Simulation Research on the Effects of Air Gaps and Ambient Temperature on a 27.5 kV Power Cable

Abstract

A 27.5 kV cable is one of the important infrastructures of a high-speed railway traction power supply system, and the reliability of the cable directly affects the stability and safety of the high-speed railway power supply. The cable runs in the complex environment of the laying site and will inevitably face the influence of electrical stress and thermal stress, resulting in air gap and insulation deterioration, which poses a threat to the safety of a high-speed railway traction power supply system. In this paper, an electric–thermal coupling model is built and simulated under normal operating conditions and different cable damage conditions. The distributions of the electric field and thermal field under different conditions of cables are explored. The weak points of a cable with poor heat resistance and easily produced air gaps are found. The influence of various temperature differences on a damaged air gap inside the cable is studied. Finally, the damage mechanism of a further increase in the cable’s air gap caused by partial discharge of the air gap is proven. This study provides a theoretical basis for inhibiting cable degradation and prolonging cable life.

1. Introduction

Due to the restriction of line paths and other reasons, the traction power supply system of an electrified railway is more and more dependent on power cables for transport electric energy [1,2,3,4,5,6]. With the development of high-speed railways, the reliable operation of cables directly affects the stability and safety of a traction power supply system [7,8,9]. Cables are one of the weakest links in the traction power supply of an electrified railway [10,11]. During operation of the power system, the cable inevitably faces the influence of electrical stress and thermal stress [12,13,14,15]. The internal heat and cold of the cable alternates, the interlayer stress changes, the interface is not tightly bonded, and structural stratification occurs, which leads to deterioration of the cable and aggravates the development of air gap defects inside the cable terminal, resulting in electric field distortion [16,17,18,19]. As a result, safe operation of the cable terminal is damaged, posing a potential threat to the overall safety and performance of the system. Therefore, it is of great significance to study the distributions of the temperature field and the electric field inside a cable and the mechanism of air gap development under different air gap damage conditions, as well as the influence of environmental temperature differences on the internal temperature of the cable, to improve cable life and ensure the safe and stable operation of high-speed trains.

Aiming at the typical defects of power cable air gaps, a large number of experiments and simulation studies have been carried out. References [20,21,22] found that under any field strength and temperature gradient, the dielectric properties such as the conductivity of different dielectrics have an impact on the space charge and electric field intensity distribution of the insulation layer of a cable, resulting in degradation of the cable. Therefore, the influence of internal temperature differences and environmental temperature gradients on the degradation of a cable cannot be ignored. Scholars [23,24,25,26] discovered the thermal aging effect caused by temperature on a cable and observed the effect of thermal aging on the electrical properties of crosslinked polyethylene, where temperature had a profound effect on the cable. However, the above research focused on the influence of air gap defects on cable aging, ignoring the cause of cable air gaps, that is, the process of air gap defect aggravation. Traditional power cable air gap defect experimental research has considerable flaws. On the one hand, it is a long process to design the sample air gap defect of a power cable and simulate the increase in the air gap defect of the power cable in an experiment, while an increase in the air gap defect of a power cable due to electrothermal coupling damage is a microscopic process. It is difficult to observe the microscale defect aggravation of power cables on a longer time scale. On the other hand, at present, the main means to study defects of power cables is to simulate the normal operating conditions of power cables and to observe the temperature changes in power cables during experiments by means of infrared cameras. However, due to the complex structure of power cables and the combination of various materials, infrared cameras can only observe temperature changes in the outer layer. The internal temperature variation of power cables cannot be well characterized. However, power cable simulation research can overcome the difficulties in experimental research, such as a complex structure that is not easy to observe and micro-changes that are not easy to detect, to realize the study of power cable air gap defects.

In past power cable simulation studies, references [27,28,29] used finite element analysis to analyze the influence of air gap defects on cable terminals. It was proven that air gap defects can cause distortion of the electric field in the insulation layer. By the finite element method, scholars [30,31] analyzed changes in cables and surrounding soil temperature increases under different laying conditions, evaluated the electromagnetic environment near power cables and quantitatively evaluated the effect of magnetic shielding. The problem of electric field distortion and temperature increases in power cables can be well studied with the finite element method. However, a cable runs in the complex environment of the laying site and will inevitably face the influence of electrical stress and thermal stress, resulting in air gap and insulation deterioration, which poses a threat to the safety of a high-speed railway traction power supply system. At present, studies on the internal damage process of power cables under different air gap defects and different ambient temperatures are still lacking. However, this study evaluated the impact of air gap and ambient temperature on power cables by analyzing the results of a electrothermal coupling model under normal and different cable damage conditions, improved the damage mechanism of power cables and studied how to reduce the damage to power cables. Improving the life of power cables is of great help. In order to ensure the safe operation of an electrified high-speed railway, it is urgent to research the influence of air gap defects of a 27.5 kV power cable with more special and harsh working conditions.

In this paper, an electric–thermal field coupling model was built and simulated under different working conditions, including normal operation and cable damage. The distributions of the electric field and thermal field under different conditions of cables were explored. It was found that the cable has poor heat resistance and easily produces air gaps. The influence of various temperature differences on a damaged air gap inside a cable was studied. Finally, the damage mechanism of partial discharge of an air gap, leading to a further increase in the cable air gap, is proven.

2. Cable Model Construction

In this study, an EN50264 standard 27.5 kV semi-rigid high-voltage cable and terminal are used for modeling [32]. The EN 50264 standard provides important input parameters for cable simulation such as material, geometric structure, thermal characteristics and electrical properties, which can greatly improve the accuracy and practical applicability of the simulation. Especially in complex, high-safety scenarios such as railway environments, the guidance provided by the standard can be used to develop safer and more efficient cable designs. The cable model and its terminal structure are mainly composed of a cable core and seven layers of an insulation structure [32], as shown in Figure 1. The outermost layer is an umbrella skirt to provide creepage distance; the second, third, fourth and sixth layers are insulated tubes, which play the main role of withstanding voltage; and the fifth and seventh layers are stress control tubes, which are used to improve the electric field distribution at the end of the cable and suppress electric field distortion.

2.1. Model Structure and Geometry

The simulation used COMSOL Multiphysics 6.1 finite element software to build the electro–thermal coupling simulation model of a 27.5 kV electrified railway cable, as shown in Figure 2. Based on the above simulation model, a single-phase alternating current with an amplitude of 27.5 kV and a frequency of 300 A of 50 Hz was applied to both ends of the cable, and a grounding was set on the shielding layer. By setting the external environment, the temperature and the distribution law of the temperature field inside the cable and its terminal under external temperature changes were explored.

The types and geometric settings of the materials inside the power cable are shown in

Table 1. Cable and terminal material type and geometry.

Structure	Materials	Outside Radius /(mm)
Cable core	Copper-aluminum alloy	9.77
Semiconductor layer	Semiconductor polymer	19.57
stress control tube	Polymer materials	18.27
Glue	Hot melt glue	/
heat shrink tube	PE	23.77
Sheathing layer	PVC	23.92
Umbrella skirt	Rubber	27.12

. The electrical conductivity, relative dielectric constant, thermal conductivity and Poisson value of the materials inside the power cable were obtained through actual measurements, as shown in

Table 2. Cable and terminal material parameters.

Structure	Electric Conductivity /(S/m)	Relative Dielectric Constant /(1)	Thermal Conductivity /(W/(m·k))	Poisson Ratio /(P)
Cable core	5.998 × 107	1	400	0.35
Semiconductor layer	2	100	10	0.25
stress control tube	1.3 × 10−9	25.3	35.3	0.44
Glue	7.7	0.5 × 10−8	10	0.38
heat shrink tube	0.25 × 10−10	3.34	0.25	0.22
Sheathing layer	1 × 10−18	2.6	0.46	0.38
Umbrella skirt	0.8 × 10−18	0.85	2.25	0.26

.

2.2. Boundary Conditions and Formulas

After the material was set up, the conductor was loaded with current, the solid loaded heat transfer module, and physical field coupling boundary conditions of a joule heat source, heat conduction and thermal expansion were established. The specific process was as follows: In the electric field, material resistivity changes with temperature, the skin effect and conductivity under the influence of pressure were considered, while the proximity effect was ignored. Contact thermal resistance under the influence of a joule heat source and pressure was considered in the thermal field, and eddy current loss under the action of the magnetic field was ignored in the heat source. The electric field affected the joule heat source in the thermal field, and the thermal field affected material resistivity in electrical stress analysis; therefore, the electric field and thermal field showed bidirectional coupling.

Firstly, the solid heat transfer control equation was constructed as follows:

$${\rho }_T{C}_P{\displaystyle \frac{\mathit{\partial }T}{\mathit{\partial }t}}-{\lambda }_T{\nabla }^{2}T=Q_E$$

(1)

Here, $t$ is the time; ${\rho }_T$ is the density of the material at temperature $T(K)$; $C_P$ is the specific heat capacity of the material at constant pressure; ${\lambda }_T$ is the thermal conductivity of the material at temperature $T$; and $Q_E$ is the joule heat source, calculated by the following formula:

$$Q_E=J\cdot E$$

(2)

Here, $J$ is the current density of the contact source, and $E$ is the electric field inside the contact source. $J$ and $E$ are solved by the electric field control equation satisfying Ohm ’s law and the current conservation law:

$$\begin{array}{l}J={\sigma }_T\cdot E\\ \nabla \cdot J=0\\ E=-\nabla \phi \end{array}$$

(3)

Here, ${\sigma }_T$ is the conductivity of the contact material at temperature T, and $\phi$ is the electric potential. When solving the electric field control equation, linear temperature change characteristics and the skin effect of conductivity should also be considered:

$${\sigma }_T(T)={\displaystyle \frac{1}{{\rho }_{20}[1+{\alpha }_{20}(T-293.15)]}}$$

(4)

This study focused on the transient process. The construction process of the electro–thermal coupling simulation model is shown in Figure 3.

3. Cable Thermal Field Research

Under preset conditions, the thermal field simulation of the simulation model was carried out to obtain the cable temperature distribution. The simulation results are shown in Figure 4. By comparing the temperatures of different structures, it was found that the core is the heat source of the cable terminal, and the highest temperature is 105 °C, as shown in Figure 4a. At the same time, it was observed that the temperature deceases with increasing distance from the cable core. When in the shield layer and the glue, the temperature near the stress tube approached the air temperature. When the cable was energized and heated, due to the varying thermal conductivity and temperature increases in different structural materials, the effects of temperature increases and thermal expansion had a strong influence on the deformation of the cable, which easily leads to the generation of air gaps and aggravates the aging and failure of a cable. Therefore, in order to further study temperature increases in different model structures when the cable is energized, internal temperature increases in the cable and terminal were calculated, as shown in Figure 4b. It was found that temperature increases between the outer semiconductor, the insulating layer and the junction of the stress control tube (x = 385 mm and x = 430 mm) is the largest. In practical engineering, the junction of the semiconductor, insulating layer and stress control tube of the cable is more prone to abnormal deterioration and failure [8,33]. The simulation results of the cable thermal field model were consistent with the actual project, which also proves that the huge temperature difference between the semiconductor layer, insulation layer and stress control tube is an important reason for the deterioration and failure of a cable. In the following research, the thermoelectric coupling simulation based on cables further revealed the damage and aging mechanisms of cables caused by temperature differences.

Electrified railway cables are in an exposed environment, and the temperature of the exposed environment will vary greatly over time. Different ambient temperatures caused by different times aggravate the aging of cables. In order to further study the influence of ambient temperature changes caused by different times on the distribution of the cable internal temperature, according to the ambient temperature of typical cable laying [34,35], the formula that defines the ambient temperature of an electrified railway cable over time is as follows:

$$T=\left\{\begin{array}{cc}({\displaystyle \frac{2}{45}})\cdot t+293.15& 0<t\le 450\\ 313.15& 450<t\le 1800\\ (-{\displaystyle \frac{3}{45}})\cdot (t-2700)+253.15& 1800<t\le 2700\\ 253.15& 2700<t\le 4050\end{array}\right.$$

(5)

Based on the above definition formula for changes in ambient temperature over time in electrified railway cables, a cable working environment temperature change curve with time was developed, as shown in Figure 5. It was found that t = 0 s to t = 4000 s can be divided into four zones, and t = 0 s to 450 s is the temperature increase zone. T = 450 s to t = 2700 s is the higher-temperature stable region, t = 2700 s to t = 4000 s is the temperature-drop zone, and t = 0 s to 450 s is the lower-temperature stable zone. In the four zones, the temperature difference from t = 1800 s to t = 2700 s—the temperature-drop zone—is the largest, which easily leads to cable air gaps and exacerbates cable aging. Therefore, the temperature difference from t = 2000 s to t = 2040 s in the temperature-drop zone was selected to further study the effect of environmental temperature differences on the cable temperature distribution.

As shown in Figure 6, the temperature change inside the cable occurred at 385 mm and 405 mm when the ambient temperature changed from t = 2000 s to t = 2040 s. It was found that the temperature at the cable core and the semiconductor layer are significantly reduced, and the temperature gradient is 3000 K/m. The temperature at the semiconductor layer and stress control tube decreased first and then increased. The maximum temperature gradient was 5000 K/m. The maximum temperature drop gradient at the junction of the stress control tube and insulating layer was 1400 K/m. In the cable terminal, the temperature was the most unevenly distributed at the semiconductor layer and stress control tube, and then the stress between layers change; the interface was not tightly bonded, and an air gap was generated to aggravate stratification of the structure, resulting in deterioration of the cable. The second was between the cable core and the semiconductor layer, and the last was between the stress control tube and the insulating layer.

4. Cable Electrical Field Research

In order to study the damage mechanism of partial discharge leading to further increases in the cable air gap, the specific distribution of the interface electric field in the XLPE/EPDM composite interface discharge area under AC voltage was investigated using the cable model. Then, the electric field distribution characteristics between air gap composite interfaces were simulated and calculated by the electrostatic field analysis module, and the insulation degradation mechanism of the 27.5 kV cable caused by the air gap was analyzed. The air gap defect mainly occurred between the primary insulation layer and stress control tube in the cable model, as shown in Figure 7a. The air gap length was 20 mm, and the thickness was 2 mm. The electric field simulation calculation of the cable model with air gap defects was carried out, and an air gap electric field cloud map was obtained, as shown in Figure 7b. When there was an air gap defect inside the cable terminal, the electric field inside the air gap was seriously distorted, the maximum air gap electric field strength reached 6.5 × 10⁶ V/m, and the ionization field strength of super air (3 × 10⁶ V/m) was doubled, which is prone to partial discharge inside the cable, aggravation of cable insulation deterioration and cable aging, which affect the performance and stability of the cable.

By simulating the interior of the cable under different temperature changes, an air gap temperature diagram under different temperature changes was obtained, and the influence of different temperature changes on the air gap was studied, as shown in Figure 8. The results show that a decrease in ambient temperature has a greater influence on the temperature in the air gap than an increase in ambient temperature.

Further research identified the maximum temperature of the cable under different temperatures and different environmental temperature changes, as shown in Figure 9. When the ambient temperature decreased from 20 °C to 0 °C, the air gap temperature increased the most, reaching 319.87 K. When the ambient temperature was 20 °C to 0 °C, the air gap temperature inside the cable was the highest. Under the alternating action of internal and external cold and heat, the interlayer stress changed, and the interface was not tightly bonded. With deformation inside the cable, the air gap developed further, and the cable deteriorated.

Cable air gaps are prone to partial discharge, and the energy generated by discharge caused the air gap temperature to change sharply, which further aggravated the deformation of the air gap and aging of the cable; air gaps may cause potential threats to the stability and security of a traction power supply system. In order to study the influence of air gap thickness on the internal temperature of a cable during operation, a cable model with different air gap thicknesses was built, as shown in Figure 10. The air gaps between the stress control tube and the primary insulation layer were 1 mm, 2 mm, 3 mm, 4 mm, 5 mm and 6 mm.

The electro–thermal coupling simulation of air gaps with different thicknesses was carried out, and electro–thermal field diagrams of air gaps with different thicknesses were calculated, as shown in Figure 11a,c. It was found that when an air gap increased from 1 mm to 6 mm, the temperature and the temperature distribution range of the air gap decreased. When the air gap is 1 mm, the minimum temperature is 309.90 °C. When the air gap is 6 mm, the maximum temperature is 319.98 °C. In order to further study the influence of air gap temperature on a cable, an electric field diagram of air gaps with different thicknesses was observed, as shown in Figure 11b,c. It was found that when the air gap is 1 mm, the electric field intensity in the air gap is the highest, partial discharge is more likely to occur, the initial electron generation rate of partial discharge has a strong influence on air gap temperature, and stronger partial discharge leads to a greater temperature difference. When the air gap was small, the electric field intensity in the air gap was greatly affected, and the temperature change was more severe, leading to the further expansion of the air gap and deterioration of and damage to the cable.

5. Conclusions

By analyzing the results of the electric–thermal coupling model under normal working conditions and different cable damage conditions, we evaluated the effect of air gaps on power cables and drew the following conclusions:

(1)

The temperature distribution of the cable under different conditions was explored. It was found that the temperature difference at the junction of the outer semiconductor, insulating layer and stress control tube of the cable is the largest, and the distribution at the semiconductor layer and stress control tube is the most uneven. which is morelikely to produce an air gap to aggravate the structural stratification, resulting in cable degradation.

(2)

The influence of different temperature differences on the temperature of a cable air gap was studied. It was found that a decrease in the ambient temperature has a greater influence on the temperature in the air gap than an increase in the ambient temperature. When the ambient temperature decreased from 20° to 0°, the air gap temperature was the highest, reaching 319.87 K.

(3)

The electrothermal field distribution law of cable air gaps with different thicknesses was found. When air gap thickness is smaller, the electric field strength in the air gap is higher, and partial discharge is more likely to occur, resulting in a greater cold and heat alternating effect and a further increase in the air gap.

The results of this study can provide a theoretical basis for restraining cable deterioration and prolonging cable life to ensure the stability and safety of traction power supply systems.

In the future, in order to further study the influence of air gaps and ambient temperature on power cables, power cable samples with different air gaps were designed. An infrared camera was used to observe the influence trends of different air gaps and different ambient temperatures on cable temperature changes, which were then compared with those of the model to verify the accuracy and feasibility of the power cable defect model proposed in this study.