基于线性Bregman方法的缺失负荷数据低秩矩阵补全

摘要

针对电力负荷预测原始资料出现的数据缺失现象对提高预测精度带来的不利影响,提出基于低秩矩阵补全理论的缺失负荷数据恢复方法.通过分析电力负荷数据的低秩性特点,基于线性近似的原则构建低秩矩阵,推导基于线性Bregman方法的低秩矩阵补全算法.使用该算法对我国南方某电网负荷数据缺失值进行恢复,计算并分析恢复算法的误差以及其分布情况,并与传统插值和外推方法的误差分布进行对比.结果表明,相比传统方法,基于低秩矩阵的数据补全算法具有更高的精度和更强的鲁棒性.%In allusion to the problem of data missing of source materials in power load prediction which may bring bad effect on prediction accuracy,this paper presents a recovery method for missing load data based on low rank matrix Completion theory. By analyzing low rank characteristic of power load,it constructs the low rank matrix on the basis of proximate linear principle and deduces the low rank matrix Completion algorithm based on the linear Bregman. It uses this algorithm to re-cover missing values of load data of one south power grid,calculates and analyzes errors of this recovery algorithm and error distribution. It also compares error distribution of the proposed algorithm with that of the traditional interpolation and ex-trapolation method. The result indicates compared with the traditional method,this data Completion algorithm based on low rank matrix has higher precision and strong robustness.