Approximation of feasible sets in energy system applications via convex optimization

In this paper we present and compare two interior point methods for ellipsoidal approximations of feasible sets defined by linear inequalities. The two procedures (primal-dual maximum volume MaxVE and a linear matrix inequality-based method LMI) are compared on a Simultaneous Feasibility Test (SFT) in power system contingency analysis. The methods simultaneously determine optimal analytic center of the approximating ellipsoid, and its shape matrix for maximal volume inner approximation. The methods are potentially useful optimization in deregulated power markets, for example Security-Constrained Economic Dispatch (SCED). The applicability of the two methods is demonstrated on two characteristic test examples: 1) small-size with 6 buses and 3 generators, where visual representation of feasible region are possible, and 2) medium-size with 68 buses and 16 generators.