# Significance of Harmonic Filters by Computation of Short-Time Fourier Transform-Based Time–Frequency Representation of Supply Voltage

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## Abstract

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## 1. Introduction

- The frequency domain representation of harmonics based on mathematical equations;
- The short-time Fourier transform-based representation of harmonics;
- Generation of the waveforms of voltage and current waveforms at the supply side and load side by the simulation of a power system in a MATLAB environment;
- Keeping in view the power quality in terms of the supply voltage and load current, the supply voltage is considered for analysis;
- A spectrogram of the supply voltage is visualized for different windows of Hamming, Kaiser, and Blackman windows;
- Using the time and frequency domain representation for a length, the Hamming window is chosen for analysis;
- Using the Hamming window for small and large window lengths, the spectrogram is analyzed for supply voltage with and without filters;
- A reduction in the power distribution is observed for the spectrogram of the supply voltage after connecting the filters;
- This indicates a reduction in the harmonic content;
- The results are validated by a calculation of the total harmonic distortion;
- The renewable energy source is integrated into the system, and the effect of the filter’s presence is observed.

#### 1.1. Analysis of Harmonic Content Present in a Signal

#### 1.1.1. Information about Frequency Content

#### 1.1.2. Extraction of Additional Information Using Time–frequency Representation

_{1RMS}(t), instantaneous RMS voltage, V

_{RMS}(t), instantaneous total waveform distortion, V

_{TWD}(t), instantaneous total harmonic distortion, V

_{THD}(t), and instantaneous total nonharmonic distortion, V

_{TnHD}(t). According to IEEE Recommended Practice for Monitoring Electric Power Quality (IEEE Standard 1159-1995) [30], harmonics come under the category of waveform distortion in the classification of power quality disturbances. Harmonics are voltages or currents having integer multiples of fundamental frequency [31], and harmonics have a 0 to 9 kHz typical spectral content with a steady-state duration and a 0 to 20% variation in the magnitude of the voltage.

#### 1.1.3. Role of Harmonic Filters

^{th}-order multiple of the fundamental frequency, and the quality factor is 7. For the C-type high-pass filter, the tuning frequency is in the 3

^{rd}-order multiple of the fundamental frequency, and the quality factor is 2. The voltage injection into the system is made through which reactive power is controlled, resulting in control of the reactive power, resulting in a balanced and distortion-free supply voltage. Different types of filters are connected at the supply side and load side. Table 2 depicts the different types of filters used in the simulated system to analyze the supply voltage before and after connecting the filters. Shunt filters and series filters, defined by way of the connection, respectively, inject the shunt current and series voltage into the distribution line based on the requirement.

## 2. Materials and Methods

#### 2.1. Application of Fourier Transform for Harmonics Signal

#### 2.1.1. Generation of Harmonics in Time and Frequency Domains

_{1}, α

_{2}, α

_{5}, and α

_{7}.

#### 2.1.2. Short-Time Fourier Transform-Based Representation of Harmonics Signal

#### 2.2. Voltage and Current Waveforms Obtained at Supply and Load Sides

#### Generation of Waveforms in Time Domain

#### 2.3. Analysis of Supply Voltage

#### 2.3.1. Spectrogram-Based Representation of Supply Voltage

#### 2.3.2. Representation of Different ‘Windows’ in Time and Frequency Domains

#### 2.3.3. Effect of Variations in STFT Analysis for Different Sizes in WINDOW length

## 3. THD Analysis

## 4. Integration of Renewable Energy Sources with Stochastic Behavior to Show Effect of Filter

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 5.**(

**a**) Spectrogram of the reference sine signal with the color map. (

**b**) Spectrogram of harmonics signal with time on the abscissa and the frequency on the ordinate.

**Figure 6.**(

**a**) Voltage waveform at sending end. (

**b**) Current waveform at sending end. (

**c**) Voltage waveform at receiving end without harmonic filters. (

**d**) Current waveform at receiving end without harmonic filters.

**Figure 7.**(

**a**) Voltage waveform at sending end. (

**b**) Current waveform at sending end. (

**c**) Voltage waveform at receiving end with harmonic filters. (

**d**) Current waveform at receiving end with harmonic filters.

**Figure 8.**(

**a**) Supply voltage before connecting harmonic filters. (

**b**) Supply voltage after connecting harmonic filters. (

**c**) Spectrogram of supply voltage before connecting harmonic filters using a Blackman window. (

**d**) Spectrogram of supply voltage after connecting harmonic filters using a Blackman window. (

**e**) Spectrogram of supply voltage before connecting harmonic filters using a Kaiser window. (

**f**) Spectrogram of supply voltage after connecting harmonic filters using a Kaiser window. (

**g**) Spectrogram of supply voltage before connecting harmonic filters using a Hamming window. (

**h**) Spectrogram of supply voltage after connecting harmonic filters using a Hamming window.

**Figure 9.**Hamming window in (

**a**) the time domain and (

**b**) the frequency domain, representing a length of 64 in the time domain.

**Figure 10.**Kaiser window in (

**a**) the time domain and (

**b**) the frequency domain, representing a length of 64 in the time domain.

**Figure 11.**Blackman window in (

**a**) the time domain and (

**b**) the frequency domain, representing a length of 64 in the time domain.

**Figure 12.**(

**a**) STFT for supply voltage using the Hamming window of a segment length size of 120 before connecting harmonic filters. (

**b**) STFT for supply voltage using the Hamming window of a segment length size of 120 after connecting harmonic filters. (

**c**) STFT for supply voltage using the Hamming window of a segment length size of 1600 before connecting harmonic filters. (

**d**) STFT for supply voltage using a Hamming window of a segment length size of 1600 after connecting harmonic filters.

**Figure 15.**Characteristics of PV array: (

**a**) current versus voltage and (

**b**) power versus voltage for different temperatures of 25 °C and 45 °C.

**Figure 16.**(

**a**) Supply voltage after integration of PV source into the system without harmonic filters. (

**b**) Supply voltage after integration of PV source into the system with harmonic filters.

**Figure 17.**(

**a**) Spectrogram after integration of PV source into the system without harmonic filters. (

**b**) Spectrogram after integration of PV source into the system with harmonic filters.

Type | Quantity and Values |
---|---|

Three-phase voltage source | Phase-to-phase voltage = 500 kV |

Source resistance = 0 Ω | |

Source inductance = 98.03 mH | |

Distribution line | Resistance = 26. 07 Ω |

Inductance = 48.86 mH | |

Three-phase transformer | Nominal power = 1200 MVA |

Winding 1 voltage = 450 kV | |

Winding 2 voltage = 200 kV | |

Winding 3 voltage = 200 kV | |

Three-phase nonlinear load | Bridge rectifier |

**Table 2.**Different types of filter configurations used as harmonic filters, used as a single filter or in combination, each having a nominal line-to-line voltage of 500 kV, and 50 Hz with a nominal reactive power var is 150 Mvar.

Series Capacitor | Double-Tuned Filter | High-Pass Filter | C-Type High-Pass Filter |
---|---|---|---|

Type | Quantity and Values |
---|---|

Solar PV array | Sun irradiance = 1000 W/m^{2} |

Cell temperature = 45 °C Number of parallel strings = 88 | |

Series-connected modules per string = 7 |

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## Share and Cite

**MDPI and ACS Style**

Priyadarshini, M.S.; Krishna, D.; Kumar, K.V.; Amaresh, K.; Goud, B.S.; Bajaj, M.; Altameem, T.; El-Shafai, W.; Fouda, M.M.
Significance of Harmonic Filters by Computation of Short-Time Fourier Transform-Based Time–Frequency Representation of Supply Voltage. *Energies* **2023**, *16*, 2194.
https://doi.org/10.3390/en16052194

**AMA Style**

Priyadarshini MS, Krishna D, Kumar KV, Amaresh K, Goud BS, Bajaj M, Altameem T, El-Shafai W, Fouda MM.
Significance of Harmonic Filters by Computation of Short-Time Fourier Transform-Based Time–Frequency Representation of Supply Voltage. *Energies*. 2023; 16(5):2194.
https://doi.org/10.3390/en16052194

**Chicago/Turabian Style**

Priyadarshini, M. S., D. Krishna, Kurakula Vimala Kumar, K. Amaresh, B. Srikanth Goud, Mohit Bajaj, Torki Altameem, Walid El-Shafai, and Mostafa M. Fouda.
2023. "Significance of Harmonic Filters by Computation of Short-Time Fourier Transform-Based Time–Frequency Representation of Supply Voltage" *Energies* 16, no. 5: 2194.
https://doi.org/10.3390/en16052194