ACO in MPPT

For implementing ACO in MPPT, most of the ants' behavior is considered. Here, ants are initialized first and the objective function is set by considering the irradiation and temperature exposure of each panel. The procedure followed in the ACO algorithm for optimization is given below [50]:

Step 1: Initialize all ants and evaluate K random solutions.

Step 2: Rank solutions according to their fitness value.

Step 3: Perform a new solution.

Step 4: Observe the ant that has the global best position (solution).


Step 7: If satisfied, then the existing solution is the global best value, else go to Step 3. Step 8: End.

For finding the pheromone concentration, the formula is given as:

$$\mathbf{T}\_{\text{i}\parallel} = \rho \mathbf{T}\_{\text{i}\parallel}(\mathbf{t} - \mathbf{1}) + \Delta \mathbf{T}\_{\text{i}\parallel} \tag{13}$$

In the above equation

t = 1, 2, 3, ... , T

Tij is the revised concentration of the pheromone

ΔTij is the change in pheromone concentration

ρ is the pheromone concentration rate.

The main function of ACO is to track the global peak power operating point at which the PV system operates.

$$\begin{aligned} \text{Fitness function} &= \text{Panel } 1 \left( \mathbf{V}\_1 \times \left( \mathbf{I} (\mathbf{S}\_1, \mathbf{T}\_1) \right) \right) + \text{Panel } 2 \left( \mathbf{V}\_2 \times \left( \mathbf{I} (\mathbf{S}\_2, \mathbf{T}\_2) \right) \right) + \\ &\quad \text{Panel } 3 \left( \mathbf{V}\_3 \times \left( \mathbf{I} (\mathbf{S}\_3, \mathbf{T}\_3) \right) \right) + \dots \text{ + panel } \text{N} \left( \mathbf{V}\_N \times \left( \mathbf{I} (\mathbf{S}\_N, \mathbf{T}\_N) \right) \right) \end{aligned} \tag{14}$$

where V1, S1, and T1 represent the panel 1 voltage, irradiance, and temperature, respectively, and so on for the other panels.

In references [42,52], the authors have used an ACO algorithm to improve the PV system efficiency for a partial shading condition. Apart from the MPPT techniques, the ACO has wide application such as optimization in hydro-electric generation scheduling, optimal reactive power dispatch for line loss reduction, microwave corrugated filter design, etc. [53–55]. For further improving the ACO performance, i.e., its convergence speed and ease of operation, it can also be combined with various evolutionary and conventional algorithms. The ACO algorithm performs excellently for partially shaded PV modules with improved system performance [56,57]. In reference [58], an ACO-PSO-based MPPT technique is given for a partially shaded PV system. The proposed hybrid algorithm is implemented with an inter-leaved boost converter, which improves the output power and provides a constant voltage to the load. The authors in reference [59] have proposed a hybrid algorithm by considering the simplest conventional and widely used P&O (perturb and observe) with ACO. P&O fails during partial shading and falls on local MPP, hence in the hybrid algorithm, ACO helps the algorithm converge towards the GMPP. This hybrid algorithm improves the system performance and reliability.

### *3.4. Artificial Bee Colony (ABC)*

This swarm technology-based meta-heuristic algorithm is used to solve multi-dimensional and multi-modal problems. The algorithm was proposed by Karaboga [60]. It is inspired by various behaviors of honeybees such as foraging, learning, memorizing, and sharing of information for optimization [61–63]. For the ABC algorithm, food locations are considered as effective solutions and the amount of nectar it produces defines the quality of the food source (i.e., fitness of the food source) [64]. Here, the bees are classified into three categories (first one is called employed bees, second one is onlooker bees, and the third one is scout bees), and the three types of bees perform mostly three types of foraging behavior, which are first searching the food source, then employing the employed bees for getting the food from the food source, and lastly, discarding the food source due to its lack of nectar quality [15,27]. The employed bees search for food or find the food location. The bee that makes decision regarding the food source is called the onlooker bee. The food sources discovered by the employed bees that cannot be improved are discarded, and the employed bees that found them become scout bees. Here, the number of bees is equal to the number of employed scout bees and onlooker bees. Flowchart of ABC algorithm is given in Figure 7.

**Figure 7.** ABC algorithm.

ABC as the MPPT

For analyzing the MPPT technique based on the ABC algorithm, every candidate solution is considered as duty cycle "d" of the dc–dc converter. Hence, here the optimization function has only one parameter "d" to be optimized. Let us consider a D-dimensional problem having NP food sources has to be optimized, where NP is the number of number of bees in the search space. Hence, by assuming that each food source has one employed bee, then the ith food source location for the tth iteration is given by

$$\mathbf{X}\_{\rm i}^{\rm t} = \begin{bmatrix} \mathbf{x}\_{\rm i1'}^{\rm t} \mathbf{x}\_{\rm i2'}^{\rm t} \mathbf{x}\_{\rm i3'}^{\rm t} \dots \mathbf{x}\_{\rm id}^{\rm t} \dots \mathbf{x}\_{\rm iD}^{\rm t} \end{bmatrix}^{\rm T} \tag{15}$$

Randomly generate the food source as:

$$\mathbf{x}\_{\rm id} = \mathbf{L}\_{\rm d} + \mathbf{r}(\mathbf{U}\_{\rm d} - \mathbf{L}\_{\rm d}) \tag{16}$$

where Ud and Ld are upper and lower limit for the dth dimension problem, and r is a random number whose value is chosen between [0,1].

In the next step, the employed bees search for a new food source Vi near to Xi along with a randomly selected dimension d:

$$\mathbf{v}\_{\rm id} = \mathbf{x}\_{\rm id} + \beta \left(\mathbf{x}\_{\rm id} - \mathbf{x}\_{\rm id}\right) \tag{17}$$

where vid is the new food source; j is a randomly chosen vector where i - j ∈ (1, 2, 3, ... NP) and β is a randomly chosen value between [1,−1].

In the above condition, if it is found that the new food source is better than that of the old one, then the new food source gets updated, whereas the old one is discarded; else, the old food source remains in the next iteration [15].

Again, the available food source information is shared with onlooker bees and the food source is selected by the onlooker bees based on a probability criteria:

$$P\_{\mathbf{i}} = \frac{\text{fitness}\_{\mathbf{i}}}{\sum\_{\mathbf{n}=1}^{N\_{\mathbf{P}}} \text{fitness}\_{\mathbf{n}}} \tag{18}$$

In this step, the employed bees also ge<sup>t</sup> updated with the help of a greedy selection process. In the next step, after the prescribed number of iterations or when the limit values for the new food source quality have not improved, then the food source gets abandoned and goes for termination. The bees associated with the abandoned food sources become scout bees and search for new available food sources and checks for termination criteria. If the available solutions are acceptable and maximum iterations are reached, then the process terminates; otherwise, it continues the search.

The performance analysis of the ABC algorithm is given in reference [65]. Here, the performance of the algorithm is compared with PSO, DE, and other evolutionary algorithms for multi-modal and multi-functional problems where ABC is found to be giving better result compared to others. ABC has successfully been implemented for leaf-constrained minimum spanning problems too [66]. In reference [67], the authors have done a comparative study of the ABC algorithm for a large set of numerical optimization problems and the results obtained are compared with population-based algorithms. It was found that the results obtained by ABC are superior, and in some cases, same as the population-based algorithms where ABC has the advantage of having less control parameters than others. ABC-based MPPT techniques for PV system are given in Reference [68] and the results are compared with the P&O algorithm where the ABC-based MPPT gives a better performance. From various researchers, the e ffectiveness of the ABC algorithm as an MPPT technique for both uniform and partial shading conditions are shown and found to be better than the existing techniques [69–71]. A modified ABC algorithm (MABC) is presented in reference [72] whose performance is compared with the genetic algorithm (GA), PSO, and ABC, and was found to be more suitable for reducing the power loss of PV modules during a partial shading condition.

### *3.5. Bacteria Foraging Optimization Algorithm (BFOA)*

This is a nature-inspired algorithm that is inspired by various foraging behaviors of *Escherichia Coli (E. Coli)*. The *E. Coli* bacteria present inside the intestine of humans and animals possesses various multi-functional foraging behaviors so as to maximize the consumption of energy per unit time for one particular foraging process. When the foraging process occurs due to the environmental conditions, the bacterium with a high fitness value or those that are able to withstand the environmental changes continue to survive and the others ge<sup>t</sup> eliminated [73]. These bacteria follows four basic steps for getting to a nutrient-rich location, i.e., for foraging. These four steps are chemotaxis, swarming, reproduction, and elimination-dispersal [74].
