We present a two-dimensional model of a bulk heterojunction solar cell in which we include the effects of optical interference, exciton diffusion, charge separation via the formation of polaron pairs, and charge transport in two separate interpenetrating phases. Our model shows that the current is increased by an order of magnitude with a full optical model compared to assuming that absorbed photons have a Lambertian profile, and depends much more strongly on applied bias when dissociation via polaron pairs is considered. We find a power efficiency at solar intensities of 1-3% depending on the morphology, and show that the fill factor decreases from 40% at low intensities to 20% at solar intensities because of the increase in the open circuit voltage and decreases much more rapidly at higher intensities due to the decrease in the power efficiency.