# Harmonic Distortion Prediction Model of a Grid-Tie Photovoltaic Inverter Using an Artificial Neural Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Site

#### 2.2. Measurement Procedure

## 3. Analysis of the Measured Data

#### 3.1. Meteorological Data

#### 3.2. Power Quality Measurement Analysis

_{i}represents the effective current of the harmonic order i:

## 4. Current Harmonics Forecasting with ANN

_{1}, x

_{2}, …, x

_{n}are input values, w

_{k}

_{1}, w

_{k}

_{2}, …, w

_{kn}are synaptic weights, b

_{k}is a bias, and G(u

_{k}) is the activation function [20]. The output value u

_{k}is defined as in Equation (3), while the output of the neuron y

_{k}is calculated as in Equation (4).

_{pred}is the predicted value, and I

_{meas}is the experimentally measured value.

_{i}is the i-th output value between 0 and 1, x

_{i}is the i-th input value of parameter, x

_{min}is the minimum input value of the parameter in a set, and x

_{max}is the maximum input value of the parameter in a set.

#### 4.1. ANN Model Evaluation

_{meas,i}is the experimentally measured value of sample I, I

_{pred,i}is the predicted value of sample i, ${\overline{I}}_{\mathrm{meas}}$ is the average of the experimentally measured values, and ${\overline{I}}_{\mathrm{pred}}$ is the average of predicted values.

#### 4.2. Simulations, Results, and Discussion

_{amb}); and version 3 with three input variables, i.e., solar irradiance, ambient temperature, and time of the day (t).

_{amb}) input variables, respectively, while Table 7 shows the performance of the MLPNN with three input variables (G, T

_{amb}, and t).

_{amb}, and t) and two hidden layers produced the best results considering the overall accuracy (all four current harmonics). If we observe the prediction accuracy of each current harmonic individually, MLPNN 3 demonstrated the best performance for the prediction of the 5th current harmonic. If we compare the results by the coefficient of correlation R (0.9381). MLPNN 1 had the best performance for the prediction of the 7th current harmonic (R = 0.971), while MLPNN 6 showed the best performance for the predictions of the 11th (R = 0.9469) and 13th (R = 0.8801) current harmonics.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the 10-kWp PV plant and part of the data acquisition system used for the measurements.

**Figure 2.**Equipment used to obtain measurements for our analysis: (

**a**) PV plant strings; (

**b**) PV plant inverter Kaco Powador 12.0 TL3; (

**c**) pyranometer Kipp&Zonnen SMP3; and (

**d**) power quality analyzer Fluke 1760.

**Figure 4.**Effective current values of the 1st, 5th, 7th, 11th, and 13th current harmonics during a sunny day (21 August 2018).

**Figure 5.**Effective current values of the 1st, 5th, 7th, 11th, and 13th current harmonics during a partially cloudy day (15 April 2018).

**Figure 6.**The current harmonic spectrum on a partially cloudy day (15 April 2018) and a sunny day (21 August 2018).

**Figure 7.**The absolute THDI calculated from the 2nd to the 40th current harmonics and the absolute THDI calculated from 5th, 7th, 11th, and 13th current harmonic.

**Figure 10.**Multilayer perceptron neural network (MLPNN) architecture [20].

**Figure 11.**Neuron model diagram [20].

**Figure 13.**The mean squared error (MSE) of the artificial neural network (ANN) training for different types of optimizers.

**Figure 14.**Coefficients of correlation R of the predictions of the 5th, 7th, 11th, and 13th current harmonics of the MLPNN models.

**Table 1.**Technical characteristics of the photovoltaic (PV) plant inverter [17].

Manufacturer | Kaco |
---|---|

Model | Powador 12.0 TL3 |

Circuit design | 6-pulse transformerless IGBT ^{1} |

DC side | |

Parameter | Value |

Maximum PV generator input power (kW) | 12 |

Maximum power point voltage range (V) | 280–800 |

Starting voltage (V) | 250 |

Maximum open-circuit voltage (V) | 1000 |

Number of string inputs | 2 |

Maximum short-circuit current (A) | 22.4 |

AC side | |

Rated power (kW) | 10 |

Rated current (A) | 14.5 |

Grid voltage (V) | 400/230 |

Distortion factor (THDI) (%) | 2.22 |

Maximum efficiency (%) | 98 |

European efficiency (%) | 97.5 |

^{1}IGBT: insulated gate bipolar transistor.

Parameter | Solar Irradiance | Ambient Temperature |
---|---|---|

Mean value | 175.17 W/m^{2} | 14.65 °C |

Minimum value | 7.26 W/m^{2} | −11.21 °C |

Maximum value | 1172.03 W/m^{2} | 37.16 °C |

Standard deviation | 248.91 W/m^{2} | 9.76 °C |

Coefficient of variation | 1.42 | 0.67 |

Parameter | 5th Current Harmonic (A) | 7th Current Harmonic (A) | 11th Current Harmonic (A) | 13th Current Harmonic (A) |
---|---|---|---|---|

Mean value | 0.0147 | 0.0142 | 0.0137 | 0.0130 |

Maximum value | 0.8489 | 0.4733 | 0.4310 | 0.2915 |

Minimum value | 0.1354 | 0.0961 | 0.0752 | 0.0437 |

Standard deviation | 0.1278 | 0.0911 | 0.0662 | 0.0402 |

Coefficient of variation | 1.0596 | 1.0550 | 1.1374 | 1.0869 |

Model Name | Input Parameters | Architecture |
---|---|---|

MLPNN 1 | G | 1-11-4 |

MLPNN 2 | G, T_{amb} | 2-11-4 |

MLPNN 3 | G, T_{amb}, t | 3-11-4 |

MLPNN 4 | G | 1-11-5-4 |

MLPNN 5 | G, T_{amb} | 2-11-5-4 |

MLPNN 6 | G, T_{amb}, t | 3-11-5-4 |

Model Version | Current Harmonic | Validation | |||
---|---|---|---|---|---|

R | d | RMSE (A) | MAE (A) | ||

MLPNN 1 (1-11-4) | 5th | 0.9356 | 0.9555 | 0.0693 | 0.0455 |

7th | 0.971 | 0.9804 | 0.032 | 0.0221 | |

11th | 0.9437 | 0.9598 | 0.0376 | 0.0252 | |

13th | 0.8459 | 0.8426 | 0.0374 | 0.021 | |

MLPNN 2 (1-11-5-4) | 5th | 0.9358 | 0.9563 | 0.0687 | 0.0454 |

7th | 0.9706 | 0.9798 | 0.0323 | 0.022 | |

11th | 0.9437 | 0.9599 | 0.0375 | 0.0245 | |

13th | 0.8534 | 0.8567 | 0.0363 | 0.0216 |

Model Version | Current Harmonic | Validation | |||
---|---|---|---|---|---|

R | d | RMSE (A) | MAE (A) | ||

MLPNN 3 (1-11-4) | 5th | 0.9381 | 0.9662 | 0.0658 | 0.0438 |

7th | 0.9676 | 0.9804 | 0.0324 | 0.0224 | |

11th | 0.9465 | 0.972 | 0.0336 | 0.0217 | |

13th | 0.8712 | 0.9124 | 0.0309 | 0.0185 | |

MLPNN 4 (1-11-5-4) | 5th | 0.9354 | 0.9647 | 0.0673 | 0.0436 |

7th | 0.9626 | 0.9771 | 0.0343 | 0.0222 | |

11th | 0.945 | 0.9702 | 0.0345 | 0.0235 | |

13th | 0.8743 | 0.9225 | 0.03 | 0.0193 |

Model Version | Current Harmonic | Validation | |||
---|---|---|---|---|---|

R | d | RMSE (A) | MAE (A) | ||

MLPNN 5 (1-11-4) | 5th | 0.9376 | 0.9664 | 0.066 | 0.045 |

7th | 0.9634 | 0.9801 | 0.033 | 0.0222 | |

11th | 0.9429 | 0.9694 | 0.0362 | 0.024 | |

13th | 0.8678 | 0.926 | 0.0299 | 0.0183 | |

MLPNN 6 (1-11-5-4) | 5th | 0.9369 | 0.9666 | 0.0651 | 0.0428 |

7th | 0.9686 | 0.9834 | 0.0306 | 0.0201 | |

11th | 0.9469 | 0.9722 | 0.034 | 0.0229 | |

13th | 0.8801 | 0.9253 | 0.0293 | 0.0191 |

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**MDPI and ACS Style**

Žnidarec, M.; Klaić, Z.; Šljivac, D.; Dumnić, B.
Harmonic Distortion Prediction Model of a Grid-Tie Photovoltaic Inverter Using an Artificial Neural Network. *Energies* **2019**, *12*, 790.
https://doi.org/10.3390/en12050790

**AMA Style**

Žnidarec M, Klaić Z, Šljivac D, Dumnić B.
Harmonic Distortion Prediction Model of a Grid-Tie Photovoltaic Inverter Using an Artificial Neural Network. *Energies*. 2019; 12(5):790.
https://doi.org/10.3390/en12050790

**Chicago/Turabian Style**

Žnidarec, Matej, Zvonimir Klaić, Damir Šljivac, and Boris Dumnić.
2019. "Harmonic Distortion Prediction Model of a Grid-Tie Photovoltaic Inverter Using an Artificial Neural Network" *Energies* 12, no. 5: 790.
https://doi.org/10.3390/en12050790