We present a combined numerical charge transport and morphology model to describe the current density-voltage (j-V) characteristics of three different, benchmark polymer: fullerene bulk heterojunction organic solar cells in which the device performance critically depends on the processing conditions or composition of the active layer. We find that an accurate description of the j-V characteristics over a broad bias range can be obtained when the actual complex, three-dimensional (3D) phase separation is represented by a simplified 2D or even 1D description. The morphological device model allows predicting the potential for increasing device performance by further optimizing the morphology. The optimal simplified morphology consists of two, relatively thin alternating vertically oriented slabs, that allow for fast lateral separation of photocreated holes and electrons. This morphology can effectively be described as 1D.