# An Inductive Active Filtering Method for Low-Voltage Distribution Networks

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## Abstract

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## 1. Introduction

## 2. The Main Circuit Topology of the Distribution Network under the Hybrid Inductive and Active Filter System

## 3. Structure and Operation Principle of the Hybrid Inductive and Active Filter System

## 4. Controller Design and Parameter Tuning

#### 4.1. Impedance Tuning of the Filtering Winding and Fully Tuned Filtering Branch

#### 4.2. Filtration Performance Analysis Considering Different K

#### 4.3. Voltage Source Inverter Control System Design

#### 4.3.1. Harmonic Damping Control of the Voltage Source Inverter

#### 4.3.2. Zero-Value Impedance Control of the Voltage Source Inverter

## 5. Case Study

#### 5.1. Filtration Performance Considering Balanced Three-Phase Loads

#### 5.2. Filtration Performance Considering Unbalanced Three-Phase Loads

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Topologies of the distribution networks considering the HAPF and proposed HIAF system. (

**a**) Topologies of distribution networks considering the HAPF system. (

**b**) Topologies of distribution networks considering the proposed HIAF system.

**Figure 5.**The sensitivity function values under a different K. (

**a**) Considering the effect of the load-side harmonic current ${I}_{Ln}$ to the grid-side harmonic current ${I}_{sn}$. (

**b**) Considering the effect of the harmonic voltage ${V}_{sn}$ at the grid side to the grid-side harmonic current ${I}_{sn}$.

**Figure 6.**Inductive active filter harmonic damping control system block diagram. (

**a**) VSI harmonic damping control block diagram of a classic HIAF system. (

**b**) VSI harmonic damping control block diagram of the proposed HIAF system. Star* means reference value.

**Figure 9.**Dynamic response of the grid-side and load-side currents in the HIAF system. (

**a**) Dynamic responses of the three-phase grid-side currents ${i}_{s}$ (

**b**) Dynamic responses of the three-phase load-side currents ${i}_{L2}$.

**Figure 10.**Distortion rate of the grid-side currents with and without the proposed HIAF system. (

**a**) The distortion rate of the transformer’s grid-side winding current considering the 5th and 7th fully tuned filtering branches. (

**b**) The distortion rate of the transformer’s grid-side winding current considering the proposed HIAF system.

**Figure 12.**Current waveform of the transformer’s grid-side winding under different operating scenarios. (

**a**) Dynamic current responses without any filtering device. (

**b**) Dynamic current responses of the inductive filtering (IF) method considering the 5th and 7th fully tuned branches. (

**c**) Dynamic current responses of the inductive filtering (IF) method considering the 5th, 7th, 11th, and 13th filters. (

**d**) Dynamic current responses of the inductive filtering (IF) method considering the 3rd, 5th, 7th, 9th, 11th, and 13th filters. (

**e**) Dynamic current responses under the proposed HIAF system.

**Figure 13.**The current distortion rate of the transformer’s grid-side winding under different operating scenarios. (

**a**) The distortion rate of transformer’s grid-side winding current without any filtering device. (

**b**) The distortion rate of transformer’s grid-side winding current without any filtering device considering the 5th and 7th fully tuned branches. (

**c**) The distortion rate of transformer’s grid-side winding current considering the 5th, 7th, 11th, and 13th fully tuned branches. (

**d**) The distortion rate of transformer’s grid-side winding current considering the 5th, 7th, 11th, 13th, 3rd, and 9th fully tuned branches. (

**e**) The distortion rate of the transformer’s grid-side winding current under the proposed HIAF system.

**Figure 14.**The load-side winding current waveform under different operating scenarios. (

**a**) Dynamic current responses without any filtering device. (

**b**) Dynamic current responses considering the 5th and 7th fully tuned branches. (

**c**) Dynamic current responses under the proposed HIAF system.

**Figure 15.**Current distortion rate of the transformer’s load-side winding under different operating scenarios. (

**a**) The distortion rate of the transformer’s load-side winding current without any filtering device. (

**b**) The distortion rate of transformer’s load-side winding current considering the 5th and 7th fully tuned branches. (

**c**) The distortion rate of transformer’s load-side winding current under the proposed HIAF system.

**Figure 16.**Influence of the harmonic damping control coefficient on the filtering effect under an unbalanced load. (

**a**) Dynamic three-phase currents under the proposed HIAF system (K = 500). (

**b**) Dynamic three-phase currents under the proposed HIAF system (K = 2000).

**Figure 17.**Phase A current distortion rate under an unbalanced load with different harmonic damping control coefficients. (

**a**) The distortion rate of the phase A current (K = 500). (

**a**) The distortion rate of the phase A current (K = 2000).

Parameters | DivisionV | Parameters | DivisionV |
---|---|---|---|

Rate capacity | 30 kVA | R2(pu)of Winding2 | 0.0228 |

Winding1 voltage V1 | 10 kV | R3(pu)of Winding3 | 0.0261 |

Winding2 voltage V2 | 0.4 kV | L1(pu)of Winding1 | 0.0423 |

Winding3 voltage V3 | 0.4 kV | L2(pu)of Winding2 | 0.016 |

R1(pu)of Winding1 | 0.01778 | L3(pu)of Winding3 | 0.00096 |

n-Order | L/H | C/F |
---|---|---|

5th branch | 0.020637122 | 1.96386 × 10^{−5} |

7th branch | 0.014445986 | 1.43139 × 10^{−5} |

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## Share and Cite

**MDPI and ACS Style**

Li, D.; Zhang, X.; Deng, X.; Li, C. An Inductive Active Filtering Method for Low-Voltage Distribution Networks. *Machines* **2021**, *9*, 258.
https://doi.org/10.3390/machines9110258

**AMA Style**

Li D, Zhang X, Deng X, Li C. An Inductive Active Filtering Method for Low-Voltage Distribution Networks. *Machines*. 2021; 9(11):258.
https://doi.org/10.3390/machines9110258

**Chicago/Turabian Style**

Li, Delu, Xiao Zhang, Xianming Deng, and Changyi Li. 2021. "An Inductive Active Filtering Method for Low-Voltage Distribution Networks" *Machines* 9, no. 11: 258.
https://doi.org/10.3390/machines9110258