Solving Nonlinear Single-Unit Commitment problems with ramping constraints

We present a dynamic programming algorithm for solving the Single-Unit Commitment (1UC) problem with ramping constraints and arbitrary convex cost functions. The algorithm is based on a new approach for efficiently solving the single-unit Economic Dispatch (ED) problem with ramping constraints and arbitrary convex cost functions, improving on previously known ones that were limited to piecewise-linear functions. For simple convex functions, such as the quadratic ones typically used in applications, the solution cost of all the involved (ED) problems, comprised that of finding an optimal primal and dual solution, is~$O(n^3)$. Coupled with a special visit of the state-space graph in the dynamic programming algorithm, that enables one to solve (1UC) with simple convex functions in~$O(n^3)$ overall.