# Harmonic Detection for Power Grids Using Adaptive Variational Mode Decomposition

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed AVMD Algorithm for Harmonic Detection

#### 2.1. VMD AlgorithmTheory

**{u**= {u

_{k}}_{1},…,u

_{K}} are the decomposed modal components for each BLIMFs;

**{ω**= {ω

_{k}}_{1},…,ω

_{K}} are the central frequencies for each BLIMFs.

#### 2.2. Inner Loop

_{k}) of the finite bandwidth, the modal center frequency (ω

_{k}), and the Lagrange multiplier (λ) are sequentially updated in accordance with Equations (3), (4), and (5), respectively. The BLIMFs can be obtained through the following implementation process.

_{k}) and the center frequency (ω

_{k}) are updated step by step in accordance with Formulas (3) and (4) as

#### 2.3. OuterLoop

## 3. Harmonic Detection Based on the AVMD Algorithm in Power System

_{0}are the amplitude, frequency, and phase of the harmonic signal, respectively.

## 4. Results and Analysis

#### 4.1. Test Signal Analysis

#### 4.2. Analysis of the Measured Data

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Waveform and FFT spectrum of the original test signal: (

**a**) The waveform of original test signal; (

**b**) FFT spectrum of test signal containing noise.

**Figure 4.**BLIMFs decomposed by AVMD and their FFT spectrum: (

**a**) AVMD decomposition for test signal x(t); (

**b**) FFT spectrum of BLIMFs decomposed by AVMD.

**Figure 5.**EMD decomposition results of the test signal. (

**a**) EMD decomposition results of the test signal. (

**b**) The FFT spectrum of IMF decomposed by EMD.

**Figure 7.**Waveform and FFT spectrum of the measured current signal containing harmonics. (

**a**) Waveform of measured current signal containing harmonics. (

**b**) FFT spectrum of measured current signal containing harmonics.

Algorithm | Harmonic | Frequency (Hz) | Amplitude | Phase (°) | Calculation Time (s) |
---|---|---|---|---|---|

Theoretical values | Fundamental | 50 | 1.0000 | 0 | - |

Third | 150 | 0.2000 | 30.0000 | ||

Fifth | 250 | 0.1500 | 45.0000 | ||

AVMD + HT | Fundamental | 49.99 | 0.9972 | 0.2416 | 4.144 |

Third | 149.93 | 0.1987 | 29.1432 | ||

Fifth | 250.01 | 0.1495 | 46.4916 | ||

EMD + HT | Fundamental | 49.12 | 0.9726 | 0.3021 | 0.854 |

Third | 148.24 | 0.1432 | 28.7495 | ||

Fifth | 250.79 | 0.1846 | 48.5782 | ||

FFT | Fundamental | 49.80 | 0.498 | - | 0.506 |

Third | 149.25 | 0.1024 | - | ||

Fifth | 250.31 | 0.0853 | - |

Parameter | Harmonic | AVMD + HT | EMD + HT | FFT |
---|---|---|---|---|

Frequency (Hz) | Fundamental | 0.01 | 0.88 | 0.20 |

Third | 0.07 | 1.76 | 0.75 | |

Fifth | 0.01 | 0.79 | 0.31 | |

Amplitude | Fundamental | 0.0028 | 0.0274 | 0.5020 |

Third | 0.0013 | 0.0568 | 0.0976 | |

Fifth | 0.0005 | 0.0346 | 0.0647 | |

Phase (°) | Fundamental | 0.2416 | 0.3021 | - |

Third | 0.8586 | 1.2505 | - | |

Fifth | 1.4916 | 3.5782 | - |

SNR/dB | Harmonic | AVMD + HT | EMD + HT | ||||
---|---|---|---|---|---|---|---|

Frequency (Hz) | Amplitude | Phase (°) | Frequency (Hz) | Amplitude | Phase (°) | ||

20 | Fundamental | 49.75 | 0.992 | 0.241 | 48.69 | 0.953 | 0.472 |

Third | 148.95 | 0.190 | 29.014 | 147.39 | 0.136 | 26.87 | |

Fifth | 250.96 | 0.145 | 47.623 | 251.84 | 0.195 | 50.03 | |

10 | Fundamental | 49.37 | 0.987 | 0.2380 | 47.39 | 0.905 | 0.642 |

Third | 148.32 | 0.188 | 28.982 | 145.87 | 0.114 | 25.06 | |

Fifth | 249.06 | 0.138 | 47.058 | 253.06 | 0.220 | 53.41 |

Algorithm | SNR (dB) |
---|---|

AVMD + HT | 35.9781 |

EMD + HT | 7.9432 |

Algorithm | Harmonic | Frequency (Hz) | Amplitude (KA) | Phase (°) | Calculation Time (s) |
---|---|---|---|---|---|

AVMD + HT | Fundamental | 59.0134 | 5.0320 | 0.2040 | 13.57 |

3rd | 179.9635 | 0.2937 | 35.8794 | ||

5th | 300.4672 | 0.8210 | 10.1359 | ||

7th | 419.3951 | 0.1435 | 89.9012 | ||

11th | 658.9123 | 0.6540 | 51.0432 | ||

13th | 781.8643 | 0.3028 | 1.2051 | ||

EMD + HT | Fundamental | 59.3473 | 5.5027 | 0.34570 | 2.2 |

5th | 301.6321 | 0.9431 | 112.1425 | ||

11th | 660.3748 | 0.6031 | 50.2937 | ||

FFT | Fundamental | 60.1538 | 1.536 | - | 0.7 |

3rd | 180.3241 | 0.1257 | - | ||

5th | 300.6412 | 0.2014 | - | ||

7th | 420.4689 | 0.06329 | - | ||

11th | 659.9677 | 0.185 | - | ||

13th | 780.1237 | 0.0985 | - |

Algorithm | SNR (dB) |
---|---|

AVMD + HT | 32.6327 |

EMD + HT | 8.5714 |

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**MDPI and ACS Style**

Cai, G.; Wang, L.; Yang, D.; Sun, Z.; Wang, B.
Harmonic Detection for Power Grids Using Adaptive Variational Mode Decomposition. *Energies* **2019**, *12*, 232.
https://doi.org/10.3390/en12020232

**AMA Style**

Cai G, Wang L, Yang D, Sun Z, Wang B.
Harmonic Detection for Power Grids Using Adaptive Variational Mode Decomposition. *Energies*. 2019; 12(2):232.
https://doi.org/10.3390/en12020232

**Chicago/Turabian Style**

Cai, Guowei, Lixin Wang, Deyou Yang, Zhenglong Sun, and Bo Wang.
2019. "Harmonic Detection for Power Grids Using Adaptive Variational Mode Decomposition" *Energies* 12, no. 2: 232.
https://doi.org/10.3390/en12020232