H.B. Keller Colloquium
Our power system is becoming over the coming decade more dynamic, distributed, uncertain, autonomous, and open. We will motivate some of the emerging problems in this transformation and give a sample of solutions for illustration. Specifically we describe a sufficient condition for exact semidefinite relaxation of the nonconvex optimal power flow (OPF) problems on a distribution network that contains loops. We characterize the class of OPF problems for which both semidefinite relaxation is exact and any local optima are globally optimal. These results offer the first explanation of the overwhelming empirical observation that OPF, though NP-hard in theory, seems easy in practice in that both relaxations and local algorithms tend to produce global optima. Rising uncertainty demands closing the loop and solving time-varying OPF problems. We describe simple algorithms for tracking a KKT point of time-varying nonconvex OPF problems. All these algorithms assume we know the topology and line parameters of the network, which are often unavailable or inaccurate. Yet, new measurement infrastructures are being deployed at scale. We describe how to learn network admittance matrix from these measurements. Finally, we describe an open-source testbed that is being developed at Caltech that will provide fine-grained real electric vehicle (EV) charging data, data-driven grid simulators, and a live testbed for novel EV charging algorithms.