Learning Fast Approximations for Nonconvex Optimization Problems via Deep Learning with Applications to Power Systems

Abstract

Nonlinear convex optimization has provided a great modeling language and a powerful solution tool for the control and analysis of power systems over the last decade. A main challenge today is solving non-convex problems in real-time. However, if an oracle can guess, ahead of time, a high quality initial solution, then most non-convex optimization problems can be solved in a limited number of iterations using off-the-shelf solvers. In this proposal, we study how deep learning can provide good approximations for real-time power system applications. These approximations can act as good initial solutions to any exact algorithm. Alternatively, such approximations could be satisfactory to carry out real-time operations in power systems. First, we address the problem of joint power system state estimation and bad data identification. We propose a deep learning model that provides high quality approximations in milliseconds. Second, we address the problem multi-step ahead power system state forecasting and advocate sequence-to-sequence models for better representation. Lastly, we study the problem of learning fast approximations to intialize linear programming solvers. We cast the problem as a simple learning task and propose a deep learning model.