions. To further improve location performance, the model integrated data from smart meters (SMs) and micro-phasor measurement units (μPMUs). These sources help reduce the fault search space and suppress interference caused by false or missed alarms from feeder terminal units (FTUs). A logic-based section location model was developed based on the improved switching function, SM and μPMU constraints, and additional system constraints. Using three transformation principles between logical and algebraic relations, the model was linearized and transformed into a mixed-integer linear programming problem solvable in Matlab with the GUROBI optimizer. Simulation tests were conducted on a 10-node system and an IEEE 33-node distribution network with dual power sources. Test scenarios included single faults, simple double faults, and complex multiple faults. FTU false and missed alarms were introduced to simulate real-world measurement disturbances. The proposed method successfully identified fault sections under all test conditions. In a typical case where the main source and DG generated opposing fault currents on a shared line, traditional switching functions incorrectly computed the expected FTU state as zero, resulting in location failure. The improved function correctly calculated the expected state. With SM and μPMU data incorporated, the model maintained accurate fault localization even under distorted FTU measurements. For the 10-node and 33-node systems, the average solution times were 0.4 and 2.1 seconds, respectively. These were much faster than those of convolutional neural networks (CNNs) or intelligent optimization algorithms. The latter were more sensitive to false or missed alarms from FTUs. The simulation results lead to the following conclusions: (1) Traditional switching functions cannot accurately compute the expected FTU state on shared branches with multiple sources. (2) The improved switching function reflects the directional distribution of fault current under complex multiple faults. It ensures accurate fault section location in distribution networks with complex multiple faults. (3) The three transformation principles enable equivalent linearization of the logic-based section location model, ensuring efficient computation while maintaining adaptability to complex multiple fault scenarios.
王秋杰, 甘德伟, 谭洪, 陈槿然, 闫飞. 面向台风灾害的配电网故障区段定位混合整数线性规划方法[J]. 电工技术学报, 2026, 41(7): 2223-2236.
Wang Qiujie, Gan Dewei, Tan Hong, Chen Jinran, Yan Fei. A Mixed-Integer Linear Programming Method for Fault Section Location in Distribution Networks under Typhoon Disasters. Transactions of China Electrotechnical Society, 2026, 41(7): 2223-2236.
[1] 肖娟霞, 李勇, 韩宇, 等. 计及台风时空特性和灵活性资源协同优化的配电网弹性提升策略[J]. 电工技术学报, 2024, 39(23): 7430-7446. Xiao Juanxia, Li Yong, Han Yu, et al.Resilience enhancement strategy for distribution networks considering the spatiotemporal characteristics of typhoon and the collaborative optimization of flexible resources[J]. Transactions of China Electrotechnical Society, 2024, 39(23): 7430-7446. [2] 朱晓荣, 司羽. 考虑物理-信息-交通网耦合的配电网多时段动态供电恢复策略[J]. 电工技术学报, 2023, 38(12): 3306-3320. Zhu Xiaorong, Si Yu.Multi-period dynamic power supply restoration strategy considering physical-cyber-traffic network coupling[J]. Transactions of China Electrotechnical Society, 2023, 38(12): 3306-3320. [3] 蔡胜, 徐振钦, 谢云云, 等. 计及冷负荷启动时变特性的弹性配电网供电恢复[J]. 电工技术学报, 2025, 40(1): 139-151. Cai Sheng, Xu Zhenqin, Xie Yunyun, et al.A service restoration method for resilient distribution systems considering time-varying characteristic of cold load pickup[J]. Transactions of China Electrotechnical Society, 2025, 40(1): 139-151. [4] 温紫豪, 任洲洋, 董朝阳, 等. 跨区资源共享的多区域电-氢综合能源系统灾后恢复策略[J]. 电工技术学报, 2025, 40(11): 3486-3501. Wen Zihao, Ren Zhouyang, Dong Zhaoyang, et al.Post-disaster recovery strategy for multi-regional electricity-hydrogen integrated energy system with cross-regional resource sharing[J]. Transactions of China Electrotechnical Society, 2025, 40(11): 3486-3501. [5] 王秋杰, 金涛, 申涛, 等. 利用多因素降维的配电网区段定位完全解析模型[J]. 电工技术学报, 2019, 34(14): 3012-3024. Wang Qiujie, Jin Tao, Shen Tao, et al.A complete analytic model of section location in distribution network based on multi-factor dimensionality deduction[J]. Transactions of China Electrotechnical Society, 2019, 34(14): 3012-3024. [6] 李君, 何敏, 黄守道, 等. 基于相位差的小电阻接地有源配电网接地故障保护算法[J]. 电工技术学报, 2024, 39(23): 7418-7429. Li Jun, He Min, Huang Shoudao, et al.Grounding fault protection algorithm of small resistance earthing active distribution network based on phase difference[J]. Transactions of China Electrotechnical Society, 2024, 39(23): 7418-7429. [7] 黄南天, 程铎, 蔡国伟. 基于改进时空图神经网络的高渗透率有源配电网故障定位[J]. 电力系统自动化, 2025, 49(10): 112-122. Huang Nantian, Cheng Duo, Cai Guowei.Fault location for active distribution network with high penetration rate based on improved spatio-temporal graph neural network[J]. Automation of Electric Power Systems, 2025, 49(10): 112-122. [8] 杜红卫, 孙雅明, 刘弘靖, 等. 基于遗传算法的配电网故障定位和隔离[J]. 电网技术, 2000, 24(5): 52-55. Du Hongwei, Sun Yaming, Liu Hongjing, et al.Fault section diagnosis and isolation of distribution networks based on genetic algorithm[J]. Power System Technology, 2000, 24(5): 52-55. [9] 卫志农, 何桦, 郑玉平. 配电网故障区间定位的高级遗传算法[J]. 中国电机工程学报, 2002, 22(4): 127-130. Wei Zhinong, He Hua, Zheng Yuping.A refined genetic algorithm for the fault sections location[J]. Proceedings of the CSEE, 2002, 22(4): 127-130. [10] 李宗博, 崔一嘉, 王昊晴, 等. 含逆变型分布式电源的配电网馈线终端告警信息校正及故障定位方法[J]. 电工技术学报, 2025, 40(4): 1268-1286. Li Zongbo, Cui Yijia, Wang Haoqing, et al.Method of alarm information correction and fault location for distribution network with inverter-interfaced distributed generation[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 1268-1286. [11] Ganivada P K, Jena P.A fault location identification technique for active distribution system[J]. IEEE Transactions on Industrial Informatics, 2022, 18(5): 3000-3010. [12] Trindade F C L, Freitas W, Vieira J C M. Fault location in distribution systems based on smart feeder meters[J]. IEEE Transactions on Power Delivery, 2014, 29(1): 251-260. [13] 王志远, 高湛军, 张健磊, 等. 考虑短路及断线故障的有源配电网保护[J]. 电力系统自动化, 2021, 45(12): 133-141. Wang Zhiyuan, Gao Zhanjun, Zhang Jianlei, et al.Protection for active distribution network considering short-circuit and broken-line faults[J]. Automation of Electric Power Systems, 2021, 45(12): 133-141. [14] Zhang Ying, Wang Jianhui, Khodayar M E.Graph-based faulted line identification using micro-PMU data in distribution systems[J]. IEEE Transactions on Smart Grid, 2020, 11(5): 3982-3992. [15] 张健磊, 高湛军, 陈明, 等. 考虑复故障的有源配电网故障定位方法[J]. 电工技术学报, 2021, 36(11): 2265-2276. Zhang Jianlei, Gao Zhanjun, Chen Ming, et al.Fault location method for active distribution networks considering combination faults[J]. Transactions of China Electrotechnical Society, 2021, 36(11): 2265-2276. [16] Majidi M, Etezadi-Amoli M, Fadali M S.A sparse-data-driven approach for fault location in transmission networks[J]. IEEE Transactions on Smart Grid, 2017, 8(2): 548-556. [17] 周湶, 郑柏林, 廖瑞金, 等. 基于粒子群和差分进化算法的含分布式电源配电网故障区段定位[J]. 电力系统保护与控制, 2013, 41(4): 33-37. Zhou Quan, Zheng Bolin, Liao Ruijin, et al.Fault-section location for distribution networks with DG based on a hybrid algorithm of particle swarm optimization and differential evolution[J]. Power System Protection and Control, 2013, 41(4): 33-37. [18] 郭壮志, 陈涛, 洪俊杰, 等. 基于故障辅助因子的配电网高容错性故障区段定位方法[J]. 电力自动化设备, 2017, 37(7): 93-100. Guo Zhuangzhi, Chen Tao, Hong Junjie, et al.High-tolerance faulty section locating based on fault accessory factors for distribution network[J]. Electric Power Automation Equipment, 2017, 37(7): 93-100. [19] 郭壮志, 徐其兴, 洪俊杰, 等. 配电网故障区段定位的互补约束新模型与算法[J]. 中国电机工程学报, 2016, 36(14): 3742-3751. Guo Zhuangzhi, Xu Qixing, Hong Junjie, et al.A novel fault section location model with complementarity constraints and its optimization algorithm for distribution network[J]. Proceedings of the CSEE, 2016, 36(14): 3742-3751. [20] 郭壮志, 徐其兴, 洪俊杰, 等. 配电网快速高容错性故障定位的线性整数规划方法[J]. 中国电机工程学报, 2017, 37(3): 786-795. Guo Zhuangzhi, Xu Qixing, Hong Junjie, et al.Integer linear programming based fault section diagnosis method with high fault-tolerance and fast performance for distribution network[J]. Proceedings of the CSEE, 2017, 37(3): 786-795. [21] 何瑞江, 胡志坚, 李燕, 等. 含分布式电源配电网故障区段定位的线性整数规划方法[J]. 电网技术, 2018, 42(11): 3684-3692. He Ruijiang, Hu Zhijian, Li Yan, et al.Fault section location method for DG-DNs based on integer linear programming[J]. Power System Technology, 2018, 42(11): 3684-3692. [22] Jiang Yazhou.Data-driven fault location of electric power distribution systems with distributed generation[J]. IEEE Transactions on Smart Grid, 2020, 11(1): 129-137. [23] Wang Qiujie, Jin Tao, Mohamed M A, et al.A novel linear optimization method for section location of single-phase ground faults in neutral noneffectively grounded systems[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 3513410. [24] 国家电网有限公司. 分布式电源接入配电网设计规范: Q/GDW 11147—2017[S].北京: 国家电网有限公司, 2018. [25] 董张卓, 刘魁, 张倍倍. 含分布式电源配电网通用故障电流计算方法[J]. 电力系统保护与控制, 2019, 47(18): 161-168. Dong Zhangzhuo, Liu Kui, Zhang Beibei.A general fault current calculation method for distribution network with distributed generation[J]. Power System Protection and Control, 2019, 47(18): 161-168. [26] 滕林, 刘万顺, 貟志皓, 等. 电力系统暂态稳定实时紧急控制的研究[J]. 中国电机工程学报, 2003, 23(1): 64-69. Teng Lin, Liu Wanshun, Yun Zhihao, et al.Study of real-time power system transient stability emergency control[J]. Proceedings of the CSEE, 2003, 23(1): 64-69. [27] 彭放, 高厚磊, 郭一飞, 等. 构网逆变电源故障穿越控制策略及其对保护影响的研究综述[J]. 电网技术, 2024, 48(9): 3673-3685. Peng Fang, Gao Houlei, Guo Yifei, et al.A review of fault ride-through control strategies of grid-forming inverter-based resources and the influence on protection[J]. Power System Technology, 2024, 48(9): 3673-3685.
2026, Vol. 41 
