  In this paper we present a stochastic scenario-based model predictive control
(MPC) approach for the operation of islanded microgrids with high share of
renewable energy sources. We require that the stored energy remains within
given bounds with a certain probability using risk-based constraints as convex
approximations of chance constraints. We show that risk constraints can
generally be cast as conic constraints and, unlike chance constraints, can
control both the number and average magnitude of constraint violations. Lastly,
we demonstrate the risk-constrained stochastic MPC in a numerical case study.
