Verification of power grid voltage constraint satisfaction-A barrier certificate approach

This paper addresses verification of voltage constraint satisfaction in power systems with distributed production and time-varying consumption. Due to increasing penetration of renewable generation units and additional demand from e.g., electrical vehicles, voltage constraint satisfaction is seen as one of the major future challenges of power system operators. We show that ensuring voltage constraints in power systems is equivalent to finding a barrier function for a differential algebraic system. In order to compute the barrier function we reformulate the original problem to polynomial form and cast it as a sum of squares (SOS) feasibility problem, solvable using available tools.