# Enhanced Solar Photovoltaic System Management and Integration: The Digital Twin Concept
## 3 Digital Twins for Solar Photovoltaics
### PV DT Technologies
#### 3.3.2 PV Module and Mounting Structure  
The development of a full PV array DT is a multidimensional modeling process. This means it requires multi-physics and mechanical or structural modeling, which include models of the optical [78; 79], electrical [80], and thermal processes [81]; the mechanical [82] and mounting structures [83; 84]; and the global location/landscape/terrain [85]. Each of these is vital to the reliability of the information provided by the DT. However, the purpose of the DT may vary in how the actual modeling is implemented. If the aim of the DT is not to compare the performance of an ideal solar module to the performance of the physical counterpart, the intrinsic processes listed above may be bypassed using the historical time-series energy production compared to data from WEC sensors. For a robust and reliable PV DT, combining the opto-electro-thermal modeling (Equations (1)-(6)) of the PV module with the system's physical properties, dimensions, and installation parameters is essential. This provides the global framework for in-depth analysis and maintenance optimization, especially for large utility-scale installation.  
* **Optical Equation [79]:** \[G=\int_{E_{g}}^{\infty}g_{E}(E)\,dE\] (1) where \(E_{g}\) is the band gap energy, and \(g_{E}\) (\(E\)) is the optical generation profile for every excitation energy.
* **Electrical Equation [80]:** \[I_{\text{output}}=I_{\text{ph}}-I_{0c}\left[\exp\left(\frac{V+IR_{sc}}{V_{t}} \right)-1\right]-\frac{V+IR_{sc}}{R_{pc}}\] (2) where \(I_{\text{ph}}\) is the photocurrent generated by the incident solar radiation, \(I_{0c}\) is the reverse saturation current, \(V\) is the output voltage, \(V_{t}=\gamma k_{B}T_{3}/q\) is the thermal voltage of the diode, \(\gamma\) is the ideality factor of the diode, \(k_{B}\) is the Boltzmann constant (1.3806503 \(\times\) 10\({}^{-23}\) J/K), \(T_{3}\) is the temperature of the solar cell calculated in the thermal model, \(q\) is the electron charge (1.60217646 \(\times\) 10\({}^{-19}\) C), and \(R_{sc}\) and \(R_{pc}\) are the series resistance and parallel resistance, respectively.
* **Thermal Equation [81]:** \[\rho_{i}c_{pi}\frac{\partial T_{i}}{\partial t}+\
abla\cdot(-\lambda_{i} \
abla T_{i})=0\] (3) \[-n\cdot q=G\tau_{i}-P_{e}\] (4)\[-n\cdot q=G\alpha_{i}+h(T_{a}-T_{\rm amb})+\sigma e_{1}F_{\rm sky}\Big{(}T_{a}^{4}-T_ {\rm sky}^{4}\Big{)} \tag{5}\]  
\[-n\cdot q=h(T_{b}-T_{\rm amb})+\sigma e_{5}F_{\rm grow}\Big{(}T_{b}^{4}-T_{\rm grow }^{4}\Big{)} \tag{6}\]  
where \(i\) denotes the number of layers in the solar cell, \(\rho\) is the density of the bulk material, \(c_{p}\) is the specific heat capacity, \(T\) is the temperature, \(\lambda\) is the heat conductivity, \(n\) is the outward unit normal to the boundary, \(q\) is the heat flux on the boundary, \(G\) is the solar irradiance, \(\tau_{i}\) is the transitivity of the glass, \(P_{e}\) is the power output intensity, \(\alpha_{i}\) is the absorptivity of the glass surface, \(h\) is the convective heat transfer coefficient, \(T_{\rm amb}\) is the ambient temperature, \(\sigma\) is the Stefan-Boltzmann constant, \(e_{1}\) is the emissivity of the glass surface, \(F_{\rm sky}\) is the view factor between the front surface and the sky, \(T_{\rm sky}\) is the sky temperature, \(e_{5}\) is the emissivity of the back surface, \(F_{\rm grow}\) is the view factor between the back surface and the ground, \(T_{a}\) and \(T_{b}\) are the temperatures at the topmost and bottom layers, respectively, and \(T_{\rm grow}\) is the ground temperature.  
In addition, the global location/landscape/terrain needs to be defined, for example, as rooftop, ground mount, floating system, etc. The modeling of the mounting structure and terrain varies depending on the mounting structure used. Often, the mounting structure is not modeled except in specific applications that involve forecasting the yield or the expected use of autonomous systems.