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

Abstract

This study analyzes and evaluates the feasibility of a harmonic suppression traction transformer (HSTT) for harmonic reduction in railway systems. This new type of transformer can improve the power quality of railway systems by preventing high-frequency harmonic currents from injecting into the traction grid. As the physical size of available space in high-speed trains is strictly limited, low space-occupying filtering techniques are needed. Therefore, an HSTT with integrated filtering inductors (IFIs) capable of being implemented in regular trains is proposed. Taking advantage of the HSTT, a specially constructed inductive-capacitive-inductive (LCL)-type filter is used for harmonic suppression instead of a regular LCL-type filter. The proposed filter is composed of an integrated inductor, leakage inductor of the traction transformer, and an external filter capacitor. In this paper, we analyze the topology of the proposed system, construct a mathematical model to reveal the magnetic decoupling theory of IFIs, and discuss the design and calculation procedures of the HSTT with IFIs. The field circuit coupling simulation of the HSTT with IFIs is performed to validate the effectiveness of the proposed system. Finally, the practical operation based on a 10 kVA prototype shows that the proposed scheme can not only suppress the high-order frequency harmonics but also decrease the installed space of filter devices.

1. Introduction

In recent years, with the rapid development of the China Railway High-Speed (CRH) infrastructure, the total operation mileages reached more than 29,000 km by the end of 2018. As AC–DC–AC traction converters are widely used in CRH locomotives, the pulse-width modulation (PWM) technologies applied in the line-side converters of the traction drive systems can contribute to the high power factor when supplying the traction loads. However, this inevitably produces high-frequency harmonics, leading to issues such as high-frequency resonance and electromagnetic interference (EMI), threatening the stable operations of railway transportation systems [1,2,3].

To address the aforementioned issue, researchers and engineers have proposed several approaches. These can be divided into two categories, which are from the perspectives of the traction power supply system and the traction drive system, respectively. Some studies focus on resonance suppression from the traction power supply system. Measures are taken to dampen the harmonics of traction power supply systems by using passive or active methods. Although the passive power filter can suppress the harmonic current [4], this may result in system instability. The employment of an active power filter (APF) can suppress the harmonics dynamically as well as avoid harmonic resonance in the system [5], but typically at a relatively higher cost.

The alternative solution for resonance suppression is from the perspective of the traction drive system. For example, online and offline optimal PWM schemes are proposed to eliminate resonance harmonics [6,7,8,9], but these schemes are sensitive to the traction networks’ parameters. Additionally, the Class-120 locomotives in German railways implement a tuned harmonic filter between the pantograph voltage winding of the input transformer (see Figure 1a). Considering the fact that the high-voltage side typically requires large, heavy-weight passive filters, the loss will be high using passive damping. An active harmonic compensator can interact with the traction drive system through transformer winding (see Figure 1b) [10], but the additional APF will be costly. The BR 101 instrument features a passive harmonics filter instead of an APF (see Figure 1c) [11], in which the filter is damped with resistive devices, thus causing losses. Song et al. proposed a single-phase traction converter with an inductive-capacitive-inductive (LCL)-type filter to suppress high-frequency resonance in high-speed railways (see Figure 1d) [12]. This approach can attenuate the high-frequency harmonics in the grid current and damp the LCL-type filter with active damping methods, while maintaining a relatively lower cost. It is noted that the capacitor of the LCL-type filter can prevent the high-frequency harmonics from flowing into the traction transformer by forming a circulation path for high-frequency harmonics. Hence, the losses, vibration, and noises of traction transformers can be dampened effectively.

Although the LCL-type filter scheme can effectively suppress the high-frequency harmonics, additional harmonic filters should be installed in high-speed trains. Due to the limited space in high-speed trains for stacking air-core inductors, the space required for LCL-type filter devices needs to be reduced. To this end, the magnetic integration technique is an effective solution. A magnetic integration theory is introduced in [13,14], in which the two inductors of LCL-type filters are integrated into an EE-type (which means the shape of the iron core is like the character E) core structure. The weak coupling effect observed in those inductors will impose a negative impact on the performance of the LCL-type filter. To address this problem, the coupling coefficient can be utilized to form an inductive-inductive-capacitive-inductive (LLCL)-type filter to suppress the most predominant harmonic currents [15]. In [16], an active magnetic decoupling method is proposed by winding a decoupling winding in series with the filter capacitor around the common I-type core. Therefore, the harmonic attenuation capability can be realized and the volume of the filtering device can be reduced to a large extent. In [17], the grid side inductor of an LCL-type filter is integrated with the leakage inductance of the transformer, but the authors do not investigate the integration of the converter-side inductor of the LCL-type filter.

Although these existing magnetic integration methods can reduce the coverage space of LCL-type filter equipment, they may not be suitable for use in traction drive systems. To address this issue, this paper proposes a harmonic suppression traction transformer (HSTT) with integrated filtering inductors (IFIs) [18] for high-speed trains. Based on this, an innovative magnetic integrated LCL-type filter can satisfy the power quality requirements, while being well-suited for limited space available on locomotives. Each IFI winding is composed of two series-connected sub-windings with the same turns and opposite directions. Similar structures have been applied to a distribution transformer [19], rectifier transformer [20], and inductive filtering transformer [21,22]. The proposed IFI method has the merits of a simple inductance design, good linearity of inductance, low impact on transformer operation, and ease of manufacture and application.

The contributions of this paper are listed as follows:

• 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.

The remainder of this paper is organized as follows. The topology structure of the grid-side traction converter with an LCL-type filter is described in Section 2, along with the magnetic analysis of the proposed HSTT with IFIs. Moreover, a step-by-step calculation and design guidance of the HSTT with IFIs is introduced in Section 3. In Section 4, the simulations and experiments are performed to verify the effectiveness of the proposed concepts. Finally, Section 5 draws a conclusion.

2. Description and Magnetic Analysis of the HSTT with IFIs

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

Figure 2 shows the proposed circuit topology of an IFI-based, single-phase LCL-type converter unit. An LCL-type filter is composed of the leakage inductance (L_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.

Figure 3 depicts the structure of the HSTT with IFIs. The proposed HSTT is a single-phase transformer with split multiwindings, where the iron core adopts the “C-core” core type with two core limbs. On each core limb, two coils of the high-voltage (HV) winding and two split windings of the low-voltage (LV) winding are concentrically wound. The HV windings are connected in parallel, and the LV windings operate independently. Designed for insulation, the HV winding is generally arranged outside of the LV winding. Moreover, compared with the conventional traction transformer, the proposed HSTT adds two additional sub-windings in each unit to constitute an IFI, which is arranged inside the LV windings.

2.2. Magnetic Analysis of the IFI Windings

Figure 4a shows the schematic diagrams of the IFI windings. For instance, IFI 1 windings are composed of two series-connected sub-windings, a and b, which are sub-windings wound around the same magnetic core with the same turns and structural dimensions. Moreover, each sub-winding convolves in the opposite direction. Figure 4b shows the magnetic field distribution of the IFI 1 windings. The magnetic flux generated by the energized IFI winding 1 can be divided into the main magnetic flux and leakage magnetic flux; the former passes completely through the magnetic core, and the latter passes through the oil or air. The main magnetic flux (${\dot{\Phi }}_1$) and the leakage magnetic flux (${\dot{\Phi }}_{1\mathsf{\sigma }}$) of IFI 1 windings can be derived as

$$\{\begin{array}{l}{\dot{\Phi }}_1={\dot{\Phi }}_{\mathrm{a}}+{\dot{\Phi }}_{\mathrm{b}}\hfill \\ {\dot{\Phi }}_{1\mathsf{\sigma }}={\dot{\Phi }}_{\mathrm{a}\mathsf{\sigma }}+{\dot{\Phi }}_{\mathrm{b}\mathsf{\sigma }}\hfill \end{array}$$

(1)

where ${\dot{\Phi }}_{\mathrm{a}}$ and ${\dot{\Phi }}_{\mathrm{b}}$ represent the main magnetic flux generated by the sub-winding a and sub-windings b, respectively; ${\dot{\Phi }}_{\mathrm{a}\mathsf{\sigma }}$ and ${\dot{\Phi }}_{\mathrm{b}\mathsf{\sigma }}$ represent their leakage magnetic fluxes, respectively.

Referring to Figure 4b, the expressions of the main magnetic flux can be described as

$$\{\begin{array}{l}{\dot{\Phi }}_{\mathrm{a}}=\frac{{\dot{F}}_{\mathrm{a}}}{R_{\mathrm{a}}}=\frac{N_{\mathrm{a}}{\dot{I}}_{\mathrm{a}}}{R_{\mathrm{a}}}\hfill \\ {\dot{\Phi }}_{\mathrm{b}}=\frac{{\dot{F}}_{\mathrm{b}}}{R_{\mathrm{b}}}=\frac{N_{\mathrm{b}}{\dot{I}}_{\mathrm{b}}}{R_{\mathrm{b}}}\hfill \end{array}$$

(2)

where ${\dot{F}}_{\mathrm{k}}$ (k = a, b) represents the magnetomotive force of the sub-winding k, N_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.

Because the two sub-windings are wound on the same core with the same turns, it can be deduced that R_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

$$\{\begin{array}{l}{\dot{\Phi }}_{\mathrm{a}}=\frac{N^{\prime }{\dot{I}}_1}{R}\hfill \\ {\dot{\Phi }}_{\mathrm{b}}=-\frac{N^{\prime }{\dot{I}}_1}{R}\hfill \end{array}$$

(3)

Then, the expression of the leakage flux can be given by

$$\{\begin{array}{l}{\dot{\Phi }}_{\mathrm{a}\mathsf{\sigma }}=\frac{{\dot{F}}_{\mathrm{a}}}{R_{\mathrm{a}\mathsf{\sigma }}}=\frac{N_{\mathrm{a}}{\dot{I}}_{\mathrm{a}}}{R_{\mathrm{a}\mathsf{\sigma }}}\hfill \\ {\dot{\Phi }}_{\mathrm{b}\mathsf{\sigma }}=\frac{{\dot{F}}_{\mathrm{b}}}{R_{\mathrm{b}\mathsf{\sigma }}}=\frac{N_{\mathrm{b}}{\dot{I}}_{\mathrm{b}}}{R_{\mathrm{b}\mathsf{\sigma }}}\hfill \end{array}$$

(4)

where R_kσ represents the magnetic resistance of the magnetic path of the sub-winding k in oil or air.

The leakage magnetic fields of the two sub-windings are established in different spatial regions, thus, we have R_aσ ≠ R_bσ. Substituting Equations (3) and (4) into (1) yields

$$\{\begin{array}{l}{\dot{\Phi }}_1={\dot{\Phi }}_{\mathrm{a}}+{\dot{\Phi }}_{\mathrm{b}}=\frac{N^{\prime }{\dot{I}}_1-N^{\prime }{\dot{I}}_1}{R}=0\hfill \\ {\dot{\Phi }}_{1\mathsf{\sigma }}={\dot{\Phi }}_{\mathrm{a}\mathsf{\sigma }}+{\dot{\Phi }}_{\mathrm{b}\mathsf{\sigma }}\hfill \end{array}$$

(5)

Equation (5) clearly illustrates that because the main magnetic fluxes generated by the two sub-windings are opposite in direction and have the same amplitude, therefore, the total main magnetic flux of IFI winding 1 in the core is zero. That is to say, the magnetic flux of IFI winding 1 depends on the leakage magnetic flux of the two sub-windings. Thus, the inductance value of each IFI winding can be calculated by the magnetic field energy method.

2.3. Magnetic Analysis of the HSTT with IFIs

Figure 5 depicts a transformer winding T, iron core, and two IFI windings. The transformer windings T represents the HV or LV windings of the HSTT. IFI windings 1 and 2 are averaged and divided into sub-windings a and b, and sub-windings c and d, respectively. Here, sub-windings a and b, as well as sub-windings c and d, are of a symmetrical mirror relationship to winding T. As already mentioned, the main magnetic flux in the iron core generated by IFI windings 1 and 2 is zero. This means the main magnetic flux decoupling between the IFI windings and other windings can be realized.

Due to the mirror symmetry arrangement of sub-windings a and b to winding T, the equations of the mutual inductance between winding T and the two sub-windings a and b can be obtained as

$$\begin{array}{l}{M}_{\mathrm{T}-\mathrm{a}}\approx -M_{\mathrm{T}-\mathrm{b}}\\ M_{\mathrm{a}-\mathrm{T}}\approx -M_{\mathrm{b}-\mathrm{T}}\end{array}$$

(6)

The current in winding T is denoted as I_T, by which the mutual flux linkage in sub-windings a and b are motivated, and thus expressed as ψ_q-T = M_a-TI_T and ψ_b-T = M_b-TI_T, respectively. Thus, the induction electromotive forces (EMF) of the sub-windings a and b can be expressed as

$$\begin{array}{l}{E}_{\mathrm{a}}=-\frac{d{\psi }_{\mathrm{a}-\mathrm{T}}}{dt}\\ E_{\mathrm{b}}=-\frac{d{\psi }_{\mathrm{b}-\mathrm{T}}}{dt}\end{array}$$

(7)

As a result, the composite EMF in the winding 1 induced by winding T can be obtained as

$$E_{1-\mathrm{T}}=E_{\mathrm{a}-\mathrm{T}}+E_{\mathrm{b}-\mathrm{T}}=-\left(M_{\mathrm{a}-\mathrm{T}}+M_{\mathrm{b}-\mathrm{T}}\right)\frac{d{I}_{\mathrm{T}}}{dt}\approx 0$$

(8)

Similarly, it can be concluded that the EMF of winding T generated by the current in IFI winding 2 is also approximately equal to 0. Consequently, the power decoupling between the IFI winding and the transformer windings can be realized.

The EMF in winding 1 induced by winding 2 can be expressed as

$$E_{1-2}=E_{1-\mathrm{c}}+E_{1-\mathrm{d}}=-(M_{\mathrm{a}-\mathrm{c}}+M_{\mathrm{b}-\mathrm{c}})\frac{d{I}_2}{dt}-(M_{\mathrm{a}-\mathrm{d}}+M_{\mathrm{b}-\mathrm{d}})\frac{d{I}_2}{dt}$$

(9)

The mutual inductance of the windings of the integrated inductor can be achieved as below

$$\begin{array}{l}{M}_{\mathrm{a}-\mathrm{c}}\approx -M_{\mathrm{a}-\mathrm{d}}\\ M_{\mathrm{b}-\mathrm{c}}\approx -M_{\mathrm{b}-\mathrm{d}}\end{array}$$

(10)

By substituting Equation (10) into (9), we have E_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.

It can be concluded that based on the proposed inductor integration method, the IFIs can be obtained with the linearity inductance. Moreover, the IFIs can operate independently with other windings of the traction transformer.

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

3.1. LCL-Type Filter Design

To ensure the harmonics suppression effect and steady operation of the LCL-type converter system, the parameters of the LCL-type filter should be specifically designed [23,24,25,26,27,28].

Generally, the reactive power, which is supported by the capacitor, should not exceed 5% of the rated power of the system. Hence, the capacitor of the LCL-type filter can be derived as

$$C_{\mathrm{f}}\le \frac{5\%P_{\mathrm{n}}}{2\pi f_{\mathrm{n}}{V}_{\mathrm{g}}^2}$$

(11)

where P_n is the rated power of the system, and f_n is the fundamental frequency of the traction grid.

The inductance of the converter side is determined by the modulation method and the permissible maximum current fluctuation. As the unipolar modulation is applied for the traction converter [29] and the current restrictions of the converter side current are set in the range of 30–40% of the rated current [12], the inductance of the converter side inductor can be obtained with

$$L_{\mathrm{f}}\ge \frac{U_{\mathrm{dc}}}{8f_{\mathrm{s}}\Delta i_{\max }}$$

(12)

where f_s represents the switching frequency of the converter and Δi_max is the permissible maximum converter side current fluctuation.

The ratio of the grid-side high-order harmonic current to converter-side high-order harmonic current can be derived as

$$N=\frac{i_{\mathrm{g}}\left(k\right)}{i_{\mathrm{f}}\left(k\right)}=\frac{1}{\left|1-L_{\mathrm{g}}{C}_{\mathrm{f}}{\omega }_{\mathrm{k}}^2\right|}$$

(13)

where ω_k is the double switching angular frequency and k is the order of the harmonic current.

As an appropriate attenuation coefficient of N should be chosen to suppress the high-frequency harmonics in the grid-side current, the inductance of L_g can be calculated as

$$L_{\mathrm{g}}=\frac{N}{\left(N-1\right){\omega }_{\mathrm{k}}^2{C}_{\mathrm{f}}}$$

(14)

The resonant frequency of the LCL-type filter yields

$$f_{\mathrm{res}}=\frac{1}{2\pi }\sqrt{\frac{L_{\mathrm{g}}+L_{\mathrm{f}}}{L_{\mathrm{g}}{L}_{\mathrm{f}}{C}_{\mathrm{f}}}}$$

(15)

To guarantee the stability of the entire system, the resonant frequency of the LCL-type filter must be set within a reasonable range. In this paper, it should be limited in the following range

$$5f_{\mathrm{n}}<f_{\mathrm{res}}<f_{\mathrm{s}}$$

(16)

3.2. Dimension-Based Method

Based on the designed parameters of the two inductors of the LCL-type filter, Figure 5 shows the dimension-based method (DBM) [18,19], which is devoted to designing the practical structure parameters of proposed HSTT with IFIs.

As shown in Figure 2, the LCL-type filter consists of L_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 N₁. L_f consists of sub-windings W₁ and W₂, and the turns are both equal to N₂. According to the dimension-based method, the inductance of the LCL-type filter can be determined by

$$L_{\mathrm{g}}=\frac{2\pi {\mu }_0{N}_1{}^2{\rho }_1}{l_{\mathrm{y}}}\Sigma D_1$$

(17)

$$L_{\mathrm{f}}=\frac{2\pi {\mu }_0{N}_2{}^2{\rho }_2}{l_{\mathrm{x}}}\Sigma D_2$$

(18)

where ${\mu }_0=4\pi \times {10}^{-7}\raisebox{1ex}{$\mathrm{H}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.$, and

$$\{\begin{array}{l}{\rho }_1=1-\frac{a_1+a_2+a_{12}}{\pi l_{\mathrm{y}}}\\ \Sigma D_1=\frac{r_1{a}_1+r_2{a}_2}{3}+a_{12}{r}_{12}\end{array}$$

(19)

$$\{\begin{array}{l}{\rho }_2=1-\frac{1}{\pi u}\left(1-e^{-\pi u}\right)\left[1-0.5e^{-2\pi v}\left(1-e^{-\pi u}\right)\right]\\ u=\frac{H_{\mathrm{x}}}{b_0+2b_1}\\ v=\frac{r}{b_0+2b_1}\\ \Sigma D_2=r_{\mathrm{av}}\left(b_0+\frac{2}{3}{b}_1\right)\end{array}$$

(20)

3.3. Inductance Matrix Based Calculation

The structural parameters of the HSTT with IFIs can be achieved via the DBM. On this basis, the inductance matrix-based calculation (IMBC) methods are used to verify the coupling effect of the inductors. The IMBC methods include the reduced-order inductance matrix method (ROIMM) [19] and the short-circuit impedance matrix method [30]. Based on the inductance matrix of the windings of the HSTT with IFIs, which are calculated by the finite-element simulations method, the leakage inductances of the traction transformer and inductances of the IFIs can be obtained with IMBC methods.

The coupling coefficient matrix of the HSTT with IFIs can be calculated by

$$k_{\mathrm{pq}}=\frac{M_{\mathrm{pq}}}{\sqrt{L_{\mathrm{p}}{L}_{\mathrm{q}}}}$$

(21)

where L_p and L_q represent the self-inductance of each winding, and M_pq represents the mutual inductance of windings p and q.

Figure 7 shows the flowchart of the design and calculation procedure of the proposed HSTT with IFIs. Starting with some selected initial values (P_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

In order to ensure the stability of the entire system, the main challenge here is to suppress the resonance caused by the LCL-type filter. There are usually two solutions, namely the passive damping method and the active damping method. Since the passive damping method inevitably leads to more loss compared to the active damping method, the active damping method seems more attractive for high-power applications. The active damping can be realized by the feedback of different state variables [31]. Figure 8 shows the capacitive current-based feedback control method [32]. This damping method is adopted in this paper because of its simple realization. Here, v_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

Figure 9 shows the implementations of the field-circuit coupling simulation of the traction drive system with an HSTT, which is built in ANSYS/Maxwell and ANSYS/Simplorer to verify the correctness of the proposed magnetic integration method. The simulation parameters are shown in

Table 1. Parameters of the HSTT with IFIs and traction drive system for simulation.

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 Lg	1.1 mH
	Converter side inductor Lf	1.46 mH
	Filter capacitor Cf	180 μF

.

According to the dimension-based method, the physical structure parameters of the HSTT with IFIs can be deduced. Figure 9a shows the three-dimensional (3D) model of the HSTT with the IFIs, which is established in ANSYS/Maxwell. Figure 9b depicts the magnetization (B-H) curve of the 30Q130 silicon steel from which the transformer core is made. Figure 9c shows the model built in the ANSYS/Simplorer.

The self- and mutual-inductance matrices covering all windings in the transformer can be calculated in the ANSYS/Maxwell simulation environment. Then, according to the ROIMM [21], the inductance matrix of the 12-order matrix, represented as M¹², can be obtained, as shown in the Appendix A. According to Equation (21), the coupling factors matrix K¹² 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. Simulated inductances of the HSTT with IFIs.

Inductances	Unit 1	Unit 2	Unit 3	Unit 4
Lg	1.095 mH	1.096 mH	1.094 mH	1.095 mH
Lf	1.4611 mH	1.4649 mH	1.4603 mH	1.4605 mH

. 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.

To further prove the harmonics suppression effect of the IFI-based LCL-type scheme, simulation comparisons of filtering performance of the IFI-based L-type filter, IFI-based LCL-type filter, and discrete inductor-based LCL-type filter are performed in this section. It is worth noting that the external circuit is added to the finite element model in ANSYS/Simplorer, so as to develop the field-circuit coupling simulations. Particularly, the external electric circuit model mainly contains an AC source with 25 kV rated voltage, line-side traction converters with equivalent load, and the control part of the system.

Figure 10 shows the simulation results of secondary-side current (i_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.

Figure 12 shows the waveforms of the grid-side voltages (v_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

A 10 kVA prototype of the HSTT with two IFIs and its experiment platform is established. The parameters of the prototype and experimental platform are listed in

Table 3. Parameters of the HSTT and converter system.

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 Lf	1.0 mH
The capacitance of LCL-type filter Cf	30 uF
The resistive load	33.5 Ω

.

Table 4. Inductances obtained by different methods.

Inductances	Designed Value	Calculated Value	Simulated Value	Measured Value
Lg1	0.7 mH	0.71 mH	0.698 mH	0.764 mH
Lg2	0.7 mH	0.71 mH	0.698 mH	0.765 mH
Lf1	1.0 mH	1.03 mH	1.04 mH	1.056 mH
Lf2	1.0 mH	1.03 mH	1.03 mH	1.042 mH

shows the results of the designed, calculated, simulated, and measured inductance of the HSTT with IFIs. The errors of the two IFIs are within the allowed range. Thus, the validity of the design method is proven. Furthermore, the measured coupling factors of the integrated inductors with traction windings are shown in Equation (22), where h1, l1, and i1 represent the high-voltage windings, low-voltage windings, and IFI windings, respectively, and the same for {h2, l2, i2}. From Equation (22), it can be seen that the values of coupling factors between IFIs and transformer windings are below 0.01, which verifies the decoupling performance of the proposed method.

$$\begin{array}{l}{k}^6=\left[\begin{array}{cccccc}{k}_{\mathrm{h}1}& k_{\mathrm{h}1\mathrm{h}2}& k_{\mathrm{h}1\mathrm{l}1}& k_{\mathrm{h}1\mathrm{l}2}& k_{\mathrm{h}1\mathrm{i}1}& k_{\mathrm{h}1\mathrm{i}2}\\ k_{\mathrm{h}2\mathrm{h}1}& k_{\mathrm{h}2}& k_{\mathrm{h}2\mathrm{l}1}& k_{\mathrm{h}2\mathrm{l}2}& k_{\mathrm{h}2\mathrm{i}1}& k_{\mathrm{h}2\mathrm{i}2}\\ k_{\mathrm{l}1\mathrm{h}1}& k_{\mathrm{l}1\mathrm{h}2}& k_{\mathrm{l}1}& k_{\mathrm{l}1\mathrm{l}2}& k_{\mathrm{l}1\mathrm{i}1}& k_{\mathrm{l}1\mathrm{i}2}\\ k_{\mathrm{l}2\mathrm{h}1}& k_{\mathrm{l}2\mathrm{h}2}& k_{\mathrm{l}2\mathrm{l}1}& k_{\mathrm{l}2}& k_{\mathrm{l}2\mathrm{i}1}& k_{\mathrm{l}2\mathrm{i}2}\\ k_{\mathrm{i}1\mathrm{h}1}& k_{\mathrm{i}1\mathrm{h}2}& k_{\mathrm{i}1\mathrm{l}1}& k_{\mathrm{i}1\mathrm{l}2}& k_{\mathrm{i}1}& k_{\mathrm{i}1\mathrm{i}2}\\ k_{\mathrm{i}2\mathrm{h}1}& k_{\mathrm{i}2\mathrm{h}2}& k_{\mathrm{i}2\mathrm{l}1}& k_{\mathrm{i}2\mathrm{l}2}& k_{\mathrm{i}2\mathrm{i}1}& k_{\mathrm{i}2}\end{array}\right]\\ =\left[\begin{array}{cccccc}1& 0.9935& 0.9995& 0.9928& 1.28\mathrm{e}-3& 1.79\mathrm{e}-3\\ 0.9935& 1& 0.9926& 0.9990& 1.31\mathrm{e}-3& 2.27\mathrm{e}-3\\ 0.9995& 0.9926& 1& 0.9926& 1.54\mathrm{e}-3& 1.85\mathrm{e}-3\\ 0.9928& 0.9990& 0.9926& 1& 1.85\mathrm{e}-3& 2.38\mathrm{e}-3\\ 1.28\mathrm{e}-3& 1.31\mathrm{e}-3& 1.54\mathrm{e}-3& 1.85\mathrm{e}-3& 1& 0.038\\ 1.79\mathrm{e}-3& 2.27\mathrm{e}-3& 1.85\mathrm{e}-3& 2.38\mathrm{e}-3& 0.038& 1\end{array}\right]\end{array}$$

(22)

Figure 14 compares the coverage area of the HSTT with IFIs to that with discrete inductors. It can be seen that the HSTT with IFIs (10 kVA) needs a coverage area of 0.051 m². 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 m². 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.

Figure 15 shows the experimental platform, which is used to verify the high-frequency harmonics suppression effect with the proposed method. The DSP-TMS320F28335 (Texas Instruments, Dallas, USA) is used to sample signals and implement the control algorithm in this platform, and an oscilloscope is used to display the voltage and current waveforms.

Figure 16 shows the experimental results when the prototype of the HSTT with IFIs is adopted as an LCL-type filter, while Figure 17 shows the experimental results of LCL-type filtered single-phase converter, which is composed of the HSTT combined with discrete inductors. Clearly, both systems can operate stably, and the waveform of the grid-side current is nearly sinusoidal and in phase with the grid voltage. Furthermore, from those figures, the current ripple of double the switching frequency is damped to almost the same level, which is also within the allowed range. Therefore, the effectiveness of the proposed scheme for high-frequency suppression can be validated.

5. Conclusions

In this paper, a scheme for a single-phase LCL-type converter is adopted in the traction drive system for high-frequency harmonics suppression. Considering that the space in high-speed trains is extremely limited, an innovative HSTT with IFIs is proposed. The IFI has an effective magnetic decoupling structure, and the installation space of the filter device can be greatly reduced. Simulation and experimental results show that the proposed IFI-based LCL-type filter scheme can achieve similar harmonic attenuation performance as the discrete LCL-type filter scheme. The IFI method can also be applied to other engineering practices.