A Sparse Linear Model and Significance Test for Individual Consumption Prediction

Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well. Existing prediction methods usually have high relative errors that can be larger than 30% and have difficulties accounting for heterogeneity between individual users. In this paper, we propose a method to improve prediction accuracy of individual users by adaptively exploring sparsity in historical data and leveraging predictive relationship between different users. Sparsity is captured by popular least absolute shrinkage and selection estimator, while user selection is formulated as an optimal hypothesis testing problem and solved via a covariance test. Using real world data from PG&E, we provide extensive simulation validation of the proposed method against well-known techniques such as support vector machine, principle component analysis combined with linear regression, and random forest. The results demonstrate that our proposed methods are operationally efficient because of linear nature, and achieve optimal prediction performance. Pan Li and Baosen Zhang are with the Department of Electrical Engineering, University of Washington, Seattle, WA, 98195, (email: {pli69, zhangbao}@uw.edu). Yang Weng and Ram Rajagopal are with the Civil and Environmental Department, Stanford University, Stanford, CA, 94035, (email: {yangweng, ramr}@stanford.edu). 2 Estimated consumption at time t. Estimated variance of the noise. Electric load forecasting is an important problem in the power engineering industry and have received extensive attention from both industry and academia over the last century. Many different forecasting techniques have been developed during this time. The authors in [1] present a comprehensive literature review on different methods related to load forecasting, from regression models to expert systems. Time series methods are further discussed in [2]. A thorough research on load and price forecasting is presented in [3]. A common theme among many of the established methods is that they are used to forecast relative large loads, from substations serving megawatts to transmission networks serving more than gigawatts of power [4]. Recent advances in technology such as smart meters, bidirectional communication capabilities and distributed energy resources have made individual households active participants in the power system. Many applications and programs based on these new technologies require estimating the future load of individual homes.