基于曲线相似与低秩矩阵的缺失电量数据补全方法

低压台区用电数据是电网运营中众多高级应用的基础。然而，在泛在电力物联网数据采集、传输、储存管理的过程中，会不可避免地出现数据缺失的情况，在一定程度上影响上层高级应用。针对这一问题，文章研究并提出曲线相似与低秩矩阵填充理论相结合的用电数据缺失补全方法。首先通过分析电量数据矩阵奇异值分布，揭示其低秩特性，完成数据恢复可行性判定。在此基础上，考虑用电曲线之间的差异性，提出预填充-曲线相似分类-二次填充的数据恢复方法，在对电量矩阵进行预填充之后，对于每一条待恢复的用电量曲线，基于考虑数据缺失的曲线相似性测度，找到与其最为相似的k条曲线构成数据矩阵，之后再次应用低秩矩阵填充理论恢复缺失数据，以提高恢复精度。以华北某电网居民用户电量数据进行试验，并将文章提出的方法与经典插值补齐法相比较，验证了所提出的电量曲线聚类与矩阵填充相结合的方法可以更有效补齐缺失电量数据。

Missing Load Data Completion Based on Curve Similarity and Low-Rank Matrix

Many advanced applications in the power grid are based on load data. However,in the process of data collection,transmission and storage,there will inevitably meet with data missing,which may bring bad effect to data analysis. In allusion to the above problem,this paper proposes a missing data completion strategy combining load curve similarity and singular value threshold algorithm. Firstly,through analyzing the distribution of singular values in electric data matrix,a low rank characteristic is revealed. On the basis of that,considering the differences between power consumption curves,a data recovery method of pre-filling,curve similarity classification and secondary filling is proposed. After the prefilling,for each power curve to be recovered,the k curves which are most similar to it are found on the basis of the improved similarity index to form the data matrix,and then the low-rank matrix completion is applied again. Through the above steps,the missing recovery is supposed to be improved. The load data from the power grid in north China is used for test,and the method proposed is compared with the classical interpolation method to verify the effectiveness. Results prove that the combination of load curve similarity and singular value thresholding( SVT) can effectively complete the missing data and provide strong support for load data repair.