Non-proportional Repartition Rules Optimize Environmental Flows and Energy Production

In order to meet the growing demand for energy, the development of hydropower leads to an increase of the river exploitation by human activities. Thereby, water management has become a major issue in the energy transition. A better definition of the flow release rules is now required to improve the Minimal Flow Requirement (MFR) concept, which has long been used in spite of its environmental inconsistency. In this work, we present a class of non-proportional redistribution rules that broadens the spectrum of dynamic flow releases based on proportional redistribution for run-of-the-river power plants. We adapt the mathematical form of the Fermi-Dirac statistical distribution to engineer a novel class of redistribution functions. In particular, such functions are used to define the fraction of water allocated to the environment depending on the inflow at the intake. The theoretical background as well as the economic interpretation is presented, and the ability to generate variable flow releases carefully discussed. MFR, proportional and non-proportional distribution policies are then applied to a real case study and their respective economic and environmental efficiencies quantitatively compared. We show that non-proportional distribution policies allow for operating conditions actually close to the Pareto frontier, which improve both efficiencies with respect to those obtained from some traditional MFR and proportional policies.