# A Novel Harmonic Suppression Traction Transformer with Integrated Filtering Inductors for Railway Systems

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## Abstract

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## 1. Introduction

- An HSTT with integrated filtering inductors is proposed;
- The principle of magnetic decoupling of the IFIs is analyzed;
- The design process of the HSTT with IFIs is specifically introduced;
- The proposed method is verified in terms of volume reduction and harmonic suppression effect.

## 2. Description and Magnetic Analysis of the HSTT with IFIs

#### 2.1. Descriptions of the Traction Drive System with IFI-Based LCL-Type Filter

_{g}) of the traction transformer, an added filter capacitor (C

_{f}), and an IFI (L

_{f}). C

_{d}is the DC-link capacitor; R

_{L}is the equivalent resistor of a load from the traction drive system; v

_{g}is the voltage of the traction grid, i

_{g}and i

_{f}are the grid-side current and converter-side current, respectively; i

_{s}is the secondary current of the traction transformer; v

_{c}and i

_{c}are the voltage and current of the filter capacitors, respectively. Here, u

_{ab}is the input voltage of converter, and u

_{dc}and i

_{dc}represent the DC-side voltage and current, respectively.

#### 2.2. Magnetic Analysis of the IFI Windings

_{k}is the number of turns of the sub-winding k; ${\dot{I}}_{\mathrm{k}}$ is the current flowing through the sub-winding k; R

_{k}= l/(μA

_{c}) represents the magnetic resistance of the magnetic path of the sub-winding k in the core, where l is the magnetic path length, A

_{c}is the cross-sectional area, and μ is the core permeability.

_{a}= R

_{b}= R and N

_{a}= N

_{b}= N′. Moreover, as the current flows through the two sub-windings in opposite directions, the following equation can be obtained as

_{kσ}represents the magnetic resistance of the magnetic path of the sub-winding k in oil or air.

_{aσ}≠ R

_{bσ}. Substituting Equations (3) and (4) into (1) yields

#### 2.3. Magnetic Analysis of the HSTT with IFIs

_{T}, by which the mutual flux linkage in sub-windings a and b are motivated, and thus expressed as ψ

_{q-T}= M

_{a-T}I

_{T}and ψ

_{b-T}= M

_{b-T}I

_{T}, respectively. Thus, the induction electromotive forces (EMF) of the sub-windings a and b can be expressed as

_{1–2}≈ 0. A similar conclusion can be drawn that the EMF E

_{2–1}is approximately equal to zero. Thus, the magnetic decoupling of IFI windings with transformer windings and other IFI windings can be realized.

## 3. Math Design and Calculations Methods of the HSTT with IFIs

#### 3.1. LCL-Type Filter Design

_{n}is the rated power of the system, and f

_{n}is the fundamental frequency of the traction grid.

_{s}represents the switching frequency of the converter and Δi

_{max}is the permissible maximum converter side current fluctuation.

_{k}is the double switching angular frequency and k is the order of the harmonic current.

_{g}can be calculated as

#### 3.2. Dimension-Based Method

_{g}and L

_{f}, where L

_{g}is the leakage inductance of the traction transformer. Figure 6 shows the dimension of the HSTT with IFIs, where the turns of the HV winding of the traction transformer is set as N

_{1}. L

_{f}consists of sub-windings W

_{1}and W

_{2}, and the turns are both equal to N

_{2}. According to the dimension-based method, the inductance of the LCL-type filter can be determined by

#### 3.3. Inductance Matrix Based Calculation

_{p}and L

_{q}represent the self-inductance of each winding, and M

_{pq}represents the mutual inductance of windings p and q.

_{n}, V

_{g}, f

_{n}, U

_{dc}, f

_{s}, Δi

_{max}, N), the LCL-type filter parameters can be obtained by Equations (11), (12), and (14). Then, it is confirmed whether the resonant frequency of the LCL-type filter meets the limitations given by Equation (16) or not. Therefore, the qualified LCL-type filter parameters can be acquired. Subsequently, with the reference value of the two inductors of L

_{g}and L

_{f}, the basic structural parameters of the proposed HSTT with IFIs can be obtained via Equations (19) and (20). Then, the finite element model of the HSTT with IFIs can be built with its structural parameters, so the inductance matrix of the HSTT with IFI windings can be calculated. The inductance of the HSTT and IFIs can be obtained by the IMBC methods afterward. The design and calculation procedure of the HSTT with IFIs ends if the calculated inductances meet the designed error (ε).

## 4. Simulation and Experiment Results

#### 4.1. Control Method

_{g}is the voltage of the traction grid, i

_{g}and i

_{f}are the grid-side current and converter-side current, respectively; v

_{c}and i

_{c}are the voltage and current of the filter capacitors, respectively; v

_{cov}and v

_{r}are the input voltage and reference input voltage of the converter, respectively. K

_{pwm}denotes the equivalent gain of PWM converter.

#### 4.2. Field-Circuit Coupling Simulation

^{12}, can be obtained, as shown in the Appendix A. According to Equation (21), the coupling factors matrix K

^{12}can be obtained. The inductances of the HSTT with IFIs can be calculated with IMBC methods, and the specifications of L

_{g}and L

_{f}are presented in Table 2. Compared with the designed values of the inductances in Table 1, the error between simulation value and the designed value of the inductances is below 5 %. Thus, the inductance is in good accordance with the design requirements. Moreover, as the coupling factor of IFI windings with transformer windings is below 1 %, the high-decoupling characteristics of IFI windings demonstrated in Section 2 can be verified.

_{s1}) of the HSTT with two different filter types. Figure 11 shows the comparison of the harmonic spectra of the secondary-side current in three cases. It can be inferred from Figure 10 and Figure 11 that IFI-based L-type filter schemes and LCL-type filter schemes can both operate stably. Moreover, the IFI-based LCL-type filter schemes can better suppress high-frequency harmonics. Besides, the same level of harmonic suppression effect can be obtained as with the discrete inductor-based LCL-type filter scheme.

_{g}) and grid-side currents (i

_{g}) of the HSTT with four secondary windings. It is clear that the grid-side currents of all the cases can operate in phases with the grid-side voltage, and they are highly sinusoidal. Figure 13 shows the comparative results of the harmonic spectra of the grid-side current for the above-mentioned three cases. The harmonic spectrum of the grid-side currents with the L-type filter scheme distributes around 4400 Hz due to the phase shift control, but the IFI-based and discrete inductor-based LCL-type filter schemes can dampen these high-frequency harmonic currents on the train side to almost the same level. Therefore, the effectiveness of the IFI-based LCL-type filter scheme for high-frequency harmonics suppression can be confirmed.

#### 4.3. Practical Operations

^{2}. In order to avoid the electromagnetic interference between equipment, the regular HSTT (10 kVA) with a configuration of separated hollow inductors covers an area of 0.083 m

^{2}. This indicates that the total installed area of equipment can be reduced by 38.5% when IFIs are adopted. Furthermore, in practical application, the inductance of the IFIs and capacity of the transformer is usually much larger, which will result in a smaller installed area. As a result, a high power density LCL-type filter system is implemented.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

**M**and corresponding coupling efficiency matrix

^{12}**K**covering all windings of the prototype of the transformer integrated with the integrated inductor as below (unit = mH). Here, h1, l1, and i1 represent the high-voltage windings, low-voltage windings, and IFI windings, respectively; the same is true for {h2, l2, i2}, {h3, l3, i3}, and {h4, l4, i4}.

^{12}## References

- Hu, H.; Shao, Y.; Tang, L.; Ma, J.; He, Z.; Gao, S. Overview of harmonic and resonance in railway electrification systems. IEEE Trans. Ind. Appl.
**2018**, 5, 5227–5245. [Google Scholar] [CrossRef] - He, Z.; Hu, H.; Zhang, Y.; Gao, S. Harmonic resonance assessment to traction power-supply system considering train model in China high-speed railway. IEEE Trans. Power Del.
**2013**, 4, 1735–1743. [Google Scholar] [CrossRef] - Liu, J.; Yang, Q.; Zheng, T.Q. Harmonic analysis of traction networks based on the CRH380 series EMUs accident. In Proceedings of the IEEE Transportation Electrification Conference and Expo (ITEC), Dearborn, MI, USA, 18–20 June 2012. [Google Scholar]
- Hu, H.; He, Z.; Gao, S. Passive filter design for China high-speed railway with considering harmonic resonance and characteristic harmonics. IEEE Trans. Power Del.
**2014**, 30, 505–514. [Google Scholar] [CrossRef] - Tan, P.-C.; Loh, P.C.; Holmes, D.G. A robust multilevel hybrid compensation system for 25-kV electrified railway applications. IEEE Trans. Power Electron.
**2004**, 4, 1043–1052. [Google Scholar] [CrossRef] - Holtz, J.; Krah, J. Adaptive optimal pulse-width modulation for the line-side converter of electric locomotives. IEEE Trans. Power Electron.
**1992**, 1, 205–211. [Google Scholar] [CrossRef] - Zhang, R.; Lin, F.; Yang, Z.; Cao, H.; Liu, Y. A harmonic resonance suppression strategy for a high-speed railway traction power supply system with a SHE-PWM four-quadrant converter based on active-set secondary optimization. Energies
**2017**, 10, 1567. [Google Scholar] [CrossRef] - Cui, H.; Song, W.; Fang, H.; Ge, X.; Feng, X. Resonant harmonic elimination pulse width modulation-based high-frequency resonance suppression of high-speed railways. IET Power Electron.
**2015**, 5, 735–742. [Google Scholar] [CrossRef] - Song, K.; Konstantinou, G.; Mingli, W.; Acuna, P.; Aguilera, R.P.; Agelidis, V.G. Windowed SHE-PWM of interleaved four-quadrant converters for resonance suppression in traction power supply systems. IEEE Trans. Power Electron.
**2016**, 10, 7870–7881. [Google Scholar] [CrossRef][Green Version] - Krah, J.-O.; Holtz, J. Total compensation of line-side switching harmonics in converter-fed AC locomotives. IEEE Trans. Ind. Appl.
**1995**, 6, 1264–1273. [Google Scholar] [CrossRef] - Aceiton, R.; Weber, J.; Bernet, S. Input filter for a power electronics transformer in a railway traction application. IEEE Trans. Ind. Electron.
**2018**, 12, 9449–9458. [Google Scholar] [CrossRef] - Song, W.; Jiao, S.; Li, Y.W.; Wang, J.; Huang, J. High-frequency harmonic resonance suppression in high-speed railway through single-phase traction converter with LCL filter. IEEE Trans. Transport. Electrif.
**2016**, 3, 347–356. [Google Scholar] [CrossRef] - Lee, K.-J.; Park, N.-J.; Kim, R.-Y.; Ha, D.-H.; Hyun, D.-S. Design of an LCL filter employing a symmetric geometry and its control in grid-connected inverter applications. In Proceedings of the IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008. [Google Scholar]
- Pan, D.; Ruan, X.; Bao, C.; Li, W.; Wang, X. Magnetic integration of the LCL filter in grid-connected inverters. IEEE Trans. Power Electron.
**2013**, 4, 1573–1578. [Google Scholar] [CrossRef] - Fang, J.; Li, H.; Tang, Y. A magnetic integrated LLCL filter for grid-connected voltage-source converters. IEEE Trans. Power Electron.
**2016**, 3, 1725–1730. [Google Scholar] [CrossRef] - Li, X.; Fang, J.; Lin, P.; Tang, Y. Active magnetic decoupling for improving the performance of integrated LCL-filters in grid-connected converters. IEEE Trans. Ind. Electron.
**2017**, 2, 1367–1376. [Google Scholar] [CrossRef] - Pleite, J.; Valdivia, V.; Zumel, P.; Gonzalez, C. Transformer and Series Inductance Integration for Harmonic Filtering in PWM Inverters Based in a Simple Design Procedure. In Proceedings of the IEEE International Symposium on Industrial Electronics, Vigo, Spain, 4–7 June 2007. [Google Scholar]
- Liang, C.; Luo, L.; Li, Y.; Xu, J.; Qi, Q.; Chen, Y.; Zhou, G.; Deng, M. An integrated harmonic-filtering transformer for low-voltage distribution systems. IEEE Trans. Magn.
**2015**, 11, 1–4. [Google Scholar] - Xu, J.; Gu, X.; Liang, C.; Bai, Z.; Kubis, A. Harmonic suppression analysis of a harmonic filtering distribution transformer with integrated inductors based on field–circuit coupling simulation. IET Gener. Trans. Distrib.
**2017**, 3, 615–623. [Google Scholar] [CrossRef] - Li, Y.; Peng, Y.; Liu, F.; Sidorov, D.; Panasetsky, D.; Liang, C.; Luo, L.; Cao, Y. A controllably inductive filtering method with transformer-integrated linear reactor for power quality improvement of shipboard power system. IEEE Trans. Power Del.
**2016**, 4, 1817–1827. [Google Scholar] [CrossRef] - Zhang, M.; Li, Y.; Liu, F.; Li, W.; Peng, Y.; Wu, W.; Cao, Y. Cooperative Operation of DG Inverters and a RIHAF for Power Quality Improvement in an Integrated Transformer-Structured Grid-Connected Microgrid. IEEE Trans. Ind. Appl.
**2018**, 2, 1157–1170. [Google Scholar] [CrossRef] - Liu, Q.; Li, Y.; Luo, L.; Peng, Y.; Cao, Y. Power quality management of PV power plant with transformer integrated filtering method. IEEE Trans. Power Del.
**2018**, 3, 941–949. [Google Scholar] [CrossRef] - Liu, Q.; Peng, L.; Kang, Y.; Tang, S.; Wu, D.; Qi, Y. A novel design and optimization method of an LCL filter for a shunt active power filter. IEEE Trans. Ind. Electron.
**2013**, 8, 4000–4010. [Google Scholar] [CrossRef] - Jalili, K.; Bernet, S. Design of LCL filters of active-front-end two-level voltage-source converters. IEEE Trans. Ind. Electron.
**2009**, 5, 1674–1689. [Google Scholar] [CrossRef] - Liserre, M.; Blaabjerg, F.; Hansen, S. Design and control of an LCL-filter-based three-phase active rectifier. IEEE Trans. Ind. Appl.
**2005**, 5, 1281–1291. [Google Scholar] [CrossRef] - Tang, Y.; Loh, P.C.; Wang, P.; Choo, F.H.; Gao, F.; Blaabjerg, F. Generalized design of high performance shunt active power filter with output LCL filter. IEEE Trans. Ind. Electron.
**2011**, 3, 1443–1452. [Google Scholar] [CrossRef] - Bao, C.; Ruan, X.; Wang, X.; Li, W.; Pan, D.; Weng, K. Step-by-step controller design for LCL-type grid-connected inverter with capacitor–current-feedback active-damping. IEEE Trans. Power Electron.
**2013**, 3, 1239–1253. [Google Scholar] - Said-Romdhane, M.; Naouar, M.; Belkhodja, I.; Monmasson, E. An improved LCL filter design in order to ensure stability without damping and despite large grid impedance variations. Energies
**2017**, 10, 336. [Google Scholar] [CrossRef][Green Version] - Chang, G.W.; Lin, H.-W.; Chen, S.-K. Modeling characteristics of harmonic currents generated by high-speed railway traction drive converters. IEEE Trans. Power Del.
**2004**, 2, 766–773. [Google Scholar] [CrossRef] - Xie, B.; Li, X.; Chen, Q.; Zhang, Y.; Wang, J. Calculation of the circulating current and short- circuit impedance of a 3000kVA HTS transformer with split types of windings. In Proceedings of the International Conference on Electrical Machines and Systems (ICEMS), Seoul, Korea, 8–11 October 2007. [Google Scholar]
- Yoon, S.-J.; Lai, N.; Kim, K.-H. A systematic controller design for a grid-connected inverter with LCL filter using a discrete-time integral state feedback control and state observer. Energies
**2018**, 11, 437. [Google Scholar] [CrossRef][Green Version] - Lorzadeh, I.; Askarian Abyaneh, H.; Savaghebi, M.; Bakhshai, A.; Guerrero, J.M. Capacitor current feedback-based active resonance damping strategies for digitally-controlled inductive-capacitive-inductive-filtered grid-connected inverters. Energies
**2016**, 9, 642. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Harmonics compensation methods for AC locomotives: (

**a**) passive harmonic filter (compensation on the high-voltage side), (

**b**) active harmonic compensator, (

**c**) passive harmonic filter (compensation with additional filter windings), and (

**d**) LCL-type filter compensation on the low-voltage side.

**Figure 3.**Structure of the harmonic suppression traction transformer (HSTT) with integrated filtering inductors (IFIs).

**Figure 4.**Schematic diagram of IFI windings: (

**a**) winding structure diagram; (

**b**) magnetic flux distribution diagram.

**Figure 9.**Field-circuit coupling simulations for the (

**a**) 3D finite-element model of the HSTT, (

**b**) B-H curve of the transformer core, and (

**c**) model diagram.

**Figure 10.**Simulated waveforms of secondary-side current (i

_{s}

_{1}): (

**a**) IFI-based L-type filter; (

**b**) discrete inductor-based LCL-type filter; (

**c**) IFI-based LCL-type filter.

**Figure 11.**Comparison of simulated fast Fourier transform (FFT) analysis result of secondary-side current (i

_{s}

_{1}).

**Figure 12.**Simulated waveforms of grid voltage (v

_{g}) and grid current (i

_{g}) for: (

**a**) IFI-based L-type filter; (

**b**) discrete inductor-based LCL-type filter; and (

**c**) IFI-based LCL-type filter.

**Figure 14.**Comparison between the covering area of the HSTT with IFIs and that of discrete inductors (units = mm).

**Figure 16.**Experimental results of the HSTT with an IFI-based LCL-type filtered single-phase converter.

**Figure 17.**Experimental results of the HSTT with a discrete inductor-based LCL-type filtered single-phase converter.

Elements | Parameters | Values |
---|---|---|

Traction Grid | Voltage | 27,500 V |

Frequency | 50 Hz | |

Traction transformer | Turns ratio | 77/3 |

Traction Converter | Rated power | 1.385 MW |

Switching frequency | 550 Hz | |

DC-link voltage | 2400 V | |

DC-link Capacitor | 3000 μF | |

The Resistive load | 6 Ω | |

LCL-type filter | Grid side inductor L_{g} | 1.1 mH |

Converter side inductor L_{f} | 1.46 mH | |

Filter capacitor C_{f} | 180 μF |

Inductances | Unit 1 | Unit 2 | Unit 3 | Unit 4 |
---|---|---|---|---|

L_{g} | 1.095 mH | 1.096 mH | 1.094 mH | 1.095 mH |

L_{f} | 1.4611 mH | 1.4649 mH | 1.4603 mH | 1.4605 mH |

Parameters | Values |
---|---|

The rated power | 5 kW |

Turns ratio of the transformer | 220/220 |

The rated current of the converter | 22.7 A |

Grid frequency | 50 Hz |

DC link reference voltage | 400 V |

The capacitor of the DC link | 3000 μF |

Switching frequency | 10 kHz |

The inductance in the discrete inductors L_{f} | 1.0 mH |

The capacitance of LCL-type filter C_{f} | 30 uF |

The resistive load | 33.5 Ω |

Inductances | Designed Value | Calculated Value | Simulated Value | Measured Value |
---|---|---|---|---|

L_{g1} | 0.7 mH | 0.71 mH | 0.698 mH | 0.764 mH |

L_{g2} | 0.7 mH | 0.71 mH | 0.698 mH | 0.765 mH |

L_{f1} | 1.0 mH | 1.03 mH | 1.04 mH | 1.056 mH |

L_{f2} | 1.0 mH | 1.03 mH | 1.03 mH | 1.042 mH |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Xu, J.; Shuai, Z.; Li, Y.; Peng, Y.; Liang, C.; Cui, G.; Hu, S.; Zhang, M.; Xie, B. A Novel Harmonic Suppression Traction Transformer with Integrated Filtering Inductors for Railway Systems. *Energies* **2020**, *13*, 473.
https://doi.org/10.3390/en13020473

**AMA Style**

Liu Y, Xu J, Shuai Z, Li Y, Peng Y, Liang C, Cui G, Hu S, Zhang M, Xie B. A Novel Harmonic Suppression Traction Transformer with Integrated Filtering Inductors for Railway Systems. *Energies*. 2020; 13(2):473.
https://doi.org/10.3390/en13020473

**Chicago/Turabian Style**

Liu, Yuxing, Jiazhu Xu, Zhikang Shuai, Yong Li, Yanjian Peng, Chonggan Liang, Guiping Cui, Sijia Hu, Mingmin Zhang, and Bin Xie. 2020. "A Novel Harmonic Suppression Traction Transformer with Integrated Filtering Inductors for Railway Systems" *Energies* 13, no. 2: 473.
https://doi.org/10.3390/en13020473