奇异值分解方法在日负荷曲线降维聚类分析中的应用

Application of Singular Value Decomposition Algorithm to Dimension-reduced Clustering Analysis of Daily Load Profiles

负荷曲线聚类对负荷预测、电网规划和需求侧响应等应用有重要意义,但是海量的历史负荷曲线为数据存储和计算效率带来了挑战。为此,提出一种基于奇异值分解的日负荷曲线降维聚类方法。首先利用奇异值分解将日负荷曲线数据旋转变换至新的坐标系中,求解出的奇异值反映了相应坐标轴的重要程度。然后,将负荷曲线在各坐标轴上的坐标作为降维指标,用以反映负荷曲线的主要特征,再依据奇异值下降趋势确定指标的数目。最后,以各坐标轴对应的奇异值作为指标权重,采用基于加权欧式距离的K-means算法对日负荷曲线进行聚类。算例结果表明所提方法运行时间短、鲁棒性好,可以提高负荷曲线聚类的准确性。

Load profiles clustering is of great significance for the load forecasting, power grid planning and demand response, but massive historical load profiles introduce great challenges for the data storage and computation efficiency. To solve this problem, a dimension-reduced clustering method for daily load profiles is proposed based on singular value decomposition, Firstly, daily load profiles are transformed into a new coordinate system by singular value decomposition, and the singular values reflect the importance of different axes. Then, the dimension-reduced index is defined as the projected values of load profiles on axes to represent the main features of load profiles. The number of dimension-reduced indices is determined by the decreasing trend of singular values. Finally, the singular values are selected as the weight of corresponding axes and the weighted K-means algorithm is adopted to classify daily load profiles. Cases studies verify that the proposed method has the advantages of short running time, good robustness and better classification results.