Solving short-term electric hydrothermal scheduling problems by exponential multiplier methods†

Abstract

The short-term electric hydrothermal scheduling (STEHS) problem consists in optimizing the production of hydro and thermal electric generation units over a short time period (up to one week long). The problem described in this work can be modelled as a nonlinear network flow problem with linear and nonlinear side constraints. The minimization of this kind of problem can be performed by exploiting the efficiency of network flow techniques. It lies in minimizing approximately a series of augmented Lagrangian functions including only the side constraints, subject to balance constraints in the nodes and capacity bounds. One of the drawbacks of the multiplier methods with quadratic penalty function is that the augmented Lagrangian is not twice differentiable when it is applied to problems with inequality constraints. This article overcomes this difficulty by using the exponential multiplier method. In order to improve the performance some parameters are tuned. The efficiency of this method over STEHS test problems is illustrated by comparing its CPU-times with those of the quadratic multiplier method and with those of the general purpose codes MINOS, SNOPT, and KNITRO. Numerical results are promising. †The research was partially supported by grant MCYT DPI 2005-09117-C02-01.