Electric Power ›› 2025, Vol. 58 ›› Issue (9): 124-137.DOI: 10.11930/j.issn.1004-9649.202503050
• New-Type Power Grid • Previous Articles Next Articles
Received:2025-03-17
															
							
															
							
															
							
																	Online:2025-09-26
															
							
							
																	Published:2025-09-28
															
							
						Supported by:LIN Jikeng, SHI Tao. Frequency Control Method for Regional Power Grids Based on Model Predictive Control[J]. Electric Power, 2025, 58(9): 124-137.
| 机组编号 | 容量/MW | 惯性时间 常数/s  | 机组编号 | 容量/MW | 惯性时间 常数/s  | |||||
| G1 | 1000 | 8.53 | G9 | 1000 | 6.45 | |||||
| G2 | 700 | 7.03 | G10 | 1000 | 6.20 | |||||
| G3 | 800 | 7.58 | W1 | 300 | 3.30 | |||||
| G4 | 800 | 6.86 | W2 | 400 | 3.50 | |||||
| G5 | 600 | 6.60 | W3 | 350 | 4.00 | |||||
| G6 | 800 | 6.48 | W4 | 300 | 3.10 | |||||
| G7 | 700 | 7.64 | BESS | 100 | 0 | |||||
| G8 | 700 | 5.43 | 
Table 1 Capacity and inertia constant of generators
| 机组编号 | 容量/MW | 惯性时间 常数/s  | 机组编号 | 容量/MW | 惯性时间 常数/s  | |||||
| G1 | 1000 | 8.53 | G9 | 1000 | 6.45 | |||||
| G2 | 700 | 7.03 | G10 | 1000 | 6.20 | |||||
| G3 | 800 | 7.58 | W1 | 300 | 3.30 | |||||
| G4 | 800 | 6.86 | W2 | 400 | 3.50 | |||||
| G5 | 600 | 6.60 | W3 | 350 | 4.00 | |||||
| G6 | 800 | 6.48 | W4 | 300 | 3.10 | |||||
| G7 | 700 | 7.64 | BESS | 100 | 0 | |||||
| G8 | 700 | 5.43 | 
| 机组 | 基准功率/ MW  | 最小出力/ MW  | 最大出力/ MW  | 速率/ (MW·min–1)  | ||||
| G2 | 520.8 | 200 | 680 | 15.0 | ||||
| G3 | 650.0 | 250 | 790 | 15.0 | ||||
| G4 | 100.0 | 250 | 790 | 25.0 | ||||
| G5 | 650.0 | 240 | 600 | 12.3 | ||||
| G7 | 260.0 | 50 | 700 | 20.0 | ||||
| G10 | 250.0 | 200 | 950 | 12.3 | ||||
| BESS | 0 | –100 | 100 | 60.0 | 
Table 2 Generator unit output parameters
| 机组 | 基准功率/ MW  | 最小出力/ MW  | 最大出力/ MW  | 速率/ (MW·min–1)  | ||||
| G2 | 520.8 | 200 | 680 | 15.0 | ||||
| G3 | 650.0 | 250 | 790 | 15.0 | ||||
| G4 | 100.0 | 250 | 790 | 25.0 | ||||
| G5 | 650.0 | 240 | 600 | 12.3 | ||||
| G7 | 260.0 | 50 | 700 | 20.0 | ||||
| G10 | 250.0 | 200 | 950 | 12.3 | ||||
| BESS | 0 | –100 | 100 | 60.0 | 
| 参数 | 取值 | 参数 | 取值 | |||
| 0.05 | 0.05 | |||||
| 0.05 | 1 | |||||
| 0.05 | 5 | |||||
| 0.05 | 0.2 | |||||
| 0.08 | 5 | |||||
| 0.3 | 0.43 | |||||
| 0.33 | 0.05 | |||||
| 7 | 1 | |||||
| 0.3 | 0.2 | |||||
| 0.08 | 1 | |||||
| 0.2 | 2 | |||||
| 5 | 20 | |||||
| 0.43 | 
Table 3 Parameters of unit regulation systems
| 参数 | 取值 | 参数 | 取值 | |||
| 0.05 | 0.05 | |||||
| 0.05 | 1 | |||||
| 0.05 | 5 | |||||
| 0.05 | 0.2 | |||||
| 0.08 | 5 | |||||
| 0.3 | 0.43 | |||||
| 0.33 | 0.05 | |||||
| 7 | 1 | |||||
| 0.3 | 0.2 | |||||
| 0.08 | 1 | |||||
| 0.2 | 2 | |||||
| 5 | 20 | |||||
| 0.43 | 
| 控制方法 | δCPS1/% | E(|EAC|)/MW | E(| | |||
| PI | 105.24 | 26.95 | ||||
| 确定性方法 | 181.10 | 8.78 | ||||
| 文献[ | 184.70 | 5.70 | ||||
| 本文方法 | 196.08 | 3.48 | 
Table 4 Performance comparison of different methods
| 控制方法 | δCPS1/% | E(|EAC|)/MW | E(| | |||
| PI | 105.24 | 26.95 | ||||
| 确定性方法 | 181.10 | 8.78 | ||||
| 文献[ | 184.70 | 5.70 | ||||
| 本文方法 | 196.08 | 3.48 | 
| 考虑因素 | |EAC|/MW | | | δCPS1/% | |||||||
| 均值 | 最大值 | 均值 | 最大值 | |||||||
| 本文 | 3.48 | 11.65 | 196.08 | |||||||
| 负荷 | 9.74 | 31.98 | 189.04 | |||||||
| 新能源 | 4.08 | 14.32 | 195.68 | |||||||
| 惯量 | 10.80 | 25.59 | 189.51 | |||||||
| 频率 | 10.67 | 35.86 | 188.78 | |||||||
Table 5 Comparison of various indicators for different methods
| 考虑因素 | |EAC|/MW | | | δCPS1/% | |||||||
| 均值 | 最大值 | 均值 | 最大值 | |||||||
| 本文 | 3.48 | 11.65 | 196.08 | |||||||
| 负荷 | 9.74 | 31.98 | 189.04 | |||||||
| 新能源 | 4.08 | 14.32 | 195.68 | |||||||
| 惯量 | 10.80 | 25.59 | 189.51 | |||||||
| 频率 | 10.67 | 35.86 | 188.78 | |||||||
| 1 |  
											张磊, 马晓伟, 王满亮, 等. 互联新能源电力系统区内AGC机组分布式协同控制策略[J]. 中国电力, 2025, 58 (3): 8- 19. 
																							 DOI  | 
										
|  
											ZHANG Lei, MA Xiaowei, WANG Manliang, et al. Distributed collaborative control strategy for intra-regional AGC units in interconnected power system with renewable energy[J]. Electric Power, 2025, 58 (3): 8- 19. 
																							 DOI  | 
										|
| 2 | ABAZARI A, MONSEF H, WU B. Load frequency control by de-loaded wind farm using the optimal fuzzy-based PID droop controller[J]. IET Renewable Power Generation, 2019, 13 (1): 180- 190. | 
| 3 |  
											ZHANG CK, JIANG L, WU Q H, et al. Delay-dependent robust load frequency control for time delay power systems[J]. IEEE Transactions on Power Systems, 2013, 28 (3): 2192- 2201. 
																							 DOI  | 
										
| 4 |  
											薛飞, 李宏强, 田蓓, 等. 储能辅助的孤岛微网自适应事件触发二次调频策略[J]. 中国电力, 2023, 56 (9): 196- 205. 
																							 DOI  | 
										
|  
											XUE Fei, LI Hongqiang, TIAN Bei, et al. Adaptive event-triggered secondary frequency control in islanded microgrids with auxiliary energy storage systems[J]. Electric Power, 2023, 56 (9): 196- 205. 
																							 DOI  | 
										|
| 5 |  
											MI Y, FU Y, WANG CS, et al. Decentralized sliding mode load frequency control for multi-area power systems[J]. IEEE Transactions on Power Systems, 2013, 28 (4): 4301- 4309. 
																							 DOI  | 
										
| 6 |  
											PEDDAKAPU K, MOHAMED MR, SRINIVASARAO P, et al. A state-of-the-art review on modern and future developments of AGC/LFC of conventional and renewable energy-based power systems[J]. Renewable Energy Focus, 2022, 43, 146- 171. 
																							 DOI  | 
										
| 7 | 席磊, 杜雄, 李彦营, 等. 基于具有强化学习思想的集成学习自动发电控制算法[J]. 南方电网技术, 2023, 17 (7): 74- 82. | 
| XI Lei, DU Xiong, LI Yanying, et al. Automatic generation control algorithm based on ensemble learning with the idea of reinforcement learning[J]. Southern Power System Technology, 2023, 17 (7): 74- 82. | |
| 8 | 陈宋宋, 张路涛, 周颖, 等. 面向新能源并网的分布式AGC协同算法[J]. 南方电网技术, 2023, 17 (4): 58- 68. | 
| CHEN Songsong, ZHANG Lutao, ZHOU Yin, et al. Distributed AGC cooperative algorithm for new energy grid connection[J]. Southern Power System Technology, 2023, 17 (4): 58- 68. | |
| 9 | YU T, ZHOU B, CHAN K W, et al. Stochastic optimal relaxed automatic generation control in non-Markov environment based on multi-step Q(λ) learning[J]. IEEE Transactions on Power Systems, 2011, 26 (3): 1272- 1282. | 
| 10 |  
											张孝顺, 余涛, 唐捷. 基于分层相关均衡强化学习的CPS指令优化分配算法[J]. 电力系统自动化, 2015, 39 (8): 80- 86. 
																							 DOI  | 
										
|  
											ZHANG Xiaoshun, YU Tao, TANG Jie. Optimal CPS command dispatch based on hierarchically correlated equilibrium reinforcement learning[J]. Automation of Electric Power Systems, 2015, 39 (8): 80- 86. 
																							 DOI  | 
										|
| 11 | 李彦营, 席磊, 郭宜果, 等. 基于权重双Q-时延更新学习算法的自动发电控制[J]. 中国电机工程学报, 2022, 42 (15): 5459- 5470. | 
| LI Yanying, XI Lei, GUO Yiguo, et al. Automatic generation control based on the weighted double Q-delayed update learning algorithm[J]. Proceedings of the CSEE, 2022, 42 (15): 5459- 5470. | |
| 12 | 柳丹, 任建宇, 席磊, 等. 基于高维协同软演员-评论家的多智能体自动发电控制[J]. 南方电网技术, 2025, 19 (4): 93- 106. | 
| LIU Dan, REN Jianyu , XI Lei, et al. Multi-agent automatic power generation control based on high dimensional collaborative soft actor-critic[J]. Southern Power System Technology, 2025, 19 (4): 93- 106. | |
| 13 |  
											YANG F, HUANG D, LI D, et al. Data-driven load frequency control based on multi-agent reinforcement learning with attention mechanism[J]. IEEE Transactions on Power Systems, 2023, 38 (6): 5560- 5569. 
																							 DOI  | 
										
| 14 | 刘向杰, 孔小兵. 电力工业复杂系统模型预测控制: 现状与发展[J]. 中国电机工程学报, 2013, 33 (5): 79- 85, 14. | 
| LIU Xiangjie, KONG Xiaobing. Present situation and prospect of model predictive control application in complex power industrial process[J]. Proceedings of the CSEE, 2013, 33 (5): 79- 85, 14. | |
| 15 |  
											周念成, 付鹏武, 王强钢, 等. 基于模型预测控制的两区域互联电网AGC系统研究[J]. 电力系统保护与控制, 2012, 40 (22): 46- 51. 
																							 DOI  | 
										
|  
											ZHOU Niancheng, FU Pengwu, WANG Qianggang, et al. Research on AGC of two area interconnected power system based on MPC[J]. Power System Protection and Control, 2012, 40 (22): 46- 51. 
																							 DOI  | 
										|
| 16 |  
											LIU XJ, ZHANG Y, LEE KY, et al. Coordinated distributed MPC for load frequency control of power system with wind farms[J]. IEEE Transactions on Industrial Electronics, 2017, 64 (6): 5140- 5150. 
																							 DOI  | 
										
| 17 |  
											虞临波, 寇鹏, 冯玉涛, 等. 风储联合发电系统参与频率响应的模型预测控制策略[J]. 电力系统自动化, 2019, 43 (12): 36- 43. 
																							 DOI  | 
										
|  
											YU Linbo, KOU Peng, FENG Yutao, et al. Model predictive control strategy for combined wind-storage system to participate in frequency response[J]. Automation of Electric Power Systems, 2019, 43 (12): 36- 43. 
																							 DOI  | 
										|
| 18 | 孙舶皓, 汤涌, 叶林, 等. 基于随机分层分布式模型预测控制的风电集群频率控制规划方法[J]. 中国电机工程学报, 2019, 39 (20): 5903- 5914. | 
| SUN Bohao, TANG Yong, YE Lin, et al. A programming method for wind power cluster frequency control based on S-H-DMPC[J]. Proceedings of the CSEE, 2019, 39 (20): 5903- 5914. | |
| 19 |  
											YANG DY, WANG B, CAI GW, et al. Inertia-adaptive model predictive control-based load frequency control for interconnected power systems with wind power[J]. IET Generation, Transmission and Distribution, 2020, 14 (22): 5029- 5036. 
																							 DOI  | 
										
| 20 |  
											LIU LK, HU ZC, MUJEEB A. Automatic generation control considering uncertainties of the key parameters in the frequency response model.[J]. IEEE Transactions on Power Systems, 2022, 37 (6): 4605- 4617. 
																							 DOI  | 
										
| 21 | SHEN Y K, WU W C, SUN S M. Stochastic model predictive control based fast-slow coordination automatic generation control[J]. IEEE Transactions on Power Systems, 2023, 39 (3): 1- 13. | 
| 22 | 张怡, 刘向杰. 互联电力系统鲁棒分布式模型预测负荷频率控制[J]. 控制理论与应用, 2016, 33 (5): 621- 630. | 
| ZHANG Y, LIU X J. Robust distributed model predictive control for load frequency control of uncertain power systems[J]. Control Theory & Applications, 2016, 33 (5): 621- 630. | |
| 23 | 杨冬锋, 朱军豪, 姜超, 等. 基于分布式模型预测的高比例风电系统多源协同负荷频率控制策略[J]. 电网技术, 2024, 48 (7): 2804- 2814. | 
| YANG D F, ZHU J H, JIANG C, et al. High proportion wind power system multi-source collaborate load frequency control strategy based on distributed model prediction[J]. Power System Technology, 2024, 48 (7): 2804- 2814. | |
| 24 | 刘家豪, 王程, 毕天姝. 面向新能源电力系统频率时空动态的节点等效惯量指标及其应用[J]. 中国电机工程学报, 2023, 43 (20): 7773- 7789. | 
| LIU Jiahao, WANG Cheng, BI Tianshu. Node equivalent inertia index for temporal-spatial frequency dynamics of renewable energy power system and its applications[J]. Proceedings of the CSEE, 2023, 43 (20): 7773- 7789. | |
| 25 | 夏飞, 袁博, 彭道刚, 等. 基于信息量准则的锂离子电池变阶RC等效电路模型建模及优化方法[J]. 中国电机工程学报, 2018, 38 (21): 6441- 6451, 6506. | 
| XIA Fei, YUAN Bo, PENG Daogang, et al. Modeling and optimization of variable-order RC equivalent circuit model for lithium ion batteries based on information criterion[J]. Proceedings of the CSEE, 2018, 38 (21): 6441- 6451, 6506. | |
| 26 |  
											ZHANG JB, XU HC. Online Identification of Power System Equivalent Inertia Constant[J]. IEEE Transactions on Industrial Electronics, 2017, 64 (10): 8098- 8107. 
																							 DOI  | 
										
| 27 | 邓齐林, 邱天宇, 申富饶, 等. 一种自适应在线核密度估计方法[J]. 软件学报, 2020, 31 (4): 1173- 1188. | 
| DENG Qilin, QIU Tianyu, SHEN Furao, et al. Adaptive online kernel density estimation method[J]. Journal of Software, 2020, 31 (4): 1173- 1188. | |
| 28 | FLAM J T. The linear model under Gaussian mixture inputs: selected problems in communications[D]. Trondheim: Norwegian University of Science and Technology, 2013. | 
| 29 | 严儒井. 多重不确定性下区域综合能源系统的供需协调规划研究[D]. 北京: 华北电力大学(北京), 2022: 31–33. | 
| YAN Rujing. Research on supply and demand coordination planning of regional integrated energy system under multiple uncertainties[D]. Beijing: North China Electric Power University, 2022: 31–33. | |
| 30 | 黄越辉, 曲凯, 李驰, 等. 基于K-means MCMC算法的中长期风电时间序列建模方法研究[J]. 电网技术, 2019, 43 (7): 2469- 2476. | 
| HUANG Yuehui, QU Kai, LI Chi, et al. Research on modeling method of medium- and long-term wind power time series based on K-means MCMC algorithm[J]. Power System Technology, 2019, 43 (7): 2469- 2476. | |
| 31 |  
											李世春, 宋秋爽, 薛臻瑶, 等. 含风电虚拟惯性响应的新能源电力系统惯量估计[J]. 电力工程技术, 2023, 42 (2): 84- 93. 
																							 DOI  | 
										
|  
											LI Shichun, SONG Qiushuang, XUE Zhenyao, et al. Inertia estimation of new energy power system with virtual inertia response of wind power[J]. Electric Power Engineering Technology, 2023, 42 (2): 84- 93. 
																							 DOI  | 
										
| [1] | MAN Linkun, WU Keming, CHI Cheng, YOU Jinshi, ZHAO Zitong, ZHANG Yajian. Adaptive Load Frequency Control Strategy for Interconnected Power Systems Considering Stochastic Access/Exit Behaviors of Energy Storage Systems [J]. Electric Power, 2025, 58(9): 164-174. | 
| [2] | GAO Fangjie, SUN Yujie, LI Yi, LE Ying, ZHANG Jiguang, XU Chuanbo, LIU Dunnan. Robust Optimization Scheduling of Island Multi-energy Microgrid Considering Offshore Wind Power to Hydrogen [J]. Electric Power, 2025, 58(7): 68-79. | 
| [3] | KONG Lingguo, TIAN Yangjin, KANG Jiandong, FANG Lei, LIU Chuang, CAI Guowei. Bi-level Optimization Configuration for Offshore Independent Energy Islands Considering Coordination of Multiple Electrolyzers under Uncertainties [J]. Electric Power, 2025, 58(7): 80-90, 104. | 
| [4] | ZHANG Bohang, QI Jun, XIE Luyao, ZHANG Youbing, ZHANG Boyang. Distributed Model Predictive Frequency Control of Interconnected Power Systems Considering Demand Response [J]. Electric Power, 2025, 58(7): 105-114. | 
| [5] | ZHOU Kai, TAO Zhengshun, PAN Tinglong, XU Dezhi. Balancing Control Strategy for Energy Storage Lithium Battery Pack Based on CCS-MPC [J]. Electric Power, 2025, 58(7): 177-186. | 
| [6] | ZHAI Zhe, CHEN Ziyu, LIU Qixing, LIANG Yanjie, LI Zhiyong. An Electricity Market Trading Model for Distributed Resource Aggregators Considering Risk Management [J]. Electric Power, 2025, 58(6): 56-66, 155. | 
| [7] | TAN Qinliang, HE Jiaming, LV Hanyu, DING Yihong. Optimization of Low-Carbon Technology Adoption Decision for Generation Enterprises Considering Cost Uncertainty [J]. Electric Power, 2025, 58(5): 62-73. | 
| [8] | CHEN Minghongtian, GENG Jianghai, ZHAO Yuze, XU Peng, HAN Yushan, ZHANG Yuming, ZHANG Zimo. Two-Stage Stochastic Optimization Based Weekly Operation Strategy for Electric-Hydrogen Coupled Microgrid [J]. Electric Power, 2025, 58(5): 82-90. | 
| [9] | WANG Li, JIANG Yuxiang, ZENG Xiangjun, ZHAO Bin, LI Junhao. Secondary Frequency Control of Islanded Microgrid Based on Deep Reinforcement Learning [J]. Electric Power, 2025, 58(5): 176-188. | 
| [10] | WANG Jinfeng, LI Jinpeng, XU Yinliang, LIU Haitao, HE Jinxiong, XU Jianyuan. Distributed Optimization for VPP and Distribution Network Operation Considering Uncertainty and Green Certificate Market [J]. Electric Power, 2025, 58(4): 21-30, 192. | 
| [11] | Yunrui WU, Jianpo ZHANG, Xincheng TIAN, Kaifeng YING, Zhong CHEN. Improved Coordinated Control Strategy of Multi-terminal DC Grids Considering Frequency Adaptation and Fast Stabilization Characteristics [J]. Electric Power, 2025, 58(3): 31-42. | 
| [12] | Mingbing LI, Qiang LI, Xiyang GUAN, Haoyang ZHOU, Rui LU, Yankun FENG. Market Oriented Low-Carbon Optimal Scheduling of Virtual Power Plants Considering Multiple User-Side Resources Coordination [J]. Electric Power, 2025, 58(2): 66-76. | 
| [13] | Changhao XU, Weidong GUAN, Yue WANG, Jinshuai ZHANG, Peng WANG, Ning ZHOU, Bowen SHANG. Two-Layer MPC Virtual Inertia Control Strategy for Small-Scale Variable-Speed Pumped Storage Unit with Full-Size Converter [J]. Electric Power, 2025, 58(2): 216-226. | 
| [14] | YANG Xiong, LI Juan, JIANG Yunlong, LI Hongmei, XU Wanyun, LI Xiaolu, GUO Ruipeng. An Optimal Scheduling Method for Demand-Side Resource Clustering in Distribution Networks Based on Customer Directrix Load Reconfiguration [J]. Electric Power, 2025, 58(10): 163-170. | 
| [15] | WANG Zezhou, MAO Linming, PAN Keqin, CHU Jianxin, CHEN Gang. Affine Power Flow Calculation Method for Low-voltage Distribution Systems Considering the Uncertainty of Distributed Photovoltaic Output [J]. Electric Power, 2025, 58(10): 188-194. | 
| Viewed | ||||||
| 
										Full text | 
									
										 | 
								|||||
| 
										Abstract | 
									
										 | 
								|||||

