A generalized theoretical methodology to forecast flow coefficient, head coefficient and efficiency of Pumps-as-Turbines (PaTs)

Among the most used hydraulic machines in the small-scale hydropower sector, Pump-as-Turbine (PaT) technology is suitable for both practical and economical aspects. These machines are already profitably applied in remote and rural zones for electricity production and in energy recovery applications in both civil and industrial plants, like Water Distribution Networks (WDNs) and chemical plants. Several studies aimed to provide theoretical formulas able to forecast flow rate and head at the Best Efficiency Point (BEP) in turbine mode obtaining, however, contrasting results and a lack of generalization. In this work, a generalized theoretical methodology for forecasting the flow rate, the head and the efficiency of PaTs at their BEP is studied. Specific correlations between the non-dimensional parameters of PaTs in pump and in turbine mode are presented and discussed. The accuracy of the presented methodology is compared to the ones available in literature showing a good generalization capability and a significant improvement in forecasting the behaviour of the PaT, starting from the available performance characteristics in pump mode.