A comparison of static and dynamic models for hydro production in generation scheduling problems

Static piecewise linear models for hydro production are largely employed when a generation scheduling problem is formulated as a linear or mixed integer optimization program. Even though such models may provide a satisfactory representation of hydro generation as compared to the real nonlinear function, breakpoints of the function become natural candidates to optimal solutions of the problem. Such behavior might be an inconvenience for real market applications, where small deviations in hydro generation may lead to significant variations in GENCOs revenues. This drawback can be overcome by increasing the number of breakpoints in the static model to very large values, or by employing a dynamic model where linear approximations are adjusted as the solving procedure of the problem evolves. This paper compares the performance of static and dynamic models for hydro production in optimal generation scheduling problems, regarding CPU times and quality of the solution. Results are presented for test cases based on the real Brazilian hydroelectric system.