  Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental
problems in short-term electric power systems planning that are traditionally
solved sequentially. The state-of-the-art mostly uses a direct current flow
approximation of the power flow equations in the UC-level and the generator
commitments obtained are sent as input to the OPF-level. However, such an
approach can yield infeasible or suboptimal generator schedules. In this paper,
we aim to simultaneously solve the UC Problem with alternating current (AC)
power flow equations, which combines the challenging nature of both UC and OPF
problems. Due to the highly nonconvex nature of the AC flow equations, we
utilize the mixed-integer second-order cone programming (MISOCP) relaxation of
the UC Problem as the basis of our solution approach. For smaller instances, we
develop two different algorithms that exploit the recent advances in the OPF
literature and obtain high-quality feasible solutions with provably small
optimality gaps. For larger instances, we propose a novel Lagrangian
decomposition based approach that yields promising results.
