4.1.1. Perturb and Observe

The P&O MPPT technique is widely used due to its simplicity, ease of implementation, fewer sensor requirements, and low actualized costs [23,24]. It is an iterative method of tracking MPP. This technique works on the principle of minor change in PV array voltage and monitors the resulting impact on power. This is achieved by varying the duty cycle of the DC–DC converter employed in the system. With these perturbations, the change in power can be determined. If power is increased by increasing the voltage, the operating point of the PV module is on the left side of the P–V curve. If, on the other hand, power is reduced with the increase in voltage, the PV module operating point is on the right side of the P–V curve. As a result, for tracking MPP, the direction of perturbation must be such that it converges towards a precise end. Thereafter, this iteration process is continued until MPP is reached. Though the conventional P&O technique works well in stable environmental conditions, it fails to track MPP in PSCs [25]. To overcome this drawback, P&O are modified, as reported in [26]. Steps to demonstrate the working of this technique are shown in Figure 8.

**Figure 8.** P&O-based MPPT technique [24].

## 4.1.2. Incremental Conductance

This technique is an improved version of P&O and can track MPP in a rapidly changing environment [27,28]. The principle fact of this technique is based on computing the slope of power "p" on the P–V curve. Since instantaneous power is given as the product of instantaneous voltage and current,

$$p = v \times i \tag{5}$$

The P–V curve slope can be computed as

$$
\partial p/\partial v = \frac{\partial (v \times i)}{\partial v}
$$

$$
= i + v \left(\frac{\partial i}{\partial v}\right) \tag{6}
$$

The following conditions can be drawn from Equation (6):


As a result, the INC approach tracks MPP by comparing incremental conductance with instantaneous one [28]. Although INC can show zero oscillations in steady state, it acts the same as the P&O technique in transition states. Figure 9 shows the flowchart of the INC approach for tracking MPP.

**Figure 9.** INC-based MPPT technique [27].

4.1.3. Fractional Open-Circuit Voltage Technique

FOCV MPPT technique is an indirect scheme to track MPP and can be utilized for low-power functions. This technique utilizes the principle that shows linear relationship between Vmpp and Voc:

$$V\_{mpp} \approx b \times V\_{oc} \tag{7}$$

"b" lies in a range of 0.71 < b < 0.78 [29]. Its value is mainly dependent on module and environmental conditions. Although the technique is simple, FOCV suffers from power loss while sampling Voc. A flowchart of the FOCV method is shown in Figure 10.

**Figure 10.** FOCV-based MPPT technique [29].

4.1.4. Fractional Short-Circuit Current Technique

This technique is also an indirect method for tracking MPP and is similar to FOCV. The FSCC technique utilizes the fact that there exists a linear association between Impp and Isc:

$$I\_{mpp} \approx d \times I\_{sc} \tag{8}$$

The range of "d" lies in 0.78<d< 0.92 [30]. This technique also suffers from the drawback of power loss while measuring Isc during MPPT. A flowchart of the FSCC technique is shown in Figure 11.

**Figure 11.** FSCC-based MPPT technique [30].

These conventional techniques are still used as a baseline for tracking GMPP in PSCs. Table 1 summarizes recently reported works based on these principles, followed by a discussion of their pros and cons in Table 2.


**Table 1.**

Taxonomy on recent reported work on

conventional

 techniques to track GMPP.


**Table 2.** Pros and cons of recent work based on conventional techniques.

#### *4.2. Swarm Intelligence MPPT Techniques*

This section of the paper explains various swarm intelligence MPPT techniques in detail and reports the recent work done with these techniques to enhance MPPT along with their pros and cons in Tables 3 and 4 respectively.

#### 4.2.1. Ant colony Optimization

Ants' cooperative search behavior for the shortest path between source food and their colony motivates ACO. Firstly, ants scurry about aimlessly. When any ant finds a food source, they return to their home along with the food, leaving pheromone trails at their back. This pheromone is composed of particular artificial compounds that are received by living organisms to send messages or codes to other members of the same class. If other colony ants come across such a route, they will follow it to the food source rather than roaming randomly.

They leave pheromones when they return to their territory, boosting the existing pheromone strength. The potency of the pheromone is condensed as pheromone dissipates over time. The ants ultimately regulate and find the shortest path to the food source.

The procedure starts with a single colony of (artificial) ants that has been randomly positioned in that colony. Suppose ants are represented by N parameters. Each ant in the colony uses its magnetic power to entice another ant. They travel from the lower potency zone to the higher potency zone on the basis of attractive force. The attractive power resolute after each iteration cycle and the ants travel in the direction of the best option based on the results.

Consider a problem in which "n" artificial ants (parameters) must be tuned so that A ≥ n. The solution register stores "A", which represents the primarily created arbitrary solutions. The result afterwards sited according to their fitness significance, f (si), is shown in Equation (9):

$$\mathbf{f}(\mathbf{s}\_1) \le \mathbf{f}(\mathbf{s}\_2) \le \mathbf{f}(\mathbf{s}\_3) \le \mathbf{f}(\mathbf{s}\_4) \dots \dots \dots \dots \dots \dots \dots \le \mathbf{f}(\mathbf{s}\_{\mathbf{n}}) \tag{9}$$

Similarly, fresh arrangements are created to determine the placements of these ants with the help of Gaussian kernel function sampling for ith dimensions and kth solution as [46]

$$\mathbf{G}\_{l}(\mathbf{x}) = \sum\_{k=1}^{A} w\_{k} \mathbf{g}\_{k}^{i}(\mathbf{x}) = \sum\_{k=1}^{A} w\_{k} \frac{1}{\sqrt{2\pi} \tilde{a}\_{k}^{i}} e^{\left[-\frac{\left(x-\mu\_{k}^{i}\right)^{2}}{2\left(k\_{k}\right)^{2}}\right]} \tag{10}$$

α5i k, ˆμ<sup>i</sup> <sup>k</sup>, and wk can be evaluated as

$$
\bar{\boldsymbol{\kappa}}\_k^{\dot{i}} = \epsilon \sum\_{\mathbf{k}=1}^{\mathbf{A}} \frac{\left| \mathbf{s}\_{\mathbf{k}}^{\dot{i}} - \mathbf{s}\_{\mathbf{k}}^{\dot{i}} \right|}{\mathbf{A} - 1} \tag{11}
$$

$$\boldsymbol{\mu}\_{k}^{i} = \left[ \boldsymbol{\mu}\_{1\prime}^{i}, \boldsymbol{\mu}\_{2\prime}^{i}, \dots, \boldsymbol{\mu}\_{k\prime}^{i}, \dots, \dots, \boldsymbol{\mu}\_{A}^{i} \right] = \left[ s\_{1\prime}^{i} s\_{2\prime}^{i}, \dots, s\_{k\prime}^{i}, \dots, s\_{A}^{i} \right] \tag{12}$$

$$w\_k = \frac{1}{\mathcal{Q}A} \frac{1}{\sqrt{2\pi}} e^{\left[-\frac{\left(k-1\right)^2}{2\left(\rho A\right)^2}\right]}}\tag{13}$$

The investigative cycle will be continual depending on the quantity of parameters that needs to be improved. First, we generate "B" novel solutions that sum up the initial "A" solutions. Afterwards, A + B solutions must be placed in the search box. Soon after, A's most effective arrangements are re-established. The entire cycle is thus re-hashed for the required amount of iterations [47]. Effective tracking of GMPP, high convergence rate, and a lesser number of iteration makes ACO more advantageous than traditional MPPT techniques. A flowchart of ACO is shown in Figure 12.

**Figure 12.** ACO-based MPPT technique [47].

4.2.2. Particle Swarm Optimization

PSO is a random search technique. It utilizes the principle of maximizing nonlinear continuous function. It follows the rules of natural manner of fish schooling and flock gathering. Several combined birds are used in this technique, each of which represents a particle. In search space, every particle has a fitness value mapped by a vector of position and velocity. The direction and steps of every particle are determined by their fitness value. Following that, all particles present a solution by combining the information gathered during their own search process to arrive at the optimal solution. This technique starts with random solution groups based on particles position and velocity in the search area. With the help of cerebral and social trade-off, the fitness value of particles is adjusted after each iteration. Because of the trade off, shifts in individual and community best position are obtained. Individual particles' best position is also remembered by every particle while also accumulating the global best position [48].

After each cycle, the swarm tries to determine the optimum solution by stimulating the position and velocity. Following that, a global maximum is swiftly achieved by each particle. For the kth cycle, the nth molecule refreshes the condition with position "Y" and velocity "v" as given below

$$
\omega\_n(k+1) = \omega \upsilon\_n(k) + a\_1 \mu\_1 \left( p\_{p, \text{best}-k} - \chi\_n(k) \right) + a\_2 \mu\_2 \left( p\_{\text{g.best}} - \chi\_n(k) \right) \tag{14}
$$

$$Y\_n(k+1) = Y\_n(k) + v\_n(k+1) \tag{15}$$

$$n = 1, 2, 3, \ldots, \ldots, \ldots, \ldots, N$$

If, with an improvised scenario as in Equation (16), the initialization requirement is satisfied, the technique update is in line with Equation (17):

$$ft(Y\_{n-k}) \, > \, ft\left(p\_{p,\,best-k}\right) \tag{16}$$

$$p\_{p,\text{ best}-k} = \mathbb{Y}\_{n-k} \tag{17}$$

"ft" must be maximized. Figure 13 shows the flowchart of the PSO algorithm to track GMPP.

**Figure 13.** PSO-based MPPT technique [48].

4.2.3. Artificial Bee Colony

The ABC approach is based on honey bees' foraging intelligence. This approach is a sensible, modern, and speculative global optimization technique. Honey bees reside inside their hives and use a chemical exchange (pheromones) and the shake dance for their communication. If a bee finds a honey source (food), it takes food back to its hive by performing a shake dance to trade off the food-source site. The potency and duration of the shake dance show the richness of the food source discovered.

Three classes of artificial bee are formed by ABC algorithm, i.e., employed, scouts, and spectator bees. The hive is divided equally between employed and spectator bees. The main aim of whole bees group is to find the best honey source. Employed bees seek out a honey source (food) initially. They revisit their hive and communicate their findings with other groups of bees through shake dance movements. By carefully examining the shake dance of employee bees, spectator bees try to find the food source, while scout bees imprecisely search for new food sources. Thus, with this communication and coordination amongst them, artificial honey bees arrive at ideal solutions in the possible shortest time [49,50]. The ABC algorithm uses five phases to track GMPP as discussed below.
