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Demand response is designed to motivate electricity customers to modify theirloads at critical time periods. The accurate estimation of impact of demandresponse signals to customers' consumption is central to any successfulprogram. In practice, learning these response is nontrivial because operatorscan only send a limited number of signals. In addition, customer behavior alsodepends on a large number of exogenous covariates. These two features lead to ahigh dimensional inference problem with limited number of observations. In thispaper, we formulate this problem by using a multivariate linear model and adoptan experimental design approach to estimate the impact of demand responsesignals. We show that randomized assignment, which is widely used to estimatethe average treatment effect, is not efficient in reducing the variance of theestimator when a large number of covariates is present. In contrast, we presenta tractable algorithm that strategically assigns demand response signals tocustomers. This algorithm achieves the optimal reduction in estimationvariance, independent of the number of covariates. The results are validatedfrom simulations on synthetic data.

An Optimal Treatment Assignment Strategy to Evaluate Demand Response Effect