Improved Inflow Modeling in Stochastic Dual Dynamic Programming

Abstract

Stochastic dual dynamic programming (SDDP) is a widely used technique for operation optimization of large-scale hydropower systems in which reservoir inflow uncertainty is modeled with discrete scenarios produced by statistical time series models, such as the family of periodic auto-regressive (PAR) models. It is a common practice in statistical modeling of hydrologic time series to fit a well-known probability distribution (usually normal distribution) to the data by applying proper transformation. Box-Cox transformation is a commonly used transformation in the case of normal distribution fitting. The convexity requirement of SDDP means that nonlinearly transformed time series cannot be used for statistical inflow model calibration. In this paper, a linear approximation is proposed to estimate the expected value of the next stage inflow. In the proposed approach, next-stage inflows are estimated by a model that uses transformed time series. Furthermore, using the proposed linear approximation, it is shown that it is possible to utilize the time series transformed by Box-Cox transformation for scenario generation in SDDP. The Karoon multireservoir system in Iran has been used as a case study in order to show the effectiveness of the proposed method. Some concluding remarks have also been provided by comparing the results of the two SDDP models, with and without the proposed linear approximation.