Concentrated photovoltaic is a promising route to achieve high efficiency solar conversion. Concentration of sunlight increases the irradiation on panel along with its temperature. At higher temperature, the efficiency of the cells drops necessitating active cooling. However, flow of a coolant consumes pumping-power leading to reduction in net power output. These two counter-acting factors lead to a two-stage optimization for designing an advection cooled concentrated photovoltaic (ACCPV) system. Here, we attempt developing a design methodology where standard numerical scheme for solving a multi-level conjugate heat problem is utilized to obtain optimal operating conditions in terms of the coolant flow rate, and the sunlight concentration ratio for a series of widely used photovoltaic materials: a-Si, m-Si, p-Si, CIGS, CdTe. For the chosen ACCPV geometry, the estimated concentration ratios are computed to be 7, 9, 9, 16 and 20 for m-Si, p-Si, CIGS, p-Si and CdTe cells, respectively. Even though the estimated values of optimal parameters depend on the choice of PV material, coolant and the geometry of the system, the methodology presented here is universally applicable for any such ACCPV system. The general intuition - higher the irradiation, better the performance - is demonstrated to be false through the present analysis.