Distributionally Robust Optimization-Based Decomposition Method for Medium- and Long-Term Contracts of Large-Scale Energy Bases

doi:10.11930/j.issn.1004-9649.202504023

Abstract

Abstract:

With the gradual construction and commissioning of large-scale energy bases, the medium- and long-term contracted energy of their supporting thermal power units needs to be decomposed into hourly scales for dispatching plans. To address the challenge of coordinating the decomposition of contract energy with inter-provincial power transmission requirements, a distributionally robust optimization-based decomposition method for medium- and long-term contracts of large-scale energy bases is proposed. Firstly, a deterministic optimization model for medium- and long-term contract decomposition is developed to maximize thermal power contract fulfillment and minimize generation costs while complying with standard transmission curve requirements. Secondly, a fuzzy set for renewable energy output uncertainty is constructed based on the empirical distribution formed from historical samples and a Wasserstein ball, and accordingly a distributionally robust optimization model is established. Finally, the model is transformed into a mixed-integer linear programming problem based on the strong duality theorem and affine adjustment strategy. The case study results demonstrate that the proposed method effectively balances the aggressiveness and conservatism of decisions, supporting the optimal dispatch of large-scale energy bases in electricity market environment.

Key words: large-scale energy base, contract energy decomposition, distributionally robust optimization, Wasserstein distance, optimal dispatch

SUN Tian, WANG Guoyang, LI Yinxiao, FAN Menghua, TANG Chenghui, GUO Hongye. Distributionally Robust Optimization-Based Decomposition Method for Medium- and Long-Term Contracts of Large-Scale Energy Bases[J]. Electric Power, 2025, 58(11): 38-48.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202504023

https://www.electricpower.com.cn/EN/Y2025/V58/I11/38

Figures/Tables 14

Fig.1 Power transmission structure of large-scale energy bases

Fig.2 The Wasserstein ball of radius $ \varepsilon $ centered at $ {\hat {\mathcal{P}}_N} $

Fig.3 Structure of large-scale energy base

Fig.4 The wind power output prediction and standard power transmission curves

Table 1 Parameters of thermal units

项目	机组编号
项目	1	2	3	4	5	6	7
最大出力/MW	660	660	660	660	660	660	350
最小出力/MW	198	198	198	198	198	198	105
爬坡能力/(p.u.·min^–1)	0.015	0.015	0.015	0.015	0.015	0.015	0.015
启动成本/万元	60	60	60	60	60	60	35
空载运行成本/万元	2.5	2.5	2.5	2.5	2.5	2.5	1.0
变动运行成本/ (元·(MW·h)^–1)	263	246	266	268	263	269	296
合同电量/(MW·h)	9041	9041	9041	9041	9041	9041	4795

Fig.5 Power generation output by unit type

Fig.6 Thermal power contract deviation volume under out-of-sample scenarios

Table 2 Optimal dispatch results

优化方法	目标函数/ 万元	峰时段外送功率/MW	总外送电量/(MW·h)
分布鲁棒优化	1 979.52	5 374.20	94 048.50
随机优化	1 786.54	5 409.15	94 660.31
鲁棒优化	2 204.05	5 363.20	93 856.02

Table 3 Out-of-sample validation results

优化方法	平均合同电量偏差/(MW·h)	最大合同电量偏差/(MW·h)	平均发电成本/万元	最大发电成本/万元
分布鲁棒优化	972.69	5 193.22	1 554.02	1 703.60
随机优化	888.67	5 493.45	1 562.43	1 711.66
鲁棒优化	1 371.82	5 035.08	1 539.07	1 691.85

Fig.7 Objective function under different sample sizes

Fig.8 Thermal power contract energy deviation under different sample sizes

Fig.9 Objective function at different confidence levels

Fig.10 Thermal power contract energy deviation at different confidence levels

Fig.11 Thermal power contract energy deviation under different deviation penalty coefficients

References 30

1	国家发展改革委, 国家能源局. 关于促进新时代新能源高质量发展的实施方案[EB/OL]. (2022-05-14)[2025-07-25]. https://www.gov.cn/zhengce/content/2022-5/30/content_5693013.htm.
2	徐文哲, 张哲任, 徐政. 适用于大规模纯新能源发电基地送出的混合式直流输电系统[J]. 中国电力, 2023, 56 (4): 17- 27.
	XU Wenzhe, ZHANG Zheren, XU Zheng. A hybrid HVDC topology suitable for large-scale pure clean energy power base transmission[J]. Electric Power, 2023, 56 (4): 17- 27.
3	夏清, 陈启鑫, 谢开, 等. 中国特色、全国统一的电力市场关键问题研究(2): 我国跨区跨省电力交易市场的发展途径、交易品种与政策建议[J]. 电网技术, 2020, 44 (8): 2801- 2808.
	XIA Qing, CHEN Qixin, XIE Kai, et al. Key issues of national unified electricity market with Chinese characteristics (2): development path, trading varieties and policy recommendations for inter-regional and inter-provincial electricity markets[J]. Power System Technology, 2020, 44 (8): 2801- 2808.
4	关立, 常江, 孙大雁, 等. 省间电力现货市场试运行分析及思考[J]. 电力系统自动化, 2024, 48 (11): 2- 10.
	GUAN Li, CHANG Jiang, SUN Dayan, et al. Analysis and reflection on trial operation of inter-provincial electricity spot markets in China[J]. Automation of Electric Power Systems, 2024, 48 (11): 2- 10.
5	李明轩, 范越, 汪莹, 等. 新能源大基地风光储容量协调优化配置[J]. 电力自动化设备, 2024, 44 (3): 1- 8.
	LI Mingxuan, FAN Yue, WANG Ying, et al. Coordinated optimal configuration of wind-photovoltaic-energy storage capacity for large-scale renewable energy bases[J]. Electric Power Automation Equipment, 2024, 44 (3): 1- 8.
6	李晖, 刘栋, 秦继朔, 等. 考虑风光出力不确定性的新能源基地直流外送随机规划方法研究[J]. 电网技术, 2024, 48 (7): 2795- 2803.
	LI Hui, LIU Dong, QIN Jishuo, et al. Stochastic planning method for UHVDC transmission of renewable energy power base considering wind and photovoltaic output uncertainties[J]. Power System Technology, 2024, 48 (7): 2795- 2803.
7	崔杨, 李崇钢, 赵钰婷, 等. 考虑风-光-光热联合直流外送的源-网-荷多时段优化调度方法[J]. 中国电机工程学报, 2022, 42 (2): 559- 573.
	CUI Yang, LI Chonggang, ZHAO Yuting, et al. Source-grid-load multi-time interval optimization scheduling method considering wind-photovoltaic-photothermal combined DC transmission[J]. Proceedings of the CSEE, 2022, 42 (2): 559- 573.
8	李湃, 王伟胜, 黄越辉, 等. 大规模新能源基地经特高压直流送出系统中长期运行方式优化方法[J]. 电网技术, 2023, 47 (1): 31- 44.
	LI Pai, WANG Weisheng, HUANG Yuehui, et al. Method on optimization of medium and long term operation modes of large-scale renewable energy power base through UHVDC system[J]. Power System Technology, 2023, 47 (1): 31- 44.
9	杜刚, 赵冬梅, 刘鑫. 计及风电不确定性优化调度研究综述[J]. 中国电机工程学报, 2023, 43 (7): 2608- 2627.
	DU Gang, ZHAO Dongmei, LIU Xin. Research review on optimal scheduling considering wind power uncertainty[J]. Proceedings of the CSEE, 2023, 43 (7): 2608- 2627.
10	贺帅佳, 阮贺彬, 高红均, 等. 分布鲁棒优化方法在电力系统中的理论分析与应用综述[J]. 电力系统自动化, 2020, 44 (14): 179- 191.
	HE Shuaijia, RUAN Hebin, GAO Hongjun, et al. Overview on theory analysis and application of distributionally robust optimization[J]. Automation of Electric Power Systems, 2020, 44 (14): 179- 191.
11	OZTURK U A, MAZUMDAR M, NORMAN B A. A solution to the stochastic unit commitment problem using chance constrained programming[J]. IEEE Transactions on Power Systems, 2004, 19 (3): 1589- 1598.
12	彭院院, 周任军, 曾子琪, 等. 参与气电市场的虚拟电厂内部优化随机模型[J]. 中国电力, 2020, 53 (9): 181- 188.
	PENG Yuanyuan, ZHOU Renjun, ZENG Ziqi, et al. Internal optimization stochastic model of virtual power plant participating in gas and electricity market[J]. Electric Power, 2020, 53 (9): 181- 188.
13	ZHAO C Y, WANG Q F, WANG J H, et al. Expected value and chance constrained stochastic unit commitment ensuring wind power utilization[J]. IEEE Transactions on Power Systems, 2014, 29 (6): 2696- 2705.
14	WANG J, BOTTERUD A, BESSA R, et al. Wind power forecasting uncertainty and unit commitment[J]. Applied Energy, 2011, 88 (11): 4014- 4023.
15	WU L, SHAHIDEHPOUR M, LI T. Stochastic security-constrained unit commitment[J]. IEEE Transactions on Power Systems, 2007, 22 (2): 800- 811.
16	KARAMI M, SHAYANFAR H A, AGHAEI J. Scenario-based security-constrained hydrothermal coordination with volatile wind power generation[J]. Renewable & Sustainable Energy Reviews, 2013, 28, 726- 737.
17	GORISSEN B L, YANIKOGLU I, DEN H. A practical guide to robust optimization[J]. Omega, 2015, 53, 124- 137.
18	汲国强, 吴文传, 张伯明. 考虑风电不确定性的机组检修鲁棒优化方法[J]. 中国电机工程学报, 2015, 35 (12): 2919- 2926.
	JI Guoqiang, WU Wenchuan, ZHANG Boming. Robust optimization method of generator maintenance schedule considering wind power integration[J]. Proceedings of the CSEE, 2015, 35 (12): 2919- 2926.
19	杜浩程, 李世龙, 巨云涛, 等. 基于压缩开关候选集合的分布鲁棒配电网重构方法[J]. 中国电力, 2024, 57 (10): 12- 24, 35.
	DU Haocheng, LI Shilong, JU Yuntao, et al. Linear active disturbance rejection control parameter tuning method for energy storage converter with enhanced stability[J]. Electric Power, 2024, 57 (10): 12- 24, 35.
20	WIESEMANN W, KUHN D, SIM M. Distributionally robust convex optimization[J]. Operations Research, 2014, 62 (6): 1358- 1376.
21	MOHAJERIN E P, KUHN D. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations[J]. Mathematical Programming, 2018, 171 (1-2): 115- 166.
22	朱晓荣, 山雨琦. 考虑灵活性的储能容量多阶段分布鲁棒规划[J]. 电力自动化设备, 2023, 43 (6): 152- 159, 167.
	ZHU Xiaorong, SHAN Yuqi. Multi-stage distributionally robust planning of energy storage capacity considering flexibility[J]. Electric Power Automation Equipment, 2023, 43 (6): 152- 159, 167.
23	ZHU R J, WEI H, BAI X Q. Wasserstein metric based distributionally robust approximate framework for unit commitment[J]. IEEE Transactions on Power Systems, 2019, 34 (4): 2991- 3001.
24	DUAN C, FANG W L, JIANG L, et al. Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric[J]. IEEE Transactions on Power Systems, 2018, 33 (5): 4924- 4936.
25	WANG C, GAO R, QIU F, et al. Risk-based distributionally robust optimal power flow with dynamic line rating[J]. IEEE Transactions on Power Systems, 2018, 33 (6): 6074- 6086.
26	FOURNIER N, GUILLIN A. On the rate of convergence in Wasserstein distance of the empirical measure[J]. Probability Theory and Related Fields, 2015, 162, 707- 738.
27	ZHAO C Y, GUAN Y P. Data-driven risk-averse stochastic optimization with Wasserstein metric[J]. Operations Research Letters, 2018, 46 (2): 262- 267.
28	JABR R A. Adjustable robust OPF with renewable energy sources[J]. IEEE Transactions on Power Systems, 2013, 28 (4): 4742- 4751.
29	DUAN C, JIANG L, FANG W L. Data-driven affinely adjustable distributionally robust unit commitment[J]. IEEE Transactions on Power Systems, 2018, 33 (2): 1385- 1398.
30	GAO R, KLEYWEGT A. Distributionally robust stochastic optimization with Wasserstein distance[J]. Mathematics of Operations Research, 2023, 48 (2): 603- 655.

[1]	FU Chengcheng, ZHANG Chunyan, LIU Jianye, JIA Dexiang, LI Dan, WANG Su. Optimal Dispatching Method of Demand-Side Resources with Load Aggregator Participation [J]. Electric Power, 2025, 58(8): 1-11.
[2]	DING Xiaoqiang, YUAN Zhi, LI Ji. Cooperative Operation Optimization for Multi-region Hydrogen-Integrated Integrated Energy System Based on Hybrid Wasserstein Two-Stage Distributionally Robust [J]. Electric Power, 2025, 58(7): 1-14.
[3]	XU Shijie, HU Bangjie, ZHAO Liang, WANG Pei. Research on Optimal Dispatch with Source-Load Coordination for Micro-energy Grid Based on Energy-Carbon Coupling Model [J]. Electric Power, 2025, 58(4): 1-12.
[4]	Yumin ZHANG, Yanbin Yin, Xingquan JI, Pingfeng YE, Donglei SUN, Aiquan SONG. Optimal Dispatch of Integrated Electric-Heat Energy System Considering Supply Flexibility of Heat Networks Under Different Operation States [J]. Electric Power, 2025, 58(2): 88-102.
[5]	Suwei ZHAI, Yinyin LI, Fan DU, Wenyun LI, Kaiyan PAN, Junkai LIANG. Distributed Reactive Power Control Strategy of Distribution Network Considering Massive Distributed Energy Access [J]. Electric Power, 2024, 57(8): 138-144.
[6]	Caijuan QI, Baosheng CHEN, Dongni WEI, Zhao YANG. Distributionally Robust Optimal Configuration for Shared Energy Storage Based on Stackelberg Game Pricing Model [J]. Electric Power, 2024, 57(7): 40-53.
[7]	Yao ZHAO, Yongjiang CHEN, Kunhua JI, Yun WANG. Distribution Network Topology Identification Based on Finite Key Nodes and Wasserstein Distance [J]. Electric Power, 2024, 57(4): 151-161.
[8]	Zhipeng LV, Zhenhao SONG, Lisheng LI, Yang LIU. Optimization Scheduling of Integrated Energy System Scheduling in Industrial Park containing Electric Vehicles [J]. Electric Power, 2024, 57(4): 25-31.
[9]	Dongshun ZHANG, Hengli QUAN, Hua XIE, Zhihong XU, Yayun TAO, Huisheng WANG. Dispatching Strategy of Park-Level Integrated Energy System Considering Carbon Trading Mechanism and Hydrogen Blending Natural Gas [J]. Electric Power, 2024, 57(2): 183-193.
[10]	Zhiwei LIU, Yue MA, Zhicheng SHA, Yunshu SHAO, Yuanfang NIU, Xiaoming DONG, Chengfu WANG. Distributionally Robust Operation for Flexible Distribution Networks Considering Multi-correlation of Renewable Power Generation [J]. Electric Power, 2024, 57(12): 97-108.
[11]	Wenhao CHAO, Zhi YUAN, Ji LI. Optimal Dispatch of Power System with P2G-Wind-Thermal-Nuclear-Carbon Capture Units [J]. Electric Power, 2024, 57(1): 183-194.
[12]	Zhiyuan SUN, Boya PENG, Yan SUN. Optimal Dispatch Strategy of Power and Electricity Balance Based on Multi-Energy Complementation [J]. Electric Power, 2024, 57(1): 115-122.
[13]	Chao ZHANG, Dongmei ZHAO, Yu JI, Ying ZHANG. Real Time Optimal Dispatch of Virtual Power Plant Based on Improved Deep Q Network [J]. Electric Power, 2024, 57(1): 91-100.
[14]	QI Caijuan, CHE Bin, YANG Yan, CHEN Baosheng. Master-Slave Game-Based Robust Pricing Method of Shared Energy Storage Considering Renewable Energy Accommodation and Energy Storage Participating in Frequency Modulation [J]. Electric Power, 2023, 56(8): 26-39.
[15]	Qiang LI, Yao WANG, Yingying HU, Xiaoming ZHENG, Linna ZHANG, Yongming JING. Multi-Stage Coordinated Planning Method for Transmission Network and Energy Storage Considering Carbon Trading Cost [J]. Electric Power, 2023, 56(12): 199-205.