Mixed integer linear programming formulations for the hydro production function in a unit-based short-term scheduling problem

The growing complexity of power system operation demands a greater performance of the modeling approaches, even for generation technologies already consolidated as hydroelectricity. Five mixed integer linear programming formulations for modeling the hydro production function (HPF) are compared: four based on previous references (the traditional method based on a single concave piecewise linear flow-power function, the rectangle method, the logarithmic independent branching 6-stencil method, and the quadrilateral method), and one firstly presented in the paper (the parallelogram method). The comparison is made in the context of daily and weekly hydro scheduling problems of a hypothetical three-plant system on different national day-ahead markets and using different levels of detail in the HPF discretization and time limits. The discussion of results is focused around the relative accuracy, effectiveness, and speed of the analyzed methods to solve the scheduling problems in order to aid in making the most appropriate choice depending on the time horizon. This discussion shows the logarithmic independent branching 6-stencil method as one of the most accurate, the parallelogram method as one of the most effective, and the traditional method based on a single concave piecewise linear flow-power function as the fastest one.

Automated summary

The study compares five mixed integer linear programming formulations for modeling the hydro production function, discussing their accuracy, effectiveness, and speed in solving hydro scheduling problems to help make the most appropriate choice depending on the time horizon. The logarithmic independent branching 6-stencil method is identified as one of the most accurate, the parallelogram method as one of the most effective, and the traditional method based on a single concave piecewise linear flow-power function as the fastest one.