Abstract: This talk deals with nonconvex power flow and power system state estimation problems, which play a central role in dynamic monitoring and operation of electric power networks. The objective of the power flow problem is to obtain the state of the system from a set of noiseless measurements, whereas the state estimation problem deals with noisy measurements. The semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations are then leveraged to cope with the inherent nonconvexity of the power flow problem.
It is shown that both conic relaxations recover the true power flow solution under mild conditions. By capitalizing on this result, a penalized convex problem is designed for the state estimation. This penalized SDP problem is obtained from the aforementioned SDP relaxation, by adding a weighted least absolute value penalty for fitting noisy measurements. Strong theoretical results are derived to quantify the optimal solution of the penalized SDP, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector. Numerical results on benchmark systems will be demonstrated to corroborate the merits of the proposed convexification framework.
Bio: Yu Zhang is an assistant professor in the ECE Department of the University of California, Santa Cruz. He received a Ph.D. in electrical engineering from the University of Minnesota. His research interests span the broad areas of smart power grids, signal processing, data analytics, optimization. and learning.