## 3 MPPT Techniques
### Intelligent MPPT Techniques
#### 3.3.5 Grey Wolf Optimization  
The GWO method is proposed to tackle the nonlinear problems based on the social behavior of grey wolves in nature [114]. As observed in Figure 14, grey wolves live in packs of 5 to 12 animals and have a clear dominating order. Based on their capacity to pursue prey, grey wolves are categorized into the following four groups: alpha, beta, delta, and omega. When creating the GWO algorithm, the alpha wolves are regarded as the best solution. As a result, beta wolves are the second best solution in the pack, and delta wolves are the third best. In the pack, the leftover wolves are classified as the omega category. The hunting behaviors of grey wolves, such as encircling, hunting, and attacking prey, are used to design the GWO algorithm for optimization problems. This hunting behavior can be expressed mathematically as follows:  
\[\overset{\rightarrow}{D}=|\overset{\rightarrow}{C}.\overset{\rightarrow}{X^ {n}}-\overset{\rightarrow}{X^{n}}| \tag{27}\]  
\[\overset{\rightarrow}{X}^{n+1}=\overset{\rightarrow}{X^{n}}+\overset{ \rightarrow}{A.D} \tag{28}\]  
Figure 13: Flow chart of GO. The coefficient vectors \(\overset{\rightarrow}{A}\), \(\overset{\rightarrow}{C}\) can be obtained as follows:  
\[\overset{\rightarrow}{A}=2\overset{\rightarrow}{a}.\overset{\rightarrow}{r}_{1} -\overset{\rightarrow}{a} \tag{29}\]  
\[\overset{\rightarrow}{C}=2.\overset{\rightarrow}{r}_{2} \tag{30}\]  
where \(\overset{\rightarrow}{r}_{1}\), \(\overset{\rightarrow}{r}_{2}\) are the random numbers between 0 and 1, and \(\overset{\rightarrow}{a}\) is linearly varied from 2 to 0. The hunt is typically led by alphas known as leaders, who are followed by betas and deltas who may hunt on occasion. The wounded wolves in the pack are cared for by delta and omega. As a result, we refer to alpha as the candidate solution that has a better understanding of the location of prey. When the prey stops moving, the grey wolves finish the hunt. Grey wolves hunting behavior can be expressed as follows:  
\[\overset{\rightarrow}{D}_{\alpha}=\left|\overset{\rightarrow}{C}_{1}.\overset {\rightarrow}{X}_{\alpha}-\overset{\rightarrow}{X}\right|\text{; }\overset{ \rightarrow}{D}_{\beta}=\left|\overset{\rightarrow}{C}_{1}.\overset{ \rightarrow}{X}_{\beta}-\overset{\rightarrow}{X}\right|\text{; }\overset{ \rightarrow}{D}_{\delta}=\left|\overset{\rightarrow}{C}_{1}.\overset{ \rightarrow}{X}_{\delta}-\overset{\rightarrow}{X}\right| \tag{31}\]  
\[\overset{\rightarrow}{X}_{1}=\overset{\rightarrow}{X}_{\alpha}-\overset{ \rightarrow}{A}_{1}.\left(\overset{\rightarrow}{D}_{\alpha}\right)\text{; }\overset{\rightarrow}{X}_{2}=\overset{\rightarrow}{X}_{\beta}-\overset{ \rightarrow}{A}_{2}.\left(\overset{\rightarrow}{D}_{\beta}\right)\text{; }\overset{\rightarrow}{X}_{3}=\overset{\rightarrow}{X}_{\delta}-\overset{ \rightarrow}{A}_{3}.\left(\overset{\rightarrow}{D}_{\delta}\right) \tag{32}\]  
\[\overset{\rightarrow}{X}^{n+1}=\frac{\overset{\rightarrow}{X}_{1}+\overset{ \rightarrow}{X}_{2}+\overset{\rightarrow}{X}_{3}}{3} \tag{33}\]  
The block diagram of the PV system with the MPPT technique is presented in Figure 6. The output power is calculated for each grey wolf, or duty ratio, once the Vpv and IPv have been measured using sensors. The flow chart of GWO is presented in Figure 15.  
The P-V curve is classified as having multiple peaks with several local peaks (LPs) and one global peak (GP) during partial shading. It is worth noting that once the wolves locate the MPP, their correlated coefficient vectors approach zero. The suggested method aims to combine GWO with direct duty-cycle control, i.e., the duty cycle is maintained at a constant value at the MPP, reducing the steady-state oscillations present in conventional MPPT techniques, and finally, power loss due to oscillation is reduced, leading to higher system efficiency. The GWO-based MPPT is implemented by defining duty cycle D as a grey wolf.