Upconverter materials and upconverter solar devices were recently investigated with broad-band excitation revealing the great potential of upconversion to enhance the efficiency of solar cell at comparatively low solar concentration factors. In this work first attempts are made to simulate the behavior of the upconverter β-NaYF4 doped with Er3+ under broad-band excitation. An existing model was adapted to account for the lower absorption of broader excitation spectra. While the same trends as observed for the experiments were found in the simulation, the absolute values are fairly different. This makes an upconversion model that specifically considers the line shape function of the ground state absorption indispensable to achieve accurate simulations of upconverter materials and upconverter solar cell devices with broadband excitations, such as the solar radiation.