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In this study, a rigorous mathematical method is proposed for dealing with the ramp-rate limits in unit commitment and the rotor fatigue effect in economic dispatch. An iterative procedure is employed to coordinate the unit commitment and the power dispatch for obtaining an economical solution within a reasonable time. The Lagrangian relaxation method is used to generate the unit commitment schedule with relaxed power balance constraints. A network model is adopted to represent the dynamic process of operating a unit over the entire study time span, as the required unit commitment schedule can be achieved by searching for the shortest path in the network. In order to find the global optimal solution for the economic dispatch problem within personal computer resources, a piecewise linear model is used for thermal units. Furthermore, linear programming is used in optimizing the benefits of ramping the units, with low operating cost against the cost of shortening the service life of the turbine rotor. In this regard, linear programming is used to dispatch the power generation among committed units by considering a ramping penalty for the fatigue effect in rotor shafts, while preserving the operational constraints of the system as well as the generating units.>
Wang et al. (Sat,) studied this question.