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Optimization of the operation of a two-resevoir hydropower system Nash, Garth Andrew

Abstract

A method for optimizing the operation of a system of two hydraulically separate reservoirs serving the same demand area for hydropower production is described. The reservoir system is assumed to be operated, and import and export decisions made, so as to maximize the value of energy produced while considering the value of water stored in the reservoirs at the end of the model time horizon. The optimization considers uncertain reservoir inflows, energy demands, and electricity prices, and is subject to physical and operational constraints. The proposed method consists of two cascaded models. A longer-term monthly model based upon dynamic programming and linear programming is used to estimate the value of water stored in each reservoir as a function of the storage in both reservoirs, as well as the marginal values of water storage in the two reservoirs. Linear programming is used to evaluate the recursive equation in the dynamic program by making tradeoffs between releasing water, making energy trades, and keeping water in storage for the next month. The monthly energy value functions are input to the shorter-term model, which is based upon stochastic linear programming with recourse. The shorter-term model allows for the planning of operations and the calculation of marginal water values over periods shorter than one month. The time horizon in the shorter-term model is divided into time steps that may be of variable duration. Uncertainty in the model is handled through a scenario tree. Scenarios describe the values assumed by the inflows, demands, and prices in each time step. Sub-periods allow for the consideration of on- and off-peak periods. Application of the proposed model is made to a system based roughly on the two main river systems in the B C Hydro system—the Peace and Columbia. It is found that the marginal value of storage in the Columbia Reservoir is generally dependent upon the storage in both the Columbia and Peace Reservoirs, and vice versa. Regions of storage existed in which the marginal energy value in one reservoir was independent of storage in the second, although no general rules for identifying these regions were found.

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