## 5 Advanced MPPT Techniques
### Metaheuristic MPPT Techniques
#### 5.2.2 Bio-Inspired Algorithms  
Bio-inspired MPPT algorithms draw inspiration from natural processes and behaviors observed in animals and biological systems. These algorithms mimic these natural phenomena to solve the MPPT problem, often through swarm intelligence, evolutionary strategies, or other bio-inspired mechanisms [83]. The Cuckoo Search Optimization (CSO) MPPT algorithm is an advanced optimization technique inspired by the brood parasitism of cuckoo birds, where solutions are treated as cuckoo eggs laid in host nests [84]. Figure 16 indicates the flowchart of the CSO MPPT, where \(a\) is the scaling factor and \(n\) is the population size. This algorithm iteratively explores and exploits potential solutions to identify the optimal MPP by mimicking the natural behavior of cuckoos. Its advantages include robust performance in dynamic environments and a strong capability to avoid local optima, leading to faster convergence compared to traditional methods. However, it can be more complex and computationally intensive, requiring careful parameter tuning to achieve optimal results [85,86]. In the CSO algorithm, Levy flights represent a random walk of cuckoo birds, defined by the following equations. Here, \(y\) is the probability density, \(\lambda\) represents the variance, and \(l\) denotes the flight length. \(x_{i}{}^{t}\) is the sample, while \(\alpha\) indicates the step size. The variables \(t\) and \(i\) refer to the number of iterations and samples, respectively. The value of \(\alpha\) is the step size, where \(\alpha_{0}\) is the initial step size. Additionally, \(x_{j}{}^{(t)}\) and \(x_{i}{}^{(t)}\) are the two samples. By using Levy flights for step size, CSO achieves faster convergence. \[y=l^{-\lambda},\ \ (1<\lambda<3) \tag{14}\]  
\[x_{i}^{(t+1)}=x_{i}^{t}+\alpha\oplus L\acute{e}vy(\lambda) \tag{15}\]  
\[a=a_{0}(x_{i}^{(t)}-x_{i}^{(t)}) \tag{16}\]  
The Firefly Optimization (FO) MPPT algorithm is inspired by the natural behavior of fireflies, which use light flashes to attract mates and communicate [87]. Figure 17 depicts the flowchart of the FO MPPT. In this algorithm, the search for the optimal MPP is modeled as a swarm of fireflies, where each firefly represents a potential solution and moves through the solution space based on the attractiveness of other fireflies, which is related to their brightness or power output. The advantages of this method include its ability to effectively explore a wide solution space, maintain a balance between exploration and exploitation, and adapt to varying conditions, leading to improved convergence and accuracy in reaching the MPP. However, the algorithm can be computationally demanding and may require fine-tuning of its parameters to achieve optimal performance, which can be a drawback compared to simpler MPPT techniques [88,89]. Following equations are used for the FO algorithm, where \(D\) represents the dimension, \(x_{i,k}\) is the \(k\)-th dimension of the \(i\)-th firefly, \(x_{i,k}\) is the \(k\)-th dimension of the \(j\)-th firefly, \(r_{ij}\) is the distance between the \(i\)-th and \(j\)-th fireflies, \(\beta_{0}\) is the attractiveness at \(r=0\), \(e\) is the mathematical constant, \(\gamma\) is the absorption coefficient, and \(\alpha\) is a random movement factor within the range of [0, 1]. \[r_{ij}=\left\|x_{i}-x_{j}\right\|=\sqrt{\sum_{k=1}^{D}\left(x_{i,k}-x_{j,k} \right)^{2}} \tag{17}\]  
\[\beta(r_{ij})=\beta_{0}e^{-\gamma r^{2}ij} \tag{18}\]  
\[x_{i}=x_{i}+\beta_{0}e^{-\gamma r^{2}ij}\left(x_{i}-x_{j}\right)+\alpha(rand- 0.5) \tag{19}\]Flower Pollination Algorithm  
The Flower Pollination (FP) MPPT algorithm is inspired by the process of flower pollination and is used in MPPT to optimize power extraction from PV systems. Figure 18  
Figure 16: Flowchart of the CSO MPPT. Figure 17: Flowchart of the FO MPPT. displays the flowchart of the FP MPPT, where \(P\) refers to the probability factor and _Rand_ refers to a random number generated within a specified range.