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The unconvertible portion of incident radiation on solar panels causes an increase in their temperature and a decrease in efficiency due to the negative temperature coefficient of the maximum power. This problem is dealt with through the use of cooling systems to lower the temperature of photovoltaic (PV) panels. However, the developments are focused on the loss of efficiency or extract the heat out of the solar panel, rather than optimizing the solution to produce a net gain in the electric power output. Therefore, this study proposes the analytical model for the cell temperature, irradiance and design of absorbers. Furthermore, the cooling systems for the hybrid solar panels were developed through analytical modeling of the solar cell temperature behavior and heat exchange between the fluid and back surface of the PV module in MATLAB. The design parameters such as mass flow rate, input power, solar cell temperature, velocity, height, number of passes and maximum power output were optimized through a multi-objective, multivariable optimization algorithm to produce a net gain in the electrical power. Three layouts of heat absorbers were considered—i.e., single-pass ducts, multi-pass ducts, and tube-type heat absorbers. Water was selected as a cooling medium in the three layouts. The optimized results were achieved for the multi-pass duct with 31 passes that delivered a maximum power output of 186.713 W at a mass flow rate of 0.14 kg/s. The maximum cell temperature achieved for this configuration was 38.810 °C at a velocity of 0.092 m/s. The results from the analytical modeling were validated through two-way fluid-solid interaction simulations using ANSYS fluent and thermal modules. Analyses revealed that the multi-pass heat absorber reduces the cell temperature with the least input power and lowest fluid mass flow rate to produce the highest power output in the hybrid PV system.