Mathematics Colloquia and Seminars

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In this talk, we will first focus on the non-convex power flow and power system state estimation problems, which play a central role in monitoring and operation of electric power grids. The power flow problem aims at obtaining all voltage phasors from a set of noiseless observations, whereas the state estimation deals with noisy measurements. The semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations are leveraged to cope with the inherent non-convexity of the two problems. It is shown that both conic relaxations recover the true power flow solution under mild conditions. A penalized SDP is then designed for the state estimation task. We drive an upper bound to quantify the optimal solution of the SDP, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector. In the second part of the talk, we will quickly demonstrate recent results for electricity market inference and energy disaggregation solved by advanced machine learning techniques.