基于分布鲁棒优化的大型能源基地中长期合同分解方法

doi:10.11930/j.issn.1004-9649.202504023

中国电力 ›› 2025, Vol. 58 ›› Issue (11): 38-48.DOI: 10.11930/j.issn.1004-9649.202504023

• 推进全国统一电力市场建设关键技术与机制 • 上一篇下一篇

基于分布鲁棒优化的大型能源基地中长期合同分解方法

孙田¹^,²(), 王国阳¹(), 李寅晓²(), 范孟华³(), 唐程辉³(), 郭鸿业²()

1. 北京电力交易中心有限公司，北京　100031
2. 新型电力系统运行与控制全国重点实验室（清华大学电机工程与应用电子技术系），北京　100084
3. 国网能源研究院有限公司，北京　102209

收稿日期:2025-04-09 修回日期:2025-08-11 发布日期:2025-12-01 出版日期:2025-11-28
作者简介:
孙田（1992），女，博士研究生，高级工程师，从事电力市场研究，E-mail：tian-sun@sgcc.com.cn
王国阳（1995），男，硕士，工程师，从事电力系统、电力市场研究，E-mail：wang-guoyang@sgcc.com.cn
李寅晓（1996），男，通信作者，博士，助理研究员，从事电力市场、电力系统优化研究，E-mail：liyinxiao2023@mail.tsinghua.edu.cn
范孟华（1983），女，博士，高级工程师（教授级），从事电力市场研究，E-mail：fanmenghua@sgeri.sgcc.com.cn
唐程辉（1990），男，博士，高级工程师，从事电力市场研究，E-mail：immocy@163.com
郭鸿业（1993），男，博士，副研究员，从事电力市场、源网荷储市场化互动、人工智能与大数据分析等研究，E-mail：hyguo@tsinghua.edu.cn
基金资助:
国家电网有限公司科技项目（全国统一电力市场框架下促进大型能源基地开发利用的电力市场交易机制及关键技术研究，5108-202457041A-1-1-ZN）。

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

SUN Tian¹^,²(), WANG Guoyang¹(), LI Yinxiao²(), FAN Menghua³(), TANG Chenghui³(), GUO Hongye²()

1. Beijing Power Trading Center Co., Ltd., Beijing 100031, China
2. State Key Laboratory of Power System Operation and Control (Department of Electrical Engineering, Tsinghua University), Beijing 100084, China
3. State Grid Energy Research Institute Co., Ltd., Beijing 102209, China

Received:2025-04-09 Revised:2025-08-11 Online:2025-12-01 Published:2025-11-28
Supported by:
This work is supported by Science and Technology Project of SGCC (Study on the Electricity Market Trading Mechanism and Key Technologies to Promote the Development and Utilisation of Large Energy Bases under the Framework of the National Unified Electricity Market, No.5108-202457041A-1-1-ZN)．

摘要/Abstract

摘要：

随着大型能源基地的逐步建设投产，其配套火电机组的中长期合同电量需要分解到小时级尺度以制定调度计划。针对中长期合同分解与省间送电要求难以协同的问题，提出基于分布鲁棒优化的大型能源基地中长期合同分解方法。首先，在满足标准送电曲线的要求下，以尽可能完成火电合同电量与最小化发电成本为目标成本建立确定性中长期合同分解优化模型。其次，基于由历史样本形成的经验分布与Wasserstein球构建可再生能源出力不确定性的模糊集，并依此建立分布鲁棒优化模型。最后，基于强对偶定理与仿射调整策略将模型转化为混合整数线性规划问题进行求解。算例结果表明所提方法能够有效兼顾决策的激进性与保守性，支撑电力市场环境下大型能源基地的优化调度。

关键词: 大型能源基地, 合同电量分解, 分布鲁棒优化, Wasserstein距离, 优化调度

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

孙田, 王国阳, 李寅晓, 范孟华, 唐程辉, 郭鸿业. 基于分布鲁棒优化的大型能源基地中长期合同分解方法[J]. 中国电力, 2025, 58(11): 38-48.

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.

导出引用管理器 EndNote|Ris|BibTeX

链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202504023

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

图/表 14

图 1 大型能源基地外送结构示意

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

图 2 以$ {\hat {\mathcal{P}}_N} $为中心、半径为$ \varepsilon $的Wasserstein球

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

图 3 大型能源基地结构

Fig.3 Structure of large-scale energy base

图 4 风电预测出力与标准送电曲线

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

表 1 火电机组参数

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

图 5 各类型机组发电功率

Fig.5 Power generation output by unit type

图 6 样本外抽样场景下的火电合同偏差量

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

表 2 优化调度结果

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

表 3 样本外验证结果

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

图 7 不同样本数量下的目标函数

Fig.7 Objective function under different sample sizes

图 8 不同样本数量下的火电合同电量偏差

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

图 9 不同置信水平下的目标函数

Fig.9 Objective function at different confidence levels

图 10 不同置信水平下的火电合同电量偏差

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

图 11 不同偏差惩罚系数下的火电合同电量偏差

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

参考文献 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. DOI
	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. DOI
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. DOI
	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. DOI
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. DOI
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. DOI
	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. DOI
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. DOI
14	WANG J, BOTTERUD A, BESSA R, et al. Wind power forecasting uncertainty and unit commitment[J]. Applied Energy, 2011, 88 (11): 4014- 4023. DOI
15	WU L, SHAHIDEHPOUR M, LI T. Stochastic security-constrained unit commitment[J]. IEEE Transactions on Power Systems, 2007, 22 (2): 800- 811. DOI
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. DOI
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. DOI
	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. DOI
20	WIESEMANN W, KUHN D, SIM M. Distributionally robust convex optimization[J]. Operations Research, 2014, 62 (6): 1358- 1376. DOI
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. DOI
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. DOI
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. DOI
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. DOI
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. DOI
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. DOI
28	JABR R A. Adjustable robust OPF with renewable energy sources[J]. IEEE Transactions on Power Systems, 2013, 28 (4): 4742- 4751. DOI
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. DOI
30	GAO R, KLEYWEGT A. Distributionally robust stochastic optimization with Wasserstein distance[J]. Mathematics of Operations Research, 2023, 48 (2): 603- 655. DOI

[1]	丁小强, 袁至, 李骥. 基于混合Wasserstein两阶段分布鲁棒的多区域含氢综合能源系统合作运行优化[J]. 中国电力, 2025, 58(7): 1-14.
[2]	张瀚公, 谢丽蓉, 王层层, 任娟, 卞一帆, 韩宪超. 考虑氢能多元利用的综合能源系统低碳灵活调度[J]. 中国电力, 2025, 58(7): 38-53.
[3]	魏春晖, 单林森, 胡大栋, 高乾恒, 张新松, 薛晓岑. 面向需求响应的园区虚拟电厂优化调度策略[J]. 中国电力, 2025, 58(6): 112-121.
[4]	许世杰, 胡邦杰, 赵亮, 王沛. 基于能碳耦合模型的微能源网源荷协同优化调度研究[J]. 中国电力, 2025, 58(4): 1-12.
[5]	沈舒仪, 王国腾, 但扬清, 孙飞飞, 黄莹, 徐政. 频率偏差与电压刚度约束下多馈入直流优化调度方法[J]. 中国电力, 2025, 58(3): 132-141.
[6]	李明冰, 李强, 管西洋, 周皓阳, 卢瑞, 冯延坤. 市场环境下考虑多元用户侧资源协同的虚拟电厂低碳优化调度[J]. 中国电力, 2025, 58(2): 66-76.
[7]	周建华, 梁昌誉, 史林军, 李杨, 易文飞. 计及阶梯式碳交易机制的综合能源系统优化调度[J]. 中国电力, 2025, 58(2): 77-87.
[8]	张玉敏, 尹延宾, 吉兴全, 叶平峰, 孙东磊, 宋爱全. 计及热网不同运行状态下灵活性供给能力的综合能源系统优化调度[J]. 中国电力, 2025, 58(2): 88-102.
[9]	闫志彬, 李立, 阳鹏, 宋蕙慧, 车彬, 靳盘龙. 考虑构网型储能支撑能力的微电网优化调度策略[J]. 中国电力, 2025, 58(2): 103-110.
[10]	许文俊, 马刚, 姚云婷, 孟宇翔, 李伟康. 考虑绿证-碳交易机制与混氢天然气的工业园区多能优化调度[J]. 中国电力, 2025, 58(2): 154-163.
[11]	杨雄, 李娟, 姜云龙, 李红梅, 徐婉云, 李晓露, 郭瑞鹏. 基于负荷准线重构的配电网需求侧资源集群优化调度方法[J]. 中国电力, 2025, 58(10): 163-170.
[12]	翟苏巍, 李银银, 杜凡, 李文云, 潘凯岩, 梁峻恺. 考虑海量分布式能源接入的配电网分布式无功控制策略[J]. 中国电力, 2024, 57(8): 138-144.
[13]	齐彩娟, 陈宝生, 韦冬妮, 杨钊. 考虑主从博弈定价模式的共享储能分布鲁棒优化配置方法研究[J]. 中国电力, 2024, 57(7): 40-53.
[14]	王云龙, 韩璐, 罗树林, 吴涛. 集成电动汽车的家庭电热综合能源系统负荷调度优化[J]. 中国电力, 2024, 57(5): 39-49.
[15]	吕志鹏, 宋振浩, 李立生, 刘洋. 含电动汽车的工业园区综合能源系统优化调度[J]. 中国电力, 2024, 57(4): 25-31.

基于分布鲁棒优化的大型能源基地中长期合同分解方法

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

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 14

参考文献 30

相关文章 15

编辑推荐

Metrics

模态框（Modal）标题

基于分布鲁棒优化的大型能源基地中长期合同分解方法

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

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 14

参考文献 30

相关文章 15

编辑推荐

Metrics