# Power Quality Enhancement in a Grid-Integrated Photovoltaic System Using Hybrid Techniques
## 5 Modeling of the PV Array  
The number of PV modules is optimized to reduce the cost of energy, which covers the load demand. Additionally, the output power of the PV module is mainly based on the temperature, manufacturing characteristics, and geographical locations. The PV system voltage and capacity are determined by connecting the PV panel either in parallel or in a series connection [16]. The MPPT method is considered in the PV system to increase the PV output power. Table 1 clearly depicts the specific value of parameters of the PV array of the module.  
Equation (1) is used to identify the output power that depends on the \(I_{M}\) and \(V_{M}\), which denote the maximum current and voltage, respectively.  
\[P_{MPPT}(t)=I_{MPPT}(t)\times V_{MPPT}(t) \tag{1}\]  
The current and voltage of MPPT are given in Equations (2) and (3), respectively.  
\[I_{MPPT}(t)=I_{SC}\bigg{\{}1-C_{1}\bigg{[}exp\bigg{(}\frac{V_{M}}{C_{2}\times V _{OC}}\bigg{)}\bigg{]}\bigg{\}}+\Delta I(t) \tag{2}\]  
\[V_{MPPT}(t)=V_{M}+\mu V_{OC}\cdot\Delta T(t) \tag{3}\]  
where the short circuit current is represented as \(I_{SC}\); \(C_{1}\), and \(C_{2}\) are the capacitances; \(V_{M}\) is the maximum voltage; and the open circuit voltage is represented as \(V_{OC}\).  
\(C_{1}\), \(C_{2}\), \(\Delta I(t)\), and \(\Delta T(t)\) of Equations (2) and (3) are expressed in Equations (4)-(7), respectively.  
\[C_{1}=\bigg{(}1-\frac{I_{M}}{I_{SC}}\bigg{)}\times exp\bigg{(}-\frac{V_{M}}{C_{ 2}\times V_{OC}}\bigg{)} \tag{4}\]  
\[C_{2}=\bigg{(}\frac{V_{M}}{V_{OC}}-1\bigg{)}\times\bigg{[}\text{ln}\bigg{(}1- \frac{I_{M}}{I_{SC}}\bigg{)}\bigg{]}^{-1} \tag{5}\]  
\[\Delta I(t)=I_{SC}\bigg{(}\frac{GT(t)}{G_{ref}}-1\bigg{)}+\alpha_{1,sc}\times \Delta T(t) \tag{6}\]  
\[\Delta T(t)=T_{c}(t)-T_{c,ref} \tag{7}\]  
The \(I_{M}\) is the maximum current, the incident radiation on the PV surface is represented as \(GT(t)\), and \(\alpha_{1,sc}\) signifies the constant value during short-circuit operation. The cell temperature is represented as \(T_{c}\), and the PV temperature in the standard condition is represented as \(T_{c,ref}\). The MPPT technique computes the panel operating voltage and current period (POVCP) and measures the instantaneous power. The efficiency of the MPPT technique is improved by minimizing the steady-state oscillation and eliminating the variable irradiance level. The dynamic perturbation step size is used to minimize the oscillation, whereas boundary conditions are introduced to avoid the diverging characteristic of MPP. The general block diagram of the MPPT technique is shown in Figure 1.  
Similarly, the operating point of MPP oscillates around the consecutive samples. However, the oscillation is found by a special mechanism and the perturbation size is minimized until it achieves a positive minimum value [17]. Here, less power tolerance is allowed to handle the small flickers that occur in the power issue. The consecutive samples have a difference in power (\(\Delta P\)), due to the small oscillations. The size of perturbation achieves a minimum value because the \(\Delta P/P\) value is maintained below the threshold limit (\(T_{r1}\)).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline The voltage at maximum power point, Vmp & 54.7 V \\ Temperature coefficient of Voc & \(-0.27269\) (\%/\({}^{\circ}\)C) \\ Temperature coefficient of Isc & 0.061745 (\%/\({}^{\circ}\)C) \\ Shunt resistance & 269.5934 ohms \\ Short-circuit current, Isc & 5.96 A \\ Series resistance & 0.37152 ohms \\ Open circuit voltage, Voc & 64.2 V \\ Maximum power & 305.226 W \\ Light generated current, IL & 6.0092 A \\ Diode saturation current & 0.000063 \(\times\) 10\({}^{-5}\)A \\ Diode ideality factor & 0.94504 \\ Current at maximum power point of Isc & 5.58 A \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specification of the PV array.