考虑解析化动态频率约束的输-储协同鲁棒规划方法

doi:10.11930/j.issn.1004-9649.202511031

中国电力 ›› 2026, Vol. 59 ›› Issue (5): 150-163.DOI: 10.11930/j.issn.1004-9649.202511031

考虑解析化动态频率约束的输-储协同鲁棒规划方法

陈鸿琳¹(), 罗澍忻¹(), 徐蔚¹(), 吴广大²(), 王诗超²()

1. 广东电网有限责任公司电网规划研究中心，广东省广州市　510080
2. 中国能源建设集团广东省电力设计研究院有限公司，广东省广州市　510663

收稿日期:2025-11-12 修回日期:2026-02-10 发布日期:2026-05-15 出版日期:2026-05-28
作者简介:陈鸿琳（1992），女，通信作者，博士，从事电力系统优化与控制、新能源消纳等研究，E-mail：eehonglinchen@163.com

罗澍忻（1987），男，博士，高级工程师，从事电网规划等研究，E-mail：luoshuxin@gd.csg.cn
徐蔚（1984），男，高级工程师，硕士，从事电力系统规划与分析研究，E-mail：153805379@qq.com
吴广大（1986），男，高级工程师，硕士，从事柔性直流换流站技术研究，E-mail：ccp222584369@126.com
王诗超（1988），女，高级工程师，硕士，从事电力系统规划、海上风电并网技术研究，E-mail：wangshichao@gedi.com.cn
基金资助:
汕头、潮州国管海域海上风电统一输电规划项目（031000QQ00240024）；智能电网国家科技重大专项项目（2025ZD0805304）。

A robust coordinated planning method for transmission system and storage considering analytical frequency dynamics constraints

CHEN Honglin¹(), LUO Shuxin¹(), XU Wei¹(), WU Guangda²(), WANG Shichao²()

1. Power Grid Planning Research Center, Guangdong Power Grid Co., Ltd., Guangzhou, Guangdong 510080, China
2. China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd., Guangzhou, Guangdong 510663, China

Received:2025-11-12 Revised:2026-02-10 Online:2026-05-15 Published:2026-05-28
Supported by:
This work is supported by Unified Power Transmission Planning Project for Offshore Wind Power in the State-Managed Sea Areas of Shantou and Chaozhou (No.031000QQ00240024); Smart Grid-National Science and Technology Major Project (No.2025ZD0805304).

摘要/Abstract

摘要：

为应对海上风电出力不确定性对电力系统频率安全与输电网规划带来的挑战，提出了一种考虑解析化动态频率约束的输-储协同鲁棒规划方法。首先，构建了包含输电网上层规划与下层运行调度的双层优化框架，上层以系统投资与运行总成本最小为目标，规划满足负载率约束的输电线路；下层考虑输电网与储能系统（energy storage system，ESS）的协同运行，并引入频率响应特性建模，确保系统在扰动下具备动态频率安全性。随后，利用强对偶理论将双层模型转化为易于求解的单层模型。进一步，采用对抗场景生成（adversarial scenario generation，ASG）方法构建极端风险场景，基于1-∞范数混合不确定集描述海上风电与负荷的概率分布不确定性，并利用条件风险价值（conditional value-at-risk，CVaR）度量其带来的风险损失，从而建立输-储协同分布鲁棒优化模型，同时使用列与约束生成（column and constraint generation，C&CG）算法进行求解。基于IEEE 24节点系统的仿真结果表明，该方法在提升系统频率安全性的同时，能够有效缓解线路重载问题，得到经济性与鲁棒性兼顾的规划方案。

关键词: 输电网, 海上风电, 动态频率约束, 双层规划, 条件风险价值, 分布鲁棒优化

Abstract:

To address the challenges posed by the uncertainty of offshore wind power output to power system frequency security and transmission network planning, this paper proposes a transmission-storage coordinated robust planning method considering analytical dynamic frequency constraints. First, a bi-level optimization framework is formulated, consisting of upper-level transmission network planning and lower-level operation scheduling; the upper level aims to minimize the total system investment and operation cost while planning transmission lines that satisfy load rate constraints, and the lower level considers the coordinated operation of the transmission network and energy storage system (ESS) with frequency response modeling to guarantee dynamic frequency security under disturbances. Then, the bi-level model is transformed into a tractable single-level model via strong duality theory. Furthermore, an adversarial scenario generation (ASG) method is employed to construct extreme risk scenarios, the probabilistic uncertainty of offshore wind power and load is characterized by a 1-∞ norm hybrid uncertainty set, and conditional value-at-risk (CVaR) is adopted to quantify the corresponding risk loss, based on which a transmission-storage coordinated distributionally robust optimization model is established and solved by the column-and-constraint generation (C&CG) algorithm. Simulation results on the IEEE 24-bus system demonstrate that the proposed method can enhance system frequency security, effectively alleviate line overloading, and yield planning schemes with favorable economic efficiency and robustness.

Key words: transmission network, offshore wind power, frequency dynamics constraints, bi-level programming, CVaR, distributionally robust optimization

陈鸿琳, 罗澍忻, 徐蔚, 吴广大, 王诗超. 考虑解析化动态频率约束的输-储协同鲁棒规划方法[J]. 中国电力, 2026, 59(5): 150-163.

CHEN Honglin, LUO Shuxin, XU Wei, WU Guangda, WANG Shichao. A robust coordinated planning method for transmission system and storage considering analytical frequency dynamics constraints[J]. Electric Power, 2026, 59(5): 150-163.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202511031

https://www.electricpower.com.cn/CN/Y2026/V59/I5/150

图/表 15

图 1 双层优化框架

Fig.1 The double-layer optimization framework

图 2 频率响应特性曲线

Fig.2 Frequency response characteristic curve

图 3 对抗场景生成方法流程

Fig.3 Flow of the adversarial scenario generation method

图 4 采用C&CG算法求解考虑CVaR的输储协同分布鲁棒规划模型的流程

Fig.4 Flow of solving CVaR-considered transmission and storage collaborative distributionally robust planning model using C&CG algorithm

图 5 算例仿真拓扑

Fig.5 Example simulation topology

表 1 设备参数设置

Table 1 Device parameter settings

设备	接入位置	参数
常规机组容量/(kV·A)	节点1、2	192
	节点7、22	300
	节点13	591
	节点15	215
	节点16	155
	节点18、21	400
	节点23	660
海上风电容量/(kV·A)	节点19	900
ESS容量/(kV·A)	节点17	500
ESS初始荷电量/%		50
ESS功率上限/kW		50

图 6 海上风电和负载典型场景

Fig.6 Typical scenarios of offshore wind power and loads

表 2 各策略下的规划成本结果对比

Table 2 Comparison of planning cost results under various strategies

策略	F^UL/10⁶元	F^L/10⁶元	F^G/10⁶元	F^OS/10⁶元
1	21.6511	3.5148	17.6170	0.5223
2	21.5325	3.5642	17.4458	0.5223
3	21.5807	3.6137	17.3990	0.5680

图 7 不同场景下的频率变化率与频率最低点

Fig.7 Rate of change of frequency and frequency nadir under different scenarios

图 8 负载增量扰动下多电源频率响应及时序出力特性

Fig.8 Diagram of frequency response and time-series output characteristics of multi-power sources under load increment disturbance

图 9 输储协同规划状态变化曲线

Fig.9 Coordinated transmission and storage planning state change curve

图 10 线路重载情况

Fig.10 Schematic diagram of line overload condition

图 11 考虑线路负载率约束后的线路规划结果

Fig.11 Line planning results after considering line load rate constraints

表 3 考虑线路负载率约束前后重要线路的结果对比

Table 3 Comparison of results of key lines before and after considering line load rate constraints

线路	考虑负载率约束前		考虑负载率约束后
线路	平均负载率/%	重载率/%	平均负载率/%	重载率/%
1-3	14.99	11.71	12.41	0
1-5	9.74	10.46	8.144	0
3-24	16.188	5.29	9.22	0
7-8	49.17	50.25	34.67	7.01
8-9	44.15	52.71	41.16	14.66
13-23	27.12	19.86	3.75	0
17-18	46.8	73.44	24.35	25.01

图 12 考虑线路负载率约束前后的线路平均负载率变化

Fig.12 Graph of changes in average line load rate before and after considering line load rate constraints

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考虑解析化动态频率约束的输-储协同鲁棒规划方法

A robust coordinated planning method for transmission system and storage considering analytical frequency dynamics constraints

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考虑解析化动态频率约束的输-储协同鲁棒规划方法

A robust coordinated planning method for transmission system and storage considering analytical frequency dynamics constraints

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