Abstract
Accurate photovoltaic module performance prediction under low-light conditions remains challenging for energy yield estimation, especially in Northern Europe where over 50% of annual irradiance falls below 400 W/m². We present a three-parameter beta-fit model that characterizes non-linear module efficiency across the full irradiance spectrum using compact empirical descriptors. The model describes the low-irradiance response using empirical parameters: the limiting relative efficiency loss α and the curvature parameter β. Near reference irradiance, the first-order response is primarily determined by their product, α and β. Accordingly, α and β should be interpreted jointly, rather than as independent physical measures. This approach enables meaningful comparisons of fitted low-irradiance responses among modules when equivalent-circuit parameters are unavailable. We developed a comprehensive Python analysis toolchain with robust statistical filtering, temperature normalization, and constrained non-linear regression with optional weighting for the critical 100–400 W/m² range. Field validation using long-term outdoor monitoring data from commercial crystalline silicon modules demonstrates excellent performance with root-mean-square errors below 0.5% absolute efficiency. An extended four-parameter formulation incorporating a high-irradiance correction term (γ) addresses systematic deviations which were found in controlled laboratory flash measurements. We implemented a statistical binning method that reduces outdoor data scatter while preserving underlying physical behavior. Comparative yield simulations across European locations reveal the beta-fit approach can produce estimated yield differences of up to 0.5% relative to conventional linear assumptions, with larger differences at higher latitudes. The methodology requires only standard input data, making it practical when full manufacturer equivalent-circuit specifications are unavailable, while providing standardized parameters.