Linear programming formulations for the hydro production function in a water value calculation

The global transition toward sustainability demands improved modeling approaches for energy sources like hydroelectricity. This study compares five linear programming formulations for modeling the hydro production function: four derived from prior works (the typical method based on a single concave piecewise linear flow-power function, a new parameterization of it, the upper convex hull method, and a linear version of the logarithmic independent branching 6-stencil method) and a novel approach introduced here (the binary function method). The comparison focuses on water value calculations, and subsequent scheduling simulations, for three hypothetical hydropower plants with varying reservoir regulation capacities across three national day-ahead electricity markets, using daily and weekly stages. The results highlight the linear version of the logarithmic independent branching 6-stencil method as the most accurate. For effectiveness, this method and the binary function method excel in daily and weekly stages, respectively. The classical parameterization of the single concave piecewise linear flow-power function is the fastest, while the new parameterization proposed here offers the best trade-off between effectiveness and speed. These findings provide actionable insights for selecting the most suitable method based on the stage length and reservoir regulation capacity, aiding in the optimization of hydropower operations in increasingly competitive electricity markets.