Rank-constrained semidefinite program for unit commitment

Unit Commitment (UC) is a combinatorial optimization problem that can be posed as minimizing a quadratic objective function under quadratic constraints. This paper presents a solution to UC based on Semidefinite Programming (SDP). In particular, it shows that an approximate solution can be obtained by using Shor’s semidefinite relaxation scheme together with a rank constraint enforced via convex iteration. The approximate solution has the majority of Boolean variables set by the SDP solver to either 0 or 1; it is modified by a simple heuristic to yield a feasible schedule. The proposed SDP formulation employs 3 × 3 semidefinite matrices and therefore requires computational effort that increases only moderately with problem size. Numerical results on test systems with up to 100 units dispatched over a period of 24 h show that the method is robust and produces schedules that are comparable with those from previous techniques.

► The unit commitment solution is obtained using semidefinite programming.
► The approach requires solving Shor’s semidefinite relaxation.
► The rank-1 constraint is approximately enforced via convex iteration.
► The computational effort increases moderately with problem size.
► The solution quality is comparable with that from previous techniques.