Energy Pricing and Dispatch for Smart Grid Retailers Under Demand Response and Market Price Uncertainty

TLDR

The paper proposes a two‑stage, two‑level model for energy pricing and dispatch that positions a smart‑grid retailer as an intermediary between the wholesale market and consumers. Demand response is modeled as a Stackelberg game in the first stage, while a risk‑averse dispatch under price uncertainty is formulated as a linear robust optimization; the resulting problem is converted to a MILP using KKT conditions, disjunctive constraints, and duality, with a heuristic for parameter selection and an auxiliary LP to improve bidding strategies. Case studies confirm that the proposed model and heuristic yield valid, profit‑enhancing dispatch strategies across the uncertainty set.

Abstract

This paper proposes a two-stage two-level model for the energy pricing and dispatch problem faced by a smart grid retailer who plays the role of an intermediary agent between a wholesale energy market and end consumers. Demand response of consumers with respect to the retail price is characterized by a Stackelberg game in the first stage, thus the first stage has two levels. A risk-aversive energy dispatch accounting for market price uncertainty is modeled by a linear robust optimization with objective uncertainty in the second stage. The proposed model is transformed to a mixed integer linear program (MILP) by jointly using the Karush-Kuhn-Tucker (KKT) condition, the disjunctive constraints, and the duality theory. We propose a heuristic method to select the parameter in disjunctive constraints based on the interpretation of Lagrange multipliers. Moreover, we suggest solving an additional linear program (LP) to acquire a possible enhanced bidding strategy that guarantees a Pareto improvement on the retailer's profit over the entire uncertainty set. Case studies demonstrate the proposed model and method is valid.