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Optimal discretization of net head dependency in heterogeneous multi-reservoir hydroelectric systems

Modeling the net head dependency of hydro-power plants constitutes a severe challenge from the optimization point of view. One possible approach is to pre-establish a discrete set of representative net heads and to formulate the hydro scheduling problem assigning binary variables to activate the net head that better matches the reservoir level at each time interval. Given that increasing the number of binary variables can compromise the complexity of the resulting problem, the total number of discrete possible values must be bounded. In the case of multi-reservoir systems with heterogeneous power plants, the common practice of assigning the same number of discrete values for all the power plants could not be efficient as some binary variables might be providing too much accuracy in plants with a low impact on the global results, whereas plants with higher impact could be poorly represented. Given a maximum number of available binary variables, this paper presents a method to determine how many different net head values should be used for each power plant based on their technical characteristics. The proposed method is applied to a realistic system with satisfactory results.