A model, derived from the detailed balance model from Shockley and Queisser, has been adapted to monolithically grown GaAsP/Si tandem dual junction solar cells. In this architecture, due to the difference of lattice parameters between the silicon bottom cell - acting as the substrate - and the GaAsP top cell, threading dislocations (TDs) arise at the IIIV/ Si interface and propagate in the top cell. These TDs act as non-radiative recombination centers, degrading the performances of the tandem cell. Our model takes into account the impact of TDs by integrating the NTT model developed by Yamaguchi et. al. Two surface geometries have been investigated: flat and ideally textured. Finally the model considers the luminescent coupling (LC) between the cells due to reemitted photons from the top cell cascading to the bottom cell. Without dislocations, LC allows a greater flexibility in the cell design by rebalancing the currents between the two cells when the top cell presents a higher short-circuit current. However we show that, as the TD density (TDD) increases, nonradiative recombinations take over radiative recombinations in the top cell and the LC is quenched. As a result, nonoptimized tandem cells with higher short-circuit current in the top cell experience a very fast degradation of efficiency for TDDs over 104cm-2. On the other hand optimized cells with matching currents only experience a small efficiency drop for TDDs up to 105cm-2. High TDD cells therefore need to be current-matched for optimal performances as the flexibility due to LC is lost.