Day-Ahead Offering for Virtual Power Plants: A Stochastic Linear Programming Reformulation and Projected Subgradient Method

TL;DR

This paper develops a novel stochastic linear programming approach with a projected subgradient method for day-ahead VPP market offerings, improving computational efficiency under uncertainty.

Contribution

It introduces a new inner approximation-based projected subgradient method and reformulates the robust second-stage problem as an LP for better tractability.

Findings

Achieves about two orders of magnitude speedup over existing methods.

Maintains solution quality while significantly reducing computation time.

Provides a scalable approach for VPP day-ahead market participation.

Abstract

Virtual power plants (VPPs) are an emerging paradigm that aggregates distributed energy resources (DERs) for coordinated participation in power systems, including bidding as a single dispatchable entity in the wholesale market. In this paper, we address a critical operational challenge for VPPs: the day-ahead offering problem under highly intermittent and uncertain DER outputs and market prices. The day-ahead offering problem determines the price-quantity pairs submitted by VPPs while balancing profit opportunities against operational uncertainties. First, we formulate the problem as a scenario-based two-stage stochastic adaptive robust optimization problem, where the uncertainty of the locational marginal prices follows a Markov process and DER uncertainty is characterized by static uncertainty sets. Then, motivated by the outer approximation principle of the column-and-constraint generation (CC&G) algorithm, we propose a novel inner approximation-based projected subgradient method. By exploiting the problem structure, we propose two novel approaches to improve computational tractability. First, we show that under mild modeling assumptions, the robust second-stage problem can be equivalently reformulated as a linear program (LP) with a nested resource allocation structure that is amenable to an efficient greedy algorithm. Furthermore, motivated by the computational efficiency of solving the reformulated primal second-stage problem and the isotonic structure of the first-stage feasible region, we propose an efficient projected subgradient algorithm to solve the overall stochastic LP problem. Extensive computational experiments using real-world data demonstrate that the overall projected subgradient descent method achieves about two orders of magnitude speedup over CC&G while maintaining solution quality.