A simulation model for operating a multipurpose multireservoir system

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Abstract
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.