Algorithm design for optimal power flow, security-constrained unit commitment, and demand response in energy systems

Energy management is of prime importance for power system operators to enhance the use of the existing and new facilities, while maintaining a high level of reliability. In this thesis, we develop analytical models and efficient algorithms for energy management programs in transmission and distribution networks. First, we study the optimal power flow (OPF) in ac-dc grids, which is a non-convex optimization problem. We use convex relaxation techniques and transform the problem into a semidefinite program (SDP). We derive the sufficient conditions for zero relaxation gap and design an algorithm to obtain the global optimal solution. Subsequently, we study the security-constrained unit commitment (SCUC) problem in ac-dc grids with generation and load uncertainty. We introduce the concept of conditional value-at risk to limit the net power supply shortage. The SCUC is a nonlinear mixed-integer optimization problem. We use ℓ₁-norm approximation and convex relaxation techniques to transform the problem into an SDP. We develop an algorithm to determine a near-optimal solution. Next, we target the role of end-users in energy management activities. We study demand response programs for residential users and data centers. For residential users, we capture their coupled decision making in a demand response program with real-time pricing as a partially observable stochastic game. To make the problem tractable, we approximate the optimal scheduling policy of the residential users by the Markov perfect equilibrium (MPE) of a fully observable stochastic game with incomplete information. We develop an online load scheduling learning algorithm to determine the users’ MPE policy. Last but not least, we focus on the demand response program for data centers in deregulated electricity markets, where each data center can choose a utility company from multiple available suppliers. We model the data centers’ coupled decisions of utility company choices and workload scheduling as a many-to-one matching game with externalities. We characterize the stable outcome of the game, where no data center has an incentive to unilaterally change its strategy. We develop a distributed algorithm that is guaranteed to converge to a stable outcome.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat