The paper deals with the three-dimensional theoretical and numerical investigation of the electrical performance of a Photovoltaic System (PV) with active fluid cooling (PVFC) in order to increase its efficiency in converting solar radiation into electricity. The paper represents a refinement of a previous study by the authors in which a one-dimensional theoretical model was presented to evaluate the best compromise, in terms of fluid flow rate, of net power gain in a cooled PV system. The PV system includes 20 modules cooled by a fluid circulating on the bottom, the piping network, and the circulating pump. The fully coupled thermal and electrical model was developed in a three-dimensional geometry and the results were discussed with respect to the one-dimensional approximation and to experimental tests. Numerical simulations show that a competitive mechanism between the power gain due to the cell temperature reduction and the power consumption of the pump exists, and that a best compromise, in terms of fluid flow rate, can be found. The optimum flow rate can be automatically calculated by using a semi-analytical approach in which irradiance and ambient temperature of the site are known and the piping network losses are fully characterized.