The importance for reliable forecasts of incoming solar radiation is growing rapidly, especially for those countries with an increasing share in photovoltaic (PV) power production. The reliability of solar radiation forecasts depends mainly on the representation of clouds and aerosol particles absorbing and scattering radiation. Especially under extreme aerosol conditions, numerical weather prediction has a systematic bias in the solar radiation forecast. This is caused by the design of numerical weather prediction models, which typically account for the direct impact of aerosol particles on radiation using climatological mean values and the impact on cloud formation assuming spatially and temporally homogeneous aerosol concentrations. These model deficiencies in turn can lead to significant economic losses under extreme aerosol conditions. For Germany, Saharan dust outbreaks occurring 5 to 15 times per year for several days each are prominent examples for conditions, under which numerical weather prediction struggles to forecast solar radiation adequately. We investigate the impact of mineral dust on the PV-power generation during a Saharan dust outbreak over Germany on 4 April 2014 using ICON-ART, which is the current German numerical weather prediction model extended by modules accounting for trace substances and related feedback processes. ... mehrWe find an overall improvement of the PV-power forecast for 65 % of the pyranometer stations in Germany. Of the nine stations with very high differences between forecast and measurement, eight stations show an improvement. Furthermore, we quantify the direct radiative effects and indirect radiative effects of mineral dust. For our study, direct effects account for 64 %, indirect effects for 20 % and synergistic interaction effects for 16 % of the differences between the forecast including mineral dust radiative effects and the forecast neglecting mineral dust.