## 5 Advanced MPPT Techniques
### Metaheuristic MPPT Techniques
#### 5.2.1 Optimization-Based Algorithms  
Optimization-based MPPT algorithms focus on solving the MPPT problem through mathematical and numerical optimization techniques. These algorithms often involve formulating the MPPT as an optimization task and using algorithms designed to find the optimal solution. Figure 11: General outline of the flowchart for metaheuristic MPPT techniques. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Tracking Algorithm** & **Sensed** & **Circuity** & **Tracking Speed** & **Implementation Complexity** & **True MPPT** & **Accuracy** & **Cost** \\ \hline FLC & V, I & A/D & Slow & Low & Yes & Medium & Low \\ ANN & V, I & D & Medium & Medium & Yes & Medium & Medium \\ FS & G, T or I, T & D & Medium & Low & Varies & High & Low \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of smart MPPT algorithms [29; 53; 66]. The Particle Swarm Optimization (PSO) MPPT algorithm is an advanced technique used to maximize the power output of PV systems by mimicking the social behavior observed in flocks of birds or schools of fish [68]. In the flowchart of the PSO MPPT, as shown in Figure 12, a swarm of candidate solutions, or particles, converges on the MPP by iteratively adjusting the DC-DC converter's duty cycle based on the collective behaviors, where \(i\) refers to the iteration counter. Each particle adjusts its position (\(P_{best}\)) based on its own experience and that of its neighbors, gradually converging toward the optimal solution (\(G_{best}\)). Once the algorithm terminates, output the optimal duty cycle and the corresponding MPP. The main advantage of PSO is its ability to effectively handle complex, non-linear, and multi-modal optimization problems, often yielding superior performance. It is particularly useful in systems with dynamic or unpredictable environmental conditions. However, PSO can be computationally intensive, necessitating careful parameter tuning for optimal performance, and it often involves a more complex implementation than simpler traditional MPPT methods. The initial conditions and the specific design of the PSO parameters can affect the algorithm's effectiveness [69; 70; 71]. The following equations are used to update each particle's position and velocity. Here, \(x_{i}\) and \(\Phi_{i}\) represent the position and velocity of each particle, respectively. \(k\) denotes the iteration count, \(w\) is the inertia weight, \(c_{1}\) and \(c_{2}\) are acceleration coefficients, and \(r_{1}\) and \(r_{2}\) are random values uniformly distributed between 0 and 1. \[x_{i}^{k+1}=x_{i}^{k}+\Phi_{i}^{k+1} \tag{6}\]  
\[\Phi_{i}^{k+1}=w\Phi_{i}^{k}+c_{1}r_{1}\Big{\{}P_{best}-x_{i}^{k}\Big{\}}-c_{2 }r_{2}\Big{\{}G_{best}-x_{i}^{k}\Big{\}} \tag{7}\]  
The Grey Wolf Optimization (GWO) MPPT algorithm is based on the hunting behavior and social hierarchy of grey wolves [72]. Figure 13 depicts the flowchart of the GWO MPPT, where \(i\) represents the index of the individual wolf within the population and \(k\) represents the current iteration number. In this algorithm, a population of candidate solutions, represented as wolves, is used to search for the MPP of a PV system. The wolves are categorized into alpha, beta, delta, and omega roles, with alpha wolves leading the search and beta and delta wolves assisting them. The algorithm mimics the pursuit and encirclement strategies of wolves during hunting to explore and exploit the solution space effectively [73]. One of the main advantages of the GWO algorithm is its robustness and ability to converge quickly to the MPP, even in complex and dynamic conditions. It generally performs well in finding optimal solutions with fewer iterations compared to some other optimization algorithms. However, the GWO algorithm's computational complexity can be higher than simpler MPPT methods, making it less suitable for systems with limited processing power. The PV module output power is calculated using the voltage and current measurements for the grey wolves, which represent the duty ratios [74; 75].