Steepest descent optimization based on increasing/decreasing variable pair for economic dispatch of power system

The mathematical model for economic dispatch of power system is a non-convex and nonlinear mathematical programming when some of units' cost functions are piecewise quadratic or have a negative quadratic coefficient, which gives rise to more difficulties on searching for the local/global optimum. This paper proposes a steepest descent optimization method based on increasing/decreasing variable pair. In each iterating, only one pair of state variables will be modified: one variable will increase, and the other will decrease with an identical step length. The step length is controlled dynamically under a set of principles to satisfy all the constraints; meanwhile, the increasing/decreasing variable pair is selected dynamically from all variable pairs and it has the smallest partial derivative sum to insure every iterating is along the deepest decent direction. The partial derivative is of the original objective function to variable. The method could get a global optimum for a convex programming and a local optimum for a non-convex one. In addition, an improved steepest descent optimization method based on increasing/decreasing variable pair that combines evolutionary strategy is proposed. The improved method can keep rapidness of original algorithm and get the global optimal solution. The results of sample systems indicate the practicability and effectiveness of these two methods.