# 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

- Wang, X.; Li, Y.W.; Blaabjerg, F.; Loh, P.C. Virtual-Impedance-Based Control for Voltage-Source and Current-Source Converters. IEEE Trans. Power Electron.
**2015**, 30, 7019–7037. [Google Scholar] [CrossRef] - Mehrasa, M.; Pouresmaeil, E.; Zabihi, S.; Rodrigues, E.M.; Catalão, J.P. A control strategy for the stable operation of shunt active power filters in power grids. Energy
**2016**, 96, 325–334. [Google Scholar] [CrossRef] - Aleem, S.A.; Zobaa, A.; Aziz, M.M.A. Optimal C-Type Passive Filter Based on Minimization of the Voltage Harmonic Distortion for Nonlinear Loads. IEEE Trans. Ind. Electron.
**2011**, 59, 281–289. [Google Scholar] [CrossRef] - Kazemi-Robati, E.; Sepasian, M.S. Passive harmonic filter planning considering daily load variations and distribution system reconfiguration. Electr. Power Syst. Res.
**2019**, 166, 125–135. [Google Scholar] [CrossRef] - Ouchen, S.; Betka, A.; Gaubert, J.-P.; Abdeddaim, S. Simulation and real time implementation of predictive direct power control for three phase shunt active power filter using robust phase-locked loop. Simul. Model. Pr. Theory
**2017**, 78, 1–17. [Google Scholar] [CrossRef] - Biricik, S.; Redif, S.; Özerdem, Ö.C.; Khadem, S.K.; Basu, M. Real-time control of shunt active power filter under distorted grid voltage and unbalanced load condition using self-tuning filter. IET Power Electron.
**2014**, 7, 1895–1905. [Google Scholar] [CrossRef] [Green Version] - Jafrodi, S.T.; Ghanbari, M.; Mahmoudian, M.; Najafi, A.; Rodrigues, E.M.G.; Pouresmaeil, E. A Novel Control Strategy to Active Power Filter with Load Voltage Support Considering Current Harmonic Compensation. Appl. Sci.
**2020**, 10, 1664. [Google Scholar] [CrossRef] [Green Version] - Yang, L.; Yang, J.; Gao, M.; Watson, A.; Wheeler, P. Current Control of LCL-Type Shunt APFs: Damping Characteristics, Stability Analysis, and Robust Design Against Grid Impedance Variation. IEEE J. Emerg.
**2021**, 9, 5026–5042. [Google Scholar] [CrossRef] - Luo, Z.; Su, M.; Sun, Y.; Zhang, W.; Lin, Z. Analysis and control of a reduced switch hybrid active power filter. IET Power Electron.
**2016**, 9, 1416–1425. [Google Scholar] [CrossRef] - Heathcote, M. J & P Transformer Book; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar] [CrossRef]
- Forrest, J.; Allard, B. Thermal Problems Caused by Harmonic Frequency Leakage Fluxes in Three-Phase, Three-Winding Converter Transformers. IEEE Trans. Power Deliv.
**2004**, 19, 208–213. [Google Scholar] [CrossRef] - Li, Y.; Luo, L.; Rehtanz, C.; Ruberg, S.; Yang, D.; Xu, J. An Industrial DC Power Supply System Based on an Inductive Filtering Method. IEEE Trans. Ind. Electron.
**2011**, 59, 714–722. [Google Scholar] [CrossRef] - Li, Y.; Luo, L.; Rehtanz, C.; Rüberg, S.; Liu, F. Realization of Reactive Power Compensation Near the LCC-HVDC Converter Bridges by Means of an Inductive Filtering Method. IEEE Trans. Power Electron.
**2012**, 27, 3908–3923. [Google Scholar] [CrossRef] - Luo, L.; Li, Y.; Nakamura, K.; Krost, G.; Li, J.; Xu, J.; Liu, F. Harmonic Characteristics of New HVDC Transmission System Based on New Converter Transformer. In Proceedings of the 2008 Third International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, Nanjing, China, 6–9 April 2008; pp. 1868–1872. [Google Scholar] [CrossRef]
- Li, Y.; Luo, L.; Rehtanz, C.; Yang, D.; Rüberg, S.; Liu, F. Harmonic Transfer Characteristics of a New HVDC System Based on an Inductive Filtering Method. IEEE Trans. Power Electron.
**2011**, 27, 2273–2283. [Google Scholar] [CrossRef] - Peng, Y.; Li, Y.; Liu, F.; Luo, L.; Cao, Y. A New Shipboard Power Supply System Based on a Rectifier Transformer with Integrated Filtering Reactor. In Proceedings of the 2016 IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific), Busan, Korea, 1–4 June 2016; pp. 402–406. [Google Scholar]
- Liang, C.; Xu, J.; Luo, L.; Li, Y.; Qi, Q.; Gao, P.; Fu, Y.; Peng, Y. Harmonic Elimination Using Parallel Delta-Connected Filtering Windings for Converter Transformers in HVDC Systems. IEEE Trans. Power Deliv.
**2016**, 32, 933–941. [Google Scholar] [CrossRef] - Li, Y.; Yao, F.; Cao, Y.; Liu, W.; Liu, F.; Hu, S.; Luo, L.; Zhang, Z.; Chen, Y.; Zhou, G.; et al. An Inductively Filtered Multiwinding Rectifier Transformer and Its Application in Industrial DC Power Supply System. IEEE Trans. Ind. Electron.
**2016**, 63, 3987–3997. [Google Scholar] [CrossRef] - Zhang, X.; Li, C.; Li, D.; Jiang, S. Study on Operation Parameter Characteristics of Induction Filter Distribution Transformer in Low-Voltage Distribution Network. IEEE Access
**2021**, 9, 78764–78773. [Google Scholar] [CrossRef] - Li, Y.; Liu, Q.; Hu, S.; Liu, F.; Cao, Y.; Luo, L.; Rehtanz, C. A Virtual Impedance Comprehensive Control Strategy for the Controllably Inductive Power Filtering System. IEEE Trans. Power Electron.
**2016**, 32, 920–926. [Google Scholar] [CrossRef] - Li, Y.; Rehtanz, C.; Yang, D.; Ruberg, S.; Luo, L. Feasibility Study on Application of Voltage Source Inductive Filtering Converter in HVDC-Light Systems. In Proceedings of the 2010 Asia-Pacific Power and Energy Engineering Conference, Chengdu, China, 28–31 March 2010; pp. 1–4. [Google Scholar]
- Li, Y.; Saha, T.; Krause, O.; Cao, Y.; Rehtanz, C. An Inductively Active Filtering Method for Power-Quality Improvement of Distribution Networks With Nonlinear Loads. IEEE Trans. Power Deliv.
**2013**, 28, 2465–2473. [Google Scholar] [CrossRef] - Peng, Y.; Li, Y.; Lee, K.Y.; Liu, F.; Yang, F.; Hu, B. A Wind Power Integrated System Based on a Controllably Inductive Filtering and Compensation Method. In Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA, 16–20 July 2017; pp. 1–5. [Google Scholar] [CrossRef]
- Yu, J.; Li, Y.; Cao, Y.; Xu, Y. An impedance-match design scheme for inductively active power filter in distribution networks. Int. J. Electr. Power Energy Syst.
**2018**, 99, 638–649. [Google Scholar] [CrossRef]

**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