基于集合卡尔曼滤波与相空间重构的负荷预测方法研究

Research of load forecasting method based on ensemble Kalman filter and phase⁃space reconstruction

提出一种基于集合卡尔曼滤波和相空间重构的组合模型来优化预测结果。对于负荷数据时间序列,首先使用延迟坐标嵌入方法对其进行相空间重构。基于局部平均法对下一时刻的负荷状态进行预测,其中最临近向量的数目采用循环迭代的方式选取,以获得对不同负荷序列的自适应性。根据无迹变换理论,对负荷预测值选取合适数量的Sigma点组成集合并使用集合卡尔曼滤波器进行数据同化,从而能够在容忍采样噪声的同时给出负荷的最优估计。以非侵入式量测方式获取河北保定市50个家庭用户的负荷数据作为训练集进行试验,给出了电热水器和空调负荷以及家庭总负荷的预测结果和误差分析。结果显示,与单纯基于相空间重构的预测结果进行比较,该组合模型具有更好的预测性能,且对分项电器负荷和家庭总负荷均具有较好的适应性。

A load forecasting technique based on a combined model formed by ensemble Kalman filter(EnKF)and phase⁃space reconstruction(PSR)is proposed to optimize forecasting results.For the load data time⁃series,phase⁃space reconstruction is firstly implemented using delayed coordinate embedding.Future load states can be predicted by local averaging.To achieve adaptive fea⁃ture to different load time⁃series,cyclic iterative calculation is used to select the number of nearest vectors.According to unscent⁃ed transformation theory,ensemble is formed by appropriate num⁃ber of Sigma points of the predicted load value and data assimila⁃tion can be realized using ensemble Kalman filter.Therefore,opti⁃mum estimation can be obtained while measurement noise exists.Using non⁃instrusive measurement,forecasting results and error analysis for loads of electrical water heater and air⁃conditioner as well as total household are done by adopting 50 end users data from Baoding of Hebei province as training data set.The results show that,compared to those derived from pure phase⁃space recon⁃struction forecasting,the proposed method features have better forecasting performance and good adaption both for individual ap⁃pliance load and total household load.