Optimization models and algorithms for electricity markets, redispatch, and market interactions

This thesis studies electricity and redispatch markets from an operations research perspective, with a focus on market-clearing models, equilibrium analysis, and algorithmic solutions under network constraints. In particular, the thesis examines how market outcomes are affected by nonconvexities, decomposition strategies, and the level of detail adopted in network modeling. Chapter 2 provides a critical examination and technical reconstruction of an existing equilibrium framework for competitive electricity markets with price-taking participants in both convex and nonconvex settings. It revisits the approaches introduced in the literature, reorganizes its main theoretical components, and presents in full several proofs that were omitted or only briefly outlined in the original source. The chapter’s main original contribution lies in extending the framework to an Alternating Current Optimal Power Flow setting, where the same theoretical logic is examined in a different modeling environment and complemented by a computational test case. Chapter 3 addresses the computational solution of a day-ahead market-clearing problem with demand response and Direct Current Optimal Power Flow (DCOPF) constraints. It proposes a non-monotone restart and acceptance framework for accelerated Alternating Direction Method of Multipliers (ADMM), based on a sliding-window residual criterion, and uses it to compare several acceleration schemes under a unified computational setting. The computational study shows that the effectiveness of acceleration depends significantly on the interaction between the chosen method, the problem instance, and the safeguard configuration. Chapter 4 adopts a modeling perspective on centralized redispatch. It compares a zonal formulation and a DC power-flow-based formulation, both including reserve-related mechanisms, and evaluates their outcomes through dedicated recovery models designed to restore nodal feasibility while limiting deviations from prior market results. The computational analysis shows that incorporating nodal network constraints directly into the redispatch model can improve overall economic performance without materially increasing computational burden. It also highlights relevant trade-offs among alternative recovery formulations in terms of cost, tractability, and robustness under changing operating conditions. Overall, the thesis contributes to the study of electricity markets by combining critical analysis of existing equilibrium theory with original work on algorithmic design and redispatch modeling, with particular emphasis on the role of network constraints in determining feasible and economically efficient outcomes.