An integrated learning and optimization approach to optimal dynamic retail electricity pricing of residential and industrial consumers

Residential and industrial consumers are important price-sensitive electricity consumers in the electricity retail market. To effectively manage these demand response resources, this paper investigates the optimal dynamic retail electricity pricing of residential and industrial consumers and proposes an integrated learning and optimization pricing strategy. The strategy determines customized electricity prices of consumers, while considering consumers' price-elastic demand responses (DRs) and the privacy of industrial consumers' electricity consumption patterns (ECPs). The retailer's interaction with consumers is modeled through a bi-level programming framework, where the retailer determines electricity prices and dispatch in the upper level and consumers respond by adjusting their electricity demands in the lower level. Residential consumers' DRs are captured using optimization models that minimize electricity usage deviation penalties and expected purchase costs. For industrial consumers, their DRs are learned through a regression multi-layer perceptron (MLP), trained exclusively on historical electricity price-demand data without accessing any private information regarding their ECPs. The established MLP is analytically formulated and the established nonlinear bi-level programming model is transformed into a mixed integer linear single-level programming model. The transformation involves implementing the Karush–Kuhn–Tucker single-level reformulation, the convex relaxation of bilinear terms, and mixed integer linearization reformulations of the obtained MLP and complementary constraints. To reduce the errors introduced by convex relaxation, a sequential bound-tightening algorithm that adaptively narrows the convex relaxation ranges is developed. Numerical experiments demonstrate the effectiveness of the proposed pricing strategy in guiding consumers' electricity consumption behaviors while respecting the privacy of industrial production. The impact of the data-driven modeling approach on the decision is also discussed.