Efficiency of ultrathin flexible solar photovoltaic silicon microcell arrays can be significantly improved using nonimaging solar concentrators. A fluorophore is introduced to match the solar spectrum and the low-reflectivity wavelength range of Si, reduce the escape losses, and allow the nontracking operation. In this paper we optimize our solar concentrators using a luminescent/nonluminescent photon transport model. Key modeling results are compared quantitatively to experiments and are in good agreement with the latter. Our solar concentrator performance is not limited by the dye self-absorption. Bending deformations of the flexible solar collectors do not result in their indirect gain degradation compared to flat solar concentrators with the same projected area.