Distributed Optimization Methods for Monitoring and Operating Electric Power Systems

Abstract

Increasing power demands, aging infrastructure, and growth in renewable energy production necessitate new strategies for grid operations. To achieve reliable operations in this setting, it is important to shift away from centralized control paradigms to distributed approaches that 1) allow for quicker solution times by decomposing the problem to be solved in parallel and 2) avoid communication bottlenecks that result from all data and measurements being sent to a centralized location. Since power systems are interconnected systems, decoupling such problems is challenging. This dissertation studies how to improve monitoring and operation of networked systems, specifically electric power grids, through distributed optimization and scientific computing. The thesis focuses on two areas. In the first part, we design fully distributed algorithms for power system state estimation under both linear and nonlinear measurement models. For the nonlinear setting, we develop a distributed Gauss-Newton method. The main computational burden is solving a series of large, sparse linear systems. Iterative linear solvers based on matrix-splitting techniques are developed to exploit the sparsity pattern induced by the underlying network structure and physical laws of power networks. In addition, a distributed unscented Kalman filter is proposed to improve upon the state estimator by incorporating information from past measurements. Advantages of the proposed distributed approaches include increased scalability in terms of both computation and communication. The second part of this thesis concerns the operation of power grids, in particular how to determine the optimal set points for the system. The use of primal-dual interior point (PDIP) methods for the optimal power flow (OPF) problem and the security-constrained OPF problem is studied. We design domain decomposition techniques, as well as reduction and reordering schemes, to parallelize the PDIP method by exploiting sparsity structure. Last, distributed energy resources (DERs) subject to uncertainty and various dynamic constraints are increasingly participating in electricity production and demand. A computationally tractable approximation for polyhedral projections is proposed to quantify the aggregate capability of distributed energy resources. This work contributes to the question of how to utilize DERs to improve and support bulk grid operations.