Photovoltaic (PV) modules are sensitive to the spectral distribution of solar irradiance. Although numerical weather prediction (NWP) models compute irradiance in several spectral bands, only broadband quantities are provided in the standard outputs used for PV forecasts. This study investigates how this lack of information impacts PV power estimation. A physical PV model is first designed that accounts for the spectral distribution of irradiance and the spectral response of the panels. This model is evaluated using measurements performed at Site Instrumental de Recherche par Teledetection Atrnospherique (SIRTA), Palaiseau, France. The mean relative difference between simulated and measured PV power for a monocrystalline silicon module of 250 W nominal power is -0.9%, and the mean bias is -2.0 W. This model is then used to investigate the impact of solar zenith angle and clouds on the performance of PV modules. PV performance can increase in cloudy conditions by 5% through spectral filtering of near-infrared irradiance, and by 18% when only the useful irradiance is considered to compute performance. This spectral effects is not captured by the PV model when only broadband irradiances are used. In such case errors up to 15% are obtained in simulated PV power compared to using a state-of-the-art NWP model providing irradiance in 14 spectral bands. More generally, broadband global horizontal irradiance appears insufficient for accurate PV power modelling, highlighting the added value of spectrally-and-angularly-refined irradiances. This stresses that PV models should use more detailed irradiance inputs, which could be easily achieved by exploiting internal variables of NWP models.