Probabilistic long-term reservoir operation employing copulas and implicit stochastic optimization

This paper explores and combines implicit stochastic optimization (ISO) with copula functions to simulate long-term operating policies for a hydropower reservoir located in the Northeastern region of Brazil. Overall, ISO is considered as one of the most reliable techniques to derive long-term reservoir operating rules for reservoirs. This method employs a deterministic optimization model to estimate the optimal reservoir allocations under different inflow scenarios and later constructs operating rules for each month by relating the ensemble of the optimal releases, the initial storage volume and future inflow values. Those rules are generally established by fitting approaches including linear regression or nonlinear methods. This work illustrates the applicability to combine copulas with ISO to define reservoir operation policies based on a probabilistic procedure. Firstly, synthetic streamflow scenarios are simulated using a periodic vine copula model. Afterward, optimal release data are estimated by ISO for a set of inflow scenarios. Joint probability distribution functions based on copulas are constructed in order to forecast the expected release, conditioned to the initial reservoir volume and future inflows data. Results indicate that the proposed model represents a flexible approach to construct operating rules and derive long-term reservoir operating policies with low variability, allowing to reproduce different dependence structures of simulated data.