Assessing solution quality and computational performance in the long-term generation scheduling problem considering different hydro production function approaches

The long-term generation scheduling (LTGS) problem aims at finding a generation policy that minimizes an objective function over a multi-year planning horizon. A crucial aspect of this problem is the Hydropower Production Function (HPF), which relates power with head, turbined outflow, and efficiency of the generating units. Given that the LTGS is a large-scale stochastic optimization problem, the HPF is modeled in a simplified manner. However, considering the high-performance computers currently available and the recent advances in stochastic optimization algorithms, it is possible to enhance the HPF modeling to use the energy resources more efficiently. This paper proposes a piecewise linear model of HPF that considers the plant generation as a function of the volume and the total outflow. Unlike previous works, the HPF also considers the (nonlinear) efficiency function of each generating unit. The paper also presents a comparison between the proposed HPF and a one-dimensional HPF known as constant productivity. The generation policy and the computational burden are analyzed using an optimization-simulation process based on Stochastic Dual Dynamic Programming algorithm. The computational tests use data of a large-scale electrical power system, which corresponds to about 90% of the Brazilian system.