Optimization Models and Algorithms for Nonconvex Planning, Pricing and Operational Problems in Power Systems and Energy Markets

Optimization models are widely used in power system engineering to improve efficiency and cost effectiveness. The main challenge in power system optimization is nonconvexities that arise from various sources, such as binary decisions for investment or commitment for power generators and nonlinear physical constraints for electric current. The primary focus of this thesis is on important nonconvex planning and operational optimization problems in power systems and energy markets. We improve decision making for such problems by proposing suitable models and developing algorithms to efficiently solve them. We illustrate their benefits by extensive case studies. First, we study a generation capacity expansion problem that combines investment planning with unit commitment. We incorporate revenue adequacy constraints in a two-stage generation expansion planning model. After making generation investment decisions in the first stage, we determine the commitment schedule and production levels, as well as electricity prices, in the second stage. To approximate a market equilibrium, we use the duality gap between the second-stage nonconvex unit commitment model and its linearly-relaxed dual as a regularizer. Next, we propose a framework to derive solutions for discrete energy market and game theory problems using copositive programming. It was shown that a nonconvex mixed-binary quadratic program can be reformulated as a convex program, which has strong duality under mild conditions via copositive programming. Through this (duality) perspective, we propose a new pricing mechanism for nonconvex energy markets that has desirable properties, and a novel method for obtaining Nash equilibria for discrete games using the theoretical results we prove. To facilitate implementation, we design a cutting plane algorithm for solving copositive programs exactly. Lastly, we consider the alternating current optimal transmission switching (ACOTS) problem, whose models contain nonconvex structures such as binary variables and multilinear terms. We propose a variety of ways to strengthen the quadratic convex ACOTS relaxation model from the literature, such as linearizing multilinear terms with the extreme-point representation, and adding several types of valid inequalities. In particular, we derive a novel kind of cycle-based polynomial constraints, which can be added iteratively in a branch-and-cut framework.Ph.D