Multi-Plant Hydro Power Production Function Modeling: Application To The Stochastic Mid-Term Hydrothermal Planning Problem

This work proposes the modeling and application of the so-called "multi-hydro plants'' for the stochastic mid-term hydrothermal planning problem. The approach consist in aggregating sub-cascades of hydroelectric plants based on the fact that the operation of the cascades is dictated only by decisions on the release of the reservoirs with regularization capacity, and the operation of run-of-the-river plants is a consequence of such decisions. As a consequence, we obtain a formulation of the problem with a smaller number of variables and constraints, without any loss of representation of the physical and operation constraints of the hydro plants. This yields a reduction in the computational time to solve typical stochastic hydrothermal coordination problems of more than 20%, and results are presented for a real case of the Brazilian system. Furthermore, there is even a gain in accuracy of about 6% in the approximation of the non-concave hydro production function, and an analytical investigation regarding this aspect is conducted.