A Method for Grouping and Equivalent Modeling of Wind Farms Based on Single-Machine Scanning and Curve Shape Clustering
Guo Hao1, Liu Chongru1, Lü Yipeng1, Su Chenbo2, Zheng Le1
1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Source North China Electric Power University Beijing 102206 China; 2. Department of Electrical Engineering Tsinghua University Beijing 100084 China
Abstract：The simplified model of grouping and equivalent of wind turbines, inspired by the coherent equivalent method in power systems, has been widely applied. For wind turbines, the transient responses after faults under different operating conditions exhibit significant differences. To achieve accurate grouping, it should be based on the similarity of transient responses. However, most existing wind turbine grouping methods rely on steady-state conditions represented by wind speed, state variables, etc., which struggle to meet simulation demands in terms of grouping and equivalent accuracy. While some methods directly cluster transient response curves, they require access to unit-level transient response data, limiting their practicality. To address the challenge of balancing effectiveness and practicality in wind turbine grouping and equivalent, this paper proposes a method based on single-unit scanning and curve shape clustering. Essentially focusing on transient responses, this method only requires steady-state data and fault scenarios for application, ensuring both effectiveness and practicality. Firstly, by setting different wind speeds, voltages, and fault conditions for individual wind turbines, key influencing factors and dynamic responses are selected through comparative analysis. This single-unit scanning simulation method enables the acquisition of clustering data while establishing a link between steady-state points and dynamic characteristics. Secondly, considering the actual process of aggregation and equivalent, the correlation coefficient is chosen as the similarity evaluation index between transient responses. Thirdly, by comparing various classical clustering methods, the K-Means clustering algorithm, which is most suitable for this problem, is selected and further optimized using a crested porcupine optimizer optimization algorithm to improve clustering effectiveness. Finally, a time series clustering algorithm capable of effectively capturing shape differences is implemented to precisely categorize transient responses, combining the link between steady-state points and dynamic responses established in the first step to achieve practical and high-precision wind turbine grouping. Applying the proposed grouping method to a typical direct-drive wind turbine model, the grouping results under full fault conditions are in complete agreement with the distinct grouping boundaries derived from theoretical analysis. In contrast, traditional methods based on steady-state quantities yield significantly different grouping boundaries, demonstrating that the proposed grouping index enables precise grouping based on transient responses. Regarding clustering algorithms, the K-Means algorithm outperforms six other algorithms across three evaluation metrics. By repeatedly clustering and calculating the evaluation metrics, the proposed improved method shows slight improvements in the mean values of the three metrics compared to the original method, with the variance reduced to within 1% of the original method, indicating the effectiveness of the modified K-Means algorithm. Finally, PSCAD simulation cases for three types of faults verify the equivalence. Compared to traditional wind speed clustering methods, the proposed method reduces the average relative error by approximately 60% to 90% and the maximum absolute error by approximately 50% to 90%, indicating its superior performance in grouping and equivalent effectiveness. In conclusion, this paper finds that: (1) The primary influencing factors of the low-voltage ride-through dynamic characteristics of direct-drive wind turbines are wind speed and fault conditions, with active power being the primary manifestation of dynamic characteristic differences, while reactive power differences are minimal. (2) Measuring time series similarity using the linear correlation coefficient effectively captures the linear relationships between curves, making it suitable for wind turbine grouping and equivalent problems. The crested porcupine optimizer algorithm improved K-Means algorithm achieves optimal clustering results. (3) By acquiring transient time series through single-unit scanning and using them as clustering data, clustering dynamic characteristics to obtain steady-state point grouping boundaries, and then performing wind farm grouping and equivalent, this method significantly improves equivalent accuracy while ensuring practicality.
郭昊, 刘崇茹, 吕懿澎, 苏晨博, 郑乐. 基于单机扫描与曲线形状聚类的风电场分群等值方法[J]. 电工技术学报, 2025, 40(19): 6072-6084.
Guo Hao, Liu Chongru, Lü Yipeng, Su Chenbo, Zheng Le. A Method for Grouping and Equivalent Modeling of Wind Farms Based on Single-Machine Scanning and Curve Shape Clustering. Transactions of China Electrotechnical Society, 2025, 40(19): 6072-6084.
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