Including daily constraints in a monthly reservoir operation model for low-flow

In many real-world situations, operation of water resources systems are subject to constraints which are formulated on a daily basis. Since mathematical models (simulation or optimization models) are often developed on a monthly basis to avoid dimensionality problems and to reduce necessary computer time, some degree of approximation is necessary. Two examples are presented in order to show how this approximation can be done:

• •- a reservoir is operated for hydroelectric power production and low-flow augmentation is provided on a daily basis as a function of inflows (Lech River System in Germany)
• •- a reservoir is operated optimally for daily low-flow augmentation at a control gage downstream. The model includes also mandatory releases as constraints (Wupper River System in Germany).

In the first example the daily requirements are part of the constraints in the system, while in the second example the daily constraint concerns directly the objective function. Further, in the first case water can be saved and in the second case more water is needed as compared to calculations on a monthly basis.These examples are presented to show two solutions using envelope curves but other possibilities (i.e., regression analysis, constraints, coefficients) could be considered.