Coordinated Load Restoration Method of Transmission and Distribution Networks Considering the Uncertainties of Centralized and Distributed Renewable Energy Sources
Chen Yanbo, Qiang Tuben, Tian Haoxin, Li Xiaonan, Zhang Zhi
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China
Abstract：In recent years, low-probability but high-risk events including extreme weather, natural disasters, and cyberattacks have been occurring with increasing frequency. The large-scale blackouts triggered by these incidents not only pose a grave threat to the reliable supply of electricity but also inflict enormous economic losses, emerging as a major issue that demands urgent resolution in the context of the new electricity system. Furthermore, with the continuous growth in the proportion of renewable energy sources installed capacity, the scale and complexity of the transmission and distribution networks have significantly increased, which further exacerbates the operational risks of the system under extreme events. In the context of large-scale integration of renewable energy sources, its inherent uncertainty makes it difficult for traditional load restoration methods to meet actual demand. Conducting research on load restoration methods that take into account the uncertainties of renewable energy sources and formulating scientific and rational load restoration strategies are of significant theoretical importance and practical relevance. To address these issues, a coordinated load restoration method of transmission and distribution networks considering the uncertainties of centralized and distributed renewable energy sources is proposed. Firstly, taking into account the repair progress of transmission and distribution network lines, the flexible adjustment characteristics of soft open points and network reconfiguration strategies are considered to establish load restoration models for transmission and distribution networks. Secondly, the fuzzy chance constraint method is used to model the power output of renewable energy sources on both sides of the transmission and distribution networks, thereby constructing a coordinated load restoration model of transmission and distribution networks that accounts for uncertainties. On this basis, a Peaceman-Rachford splitting-embedded adaptive regularized alternating direction method of multipliers (PR-AR-ADMM) is proposed to decompose the proposed model into sub-optimization models for distributed solution of the transmission and distribution networks. Simulation analyses are conducted using the modified T30D2 and T118D30 transmission-distribution systems as case studies, drawing the following conclusions: (1) The uncertainties of renewable energy sources output on both sides of the transmission and distribution networks are simultaneously considered and modeled using the fuzzy chance constraint method. Through comparative analysis, it can be concluded that setting a reasonable confidence level can improve restoration performance while controlling restoration costs using renewable energy sources, achieving a balance between safety and economy, and providing scientific basis for optimized decision-making in load restoration. (2) By integrating soft open points with the tie switch-based network reconfiguration strategy, the interactive power at the transmission-distribution boundary is optimized, enhancing the mutual support capability between the transmission and distribution networks and improving the overall restoration performance of the system. Compared to the strategy that only considered the tie switch-based network reconfiguration, the proposed strategy reduces the total restoration cost by 65 630 CNY and advances the completion time of restoration by 15 min. (3) The proposed PR-AR-ADMM can efficiently solve the distributed optimization model for coordinated load restoration in transmission and distribution networks, demonstrating good computational efficiency and solution accuracy. Compared to the traditional alternating direction method of multipliers, the PR-AR-ADMM reduces the computation time by 63.04%, decreases the number of iterations by 19, and narrows the optimization gap to 0.48%.
陈艳波, 强涂奔, 田昊欣, 李小楠, 张智. 考虑集中式与分布式新能源不确定性的输配协同负荷恢复方法[J]. 电工技术学报, 2026, 41(7): 2281-2299.
Chen Yanbo, Qiang Tuben, Tian Haoxin, Li Xiaonan, Zhang Zhi. Coordinated Load Restoration Method of Transmission and Distribution Networks Considering the Uncertainties of Centralized and Distributed Renewable Energy Sources. Transactions of China Electrotechnical Society, 2026, 41(7): 2281-2299.
[1] 别朝红, 卞艺衡, 张理寅, 等. 新型电力系统应对极端事件的风险防范与应急管理关键技术[J]. 中国电机工程学报, 2024, 44(18): 7049-7068. Bie Zhaohong, Bian Yiheng, Zhang Liyin, et al.Key technologies of risk prevention and emergency management against extreme events for new power systems[J]. Proceedings of the CSEE, 2024, 44(18): 7049-7068. [2] 钟海旺, 张广伦, 程通, 等. 美国得州2021年极寒天气停电事故分析及启示[J]. 电力系统自动化, 2022, 46(6): 1-9. Zhong Haiwang, Zhang Guanglun, Cheng Tong, et al.Analysis and enlightenment of extremely cold weather power outage in Texas, U.S. in 2021[J]. Automation of Electric Power Systems, 2022, 46(6): 1-9. [3] Wu Liguang, Yu Runling, Xiang Chunyi, et al.Extreme impacts of four landfalling tropical cyclones in China during the 2024 peak season[J]. Advances in Atmospheric Sciences, 2025, 42(5): 817-824. [4] 覃智君, 侯云鹤, 李大虎, 等. 输电网负荷恢复方案的优化计算方法[J]. 电工技术学报, 2016, 31(8): 116-124. Qin Zhijun, Hou Yunhe, Li Dahu, et al.Optimization method for constructing load restoration strategy of transmission systems[J]. Transactions of China Electrotechnical Society, 2016, 31(8): 116-124. [5] 顾雪平, 魏佳俊, 白岩松, 等. 基于分层模型预测控制的含风电电力系统恢复在线决策方法[J]. 电工技术学报, 2025, 40(5): 1471-1486. Gu Xueping, Wei Jiajun, Bai Yansong, et al.Online decision-making method for wind power integrated power system restoration based on hierarchical model predictive control[J]. Transactions of China Electro-technical Society, 2025, 40(5): 1471-1486. [6] 李少岩, 张友好, 顾雪平. 计及短路故障影响的含风电电力系统恢复决策优化方法[J]. 中国电机工程学报, 2023, 43(20): 7827-7842. Li Shaoyan, Zhang Youhao, Gu Xueping.Optimi-zation method of restoration decision-making for wind integrated power system considering the effects of short-circuit fault[J]. Proceedings of the CSEE, 2023, 43(20): 7827-7842. [7] 张博, 马梓耀, 王辰, 等. 含光储充一体化电站的城市交直流混合配电网韧性提升策略[J]. 电力系统自动化, 2023, 47(12): 28-37. Zhang Bo, Ma Ziyao, Wang Chen, et al.Resilience improvement strategy for urban AC/DC hybrid distribution network with photovoltaic-storage-charging integrated station[J]. Automation of Electric Power Systems, 2023, 47(12): 28-37. [8] 刘玉玲, 张峰, 张刚, 等. 考虑分布式电源的配电网灾中-灾后两阶段协同韧性恢复决策[J]. 电力系统自动化, 2024, 48(2): 48-59. Liu Yuling, Zhang Feng, Zhang Gang, et al.In-and post-disaster two-stage coordinated resilience recovery decision of distribution network considering distributed generators[J]. Automation of Electric Power Systems, 2024, 48(2): 48-59. [9] Zhao Jin, Wang Hongtao, Liu Yutian, et al.Coordinated restoration of transmission and distribution system using decentralized scheme[J]. IEEE Transactions on Power Systems, 2019, 34(5): 3428-3442. [10] Monteiro M R, Zambroni de Souza A C, Abdelaziz M M A. Hierarchical load restoration for integrated transmission and distribution systems with multi-microgrids[J]. IEEE Transactions on Power Systems, 2024, 39(6): 7050-7063. [11] 韩讴竹, 陈志铭, 丁涛, 等. 计及风电不确定性的电力系统黑启动恢复模型[J]. 电网技术, 2023, 47(8): 3289-3304. Han Ouzhu, Chen Zhiming, Ding Tao, et al.Power system black-start restoration model considering wind power uncertainties[J]. Power System Technology, 2023, 47(8): 3289-3304. [12] 王晓卫, 康乾坤, 梁振锋, 等. 考虑5G基站储能参与配电网供电恢复研究[J]. 电工技术学报, 2024, 39(11): 3538-3555. Wang Xiaowei, Kang Qiankun, Liang Zhenfeng, et al.Distribution network restoration supply method considers 5G base station energy storage participation[J]. Transactions of China Electrotechnical Society, 2024, 39(11): 3538-3555. [13] 陈继明, 徐乾, 李勇, 等. 计及源荷不确定性和碳捕集虚拟电厂的电-气互联系统优化调度[J]. 太阳能学报, 2023, 44(10): 9-18. Chen Jiming, Xu Qian, Li Yong, et al.Optimal dispatch of electricity-natural gas interconnection system considering source-load uncertainty and virtual power plant with carbon capture[J]. Acta Energiae Solaris Sinica, 2023, 44(10): 9-18. [14] 臧天磊, 刘云飞, 王世俊, 等. 计及故障传播效应的配电信息物理系统多时段维修-恢复协同策略[J]. 电力自动化设备, 2024, 44(12): 247-256. Zang Tianlei, Liu Yunfei, Wang Shijun, et al.Multi-period maintenance and restoration collaborative strategy for cyber physical distribution system considering fault propagation effect[J]. Electric Power Automation Equipment, 2024, 44(12): 247-256. [15] 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. [16] 刘磊. 基于智能软开关的配电网故障恢复研究[J]. 电气技术, 2024, 25(9): 27-32, 37. Liu Lei.Research on fault recovery process of distribution network based on soft open point[J]. Electrical Engineering, 2024, 25(9): 27-32, 37. [17] 袁鑫, 唐昊, 刘昕, 等. 计及不确定性的输配电网协调恢复全并行分布式优化方法[J]. 电网技术, 2023, 47(6): 2463-2476. Yuan Xin, Tang Hao, Liu Xin, et al.Fully parallel distributed optimization method for coordinated recovery of transmission and distribution networks considering uncertainty[J]. Power System Technology, 2023, 47(6): 2463-2476. [18] 黄馨仪, 刘明波, 林舜江, 等. 考虑风电不确定性的输配电系统鲁棒经济调度分布式算法[J]. 电力系统自动化, 2025, 49(4): 165-177. Huang Xinyi, Liu Mingbo, Lin Shunjiang, et al.Distributed algorithm for robust economic dispatch of integrated transmission and distribution system considering wind power uncertainty[J]. Automation of Electric Power Systems, 2025, 49(4): 165-177. [19] Liu Hongli, Shi Yawei, Wang Zheng, et al.A distributed algorithm based on relaxed ADMM for energy resources coordination[J]. International Journal of Electrical Power & Energy Systems, 2022, 135: 107482. [20] Zhai Junyi, Jiang Yuning, Shi Yuanming, et al.Distributionally robust joint chance-constrained dispatch for integrated transmission-distribution systems via distributed optimization[J]. IEEE Transactions on Smart Grid, 2022, 13(3): 2132-2147. [21] 陈艳波, 方哲, 张宁, 等. 基于大语言模型绿电预测和绿电交易的园区综合能源系统集群多目标协同运行方法[J]. 高电压技术, 2024, 50(7): 2849-2863. Chen Yanbo, Fang Zhe, Zhang Ning, et al.Multi-objective collaborative operation method for park-level integrated energy system cluster based on large language model for green electricity prediction and trading[J]. High Voltage Engineering, 2024, 50(7): 2849-2863. [22] 陈艳波, 王德帅, 田昊欣, 等. 基于源荷储协调运行的电网可用输电能力优化方法[J]. 电力系统保护与控制, 2024, 52(23): 119-134. Chen Yanbo, Wang Deshuai, Tian Haoxin, et al.An optimal method for the available transfer capability of a power grid based on coordinated operation of source-load-storage[J]. Power System Protection and Control, 2024, 52(23): 119-134. [23] 万海洋, 刘文霞, 石庆鑫, 等. 城市电网灾后应急资源的集中匹配-分布调度策略[J]. 电工技术学报, 2024, 39(23): 7463-7480. Wan Haiyang, Liu Wenxia, Shi Qingxin, et al.A post-disaster centralized matching and decentralized dispatch strategy for emergency resources in urban power network[J]. Transactions of China Electrotech-nical Society, 2024, 39(23): 7463-7480. [24] 张智, 陈艳波, 刘芳, 等. 计及运行风险和需求响应的两阶段鲁棒机组组合模型[J]. 中国电机工程学报, 2021, 41(3): 961-973. Zhang Zhi, Chen Yanbo, Liu Fang, et al.Two-stage robust unit commitment model considering operation risk and demand response[J]. Proceedings of the CSEE, 2021, 41(3): 961-973. [25] 张智, 周明, 武昭原, 等. 考虑动态频率支撑的储能选址定容规划方法[J]. 中国电机工程学报, 2023, 43(7): 2708-2721. Zhang Zhi, Zhou Ming, Wu Zhaoyuan, et al.Energy storage location and capacity planning method considering dynamic frequency support[J]. Proceedings of the CSEE, 2023, 43(7): 2708-2721. [26] 陈艳波, 田昊欣, 刘宇翔, 等. 计及电动汽车需求响应的高速公路服务区光储充鲁棒优化配置[J]. 中国电机工程学报, 2025, 45(5): 1752-1767. Chen Yanbo, Tian Haoxin, Liu Yuxiang, et al.Robust optimization configuration of photovoltaic-storage-charging integrated system in expressway service area considering demand response of electric vehicles[J]. Proceedings of the CSEE, 2025, 45(5): 1752-1767. [27] 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. [28] Wang Shouxiang, Chen Sijia, Ge Leijiao, et al.Distributed generation hosting capacity evaluation for distribution systems considering the robust optimal operation of OLTC and SVC[J]. IEEE Transactions on Sustainable Energy, 2016, 7(3): 1111-1123. [29] 邓荣楠, 宋梦, 高赐威, 等. 考虑用户负荷决策依赖特性的配电网灾后恢复方法对比分析[J]. 电工技术学报, 2024, 39(23): 7447-7462. Deng Rongnan, Song Meng, Gao Ciwei, et al.Comparative analysis of distribution system load restoration considering decision-dependent behaviors of customers[J]. Transactions of China Electro-technical Society, 2024, 39(23): 7447-7462. [30] 陈艳波, 刘宇翔, 田昊欣, 等. 基于广义目标级联法的多牵引变电站光伏-储能协同规划配置[J]. 电工技术学报, 2024, 39(15): 4599-4612. Chen Yanbo, Liu Yuxiang, Tian Haoxin, et al.Collaborative planning and configuration of photovoltaic and energy storage in multiple traction substations based on generalized analytical target cascading method[J]. Transactions of China Electro-technical Society, 2024, 39(15): 4599-4612. [31] 伊博宇, 陈益广, 张少凡, 等. 输配电网同时故障下基于多时段安德森加速的协同恢复策略[J]. 电力系统自动化, 2024, 48(20): 159-170. Yi Boyu, Chen Yiguang, Zhang Shaofan, et al.Collaborative recovery strategy based on multi-period Anderson acceleration under simultaneous failures in transmission and distribution network[J]. Automation of Electric Power Systems, 2024, 48(20): 159-170. [32] 赵瑾. 考虑可再生能源参与的时空协调负荷恢复[D]. 济南: 山东大学, 2020. Zhao Jin.Studies on spatio-temporal coordination of load restoration considering renewable energy participation[D]. Jinan: Shandong University, 2020.
2026, Vol. 41 
