  A power system unit commitment (UC) problem considering uncertainties of
renewable energy sources is investigated in this paper, through a
distributionally robust optimization approach. We assume that the first and
second order moments of stochastic parameters can be inferred from historical
data, and then employed to model the set of probability distributions. The
resulting problem is a two-stage distributionally robust unit commitment with
second order moment constraints, and we show that it can be recast as a
mixed-integer semidefinite programming (MI-SDP) with finite constraints. The
solution algorithm of the problem comprises solving a series of relaxed MI-SDPs
and a subroutine of feasibility checking and vertex generation. Based on the
verification of strong duality of the semidefinite programming (SDP) problems,
we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce
a SDP relaxation for the feasibility checking problem, which is an intractable
biconvex optimization. Experimental results on a IEEE 6-bus system are
presented, showing that without any tunings of parameters, the real-time
operation cost of distributionally robust UC method outperforms those of
deterministic UC and two-stage robust UC methods in general, and our method
also enjoys higher reliability of dispatch operation.
