Optimization and Learning Methods for Electric Distribution Network Management

University of Minnesota Ph.D. dissertation.June 2019. Major: Electrical Engineering. Advisor: Nicholas Sidiropoulos. 1 computer file (PDF); ix, 108 pages.Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used Gauss-Newton approaches are not suitable for real-time estimation, often require many iterations to obtain reasonable results, and sometimes fail to converge. Learning-based approaches hold the promise for accurate real-time estimation. This dissertation presents the first data-driven approach to `learn to initialize' -- that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss-Newton. In addition, a novel learning model is also presented that utilizes the electrical network structure. The proposed neural network architecture reduces the number of coefficients needed to parameterize the mapping from the measurements to the network state by exploiting the separability of the estimation problem. The proposed approach is the first that leverages electrical laws and grid topology to design the neural network for DSSE. It is shown that the proposed approaches yield superior performance in terms of stability, accuracy, and runtime, compared to conventional optimization-based solvers. The second part of the dissertation focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with large-scale integration of renewables, where adjustments of real and reactive output power from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this dissertation leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm – a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using several multi-phase distribution networks with renewables