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 Shors 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 33 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 24h show that the method is robust and produces schedules that are comparable with those from previous techniques.
semidefinite programming unit commitment integer programming optimization methods power generation dispatch power system economics