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A power system unit commitment (UC) problem considering uncertainties ofrenewable energy sources is investigated in this paper, through adistributionally robust optimization approach. We assume that the first andsecond order moments of stochastic parameters can be inferred from historicaldata, and then employed to model the set of probability distributions. Theresulting problem is a two-stage distributionally robust unit commitment withsecond order moment constraints, and we show that it can be recast as amixed-integer semidefinite programming (MI-SDP) with finite constraints. Thesolution algorithm of the problem comprises solving a series of relaxed MI-SDPsand a subroutine of feasibility checking and vertex generation. Based on theverification of strong duality of the semidefinite programming (SDP) problems,we propose a cutting plane algorithm for solving the MI-SDPs; we also introducea SDP relaxation for the feasibility checking problem, which is an intractablebiconvex optimization. Experimental results on a IEEE 6-bus system arepresented, showing that without any tunings of parameters, the real-timeoperation cost of distributionally robust UC method outperforms those ofdeterministic UC and two-stage robust UC methods in general, and our methodalso enjoys higher reliability of dispatch operation.

A Mixed-Integer SDP Solution Approach to Distributionally Robust Unit Commitment with Second Order Moment Constraints