An optimization problem in deregulated electricity markets solved with the nonsmooth maximum principle

In this paper, the new short-term problems that are faced by a generation company in a deregulated electricity market are addressed and a optimization algorithm is proposed. Our model of the spot market explicitly represents the price of electricity as an uncertain exogenous variable. We consider a very complex problem of hydrothermal optimization with pumped-storage plants, so the problem deals with non-regular Lagrangian and non-holonomic inequality constraints. To obtain a necessary minimum condition, the problem was formulated within the framework of nonsmooth analysis using the generalized (or Clarke’s) gradient and the Nonsmooth Maximum Principle. The optimal control problem is solved by means of an algorithm implemented in the commercial software package Mathematica. Results of the application of the method to a numerical example are presented.