Large-scale application of the Han-Powell algorithm to compact models of static and dynamic dispatch of real power

In this study some second-order algorithms derived from the Han-Powell method are applied to real power optimization both in a static and in a dynamic dispatch procedure with security constraints. These procedures employ suitable compact reduced models for large-scale applications. In the dynamic approach a time-varying load is shared among the control units by adopting a discrete formulation of the dispatch problem. This involves the subdivision of the optimization interval into a certain number of sub-intervals with constant loads and the addition, to the ordinary constraints of the static approach, of dynamic constraints on rate of change of MW output of thermal units. In particular, security constraints are modified in order to take into account their dependence on the load variability during the optimization interval. Also in the paper, a dynamic approach is shown to be needed for preventive scheduling of the thermal generation during the time periods characterized by a high rate of load variation (pick-up or drop-down hours) as well as during the online rescheduling. The robustness and the efficiency of the adopted procedures have been demonstrated by several tests on a sample network of small dimension as well as on large-scale systems. In the dynamic approach a suitably modified version of the Han-Powell algorithm is adopted which employs an alternative technique in the construction and in the updating of the Hessian matrix of the Lagrangian function. This allows us to handle large-scale problems arising from the optimization of a large system on the framework of a minute subdivision of the dispatch interval. This technique exploits and conserves in the updating phase the sparseness property of the matrix, without using the usual Broyden-Fletcher-Shanno-Goldfarb formulae.