A HYDROTHERMAL PROBLEM WITH NON-SMOOTH LAGRANGIAN

作者：Bayon Luis^*; Maria Grau Jose; del Mar Ruiz Maria; Maria Suarez Pedro

来源：Journal of Industrial and Management Optimization, 2014, 10(3): 761-776.

DOI：10.3934/jimo.2014.10.761

• Optimization
• nonsmooth analysis
• variational methods
• hydrothermal problem
• valve-point

This paper deals with the optimization of a hydrothermal problem that considers a non-smooth Lagrangian L(t, z, z%26apos;). We consider a general case where the functions L-z%26apos;(t, ., .) and L-z(t, ., .) are discontinuous in {(t, z, z%26apos;)/z%26apos; = phi(t, z)}, which is the borderline point between two power generation zones. This situation arises in problems of optimization of hydrothermal systems where the thermal plant input-output curve considers the shape of the cost curve in the neighborhood of the valve points. The problem shall be formulated in the framework of nonsmooth analysis, using the generalized (or Clarke%26apos;s) gradient. We shall obtain a necessary minimum condition and we shall generalize the known result (smooth transition) that the derivative of the minimum presents a constancy interval. Finally, we shall present an example.

• 出版日期2014-7