# Design of a Partially Grid-Connected Photovoltaic Microgrid Using IoT Technology
## 3 Microgrid Modeling and Design
### Boost Converter  
To maximize the PV array power yield for variable loads, the DC/DC boost converter controlled by a maximum power point tracking (MPPT) algorithm is generally used. The converter circuit is designed to adjust the operating point always at the maximum power point of the \(P\)-\(V\) characteristics of the array. As shown in Figure 6, the converter circuit tracks both, the array voltage and current that are typically measured by DC voltage and current sensors. The output of the controller is a duty-cycle ratio (\(D\)) that controls the gate of a switching active device (typically it is IGBT). The converter is used to effectively link the PV array to DC-AC inverter(s) and/or to charge a battery array. The extracted PV power using the converter is related to the switch duty-cycle and the load resistance (\(R_{L}\)) using the following equation [53]:  
\[P_{PV}=\frac{1}{R_{L}}\bigg{(}\frac{V_{PV}}{1-D}\bigg{)}^{2} \tag{16}\]  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value (Unit)** \\ \hline Rate power & 315 W \\ Short-circuit current & 6.14 A \\ Open-circuit voltage & 64.6 V \\ Peak current & 5.75 A \\ Peak voltage & 54.7 V \\ Peak efficiency & 19.3\% \\ Surface area & 1.63 m\({}^{2}\) \\ \hline \end{tabular}
\end{table}
Table 1: Technical specifications of the PV module used in array modeling.  
Figure 5: (**a**) _I-V_ and (**b**) _P-V_ characteristics of one module, (**c**) _I-V_ and (**d**) _P-V_ characteristics of 100-kW PV array, computed at different irradiance levels of 0.1, 0.5, and 1 kW/m\({}^{2}\).  
Owing to limitations of the switch characteristics, \(D\) must be kept within some range (\(D_{min}<D<D_{max}\)). Consequently, the load resistance limits are calculated by [53]:  
\[\frac{V_{mpp}/I_{mpp}}{\left(1-D_{min}\right)^{2}}\leq R_{L}\leq\frac{V_{mpp}/I_ {mpp}}{\left(1-D_{max}\right)^{2}} \tag{17}\]  
where \(V_{mpp}\) and \(I_{mpp}\) are the PV array voltage and current at the MPP. In this design, the duty-cycle ratio was set from 0.1 to 0.9 and the load resistance limits are obtained to be 0.93 to 73.3 \(\Omega\), computed at the STC. The converter parameters considered here are listed in Table 2. Regarding the control algorithm of the circuit, the Perturb and Observe (P&O) approach was selected here due to its simplicity, robustness, and small numbers of computed variables required to implement the power tracking process. The P&O tracking method can continuously track the MPP, in different weather conditions, regardless of the kind and location of the PV panels. This is accomplished by analyzing real-time monitoring of PV voltage and current measurements. Because the needed circuitry for implementing MPPTs is more expensive, they are often used for large projects. A pseudocode of the P&O is shown in Algorithm 1. A slight change (perturbation) in the duty-cycle (\(\Delta D\)) is injected into the circuit throughout the gate of the switch, then PV voltage and current are read (observed) by the sensors. After the change of the power (\(\Delta P\)) is continuously computed and its sign is checked if it is positive (\(\Delta P>0\)) or negative (\(\Delta P<0\)), the perturbation continues to increase (\(D_{k}+\Delta D\)) or decrease (\(D_{k}-\Delta D\)). The performance of the MPPT algorithm is commonly evaluated based on several criteria including (1) time response to rapid and slow variations in irradiance, (2) amount of power fluctuations around the maximum power point and tracking efficiency (\(TE\)). The latter parameter can be computed by [54]:  
\[TE=\frac{P_{PV-average}}{P_{PV-available}}\times 100 \tag{18}\]  
where \(P_{PV-average}\) is the average output power of the array that is actually collected by the tracking circuit, and \(P_{PV-available}\) is the available power of the array at a certain level of irradiance, which is the maximum power that may be obtained and targeted by the MPPT controller.  
Figure 6: Schematic diagram of boost converter with MPPT controller.