Automatic estimation of reservoir inflows of Alpine hydropower cascade systems using level and outflow data

Alpine hydropower reservoirs play a crucial role in the energy system as a source of renewable energy and energy storage, as well as in water management mitigating the impacts of extreme events and augmenting freshwater availability. The effective operation of hydropower reservoirs requires knowledge of the expected inflows, and the inflows prediction methods usually require the historical series of observed inflows. The reservoir inflow is often estimated because it is hardly measurable due to its spatial distribution along the reservoir sides. However, traditional methods such as the Simple Water Balance for estimating inflows can yield fluctuating and potentially negative results due to errors in water level measurement and stage-storage relationships. This study focuses on the estimation of inflow to ten reservoirs belonging to three different hydropower cascade systems situated in the Italian Alps. Two new methodologies to estimate reservoir inflow are proposed. The first (Optimized Inflow Estimation from Water Balance, OIEWB) consists of an optimization-based method and extends a known literature optimization technique to cascade reservoirs. In particular, the OIEWB method estimates the inflows to cascade reservoirs solving a bi-objective optimization problem aiming to minimize both the differences between consecutive inflow and the differences between observed and estimated water levels. It also includes an automatic calibration of the weight of the objectives according to the physical characteristics of each reservoir, avoiding any a priori calibration. The second (Filtered Inflow Estimation from Water Balance, FIEWB) consists of a low-pass filter shaped as a piecewise linear function whose slope is defined, again, by the physical characteristics of each reservoir. The low-pass filter is applied to the SWB cascade reservoir inflow to remove the high-frequency fluctuations that can be generated by measurement and estimation errors. The proposed procedures have been compared with the traditionally used ones in terms of Inflow Variability (the difference between inflow at two consecutive time steps) and Storage Error (the difference between the estimated reservoir storage and the observed one). Results show that both the OIEWB and FIEWB methods generate smoother inflows compared to the SWB, reducing the average Inflow Variability standard deviation, of 86.6% and 79.3%, respectively. However, the FIEWB does not guarantee the positivity of the inflows and can lead to large Storage Errors. The OIEWB method has been found to be more flexible and automatically adaptable to reservoirs with a wide range of physical characteristics. Nevertheless, a relationship between the OIEWB and the FIEWB has emerged. This relationship can be used to design new low-pass filters that can emulate the behavior of the OIEWB, combining the flexibility of the latter with the simplicity of the FIEWB. By contributing to provide more accurate and reliable inflow predictions, the proposed methodologies reveal their utility in optimizing cascade reservoir operation, thereby facilitating better decision-making.