Optimal Power Flow: Online Algorithm and Fast Dynamics

The optimal power flow (OPF) problem underlies numerous system operation and planning applications. The computational challenge often arises from the need to solve power flow equations explicitly or implicitly. The grid however implicitly solves power flow equations in real-time at scale for free. We propose to explicitly exploits the network as a power flow solver to carry out part of our optimization algorithm. This approach naturally adapts to evolving network conditions. Specifically, we present an algorithm that adapts controllable devices and interacts continuously with the grid which computes a power flow solution given a control action. Collectively these devices and the grid implement a gradient projection algorithm in real time. We characterize optimality and tracking properties of the algorithm. We apply this idea to a unified frequency controller at a fast timescale that integrates primary frequency regulation, secondary frequency regulation, and congestion management. We prove sufficient conditions under which the algorithm converges to a global optimum.
Steven H. Low is a Professor of the Department of Computing & Mathematical Sciences and the Department of Electrical Engineering at Caltech. He is a Senior Editor of the IEEE Transactions on Control of Network Systems and the IEEE Transactions on Network Science & Engineering, is on the editorial boards of NOW Foundations and Trends in Electric Energy Systems, and Foundations and Trends in Networking, as well as Journal on Sustainable Energy, Grids and Networks. He received his B.S. from Cornell and PhD from Berkeley, both in EE. He is an IEEE Fellow.