Improved prediction model of energy performance for variable-speed pumps-as-turbines (PATs) in micro-hydropower schemes

Abstract

The variable speed regulation in pumps-as-turbines (PATs) plays a pivotal role in micro-pumped hydro energy storage (MPHES) systems by expanding operational parameters, optimizing energy conversion efficiency, and augmenting system adaptability through enhanced dynamic response characteristics. While existing studies have proposed empirical formulas, these models are often limited to optimal operating points under specific conditions, leaving their accuracy and applicability under broader variable speed conditions insufficiently validated. This paper presents an improved prediction model for the energy performance of variable-speed PATs, integrating turbine theoretical models with composition analysis method to modify the affinity laws. The model utilizes a segmented analysis approach that classifies the affinity laws into three categories based on speed ratios, ensuring more accurate predictions across diverse operating conditions. An improved whale optimization algorithm is employed to systematically refine the coefficients of the modified affinity laws. The most optimal modification is selected through a comparison of R² values for each model. The proposed model demonstrates a significant enhancement in prediction accuracy, particularly for low and high speed ratios, with an average improvement of 10 % over existing models. This work addresses critical gaps in current PAT energy performance prediction methods and provides a more robust framework for optimizing energy efficiency in micro-hydropower systems.