基于边界法的大型机组组合模型的简化方法

doi:10.16182/j.issn1004731x.joss.23-1072

摘要/Abstract

摘要：

随着电网规模的持续扩大，市场环境下考虑网络安全约束的机组组合（security-constrained unit commitment，SCUC）模型中的变量和约束显著增加，模型的求解性能变差。当模型规模过大时，会出现现有的商用求解器无法求解的状况，造成大规模模型求解困难的问题。为实现大规模机组组合模型的快速求解，从减少模型约束数量的角度出发，提出了一种基于边界法的线性约束简化方法。通过边界法剔除模型中冗余的线性约束，可以有效降低模型规模，实现模型的快速求解。基于IEEE-39、WECC 179和IEEE-118算例，在市场环境下进行日前SCUC测试。通过对比简化前后的求解时间，表明该方法能够显著提高模型的求解速率。

关键词: 安全约束机组组合, 求解性能, 边界法, 线性约束, 快速求解

Abstract:

As the scale of power grid expands, in the market environment, the variables and constraints in the security-constrained unit commitment (SCUC) model considering power grid security constraints increase significantly and the solvability of the model reduces. When the model scale is too large, even the existing commercial solvers cannot solve it. Aiming at the model rapid solving, from the perspective of reducing the number of model constraints, a linear constraint simplification method based on the boundary method is proposed. The proposed method can effectively reduce the model's size by eliminating the redundant linear constraints. The IEEE-39, WECC 179 and IEEE-118 test cases are utilized to carry out the day-ahead SCUC testing in a market environment. Comparing the solving speed before and after simplification, the proposed method can significantly improve the solving speed of the model.

Key words: security-constrained unit commitment(SCUC), solvability, boundary method, linear constraints, rapid solving

中图分类号:

TP391

许彦平,赵明欣,秦晓辉等 . 基于边界法的大型机组组合模型的简化方法[J]. 系统仿真学报, 2024, 36(2): 296-304.

Xu Yanping,Zhao Mingxin,Qin Xiaohui,et al . A Simplification Method of Large-scale Unit Commitment Model Based on Boundary Method[J]. Journal of System Simulation, 2024, 36(2): 296-304.

图/表 13

图1

表1

模型规模

连续变量数量	$∑ i ∈ G e n (T S e g, i) N S e g$
整数变量数量	$3 N C o a l N S e g$
等式约束数量	$(N C o a l + 1) N S e g$
不等式约束数量 (不含网络安全约束)	$(5 N C o a l + N H y d r o + N W i n d + N S o l a r) N S e g$

表1

图2

图3

表2

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表5

图4

图5

表6

表7

表8

参考文献 19

1	李云达. 考虑备用共享的含风电区域电力市场日前出清模型研究[D]. 保定: 华北电力大学, 2021.
	Li Yunda. Research on the Day-ahead Clearing Model of Regional Electricity Market Including Wind Power Generation Considering Reserve Sharing[D]. Baoding: North China Electric Power University, 2021.
2	Palmintier B S, Webster M D. Heterogeneous Unit Clustering for Efficient Operational Flexibility Modeling[J]. IEEE Transactions on Power Systems, 2014, 29(3): 1089-1098.
3	Palmintier B S, Webster M D. Impact of Operational Flexibility on Electricity Generation Planning with Renewable and Carbon Targets[J]. IEEE Transactions on Sustainable Energy, 2016, 7(2): 672-684.
4	Palmintier B, Webster M. Impact of Unit Commitment Constraints on Generation Expansion Planning with Renewables[C]//2011 IEEE Power and Energy Society General Meeting. Piscataway, NJ, USA: IEEE, 2011: 1-7.
5	Palmintier B S, Webster M D. Heterogeneous Unit Clustering for Efficient Operational Flexibility Modeling[J]. IEEE Transactions on Power Systems, 2014, 29(3): 1089-1098.
6	代江, 田年杰, 姜有泉, 等. 考虑梯级耦合的水火电检修计划与机组组合协同优化[J]. 电力工程技术, 2022, 41(3): 83-91.
	Dai Jiang, Tian Nianjie, Jiang Youquan, et al. Collaborative Maintenance Scheduling and Unit Commitment for Hydropower and Thermal Power Systems Considering Cascade Hydropower Coupling[J]. Electric Power Engineering Technology, 2022, 41(3): 83-91.
7	Zhou Yuzhou, Zhai Qiaozhu, Wu Lei, et al. A Data-driven Variable Reduction Approach for Transmission-constrained Unit Commitment of Large-scale Systems[J]. Journal of Modern Power Systems and Clean Energy, 2023, 11(1): 254-266.
8	Hua Bowen, Baldick R, Wang Jianhui. Representing Operational Flexibility in Generation Expansion Planning Through Convex Relaxation of Unit Commitment[J]. IEEE Transactions on Power Systems, 2018, 33(2): 2272-2281.
9	Hua Bowen, Baldick R. A Convex Primal Formulation for Convex Hull Pricing[J]. IEEE Transactions on Power Systems, 2017, 32(5): 3814-3823.
10	曲明, 丁涛, 李立, 等. 从NP-Hard到多项式时间算法的大规模机组组合近似线性规划: 双重凸包模型[J]. 中国电机工程学报, 2022, 42(9): 3261-3275, 中插13.
	Qu Ming, Ding Tao, Li Li, et al. An Approximate Linear Program from an NP-hard to a Polynomial Time Complexity for a Large-scale Unit Commitment: Dual Convex Hull Model[J]. Proceedings of the CSEE, 2022, 42(9): 3261-3275, 中插13.
11	王砚平, 鲍威, 李赢, 等. 考虑N-1故障的安全约束机组组合模型及约束削减方法[J]. 电力自动化设备, 2021, 41(7): 167-175.
	Wang Yanping, Bao Wei, Li Ying, et al. Model and Constraint-reduction Method for Security-constrained Unit Commitment Considering N-1 Contingency[J]. Electric Power Automation Equipment, 2021, 41(7): 167-175.
12	付聪, 王砚平, 刘俊磊, 等. 基于辅助优化问题的安全约束机组组合约束削减方法[J]. 电力系统保护与控制, 2021, 49(21): 9-17.
	Fu Cong, Wang Yanping, Liu Junlei, et al. Constraint Reduction Method for Security-constrained Unit Commitment Based on an Auxiliary Optimization Problem[J]. Power System Protection and Control, 2021, 49(21): 9-17.
13	Ma Ziming, Zhong Haiwang, Cheng Tong, et al. Redundant and Nonbinding Transmission Constraints Identification Method Combining Physical and Economic Insights of Unit Commitment[J]. IEEE Transactions on Power Systems, 2021, 36(4): 3487-3495.
14	Pineda Salvador, Juan Miguel Morales, Jiménez-Cordero Asunción. Data-driven Screening of Network Constraints for Unit Commitment[J]. IEEE Transactions on Power Systems, 2020, 35(5): 3695-3705.
15	Xavier Álinson S, Qiu Feng, Ahmed Shabbir. Learning to Solve Large-scale Security-constrained Unit Commitment Problems[J]. INFORMS Journal on Computing, 2020, 33(2): 739-756.
16	黄泽荣, 彭建春, 肖文娴, 等. 关于GSDF与GGDF的合理性与最优性[J]. 电力系统保护与控制, 2009, 37(21): 7-10, 40.
	Huang Zerong, Peng Jianchun, Xiao Wenxian, et al. On the Rationality and Optimality of GSDF and GGDF[J]. Power System Protection and Control, 2009, 37(21): 7-10, 40.
17	Zhu Jizhong. Optimization of Power System Operation[M]. Hoboken: Wiley, 2008.
18	Tejada-Arango Diego A, Sánchez-Martın Pedro, Ramos Andres. Security Constrained Unit Commitment Using Line Outage Distribution Factors[J]. IEEE Transactions on Power Systems, 2018, 33(1): 329-337.
19	Paulraj S, Sumathi P. A Comparative Study of Redundant Constraints Identification Methods in Linear Programming Problems[J]. Mathematical Problems in Engineering, 2010, 2010: 723402.

规模	case39	case179
火电机组	7	21
水电机组	1	1
风电机组	1	3
光伏机组	1	4
线路	46	263

规模	case39	case179
连续变量	3 840	8 760
整数变量	504	1 512
等式约束	192	528
不等式约束 (不含网络安全约束)	912	2 712
网络安全约束数量	38 136	693 360
约束总量	43 584	706 872

算例	简化前	简化后
case39	38 136	18 459
case179	693 360	392 046

算例	简化前	简化后
case39	43 584	23 907
case179	706 872	395 286

算例		模型构建	求解	总时间
case39	简化前	6.059	3.600	9.659
case39	简化后	7.653	1.520	9.173
case179	简化前	262.565	201.226	463.791
case179	简化后	264.060	36.310	300.370