2.3.1. FPV Operating Temperature

The energy produced by a photovoltaic system depends on the electrical efficiency of the modules. The electrical efficiency of the modules (η*e*) changes with the operating temperature of the cell and is calculated using Equation (25) [45,84]:

$$
\eta\_{\rm ef} = \eta\_{ref} \times \left[1 - \beta \times \left(T\_{co} - T\_{ref}\right)\right] \tag{25}
$$

where η*re f* (%), β*re f* (%/ ◦C), *Teo* ( ◦C), and *Tref* ( ◦C) are, respectively, the reference efficiency of the panel, the temperature coefficient of the panel, the effective operating temperature of the panel, and the reference temperature.

The data collected from the FPV test bed are used to determine the effective operating temperature (*Teo*) of the FPV. The model describing the temperature dependence on the ambient temperature and the solar power in nominal operating cell temperature (NOCT) conditions is a linear model [84–86]:

$$T\_{\rm cell} = T\_{\rm mc} + k \times I\_S \qquad \quad \text{(}^\circ\text{C)}\tag{26}$$

*TCell* ( ◦C) is the operating temperature of the solar cells, *k* ( ◦C. m2/W) is the coefficient of the relationship, *IS* (W/m2) is the solar irradiance, and *Tme* ( ◦C) is the ambient temperature of the location of the solar module. This model is well-adapted for offshore, roof or ground mounted, PV systems but needs to be modified to accurately describe FPV systems. A study conducted by Kamuyu et al. [45] has proposed a solar cell temperature calculation in FPV using the air temperature, the water temperature, the solar irradiance, and the wind speed. Kamuyu et al.'s study focused on FPV mounted at a tilt angle relative to the water's surface where the air temperature and wind speed played a larger role in determining the module temperature than the water temperature. In this study, because the modules are on/under the water surface, wind speed is neglected, and the water temperature plays the dominant role in module temperature. Thus, the Kamuyu approach for pontoon-based FPV was adapted and used here with experimental data for solar flux, air temperature, water temperature, and module temperature. The approach used was a multilinear variable regression. The regression has three independent variables that are the solar irradiance (*IS*), the water temperature (*Tw*), and the air temperature (*Ta*). The last variable of the regression, the FPV module's effective operating temperature (*Teo*), depends on the previous three. The goal of the regression is to find a linear relationship between the module's effective operating temperature (*Teo*), and the three independent variables in the form of:

$$T\_{\rm av} = \alpha\_0 + \alpha\_1 T\_w + \alpha\_2 T\_a + \alpha\_3 I\_S \qquad (^{\circ}\text{C}), \tag{27}$$

where α<sup>0</sup> is a constant term; α1, α2, and α<sup>3</sup> are the regression coefficients relative to the water temperature, air temperature, and solar irradiance, respectively.

The solar module temperature dataset from the test bed has been stored in a MATLAB column vector, and the independent variables have been stored within a MATLAB numeric matrix to which an additional unit column has been added at the beginning to account for the coefficient α0. Then, the regression is performed using a dedicated MATLAB function called "regress" [87]. The "regress" function performs a multivariable regression on experimental data and outputs the coefficients of the regression as well as other values such as the R-squared value of the regression and the residuals. The experimentally obtained coefficients are used in the case study of Lake Mead to estimate the effective operating module temperatures that are, in turn, used in the energy yield simulation.
