An outer approximation of the Minkowski sum of convex conic sets with application to demand response

Flexible loads can provide services such as load-shifting and regulation to power system operators through demand response. A system operator must know the aggregate capabilities of a load population to use it in scheduling and dispatch routines such as optimal power flow and unit commitment. It is not practical for a system operator to model every single load because it would compromise tractability and require potentially unavailable information. A key challenge for load aggregators is to develop low-order models of load aggregations that system operators can use in their operating routines. In this paper, we develop a simple approximation for loads modeled by linear, second-order cone, and semidefinite constraints. It is an outer approximation of the Minkowski sum, the exact computation of which is intractable. We apply the outer approximation to loads with convex quadratic apparent power constraints and uncertainty modeled with second-order cone constraints.