Role of Flux Diverters in Reducing AC Loss in a Single-Phase 6.5 MVA HTS Traction Transformer for Chinese High-Speed Train Carrying High-Order Harmonic Currents

The traction transformer is a critical electrical component in high-speed-trains. We are currently building a 6.5 MVA superconducting traction transformer which will increase transformer efficiency to 99%, halve the weight, and avoid the fire risk of the conventional transformer system. AC loss from the transformer windings cannot exceed 2 kW to meet both the efficiency and weight targets. There are significant high frequency harmonics, particularly the $13^{\mathrm {th}}$ harmonic at 650 Hz, on the traction side of the transformer. Our previous work has shown the estimated AC loss in the transformer windings almost doubled with the addition of a 650 Hz harmonic current at the 8% level specified, which is not acceptable. Therefore, it is critical to reduce AC loss in the transformer due to high harmonics. In this study, we explored the role of flux diverters positioned at the outer ends of the high voltage (HV) and low voltage (LV) windings in restraining AC loss in the windings carrying high-order harmonic currents below 2 kW. Five different ring-shaped flux diverter designs were modelled in this work, utilizing the previously developed 2D axisymmetric model using the $H$ formulation. Simulations were carried out to study the influence of the phase of the 13th harmonic, either in phase or out of phase with respect to the fundamental current, and of the inclusion of multiple harmonics on the loss. The simulation results show that placing flux diverters near the end of the windings leads to a magnetic flux distribution in the windings with reduced radial field, and hence significantly reduces the loss. Three of the flux diverter designs achieve the loss target by limiting the AC loss to below 2 kW, with a wide/thin design having the minimum weight and a wide/thick design achieving only 6% less loss, despite being almost four times heavier.


I. INTRODUCTION
The traction transformer is one of the essential components in Chinese Fuxing high-speed trains. The efficiency of this The associate editor coordinating the review of this manuscript and approving it for publication was Zhouyang Ren . traditional traction transformer is not greater than 96% [1], [2]. To increase the transformer efficiency and reduce the system weight and the fire risk, there have been intensive worldwide developments of superconducting transformers, which are, more efficient, lighter, and low in fire risk [3]- [15]. The present paper describes modelling results which form part of concept design development for an on-going international collaboration project aiming to develop a 6.5 MVA high temperature superconducting (HTS) traction transformer with efficiency >99% and a halved system weight of 3 tons. The project is led by Beijing Jiaotong University in China in cooperation with other parties, including Robinson Research Institute, Victoria University of Wellington in New Zealand.
AC loss of the HTS transformer is the main obstacle to the project goal and must be limited to no more than 2 kW to meet the efficiency and system weight targets [12]- [15]. In addition to the AC loss, we allow for 500 W of thermal load from current leads, bushings, and other factors [16].
The high voltage (HV) windings of the transformer are directly connected to the 50 Hz power network which contains harmonics. The low voltage (LV) windings of the transformer are connected to the traction system, which incorporates converters and switches. As a result, the current in the transformer windings has substantial harmonic content [17], [18]. According to previous reports [19], on the traction side of the high-speed train transformer, the 13th harmonic is the strongest, rather than the 3rd harmonic. Table 1 gives a typical harmonic distribution for the conventional transformer in the Fuxing high-speed train. Here, we define the total harmonic distortion (THD) for a current as where I k (k = 2, 3, 4, 5, . . . ) is the RMS current of the k-th harmonic, I 1 is the RMS value of the fundamental current.
In the case that a single k-th harmonic component is considered, the THD can be written as As shown in Fig. 1, our previous work [19] calculated that the AC loss in the windings reaches 6.7 kW, far higher than our 2 kW AC loss limit, at the 8% 13 th harmonic THD given in Table 1. Most importantly, the majority of losses was generated at the end coils of the HV and LV windings. Our earlier work [16] explored numerically the reduction of the AC loss using flux diverters (FDs) to reshape the magnetic flux distribution near the transformer windings, but that work did not consider the harmonic distortion of the current. A subsequent experimental investigation [20] demonstrated both the effectiveness of flux diverters in reducing AC loss in HTS coils and the validity of our computational methods for predicting the loss reduction. The measured results also showed negligible loss in the magnetic flux diverter materials.
In this work we explore the potential of flux diverters positioned near the end of the HV and LV windings to restrain FIGURE 1. Simulated AC loss results in HTS transformer carrying rated 50 Hz current with the addition of a 13th harmonic component, plotted against THD value [10]. Here, the 13th harmonic was assumed to be in phase with the fundamental current. The dashed dotted red line denotes the 2 kW thermal criteria for both 99% efficiency and 3 tons weight. the AC loss below 2 kW in the transformer windings carrying current with high-order harmonic components. Various ring-shaped flux diverters designs are proposed and considered in the work, and the best of these is identified.

II. NUMERICAL SIMULATION
A. TRANSFORMER SPECIFICATIONS Fig. 2 shows the schematic of the 6.5 MVA single-phase HTS transformer. The transformer design contains four winding units on a single iron core where each leg of the core has two winding units around it. The transformer is designed to operate at 65 K [16]. The HV winding is wound with 4 mm-wide Fujikura wire and the LV winding is wound with 8/5 (eight 5 mm wide strands) Roebel cables, assembled from punched Fujikura strands. Table 2 gives both electrical and geometrical parameters of the transformer.

B. SIMULATION METHOD
AC loss simulation for the transformer was carried out in a 2D axisymmetric model, using the H formulation [21]- [23]. Homogenization method [24] was implemented in the simulation. The simulation is completed by solving the combination of Maxwell equations and E-J power law relation, the distinctive behavior of superconductors. In our previous paper [25], we verified an AC loss model for a 1 MVA transformer with its LV winding wound with Roebel cables. In this work, we adopted the same method for AC loss analysis of the 6.5 MVA transformer carrying distorted current with harmonic components.
The simulations were carried out using a 2D axisymmetric model for the transformer, as shown in Fig. 3. The radial and axial magnetic field components H = [H r , H z ] T are directly solved. Only the cross-section of the HV and LV windings in one unit is considered as schematized in Fig. 3. Superconducting windings are surrounded by an air domain. Current I flows in ϕ direction. The detailed modeling method can be found in our previous paper [16].
The dependence of the critical current density on the applied magnetic field is incorporated, based on measured I c (B) results divided by the cross-section area of the conductor, S. We adopted a modified Kim model [26] for the J c (B) behavior, Fitting parameters B 0 = 100 mT, k = 0.71 and α = 0.23 were determined by comparing fitted I c (B) curves with the measured results under perpendicular and parallel magnetic fields, as shown in Fig. 4. Here, B ⊥ is the radial magnetic field B r and B // is the axial magnetic field B z .  The governing equations are shown below, where µ 0 is the magnetic permeability of the free space and µ r is the relative magnetic permeability. To be effective in shaping the flux distribution to reduce the radial magnetic field component at the end windings, the FDs need to be close to the winding ends. We assume a gap g 1 between winding ends and FD, 0.5 mm. In practice, this requires both the FDs and the outer ends of both HV and LV windings to be grounded. Our previous work [16] has shown that, at the inner end of the HV and LV windings, FDs are not required because the radial magnetic field, and hence the AC loss, is low, provided the axial gap between  the upper and lower winding pairs on the core leg remains small. In this work we adopt an axial spacing g 2 of 20 mm. By varying the values of the width and height of the flux diverters, while keeping the radial center of the FD aligned with the radial center of the corresponding winding, five ring-shaped flux diverters are specified, as listed in Table 3, to investigate the AC loss reduction using flux diverters. The selected flux diverter material is the low-loss nickel-iron High-Flux powder-core material [27].

IV. SIMULATION RESULTS AND DISCUSSION
A. AC LOSS REDUCTION BY FDS WHEN ONLY THE 13 TH HARMONIC IS CONSIDERED Fig. 6 plots the waveforms of the distorted current in the HV and LV windings containing the 13th harmonic component with 8% THD at the rated current, as compared with the sinusoidal current waveform. It is observed that the maximum current amplitude of the resultant current with the 13th harmonic component is larger than that of the sinusoidal current. There are seven peaks or incipient peaks per half cycle in the distorted current waveform as opposed to the single peak in the pure sinusoid [20]. Each reversal of current produces additional AC loss. The simulated AC loss values in the 6.5 MVA transformer windings using different FD designs with 8% THD of the 13th harmonic current are plotted in Fig. 7. Here, five FD designs, #1 to #5, are considered. The green dotted line shows  the AC loss values in the transformer winding carrying the sinusoidal rated current without FDs. The black dotted and dashed line shows the AC loss in the transformer winding with 8% 13th harmonic component without FDs. The red dashed line shows the 2 kW loss target to achieve 99% efficiency and 3 tons transformer system weight. It is obvious that flux diverters can significantly reduce the AC loss in the transformer windings. Flux diverter design #3, #4 and #5 could all limit the AC loss to below 2 kW, among which FD #4 has the maximum AC loss reduction. Note that FD #3, #4 and #5 have the same thickness, but different width. The results indicate that a wider FD will achieve more AC loss reduction.  windings with FD#1 and #2 were reduced to 2.17 kW and 2.11 kW, respectively, corresponding to around 68% AC loss reduction. However, AC loss values in the windings with FD#3, #4 and #5 were further reduced to 1.96 kW, 1.83 kW and 1.77 kW, respectively, which are all below the 2 kW loss target. Fig. 8 shows the simulated AC loss values in the HV and LV windings when carrying the 13th harmonic with 8% THD plotted as a function of the FD index. A similar loss reduction trend was found in the HV and LV winding. Fig. 9 compares AC loss in each disc in the 6.5 MVA HTS transformer with/without FDs carrying sinusoidal current or current with 8% THD of the 13th harmonic at rated current. In Fig. 9(a), the loss in Disc #1 of the HV winding increases by 9% when the harmonic is added as compared to that with the sinusoidal current alone. The losses in the majority of the discs of the HV winding show obvious reduction, especially in the end discs when FD#1 and FD#5 are used, as compared to that without FDs. It is also observed that FD#5 leads to lower losses than FD#1. The indexing of the discs is indicated in Fig. 2. Fig. 9(b) indicates that there are substantial loss reductions in the LV winding as well when FD#1 and FD#5 are used, as compared to that without FDs. Again, FD#5 leads to slight better loss reduction than FD#1.
The phenomenon can be explained by the redistribution of the magnetic field in the end discs of the transformer windings when FDs are in place. Figs. 10(a)-(c) compare the radial magnetic field distribution in the HV windings at the rated current, when carrying sinusoidal current, nonsinusoidal current with 8% THD 13 th harmonic component without FD, and non-sinusoidal current with 8% THD 13 th harmonic component with FD#5. It is observed that the harmonic component increases the maximum radial magnetic field component, consistent with the 8% increase in peak current amplitude. This phenomenon is consistent with the findings in [28] that a larger amplitude of the current considering current harmonics will lead to higher AC losses. The flux diverters are effective in attracting the magnetic flux so that the magnetic flux lines run more parallel to the coil surface in the end discs of the windings. Figs. 10(d)-(f) compares the radial magnetic field distribution in the LV windings at the rated current, when LV carries sinusoidal current, non-sinusoidal current with 8% THD 13 th harmonic component without FD, and non-sinusoidal current with 8% THD 13 th harmonic component with FD#5. A similar magnetic flux reshaping effect can be observed which explains the AC loss reduction in LV windings produced by reducing the radial magnetic field around the end discs using the FDs. Fig. 11 shows waveforms for distorted currents with the 13th harmonic in-phase and out-of-phase with regard to the fundamental current, at THD = 8%. We clearly observe that the waveform with the out-of-phase 13th harmonic is notably different from that with the in-phase harmonic [29]. The current waveform with out-of-phase 13 th harmonic has two peaks in amplitude leading and lagging the peak of the fundamental and 5.3% greater in amplitude than the fundamental. The maximum amplitude for the current with the in-phase harmonic coincides with the peak in the fundamental and is 8% greater in amplitude than the fundamental. The AC loss value for the transformer with in-phase 13 th harmonic is slightly greater than that for the out-of-phase harmonic which is due to the difference in the amplitudes, as shown in Table 5. Fig. 12(a) and 12(b) plot total instantaneous loss in each winding (W) through a single 50 Hz cycle, when carrying sinusoidal current, sinusoid current plus 8% in-phase 13th harmonic current, and sinusoid current plus 8% out-ofphase 13th harmonic current, at rated current. The first half cycle, during which AC current is introduced to the initially unmagnetized superconductor, differs from subsequent half cycles in which the AC magnetization distribution in the winding is established. In practice, the AC loss per cycle is given by twice the integrated instantaneous loss in the second half cycle. In Fig. 12(a), it is obvious that more peaks of instantaneous loss occur due to the resultant current waveform shown in Fig. 11, when harmonic current is considered, either in phase or out of phase, as compared to the sinusoidal case. The peaks of instantaneous loss when carrying 8% 13th harmonic current in phase occur at different times compared to those when carrying 8% 13th harmonic current out of phase. The maximum instantaneous loss peak occurs when carrying 8% 13th harmonic current in phase, consistent with the fact that it has the maximum current amplitude. The integral of the instantaneous loss for 8% 13th harmonic current in phase is greater than that for 8% 13th harmonic current out of phase. The same effect is seen in the LV winding in Fig.12(b). Fig. 13 shows the waveforms for the distorted current with multiple harmonics listed in Table 1, either in-phase or outof-phase with regard to the fundamental current component.  The maximum amplitude for the current is 1271.96 A and 1249.16 A, 3.0% and 1.2%, respectively, greater than the amplitude of the fundamental. Note that FD#5 is used in the model to reduce the losses since it not only limits the AC loss to below 2 kW when carrying the single 13th harmonic but also has the smallest cross-section. As seen from the results in Table 6, with FD#5 the AC loss is limited to below 2 kW when the multiple harmonic components are either in-phase or out-of-phase with respect to the fundamental current.    Detailed weight values can be found in Table 7. The weight m is calculated based on the volume of flux diverters V and the density of iron ρ, m = V * ρ, as an approximation. Here, ρ = 7.874 g/cm 3 was used.

C. AC LOSS REDUCTION BY FDS WHEN A HARMONIC SPECTRUM IS CONSIDERED
As seen from Fig. 14, FD#4 has the maximum weight of 37.9 kg. FD#1 and FD#5 have relative lighter weight of  Table 1).   Fig. 7, FD#3, #4 and #5 will meet the AC loss target of 2 kW. However,FD#5 will be a preferable option in terms of both weight and loss reduction in the transformer windings. Table 8 shows an estimation of the weight of the system and its component parts for the required cooling power of 2.5 kW and for running times of 5 and 8 hours [16]. At 2.5 kW cooling power the total system after adding the weight of flux diverters still weighs less than 3000 kg even for 8 hours running time. The estimation underlines the importance of minimizing AC loss to keep the system weight within the 3-tons constraint.

V. CONCLUSION
It was evidenced by previous study that AC loss in the traction transformer windings will be significantly increased due to the harmonic current, particularly high-order harmonic. This remains a bottleneck for superconducting traction transformer application. The main contribution of this work is, for the first time, we propose to utilize flux diverters to tackle with this challenge in the traction transformer carrying high order harmonic component and harmonic spectrum, and numerical models are built to investigate the AC loss reduction by this proposal.
To constrain AC loss in the transformer windings carrying current with high-order harmonics within 2 kW, we propose to utilize flux diverters near the end of the high voltage (HV) and low voltage (LV) windings. Five different ring-shaped flux diverters were considered in this work, and AC loss calculated using a validated 2D axisymmetric model.
In this work, flux diverter rings with rectangular crosssection are considered for both HV and LV windings. The results show that using flux diverters near the end of the transformer windings leads to less perpendicular magnetic field in the end windings and hence significantly reduces the AC loss. It is obvious that the width of the flux diverters has more impact on the AC loss of the transformer winding than the thickness, and that a wider FD ring design leads to more AC loss reduction.
The simulation result shows that the addition of harmonic components distorts the current waveforms and results in higher current amplitude and hence higher AC loss in the transformer winding. The flux diverter design #5 having the smallest weight limits the AC losses in transformer windings below 2 kW, not only in the case when only the 13 th harmonic is considered, but also when the full harmonic current spectrum is considered.
The simulation results reveal that the AC loss in the transformer winding depends on the phase angle of the harmonic components, which should be considered during the design stage for accurate AC loss estimation.
The simulation results clearly show that high order harmonic components are not an insurmountable obstacle to HTS traction transformer application. Better than 99% efficiency and less than 3 tons system weight are still achievable in the HTS 6.5 MVA traction transformer fitted with low-loss flux diverters when carrying current with realistic high-order harmonic components.