The performance of solar cells in realistic operating conditions usually differs from the specified efficiency at standard test conditions (STC). Among other factors, the illumination intensity (irradiance) is often lower than at STC, which leads to a lower device efficiency. Therefore, it becomes important to optimize the output power at low-light conditions in order to achieve a high energy yield at a specific location. For this purpose, it is essential to have a detailed knowledge of the relevant parameters that govern the low-light behaviour. This study investigates the impact of the diode parameters on the low-light performance of thin-film solar cells based on chalcopyrite Cu(In,Ga) (S,Se)2 absorbers. Experimental irradiance-dependent current-voltage results are analysed with the help of an analytical model. For each parameter the contributions of its absolute value and its irradiance dependence are assessed. Additionally, relations between the diode parameters and material parameters are examined by analysing different cell variations. The results show that cell performance at low-light conditions is primarily governed by the irradiance dependence of the fill factor, which in turn is mainly determined by the parallel resistance of the device. Moreover, a reduction of the dark saturation current and the ideality factor towards lower irradiances is observed which indicates an irradiance-dependent change of recombination dynamics. The consequence is an increase of the open-circuit voltage at low-light conditions which indirectly also boosts the fill factor. The results suggest that cell optimization for low-light conditions should focus on improving the parallel resistance and tuning recombination in a way that the dark saturation current decreases with decreasing irradiance.