Short-Term Forecasting of Price-Responsive Loads Using Inverse Optimization

Abstract

Abstract-We consider the problem of forecasting the aggregate demand of a pool of price-responsive consumers of electricity. The price-response of the aggregation is modeled by an optimization problem that is characterized by a set of marginal utility curves and minimum and maximum power consumption limits. The task of estimating these parameters is addressed using a generalized inverse optimization scheme that, in turn, requires solving a nonconvex mathematical program. We introduce a solution method that overcomes the nonconvexities by solving instead two linear problems with a penalty term, which is statistically adjusted by using a cross-validation algorithm. 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 power load of a group of heating, ventilation, and air conditioning systems in buildings is simulated, and the results show that the aggregate demand of the group can be successfully captured by the proposed model, making it suitable for short-term forecasting purposes.Index Terms-Inverse optimization, load forecasting, smart grid, demand response. NOTATIONThe notation used throughout the paper is stated below for quick reference. Other symbols are defined as required. A. Indexes tTime period, ranging from 1 to T . bMarginal utility block, ranging from 1 to B. r Regressor, ranging from 1 to R. B. Decision variablesx b,t Load from energy block b and time t. P t Lower bound for electricity consumption at time t. P tUpper bound for electricity consumption at time t. u b,t Marginal utility of load block b at time t. µ Intercept for the lower load-consumption bound.

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