Efficient Methods to Compute Convex Hull Prices for Electricity Markets Using a Stochastic Gradient-Based approach

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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 uplift sum corresponds to the Lagrangian dual L(π) maximization. Our research focuses on employing a stochastic approach to resolve this problem by using the variance reduced method like SAG,SAGA,SVRG. The main observation is that these methods depend on gamma and affect too much la solution. The primary observation highlights that these methods depend highly on the gamma parameter, significantly impacting the overall solution. This sensitivity to gamma underscores the need for careful selection and tuning of this parameter to ensure optimal performance and minimize its influence on the solution.