Multipurpose Multireservoir System Research Articles

Building flood control rule curves for multipurpose multireservoir systems using controllability conditions

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 simulation model for operating a multipurpose multireservoir system

This paper describes a mathematical model used for assessing alternative policies of operation for the Trent River system in Ontario, Canada. The Trent basin is characterized by numerous reservoirs (48 were represented in the model), each with a control structure(s) in its outlet channel(s). The reservoir system is used for flood control, water supply, hydropower, and augmenting flows through the canal system during the summer period. The need for assessing alternative policies arose from growing conflicts in recent years over satisfying all of the many water‐based needs of the basin. To aid in assessing the impact of alternative policies, a simulation model was developed and applied. Every reservoir was subdivided into five storage zones (which were variable in a temporal sense). A time‐based rule curve was also prescribed to represent ideal reservoir operation. Ranges were prescribed for channel flows, which were dependent on water‐based needs. The underlying concept of the model was the functional (or mathematical) representation of the chief operator's perception of ‘Optimum’ operation and the derivation of this solution using a nested optimization submodel. ‘Penalty coefficients’ were assigned to those variables which represented deviations from ideal conditions. Different operational policies were simulated by altering relative values of these coefficients. The development and use of the model were simplified by representing the entire reservoir system in ‘capacitated network’ form and deriving optimum solutions for individual time periods with the ‘out‐of‐kilter’ algorithm. Besides being computationally efficient this algorithm simplified model development and permitted flexibility in readily using the model for a wide range of reservoir configurations and operating policies.

Comment on ‘Capacity decisions in a multipurpose multireservoir system’ by Satish Nayak and Sant R. Arora

Comment on ‘Capacity decisions in a multipurpose multireservoir system’ by Satish Nayak and Sant R. Arora

Capacity decisions in a multipurpose multireservoir system

A mathematical programing model is proposed to solve the common and formidable water resource planning problem of finding the best sites from a number of potential sites for constructing a system of reservoirs that will optimally meet the various water demands. Since flood damages and shortage costs (the primary problems the reservoirs are designed to solve) usually vary nonlinearly with the flow values, a nonlinear programing model is proposed. The fact that the variables in the objective function, which minimizes the sum of the annual amortized cost of the reservoirs and the annual flood and shortage losses less the annual recreational benefits, and the variables in the constraints are separable has been used to reduce the nonlinear problem to a separable problem. The common approximate approach to the problem, which chooses the optimal design parameters on the basis of straight historical inflow data for a specified period, was selected over the more complex ideal approach, which quantifies the stochastic nature of the historical inflows and uses the inflow distributions in an optimization model to select the design parameters. The optimization in this paper considers the flood inflows (based on a given flood frequency) and the drought inflows (based on the severest drought on record) simultaneously. The damages due to shortages may be weighted further in the objective function. The present model differs from other models in that releases are constrained only by the availability of water and their optimal values are determined by balancing damages downstream against the cost of providing storage to prevent them. The model is applied to U.S. Army Corps of Engineers data for the Minnesota River basin, and the results are compared with the plan proposed by the Corps.

A dynamic programming successive approximations technique with convergence proofs

This paper discusses a successive approximations technique based on dynamic programming. The basic idea of the method is to break up a problem containing several control variables into a number of subproblems containing only one control variable. Each subproblem has fewer state variables than the original problem; in the case where there are as many control variables as state variables, each subproblem has only one state variable. Because the computational requirements of dynamic programming increase exponentially with the number of state variables, this technique is capable of producing extremely large reductions in computational difficulty.The paper is divided into two parts. The first part describes the method in detail and works out an illustrative example. Other applications of the method, including the optimization of a multipurpose multi-reservoir water-resource system and an airline scheduling problem with 100 state variables, are discussed.The major drawback to the use of this method is the difficulty in ascertaining whether or not the true optimum solution is obtained. The second part of this paper presents proofs that the method converges to the true optimum solution for three important classes of problems, all of which are related to certain convex programming problems.