The solar collectors absorb solar irradiation and then produce thermal energy; however, they cannot generate electrical power. Electricity and thermal energy can be produced by the photovoltaic thermal module, simultaneously, while the outlet temperature of the photovoltaic thermal module is not usually high enough to provide thermal requirements of a building such as hot water or space heating. This work proposes a novel compound system created by the connection of a solar collector in series with a photovoltaic thermal module to resolve the issue of low outlet temperature in the photovoltaic thermal module and lack of electrical power in solar collectors. To examine the feasibility of this novel compound system, the performance of four systems, including photovoltaic unit, flat plate solar collector, photovoltaic thermal module, and compound system are numerically compared using a transient three-dimensional model. A parametric analysis is also performed to examine the impact of different operating conditions on the power outputs of the compound module. Furthermore, Taguchi based grey relational investigation is employed to indicate the optimum values and the contribution of operating conditions. Taguchi based grey relational examination indicates that the optimum value of mass flow rate, solar radiation, coolant inlet temperature, ambient temperature and wind speed are 50 kg/h, 1000 W/m(2), 24 degrees C, 28 degrees C and 1 m/s, respectively.