The increasing penetration of renewable generation plants in electric systems, combined with the development of effective short-term energy storage batteries, demand scheduling to be represented on an hourly basis or even in smaller time intervals. Multistage stochastic optimization in such time resolution would imply in the increase of the problem s dimension, which might result in the impossibility of solving such problems. This work presents a method that is able to take into account such small time intervals while avoiding the considerable increase of computational effort. This method consists in calculating the analytical representation of the immediate cost function that is applied in the context of stochastic dual dynamic programming (SDDP). The function represents immediate operation costs as a function of the total hydroelectric generation optimal decision. As the immediate cost function is piecewise linear, it leads to a structure very similar to the one used to approximate the future cost function (cut sets). Results of the application of the method in real electric systems are presented.