Two-stage Robust Low-carbon Optimal Scheduling for Integrated Energy Systems Considering for Multiple Uncertainties

doi:10.11930/j.issn.1004-9649.202507022

Abstract

Abstract:

To address the challenges of electricity-heat-gas coupling in integrated energy systems under multiple uncertainties, a two-stage robust optimization scheduling model is constructed that considers the multiple uncertainties from both renewable energy and equipment. Firstly, an integrated energy system model encompassing electricity, heat, and gas is established. Subsequently, with the objectives of system economy, robustness, and low-carbon performance, a two-stage robust low-carbon optimal scheduling model is established by introducing a tiered carbon trading mechanism to constrain carbon emissions. Finally, five scenarios are designed and solved using the column-and-constraint generation algorithm. Simulation results demonstrate that the proposed model effectively reduces carbon emissions of the system scheduling scheme while ensuring system robustness, thereby significantly enhancing the rationality of the scheduling scheme.

Key words: integrated energy system, multiple uncertainties, tiered carbon trading, robust optimization

YANG Huping, GONG Jianing, CHENG Ming, LI Xiangjun, LIU Changlu, ZHANG Yang. Two-stage Robust Low-carbon Optimal Scheduling for Integrated Energy Systems Considering for Multiple Uncertainties[J]. Electric Power, 2025, 58(11): 101-110, 121.

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URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202507022

https://www.electricpower.com.cn/EN/Y2025/V58/I11/101

Figures/Tables 14

References 30

1	中华人民共和国中央人民政府, 国家能源局. 关于印发《2024年能源工作指导意见》的通知(国能发规划〔2024〕22号)[Z].
2	周奕佳, 彭弘毅, 晏鸣宇. 氢-电-热综合能源系统快速风险评估方法[J]. 智慧电力, 2025, 53 (5): 1- 7.
	ZHOU Yijia, PENG Hongyi, YAN Mingyu. A rapid risk assessment method for hydrogen-electric-thermal integrated energy systems[J]. Smart Power, 2025, 53 (5): 1- 7.
3	马成元, 陈皓勇, 肖东亮. 考虑碳约束的新型电力系统跨区域优化调度研究[J]. 智慧电力, 2024, 52 (6): 38- 45.
	MA Chengyuan, CHEN Haoyong, XIAO Dongliang. Cross-region optimal dispatch of new power system considering carbon constraints[J]. Smart Power, 2024, 52 (6): 38- 45.
4	LI P, WANG Z X, WANG J H, et al. Two-stage optimal operation of integrated energy system considering multiple uncertainties and integrated demand response[J]. Energy, 2021, 225, 120256.
5	田兴涛. 电-热耦合综合能源系统安全经济优化调度方法研究[D]. 杭州: 浙江大学, 2024.
	TIAN Xingtao. Optimal Scheduling Method for Integrated Electricity and Heating Systems with Safe and Economic Guarantee[D]. Hangzhou: Zhejiang University, 2024.
6	胡福年, 张彭成, 周小博, 等. 计及灵活性资源的综合能源系统源荷协调优化调度[J]. 中国电力, 2024, 57 (5): 2- 13.
	HU Funian, ZHANG Pengcheng, ZHOU Xiaobo, et al. Coordinated optimal scheduling of source and load in integrated energy system considering flexible resources[J]. Electric Power, 2024, 57 (5): 2- 13.
7	彭春华, 郑聪, 陈婧, 等. 基于置信间隙决策的综合能源系统鲁棒优化调度[J]. 中国电机工程学报, 2021, 41 (16): 5593- 5604.
	PENG Chunhua, ZHENG Cong, CHEN Jing, et al. Robust optimal dispatching of integrated energy system based on confidence gap decision[J]. Proceedings of the CSEE, 2021, 41 (16): 5593- 5604.
8	雷杨, 赵纪峰, 丁石川, 等. 考虑双重不确定性的区域综合能源系统多阶段滚动随机规划[J]. 电力系统自动化, 2023, 47 (20): 53- 63.
	LEI Yang, ZHAO Jifeng, DING Shichuan, et al. Multi-stage rolling stochastic planning of regional integrated energy system considering dual-uncertainty[J]. Automation of Electric Power Systems, 2023, 47 (20): 53- 63.
9	ZHOU Y Z, WEI Z N, SUN G Q, et al. A robust optimization approach for integrated community energy system in energy and ancillary service markets[J]. Energy, 2018, 148, 1- 15.
10	MEI F, ZHANG J T, LU J X, et al. Stochastic optimal operation model for a distributed integrated energy system based on multiple-scenario simulations[J]. Energy, 2021, 219, 119629.
11	DOLATABADI A, MOHAMMADI-IVATLOO B, ABAPOUR M, et al. Optimal stochastic design of wind integrated energy hub[J]. IEEE Transactions on Industrial Informatics, 2017, 13 (5): 2379- 2388.
12	SOYSTER A L. Convex programming with set-inclusive constraints and applications to inexact linear programming[J]. Operations Research, 1973, 21 (5): 1154- 1157.
13	SINGH C. Convex programming with set-inclusive constraints and its applications to generalized linear and fractional programming[J]. Journal of Optimization Theory and Applications, 1982, 38 (1): 33- 42.
14	BEN-TAL A, NEMIROVSKI A. Robust solutions of uncertain linear programs[J]. Operations Research Letters, 1999, 25 (1): 1- 13.
15	彭春华, 谢鹏, 詹骥文, 等. 基于改进细菌觅食算法的微网鲁棒经济调度[J]. 电网技术, 2014, 38 (9): 2392- 2398.
	PENG Chunhua, XIE Peng, ZHAN Jiwen, et al. Robust economic dispatch of microgrid using improved bacterial foraging algorithm[J]. Power System Technology, 2014, 38 (9): 2392- 2398.
16	TAN J, WU Q W, HU Q R, et al. Adaptive robust energy and reserve co-optimization of integrated electricity and heating system considering wind uncertainty[J]. Applied Energy, 2020, 260, 114230.
17	BEN-TAL A, GORYASHKO A, GUSLITZER E, et al. Adjustable robust solutions of uncertain linear programs[J]. Mathematical Programming, 2004, 99 (2): 351- 376.
18	周特, 薛云飞, 季节, 等. 考虑电力间接碳排放不确定性的电-冷-热综合能源系统两阶段鲁棒优化方法[J]. 电网技术, 2024, 48 (1): 50- 63.
	ZHOU Te, XUE Yunfei, JI Jie, et al. Two-stage robust optimization for electricity-cooling-heat integrated energy system considering uncertainty of indirect carbon emissions of electricity[J]. Power System Technology, 2024, 48 (1): 50- 63.
19	ZENG B, ZHAO L. Solving two-stage robust optimization problems using a column-and-constraint generation method[J]. Operations Research Letters, 2013, 41 (5): 457- 461.
20	郭尊, 李庚银, 周明, 等. 考虑网络约束和源荷不确定性的区域综合能源系统两阶段鲁棒优化调度[J]. 电网技术, 2019, 43 (9): 3090- 3100.
	GUO Zun, LI Gengyin, ZHOU Ming, et al. Two-stage robust optimal scheduling of regional integrated energy system considering network constraints and uncertainties in source and load[J]. Power System Technology, 2019, 43 (9): 3090- 3100.
21	SHEN X W, GUO Q L, SUN H B. Regional integrated energy system planning considering energy price uncertainties: a two-stage stochastic programming approach[J]. Energy Procedia, 2019, 158, 6564- 6569.
22	邱海峰. 考虑不确定性的微网鲁棒优化调度研究[D]. 南京: 东南大学, 2021.
	QIU Haifeng. Robust optimal scheduling of microgrids considering uncertainties[D]. Nanjing: Southeast University, 2021.
23	杨欢红, 赵峰, 黄文焘, 等. 考虑设备变工况特性的园区综合能源系统双层优化[J]. 电力系统保护与控制, 2024, 52 (17): 115- 127.
	YANG Huanhong, ZHAO Feng, HUANG Wentao, et al. Two-level optimization for a community integrated energy system considering the off-design condition of equipment[J]. Power System Protection and Control, 2024, 52 (17): 115- 127.
24	崔杨, 郭福音, 仲悟之, 等. 多重不确定性环境下的综合能源系统区间多目标优化调度[J]. 电网技术, 2022, 46 (8): 2964- 2975.
	CUI Yang, GUO Fuyin, ZHONG Wuzhi, et al. Interval multi-objective optimal dispatch of integrated energy system under multiple uncertainty environment[J]. Power System Technology, 2022, 46 (8): 2964- 2975.
25	陈晚晴, 穆云飞, 贾宏杰, 等. 考虑设备变工况特性的区域综合能源系统优化调度方法[J]. 电网技术, 2021, 45 (3): 951- 958.
	CHEN Wanqing, MU Yunfei, JIA Hongjie, et al. Operation optimization method for regional integrated energy system considering part-load performances of devices[J]. Power System Technology, 2021, 45 (3): 951- 958.
26	ZAKRZEWSKI T, STEPHENS B. Updated generalized natural gas reciprocating engine part-load performance curves for cogeneration applications[J]. Science and Technology for the Built Environment, 2017, 23 (7): 1151- 1158.
27	周建华, 梁昌誉, 史林军, 等. 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.
	ZHOU Jianhua, LIANG Changyu, SHI Linjun, et al. Optimal scheduling of integrated energy system considering the ladder-type carbon trading mechanism[J]. Electric Power, 2025, 58 (2): 77- 87.
28	李江南, 程韧俐, 周保荣, 等. 含碳捕集及电转氢设备的低碳园区综合能源系统随机优化调度[J]. 中国电力, 2024, 57 (5): 149- 156.
	LI Jiangnan, CHENG Renli, ZHOU Baorong, et al. Stochastic optimal of integrated energy system in low-carbon parks considering carbon capture storage and power to hydrogen[J]. Electric Power, 2024, 57 (5): 149- 156.
29	陈兴龙, 曹喜民, 陈洁, 等. 绿证-碳交易机制下热电灵活响应的园区综合能源系统优化调度[J]. 中国电力, 2024, 57 (6): 110- 120.
	CHEN Xinglong, CAO Ximin, CHEN Jie, et al. Optimized dispatch of park integrated energy system with thermoelectric flexible response under green certificate-carbon trading mechanism[J]. Electric Power, 2024, 57 (6): 110- 120.
30	王利猛, 刘雪梦, 李扬, 等. 阶梯式碳交易机制下考虑需求响应的综合能源系统低碳优化调度[J]. 电力建设, 2024, 45 (2): 102- 114.
	WANG Limeng, LIU Xuemeng, LI Yang, et al. Low-carbon optimal dispatch of integrated energy system considering demand response under the tiered carbon trading mechanism[J]. Electric Power Construction, 2024, 45 (2): 102- 114.

设备	参数	取值	设备	参数	取值
EB	$ \eta _{\rm EB}^{} $	0.98	GB	$ {\eta _{\rm GB}} $	0.94
	$ H_{\rm EB}^{\max } $/kW	300		$ H_{\rm GB}^{\max } $/kW	600
	$ a_{\rm EB}^{\rm ope} $/(元·kW^–1)	0.024		$ a_{\rm GB}^{\rm ope} $/(元·kW^–1)	0.024
CHP	$ \eta _{\rm CHP}^e $	0.34	电储能	$ {\tau _{\rm ES}} $	0.001
	$ {\alpha _{\rm CHP}} $	1.48		$ \eta _{\rm ES}^{\rm cha} $	0.9
	$ P_{\rm CHP}^{\max } $/kW	500		$P_{{\text{ES}}}^{{\text{max}}}$/kW	250
	$ {L_{\rm NG}} $/(kW·m^–3)	9.7		$ E_{\rm ES}^{\min } $/kW	100
	$ a_{\rm CHP}^{\rm ope} $/(元·kW^–1)	0.04		$ E_{\rm ES}^{\max } $/kW	600
P2G	$ {\eta _{\rm P2 G}} $	0.88	FC	$ {\eta _{\rm FC}} $	0.78
	$ P_{\rm P2 G}^{\max } $/kW	550		$ P_{\rm FC}^{\max } $/kW	1 200
	$ a_{\rm P2 G}^{\rm ope} $/(元·kW^–1)	0.03		$ a_{\rm FC}^{\rm ope} $/(元·kW^–1)	0.05
热储能	$ {\tau _{\rm HS}} $	0.01	气储能	$ {\tau _{\rm GS}} $	0.01
	$ \eta _{\rm HS}^{\rm cha} $	0.95		$ \eta _{\rm GS}^{\rm cha} $	0.98
	$ \eta _{\rm HS}^{\rm dis} $	0.95		$ \eta _{\rm GS}^{\rm dis} $	0.98
	$H_{{\text{HS}}}^{{\text{max}}}$/kW	120		$G_{\rm GS}^{{\text{max}}}$/m³	30
	$ E_{\rm HS}^{\min } $/kW	100		$ E_{\rm GS}^{\min } $/m³	20
	$ E_{\rm HS}^{\max } $/kW	600		$ E_{\rm GS}^{\max } $/m³	100
	$ {E_{\rm HS,1}} $/kW	300		$ {E_{\rm GS,1}} $/m³	20

设备	参数	取值	设备	参数	取值
EB	$ \eta _{\rm EB}^{} $	0.98	GB	$ {\eta _{\rm GB}} $	0.94
	$ H_{\rm EB}^{\max } $/kW	300		$ H_{\rm GB}^{\max } $/kW	600
	$ a_{\rm EB}^{\rm ope} $/(元·kW^–1)	0.024		$ a_{\rm GB}^{\rm ope} $/(元·kW^–1)	0.024
CHP	$ \eta _{\rm CHP}^e $	0.34	电储能	$ {\tau _{\rm ES}} $	0.001
	$ {\alpha _{\rm CHP}} $	1.48		$ \eta _{\rm ES}^{\rm cha} $	0.9
	$ P_{\rm CHP}^{\max } $/kW	500		$P_{{\text{ES}}}^{{\text{max}}}$/kW	250
	$ {L_{\rm NG}} $/(kW·m^–3)	9.7		$ E_{\rm ES}^{\min } $/kW	100
	$ a_{\rm CHP}^{\rm ope} $/(元·kW^–1)	0.04		$ E_{\rm ES}^{\max } $/kW	600
P2G	$ {\eta _{\rm P2 G}} $	0.88	FC	$ {\eta _{\rm FC}} $	0.78
	$ P_{\rm P2 G}^{\max } $/kW	550		$ P_{\rm FC}^{\max } $/kW	1 200
	$ a_{\rm P2 G}^{\rm ope} $/(元·kW^–1)	0.03		$ a_{\rm FC}^{\rm ope} $/(元·kW^–1)	0.05
热储能	$ {\tau _{\rm HS}} $	0.01	气储能	$ {\tau _{\rm GS}} $	0.01
	$ \eta _{\rm HS}^{\rm cha} $	0.95		$ \eta _{\rm GS}^{\rm cha} $	0.98
	$ \eta _{\rm HS}^{\rm dis} $	0.95		$ \eta _{\rm GS}^{\rm dis} $	0.98
	$H_{{\text{HS}}}^{{\text{max}}}$/kW	120		$G_{\rm GS}^{{\text{max}}}$/m³	30
	$ E_{\rm HS}^{\min } $/kW	100		$ E_{\rm GS}^{\min } $/m³	20
	$ E_{\rm HS}^{\max } $/kW	600		$ E_{\rm GS}^{\max } $/m³	100
	$ {E_{\rm HS,1}} $/kW	300		$ {E_{\rm GS,1}} $/m³	20

场景	调度总成本/元	购电成本/元	购气成本/元	运维成本/元	碳交易成本/元	碳排放量/kg
1	34 672.54	6 309.48	2 773.47	628.30	0	32 184.53
2	35 328.64	6 042.94	28 626.10	659.89	0	32 225.86
3	35 423.52	6 590.39	28 180.77	652.35	0	32 422.17
4	37 255.30	6 285.74	28 481.98	654.62	1 832.95	31 996.38
5	37 822.76	6 007.07	28 760.42	661.39	2 393.87	31 556.53

场景	调度总成本/元	购电成本/元	购气成本/元	运维成本/元	碳交易成本/元	碳排放量/kg
1	34 672.54	6 309.48	2 773.47	628.30	0	32 184.53
2	35 328.64	6 042.94	28 626.10	659.89	0	32 225.86
3	35 423.52	6 590.39	28 180.77	652.35	0	32 422.17
4	37 255.30	6 285.74	28 481.98	654.62	1 832.95	31 996.38
5	37 822.76	6 007.07	28 760.42	661.39	2 393.87	31 556.53

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[2]	GUO Zhenglin, CHEN Shutong, TIAN Jiawen, CHEN Luan, GUO Zhongjie, HU Weihao, FU Qiang. Allocation of Multiple Resources for Integrated Energy System Based on Capacity Value Function [J]. Electric Power, 2025, 58(7): 15-23.
[3]	ZHAO Junxiang, WEN Zhong, WANG Qiujie, ZHANG Yewei. Two-Stage Robust Low-Carbon Economic Optimization for Integrated Energy System Based on Oxy-Fuel Combustion Technology [J]. Electric Power, 2025, 58(7): 24-37.
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