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UBC Theses and Dissertations

General equations for short-range optimization of a combined hydro-thermal electric system Arismunandar, Raden Artono


This thesis offers a review and an analysis of all except the less important advances of the previously developed methods and equations for optimizing the operation of an electric system of m thermal and n hydro plants. In this analysis both short-range (twenty-four hours, seven days) and long-range (one year) periods are involved. The primary objective of this thesis is to derive, using the Calculus of Variations, general differential equations for short-range optimization of combined hydro-thermal systems. The basic criterion for choosing to solve the short-range instead of the long-term problem lies in the theory of forecasting in general, the theory of forecasting of stream flows in particular, and is based on the aforementioned analysis. Tests for establishing the fact that the above general equations actually produce the desired minimum cost of operation are given in the form of three other necessary conditions and three sufficient conditions. These conditions are known in this branch of mathematics as the analogue of Legendre's condition, the Weierstrass’ analogue of the Jacobi's condition and the Weierstrass' E-function condition for a minimum. A well-known example is worked out using these conditions. In addition to the above, this thesis also proves that all previously developed methods and equations for short-term optimization are essentially equivalent, and that these formulas are merely simplified forms of the general equations developed in this treatise.

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