基于均生函数-最优子集回归模型的短期电力负荷预测方法

Method of short-term load forecasting based on mean generating function-optimal subset regression

为进一步提高电力负荷预测的精度和运算速度,针对短期负荷预测样本数据既有趋势性又有波动性的特点,采用均生函数-最优子集回归(mean generating function-optimal subset regression,MGF-OSR)建立预测模型。相对于均生函数主成分回归(mean generating function-principal component analysis,MGF-PCA)模型,该方法引入了一阶、二阶差分序列对高频部分进行拟合,又建立累加生成序列拟合其趋势,通过均值生成函数(MGF)将上述所有序列构建出预测因子矩阵,采用双评分准则进行粗选,剔除评分较低的因子,其他预报因子经组合寻优后得到最优子集并以此建立预测模型。实例分析表明,该模型预测的平均相对误差可低至2.42%,明显优于主成分回归模型的预测精度。

Power load forecasting can be divided into long-term prediction, medium-term prediction, short-term prediction and ultra short-term prediction, according to different time horizons of sample sequences. If sample sequences are different, their statistical characteristics are different. Therefore, we should adopt different forecast methods and models in this prediction process. This paper mainly discusses short-term load forecasting. Power system short-term load sample sequences not only have the characteristics of tendency and periodicity, but it also fluctuates greatly, making it difficult to forecast. In the current forecast models, there are some drawbacks, and the accuracy of fitting is not good. In order to improve the accuracy of short-term prediction, this paper established the Optimal Subset Regression （OSR） model for prediction based on the Mean Generating Function （MGF） sequence. MGF adopts m （m=INT（n/2）） different cycles to extract sample data from the original sample sequence, and x（n） to calculate their averages to get the new sequence. Then they are repeatedly extended to the length of the original sample sequence and we can get n×m matrix Fnxm called Mean Generating Function matrix. Each column vector fi（0）（t） of Fn×m can be used as a regression predictor of the original sample sequence. Furthermore, in order to fit the high frequency component of the original sample sequence, we make twice-differencing operations of original sample sequences so that we can achieve the effect of high-pass filtering. The first-order difference sequence of x（n） is x（1）（n-1） and the second-order difference sequence is x（2）（n-2）. We can get f（1）（t） andf（2）（t） by calculating the MGF extended sequence of x（1）（n-1） and x（2）（n-2） respectively, then generating accumulation extended sequence fi（3）（t） by using fi（1）（t）, SO we can get about 4m MGF extended sequence fi（0）（t）, fi（1）（t）,fi（2）（t）和fi（3）（t） （l=1,2,…, m）. In order to reduce the calculation work, we use all the predictors for roughing, using the sample sequence for simple regression. According to the couple score criterion （CSC）, we can get the CSC value of simple regression. Then we make X^2 test and keep qualified predictors, which, with bigger CSC values, are about 1/6 of the original predictors. We take these qualified predictors for free combination, generating 2p- 1 subsets, and using these subsets for regression calculation. Then we calculate again the CSC value of the regression result, and select the subset with the maximum CSC value--the optimal subset using as prediction regression equation. According to the requirements of the prediction length, we extend the length of predictive factors of the optimal subset, substituting the extension value into the regression equation, so we can get the forecast results. This paper takes a certain area in northern China as an example and uses hourly load values as the sample sequence, using the above algorithm to forecast four-hour-ahead load values. In this case, we got a total of 45 predictors, then 8 predictors by roughing, and generated 255 subsets. By regression calculation, we determined the optimal subset regression equation. By using the equation, we calculated the fitting value average error at 2.41%. According to the above method extending predictors, we identified the prediction value by regression calculation. The prediction average error is only 4.24%. Compared with principal component analysis of mean generating function model and grey model, the maximum error of prediction model was reduced by 10% or so.