# Solar Power Prediction Modeling Based on Artificial Neural Networks under Partial Shading
## 2 Photovoltaic System  
Photovoltaic systems refer to the technology of directly converting solar energy into electricity using solar cells. Solar cells are essentially two-terminal devices composed of a p-n junction. They are made from various types of semiconductors, such as mono-crystalline silicon and multi-crystalline silicon. Although other materials can achieve higher efficiency, they are commercially challenging to use. Solar systems operate through the following sequence: (1) the absorption of photons generates electron-hole pairs. (2) Ideally, minority carriers cross the junction, leading to majority carriers. (3) Electrons and holes recombine after passing through the load. Photons with lower energy than the energy bandgap of the solar cell cannot generate voltage or current. Photons with energy greater than the bandgap only generate electricity corresponding to the bandgap energy, while the remaining energy is emitted as heat. Using a semiconductor with a lower energy bandgap allows for utilizing a broader spectrum of radiation but comes with the trade-off of lower generated voltage. To represent a photovoltaic system in a formula, five parameters are usually required for a photovoltaic-system-equivalent model: photocurrent (\(I_{ph}\)), diode saturation current (\(I_{0}\)), diode ideality factor (\(n\)), series resistance (\(R_{s}\)), and shunt resistance (\(R_{sh}\)). A typical photovoltaic-system-equivalent model is shown in Figure 1[9]. Figure 1: Common equivalent circuit of photovoltaic cell. With the five parameters shown in the equivalent model, the formula for the current in the system can be expressed as follows [9]. \[I=I_{ph}-I_{0}\bigg{[}\exp\bigg{(}\frac{V+IR_{s}}{nN_{s}V_{t}}\bigg{)}-1\bigg{]}- \frac{V+IR_{s}}{R_{sh}} \tag{1}\]  
where \(N_{s}\) represents the number of cells in series and \(V_{t}(kT/q)\) represents the thermal voltage. Equation (1) involves all five parameters. The formula for \(I_{ph}\) is as follows [9]:  
\[I_{ph}=[I_{sc}+K_{i}(T-T_{STC})]\frac{I_{r}}{I_{STC}} \tag{2}\]  
where \(I_{sc}\) is the short-circuit current, \(K_{i}\) is the short-circuit current temperature coefficient, \(T\) is the input temperature (K), \(T_{STC}\) is the standard-test condition temperature (298 K), \(I_{r}\) is the input light intensity (W/m\({}^{2}\)), and \(I_{STC}\) is the irradiation condition (1000 W/m\({}^{2}\)) for a standard test. The short circuit current is the current that flows through a solar cell when the voltage across the terminals is zero, i.e., when the solar cell is short-circuited. The short-circuit current is generated by photo-carriers, and in an ideal solar cell, it represents the maximum current that can be generated in a photovoltaic system. The diode current (\(I_{0}\)) is expressed as the product of the diode saturation current and diode reverse-saturation current. Its formula is as follows [9]:  
\[I_{0}=I_{rs}\bigg{[}\frac{T_{STC}}{T}\bigg{]}^{3}\exp\bigg{[}\frac{qE_{g0}}{nk} \bigg{(}\frac{1}{T_{STC}}-\frac{1}{T}\bigg{)}\bigg{]} \tag{3}\]  
where \(k\) is the Boltzmann constant (\(1.38\times 10^{-23}\)J/K), \(q\) is the charge \(\big{(}1.6\times 10^{-19}\)C\(\big{)}\), \(E_{g0}\) is the energy band gap of the semiconductor (Si), and \(I_{rs}\) is the diode reverse-saturation current. \(I_{rs}\) is given as [9]  
\[I_{rs}=\frac{I_{sc}}{\exp\bigg{(}\frac{qV_{oc}}{nkkT}\bigg{)}-1} \tag{4}\]  
where \(V_{oc}\) is the open-circuit voltage, which can be represented by the photocurrent and diode current, as follows [10]. \[V_{oc}=\frac{nkT}{q}\text{log}\bigg{(}1+\frac{I_{ph}}{I_{0}}\bigg{)} \tag{5}\]  
The open circuit voltage is the voltage available from a solar cell when there is no current flowing through it. The open circuit voltage increases linearly with temperature. In Equation (5), the open circuit voltage is influenced by the saturation current and photocurrent of the solar cell. While there may be slight variations in the short circuit current, it is primarily affected by the saturation current.