Abstract
We study the operation of a cascade of hydropower stations for given time varying prices and given inflows. The objective is to maximize the value of the power output, under constraints on final reservoir contents. The flow of the river is modeled through nonlinear partial differential equations (PDEs), the St. Venant equations, which are solved iteratively. For the stations, empirical but smooth efficiency curves are employed. Exploiting the structure of the problem, a descent method of reduced gradient type is developed. Convexification is used to avoid getting trapped in local minima. Further scaling of the problem has been applied with rather dramatic success. MATLAB computations on a small but realistic problem are presented.
The project is funded by Vattenfall AB and the Swedish Research Council for Engineering Science.
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Lindberg, P.O., Wolf, A. (1998). Optimization of the Short Term Operation of a Cascade of Hydro Power Stations. In: Optimal Control. Applied Optimization, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6095-8_15
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DOI: https://doi.org/10.1007/978-1-4757-6095-8_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4796-3
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