考虑调频资源供需比的电力系统年度典型日概率密度聚类方法

doi:10.19595/j.cnki.1000-6753.tces.251518

Abstract
Figure/Table
References (0)
Related Citation (1)

Download: PDF (2095 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract

With the rapid development of new electric power systems, the proportion of synchronous generation capacity continues to decline, intensifying the imbalance between the supply and demand of frequency regulation resource (FRR). Traditional typical-day classification methods, which rely on load and renewable generation characteristics, can no longer satisfy the operational requirements of new electric power systems with high renewable energy penetration. To address this issue, a probability density peak clustering method considering the supply-demand ratio of FRR is proposed. The method introduces the supply-demand ratio of FRR as a key indicator in the clustering process, facilitating the identification of representative typical days across a year.
First, based on the system dynamic frequency response and the constraint on frequency nadir, a quantitative model for evaluating FRR demand was established. An optimal scheduling model incorporating the primary frequency regulation capability of conventional generators was then formulated to assess the available FRR supply. The annual FRR supply and demand data over 365 days were treated as sample points for clustering. A two-dimensional Gaussian kernel density function was employed to construct the global probability density and determine the cluster centers. Subsequently, a composite clustering index was developed based on Euclidean distance and the supply-demand ratio of FRR to achieve accurate division of typical days for FRR. Compared with conventional clustering approaches, the proposed method incorporates the supply-demand ratio of FRR as a key metric, effectively characterizing the adequacy of frequency regulation capability and revealing the probability density distribution of FRR supply and demand within each cluster. The proposed typical-day classification method can enhance the optimization and market-based procurement of FRR in power systems.
The proposed probability density peak clustering algorithm was applied to analyze the annual FRR supply-demand dataset. Results indicate that the algorithm divided the 365 daily samples into eight representative typical-day scenarios. The samples within each cluster exhibited strong temporal continuity, which benefits the formulation of stable dispatch strategies and FRR allocation schemes. According to the matching degree between FRR supply and demand, the clusters were further categorized into three operational modes: adequate, inadequate, and critical-balance modes. To validate the effectiveness and superiority of the proposed method, comparative analyses were conducted with the density peak clustering (DPC) and K-means algorithms using three evaluation metrics: the Calinski-Harabasz (CH) index, Davies-Bouldin (DB) index, and mean deviation angle of FRR supply-demand ratio. The comparison results demonstrate that the proposed method consistently outperforms DPC and K-means algorithms in all evaluation indicators, confirming its robustness and higher clustering quality.
The following conclusions can be drawn from the case studies: Compared with traditional clustering methods that rely solely on Euclidean distance, incorporating the FRR supply-demand ratio provides a more comprehensive characterization of the system's frequency regulation adequacy. Clustering the annual FRR supply-demand dataset enables the identification of representative typical days and the probability density distribution features of each cluster, providing technical support for efficient market-based procurement and optimized allocation of FRR. Evaluation based on multiple clustering validity indices shows that the proposed probability density peak clustering algorithm achieves superior performance compared with DPC and K-means, further verifying its effectiveness and advancement.

Key words： Typical operating modes frequency regulation resource assessment dynamic frequency response probabilistic density clustering

Received: 02 September 2025

PACS:

TM732

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Zhang Zhong
	Qu Xiangzhao
	Wang Qiumeng

Cite this article:

Zhang Zhong,Qu Xiangzhao,Wang Qiumeng. A Probabilistic Clustering Method for Annual Typical-Day of Power Systems Considering Supply-Demand Ratio of Frequency Regulation[J]. Transactions of China Electrotechnical Society, 0, (): 20251518-.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251518 OR https://dgjsxb.ces-transaction.com/EN/Y0/V/I/20251518

[1] 王译旋, 杨用春, 高长征. 计及典型日选取与源荷灵活性调节的优化调度研究[J]. 电力系统保护与控制, 2024, 52(10): 1-10.
Wang Yixuan, Yang Yongchun, Gao Changzheng.Optimal scheduling considering typical day selection and source load flexibility adjustment[J]. Power System Protection and Control, 2024, 52(10): 1-10 (in Chinese).
[2] 高亚静, 孙永健, 杨文海, 等. 基于非参数核密度估计和改进谱多流形聚类的负荷曲线分类研究[J]. 电网技术, 2018, 42(05): 1605-1612.
Gao Yajing, Sun Yongjian, Yang Wenhai, et al.Study on load curve's classification based on nonparametric kernel density estimation and improved spectral multi-manifold clustering[J]. Power System Technology, 2018, 42(05): 1605-1612 (in Chinese).
[3] 丁明, 解蛟龙, 刘新宇, 等. 面向风电接纳能力评价的风资源/负荷典型场景集生成方法与应用[J]. 中国电机工程学报, 2016, 36(15): 4064-4072.
Ding Ming, Xie Jiaolong, Liu Xinyu, et al.The generation method and application of wind resources/load typical scenario set for evaluation of wind power grid integration[J]. Proceedings of the CSEE, 2016, 36(15): 4064-4072 (in Chinese).
[4] 杨珺, 李凤婷, 张高航. 考虑灵活性需求的新能源高渗透系统规划方法[J]. 电网技术, 2022, 46(06): 2171-2182.
Yang Jun, Li Fengting, Zhang Gaohang.Power system planning method with high new energy penetration considering flexibility requirements[J]. Power System Technology, 2022, 46(06): 2171-2182 (in Chinese).
[5] 辛阔, 马骞, 许琴, 等. 基于月份划分与指定日类型的风电出力序列场景生成方法[J]. 电力系统自动化, 2023, 47(15): 151-161.
Xin Kuo, Ma Qian, Xu Qin, et al.Wind power output sequence scenario generation method based on monthly division and specified day type[J]. Automation of Electric Power Systems, 2023, 47(15): 151-161 (in Chinese).
[6] 游广增, 汤翔鹰, 胡炎, 等. 基于典型运行场景聚类的电力系统灵活性评估方法[J]. 上海交通大学学报, 2021, 55(07): 802-813.
You Guangzeng, Tang Xiangying, Hu Yan, et al.Flexibility evaluation method for power system based on clustering of typical operating scenarios[J]. Journal of Shanghai Jiaotong University, 2021, 55(07): 802-813 (in Chinese).
[7] Geng L, Zhao Y, Chen G.Simplified sequential simulation of bulk power system reliability via chronological probability model of load supplying capability[J]. IEEE Transactions on Power Systems, 2018, 33(3): 2349-2358.
[8] 牛奎烨, 刘金波, 汤奕, 等. 计及极端气象事件的年度系统运行场景生成方法[J]. 电网技术, 2024, 48(10). 3992-4006.
Niu Kuiye, Liu Jinbo, Tang Yi, et al.A method for generating annual system operating scenarios considering extreme meteorological events[J]. Power System Technology, 2024, 48(10): 3992-4006 (in Chinese).
[9] 郭力, 杨书强, 刘一欣, 等. 风光储微电网容量规划中的典型日选取方法[J]. 中国电机工程学报, 2020, 40(08): 2468-2479.
Guo Li, Yang Shuqiang, Liu Yixin, et al.Typical day selection method for capacity planning of microgrid with wind turbine-photovoltaic and energy storage[J]. Proceedings of the CSEE, 2020, 40(08): 2468-2479 (in Chinese).
[10] Azimi R, Ghofrani M, Ghayekhloo M.A hybrid wind power forecasting model based on data mining and wavelets analysis[J]. Energy Conversion and Management, 2016, 127: 208-225.
[11] 李春燕, 蔡文悦, 赵溶生, 等. 基于优化SAX和带权负荷特性指标的AP聚类用户用电行为分析[J]. 电工技术学报, 2019, 34(S1): 368-377.
Li Chunyan, Cai Wenyue, Zhao Rongsheng, et al.Customer behavior analysis based on affinity propagation algorithm with optimized SAX and weighted load characteristic indices[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 368-377 (in Chinese).
[12] 徐青山, 吕亚娟, 孙虹, 等. 大用户多维度可中断特性精细化分析[J]. 电工技术学报, 2020, 35(S1): 284-293.
Xu Qingshan, Lv Yajuan, Sun Hong, et al.Refined analysis of large-consumers' interruptible features from multi-dimension[J]. Transactions of China Electrotechnical Society, 2020, 35(S1): 284-293 (in Chinese).
[13] 陈鹏, 王玮, 杨建青, 等. 基于多尺度分解的风火储协同调频控制策略[J]. 太阳能学报, 2024, 45(03): 428-435.
Chen Peng, Wang Wei, Yang Jianqing, et al.Cooperative frequency regulation control strategy of wind-thermal-storage system based on multi-scale decomposition[J]. Acta Energiae Solaris Sinica, 2024, 45(03): 428-435 (in Chinese).
[14] 卓映君, 管霖, 陈亦平, 等. 基于精细化备用需求评估和跨省区备用均衡的大电网优化调度模型[J]. 电网技术, 2021, 45(04): 1438-1450.
Zhuo Yingjun, Guan Lin, Chen Yiping, et al.Optimal scheduling model of large power grid based on refined reserve demand estimation and cross-regional reserve balance[J]. Power System Technology, 2021, 45(04): 1438-1450 (in Chinese).
[15] Diao R, Hu Z C, Song Y H, et al.Cooperation Mode and Operation Strategy for the Union of Thermal Generating Unit and Battery Storage to Improve AGC Performance[J]. IEEE Transactions on Power Systems, 2023, 38(6): 5290-5301.
[16] 王杨洋, 茆美琴, 杨铖, 等. 面向多场景辅助服务的大规模电动汽车聚合可调度容量建模[J]. 电力系统自动化, 2024, 48(07): 103-115.
Wang Yangyang, Mao Meiqin, Yang Cheng, et al.Aggregated and schedulable capacity modeling of large-scale electric vehicles for multi-scenario auxiliary services[J]. Automation of Electric Power Systems, 2024, 48(07): 103-115(in Chinese).
[17] Shen Y K, Wu W C, Wang B, et al.Optimal Allocation of Virtual Inertia and Droop Control for Renewable Energy in Stochastic Look-Ahead Power Dispatch[J]. IEEE Transactions on Sustainable Energy, 2023, 14(3): 1881-1894.
[18] 关舒丰, 王旭, 蒋传文, 等. 基于可控负荷响应性能差异的虚拟电厂分类聚合方法及辅助服务市场投标策略研究[J]. 电网技术, 2022, 46(03): 933-944.
Guan Shufeng, Wang Xu, Jiang Chuanwen, et al.Classification and aggregation of controllable loads based on different responses and optimal bidding strategy of VPP in ancillary market[J]. Power System Technology, 2022, 46(03): 933-944 (in Chinese).
[19] 徐辰宇, 赵冬梅, 路秋阳, 等. 考虑逆变器资源参与的惯量及一次调频市场定价机制研究[J]. 电工技术学报, 2025, 40(21): 7029-7045.
Xu Chenyu, Zhao Dongmei, Lu Qiuyang, et al.Research on the pricing mechanism for inertia and primary frequency regulation in markets considering the participation of inverter-based resources[J]. Transactions of China Electrotechnical Society, 2025, 40(21): 7029-7045 (in Chinese).
[20] 王涛, 王廷涛, 刘芮, 等. 计及动态频率响应约束的高比例风电电力系统机组组合模型[J]. 高电压技术, 2021, 47(10): 3463-3479.
Wang Tao, Wang Tingtao, Liu Rui, et al.Unit commitment model of high proportion wind power system considering dynamic frequency response constraints[J]. High Voltage Engineering, 2021, 47(10): 3463-3479 (in Chinese).
[21] 刘翔宇, 李慧斌, 顾雪平, 等. 考虑惯量充裕度与频率变化率的互联电网在线频率安全分析[J]. 电网技术, 2023, 47(05): 1780-1788.
Liu Xiangyu, Li Huibin, Gu Xueping, et al.On-line frequency security analysis of interconnected power grid considering inertia adequacy and RoCoF[J]. Power System Technology, 2023, 47(05): 1780-1788 (in Chinese).
[22] 林恒先, 侯凯元, 陈磊, 等. 高比例风电电力系统考虑频率安全约束的机组组合[J]. 电网技术, 2021, 45(01): 1-13.
Lin Hengxian, Hou Kaiyuan, Chen Lei, et al.Unit commitment of power system with high proportion of wind power considering frequency safety constraints[J]. Power System Technology, 2021, 45(01): 1-13 (in Chinese).
[23] 安军, 李可心, 周毅博, 等. 面向抑制频率波动的新型电力系统调频能力需求评估[J]. 电工技术学报, 2025: 1-13
An Jun, Li Kexin, Zhou Yibo, et al.Frequency fluctuation suppression-oriented evaluation of frequency regulation capability requirements for new-type power systems[J]. Transactions of China Electrotechnical Society, 2025: 1-13 (in Chinese).
[24] GB/T 30370-2022, 火力发电机组一次调频试验及性能验收导则[S].
GB/T 30370-2022, Guidelines for primary frequency control testing and performance acceptance of thermal power generating units[S].
[25] 王霞, 应黎明, 卢少平. 考虑动态频率约束的一次调频和二次调频联合优化模型[J]. 电网技术, 2020, 44(08): 2858-2867.
Wang Xia, Ying Liming, Lu Shaoping.Joint optimization model for primary and secondary frequency regulation considering dynamic frequency constraint[J]. Power System Technology, 2020, 44(08): 2858-2867 (in Chinese).
[26] 谭晶, 何川, 陈保瑞, 等. 考虑水光蓄互补和直流外送的电力系统分布鲁棒优化调度方法[J]. 中国电机工程学报, 2024,44(15):5947-5960.
Tan Jing, He Chuan, Chen Baorui, et al.Distributionally robust optimal scheduling method of power system considering hydropower-photovoltaic-pumped storage complementarity and DC transmission[J]. Proceedings of the CSEE, 2024, 44(15): 5947-5960 (in Chinese).
[27] 赫德军, 武欣嵘, 俞璐. 密度聚类方法研究[J]. 通信技术, 2022, 55(02): 135-142.
He Dejun, Wu Xinrong, Yu Lu.Review of Clustering Algorithm Based on Density[J]. Communications Technology, 2022, 55(02): 135-142 (in Chinese).
[28] 张桐赫, 杜欣慧, 王帅. 一种基于核密度聚类的电力负荷模式精细化识别算法研究[J]. 数学的实践与认识, 2019, 49(08): 155-164.
Zhang Tonghe, Du Xinhui, Wang Shuai.Research on refinement recognition algorithm of power load model based on kernel density clustering[J]. Mathematics in Practice and Theory, 2019, 49(08): 155-164 (in Chinese).
[29] 张斌, 庄池杰, 胡军, 等. 结合降维技术的电力负荷曲线集成聚类算法[J]. 中国电机工程学报, 2015, 35(15): 3741-3749.
Zhang Bin, Zhuang Chijie, Hu Jun, et al.Ensemble clustering algorithm combined with dimension reduction techniques for power load profiles[J]. Proceedings of the CSEE, 2015, 35(15): 3741-3749 (in Chinese).
[30] Kwac J, Flora J, Rajagopal R.Household energy consumption segmentation using hourly data[J]. IEEE Transactions on Smart Grid, 2014, 5(1): 420-430.
[31] 赵冬梅, 宋晨铭, 冯向阳, 等. 100%新能源场景下考虑频率稳定约束的源网荷储一体化系统储能优化配置[J]. 电工技术学报, 2025, 40(07): 2146-2161.
Zhao Dongmei, Song Chenming, Feng Xiangyang, et al.The optimal configuration of energy storage in the source-grid-load-storage integrated system considering frequency stability constraints in 100% new energy scenarios[J]. Transactions of China Electrotechnical Society, 2025, 40(07): 2146-2161 (in Chinese).
[32] 江一航, 赵书强, 王慧, 等. 计及风电、调相机支撑特性的频率安全约束分布鲁棒机组组合调度方法[J]. 电工技术学报, 2025, 40(01): 80-95.
Jiang Yihang, Zhao Shuqiang, Wang Hui, et al.Distributionally robust frequency constrained unit commitment with frequency support of wind power and synchronous condenser[J]. Transactions of China Electrotechnical Society, 2025, 40(01): 80-95 (in Chinese).