2 research outputs found
Unit commitment with valve-point loading effect
Valve-point loading affects the input-output characteristics of generating
units, bringing the fuel costs nonlinear and nonsmooth. This has been
considered in the solution of load dispatch problems, but not in the planning
phase of unit commitment. This paper presents a mathematical optimization model
for the thermal unit commitment problem considering valve-point loading. The
formulation is based on a careful linearization of the fuel cost function,
which is modeled with great detail on power regions being used in the current
solution, and roughly on other regions. A set of benchmark instances for this
problem is used for analyzing the method, with recourse to a general-purpose
mixed-integer optimization solver
Non-convex nested Benders decomposition
We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size