# Comparative Estimation of Electrical Characteristics of a Photovoltaic Module Using Regression and Artificial Neural Network Models

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Models

#### 2.1. Explicit and Analytical I–V Model

#### 2.2. Five Parameters as a Function of Temperature and Solar Irradiance

## 3. Parameter Identification Approaches

#### 3.1. Multiple Regression

#### 3.2. Artificial Neural Network (ANN)

## 4. Model Verification

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**PV-equivalent circuit of a single diode with series and parallel resistance at arbitrary irradiance (G) and temperature (T).

**Figure 3.**Dependence of the five parameters on temperature and solar irradiance for the regression model (

**a**–

**e**) and ANN model (

**f**–

**j**).

**Figure 4.**Statistical metrics for the five parameters in evaluating the accuracy of the regression model and ANN model: (

**a**) RMSE and (

**b**) MAPE.

**Figure 5.**I–V curves and absolute error by simulated and experimental data (

**a**) at different irradiances and (

**b**) at different temperatures.

Parameters | $\mathbf{Regression}\text{}\mathbf{Models}\text{}\mathbf{and}\text{}{\mathit{R}}^{2}$ |
---|---|

${I}_{ph}\left(G,T\right)\left(\mathrm{A}\right)$ | $\left(\frac{G}{{G}_{0}}\right)\left[3.457+1.407\times {10}^{-3}\left(T-{T}_{0}\right)\right]$, ${R}^{2}=1.000$ |

${V}_{oc}\left(G,T\right)\left(\mathrm{V}\right)$ | $21.63\left[1-3.434\times {10}^{-3}\left(T-{T}_{0}\right)+1.752\times {10}^{-4}{V}_{t}\mathrm{ln}\left(\frac{G}{{G}_{0}}\right)\right]$, ${R}^{2}=0.9985$ |

$n\left(G,T\right)$ | $1.084\left[1-8.455\times {10}^{-4}\left(T-{T}_{0}\right)+2.749\times {10}^{-4}{V}_{t}\mathrm{ln}\left(\frac{G}{{G}_{0}}\right)\right]$, ${R}^{2}=0.96$92 |

${R}_{s}\left(G,T\right)\left(\mathrm{\Omega}\right)$ | $0.4724\frac{1+1.405\times {10}^{-2}+6.854\times {10}^{-4}{V}_{t}\mathrm{ln}\left(\frac{G}{{G}_{0}}\right)}{\left(\frac{G}{{G}_{0}}\right)\left[1+3.488\times {10}^{-2}\left(T-{T}_{0}\right)\right]}$, ${R}^{2}=0.99$38 |

${R}_{p}\left(G,T\right)\left(\mathrm{\Omega}\right)$ | $222\frac{1+1.890\times {10}^{-2}+7.246\times {10}^{-4}{V}_{t}\mathrm{ln}\left(\frac{G}{{G}_{0}}\right)}{\left(\frac{G}{{G}_{0}}\right)\left[1+2.515\times {10}^{-2}\left(T-{T}_{0}\right)\right]}$, ${R}^{2}=0.9926$ |

${I}_{0}\left(G,T\right)\left(\mathrm{A}\right)$ | $\left[{I}_{ph}\left(G,T\right)-\frac{{V}_{oc}\left(G,T\right)}{{R}_{p}\left(G,T\right)}\right]/\left[\mathrm{exp}\left(\frac{{V}_{oc}\left(G,T\right)}{n\left(G,T\right){V}_{t}}\right)-1\right]$ |

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**MDPI and ACS Style**

Lee, J.; Kim, Y.
Comparative Estimation of Electrical Characteristics of a Photovoltaic Module Using Regression and Artificial Neural Network Models. *Electronics* **2022**, *11*, 4228.
https://doi.org/10.3390/electronics11244228

**AMA Style**

Lee J, Kim Y.
Comparative Estimation of Electrical Characteristics of a Photovoltaic Module Using Regression and Artificial Neural Network Models. *Electronics*. 2022; 11(24):4228.
https://doi.org/10.3390/electronics11244228

**Chicago/Turabian Style**

Lee, Jonghwan, and Yongwoo Kim.
2022. "Comparative Estimation of Electrical Characteristics of a Photovoltaic Module Using Regression and Artificial Neural Network Models" *Electronics* 11, no. 24: 4228.
https://doi.org/10.3390/electronics11244228