Building flood control rule curves (FCRC) for multipurpose multireservoir systems involves treating simultaneously the stochasticity of future inflows and the multivariate aspect of the problem. The study demonstrates how theoretical findings concerning flood control multireservoir systems regulation obtained by Marien (1984) (the so‐called controllability conditions) can be used to build generalized FCRC in multipurpose multireservoir systems. These FCRC are generalized FCRC in the sense that they consist of a time varying constraint set on the needed empty space provisions in the different reservoirs of the system. The applicability of the proposed technique is enhanced by the derivation of new controllability conditions for systems with more than one flood control section and mandatory releases. By means of several examples, it is shown how the proposed methodology is superior to the approach which consists of lumping all the reservoirs of the system into a single imaginary reservoir. A practical example with an eight‐reservoir hydropower system in Brazil demonstrates the applicability of the methodology.
A number of theoretical results are presented concerning the necessary and sufficient conditions under which there exists a regulation for a multireservoir flood control system with given deterministic inflows such that no flooding occurs at a flood damage center situated downstream. These so‐called controllability conditions have a very simple form for a large variety of multireservoir systems; they can be reduced to the existence of a no‐flood control for a number of simple single reservoirs associated with the original system. It is then suggested how these findings can be used as an aid in the planning and operation of structural flood control systems. A practical example is given with numerical results that are impossible to obtain without the use of the theoretical findings on controllability.
A methodology is presented for the optimal design of flood control volumes in a multireservoir system with one downstream critical section. The design is optimal in the sense that the objective function attempts to minimize the penalties associated with providing the flood protection. Moreover, the method explicitly considers a set of probability constraints on the occurrence of floods. The proposed calculation scheme is easily applied to almost any type of multireservoir system. The methodology is applied to the problem of determining the flood control volumes to be provided in a hydropower system of eight reservoirs on the Parana river in Brazil. In that case the objective function consists of minimizing the total firm energy loss.
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