# Parameter Extraction of Photovoltaic Module Using Tunicate Swarm Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Problem Statement

#### 2.1. Photovoltaic Panel Module Model

^{−23}J/K), junction temperature (°K), and electron charge (1.602 × 10

^{−19}C), respectively. It is depicted in Figure 1 that only five parameters (${I}_{p}$, ${I}_{SD}$, a,$\text{}{R}_{s}$ and ${R}_{sh}$) are needed to be estimated for the minimum value of RMSE.

#### 2.2. Objective Function

## 3. Tunicate Swarm Algorithm

#### 3.1. Prevent Collisions between Candidate Solutions

#### 3.2. Step More toward the Location of the Best Solution

#### 3.3. Stick Close to the Best Solution

#### 3.4. Implementation of TSA for Parameter Extraction

_{p}), series resistance (R

_{s}), shunt resistance (R

_{sh}), diode saturation current (I

_{SD}), and diode ideality factor (a). The range of these parameters are [0–10, 0.001–2, 0–2000, 0–50, 0–100].

## 4. Results and Discussion

^{2}at 30 °C). As a result, the retrieved PV module parameters were monitored and used to create simulated I-V data. The reliability of the WOAPSO is evaluated and compared with six metaheuristics algorithms, i.e., GSA [7], SCA [8], GWO [9], PSO [10], WOA [11], PSOGSA [12], as well as other algorithms existing in the literature. For the experiment, the sample size and the objective function evaluations are set between 30 and 50,000, respectively. Furthermore, a minimum of 30 separate runs are carried out to prevent contingency.

^{®}core ™ i7-HQ CPU, 2.4 GHz, 16 GB RAM laptop.

#### 4.1. TSA for Parameter Extraction of Photowatt-PWP201 PV Module

_{p}, I

_{sd}, a, R

_{s}, R

_{sh}) for SDM of the solar PV module are presented in Table 2. The characteristics curves of current-voltage (I-V) and power-voltage (P-V) are redrawn by implementing the TSA algorithm under optimized parameters. Figure 3 demonstrates the estimated and experimental I-V and P-V characteristics curves. It can be observed that the estimated parameters show good agreement with the measured ones, which proves the efficient performance of the TSA.

^{2}and 30 °C) is less than 0.0195, which indicates that the parameters optimized by the TSA are very precise. The error relating to the measurement results for each of the 23 pair points is determined by the IAE and Relative Error (RE). The IAE and RE values are calculated using Equations (11) and (12). The curve of IAE and RE between experimental and estimated values is shown in Figure 4.

#### 4.2. Convergence Analysis

#### 4.3. Robustness and Statistics Analysis

## 5. Discussion

## 6. Conclusions

- TSA is relatively accurate and reliable at delivering the solution in terms of the RMSE compared with other algorithms such as GSA, PSOGSA, SCA, and WOA.
- The I-V and P-V characteristic curves and IAE results indicate that TSA can generate the optimized value of the estimated parameters for all the solar PV cell models compared with other algorithms.
- The statistical analysis depicts the robustness of the TSA technique in parameter estimation problems under standard operating conditions.
- The convergence curves demonstrate that the TSA obtains the best estimated parameters in terms of RMSE (5.06 $\times $ 10
^{−4}). - From the above discussion, it can be concluded that the TSA is an effective and robust technique to estimate the unknown optimized parameters of the solar PV module model under standard operating conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations and Symbols

I_{p} | Photo Diode Current |

I_{sd} | Reverse Saturation Current |

R_{s} | Series Resistance |

R_{sh} | Shunt Resistance |

A | Diode Ideality Factor |

RMSE | Root Mean Square Error |

PV | Photovoltaic |

I-V | Current-Voltage |

P-V | Power-Voltage |

MPPT | Maximum Power Point Tracking |

V_{oc} | Open Circuit Voltage |

I_{mpp} | Maximum Power Point Current |

I_{sc} | Short Circuit Current |

PSO | Particle Swarm Optimization |

WOA | Whale Optimization Algorithm |

SDM | Single diode Model |

DDM | Double diode Model |

IAE | Internal Absolute Error |

RE | Relative Error |

GSA | Gravitational Search Algorithm |

SCA | Sine Cosine Algorithm |

PSOGSA | Particle Swarm Optimization Gravitational Search Algorithm |

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**Figure 3.**Current-Voltage (I-V) and Power-Voltage (P-V) characteristics curve for estimated and experimental values for single-diode model of Photowatt-PWP201 PV Module. Symbols represent measured data, and optimized data are represented by solid lines.

**Figure 4.**(

**a**) Internal absolute error and (

**b**) relative error curve between measured and estimated current for Photowatt-PWP201 PV Module.

**Figure 5.**Convergence curve of TSA (Tunicate swarm algorithm) and the other four algorithms for single-diode model of Photowatt-PWP201 PV (Photovoltaic) Module.

**Figure 7.**Ranking of TSA (Tunicate swarm algorithm) and other compared algorithms on Photowatt-PWP201 PV panel module according to the Friedman test.

Parameters | Photowatt-PWP201 PV Module | |
---|---|---|

Lower Bound | Upper Bound | |

I_{p} (A) | 0 | 10 |

I_{sd} (µA) | 0 | 50 |

R_{s} (Ω) | 0.001 | 2 |

R_{sh} (Ω) | 0 | 2000 |

a | 0 | 100 |

Algorithms | I_{ph} (A) | R_{s} (Ω) | R_{sh} (Ω) | I_{sd} (µA) | a | RMSE |
---|---|---|---|---|---|---|

WOAPSO [18] | 1.5032 | 0.0213 | 668.27 | 0.024 | 1.502 | 8.86 × 10^{−4} |

GSA | 0.0278 | 2 | 1201.097 | 0.050 | 58.4588 | 8.80 × 10^{−3} |

PSOGSA | 0.0218 | 0.6430 | 1100.437 | 0.01 | 79.7893 | 7.156 × 10^{−3} |

SCA | 1.0063 | 0.0496 | 1107.399 | 0.039 | 1.0532 | 1.28 × 10^{−2} |

WOA | 0.0264 | 0.0113 | 588.5011 | 0.0424 | 1.4496 | 9.54 × 10^{−4} |

TSA | 0.0261 | 0.0017 | 2000 | 0.053 | 1.4727 | 5.06 × 10^{−4} |

**Table 3.**The calculated current and absolute error results of TSA (Tunicate swarm algorithm) for solar PV (Photovoltaic) module.

Observations | V_{L} (V) | I_{L} (A) | I_{sim} (A) | IAE (A) | P_{measured} (W) | P_{simulted} (W) | IAE (W) |
---|---|---|---|---|---|---|---|

1 | 0.1246 | 1.0345 | 1.0335 | 0.001 | 0.1288 | 0.1256 | 0.0032 |

2 | 0.1248 | 1.0315 | 1.0335 | 0.002 | 0.1287 | 0.1226 | 0.0061 |

3 | 1.8093 | 1.03 | 1.0335 | 0.0035 | 1.8635 | 1.8765 | 0.013 |

4 | 3.3511 | 1.026 | 1.0234 | 0.0026 | 3.4382 | 3.4354 | 0.0028 |

5 | 4.7622 | 1.022 | 1.0234 | 0.0014 | 4.8669 | 4.8766 | 0.0097 |

6 | 6.0538 | 1.018 | 1.019 | 0.001 | 6.1627 | 6.1456 | 0.0171 |

7 | 7.2364 | 1.0155 | 1.0142 | 0.0013 | 7.3485 | 7.3256 | 0.0229 |

8 | 8.3189 | 1.014 | 1.011 | 0.003 | 8.4353 | 8.4453 | 0.01 |

9 | 9.3097 | 1.01 | 1.002 | 0.008 | 9.4027 | 9.4124 | 0.0097 |

10 | 10.2163 | 1.0035 | 1.023 | 0.0195 | 10.252 | 10.245 | 0.007 |

11 | 11.0449 | 0.988 | 0.985 | 0.003 | 10.9123 | 10.9234 | 0.0111 |

12 | 11.8018 | 0.963 | 0.967 | 0.004 | 11.3651 | 11.3554 | 0.0097 |

13 | 12.4929 | 0.9255 | 0.918 | 0.0075 | 11.5621 | 11.5722 | 0.0101 |

14 | 13.1231 | 0.8725 | 0.883 | 0.0105 | 11.4499 | 11.445 | 0.0049 |

15 | 13.6983 | 0.8075 | 0.8173 | 0.0098 | 11.0613 | 11.0521 | 0.0092 |

16 | 14.2221 | 0.7265 | 0.7324 | 0.0059 | 10.3323 | 10.321 | 0.0113 |

17 | 14.6995 | 0.6345 | 0.633 | 0.0015 | 9.3268 | 9.313 | 0.0138 |

18 | 15.1346 | 0.5345 | 0.535 | 0.0005 | 8.0894 | 8.0754 | 0.014 |

19 | 15.5311 | 0.4275 | 0.4356 | 0.0081 | 6.6395 | 6.6367 | 0.0028 |

20 | 15.8929 | 0.3185 | 0.3256 | 0.0071 | 5.0618 | 5.0524 | 0.0094 |

21 | 16.2229 | 0.2085 | 0.2145 | 0.006 | 3.3824 | 3.3724 | 0.01 |

22 | 16.5241 | 0.101 | 0.111 | 0.01 | 1.6689 | 1.6564 | 0.0125 |

23 | 16.7987 | 0.008 | 0.006 | 0.002 | 0.1343 | 0.1347 | 0.0004 |

Sum of IAE | 0.0594 | 0.0927 |

**Table 4.**Statistical results of the root mean square error (RMSE) of different algorithms for Photowatt-PWP201 PV Modules.

Photowatt-PWP201 Module Model | Algorithm | RMSE | |||

Min | Mean | Max | SD | ||

GSA | 8.80 × 10^{−3} | 2.65 × 10^{−1} | 2.08 × 10^{−1} | 5.85 × 10^{−3} | |

PSOGSA | 7.156 × 10^{−3} | 6.47 × 10^{-3} | 2.83 × 10^{−1} | 1.81 × 10^{−2} | |

SCA | 1.28 × 10^{−2} | 2.26 × 10^{-1} | 6.35 × 10^{−1} | 1.78 × 10^{−2} | |

WOA | 9.54 × 10^{−4} | 2.35 ×10^{-2} | 2.63 × 10^{−1} | 2.83 × 10^{−2} | |

TSA | 5.06 × 10^{−4} | 1.45 × 10^{-3} | 2.34 × 10^{−2} | 1.25 × 10^{−3} |

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**MDPI and ACS Style**

Sharma, A.; Dasgotra, A.; Tiwari, S.K.; Sharma, A.; Jately, V.; Azzopardi, B.
Parameter Extraction of Photovoltaic Module Using Tunicate Swarm Algorithm. *Electronics* **2021**, *10*, 878.
https://doi.org/10.3390/electronics10080878

**AMA Style**

Sharma A, Dasgotra A, Tiwari SK, Sharma A, Jately V, Azzopardi B.
Parameter Extraction of Photovoltaic Module Using Tunicate Swarm Algorithm. *Electronics*. 2021; 10(8):878.
https://doi.org/10.3390/electronics10080878

**Chicago/Turabian Style**

Sharma, Abhishek, Ankit Dasgotra, Sunil Kumar Tiwari, Abhinav Sharma, Vibhu Jately, and Brian Azzopardi.
2021. "Parameter Extraction of Photovoltaic Module Using Tunicate Swarm Algorithm" *Electronics* 10, no. 8: 878.
https://doi.org/10.3390/electronics10080878