Nonlinearities in Reservoir Operation for Hydropower Production

This work presents a methodology to simplify the nonlinearities involved in reservoir operation that may contribute to the development of simulation and, particularly, optimization models applied to energy generation and multiple uses of the water in complex reservoir systems. The nonlinearities studied include water level, area and storage relations in the reservoirs, as well as evaporation. The proposed methodology uses linear and polynomial regression to simplify the level-area-storage curves, often represented by fourth degree polynomials. For evaporation, the calculation proposed is based on the history of monthly averages storages and corresponding areas before the optimization process, eliminating the need of calculating the area that represents a nonlinear constraint in the optimization problems. The methodology was added in HIDROTERM, a nonlinear programming model applied to optimize the management and operation of the Brazilian hydrothermal system, a linked network with 143 reservoirs in which 68 are run-of-river and 75 have storage to regulate flows. Using a very conservative setting, without compromising accuracy in results, all reservoirs had level-area-storage curves simplified to first or second degree polynomials. For evaporation, only two reservoirs had a difference in the standard deviation greater than 0.5% of the long term average inflow from the estimated value to the calculated one. The processing time was reduced on average by 52%. This reduction is very welcome given that a new stochastic version of the model is currently under development, originally deterministic, with a large increase in the problem's dimensions.