Decision-focused learning under decision dependent uncertainty for power systems with price-responsive demand

Contemporary power systems are experiencing a growing integration of flexible resources on the consumer side. Different from flexible demand that submits specific bids to energy markets, price-responsive demand (PRD) adjusts its power consumption without notice, simply based on the resulting electricity prices as well as internal priorities and limitations. In this paper, we demonstrate how a high penetration of PRD (the behavior of which is invisible to the operator during the day-ahead unit commitment stage) results in systematic inefficiency costs and formulate the so-termed decision-focused learning problem of learning to provide a demand forecast which, once fed as an input to the operator's economic dispatch optimization problem, results in an efficient dispatch. Interestingly, the prescribed demand forecast affects the resulting prices, which in turn affect the actual demand realization, giving rise to a decision-dependent uncertainty. Motivated by the problem's hard-to-evaluate objective function, we solve it using Bayesian optimization. The empirical evaluations demonstrate significant savings in the effective real-time system cost, compared to the current practice of using the default demand forecast. Moreover, the method is shown to achieve a system cost that is fairly close to the one achieved by a system that fully integrates PRD into the day-ahead process; but without requiring any change in the operator's existing dispatch algorithm while avoiding all efforts necessary for the integration of flexible demand, which is a widely pursued field of ongoing research.