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

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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

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TM732

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	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, 2026, 41(18): 6323-6335.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251518 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I18/6323

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