Power transformers in converter stations of the high-voltage direct current (HVDC) transmission have to withstand a composite AC and DC voltage stress during operation, which can additionally be superimposed with fast transient overvoltages. Previous studies of the authors have shown that the dielectric behaviour of oil-paper insulation systems under DC voltage stress can be explained and simulated qualitatively with a charge carrier-based approach. Therefore, the aim is to investigate the dielectric behaviour of the oil-paper insulation system at a composite voltage stress of DC and light\-ning impulse (LI) voltage under consideration of the charge carrier-based approach. The results at composite voltage stress show that the DC voltage pre-stress influences the breakdown voltage of the arrangement compared to the results at DC or LI voltage stress. Comparing the results of the unipolar and bipolar superposition, the charge carrier species have different effects on the electric field distribution at composite voltage stress and thus on the dielectric strength of the arrangement. Hence, it can be shown that the fast polarity reversal after DC voltage pre-stress at the bipolar composite voltage is more critical compared to the unipolar composite voltage stress.