A Consensus-ADMM Approach for Strategic Generation Investment in Electricity Markets

TL;DR

This paper develops a novel consensus-ADMM method to solve complex stochastic bilevel optimization problems for strategic generation investment in electricity markets, balancing computational efficiency and solution quality.

Contribution

It introduces a consensus-ADMM approach for large-scale stochastic MILP problems in electricity market investment, with bounds for solution quality assessment.

Findings

The proposed method effectively decomposes the problem by scenarios.

Trade-off identified between computational time and solution accuracy.

Bounds enable evaluation of solution quality over iterations.

Abstract

This paper addresses a multi-stage generation investment problem for a strategic (price-maker) power producer in electricity markets. This problem is exposed to different sources of uncertainty, including short-term operational (e.g., rivals' offering strategies) and long-term macro (e.g., demand growth) uncertainties. This problem is formulated as a stochastic bilevel optimization problem, which eventually recasts as a large-scale stochastic mixed-integer linear programming (MILP) problem with limited computational tractability. To cope with computational issues, we propose a consensus version of alternating direction method of multipliers (ADMM), which decomposes the original problem by both short- and long-term scenarios. Although the convergence of ADMM to the global solution cannot be generally guaranteed for MILP problems, we introduce two bounds on the optimal solution, allowing for the evaluation of the solution quality over iterations. Our numerical findings show that there is a trade-off between computational time and solution quality.