# PV Cells and Modules Parameter Estimation Using Coati Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

- ▪
- Parameter optimization for the SDM, DDM, and PV solar cell models;
- ▪
- Improving the efficiency of solar cells;
- ▪
- Introducing a coati optimization algorithm [15] designed to enhance the efficiency of PV devices;
- ▪
- Introducing an upgraded version of the coati optimization algorithm that fosters mutual learning;
- ▪
- Estimating parameters for PV models and comparing them with recent meta-heuristic methods;
- ▪
- Introducing an enhanced version of the coati optimization algorithm integrated with chaos theory.

## 2. Related Works

## 3. Methodology

#### 3.1. SMD Circuit

_{ph}represents the current produced by the photogenerated current. The SDM framework is relatively simple. First, the generated diode current I

_{d}, output current I

_{L}, shunt current I

_{sh}, and hot I

_{ph}are defined.

_{L}using Equation (1). The equations of the diode Shockley and Ohm laws are, respectively, used to obtain I

_{d}using Equation (2) and ${I}_{sh}$ applying Equation (3).

_{S}is a series resistor, R

_{sh}is a parallel resistor, V

_{L}stands for output voltage k, q stands for initial charge (1.60217646 × 10

^{−19}), and n is the ideality factor of the diode and refers to Boltzmann’s constant and equals (1.3806503 × 10

^{−23}J/K q). Here, SDM identifies five different unknown parameters (${I}_{ph}$, ${I}_{d}$, ${R}_{S}$, ${R}_{sh}$, and n), and T represents the absolute temperature.

#### 3.2. DDM Circuit

_{L}is calculated using Equation (5):

_{1}and n

_{2}represent the ideal saturation coefficient of two diodes, and ${I}_{d1}$ is the diode emission current. DDM needs to extract seven different parameters (${I}_{ph}$, ${I}_{d1}$, ${I}_{d2}$, ${R}_{S}$, ${R}_{sh}$, ${n}_{1}$, and ${n}_{2}$).

#### 3.3. PV Module Modeling

_{L}is calculated using Equation (6):

_{S}and N

_{P}represent the quantity of parallel and serial connections between PV cells. The SDM of PV modules is used in this research. The PV module should determine five unknowns (I

_{ph}, I

_{d}, R

_{S}, R

_{sh}, and n).

#### 3.4. Objective Function

**X**represents the solution consisting of different unknown parameters, and N shows the number of actual measured data.

#### 3.5. Error Metrics

#### 3.6. Coati Optimization Algorithm

- ▪
- The strategy of coatis when they attack iguanas;
- ▪
- The coatis’ escape strategy to save themselves from hunters.

#### 3.7. Proposed Flowchart

_{ph}, I

_{d}, R

_{S}, R

_{sh}, and n). If the circuit type is DDM, each solution is (I

_{ph}, I

_{d1}, I

_{d2}, R

_{S}, R

_{sh}, n

_{1}, and n

_{2}). Finally, if the circuit type is a PV module, five variables (I

_{ph}, I

_{d}, R

_{S}, R

_{sh}, and n) offer a solution to the COA algorithm. Figure 8 depicts the suggested technique’s flowchart for determining solar cell characteristics. The following are the steps of the suggested strategy for optimizing the circuit parameters of solar cells:

- ▪
- Start;
- ▪
- The parameters of SMD, DDM, and PV modules are coded as members of the COA algorithm;
- ▪
- Set parameters of the COA algorithm;
- ▪
- Set the algorithm counter to t = 1;
- ▪
- Create an initial population of random COA algorithm solution;.
- ▪
- Evaluate objective function to find solutions;
- ▪
- Determine the most optimal solution, i.e., iguanas, in each iteration;
- ▪
- Increase the COA algorithm repetition counter by one unit;
- ▪
- Find chaos parameters of the COA algorithm;
- ▪
- Update half of the solutions (coatis that have climbed trees);
- ▪
- Update half of the solutions (coatis) with the hunting mechanism of the iguana falling on the ground;
- ▪
- Update solutions using predator escape mechanism;
- ▪
- Implement opposition-based learning;
- ▪
- In each iteration, evaluate the population and solutions and choose the most optimal solution;
- ▪
- Repeat steps of the COA algorithm;
- ▪
- Select the most optimal solution or parameters of SMD, DDM, and PV modules in the last iteration;
- ▪
- Optimize the parameters of the solar module circuit;
- ▪
- Stop.

#### 3.8. The Challenges Tackled by This Paper

- Complexity of Parameter Optimization: The process of optimizing parameters within PV modules and solar cells entails grappling with intricate mathematical models and inherent uncertainties stemming from fluctuations in solar radiation and temperature;
- Requirement for Improved Optimization Algorithms: Traditional optimization algorithms may encounter difficulties in adequately managing the intricacies of parameter optimization within solar PV systems, underscoring the necessity for novel approaches such as the COA algorithm proposed herein;
- Attaining Global Optima: The task of identifying the global optimum solution for parameter optimization in solar PV systems is arduous due to the existence of numerous local optima and the expansive search space with high dimensions.

#### 3.9. The Contributions Made by This Paper to the Field

- (1)
- Innovative Optimization Strategy: Introducing a fresh optimization strategy utilizing the COA algorithm and chaotic functions, which exhibits superior effectiveness compared to existing meta-heuristic algorithms in terms of minimizing RMSE and standard deviation;
- (2)
- Enhanced Parameter Optimization: The proposed approach ensures more precise and consistent optimization of parameters within SDM, DDM, and PV modules, consequently improving power generation efficiency and the overall reliability of solar PV systems;
- (3)
- Potential for Future Research: The paper outlines future research prospects, including the exploration of LSTM neural networks for optimizing solar cell parameters and forecasting solar radiation and panel temperature. This indicates promising avenues for advancing techniques in solar energy optimization.

## 4. Results and Discussion

^{2}. A total of 36 polycrystalline silicon cells comprising a Photowatt-PWP201 module were linked in series, and at 45 °C, the current-voltage data were measured. Moreover, a total of 36 polycrystalline silicon cells, measured at 55 °C, made up the STP6-120/36 modules. A few earlier investigations were studied to gather the STP6-120/36 module’s current-voltage measurement data [29,38]. The proposed algorithm was implemented on the MATLAB 2021 platform using an Intel

^{®}i7-HQ CPU with 16 GB memory. Through parameter optimization for distinct PV modules employing the COA, the approach not only boosts output power but also reduces errors and standard deviation, surpassing traditional algorithms such as ITLBO, JSO, CPMPSO, WOA, SCA, GNDO, and MJSO. Furthermore, it outperformed competing algorithms in terms of RMSE and standard deviation, indicating its superior performance and suitability across various circuit configurations. Additionally, the method’s efficient execution time further bolsters its practical applicability. In summary, these results underscore the effectiveness and versatility of the proposed method in tackling diverse optimization challenges within solar energy systems.

#### 4.1. The Range of Parameters

#### 4.2. Results Based on SDM

#### 4.3. Results Based on DDM

#### 4.4. Results Based on STP6-120/36

#### 4.5. Ranking

#### 4.6. Time Complexity

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

COA | Coati optimization algorithm |

PV | Photovoltaic |

SDM | Single-diode model |

DDM | Double-diode model |

MPPT | Maximum power point tracking |

IEA | Energy agency |

MPP | Maximum power point |

PWM | Pulse width modulation |

GWO | Gray wolf optimization |

NGO | Northern goshawk optimization |

EVs | Electric vehicles |

HESS | Hybrid energy storage system |

ICOA | Improved coati optimization algorithm |

SD | Standard deviation |

MHs | Meta-heuristics |

RE | Relative error |

MJSO | Modified artificial jellyfish search optimizer |

GNDO | Generalized normal distribution optimization |

SCA | Sine cosine algorithm |

JSO | Jellyfish search optimizer |

QSO | Queue search optimization |

DE | Differential evolution |

PSO | Particle swarm optimization |

GA | Genetic algorithm |

GOA | Grasshopper optimization algorithms |

BA | Bat algorithms |

HHO | Harris hawks optimizer |

AOA | Arithmetic optimization algorithm |

ChOA | Chimp optimization algorithm |

WOA | Whale optimization algorithm |

IHHO-VMD | Improved Harris hawk optimization algorithm–variational mode decomposition |

MCDM | Multiple-criteria decision making |

NSGA-II | Non-dominated sorting genetic algorithm II |

PLC | Programmable logic controller |

MGO | Mountain gazelle optimizer |

IAE | Individual absolute error |

RMSE | Root mean square error |

TSA | Tree seed algorithm |

CPMPSO | Classified perturbation mutation-based particle swarm optimization |

ITLBO | Improved teaching-learning-based optimization |

AVOA | African vultures optimization algorithm |

IAOA | Arithmetic optimization algorithm |

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**Figure 1.**SDM circuit structure in PV systems [36].

**Figure 2.**DDM circuit structure in PV systems [36].

**Figure 3.**Equivalent circuit of a PV module [36].

**Figure 4.**The coati, a mammal [15].

**Figure 5.**Coatis scaring the prey, the iguana falling on the ground, and coatis hunting it [15].

**Figure 6.**Coati’s escape from the current position [15].

**Figure 7.**Chaos function to create more chaos in the COA algorithm [12].

**Figure 9.**Comparison of the measured and estimated data obtained by ICOA for SDM: (

**a**) I-V characteristic, (

**b**) P-V characteristic, and (

**c**) IAE curves.

**Figure 10.**Comparison of the measured and estimated data obtained by ICOA for DDM model: (

**a**) I-V characteristic, (

**b**) P-V characteristic, and (

**c**) IAE curves.

**Figure 11.**Comparison of the measured and estimated data obtained by ICOA for STP6-120/36 model, (

**a**) I-V characteristic, (

**b**) P-V characteristic, and (

**c**) IAE curves.

**Table 1.**Utilizing meta-heuristic optimization algorithms for parameter extraction of PV cell models.

Ref | Aim | Algorithm | Limitations | Advantages | Results |
---|---|---|---|---|---|

[10,13] | The study seeks to create a method for designing zero-energy residential structures by employing building performance simulation technology and multi-objective optimization, aiming to attain the most efficient energy-saving solutions adaptable to various climate zones in China. | NSGA-II | Challenges entail the necessity for enhancing the building energy calculation model to encompass regional nuances and the simplification of some parameters for research practicality. | The strengths of the research include the creation of a parametric design platform to determine energy consumption thresholds and photovoltaic replacement rates specific to diverse climate zones, providing valuable guidance for policymakers and standard-setting bodies. Furthermore, the study underscores the significance of holistic considerations beyond mere energy usage in residential architectural planning. | The findings indicate that near-zero energy consumption is viable in select climate zones in China, with defined photovoltaic replacement rates. Additionally, the research offers crucial guidance on fine-tuning design parameters to harmonize energy efficiency, economic viability, and residential comfort, highlighting the need to avoid overly zealous pursuit of zero-energy targets to maintain a balanced approach. |

[12] | The study aims to compare decision tree and particle swarm optimization algorithms for identifying optimal solar power plant locations, providing insights for renewable energy planning in Iran. | PSO, MCDM | The research recognizes constraints such as the unavailability of specific data such as transmission line information, potentially impacting the precision of the findings. | The article presents the application of the decision tree method in identifying prime sites for solar power plants, offering a fresh approach to environmental studies. Furthermore, it assesses the efficacy of the decision tree against the PSO method, emphasizing the decision tree’s advantage in this particular domain. | The decision tree method outperforms PSO in predicting high-potential solar energy areas, emphasizing its effectiveness in identifying optimal sites for solar projects. Employing spatial data mining techniques is advised to improve site suitability assessment for power plants, with eastern and southeastern Iran highlighted as especially favorable regions. |

[17] | The study investigates the impact of PVs and EVs on economic emission dispatch, proposes a modified WOA for optimization, and verifies its performance with simulations. | WOA | Constraints of the study encompass the intricate nature of the optimization issue, non-linear and non-convex constraints, and the necessity for meticulous consideration of diverse factors like valve point loading effects, restricted areas, and transmission losses. | The strengths of the study are found in its capacity to efficiently handle the intricate and contradictory aims of economic emission dispatching through the integration of PVs and EVs, along with proposing a customized WOA algorithm that surpasses other optimization methods in delivering superior quality results. | The findings of the study indicate that incorporating PVs and EVs into economic dispatching leads to lower emissions and energy generation costs, while the proposed modified WOA algorithm consistently yields superior quality results when compared to other optimization algorithms employed for economic load dispatch. |

[18] | The research aims to improve the performance of MPPT controllers by optimizing them with the GWO algorithm and assessing their efficiency compared to traditional methods in various conditions, focusing on response time, efficiency, and power generation. | GWO | Challenges in the study encompass the need for fine-tuning the metaheuristic algorithm when applied within a PLC mandating historical irradiation data across diverse weather conditions. | The strengths of the study are evident in the enhanced efficacy of the MPPT controller, optimized using the GWO algorithm, resulting in superior efficiency and power generation when contrasted with conventional approaches. Furthermore, the research offers valuable observations regarding the response time of various algorithms amidst changing conditions. | The research demonstrates that optimizing the MPPT controller with GWO enhances efficiency and power generation while minimizing overshooting, with GWO exhibiting faster response times than traditional algorithms. |

[16] | The research aims to mitigate the variability in photovoltaic output by suggesting a hybrid energy storage setup strategy. | IHHO-VMD | Challenges involve the possibility of constraining photovoltaic output and diminishing power generation, alongside the restricted energy storage capacity of the HESS, indicating the need for exploring improved decomposition techniques and integrating electric hydrogen into HESS, warranting further investigation. | Benefits encompass a 6.15% decrease in the hybrid energy storage system cost relative to the original algorithm as well as mitigated power fluctuations, leading to enhanced system economy and stability. | The IHHO-VMD algorithm effectively reduces energy storage system costs, enhances power allocation, and stabilizes photovoltaic grid-connected power. While MA helps mitigate power fluctuations, challenges remain with photovoltaic output and HESS capacity, warranting further exploration of improved decomposition methods and HESS expansion. |

Ref | Advantage | Description | Benefit for PV System Optimization |
---|---|---|---|

[32] | Biological inspiration | Mimics coatis’ intelligent hunting and evasion behaviors. | Novel optimization perspective, potentially leading to adaptive and resourceful solutions. |

[15] | Population-based approach | Explores multiple solutions simultaneously. | Efficiently finds global optimums in complex PV system problems. |

[33] | Integration of natural behaviors | Models coatis’ hunting and evasion behaviors for optimization. | Achieves faster convergence and more robust solutions. |

[34] | Opposition-based Learning | Diversifies exploration by generating opposite solutions. | Prevents premature convergence and encourages exploration of diverse regions. |

[35] | Chaos theory integration | Introduces randomness to escape local optima. | Enhances exploration capabilities and avoids stagnation. |

Requirements | Description |
---|---|

Optimization of solar PV parameters | Maximize the efficiency of solar PV systems by accurately optimizing their parameters. |

Reduction in environmental impact | Mitigate environmental pollution and reduce reliance on non-renewable energy sources like fossil fuels. |

Advancement of optimization techniques | Represents a significant advancement in optimization techniques for solar PV systems. |

Enhanced stability and accuracy | Improve the stability and accuracy of parameter optimization in PV modules and solar cells, thereby increasing the reliability and performance of solar energy systems. |

**Table 4.**Lower and upper range in the modules [31].

Parameters | Low Range | Upper Range |
---|---|---|

${I}_{ph}\left(A\right)$ | 0 | 2∗${I}_{sc}$ |

${I}_{sd}\left(A\right)$ | 0 | 100 × 10^{−6} |

${R}_{s}\left(\Omega \right)$ | 0 | 2 |

${R}_{sh}\left(\Omega \right)$ | 0 | 5000 |

n, ${n}_{1}$,${n}_{2}$ | 1 | 4 |

Algorithms | ${\mathit{I}}_{\mathit{p}\mathit{h}}\left(\mathit{A}\right)$ | ${\mathit{I}}_{\mathit{s}\mathit{d}}\left(\mathit{A}\right)$ | ${\mathit{R}}_{\mathit{s}}(\mathsf{\Omega})$ | ${\mathit{R}}_{\mathit{s}\mathit{h}}(\mathsf{\Omega})$ | n | RMSE |
---|---|---|---|---|---|---|

ITLBO [21] | 0.76078 | 3.11 × 10^{−7} | 0.03654 | 52.8897 | 1.47726 | 0.000773006 |

JSO [22] | 0.76079 | 3.11 × 10^{−7} | 0.03654 | 52.8882 | 1.47727 | 0.000773006 |

CPMPSO [39] | 0.76078 | 3.11 × 10^{−7} | 0.03654 | 52.8897 | 1.47726 | 0.000773006 |

WOA [38] | 0.76162 | 3.86 × 10^{−7} | 0.03530 | 45.9308 | 1.49953 | 0.001085820 |

SCA [29] | 0.7582 | 4.09 × 10^{−7} | 0.03595 | 68.8388 | 1.50500 | 0.002483415 |

GNDO [30] | 0.76078 | 3.11 × 10^{−7} | 0.03654 | 52.8897 | 1.47726 | 0.000773006 |

MJSO [31] | 0.76078 | 3.11 × 10^{−7} | 0.03654 | 52.8897 | 1.47726 | 0.000773006 |

COA [15] | 0.76078 | 3.11 × 10^{−7} | 0.03654 | 52.8897 | 1.47726 | 0.000773006 |

ICOA (proposed method) | 0.76078 | 3.11 × 10^{−7} | 0.03654 | 52.8897 | 1.47726 | 0.000773006 |

Algorithms | ${\mathit{I}}_{\mathit{p}\mathit{h}}\left(\mathit{A}\right)$ | ${\mathit{I}}_{\mathit{s}\mathit{d}1}\left(\mathit{A}\right)$ | R_{s}(Ω) | R_{sh}(Ω) | n_{1} | ${\mathit{I}}_{\mathit{s}\mathit{d}2}\left(\mathit{A}\right)$ | n_{2} | RMSE |
---|---|---|---|---|---|---|---|---|

ITLBO [21] | 0.7608 | 2.47 × 10^{−7} | 0.0368 | 53.9599 | 1.4579 | 4.78 × 10^{−7} | 1.9949 | 0.000742264 |

JSO [22] | 0.7608 | 5.38 × 10^{−7} | 0.0371 | 54.4640 | 1.7980 | 1.61 × 10^{−7} | 1.4262 | 0.000754167 |

CPMPSO [39] | 0.7608 | 7.03 × 10^{−8} | 0.0378 | 56.2715 | 1.3642 | 1.00 × 10^{−6} | 1.7963 | 0.000741937 |

WOA [38] | 0.7608 | 2.67 × 10^{−7} | 0.0368 | 51.8538 | 1.4662 | 4.10 × 10^{−8} | 1.6133 | 0.000776464 |

SCA [29] | 0.7684 | 0.00 × 10^{+0} | 0.0324 | 38.3064 | 1.1740 | 3.84 × 10^{−7} | 1.4970 | 0.007351184 |

GNDO [30] | 0.7608 | 1.00 × 10^{−6} | 0.0373 | 55.6033 | 1.9051 | 1.40 × 10^{−7} | 1.4130 | 0.000742327 |

MJSO [31] | 0.7608 | 7.03 × 10^{−8} | 0.0378 | 56.2715 | 1.3642 | 1.00 × 10^{−6} | 1.7963 | 0.000741937 |

COA [15] | 0.7607 | 7.01 × 10^{−8} | 0.0377 | 56.2716 | 1.3641 | 1.00 × 10^{−6} | 1.7964 | 0.000741936 |

ICOA (proposed method) | 0.7608 | 7.02 × 10^{−8} | 0.0377 | 56.2714 | 1.3642 | 1.00 × 10^{−6} | 1.7962 | 0.000741936 |

Algorithms | ${\mathit{I}}_{\mathit{p}\mathit{h}}\left(\mathit{A}\right)$ | ${\mathit{I}}_{\mathit{s}\mathit{d}}\left(\mathit{A}\right)$ | ${\mathit{R}}_{\mathit{s}}(\mathsf{\Omega})$ | ${\mathit{R}}_{\mathit{s}\mathit{h}}(\mathsf{\Omega})$ | N | RMSE |
---|---|---|---|---|---|---|

ITLBO [21] | 7.47528 | 1.93 × 10^{−6} | 0.16891 | 570.1972 | 44.80042 | 0.014251063 |

JSO [22] | 7.47525 | 1.93 × 10^{−6} | 0.16890 | 571.5660 | 44.80254 | 0.014251066 |

CPMPSO [39] | 7.47528 | 1.93 × 10^{−6} | 0.16891 | 570.1975 | 44.80042 | 0.014251063 |

WOA [38] | 7.50318 | 3.27 × 10^{−6} | 0.15781 | 307.7831 | 46.40846 | 0.017581962 |

SCA [29] | 7.56027 | 1.70 × 10^{−6} | 0.17318 | 323.9495 | 44.38346 | 0.052443825 |

GNDO [30] | 7.47528 | 1.93 × 10^{−6} | 0.16891 | 570.1972 | 44.80042 | 0.014251063 |

MJSO [31] | 7.47528 | 1.93 × 10^{−6} | 0.16891 | 570.1975 | 44.80042 | 0.014251063 |

COA [15] | 7.47528 | 1.92 × 10^{−6} | 0.16891 | 570.1975 | 44.80041 | 0.014251063 |

ICOA (proposed method) | 7.47528 | 1.93 × 10^{−6} | 0.16891 | 570.1974 | 44.80041 | 0.014251063 |

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**MDPI and ACS Style**

Elshara, R.; Hançerlioğullari, A.; Rahebi, J.; Lopez-Guede, J.M.
PV Cells and Modules Parameter Estimation Using Coati Optimization Algorithm. *Energies* **2024**, *17*, 1716.
https://doi.org/10.3390/en17071716

**AMA Style**

Elshara R, Hançerlioğullari A, Rahebi J, Lopez-Guede JM.
PV Cells and Modules Parameter Estimation Using Coati Optimization Algorithm. *Energies*. 2024; 17(7):1716.
https://doi.org/10.3390/en17071716

**Chicago/Turabian Style**

Elshara, Rafa, Aybaba Hançerlioğullari, Javad Rahebi, and Jose Manuel Lopez-Guede.
2024. "PV Cells and Modules Parameter Estimation Using Coati Optimization Algorithm" *Energies* 17, no. 7: 1716.
https://doi.org/10.3390/en17071716