# Centralized MPPT Control Architecture for Photovoltaic Systems Using LoRa Technology
## 2 Centralized MPPT Architecture Based on LoRa  
### Power Optimization of PV Systems  
#### 2.1.1 PV Module  
A PV cell can be characterized by the single-diode model, which is simple but accurate [32]. The schematic diagram of this model is shown in Figure 1, where \(I\) and \(V\) are the current and voltage of the PV cell, respectively. A direct current (DC) source generates \(I_{\text{ph}}\) depending on solar irradiance. Additionally, the model incorporates two resistors: \(R_{\text{sh}}\), which is associated with the diode's current leakage at the p-n junction; and \(R_{\text{s}}\), which denotes the series resistance of the PV cell. The output current is given by [PERSON]'s Current Law through Equation (1), whose right-hand terms are defined below.  
\[I=I_{\text{ph}}-I_{\text{D}}-I_{\text{sh}}. \tag{1}\]  
Ohm's Law is used in (2) to determine \(I_{\text{sh}}\):  
\[I_{\text{sh}}=\frac{V_{\text{D}}}{R_{\text{sh}}}, \tag{2}\]  
where \(V_{\text{D}}\) is the voltage across the diode. A Shockley equation of the p-n junction of the diode is presented in (3):  
\[I_{\text{D}}=I_{0}\left[\exp\left(\frac{q\,V_{\text{D}}}{n\,k\,T}\right)-1 \right], \tag{3}\]  
where \(I_{0}\) is the reverse saturation current of the diode, \(q\) is the elementary charge, \(n\) is the quality factor of the diode, \(k\) is the Boltzmann constant, and \(T\) is the thermodynamic temperature of the p-n junction. In addition, \(I_{\text{ph}}\) denotes the light-generated current in the solar cell, as shown in (4):  
\[I_{\text{ph}}=\frac{G}{G_{\text{ref}}}\,I_{\text{sc},\text{ref}}+K_{\text{ref} }\,(T-T_{\text{ref}}), \tag{4}\]  
where \(K_{\text{ref}}\) comprises a thermal factor of the short-circuit current at the reference temperature, \(T_{\text{ref}}\); \(I_{\text{sc},\text{ref}}\) is the short-circuit current at the reference temperature; and \(G\) and \(G_{\text{ref}}\) are the effective and reference irradiance, respectively.  
Assuming that all of the cells in the module are identical and not affected by uneven shading [33], the current and voltage of the PV module, \(I_{\text{pv}}\) and \(V_{\text{pv}}\), are given by (5), where \(N_{\text{p}}\) is the number of parallel circuits and \(N_{\text{s}}\) is the number of cells connected in series:  
\[I_{\text{pv}} =N_{\text{p}}\,I \tag{5}\] \[V_{\text{pv}} =N_{\text{s}}\,V.\]  
The output power of the PV module is the product of the current (\(I_{\text{pv}}\)) and voltage (\(V_{\text{pv}}\)), as shown in (6):  
\[P_{\text{pv}}=I_{\text{pv}}\,V_{\text{pv}}. \tag{6}\]  
To assess the performance of the PV module, an \(I-V\) curve was plotted, as shown in Figure 2. It showcases all of the operating points: from short circuit, where \(V_{\text{pv}}=0\) and \(I_{\text{pv}}=I_{\text{sc}}\); to open circuit, where \(I_{\text{pv}}=0\) and \(V_{\text{pv}}=V_{\text{oc}}\). The Maximum Power Point (MPP) represents the unique point on the curve that maximizes the power generated by the module. At this point, the current and voltage are denoted as \(I_{\text{MPP}}\) and \(V_{\text{MPP}}\), respectively. The PV module (or an array of PV modules) is usually connected to a DC-DC converter. The input resistance of the converter is optimal when \(R_{\text{in}}=R_{\text{opt}}=V_{\text{MPP}}/I_{\text{MPP}}\).  
Figure 1: Schematic diagram of the single-diode model circuit for PV cell characterization.  
The MPP is influenced by variations in irradiance and temperature [34], as Figure 3 illustrates. With increasing irradiance, the curves undergo nearly vertical displacement, increasing power and voltage, whereas, with rising temperature, the \(I-V\) curves contract horizontally, thereby decreasing power and voltage.  
The deviation from the MPP operating point can be compensated through the implementation of a Maximum Power Point Tracking (MPPT) system, including a DC-DC converter and a control algorithm.