## 5 Advanced MPPT Techniques
### Metaheuristic MPPT Techniques
#### 5.2.1 Optimization-Based Algorithms
GWO behavior can be modeled by the following equations, where \(\overset{\rightarrow}{X}\) and \(\overset{\rightarrow}{X_{p}}\) represent the position vectors of the grey wolf and the prey, respectively. \(t\) denotes the number of iterations, while \(\overset{\rightarrow}{A}\), \(\overset{\rightarrow}{C}\), and \(\overset{\rightarrow}{D}\) are the coefficient vectors. \(\overset{\rightarrow}{a}\) is a parameter that decreases linearly from 2 to 0, and \(\overset{\rightarrow}{r_{1}}\) and \(  
\[\stackrel{{\rightarrow}}{{A}}=2*\stackrel{{ \rightarrow}}{{a}}*\stackrel{{\rightarrow}}{{r}}_{1}-\stackrel{{ \rightarrow}}{{d}} \tag{10}\] \[\stackrel{{\rightarrow}}{{C}}=2*\stackrel{{ \rightarrow}}{{r}}_{2} \tag{11}\]  
Figure 12: Flowchart of the PSO MPPT. The Ant Colony Optimization (ACO) MPPT algorithm is inspired by the foraging behavior of ants, where ants deposit pheromones to identify successful paths and guide others [76]. Figure 14 displays the flowchart of the ACO MPPT, where \(M\) is the number of ants in the colony and \(K\) is the number of iterations. In this algorithm, the search for the MPP is modeled as a network of paths, with virtual \"ants\" exploring different solution routes and updating their pheromone trails based on the power output they encounter. Each ant explores different paths (duty cycles) and calculates the PV module output power. Successful paths that yield higher power result in increased pheromone levels on those paths. This approach allows the algorithm to effectively balance the exploration of new regions and the exploitation of known successful areas. Advantages of the ACO  
Figure 13: Flowchart of the GWO MPPT. algorithm include its robustness in handling dynamic conditions, ability to avoid local optima, and rapid convergence to the MPP by using collective intelligence. However, disadvantages include the potential for higher computational complexity and the need for careful parameter tuning to balance exploration and exploitation effectively [77; 78]. In the equations given below, \(G_{i}(x)\) represents the Gaussian kernel for the \(i\)-th dimension of the solution, while \(w\) represents the weight associated with the \(l\)-th term in the sum, \(g_{l}^{i}(x)\) denotes the \(l\)-th sub-Gaussian function for the \(i\)-th dimension. 1 is the index that runs over the sum from 1 to \(K\) and \(x\) represents a specific input. \(\mu_{l}^{i}\) and \(\sigma_{l}^{i}\) are the mean value and standard deviation for the \(i\)-th dimension of the \(l\)-th solution, respectively. \[G_{i}(x)=\sum_{l=1}^{K}w_{l}g_{l}^{i}(x) \tag{12}\]  
\[\pi_{ll(x)}=\frac{1}{\sigma_{l}^{i}\sqrt{2\pi}}exp\left(-\frac{\left(x-\mu_{l} ^{i}\right)^{2}}{2\sigma_{l}^{i}^{2}}\right) \tag{13}\]  
Figure 14: Flowchart of the ACO MPPT. The Artificial Bee Colony (ABC) MPPT algorithm is inspired by the foraging behavior of honeybees to find optimal food sources [79]. Figure 15 shows the flowchart of the ABC MPPT. It begins by initializing a population of bees, each representing a potential duty cycle. Employed bees evaluate their current positions by measuring the PV module's output power and exploring neighboring positions for improvements. This iterative process continues until convergence to the MPP is reached [80]. The advantages of the ABC algorithm include its robustness in diverse and dynamic conditions, and its capability to avoid local MPP through a balance of exploration and exploitation. However, disadvantages may include computational overhead and the need for careful parameter tuning to ensure optimal performance [81]. The optimization-based MPPT algorithms are compared in \[x_{i}^{k+1}=x_{i}^{k}+\Phi_{i}^{k+1} \tag{6}\]0