Predicting the electricity demand response via data-driven inverse optimization

Abstract

A method to predict the aggregate demand of a cluster of price-responsive consumers of electricity is discussed in this presentation. The price-response of the aggregation is modeled by an optimization problem whose defining parameters represent a series of marginal utility curves, and minimum and maximum consumption limits. These parameters are, in turn, estimated from observational data using an approach inspired from duality theory. The resulting estimation problem is nonconvex, which makes it very hard to solve. In order to obtain good parameter estimates in a reasonable amount of time, we divide the estimation problem into a feasibility problem and an optimality problem. Furthermore, the feasibility problem includes a penalty term that is statistically adjusted by cross validation. The proposed methodology is data-driven and leverages information from regressors, such as time and weather variables, to account for changes in the parameter estimates. The estimated price-response model is used to forecast the power load of a group of heating, ventilation and air conditioning systems, with positive results.