# Progress in Improving Photovoltaics Longevity
## 3 Theory: PV Electricity Generation and Degradation Rate  
### PV Electricity Generation  
The total irradiance, \(G_{F}\), on the PV surface is given by adding the beam component, \(G_{b}\), to the diffuse component, \(G_{d}\):  
\[G_{F}=G_{b}+G_{d}. \tag{1}\]  
[PERSON] et al. [22], in their recent publication, analytically calculate the direct irradiance component with the assistance of an optical model [23]. Then, based on the Perez model [24], they determine the diffuse component.  
The solar position algorithm [25], developed by the National Renewable Energy Laboratory (NREL), provides precise solar path data, such as zenith \((z)\), elevation angles \((\theta)\), and solar azimuth \((\gamma_{\text{s}})\), at any time and geographical coordinate. Alternatively, these parameters can be calculated by [26] for typical cities in Europe. The optical model is based on two irradiance components: beam and diffuse. A clear schematic illustration of these components for a PV module is presented in Figure 2.  
Figure 1: Schematic illustration of the methodology that the review followed.  
From the total solar power incident on the module, the absorbed portion is given as follows:  
\[P_{sun}=a_{m}G_{F}, \tag{2}\]  
where \(a_{m}\) is the absorptivity of the module, weighted by the solar spectrum (e.g., AM1.5 or ASTM G173-03 [27] simulated spectrum).  
For typical PV modules, which consist of \(N_{s}\) cells connected in series and \(N_{p}\) cells connected in parallel, the relationship between current and voltage is given as follows:  
\[I=I_{ph}-I_{0}\left[\exp\left(\frac{q\left(VN_{p}+R_{s}I\right)}{N_{s}N_{p}nk_ {B}T}\right)-1\right]-\frac{VN_{p}+R_{s}I}{N_{s}N_{p}R_{p}}, \tag{3}\]  
where \(I\) is the output current and \(V\) the output voltage. \(I_{ph}\), \(I_{0}\), \(N_{s}\), \(N_{p}\), \(R_{s}\), and \(R_{p}\) represent the photocurrent, the diode saturation current, the number of cells in series and in parallel, the series resistance, and the parallel resistance, respectively, \(q=1.602\times 10^{-19}\) C is the charge of the electron, \(k_{B}=1.381\times 10^{-23}\) J/K is the Boltzmann's constant, \(T\) is the temperature, and \(n\) is the diode ideality factor. It is evident from this equation that the intrinsic parameters affecting PV output are the series and parallel resistances as well as the temperature of the PV module affected by the absorbed solar irradiation given by Equation (2).  
On the assumption of no other loss occurrence, the maximum power output of a PV module is calculated by data from its current-voltage (I-V) characteristic curve, which is as follows:  
\[P_{m}=I_{MPP}V_{MPP}, \tag{4}\]  
where the subscript \"MPP\" refers to the corresponding values at the maximum power point.  
From the incident irradiance on the module, a small portion is the final power output, while the remainder is mainly converted into thermal energy. Among all PV components, solar cells with a high absorptivity coefficient are the ones with the highest temperature. Then, via conduction, heat is transferred from the solar cell to the front glass surface, which in turn exchanges heat with the environment. This heat dissipation takes place through convection and radiation. Thermal radiation, which occurs among the PV module, atmosphere, and sun, significantly impacts its performance. The description of the thermal behavior and characteristics of the PV module is beyond the objectives of this review and can be found in detail in recent studies [22].  
Figure 2: Schematic illustration of the incident irradiance with the two components (beam and diffuse) on the photovoltaic (PV) front surface. The module has a ground clearance of \(d\), a length of \(L\), and a tilt angle of \(\beta\).