  We propose a novel global solution algorithm for the network-constrained unit
commitment problem incorporating a nonlinear alternating current model of the
transmission network, which is a nonconvex mixed-integer nonlinear programming
(MINLP) problem. Our algorithm is based on the multi-tree global optimization
methodology, which iterates between a mixed-integer lower-bounding problem and
a nonlinear upper-bounding problem. We exploit the mathematical structure of
the unit commitment problem with AC power flow constraints (UC-AC) and leverage
optimization-based bounds tightening, second-order cone relaxations, and
piecewise outer approximations to guarantee a globally optimal solution at
convergence. Numerical results on four benchmark problems illustrate the
effectiveness of our algorithm, both in terms of convergence rate and solution
quality.
