A real geographical case study on superconducting cables for high speed railway with electromagnetic and environmental analysis

Abstract

High-speed railways offer significant benefits such as high speed and large passenger capacity. However, their overall energy consumption continues to increase with network expansion. High-temperature superconducting (HTS) cables represent a promising solution to improve efficiency by reducing transmission losses in traction power supply systems. To date, HTS cables have not been deployed in AC-powered high-speed railway. To evaluate the feasibility, this article presents electromagnetic analysis and a real geographical case study on HTS cables to be equipped into the AC traction power system of the Shanghai-Suzhou-Huzhou high-speed railway. An HTS cable with the stacked structure was designed and optimized, and its fundamental electromagnetic behavior and loss characteristics were systematically investigated. Furthermore, a realistic case study was conducted to evaluate power losses and environmental impacts between the proposed HTS cables and conventional copper cables. Results show that the HTS cable efficiently reduced electrical losses, and also reduced CO₂ emissions by 88%. Both the microscopic analysis and macroscopic case study highlight the potential of HTS cables to reinforce the advantages of high-speed and low-emission operation for modern high-speed railways.

Introduction

Electrification of transportation is an effective pathway to achieve the net-zero emission target¹. High-speed rail transit is a safe, environmentally friendly, and energy-efficient mode of transportation². As the number of lines increases, overall energy consumption continues to rise. Conventional power supply systems for rail transit face challenges in transmission efficiency and capacity when handling large traffic volumes. Superconductor technology can optimize the energy conversion process and reduce energy losses during transmission³, while simultaneously advancing the electrification of transportation. At present, research on superconductors in high-speed rail transit has been carried out in areas such as traction transformers^4,5, linear synchronous motors⁶, maglevs^7,8 and feeder cables⁹. Compared to conventional copper conductor cables, HTS cables offer advantages such as high capacity, low loss, transmission, and environment-friendly¹⁰.

With the declining cost of superconducting tapes, the competitiveness of HTS cables is expected to increase. Marchionini et al. predicted that HTS cables would achieve commercialization between 2025 and 2030¹¹. The United States¹², European countries^13–15, Japan^16,17, Korea^18,19, and China²⁰ have all attached great importance to the application of HTS cables and have established demonstration lines. Reported applications include superconducting substations¹⁹, dedicated high-current lines²¹, large hadron collider²² and electrolytic aluminum plants²³. Compared with conventional cable projects, the kilometer-scale HTS cable project in Shanghai²⁰ has shown significant advantages in reducing carbon emissions. This advantage becomes more pronounced with increasing cable length due to the proportional reduction in CO₂ emissions. In the transportation sector, HTS cables are being investigated for ship power systems, electric aircraft applications and railway transit system^24–28, thereby contributing to the advancement of transportation electrification. HTS cables are also well-suited for railway traction power systems.

Many DC electrified sections in Japan and France²⁹ have already initiated relevant research and trials. Conventional feeder lines between substations have been replaced with superconducting cables to solve the voltage drop problem at the end sections of the feeder arms. SuperRail^30,31 in France would install two 80-meter-long high-temperature superconducting DC cables made in parallel to improve the power supply to train stations, enhance power quality, and reduce energy losses. A comprehensive loss assessment of superconducting cable systems was presented for practical deployment in 1.5 kV DC railway networks³². An energy transmission solution has been proposed for railways using HTS DC cables to transport LH₂ and LN₂, which can reduce energy loss and CO₂ emissions³³.

However, based on our literature study, research on the application of HTS cables in AC traction systems for high-speed railways is still missing. Since traction systems operate at industrial frequency (50 Hz) and HTS cables exhibit non-negligible AC losses, it is necessary to evaluate their electromagnetic and loss characteristics under realistic conditions. Moreover, to the best of our knowledge, no real-site study has been reported for HTS cables in AC high-speed railway systems.

This article investigated the two missing aspects above, and presented fundamental electromagnetic analysis and a real geographical case study for implementing HTS cable into actual high-speed railway. An HTS cable for was designed an AC traction system of high-speed railway from Songjiang South to Chunshen in the Shanghai-Suzhou-Huzhou high-speed railway. The cable losses were reduced through optimization of the tape arrangement. In addition, a case study based on a real geographical section with multi-site HTS cable systems is conducted, providing a comprehensive comparison of power losses and environmental indicators (e.g., CO₂ emissions) between HTS cables and conventional copper cables. The results show the technical and environmental advantages of HTS cables for high-speed railways.

Design of HTS cables for traction power system of high-speed railway

Application scenario

Among the current traction power supply modes in high-speed rail systems, the Auto-Transformer (AT) power supply mode offers high voltage and low current operation. Under the same power conditions, the current is effectively halved, significantly reducing line losses. A single power supply section can extend up to 60 km, reducing the number of required substations and enabling long-distance power transmission. Additionally, the opposite directions of current in the positive and feeder lines result in mutual cancellation of external electromagnetic interference, providing excellent electromagnetic compatibility. Therefore, an application scenario based on the AT mode was selected for this design. Fig. 1 shows the traction power supply scheme.

Fig. 1.

High-speed railway traction power system (AT mode) using HTS cables.

The Songjiang South to Chunshen section of the Shanghai–Suzhou–Huzhou high-speed railway spans approximately 16 km. It is powered by the Songjiang traction substation. The line layout in this supply section is relatively straightforward and passes through residential areas, so a low electromagnetic interference solution is necessary. This makes it a suitable case for the application of HTS cables in high-speed railway. Fig. 2 shows the schematic of the system. In the design, a part of the conventional feeder line within the Songjiang traction substation’s supply zone is replaced by an AC HTS cable. The section covers a total length of 16 km.

Fig. 2.

HTS cables for the traction power system of the Songjiang South–Chunshen section (the map section was re-drawn by the authors with the basic map background by Atlist (atlist.com)).

Cable structure and parameter

Based on the specific scenario above, the HTS cable was proposed. Its 3D structural diagram and cross-sectional schematic are shown in Fig. 3. This cable adopted a stacked tape structure, where gaps existed between the tapes, and all regions between tapes were filled with copper to provide safety redundancy for fault current. The main parameters are listed in Table 1. The tape structure uses typical configuration of ReBCO tapes. The structure of the tape is shown in Figs. 4, 5, and its critical current and other parameters are listed in Table 2.

Fig. 3.

Cross-section and 3D view of the HTS cable.

Table 1.

Parameters of the HTS cable.

Structure	Outer diameter (mm)
Copper support layer	10
PPLP insulation layer	28
Shielding layer	30
LN2 cooling channel	36
Cryostat outer wall	50
Outer sheath	56

Fig. 4.

Schematic of the HTS tape.

Fig. 5.

Cable model: (a) overall structure; (b) HTS tape region.

Table 2.

Parameters of the tape.

Grade	Tape width	Tape thickness	Ic (77 K)	Substrate material
Conventional	4 mm	95 μm	114–160 A	Hastelloy

Based on the following design conditions:

1. Capacity

The installed capacity of the traction substation is 2 × (31.5 + 31.5) to 2 × (63 + 63) MVA, generally.

• (2)Voltage

The voltage of the contact and feeder network is 27.5 kV.

• (3)Power

The total power of an 8-car formation of a 350 km/h bullet train is 1 MW, and the maximum power of a Fuxing bullet train is 10 MW.

The cable was designed to simultaneously supply maximum power to two Fuxing Trains (one in each direction) with a certain design margin reserved. As a result, the cross-section of the cable conductor was designed to consist of 10 ReBCO tapes.

The thermal insulation performance of superconducting cables directly impacts their operational costs and stability. The cryostat employs a high-vacuum multi-layer insulation design, constructed with coaxial vacuum double-layer corrugated tubes. Multiple layers of insulating materials are wound around the inner tube to reduce thermal conductivity. Heat leakage in the cryostat was calculated using the following equation:

1

Here, Q represents the heat leakage of the main body cryostat (W/m), λ denotes the thermal conductivity coefficient of the cryostat (W·m^-1·K^-1), T_h is the ambient temperature (293 K), T_l indicates the operating temperature inside the superconducting cable (70 K), D₀ stands for the outer diameter of the thermostat (mm), and D₁ refers to its inner diameter (mm). Given that the required heat leakage rate is 1 W/m and λ is set at 2.2 × 10^{− 4} W/(m·K), calculations show the thickness of the cryostat should be 6.48 mm. The final thickness is therefore 7 mm.

AC loss and electromagnetic characteristics analysis

Modeling of HTS cables

Ten tapes were arranged in a tightly stacked configuration. Since other non-ferromagnetic materials in the tapes were neglected, the tightly stacked model was simplified to ten rectangular superconducting layers uniformly spaced at 100 μm (the thickness of a single tape). Each layer had a width of 4 mm and a thickness of 1 μm. These ten rectangular superconducting layers together formed the superconducting part.

To analyze the electromagnetic characteristics of the cable and calculate its AC losses, we employed the H-formulation³⁴ of Maxwell’s equations along with the E-J power law^35,36, and utilized the PDE module in the FEM software for modeling. According to Faraday’s law of electromagnetic induction:

2

Since J=∇×H, B = µH, and the relationship between the current density and the electric field in the superconductor is E = ρJ,³⁷ transformed eq. (2) in terms of the magnetic field as:

3

Where ρ is the electrical resistivity of the computational domain. For air and normal conductor regions, the resistivity is treated as a constant.

In the stacked structure, the conductor layer of the cable can be modeled as a set of long, straight conductors. Assuming that the material properties remain constant along the length of the conductor, only the 2D cross-section of the conductor layer within the tape was considered. The state variables were the two orthogonal components of the magnetic field, while the current flowed perpendicular to them. The magnetic field components are H = [H_x, H_y, 0], and the current density component was J = [0, 0, J_z]. The current density can be expressed in 2D as³⁷:

4

In the numerical model, a circular area with a radius ten times the tape width was defined as the region for analyzing the magnetic field distribution. The space was divided into three subdomains³⁴: the superconducting region (Sc), the magnetization region (Mag), and the surrounding air region (Air), as shown in Fig. 6. The modeling method can be used for the structures in Fig. 7.

Fig. 6.

Space division.

Fig. 7.

Distribution of current density and magnetic field at different time points: (a) current density (visually expanded for the 1 μm thickness), and (b) magnetic field.

Rhyner has shown that the resistivity of the superconductor follows the E–J power law³⁶:

5

Where E is the electric field, E_c is the characteristic electric field, J is the current density, J_c is the critical current density, and n is the power-law exponent of the E–J relationship, which is set to 25.

The relationship between the critical current density and the magnetic field for REBCO tapes at LN₂ temperature (77 K)³⁸ is:

6

Where J_c0 is a constant determined by the material property, k = 0.25, b = 0.6, B_c =35 mT were used in³⁹.

By adding global constraints from a general PDE module, the application of current in the superconducting region is achieved:

7

Where S is the total cross-sectional area composed of all the superconducting tapes, J_z is the component of the current density normal to the integration surface, and Iasin(2πft) is the designed current capacity of the HTS cable in the traction power supply system, in which Ia is 1000 A, f is 50 Hz.

Since the AC frequency is 50 Hz, the eddy current losses in the metallic layers can be neglected, which could be applied for different superconducting modeling methods^40,41. Additionally, as the tapes use non-magnetic substrates, there are no ferromagnetic losses. Therefore, only the hysteresis loss in the superconducting layer was considered. Since the conductor undergoes a transition from an unstable to a stable state during the first half-cycle after current, the integration is performed over the second half-cycle and then multiplied by two to obtain the average AC loss over a full cycle⁴¹:

8

To verify the validity of the model, the values obtained from the simulation required to be compared with those calculated by the Norris theoretical formula⁴². Therefore, the AC loss Q_{(Joule/cycle/m)} is further calculated as follows:

9

Electromagnetic analysis

Single tape

A simulation was conducted on a single-tape model to validate the accuracy of the established modeling and computational procedures. The analysis was performed at a frequency of 50 Hz, with the transport current ranging from 20 A to 100 A. As shown in Fig. 8, the simulation shows that the calculated AC losses fall within the range of Norris strip and Norris ellipse, indicating the reasonableness of the proposed simulation approach.

Fig. 8.

AC loss simulation of a single tape, with reference to the Norris strip and Norris ellipse.

HTS cable

Since the perpendicular component of the magnetic field has a more significant impact on the critical current, the calculation of the critical current density J_c was further simplified. Fig. 9 shows the variation of AC losses as the peak current increases from 500 A to 1000 A. At a lower current, the simulated AC losses are slightly lower than those predicted by the Norris elliptical model. As the current increases, the loss curve gradually approaches the Norris theoretical curve.

Fig. 9.

AC loss simulation of the HTS cable, with reference to the Norris strip and Norris ellipse.

Fig. 10 shows the instantaneous power losses (W/m) distribution at a total transport current amplitude of 1000 A. In Fig. 10, the overall peak instantaneous AC loss reaches 11.87 W/m. By calculation, the average AC loss over one cycle is 4.2829 W/m, corresponding to a total AC energy loss of 0.08566 J/cycle/m. Due to the symmetrical structure of the model, the behavior in the upper five tapes is consistent with that in the lower five tapes. Fig. 11 presents the current waveforms of the top five individual tapes in the cable. The first top tape carried most of the current. Fig. 7a shows the current density distribution in a 2D cross-sectional view (visually expanded for the 1 μm thickness). The current exhibits a decreasing trend from the outermost to the innermost layers of tapes, and the peak current in different tapes occurs at different times. The magnetic flux distribution inside the cable at different time instants is shown in Fig. 7b. During the first half of the AC cycle, the magnetic flux density exhibits a trend of initially increasing and then decreasing with time. The maximum magnetic flux density reaches 0.18 T and occurs near the peak of the transport current. It can be concluded that the magnetic flux density within the HTS cable increases with the magnitude of the current.

Fig. 10.

Instantaneous power loss (W/m) at a total AC transport current of 1000 A.

Fig. 11.

Current distributions of several tapes in the top part of the cable.

Optimization

To reduce the AC losses in HTS cables with the stacked structure, one feasible approach was to increase the spacing between adjacent tapes⁴³. As shown in Fig. 12, three scenarios⁴³ for tape arrangement were proposed: zero-gap, uniform-gap, and non-uniform-gap schemes. The maximum height of the HTS conductor region was constrained by the tape width (w_tape), so the cross-sectional boundary of the superconducting region was limited to 4.0 mm×4.0 mm. The gaps between adjacent tapes, denoted as g₁,g₂,…,g₉, were numbered sequentially from top to bottom.

Fig. 12.

Three scenarios for tape arrangement: (a) zero-gap, (b) uniform-gap, and (c) non-uniform-gap.

Each scheme employs a vertically symmetrical configuration. This design achieves two main benefits. First, it ensures balanced stress distribution within the cable’s internal structure to prevent deformation. Second, it maintains vertical symmetry in current flow distribution, thereby avoiding complex electromagnetic field interactions.

Uniform gap

Table 3 presents five proposed schemes with different gap sizes. Within the maximum allowed optimization region, the total thickness of the ten stacked tapes was constrained to 4.0 mm (ranging from 1.0 mm to 4.0 mm), and the maximum gap between two adjacent tapes was limited to 0.30 mm.

Table 3.

Permissible uniform gap settings for schemes.

Scheme	Gap between stacked tapes (mm)
	g1 = g2 = g3=g4 = g5 = g6=g7=g8=g9
a1	0.10
a2	0.15
a3	0.20
a4	0.25
a5	0.30

Non-uniform gap

Table 4 lists the gap configurations for the three considered patterns. Mode 1 involved a single central gap g₅, ranging from 1.0 mm to 3.0 mm (b1–b5). Mode 2 considered two distinct gaps (schemes c1–c5), where the central gap was larger than those near the top and bottom, and the difference increased gradually. Mode 3 included three distinct gaps (schemes d1–d5), with the central gap being the largest, followed by the adjacent upper and lower layers, and the outermost gaps being the smallest.

Table 4.

Permissible non-uniform gap settings for schemes.

Scheme	Gap between stacked tapes (mm)
	g3	g4	g5	g6	g7
b1	–	–	1	–	–
b2	–	–	1.5	–	–
b3	–	–	2	–	–
b4	–	–	2.5	–	–
b5	–	–	3	–	–
c1	–	1.2	0.6	1.2	–
c2	–	1	1	1	–
c3	–	0.8	1.4	0.8	–
c4	–	0.6	1.8	0.6	–
c5	–	0.4	2.2	0.4	–
d1	0.2	0.6	1.4	0.6	0.2
d2	0.3	0.6	1.2	0.6	0.3
d3	0.4	0.6	1	0.6	0.4
d4	0.5	0.6	0.8	0.6	0.5
d5	0.6	0.6	0.6	0.6	0.6

Optimized results

Among schemes with a uniform gap, a5 (the gap of 0.30 mm) resulted in the lowest AC loss, reducing the loss from 0.086 J/cycle/m (ten tapes with no gap) to 0.072 J/cycle/m. The results for non-uniform gap schemes are shown in Figs. 13, 14, 15. Among all configurations, with nearly identical values, schemes b5 and c1 showed the lowest AC losses. Compared to the original tightly stacked configuration, these optimized designs significantly reduced the loss from 0.08566 J/cycle/m (ten tapes with no gap) to 0.043 J/cycle/m. As shown in Fig. 16, introducing gap spacing altered the magnetic flux distribution, resulting in a reduction in magnetic flux density. A comparative analysis of AC loss among the original configuration and optimized schemes b5 and c1 is presented in Fig. 14. The results indicate that the optimized schemes not only reduced total AC loss but also achieved a more uniform distribution of loss across the ten tapes.

Fig. 13.

Optimized results of different schemes.

Fig. 14.

Comparison of AC loss distribution in the HTS cable before and after optimization.

Fig. 15.

Comparison of losses in a conventional copper cable and the HTS cable.

Fig. 16.

Magnetic field distribution of various schemes at different time instants (1000 A transmission current).

A real geographical case study

In the Shanghai area, the operational length of high-speed railway lines has exceeded 100 km, providing a representative case for analyzing the feasibility of HTS cable applications in traction power systems. It is reasonable to propose an expansion case of 100 km HTS cables for the traction power system of high-speed rail transport in Shanghai area, impenetrating Jinshan District, Qingpu District, Songjiang District, Minhang District, Jiading District and central Shanghai, as shown in Fig. 17. Taking scheme b5 as an example, and neglecting the additional losses of cryogenic system, if the entire line is supplied with AC at 1000 A and 50 Hz frequency, the electrical loss amounts to only 3.62 kWh per minute.

Fig. 17.

HTS cables for the traction power system of high-speed rail transport in Shanghai (an expansion case of 100 km), impenetrating Jinshan District, Qingpu District, Songjiang District, Minhang District, Jiading District and central Shanghai (the map section was re-drawn by the authors with the basic map background by Atlist (atlist.com)).

Fig. 18 shows the losses and CO₂ emissions per minute of the 16 km test line, and the results indicate that the optimized HTS cable exhibits less than 12% of the electrical loss of a conventional copper conductor cable. Based on the carbon emission factor of 0.5894 kg/kWh in Shanghai, the optimized HTS cable can reduce emissions by approximately 88%. To calculate annual energy loss, we applied two correction factors derived from actual high-speed rail operations and power supply zones: (1) Shanghai’s high-speed rail operates daily from 6:00 AM to 10:00 PM, yielding a time factor of 0.67; (2) Within each 100 km segment, at least one power supply zone is operational. Using a distance of 15 km between adjacent zones, we calculated a distance factor of 0.15. According to these two factors to consider the average operation period of high-speed railway in Shanghai area, the annual CO₂ emissions reduction can be over 891 tons, with the expansion case of 100 km.

Fig. 18.

HTS cable vs. conventional Cu cable: losses and CO₂ emissions (per minute) in the 16 km test line.

In actual operation, feeder current varies with the train operating conditions. With the continuous growth of high-speed rail demand and higher speeds, the feeder current will inevitably increase. As shown in Fig. 19, compared to the conventional copper cables, the electrical loss of HTS cables remains consistently low under varying current conditions, and their low-loss advantage becomes more significant with increasing current. Fig. 20 shows the losses comparison (per minute) with increasing cable distance. The broader adoption of HTS cables in traction power systems will reduce more energy losses and CO₂ emissions for high-speed railways.

Fig. 19.

HTS cable vs. conventional Cu cable: losses with increasing current.

Fig. 20.

HTS cable vs. conventional Cu cable: losses (per minute) with increasing cable distance, (a) only electrical losses, (b) includes electrical losses and heat leakage from the cryostat.

These findings further confirm the potential sustainable development of HTS cables in railway electrification: enabling low-loss transmission of high currents, achieving significant energy savings, and contributing to environmental objectives—thus reinforcing the dual advantages of high-speed and green operation for modern rail transit systems.

The heat leakage requirement of the cryostat in the designed cable is less than 1 W/m. If the heat leakage level of 1 W/m is considered, the loss level is shown in Fig. 20b, and the loss level still has an obvious advantage over conventional cables. Even if considering the total power consumption of cryogenic equipment, the entire power consumption of HTS cable system is still lower than that of conventional copper cable system for railway system. With the technical advancement of cryogenic equipment, the overall power consumption of HTS cables will be even lower.

Conclusion

This article presents electromagnetic analysis and a real geographical case study on a 16 km / 27.5 kV HTS cable for the traction power system of the Shanghai–Suzhou–Huzhou high-speed railway. The fundamental electromagnetic and loss behaviors of the proposed HTS cable were investigated. The results show that, compared with conventional copper cables, the optimized HTS cable achieved a substantial reduction in loss, from 0.39 J/cycle/m to 0.043 J/cycle/m, with an associated 88% decrease in CO₂ emissions. As proposed, if the HTS cable length expands to 100 km impenetrating different districts in Shanghai, the annual CO₂ reduction can be over 891 tons. Both the microscopic analysis and macroscopic case study indicate the technical feasibility and environmental advantages of HTS cables in railway electrification.

Future research may include an on-site test platform to further validate the performance of the HTS cable, which can overcome the verification limitations of this work. With the expansion of HTS cables to be used in high-speed railways, the low-loss and low-carbon benefits of HTS cables would become increasingly significant.

Author contributions

S.L.: Formal analysis, Methodology, Software, Visualization, Writing—original draft. B.S.: Conceptualization, Methodology, Supervision, Writing—original draft, Writing—review & editing. Y.C.: Software. X.C.: Methodology. L.F.: Methodology, Supervision, Writing – original draft, Writing—review & editing.

Funding

This research was funded in part by the National Natural Science Foundation of China under Grant No. 52472382 and Grant No. 52407025, and the Fundamental Research Funds for the Central Universities.

Data availability

The datasets used and/or analysed during the current study are available on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.