ABSTRACTThe use of pumps operating as turbines (PATs) is attractive to optimize the equipment costs of small hydropower plants. Unfortunately, the lack of information on the performance of PATs restricts the wide use of this technology. If a single characteristic curve is available, the behaviour of a PAT can be predicted by the application of the turbomachinery affinity law. In this paper, the reliability of the affinity law to predict the behaviour of a machine under variable speeds is discussed, and the results of this model are compared with an experimental database which includes the performance curves of five PATs operating at different speeds. The results show that the difference between the theoretical model and the experimental results is significant. Therefore, a new model, based on a relaxation of the affinity equations, has been proposed, in order to minimize the errors between the predicted and measured characteristic curves.