  We consider a robust optimization problem in an electric power system under
uncertain demand and availability of renewable energy resources. Solving the
deterministic alternating current optimal power flow (ACOPF) problem has been
considered challenging since the 1960s due to its nonconvexity. Linear
approximation of the AC power flow system sees pervasive use, but does not
guarantee a physically feasible system configuration. In recent years, various
convex relaxation schemes for the ACOPF problem have been investigated, and
under some assumptions, a physically feasible solution can be recovered. Based
on these convex relaxations, we construct a robust convex optimization problem
with recourse to solve for optimal controllable injections (fossil fuel,
nuclear, etc.) in electric power systems under uncertainty (renewable energy
generation, demand fluctuation, etc.). We propose a cutting-plane method to
solve this robust optimization problem, and we establish convergence and other
desirable properties. Experimental results indicate that our robust convex
relaxation of the ACOPF problem can provide a tight lower bound.
