Insights on short-term hydropower scheduling: On the representation of water continuity equations

In this paper we introduce a geometric analysis of reservoir dynamics in the short-term operation of hydroelectric plants with both run-off-river and storage reservoirs. Based on minimum and maximum limits on water release, we calculate upper bounds on the evolution of reservoir storage levels over a given planning horizon. The resulting analytical framework will function as a general use tool to determine the necessity for representation of water continuity equations in short-term hydropower scheduling models. We present a numerical application of our framework to the Brazilian power system. We show that the vast majority of these plants do not require the representation of water continuity equations in their short-term scheduling models, given the insignificant sensitivity of reservoir storage and reservoir elevation levels in one-day horizons for practical assumptions.