## 3 MPPT Techniques
### Intelligent MPPT Techniques
#### 3.3.6. Jaya Algorithm  
Many researchers have proposed different swarm-intelligence techniques for MPPT applications in the literature [42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65]. However, the performance of the majority of these techniques is heavily reliant on algorithm-specific parameters. For instance, in the case of PSO, cognitive parameters (c1, c2) and inertia weight are required (w); in the case of GA, crossover, mutation, and parent selection are required. Similarly, other algorithms, such as the cuckoo search (CS), ACO, the Bat algorithm, ABC, the GWO, and so on, require parameter tuning. Incorrect parameter selection or tuning may result in a suboptimal solution. To address this issue, an algorithm-specific parameters-free technique called the Jaya algorithm (JA) is introduced.  
Figure 15. Flow chart of GWO.  
[PERSON] introduced the Jaya algorithm in 2016, which was inspired by humanoid or animal activities [115]. In many cases, all humans or animals in a population are biologically distinct. However, they are all inspired by the elite or firm members of the population and seek to distance themselves from the lazy or weak members of the population. Throughout this algorithm, a candidate solution moves away from the worst solution, while simultaneously moving towards the best solution by mimicking this nature. Because of its fast convergence and simplicity, this algorithm has been effectively used to solve a variety of engineering problems [116; 117; 118; 119].  
Let p represent the size of the population (m = 1, 2-p), n represent the number of variables (v = 1, 2-n) and ITAE (Equation (39)) represent the fitness function that needs to be minimized. The ITAE identifies the population's best option as \(X_{best}\) and the population's worst solution as \(X_{worst}\). The value of the \(\epsilon\)th variable for the \(m\)th candidate in the ith iteration is given as \(X_{v,m,i}\). Then, the updated value of each variable \(X^{\prime}_{v,m,i}\) in the population can be obtained as follows:  
\[X^{\prime}_{v,m,i}=X_{v,m,i}+r_{1}*(X_{v,best,i}-|X_{v,m,i}|)-r_{2}*(X_{v,worst,i}-|X_{v,m,i}|) \tag{36}\]  
In Equation (36), all members of the population are always moving towards the best solution ('+' indication) and away from the worst solution ('-' indication). Furthermore, the equation shows that, unlike other algorithms, the proposed algorithm is not dependent on any algorithmic-specific parameters. The updated value of the population member (\(X\) (\(v\),\(m\),\(i\))) is accepted only if it is greater than the old value (\(X\) (\(v\),\(m\),\(i\))). \(r_{1}\) and \(r_{2}\) are random numbers ranging from 0 to 1.  
\[X^{\prime}_{v,m,i}=\left\{\begin{array}{cc}X_{v,m,i},&ITAE(X_{v,m,i})>ITAE \left(X^{\prime}_{v,m,i}\right)\\ &X^{\prime}_{v,m,i},&Otherwise\end{array}\right. \tag{37}\]  
The objective function of the MPPT problem optimization is to maximize the power generated by the PV arrays, which can be expressed as (38). The particle solutions are regarded as the duty cycle \(D_{i}\).  
\[P\left(D^{k+1}_{i,j}\right)>P\left(D^{k}_{i,j}\right) \tag{38}\]  
where \(P(D_{i})\) represents the instantaneous power at the duty cycle \(D_{i}\).  
The fitness function to maximize the \(PV\) output power can be expressed as follows:  
\[FF=Max\{\int\limits_{0}^{t_{sign}}t*(V_{PV}*I_{PV})*dt\} \tag{39}\]  
To use the Jaya algorithm for solar MPPT application, the initial particle solutions \(D_{i}\) are generated, and then they are iteratively updated by taking the best and worst solutions into account. The flow chart of Jaya-based MPPT is presented in Figure 16. The mathematical equation for updating particle solutions is as follows:  
\[D^{\prime}_{i,j}=D_{i,j}+r_{1}*\left(D_{i,best}-\left|D_{i,j}\right|\right)-r _{2}*\left(D_{i,worst}-\left|D_{i,j}\right|\right) \tag{40}\]