Efficient methods to compute convex hull prices for electricity markets: using a stochastic gradient-based approach

Details

Supervisors

Glineur, François

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

This thesis addresses the Unit Commitment (UC) problem, which aims to optimize energy production schedules across multiple generators to meet hourly consumer demand while minimizing costs for each participant in the electricity market. Due to the problem's non-convex constraints and binary variables, an optimal UC solution is difficult to obtain. To overcome this challenge, we employ concepts of side payments and uplifts to compensate for choosing a near-equilibrium solution. However, these compensations must be minimized. Drawing inspiration from the dual variable associated with the market constraint in a convex case, we apply Lagrangian relaxation with variable π to the UC problem. Utilizing duality theory, we demonstrate that the optimal sum of uplifts corresponds to the maximization of the Lagrangian dual L(π). Our research focuses on employing stochastic descent algorithms to approach this maximum, constituting the third layer of the problem framework. At the core of our research, we use a commercial solver like Gurobi as an oracle to generate stochastic gradients that guide the optimization process. This abstract presents our findings from experimenting with various algorithms and techniques to optimize the UC problem, emphasizing the significance of selecting an appropriate starting point and discussing the limitations of the mini-batch strategy without replacement.