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Mathematical Problems in Engineering
Volume 5, Issue 5, Pages 379-396

Multiple objective optimization of hydro-thermal systems using Ritz's method

Departamento de Matemáticas, Universidad de Oviedo, Escuela Universitaria de Ingenieria Tecnica Industrial, C/Manuel Llaneza 75, Gijón, Asturias 33208, Spain

Received 11 June 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper examines the applicability of the Ritz method to multi-objective optimization of hydro-thermal systems. The algorithm proposed is aimed to minimize an objective functional that incorporates the cost of energy losses, the conventional fuel cost and the production of atmospheric emissions such as NOx and SO2 caused by the operation of fossil-fueled thermal generation. The formulation includes a general layout of hydro-plants that may form multi-chains of reservoir network.

Time-delays are included and the electric network is considered by using the active power balance equation. The volume of water discharge for each hydro-plant is a given constant amount from the optimization interval. The generic minimization algorithm, which is not difficult to construct on the basis of the Ritz method, has certain advantages in comparison with the conventional methods.