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Center for Nonlinear Studies |
The electric power grid is undergoing transformational changes driven by several factors: Deregulation of the electricity industry and the introduction of electric markets, Rising levels of renewable penetration in the grid driven by falling costs and governmental subsidies, Integration of unconventional resources like distributed generation, microgrids and demand response. These changes mandate the need for new analysis tools that ensure safety and stability of the power system in the presence of all these uncertainties. We present several new mathematical tools to deal with this uncertainty: Using the theory of monotone operators and variational inequalities, we develop robust solvers for the nonlinear AC power flow equations that can find solutions or prove the non-existence of a solution satisfying operational constraints. Using ideas from numerical continuation and homotopy, we construct convex inner approximations of the feasible set for AC Optimal Power Flow Problem(ACOPF). These tools provide efficient and rigorous ways of performing contingency analysis against an infinite set of contingencies and finding feasible operating conditions that are robust to variations in loads/wind generation etc. In the last part of the talk, I will mention recent work on using ideas from discrete optimization and dynamic programming to solving mixed integer ACOPF problems and characterizing market power of renewable generation aggregators.
Host: Misha Chertkov