基于负荷可行域和可靠性跟踪的电力系统扩容规划及其求解算法

doi:10.16183/j.cnki.jsjtu.2024.048

摘要/Abstract

摘要：

电力系统可靠性评估计算复杂度高,难以嵌入电力系统扩容规划模型中.为了实现考虑可靠性的系统扩容规划,提出一种基于负荷可行域和可靠性跟踪的电力系统扩容规划模型及其求解算法.建立基于负荷可行域的近似距离模型,将可靠性评估中的切负荷计算从优化问题求解转变为方程求解,降低可靠性评估计算复杂度.基于近似距离模型,建立可靠性指标对设备容量的灵敏度模型,实现针对设备容量的可靠性跟踪.最后提出以可靠性提升为目标的电力系统扩容规划模型,以及基于可靠性跟踪和贪心算法的优化求解算法.结果表明:近似距离模型能够有效降低可靠性评估的计算复杂度;灵敏度模型能够正确反映设备容量变化对系统可靠性的影响;扩容规划模型及求解算法能够达到最优的系统扩容规划结果.

关键词: 扩容规划, 可靠性跟踪, 负荷可行域, 近似距离模型, 贪心算法

Abstract:

Power system reliability evaluation is a high-dimensional nonlinear problem, which is difficult to be nested into the power system expansion planning model. This paper proposes a power system expansion planning model and its solution algorithm based on load feasible region model and reliability tracking. First, it proposes an approximate distance model based on load feasible region, which transforms the optimization problem of load shedding calculation required into an equation solving. Based on this, it obtains the analytical expression of reliability sensitivity to components’ capacity and the reliability tracking oriented to capacity. Then, it proposes a reliability-oriented capacity expansion planning model, and a solution algorithm based on reliability tracking and greedy algorithm. The results show that the approximate distance model can effectively reduce the computational complexity of reliability evaluation, while the sensitivity model can accurately reflect the influence of equipment capacity on system reliability, and the capacity expansion planning model and algorithm can achieve optimal system capacity expansion planning results.

Key words: expansion planning, reliability tracking, load feasible region, approximate distance model, greedy algorithm

中图分类号:

TM715

李轩, 谢开贵, 邵常政, 胡博. 基于负荷可行域和可靠性跟踪的电力系统扩容规划及其求解算法[J]. 上海交通大学学报, 2026, 60(2): 200-210.

LI Xuan, XIE Kaigui, SHAO Changzheng, HU Bo. Power System Expansion Planning Model and Solution Algorithm Based on Load Feasible Region and Reliability Tracking[J]. Journal of Shanghai Jiao Tong University, 2026, 60(2): 200-210.

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参考文献 26

[1]	BARINGO L, BARINGO A. A stochastic adaptive robust optimization approach for the generation and transmission expansion planning[J]. IEEE Transactions on Power Systems, 2018, 33(1): 792-802. doi: 10.1109/TPWRS.2017.2713486 URL
[2]	VERÁSTEGUI F, LORCA Á, OLIVARES D, et al. An adaptive robust optimization model for power systems planning with operational uncertainty[C]// IEEE Power & Energy Society General Meeting. Montreal, QC, Canada: IEEE, 2020: 9281912.
[3]	YIN S F, WANG J H. Generation and transmission expansion planning towards a 100% renewable future[J]. IEEE Transactions on Power Systems, 2022, 37(4): 3274-3285. doi: 10.1109/TPWRS.2020.3033487 URL
[4]	YIN W Q, FENG S L, HOU Y H. Stochastic wind farm expansion planning with decision-dependent uncertainty under spatial smoothing effect[J]. IEEE Transactions on Power Systems, 2023, 38(3): 2845-2857. doi: 10.1109/TPWRS.2022.3184705 URL
[5]	BAYANI R, MANSHADI S D. Resilient expansion planning of electricity grid under prolonged wildfire risk[J]. IEEE Transactions on Smart Grid, 2023, 14(5): 3719-3731. doi: 10.1109/TSG.2023.3241103 URL
[6]	MÍNGUEZ R, VAN ACKOOIJ W, GARCÍA-BERTRAND R. Constraint generation for risk averse two-stage stochastic programs[J]. European Journal of Operational Research, 2021, 288(1): 194-206. doi: 10.1016/j.ejor.2020.05.064 URL
[7]	GARCÍA-CEREZO Á, GARCÍA-BERTRAND R, BARINGO L. Computational performance enhancement strategies for risk-averse two-stage stochastic generation and transmission network expansion planning[J]. IEEE Transactions on Power Systems, 2024, 39(1): 273-286. doi: 10.1109/TPWRS.2023.3236397 URL
[8]	王纬纶. 考虑可靠性与灵活性的输电网规划研究[D]. 济南: 山东大学, 2021.
	WANG Weilun. Study on transmission network planning considering reliability and flexibility[D]. Jinan: Shandong University, 2021.
[9]	张家浩. 基于改进粒子群算法的输电网规划方案研究[D]. 哈尔滨: 东北农业大学, 2022.
	ZHANG Jiahao. Research on transmission network planning scheme based on improved particle swarm optimization[D]. Harbin: Northeast Agricultural University, 2022.
[10]	徐岩, 张建浩. 计及故障不确定性的多阶段多目标电源扩展规划[J]. 太阳能学报, 2021, 42(12): 443-451.
	XU Yan, ZHANG Jianhao. Multi-stage multi-objective power expansion planning with fault uncertainty[J]. Acta Energiae Solaris Sinica, 2021, 42(12): 443-451.
[11]	纪静, 谢开贵, 曹侃, 等. 广东电网薄弱环节辨识及可靠性改善分析[J]. 电力系统自动化, 2011, 35(13): 98-102.
	JI Jing, XIE Kaigui, CAO Kan, et al. Weak part identification and reliability improvement analysis of Guangdong power grid[J]. Automation of Electric Power Systems, 2011, 35(13): 98-102.
[12]	郑颖, 谢开贵, 李洪兵, 等. 基于可靠性跟踪的薄弱环节辨识方法在省级电网可靠性改善中的应用研究[J]. 电测与仪表, 2015, 52(6): 118-123.
	ZHENG Ying, XIE Kaigui, LI Hongbing, et al. Application of the weak part identification based on reliability tracking method to reliability improvement of provincial power network[J]. Electrical Measurement & Instrumentation, 2015, 52(6): 118-123.
[13]	XIE K G, BILLINTON R. Tracing the unreliability and recognizing the major unreliability contribution of network components[J]. Reliability Engineering & System Safety, 2009, 94(5): 927-931. doi: 10.1016/j.ress.2008.10.009 URL
[14]	胡博, 谢开贵, 黎小林, 等. HVDC输电系统可靠性跟踪方法[J]. 中国电机工程学报, 2010, 30(10): 29-35.
	HU Bo, XIE Kaigui, LI Xiaolin, et al. Techniques of tracing the unreliability contributions of HVDC transmission system components[J]. Proceedings of the CSEE, 2010, 30(10): 29-35.
[15]	胡博, 周家浩, 王蕾报, 等. 考虑削负荷责任分摊的电力系统可靠性跟踪方法[J]. 电力系统自动化, 2020, 44(23): 64-71.
	HU Bo, ZHOU Jiahao, WANG Leibao, et al. Reliability tracking method of power system considering responsibility allocation of load shedding[J]. Automation of Electric Power Systems, 2019, 44(23): 64-71.
[16]	CAO M S, SHAO C Z, HU B, et al. Reliability tracing of the integrated energy system using the improved Shapley value[J]. Energy, 2022, 260: 124997. doi: 10.1016/j.energy.2022.124997 URL
[17]	黎小林, 曹侃, 谢开贵, 等. 基于最小二乘法的高压直流输电系统可靠性灵敏度分析[J]. 电力系统自动化, 2009, 33(18): 12-16.
	LI Xiaolin, CAO Kan, XIE Kaigui, et al. Sensitivity analysis of HVDC transmission system reliability using the least square method[J]. Automation of Electric Power Systems, 2009, 33(18): 12-16.
[18]	李生虎, 于丽萍, 马燕如, 等. 电网可靠性对可控串联补偿部件参数的灵敏度分解算法[J]. 电力系统自动化, 2016, 40(20): 20-25.
	LI Shenghu, YU Liping, MA Yanru, et al. Sensitivity decomposition algorithm of power system reliability oriented to parameters of TCSC components[J]. Automation of Electric Power Systems, 2016, 40(20): 20-25.
[19]	任震, 梁振升, 黄雯莹. 交直流混合输电系统可靠性指标的灵敏度分析[J]. 电力系统自动化, 2004, 28(14): 33-36.
	REN Zhen, LIANG Zhensheng, HUANG Wenying. Sensitivity analysis of AC/DC hybrid transmission system reliability indices[J]. Automation of Electric Power Systems, 2004, 28(14): 33-36.
[20]	赵渊. 大电力系统可靠性评估的灵敏度分析及其校正措施模型研究[D]. 重庆: 重庆大学, 2004.
	ZHAO Yuan. Sensitivity analysis of reliability evaluation of large power system and research on its correction measures model[D]. Chongqing: Chongqing University, 2004.
[21]	谢楚. 基于设备灵敏度分析的输电网可靠性优化[D]. 上海: 上海交通大学, 2013.
	XIE Chu. Reliability optimization of transmission network based on equipment sensitivity analysis[D]. Shanghai: Shanghai Jiao Tong University, 2013.
[22]	LI X, XIE K G, SHAO C Z, et al. A region-based approach for the operational reliability evaluation of power systems with renewable energy integration[J]. IEEE Transactions on Power Systems, 2024, 39(2): 3389-3400. doi: 10.1109/TPWRS.2023.3286088 URL
[23]	BILLINTON R, KUMAR S, CHOWDHURY N, et al. A reliability test system for educational purposes-basic data[J]. IEEE Transactions on Power Systems, 1989, 4(3): 1238-1244. doi: 10.1109/59.32623 URL
[24]	Probability Methods Subcommittee. IEEE reliability test system[J]. IEEE Transactions on Power Apparatus and Systems, 1979, PAS-98(6): 2047-2054. doi: 10.1109/TPAS.1979.319398 URL
[25]	GRIGG C, WONG P, ALBRECHT P, et al. The IEEE Reliability Test System—1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee[J]. IEEE Transactions on Power Systems, 1999, 14(3): 1010-1020. doi: 10.1109/59.780914 URL
[26]	赵渊, 周家启, 刘志宏. 大电网可靠性的序贯和非序贯蒙特卡洛仿真的收敛性分析及比较[J]. 电工技术学报, 2009, 24(11): 127-133.
	ZHAO Yuan, ZHOU Jiaqi, LIU Zhihong. Convergence analysis and comparison of sequential and nonsequential Monte-Carlo simulation for bulk power system reliability assessment[J]. Transactions of China Electrotechnical Society, 2009, 24(11): 127-133.

测试系统	方法	LOLP/%	EENS/ (GW·h^-1)	评估时间/s
RBTS	最优潮流模型	0.98	1.06	733
	负荷可行域模型	0.98	1.06	151
	近似距离模型	0.98	1.09	71
RTS-79	最优潮流模型	8.48	127	690
	负荷可行域模型	8.48	127	64
	近似距离模型	8.48	129	18
RTS-96	最优潮流模型	1.38	24.8	1116
	负荷可行域模型	1.38	24.8	24
	近似距离模型	1.38	25.2	15

基准方法	方法	EENS/(GW·h^-1)	误差/%
最优潮流模型	最优潮流模型	24.5	—
	灵敏度模型	24.4	-0.8
近似距离模型	近似距离模型	24.7	—
	灵敏度模型	24.7	0

序号	容量/ MW	所在节点	灵敏度	可靠性跟踪结果/ (MW·h^-1)
1	40	1	-39.31	65.94
2	10	1	-70.74	118.67
3	20	1	-54.50	91.42
4	40	1	-39.22	65.79
5	5	2	-72.61	121.81
6	5	2	-72.64	121.86
7	20	2	-62.90	105.52
8	20	2	-62.71	105.19
9	20	2	-62.94	105.58
10	20	2	-63.16	105.95
11	40	2	-49.03	82.25

排序	考虑峰值负荷		考虑全场景
排序	机组	可靠性跟踪结果/ (MW·h^-1)	机组	可靠性跟踪结果/ (MW·h^-1)
1	94	273.84	60	284.63
2	62	271.83	90	281.45
3	92	271.57	91	281.28
4	60	271.43	93	281.15
5	61	271.43	94	281.14
︙	︙	︙	︙	︙
95	24	149.01	56	97.80
96	57	147.82	22	97.71
97	89	147.37	55	97.12
98	56	146.88	88	97.06
99	90	144.73	23	96.51

序号	起始节点	终止节点	灵敏度	可靠性跟踪结果/ (MW·h^-1)
1	1	2	-3.03×10^-2	0.051
2	1	3	-3.54×10^-2	0.059
3	1	3	-3.54×10^-2	0.059
4	2	4	-1.38	2.305
5	2	4	-1.38	2.305
6	3	4	0	0
7	3	5	0	0
8	4	5	0	0
9	5	6	0	0