Linear Estimation of Treatment Effects in Demand Response: An Experimental Design Approach

Demand response aims to stimulate electricity consumers to modify their loads at critical time periods. In this paper, we consider signals in demand response programs as a binary treatment to the customers and estimate the average treatment effect, which is the average change in consumption under the demand response signals. More specifically, we propose to estimate this effect by linear regression models and derive several estimators based on the different models. From both synthetic and real data, we show that including more information about the customers does not always improve estimation accuracy: the interaction between the side information and the demand response signal must be carefully modeled. In addition, we compare the traditional linear regression model with the modified covariate method which models the interaction between treatment effect and covariates. We analyze the variances of these estimators and discuss different cases where each respective estimator works the best. The purpose of these comparisons is not to claim the superiority of the different methods, rather we aim to provide practical guidance on the most suitable estimator to use under different settings. Our results are validated using data collected by Pecan Street and EnergyPlus. NOMENCLATURE N Total number of samples. i Index of samples, i = 1, 2, ..., N . Yi(Y) Energy consumption (vector form). Ti Binary DR signal (treatment signal) for sample i. xi(x) Covariates of sample i (matrix form). d Dimension of the covariate. g(xi) or gi Treatment effect of DR signal on sample i. ḡ = 1 N ∑ i gi Average treatment effect (ATE): the average change in consumption because of demand response signals. f(xi) or fi Baseline consumption (without DR) of sample i. This work was supported by in part by NSF grant CNS-1544160 and the University of Washington Clean Energy Institute. The authors are with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195, USA (e-mail: {pli69,zhangbao}@uw.edu).