# Enhancing Global Maximum Power Point of Solar Photovoltaic Strings under Partial Shading Conditions Using Chimp Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Metaheuristic Optimization Algorithms (MOAs) for Tracking MPP

#### 2.1. Chimp Optimization Algorithm (ChOA): Background and Social Hierarchy

#### 2.2. Mathematical Model of Chimp Optimization Algorithm

- t: Current iteration
- a, m and c: Coefficient vectors
- ${\mathrm{X}}_{\mathrm{prey}}$: Prey position vector
- ${\mathrm{X}}_{\mathrm{Chimp}}$: Chimp position vector

_{Chimp}and X

_{prey}. Chaotic vector $\mathrm{m}$ is computed on several chaotic maps such that the result of the sexual motivation of chimps in the searching process. The report of this chaotic vector $\mathrm{m}$ will be explained in Section 2.4. In traditional swarm intelligent optimization techniques, all agents (particle) have identical behavior throughout the search space so that the particles are able to be treated as a group with the same hunt strategy. In the following, different strategies of chimp independent groups to revise $f$ will be modeled mathematically. The chimps’ independent groups updating process can be realized by taking any continuous function from [31].

**f**to be reduced. Each self-determining group applies their model to seek the exploration space locally as well as globally. The perfect version of the chimp optimization algorithm with distinct autonomous groups is chosen, shown in Table 1, and the dynamic coefficient of

**f**that has been proposed is shown in Figure 2. T denotes in Table 1 the maximum number of iterations, and t specifies the present iteration. These dynamic coefficients of vector

**f**have been selected with different curves and slopes to facilitate a precise searching nature for chimps’ independent groups for refining the behavior of ChOA.

#### 2.3. Exploration Phase

**.**C is a random vector in the range of [0, 2]. This parameter offers random weights for prey to check whether (C > 1) or (C < 1). It also helps ChOA to get its stochastic nature along with the optimization procedure and minimizes the chance of trapping in local optima value. C is desirable to develop continuous random values and complete the exploration phase from starting to ending period iterations. The exercise of encircling the prey by the chimps is mathematically modeled as in Equations (6) and (7):

#### 2.4. Attacking Mode (Exploitation Stage)

**f**decreases 2.5 to 0 linearly, to reinforce the procedure of attacking and exploiting the prey’s location. It is found that the scope of the vector decrement is very similar to the

**f**. The most explicit terminology is a random vector with a range of [−2

**f**and 2

**f**]. Every time, the casual value of a stretch out within the value of [−1 and 1], and the subsequent placement of a chimp may be at any location over the available position and the condition of the prey. Even though the projected blocking, driving, and chasing mechanisms in some way highlight the investigation limit, ChOA may, in any case, be in danger of trap into nearby minima. Consequently, an additional operator is essential to highlight the searching ability in the exploitation period. In this optimization algorithm, the chimps are departing to hunt the prey. As described in Figure 3, the vector $\mathrm{a}$ is modeled numerically to fit this behavior. Therefore, the disparity $\left|a\right|$ > 1 enforce the chimps to wander commencing the prey and $\left|a\right|$ < 1 power chimps to converge at the location of the prey.

#### Chaotic Maps (Sexual Motivation)

No | Name | Chaotic Map | Range |

1 | Quadratic | ${\mathrm{x}}_{\mathrm{i}+1\text{}}={\text{}\mathrm{x}}_{\mathrm{i}}^{2}-\mathrm{c},\text{}\mathrm{c}=1$ | (0, 1) |

2 | Logistic | ${\mathrm{x}}_{\mathrm{i}+1\text{}}={\text{}\mathsf{\alpha}\mathrm{x}}_{\mathrm{i}}\left(1-{\mathrm{x}}_{\mathrm{i}}\right),\text{}\mathsf{\alpha}=4$ | (0, 1) |

3 | Bernoulli | ${\mathrm{x}}_{\mathrm{i}+1\text{}}=2{\text{}\mathrm{x}}_{\mathrm{i}}$ | (0, 1) |

## 3. Testing of the ChOA on Some Fixed Dimension Benchmark Functions

_{1}and X

_{2}axes only and indicates the fitness values of the various techniques being used in contrast. The search history plots are joining towards different optimal points showing diverse optima figures nearby one global value. The movement of ideal characteristics got over various iterations can be seen and escape being hit in nearby local optima with the suggested optimization technique can be observed. The proposed algorithm has the mixed characteristics of integrated algorithms, which brought about effective and enhanced the system’s performance.

## 4. Extraction of Maximum Power Point from Solar PV System with the Proposed ChOA

#### 4.1. Modelling of PV Cell

_{oc}); (ii) Current under short-circuit (I

_{sc}); (iii) Maximum voltage near MPP (V

_{MPP}); and (iv) Current near MPP (I

_{MPP}). In contempt about this data, PV panel further required photocurrent developed at standard test condition (I

_{N}), diode reverse saturation current (I

_{o}), the resistance of the terminal of the panel (R

_{S}), shunt resistance (R

_{Sh}), and fill factor. The solar cell equivalent circuit is presented in Figure 7.

N_{s} | Total number of cells connected in series. |

N_{P} | Total number of cells connected in parallel. |

I_{0} | Saturation current of the diode in A. |

I _{PV} | Photo current generated by the cell under standard test conditions in A. |

R_{S} | Series resistance in Ω. |

R_{P} | Shunt resistance in Ω. |

a | Fill factor. |

#### 4.2. Maximum Power Extracting Controllers in PV Module during Partial Shading Condition

#### 4.3. Formulation Objective Function

${\mathrm{P}}_{\mathrm{PV}}$ | PV power in watts. |

${\mathrm{V}}_{\mathrm{PV}}$ | PV voltage in volts. |

${\mathrm{I}}_{\mathrm{PV}}$ | PV current in Amps. |

#### 4.4. ChOA Algorithm Implementation for MPPT fo Solar PV Systems

_{m}) in every cluster is solved by calculating their particular objective function (fitness function) values.

**f**coefficient of each chimp is updated by its group strategy. The vibrant coefficients of

**f**have been shown in Table 1 and Figure 2. The next stage is the driver, attacker, barrier, and chaser assessment of the available prey location. Later, every solution of the candidate revises its closeness from the prey. Likewise, the flexible regulation of the coefficients motivates the local optima prevention and quick movement towards the prey. Finally, chaotic maps comfort to speedy convergence with no getting trapped into local optima position. The pseudo-code of ChOA is given below.

Algoritm 1 Pseudocode of ChOA |

Load the chimp population (duty cycle of the DC-DC converter) Initialize the algorithm-specific parameters like f, m, a and cCompute the position of individual chimp Separate chimps aimlessly into different groups Until the stopping criterion is satisfiedDetermine the fitness function of each chimp Fitness function for Maximum power extraction from solar PV strings is $\mathrm{P}\left({\mathrm{d}}_{\mathrm{i}}^{\mathrm{K}}\right)>\mathrm{P}\left({\mathrm{d}}_{\mathrm{i}}^{\mathrm{k}-1}\right)$ d _{Attacker} = Best search agent in the chimp populationd _{Chaser} = Second best search agentd _{barrier} = Third best serach agentd _{driver} = Fourth best search agentWhile (t < maximum number of iteration)for each chimp;Extract the chimps group Update the parameters f, m and c using group strategyUse parameters f, m and c to determine a and then dend forfor each search chimpif (α < 0.5) if (|a| < 1)update location of each chimp agent else if (|a| > 1)Select random search agent end ifelse if (α > 0.5)update the position of the chimp end ifend forUpdate f, m, a and cUpdate d _{Attacker,} d_{Chaser}, d_{barrier} and d_{driver}t = t + 1 end whilereturn d_{Attacker} |

## 5. Results and Discussions

_{out}) = 330 µF. Figure 9 shows the simulation circuit of the KC200 GT PV module under different shading patterns using MATLAB 2016a software. Table 4 shows the parameters of the solar PV system.

_{1}= C

_{2}= 2, population size = 50, number of design variable equal to one, iterations = 10, weighting factor = 0.8 [10]. A small population size will lead to fast convergence and the feasibility of getting trapped to local optimal will be increased. Hence, while choosing population size in swarm intelligent techniques, e.g., PSO, adjustment between tracking accuracy, and convergence speed must be made. PSO, GWO, and ChOA algorithms are applied for observing steady and dynamic behavior of solar PV strings under shading conditions by giving random control signal (duty ratios) to the boost converter according to the algorithm mechanism. The tuning parameters of the benchmark algorithm are shown in Table 5.

_{1}= 800 W/m

^{2}, G

_{2}= 600 W/m

^{2}, G

_{3}= 400 W/m

^{2}and G

_{4}= 200 W/m

^{2}; Shading Pattern 2: G

_{1}= 1000 W/m

^{2}, G

_{2}= 1000 W/m

^{2}, G

_{3}= 500 W/m

^{2}and G

_{4}= 500 W/m

^{2}. Figure 10 shows the variation of power curves for these shading conditions, and global maximum powers (P

_{MPP}) for particular pattern, including: Pattern 1, P

_{MPP}= 267.41 W, Pattern 2: P

_{MPP}= 443.056 W, and Pattern 3, P

_{MPP}= 800.23 W.

#### 5.1. Shading Pattern1

^{2}, 600 W/m

^{2}, 400 W/m

^{2}, and 200 W/m

^{2}. The power curve of PV strings under the first shading pattern is shown in Figure 11. There are four peaks present in the Power curve during the first shading pattern. Under this shading condition, the global MPP is 257.41 W. From these simulation results, it was analyzed that the GMPP obtained under the first pattern using ChOA is 257.41 W. The tracking of the GMPP process started for ChOA and PSO algorithms by initializing the random values for the duty cycle, and then by running the algorithm duty ratio (d) is revised.

^{2}, 600 W/m

^{2}, 400 W/m

^{2}, and 200 W/m

^{2}are derived. As shown in Figure 12, the maximum power point trackers start the initialization to establish the search space to cover the entire P-V curve shown in Figure 8 under the first shading pattern to extract GMPP of 257.41 W. The simulation results obtained from chimp optimization have less oscillation during the searching process of MPP under shading conditions. In specific, the power output of the solar PV module converges to the MPP with fewer oscillations. Further, the suggested chimp algorithm converges enough rapidly, reaching to the optimal values only in few seconds, but PSO average convergence time is high from the simulation results shown in Figure 12. It is analyzed that ChOA and PSO methods have the capability of chasing global maximum power during different shading conditions. The qualitative analysis for maximum power extraction with various shading conditions is presented in Table 6.

#### 5.2. Shading Pattern 2

^{2}, 1000 W/m

^{2}, 500 W/m

^{2}, and 500 W/m

^{2}. This creates three peaks in the characteristic curve of PV module and forms a complex situation for tracking GMPP. The location of GMPP is shown in Figure 13.

^{2}, 1000 W/m

^{2}, 500 W/m

^{2}, and 1000 W/m

^{2}from Figure 13, the GMPP is 441.314 W. The exhaustive simulation results from the PV systems with proposed algorithms under a second shading pattern of 1000 W/m

^{2}, 1000 W/m

^{2}, 500 W/m

^{2}, 500 W/m

^{2}are shown in Figure 14, illustrated that the convergence time for ChOA was less comparative with the other intelligent techniques. As can be seen in Figure 12 and Figure 14, the GWO and PSO MPPT algorithms presented high disturbance in the occurrence of transients in the output voltage and power curve of boost converter, the key reasons for the existence of these oscillations are variations in the solar PV system operating conditions and load changes. Since the proposed ChOA has resulted as a devised method with a better damping of oscillations over an extensive range of operating conditions with faster speed of convergence and optimally tuning the decision variable d (duty cycle) of the power converter to get the MPP with sustained oscillations. Meanwhile, the GWO and PSO algorithm requires the complete rescan along the curve to fetch the new GMPP, according to the changes in operating conditions thereby reducing the overall system efficiency.

^{2}, 600 W/m

^{2}, 400 W/m

^{2}, and 200 W/m

^{2}. The updating procedure of ChOA coefficients permit chimps to catch Global MPP in the search space within a short span. It may be constructed that ChOA and PSO techniques are fit for identifying the GMPP, and the execution of ChOA is desirable over the PSO and GWO technique due to its faster convergence rate.

_{1}to M

_{6}for the KC200GT solar PV module within the simulation period of 1 sec. It was identified from the simulation results that the shading pattern M

_{1}will develop maximum power to the solar photovoltaic system. It was observed from the simulation results of different shading conditions that ChOA will work executively for partial shading conditions and gave better performance superior to PSO because of speed and certainty. The statistical simulation results show that the ChOA technique tracks more voltage and power output from the solar PV system compared to the PSO, GWO, and bat optimization techniques. A summary of the statistical simulation results is presented in Table 6. The statistical analysis shows that the switching signal (duty ratio) for boost converter to yield more power from solar PV module is in the range of 0.2 to 0.6 for different shading patterns (M

_{1}to M

_{6}).

**.**

## 6. Conclusions

- ❖
- For the problem of MPPT tracking under partial shading conditions dividing the chimps into four individual groups ensures exploration and exploitation of the search space.
- ❖
- The utilization of chaotic maps guides the ChOA strategy to clear up nearby optima stagnation.
- ❖
- ChOA algorithm exploits four types of population-based search agents; prevention of local optima is very high.
- ❖
- Chimps stores explore space info above the sequence of iteration. Chimps relatively use memory to preserve the conquer resolution captured until now.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

PV | Photovoltaic |

N_{s} | Total number of cells arranged in series |

N_{P} | Total number of cells arranged in parallel |

I_{0} | Saturation current of the diode in amps |

I _{PV} | Photo current generated by the cell under standard test conditions |

R_{S} | Series resistance in Ω |

R_{P} | Shunt resistance in Ω |

a | Fill factor |

E | Irradiation in W/m^{2} |

Vc | Open circuit voltage in V |

I_{SC} | Current under short-circuit in A |

I _{o} | Diode reverse saturation current in A |

I _{N} | Photocurrent developed at standard test condition in A |

V_{PP} | Voltage at MPP in V |

I_{MP} | Current near MPP in A |

P_{MP} | Power at MPP in Watts |

D | duty cycle of the power converter |

T | Simulation time in sec |

P_{PV} | PV panel power in Watts |

V_{PV} | Panel output Voltage in V |

I _{PV} | Panel output current in A |

W | Inertia weight |

C_{1} | Cognitive learning coefficient |

C_{2} | Social learning coefficient |

K | Iteration coefficient |

I | iteration count number of PSO |

${\mathrm{V}}_{\mathrm{nd}}^{\mathrm{t}}$ | Velocity of the nth particle at tth iteration |

${\mathrm{X}}_{\mathrm{nd}}^{\mathrm{t}}$ | Position of the nth particle at tth iteration |

${\mathrm{P}}_{\mathrm{nd}}^{\mathrm{t}}$ | Local best position achieved by nth particle at tth iteration |

${\mathrm{P}}_{\mathrm{gd}}^{\mathrm{t}}$ | Global best position achieved by nth particle at tth iteration |

${\varnothing}_{1},\text{}{\varnothing}_{2}$ | Random values in the rage 0 to 1 |

t | Number of current iteration |

a, m and c | Coefficient vectors |

${\mathrm{X}}_{\mathrm{prey}}$ | Prey position vector |

${\mathrm{X}}_{\mathrm{Chimp}}$ | Chimp position vector |

m | $\mathrm{Chaotic}\_\mathrm{vector}$ |

D | Distance between the chimp and prey |

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**Figure 1.**Trends in renewable energy by region [4].

**Figure 2.**Mathematical model of dynamic coefficients (

**f**) vector related to different groups of ChOA.

**Figure 6.**(

**a**) 2D function plot of F1, F2 (

**b**) Search history of Chimps (

**c**) Convergence characteristics of ChOA, GWO, and PSO techniques for the considered fixed dimension test function.

**Figure 8.**4S Arrangement under various shading patterns. (

**a**) Pattern 1. (

**b**) Pattern 2. (

**c**) P-V characteristics of a solar PV system at different shading conditions.

**Figure 9.**Simulation circuit of KC200GT series-connected PV module under different shading patterns by implementing ChOA algorithm.

**Figure 11.**Scenario of Power curve under first shading pattern like 800 W/m

^{2}, 600 W/m

^{2}, 400 W/m

^{2}and 200 W/m

^{2}.

**Figure 12.**Precise simulation results of PV strings for shading pattern of 800 W/m

^{2}, 600 W/m

^{2}, 400 W/m

^{2}, 200 W/m

^{2}proposed technique, PSO and the conventional P&O technique for weak shading pattern: (

**a**) PSO technique (

**b**) GWO technique (

**c**) ChOA technique.

**Figure 13.**Power curve under second shading pattern like 1000 W/m

^{2}, 1000 W/m

^{2}, 500 W/m

^{2}and 500 W/m

^{2}.

**Figure 14.**Precise Simulation results of PV strings for shading pattern of 1000 W/m

^{2}, 1000 W/m

^{2}, 500 W/m

^{2}, 500 W/m

^{2}proposed technique, PSO and the conventional P&O technique for weak shading pattern: (

**a**) PSO technique (

**b**) GWO technique (

**c**) ChOA technique.

**Figure 15.**Convergence curves of different algorithms for MPPT under shading pattern of 800 W/m

^{2}, 600 W/m

^{2}, 400 W/m

^{2}, and 200 W/m

^{2}.

Group | Barrier | Attacker | Driver | Chaser |
---|---|---|---|---|

f | $1.95-2{\mathrm{t}}^{1/3}/{\mathrm{T}}^{1/4}$ | $1.95-2{\mathrm{t}}^{1/4}/{\mathrm{T}}^{1/3}$ | $\left(-3\raisebox{1ex}{${\mathrm{t}}^{3}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{T}}^{3}$}\right.\right)+1.5$ | $\left(-2\raisebox{1ex}{${\mathrm{t}}^{3}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{T}}^{3}$}\right.\right)+1.5$ |

Function | Range | Dim |
---|---|---|

${\mathrm{F}}_{1}\left(\mathrm{X}\right)=4{\text{}\mathrm{X}}_{1}^{2}-2.1{\text{}\mathrm{X}}_{1}^{4}+\frac{1}{3}{\mathrm{X}}_{1}^{6}+{\mathrm{X}}_{1}{\mathrm{X}}_{2}-4{\mathrm{X}}_{1}^{2}+4{\mathrm{X}}_{2}^{4}$ | [−5, 5] | 2 |

${\mathrm{F}}_{2}\left(\mathrm{X}\right)=3.5{\text{}\mathrm{X}}_{1}^{2}-2.1{\text{}\mathrm{X}}_{1}^{4}+\frac{1}{6}{\mathrm{X}}_{1}^{6}+{\mathrm{X}}_{1}{\mathrm{X}}_{2}-6.5{\mathrm{X}}_{1}^{2}+4{\mathrm{X}}_{2}^{4}$ | [−5, 5] | 2 |

Function | ChOA | GWO | PSO | |
---|---|---|---|---|

${\mathrm{F}}_{1}\left(\mathrm{X}\right)=4{\text{}\mathrm{X}}_{1}^{2}-2.1{\text{}\mathrm{X}}_{1}^{4}+\frac{1}{3}{\mathrm{X}}_{1}^{6}+{\mathrm{X}}_{1}{\mathrm{X}}_{2}-4{\mathrm{X}}_{1}^{2}+4{\mathrm{X}}_{2}^{4}$ | Mean | −1.03163 | −1.03163 | −1.03158 |

SD | 6.25 × 10^{−16} | 2.63 × 10^{−8} | 2.95 × 10^{−5} | |

Best | −1.03163 | −1.03163 | −1.03163 | |

Worst | −1.03163 | −1.03163 | −1.03152 | |

${\mathrm{F}}_{2}\left(\mathrm{X}\right)=3.5{\text{}\mathrm{X}}_{1}^{2}-2.1{\text{}\mathrm{X}}_{1}^{4}+\frac{1}{6}{\mathrm{X}}_{1}^{6}+{\mathrm{X}}_{1}{\mathrm{X}}_{2}-6.5{\mathrm{X}}_{1}^{2}+4{\mathrm{X}}_{2}^{4}$ | Mean | −26.8026 | −26.8026 | −26.7927 |

SD | 1.00 × 10^{−14} | 5.26 × 10^{−6} | 0.010597 | |

Best | −26.8026 | −26.8026 | −26.8026 | |

Worst | −26.8026 | −26.8026 | −26.7547 |

Parameter | Value |
---|---|

Number of cells | 54 |

V_{oc}—open-circuit voltage in (V) | 32.9 V |

I_{sc}—short Circuit Current in (A) | 8.21 A |

V_{Mpp}—Maximum voltage at MPP (V) | 26.3 V |

I_{Mpp}—Maximum current at MPP (A) | 7.61 A |

P_{Mpp} (W) | 200.143 W |

Number of series-connected strings | 1 |

Number of parallel-connected strings | 1 |

Algorithm | Specification | Value |
---|---|---|

PSO | Inertia coefficient(W) | 0.8–1.2 |

Design variables | 1 | |

Number of runs | 10 | |

Cognitive and social learning coefficient (C_{1}&C_{2}) | 2 | |

Probability of search ratio | 0.02 | |

GWO | No. of agents (wolf) | 10 |

Positive Limit | 5 | |

Negative limit | −5 | |

Number of iterations | 10 | |

ChOA | f | Details given in Table 1 |

r_{1}, r_{2} | Random values | |

m | chaotic | |

No of search agents | 10 | |

iterations | 10 |

**Table 6.**Summarization of statistical simulation results like power, voltage, and current of PV module under partial shading conditions.

Different Shading Patterns | Parameter | MPPT Methods | |||
---|---|---|---|---|---|

ChOA | PSO | GWO (Mohanthy et al. [34]) | Bat (Roacha et al. [35]) | ||

M_{1} = [1000, 900, 800, 700] | Maximum power | 625.5319 W | 625.4645 W | 622.4625 W | 624.321 W |

Duty @MPP | 0.3196 | 0.4026 | 0.302 | 0.321 | |

Voltage | 115.23 V | 112.8706 V | 110.023 V | 111.212 V | |

Current | 5.5656 A | 5.5687 A | 3.975 A | 3.865 A | |

M_{2} = [800, 650, 100, 500] | Maximum power | 335.6 W | 331.2 W | 329.7 W | 329.75 W |

Duty @GMPP | 0.3296 | 0.3021 | 0.297 | 0.257 | |

Voltage | 84.57 V | 83.4 V | 80.7 V | 81.2 V | |

Current | 3.9489 A | 3.85 A | 2.95 A | 3.12 A | |

M_{3} = [650, 850, 400, 900] | Maximum power | 350.0825 W | 349.5 W | 325.5 W | 329.56 W |

Duty @GMPP | 0.6127 | 0.6027 | 0.507 | 0.527 | |

Voltage | 53.6725 V | 53.21 V | 51.5 V | 52.5 V | |

Current | 6.5915 A | 6.312 A | 6.123 A | 6.223 A | |

M_{4} = [500, 600, 1000, 400] | Maximum power | 260.2923 W | 258.2 W | 256.2 W | 257.2 W |

Duty @GMPP | 0.5163 | 0.5026 | 0.4062 | 0.496 | |

Voltage | 56.4194 V | 55.41 V | 53.55 V | 54.12 V | |

Current | 4.3234 A | 4.123 A | 4.091 A | 4.112 A | |

M_{5} = [400, 100, 850, 250] | Maximum power | 171.8035 W | 170.5W | 165.5 W | 168.5 W |

Duty @GMPP | 0.4630 | 0.4630 | 0.4203 | 0.445 | |

Voltage | 86.3148 V | 85.31 V | 84.4 V | 84.6 V | |

Current | 2.8733 A | 2.853 A | 2.583 A | 2.612 A | |

M_{6} = [350, 400, 700, 150] | Maximum power | 232.75 W | 230.133 W | 214.5 W | 216.5 W |

Duty @GMPP | 0.2704 | 0.2541 | 0.2543 | 0.252 | |

Voltage | 87.543 V | 86.4692 V | 85.54 V | 86.12 V | |

Current | 2.9210 A | 2.8177 A | 2.718 A | 2.725 A |

**Table 7.**Summary of the comparison of soft computing implemented in this work with the recent literature.

Authors | Optimization Technique for MPPT Tracking | Variable Specification | Charge Controller | Dynamic Response | Tracking Speed | Contribution of the Work |
---|---|---|---|---|---|---|

Eltamaly et al. [12] | Hybrid GWO-FLC | Duty cycle | Boost Converter | High | Fast | Developed the flow chart for hybrid GWA along with fuzzy logic controller |

Nagadurga et al. [20] | PSO | Duty Cycle | Boost Converter | Good | Slow | Proposed increment in PV power using PSO technique |

Nagadurga et al. [25] | TLBO technique | Duty Cycle | Boost Converter | Medium | Moderate | Examined the TLBO algorithm for different weather conditions |

Javad et al. [19] | FA | Voltage | Boost Converter | Medium | Fast | Proposed FA for extracting global peak power during shading conditions |

Present study | Chimp Optimization technique | Duty Cycle | Boost Converter | Fast | Moderate | Proposed chimp optimization technique for MPPT under partial shading conditions |

Optimization Technique | Parameter | Shading Pattern M _{1} | Shading Pattern M _{2} | Shading Pattern M _{3} |
---|---|---|---|---|

ChOA | Minimum iterations | 2 | 3 | 2 |

Maximum iteration | 4 | 5 | 6 | |

Convergence time to trace GMPP(s) | 0.10 | 0.12 | 0.10 | |

Efficiency | 100 | 99.99 | 99.85 | |

PSO | Minimum iterations | 2 | 4 | 3 |

Maximum iteration | 6 | 8 | 9 | |

Convergence time to trace GMPP(s) | 0.14 | 0.16 | 0.23 | |

Efficiency | 98.56 | 98.99 | 98.66 |

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## Share and Cite

**MDPI and ACS Style**

Nagadurga, T.; Narasimham, P.V.R.L.; Vakula, V.S.; Devarapalli, R.; Márquez, F.P.G. Enhancing Global Maximum Power Point of Solar Photovoltaic Strings under Partial Shading Conditions Using Chimp Optimization Algorithm. *Energies* **2021**, *14*, 4086.
https://doi.org/10.3390/en14144086

**AMA Style**

Nagadurga T, Narasimham PVRL, Vakula VS, Devarapalli R, Márquez FPG. Enhancing Global Maximum Power Point of Solar Photovoltaic Strings under Partial Shading Conditions Using Chimp Optimization Algorithm. *Energies*. 2021; 14(14):4086.
https://doi.org/10.3390/en14144086

**Chicago/Turabian Style**

Nagadurga, Timmidi, Pasumarthi Venkata Ramana Lakshmi Narasimham, V. S. Vakula, Ramesh Devarapalli, and Fausto Pedro García Márquez. 2021. "Enhancing Global Maximum Power Point of Solar Photovoltaic Strings under Partial Shading Conditions Using Chimp Optimization Algorithm" *Energies* 14, no. 14: 4086.
https://doi.org/10.3390/en14144086