**1. Introduction**

The increasing load demand on one side and the depletion of fossil fuels on the other side forces the world to look for alternative energy resources. Also, the concern regarding pollution through the greenhouse effect and other environmental issues associated with the conventional energy sources make renewable energy resources (RES) more attractive [1]. Among various non-conventional sources, solar energy is more widely used because of the abundant availability of solar irradiation on the earth's surface [2]. The photovoltaic (PV) cells convert direct sunlight into electricity, but as the solar irradiance and temperature are fluctuating in nature, as a result, it reduces the PV panel efficiency. The main drawbacks of the PV system are its highly intermittent nature, lower conversion efficiency, lower rating, high implementation cost, and maintenance issues. PV panels also ge<sup>t</sup> affected due to partial shading because of clouds, tree branches, birds, etc. These factors make it essential to deploy a dc–dc converter with an MPPT technique for tracking the maximum power point from the PV panel under all operating conditions. The MPPT control algorithm is employed along with the dc–dc converter, where the control algorithm adjusts the duty cycle according to the variation in solar irradiation and temperature, which will boost the lower voltage output of the PV system. A PV cell has very low power rating [3–6], and these cells can be connected in series or parallel according to the required current and voltage rating. The series and parallel combination constitute a PV module and the modules are connected together to form a PV array [7]. This makes power electronic interfaces indispensable in any PV system for ensuring the system voltage compatible with a load or grid [8]. PV panels can be implemented as a rooftop setup and it can also operate in standalone mode and grid-connected mode [9].

For a PV system, the output voltage depends on the temperature of the panel and the current value of the irradiance level. The PV system gives the optimum output under the standard test condition (STC-irradiance = 1000 <sup>W</sup>/m2, temperature = 25 ◦C, 1.5 air mass) [3,10]. MPPT trackers embody a control algorithm and converter to ensure that PV panels operate at MPP to render maximum possible power. This tracking scheme becomes futile when PV panels are partially shaded. In the research arena, there was a paradigm shift in MPPT algorithms as a host of research articles are being published every year on global search algorithms [8,9]. Many studies have been done toward developing an e fficient and reliable MPPT algorithm to extract the maximum operating power point from the PV panel [11–13]. Both conventional and computational intelligence algorithms are used for MPPT [14,15]. Most of the conventional algorithms perform e ffectively under uniform solar irradiation and temperature but fail to track the true maximum operating point during varying weather or partial shading conditions [16,17].

The e fficient nature-inspired algorithms based on MPPT techniques are the particle swarm optimization (P&O) algorithm, ant colony optimization (ACO) algorithm, artificial bee colony (ABC) algorithm, di fferential evolution (DE), etc. These algorithms are used for global search problems and can operate e ffectively under uniform solar irradiation and temperature, as well as partial shading and rapidly changing environmental conditions. Hybridization of these algorithms also has been done for enhancing the performance and reliability of these algorithms. In Reference [18], the authors have proposed a swarm chasing MPPT algorithm for module integrated converters and the performance is also compared with conventional P&O method. Here, the swarm-chasing technique is found to be more superior. Comparative study on well-entrenched global peak tracking algorithms is archived in a research forum [15,19]. Some researchers paid due credit to the conventional algorithms and examined whether the algorithms could be sustained during partial shading. In Reference [19], conventional and computational intelligence MPPT techniques were presented, which describes the working of each algorithm with their merits and demerits. The quest toward proposing new algorithms has not dwindled as one can witness recent research articles on global search MPPT [8,9,13,15].

In this paper, a review has been done for five evolutionary algorithms that are reliable and more pragmatic for practical deployment. This paper has been framed in such a manner that it gives a clear understanding of PV characteristics, partial shading, and MPP search mechanisms. The paper is organized in such a way that Section 2 presents PV modeling and PV characteristics analysis during both uniform irradiation condition and PSCs. Section 3 discusses the soft computing algorithms reviewed in this paper, whereas Section 4 follows a brief discussion about the reviewed algorithms. The concluding part is given in Section 5.

### **2. PV Modeling and Its Characteristic Curves**

Figure 1 depicts a general block diagram of a PV generating system. In the given diagram, a PV panel connected with a dc–dc converter and the duty cycle of the converter is controlled by the MPPT algorithm. The MPPT algorithm will sense the required parameters from the solar system, and accordingly, it modifies the converter duty cycle. Hence, under all conditions, maximum output power is obtained from the panel. Then the converter output can be directly connected to the dc load or it can also be given to ac loads by connecting them through an inverter.

**Figure 1.** Diagram of PV connected to a load.

A PV module consists of many solar cells that are generally made up of silicon material. When the light energy falls on the solar cell, then the electrons start to move and current flows. Solar cells are considered current sources. There are many types of solar cell models, among which, the single diode model is well established and a simple structure [10,20]. In this paper, a single diode model solar cell is shown in Figure 2. It is basically a diode connected in parallel with a current source along with one shunt and one series resistor. In the figure, Ipv is the current generated by light, ID is the current across diode, whereas Ish represents the current flowing through a shunt resistance Rsh, and I is the output current. For the mathematical modeling of the PV system, the basic equations are given below.

**Figure 2.** Circuit for the modelling of a single diode PV cell.

$$\mathbf{I} = \mathbf{I}\_{\rm PV} - \mathbf{I}\_{\rm o} \left[ \exp\left[\frac{\mathbf{V} + \mathbf{I}\mathbf{R}\_{\rm s}}{\mathbf{a}\mathbf{V}\_{\rm T}}\right] - 1\right] - \frac{\mathbf{V} + \mathbf{I}\mathbf{R}\_{\rm s}}{\mathbf{R}\_{\rm sh}} \tag{1}$$

where VT is the PV array thermal voltage = kT/q. IP represents the photocurrent, Io represents reverse saturation current, and Rs and Rsh represent the series and shunt resistance respectively, a is the diode ideality factor, q is the charge of the electron i.e., 1.6 × 10−<sup>19</sup> C, k represents Boltzmann's constant (1.3806503 × 10−<sup>23</sup> J/K), and T is the temperature.

$$\mathbf{I}\_{\rm o} = \mathbf{I}\_{\rm o\\_STC} \left[ \frac{\mathbf{T}\_{\rm STC}}{\mathbf{T}} \right]^3 \exp\left[ \frac{\mathbf{q} \mathbf{E}\_{\rm g}}{\mathbf{ak}} \left[ \frac{1}{\mathbf{T}\_{\rm STC}} - \frac{1}{\mathbf{T}} \right] \right] \tag{2}$$

In the above equation Eg represents band gap energy of the semi-conductor material and Io\_STC denotes the nominal saturation current at STC, TSTC is the temperature under STC (25 ◦C).

In simplified form, Io can be written as

$$\mathbf{I}\_{\rm o} = \frac{(\mathbf{I}\_{\rm sc,STC} + \mathbf{K}\_{\rm I} \Delta \mathbf{T})}{\exp\left[ (\mathbf{V}\_{\rm co,STC} + \mathbf{K}\_{\rm v} \Delta \mathbf{T}) / \mathbf{a} \mathbf{V}\_{\rm T} \right] - 1} \tag{3}$$

here Ki is the coefficient of the short circuit current, Kv is the open circuit voltage coefficient, Isc\_STC is the short circuit current under STC, Voc\_STC is the open circuit voltage under STC, and ΔT = T − TSTC.

In Figure 3a,b the I–V graph and P–V graph for different irradiation levels are shown. The I–V graph shown in Figure 3a shows that according to the temperature and irradiance, the voltage and current value also varies. Here, the current value depends on the irradiance, i.e., directly proportional, and the voltage depends on the temperature [20]. Hence, the PV operating point does not stay at the maximum operating value and it varies with the environmental conditions, which in turn, reduces the

power. Therefore, it is preferable to install more PGS than the required demand, but simultaneously, it increases the cost [21]. Therefore, the dc–dc converter with an effective MPPT technique is deployed for the PV systems to modify the converter duty cycle according to the environmental conditions and thereby tracks the maximum power point for all operating conditions. During uniform irradiance, the P–V graph shows only one peak power point, which gives the corresponding maximum voltage and current. Hence, the conventional MPPT techniques would suffice to track the true MPP and is found to be reliable.

**Figure 3.** P–V characteristics graph for different irradiation levels. (**a**) shows the current versus voltage graph for different irradiation levels; (**b**) shows the power versus voltage graph for different irradiation levels.

However, when some of the PV panels in an array receive non-uniform irradiation and temperature, i.e., they are shaded, then the power production of the shaded panel decreases relative to an unshaded one. The shaded panels absorb a large amount of current from the unshaded panels in order to operate. This condition is called hot spot formation and this damages the PV panel [22,23]. To avoid this condition, a bypass diode is connected in parallel across each panel, as shown in Figure 4a,b, which provides another way for conduction during the occurrence of partial shading [24]. As shown in Figure 4c,d, during the partial shading condition, there exist multiple peak points in the P–V characteristics graph, among which only one point is the true maximum power point. These multiple peak points are considered the local maximum power points (LMPPs), and among all the LMPPs, the true MPP is called the global maximum power point (GMPP). Most of the conventional MPPT techniques fail to identify the GMPP among all the LMPP. For this purpose, many researchers have proposed various stochastic, evolutionary, and swarm-based algorithms and hybridization of these algorithms has also been done for more reliable and effective MPP tracking.

**Figure 4.** *Cont.*

**Figure 4.** PV panels operation during partial shading conditions: (**a**) PV panels under normal operation, (**b**) PV panels under a shading condition, (**c**) I–V characteristic of PGS during partial shading, and (**d**) P–V characteristic of PGS during partial shading.

### **3. Intelligent Nature Inspired Algorithms: An Overview**

The specific evolutionary algorithms discussed are


The analysis of these algorithms has been done with respect to the convergence speed, execution, and reliability.

### *3.1. Particle Swarm Optimization (PSO)*

PSO is the most widely used algorithm used for the MPPT technique. This algorithm was discovered in 1995 by Ebehart and Kennedy. PSO is widely accepted by researchers due to its simple and easy to implementation characteristics. This algorithm is motivated by the communal activity of the crowding of birds and schooling activity of fish. PSO is a global optimization algorithm that finds the best solution in a multi-dimensional path. Therefore, it is able to track the GMPP from all local MPPs even when the PV panel is under a partial shading condition or the PV panel possesses multiple peak points. PSO uses many operating agents that share information about their respective search behavior, where all agents are termed as a particle. Here, a number of particles move in the search space in order to ge<sup>t</sup> the best solution. Each particle adjusts its movement by following the best solution and mean while searches for new solutions will be in progress [25]. The particle referred here can be voltage or duty cycle. For finding the optimal solution, the particle must follow the best position of its own or the best position of its neighbor. The mathematical representation of the PSO algorithm is given in the following equations [26,27]:

$$\mathbf{u}\_{\rm i}(\mathbf{k}+1) = \mathbf{q}\mathbf{u}\_{\rm i}(\mathbf{k}) + \mathbf{c}\_{1}\mathbf{r}1(\mathbf{p}\_{\rm best,i} - \mathbf{g}\_{\rm i}(\mathbf{k})) + \mathbf{c}\_{2}\mathbf{r}2(\mathbf{g}\_{\rm best,i} - \mathbf{g}\_{\rm i}(\mathbf{k})) \tag{4}$$

$$\mathbf{g}\_{\mathbf{i}}(\mathbf{k}+1) = \mathbf{g}\_{\mathbf{i}}(\mathbf{k}) + \mathbf{u}\_{\mathbf{i}}(\mathbf{k}+1) \tag{5}$$

where i = 1, 2, 3,..., N.

> ui—velocity of the particle gi—particle position

k—number of iterations

q—inertia weight

r1,r2—random variables which are distributed uniformly between [0,1]

c1,c2—cognitive and social co-efficient respectively

pbest—individual particle's best position

gbest—best position between all the particle's individual best position

PSO finds the global maxima voltage point according to the maximum power in the P–V graph. For this, we need to specify PSO parameters such as power and voltage value, size of the swarm, and number of iterations. PSO stores the best value as pbest and continues to update until it finds the gbest point or it satisfies the objective function [15,27,28]:

$$\mathbf{p\_{best,i}} = \mathbf{g\_i(k)} \tag{6}$$

 (8)

$$\mathbf{f}(\mathbf{g}\_i(\mathbf{k})) > \mathbf{f}(\mathbf{g}\_i(\mathbf{k}+1)) \tag{7}$$

where the function "f" is the PV panel operating power. During partial shading, the particles are re-initialized to find gbest and it must satisfy the below condition. A flowchart of the PSO algorithm is given in Figure 5.

> − <sup>P</sup>(gi)

**Figure 5.** PSO algorithm.

In Reference [24], a cost-effective PSO algorithm is presented, which uses one single pair of sensors for controlling multiple PV arrays. The algorithm is also compared with many conventional techniques, from which, the proposed algorithm is found to be more effective and it also tracks the MPP even during partial shading conditions. The authors in Reference [9] have presented a PSO algorithm integrated with an overall distribution (OD) algorithm. The OD technique is used to efficiently track the MPP during any shading conditions and is again integrated with PSO to improve the accuracy of the MPPT technique. A novel two-stage PSO MPPT is proposed in Reference [29]. Here, for partial shading conditions and to achieve improved convergence speed, a shuffled frog leaf algorithm (SFLA) with an adaptive speed factor is implemented with PSO. For partially shaded PV power systems, a modified PSO is presented in Reference [30] whose effectiveness is shown in the paper. Many studies have been done using PSO as an MPPT technique for both uniform irradiation and partially shaded conditions. However, the standard PSO performance is enhanced and modified by using hybridization and modification in the algorithm [25,28,31–35], which increases the system efficiency and is found to be more reliable.
