李军　李世昌

摘 要：针对中期或短期电力负荷预测，提出一种基于稀疏表示的特征提取建模方法。为构建预测模型，将历史电力负荷等数据构成具有时延的输入—输出数据对，将时延输入数据向量作为初始字典，采用K均值—奇异值分解（K-SVD）算法将其进行稀疏分解与变换至稀疏域以得到学习后的字典。进一步，由正交匹配追踪（OMP）算法获取相应的稀疏编码向量，再将该向量作为核极限学习机（KELM）的输入来构建全局回归模型。为了验证该方法的有效性，将所提出的方法用于不同地区的中期或短期电力负荷预测中，在同等条件下还与单一KELM、支持向量机（SVM）、极限学习机（ELM）方法以及非字典学习的其他稀疏表示建模方法进行了比较。实验结果表明，不同的稀疏表示建模方法均能取得很好的预测效果，其中所提方法具有更好的預测效果，显示出其有效性。

关键词：负荷预测;稀疏表示;特征提取; K均值—奇异值分解; 正交匹配追踪;核极限学习机

DOI：10.15938/j.emc.2020.09.017

中图分类号：TM 715

文献标志码：A

文章编号：1007-449X（2020）09-0156-09

Application of sparse representation method based on K-SVD-OMP in electricity load forecasting

LI Jun， LI Shi-chang

（School of Automation and Electrical Engineering， Lanzhou Jiaotong University， Lanzhou 730070， China）

Abstract：

For mid-term or short-term electricity load forecasting， a feature extraction modeling method based on sparse representation is proposed. The historical power load data were composed to the time-lagged input-output data pairs to build the forecasting model， using the time-lagged input data vectors as the initial dictionary， which were sparsely decomposed and transformed into the sparse domain by K-means singular value decomposition （K-SVD） algorithm to obtain the dictionary after learning. Further， the corresponding sparse coding vectors were obtained by orthogonal matching pursuit （OMP） algorithm， and then the sparse vectors are then used as the input vectors of the extreme learning machine with kernel （KELM） to build a global regression model. In order to verify the effectiveness of the employed method， it was applied to mid-term and short-term electric load forecasting instances in different areas. Compared with single KELM， support vector machine（SVM）， extreme learning machine（ELM） method as well as other forecasting methods using sparse representation with non-dictionary learning under the same conditions， experimental results show that the forecasting methods based on sparse representation algorithm achieve good forecasting results， and the methods proposed significantly improve the accuracy of load forecasting and show their effectiveness.

Keywords：load forecasting; sparse representation; feature extraction; K-means singular value decomposition; orthogonal matching pursuit; extreme learning machine with kernel

0 引 言

中、短期电力负荷预测作为电力系统规划和运营的重要组成部分，对电力部门制定发电计划、设备检修计划、电价等提供了重要的依据。因此，构建稳定、准确的中、短期电力负荷预测模型对智能电网的运行调度与发展规划有着重要意义[1-2]。

在电力负荷预测中，常见的线性或多重回归法、自回归积分滑动平均[3] （autoregressive integrated moving average，ARIMA）方法等，在精度方面往往不能满足实际需求。更先进的一类计算……