Empirical Estimation of Hydraulic Turbine Efficiency Under Aging and Partial-Load Conditions

Evaluating the efficiency of hydraulic turbines in existing hydroelectric power plants is often challenging due to the absence of complete manufacturer curves, a lack of reliable historical data, or nonexistent formal efficiency testing. This is especially common among units that have been operating for many years. While technical standards define rigorous procedures for determining efficiency under controlled conditions, there is still a lack of systematic approaches suited to data-constrained environments. This study proposes an empirical methodology for estimating the efficiency of hydraulic turbines in service. The approach is based on defining a reference efficiency value related to specific speed, followed by applying successive penalties to account for partial load operations and aging effects. The formula is expressed in the dimensionless efficiency domain and adopts a multiplicative structure that explicitly incorporates the main loss mechanisms. The methodology was then applied to a case study evaluating a Small Hydroelectric Power Plant, specifically on a 26-year-old refurbished Francis unit, yielding an estimated efficiency of approximately 79%. A comparison between linear and exponential degradation models showed a difference of less than 0.1 percentage point, while energy-balance validations showed a difference of less than 3%. The results demonstrate that this method offers a physically consistent and practical tool for assessing the performance of older hydroelectric plants, particularly under limited data availability conditions.