## 2 Proposed Test System
### Solar PV System  
A photovoltaic (PV) system operated in grid integrated mode consists of components such as solar PV plates, a boost converter, a maximum power point tracking (MPPT) system, an inverter, a grid coupling inductor and a capacitor, and a transformer. For a solar PV power generation system, the device in which actual power generation takes place (solar to electrical) is the solar panel, which consists of series and parallel combinations of solar cells. A solar cell consists of a p-n junction (p-n diode) fabricated in a thin layer of the semiconductor.Its operational characteristics are similar to the p-n diode. These characteristics also depend on the solar radiations and surface temperature of the PV plate. The electrical equivalent circuit of a solar cell is modelled using a single diode or double diode topology. Double-diode model has high accuracy under certain operating conditions. However, the single diode equivalent model is simple in nature with sufficient accuracy. This allows for the development of explicit models using the single diode model. The single diode equivalent circuit of the solar PV cell with parallel and series resistances utilized in this study is shown in Figure 2[17].  
In present study, a solar PV plant with a capacity of 1 MW was used. This consists of ten units (each with a capacity of 100 kW) connected in parallel. The relation between the output voltage (V) and current (I) for a solar cell (single-diode equivalent circuit) is expressed as below [18].  
\[I=I_{ph}-I_{0}\left\{exp\left[\frac{q(V+IR_{s})}{AKT}\right]-1\right\}-\left( \frac{V+IR_{s}}{R_{sh}}\right) \tag{3}\]  
Figure 2: Single-diode equivalent circuit of a solar cell.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Transformer** & **MVA** & **kV** & **kV** & **HV Winding** & \multicolumn{2}{c}{**LV Winding**} \\ \hline  & & **High** & **Low** & **R(\(\Omega\))** & **X(\(\Omega\))** & **R(\(\Omega\))** & **X(\(\Omega\))** \\ \hline XSST & 10 & 115 & 4.16 & 29.095 & 211.60 & 0.1142 & 0.8306 \\ \hline XFM & 5 & 4.16 & 0.48 & 0.3807 & 2.7688 & 0.0510 & 0.0042 \\ \hline XSPV & 0.1 & 4.16 & 0.260 & 0.1730 & 195.70 & 0.0007 & 0.7645 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Test Network Transformer Parameters.  
where \(I_{ph}\): photo-current of PV cell, \(I_{0}\): saturation current of PV cell, A: curve fitting factor of PV cell, \(R_{sh}\): shunt resistance of PV cell, \(R_{s}\): series resistance of PV cell, q: electronic charge, and k: Boltzmann constant.  
The magnitude of \(R_{sh}\) is infinite in short-circuit conditions. At this condition, the slope of I-V characteristics tends toward zero [18]. Hence, \(I_{ph}\) is equal to short-circuit current (\(I_{sc}\)) [17]. For a PV array organized in \(N_{p}\) parallel and \(N_{s}\) series connected solar cells, the current is expressed as follows:  
\[I=N_{p}I_{sc}-N_{p}I_{0}\left\{exp\left[\frac{q(V+I(N_{s}/N_{p})R_{s})}{N_{s} AKT}\right]-1\right\} \tag{4}\]  
The parameters simulated in this study for each module (at standard test conditions) are as follows: \(V_{oc}=64.2\) V, \(I_{sc}=5.96\) A, \(V_{mp}=54.7\) V, \(I_{mp}=5.58\) A, \(R_{s}=0.037998\)\(\Omega\), \(R_{sh}=993.51\)\(\Omega\), \(I_{0}=1.1753e^{-8}\) A, diode quality factor \(Q_{d}=1.3\), and \(I_{ph}=5.9602\) A [19]. The \(V_{mp}\) and \(I_{mp}\) are, respectively, the voltage and the current at the point of maximum power tracking.