## 2 Description of the Partially Shaded PV Energy System  
### Description of the Power and Control Circuits  
Ideally, whenever light hits the photovoltaic cell, it behaves similarly to a current source and is connected with a parallel diode. A PV module's characteristics may be acquired through an ideal model of a single diode. Practically, a single diode model consists of parallel and series resistance named as \(R_{p}\) and \(R_{s}\) respectively.The schematic diagram of a single diode model of PV is demonstrated in Figure 1.  
However, in PV cell's single diode practical model, \(R_{p}\) and \(R_{s}\) shows the losses. By using [PERSON]'s current law (KCL), mathematical equations of this model are the following:  
\[I=I_{pv}-I_{d}-I_{sh} \tag{1}\]  
where the values of \(I_{d}\) and \(I_{sh}\) are represented below in (2) and (3):  
\[I_{d}=I_{o}[exp(\frac{V+IR_{s}}{nV_{T}})-1] \tag{2}\]  
\[I_{sh}=\frac{(V+IR_{s})}{R_{sh}} \tag{3}\]  
where reverse saturation current is denoted by \(I_{o}\). The value of \(V_{T}\) is equal to  
\[V_{T}=\frac{N_{s}AKT}{q} \tag{4}\]  
diode's ideality factor is presented by \(N_{s}\), '\(K\)' stands for Boltzmann constant and '\(T\)' is expressed as the temperature of the photovoltaic cell.  
The complete governing equation of a PV cell and its output current (I) is shown by  
\[I=I_{pv}-I_{o}[exp(\frac{V+IR_{s}}{nV_{T}})-1]-\frac{(V+IR_{s})}{R_{sh}} \tag{5}\]  
Figure 1: Single diode PV model.  
DC-DC converter in PV energy systems is an integral part of the output power. There are several converters commonly used in a PV system to modify the value of output power like a buck, boost, and buck-boost converter. They decrease or increase the value of voltages according to the system requirements. Among all the other DC to DC converters, the boost converter has the advantages in terms of voltages regulation, power, and efficiency to achieve the desired results. PV energy system's output voltages should be controlled, varying the value of duty cycle of a DC-DC boost converter. For achieving this, the output voltage and connected load must be synchronized. Figure 2 presents the basic schematic diagram of the DC to DC boost converter.  
Initially, the reference voltage (\(V_{ref}\)) at GM of the PV system is adjusted then the value of \(V_{ref}\) of the boost converter is modulated to modify PV voltage as a reference voltage. The value of the duty cycle is taken from 0 to 1. The maximum energy can be harvested from the PV energy system by implementing the control algorithm in a microcontroller having zero oscillation. The mathematical equations of output capacitance, duty cycle, input capacitance, output voltage, and inductance of the boost converter are represented below in (6)-(10).  
\[C_{input}=\frac{\Delta I_{ripple}}{8\Delta V_{ripple,po}f_{switching}} \tag{6}\]  
\[DC=\frac{T_{on}}{T_{switching}} \tag{7}\]  
\[C_{output}=\frac{I_{0}}{f_{switching}8\Delta V_{ripple,load}} \tag{8}\]  
\[V_{out}=\frac{V_{int}}{1-DC} \tag{9}\]  
\[L=\frac{DCI_{o}}{2f_{switching}\Delta I_{Load}} \tag{10}\]  
where \(V_{in}\) is the input voltage, \(f_{switching}\) represents the switching frequency, \(I_{ripple}\) denotes the ripple current and DC elaborates the duty cycle of a DC-DC boost converter. In PV systems conventional techniques may be stuck on LM and do not achieve GM for maximum  
Figure 2: DC to DC Boost-Converter In PV system.  
energy harvesting. Due to this reason, bio-inspired techniques are used in this research for searching the MPP.