# Solar Power System Assessments Using ANN and Hybrid Boost Converter Based MPPT Algorithm
## 3 Analytical Approach  
### Analytical Model of PV Module  
The main background of the presented approach is discussed in Section 2. This section elaborates the mathematical mechanism for the modern MPPT based ANN system, considering the array of PVs at input side and utility grid at the receiving end. The description of used symbols are declared in Table 2. The circuitry of the PV cell contain diode for paralleling current as shown in Figure 3, which can be mathematically [32; 33; 34] defined as  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]  
where \(i_{diode}\) is the diode current, \(i_{sc}\) is the current through the parallel resistor. The \(i_{diode}\) is further explained as  
\[i_{diode}=i_{o}(e^{\frac{er_{d}}{\theta RT_{c}}}-1) \tag{2}\]  
So, the Equation (1) can be modified with Equation (2) the total current from PV cell is measured as  
\[i_{total}=i_{sc}-i_{o}(e^{\frac{er_{d}}{\theta RT_{c}}}-1) \tag{3}\]  
Parallel resistance \(R_{p}\) and series resistance \(R_{s}\) is also considered for the dynamic behavior of PV cell, however, for the proposed PV cell simulation there is computational limitation if taking both series and parallel resistance. Therefore, parallel resistance is usually neglected in PV systems bibliography. For the proposed PV cell simulation series resistance is considered and the PV cell total current is mathematically written as [35; 36]  
\[i_{total}=i_{sc}-i_{o}\{exp(\frac{e(v+i_{total}R_{s})}{\eta RT_{c}})\}-1 \tag{4}\]  
The PV system consist of \(N\) numbers of branches in parallel and each parallel branch consist of N number of PV cells in series. So, the total current from PV module under constant weather condition is  
\[i_{sc}^{N}=i_{sc}^{N}[1-exp(\frac{V^{m}-V^{m}_{oc}+R_{s}^{N}\cdot i^{N}}{N_{s} \cdot V^{c}_{T}})] \tag{5}\]  
The module current depends on some different parameters of the cell. Each variable depends on different parameters of each cell. The module short circuit current depends on number of branches and short circuit of the cell [37; 38]. \[i_{sc}^{M}=N_{p}\cdot i_{sc}^{c} \tag{6}\]  
The open circuit voltage of the module depends on the number of cells in series and the open circuit voltage of the cell. \[V^{m}_{oc}=N_{s}\times V^{c}_{oc} \tag{7}\]  
The thermal voltage of the semiconductor in the module depends on Boltzmann's constant, cell temperature and the charge of electron, i.e., 1.602 \(\times\) 10\({}^{-19}\)[39]. \[V^{c}_{T}=\frac{mKT_{c}}{e} \tag{8}\]The equivalent series resistant of the module depends on series resistance of the cell, number of parallel branches in the module and the number of cell in series in each branch. \[R_{s}^{M}=\frac{R_{s}^{c}\cdot N_{p}}{N_{s}} \tag{9}\]  
Assume that all the cell in PV system are same, so the power, voltage, and current under standard condition are  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]0  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]1  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]2  
Now the instantaneous series resistance of the PV cell can be expressed as  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]3  
Fill factor is denoted with FF and is given as  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]4  
The short circuit current of the cell itself depends on the irradiance and can be expressed as  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]5  
The open circuit voltage of the cell depends on the nominal open circuit and the actual weather condition, i.e., ambient temperature, temperature of cell, and irradiance. The open circuit voltage is expressed [40; 41] as  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]6  
Now the current generated from the PV module in term of all parameters, i.e., irradiance, temperature, voltage, etc., is  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]7  
Now assume the case that PV array consist of \(B\) number of parallel branches and each branch contain \(M\) number of module so, the array current will be equal to \(I=\sum_{i=1}^{N_{B}}\). If we consider all the panels are same and under same temperature and irradiance then the output current will be  
\[i_{total}=i_{sc}-i_{diode}, \tag{1}\]8