1. Introduction
Due to mechanical damage, contact resistance of cable joint, overcurrent operation, and so on, the temperature rise of the cable exceeds the rated value, which leads to electric shock or fire, and threatens the safety of the power grid. The cable ampacity is an important parameter to restrict the load and temperature rise of power cables. Therefore, it is necessary to simulate the distribution of temperature field and calculate cable ampacity and online monitor the temperature of cables.
There are two main calculation methods for cable temperature and ampacity: one is the analytical method obeying IEC-60287 standard [
1,
2]. This method is suitable for direct buried cables. IEC standard makes many ideal assumptions for the calculation of the cable ampacity and temperature distribution. For example, the ground surface is regarded as a constant temperature boundary, and the temperature of each layer of cables is constant. However, actual operation environment seldom meets this assumption. The other method is numerical analysis, which mainly includes boundary element method, finite difference method, finite volume method [
3] and finite element method. Compared with the analytical method, the numerical analysis method has many advantages, such as stronger operational adaptability with multiphysical field coupling analysis and simulation data is more accurate. Therefore, in recent years, numerical calculation method [
4,
5] has become a good tool to study cable thermal problems.
The works by the authors of [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17] set different boundary conditions and changed the structural parameters of cables in different environments; they obtained steady temperature field distribution of regular laying cables by analytical, numerical methods and other computational methods. Ruan, J. [
6] built a model to estimate the temperature inside the three-core cable joint based on support vector regression (SVR). Anders, G.J [
7] developed a new formula to compute the value of the internal thermal resistance of belted cables taking into account the thermal resistivity of the filler. Lee, S.J. [
8] conducted a longitudinal temperature analysis according to the structure of the refrigerant circulation system of the cable and proposed a refrigerant circulation system. Sedaghat A [
9] derived a scientifically sound and accurate thermal electric circuit for the calculation of the steady-state temperature of cables in air from first thermodynamic principles. Anders, G [
11] discussed rating calculations of underground power cables when the temperature limit is imposed on a location other than the cable conductor. Youyuan, W [
5,
13] used finite element method to calculate steady temperature field of underground cable and its influencing factors, and analyzed the calculation of current carrying capacity of cable and its influencing factors. Gaggido, C. [
15] calculated the temperature distribution and ampacity in a multilayered soil surrounding a system of three cables in the steady state in emergency situations. Doukas D. I. [
16] presented the analytical mathematical formulation to solve heat transfer equations for a 2D axisymmetric cable model and identifies temperature distribution over length and time. Works by the authors of [
18,
19,
20] introduce the calculation method of carrying capacity of different cables.
In fact, it is common that cables are laid irregularly in the actual cable trench of urban power grid, and the temperature distribution and carrying capacity of the cable trench are rarely studied. At the same time, there is almost no comparative study between IEC60287 and numerical calculation methods.
In this article, two methods are used to calculate the temperature of cable core, and a comparative analysis is made. The temperature distribution and cable ampacity of irregular distribution cable trench is studied. At the same time, an online monitoring system is designed to monitor the condition of cable trench in real-time.
2. Calculation Principle and Comparative Analysis
2.1. Physical and Environmental Parameters
The single-core cross-linked polyethylene (XLPE) low-voltage cable of 8.7/15 kV YJV 1 × 400 is taken as the research object, and its main structure is shown in
Figure 1.
The cable structure parameters and environmental parameters are shown in
Table 1 and
Table 2.
2.2. IEC-60287 Thermal Circuit Method
IEC-60287 is a common analytical method for calculating core temperature and cable ampacity. This method obtains the temperature distribution of different layers of cables by solving the equivalent thermal circuit, calculating the power loss of cables and the thermal resistance of the surrounding environment. The equivalent thermal path of the cable and its surrounding environment is shown in
Figure 2.
By thermal path model.
where
, is the power loss of the cable conductor per unit length, .
is the current effective value of the cable conductor, .
is the AC resistance of the cable conductor at the highest temperature, .
is the power loss of cable insulation layer per unit length, .
and are the loss coefficient of metal shield layer and the armor layer, respectively, constant without unit.
, and represent the thermal resistance of insulation layer, metal shield layer, outer shield layer, and surrounding medium, respectively.
is the number of cable cores, for single-core cable, .
and represent the temperature of the core and skin temperature of the cable, respectively, .
The cables studied in this article are single core cables. The thermal resistance and power loss in Equation (1) are calculated by the formula from IEC standard. The skin temperature of the cable is obtained by Equation (1), and then the conductor temperature of the cable is calculated too.
2.3. Numerical Calculation Method
2.3.1. Model of Cable Trench
We assume that the length of the cable is infinite corresponding to its cross-sectional area. In addition, in steady state operation, there is almost no temperature gradient along the cable axis. Therefore, the two-dimensional model can reflect the temperature distribution of cable trench. Because the influence of angle steel brackets is small, they are neglected in the two-dimensional model. Therefore, the two-dimensional model as the cross-section of the cable trench shown in
Figure 3 looks like triple three-loop cables float in the trench.
The cross-sectional area of inner cable trench is 0.6 m*0.8 m. Cable trench wall are 0.075 m thick, the lid is 0.1 m thick and the whole size including soil and trench is 3.15 m × 2.5 m. A total of nine cables are laid on angle steel brackets in three layers, and the current value of each phase cable is the same as 200 A, which is less than the cable ampacity. The ambient temperature is 293.15 K and the soil temperature is 287.15 K in the distance. The reference temperature is the initial temperature set by the COMSOL system, which is 293.15 K.
The following assumptions are made.
- (1)
The steady state temperature field distribution of cable trench is simulated only.
- (2)
The material properties of the cable and cable trench environments are all isotropic homogeneous media, and the physical properties of materials are constant.
- (3)
Only the balanced operation of the cables is considered.
- (4)
The metal shield or sheath layer of the cable is grounded at a single point, without considering the circulation loss of the shield layer.
2.3.2. Heat Transfer Equation
Simulating the steady-state temperature field of cable trench is a two-dimensional steady-state heat transfer problem. There are two different heat transfer equations including heat source or not:
- (1)
The heat transfer differential equation of the area containing heat source (including cable core, insulating dielectric layer, and shielding layer) is as follows.
is the temperature at the point (x, y) in the domain, °C.
is the unit volume calorific rate, .
is thermal conductivity, .
- (2)
The heat transfer differential equation of the area without heat source (including other cable layers, soil, cable trench wall, etc.) is as follows.
2.3.3. Boundary Condition
There are three main boundary conditions for heat transfer problems.
- (1)
Constant boundary temperature.
- (2)
Normal heat flow conditions with constant boundary normal heat flux density.
- (3)
The convective heat transfer conditions in the interface between solid and fluid, occurring when the temperature of the fluid and the convective heat dissipation coefficient of the fluid are known.
In the formula,
is the thermal conductivity, .
is a temperature function on the boundary.
is heat flux density, .
α is convective heat transfer coefficient, °C).
is the fluid temperature, °C.
and are the integral boundary.
According to the actual working environment of cable trench, the boundary conditions are determined as follows.
As shown in
Figure 3, the temperature does not change in the horizontal direction of the boundary 1.2 m away from the cable trench, so the left and right boundaries of the model have a normal heat flow condition. The upper boundary is the ground plane, which is directly in contact with the air flow and meets the convective heat transfer conditions, and we take 25 °C as the air temperature. The lower boundary is deep soil, which can be regarded as a constant temperature boundary condition.
For direct buried cables, cable heat is commonly considered have no effect on soil 2 m outside. In addition, the soil 1 m away from the cable trench wall is not affected. Therefore, the boundary of rectangular solution domain was set as a line 1.2 m away from cable trench wall. Meanwhile, the upper boundary took the convective boundary condition.
2.4. Thermal Process Analysis of Cable Trench
Heat generation: In the whole solution area, only the cable produces heat, which comes from the Joule heat, dielectric power loss and induced power loss of the cable. AC resistance and inductance loss of multi-group single-core cables are calculated by analytical method according to IEC60287 standard.
Heat dissipation: The thermal process of cable trench includes heat conduction, convection and radiation. Specifically, the inner part of cable body, angle steel bracket, cable trench wall and soil mainly deliver heat through heat conduction. Natural heat convection and radiation mainly happen between solid and air in cable trench, they also happen between the upper cover of cable trench and surface air.
2.5. Results and Data Analysis
The temperature field distribution of the regularly laid cable trench is calculated, as shown in
Figure 4.
It can be seen that the hottest part of the cable trench is around each cable group, and the hottest spot (310.28 K) appears at the core of the first layer cable. The lowest temperature in the cable trench is 298 K, which is basically consistent with the ambient temperature (293.15 K). The maximum temperature rise in the cable trench after thermal balance is as small as 20 K when operation current of the cable is not big enough. It can be found that the temperature of the upper cable is obviously higher than that of the bottom cable, which is due to the rise of hot air which causes the ambient temperature of the upper cable to be higher than that of the bottom cable.
According to the results of by numerical calculation, the temperature variation trend from the cable skin to the core can be obtained, which makes it possible to calculate the core temperature value with measured temperature of outer layer. The temperature of cable core is studied by taking the cable of lowest layer and near the cable trench wall. The diagram of temperature value along cable radius is shown in
Figure 1. The temperature variation along the radius of cable is shown in
Figure 5.
We can see that the temperature of the cable core is 305.68 K and the temperature difference between cable core and skin is ~1.7 K. It is inferred that the thermal conductivity of cable insulation layer is quite low and its heat dissipation ability is weak, which leads to a slight decline in temperature along the insulation layer. The temperature changes along the metal shield layer and the outer shield layer of the cable tend to ease, and the temperature decreases slightly.
The temperature of cable core is calculated by thermal circuit method and numerical calculation method respectively, and compared with the field test value (as the standard values). When the current is 200 A, the temperature calculated by thermal circuit method and numerical calculation method is 319.20 K and 310.28 K, respectively, and the field test value is 311 K.
The relative error of temperature calculated by thermal circuit method is 2.3%, and that calculated by numerical calculation method is 0.32%. Obviously, the method of calculating cable core temperature by numerical calculation is closer to the true value.
4. Online Monitoring System
4.1. System Overview
An online monitoring and prewarning system for cable trench was developed to acquire data such as cable temperature, water level of trench and smoke concentration. The scheme design and data flow chart of the monitoring system is shown in
Figure 10a, and the structure of hardware modules is shown in
Figure 10b.
The monitoring unit includes all kinds of sensor module, data acquisition module, and ZigBee wireless transmission module. The terminal node collects the temperature of cable body, joint, water level and smoke concentration respectively. The central node is installed at the outlet of cable trench, including ZigBee receiving module, General packet radio service (GPRS) transmitting module and source. Finally, a polling method is used to read the data of the terminal nodes.
GPRS transmitter module upload data to data acquisition terminal. ZigBee module has the advantages of low power consumption, low-cost, big network capacity, and enough communication distance in cable trench. So it is used for temperature data acquisition, conditioning, and data transmission between nodes. The received node data is sent to the mobile phone through GPRS by serial communication. The system consists of Zigbee coordinator and terminal nodes. The core device is the coordinator node, it establishes, initializes, and configures the network, receives and processes information from terminal nodes, and then transmits information to remote monitoring mobile phone through GPRS, namely, to fulfill real-time data sending and receiving. The data management platform has the function of receiving and analyzing data, and uses the numerical method described above to calculate the temperature of cable core quickly, accurately.
4.2. Program Design and Implementation of Monitoring System
After power-on initialization, the coordinator chooses the appropriate channel to build up its own new network, which includes the setting of PANID, the generation of short address of the coordinator and so on. Then, in the event handler function of coordinator uint16SampleApp_ProcessEvent (uint8 task_id, uint16 events), the data packet is received by calling the subfunction SampleApp_MessageMSGCB (MSGpkt). The terminal node sends the incoming signal to the coordinator to join the network. Uint16, SampleApp_ProcessEvent (uint8 task_id, uint16 events), registers events, sets numbers, send times, and so on. After setting, the function SampleApp_SendPeriodicMessage() is called to broadcast the sensor data periodically.
4.3. System Performance Testing
The infrared temperature sensor of the online monitoring system is installed aiming at the point of highest temperature of the cable obtained by the simulation. The maximum long-term permissible operating temperature of XLPE insulated cable is 90 °C, so that 90 °C was set as the temperature warning threshold of power cable. Model S20-3 infrared thermometer was selected as temperature sensor. The acquisition accuracy is 0.1 °C, which can meet the measurement accuracy requirements. The surface temperature of the object can be calculated by measuring the infrared radiation intensity emitted by the target without touching or injecting the cable. In order to test the sensitivity and accuracy of the temperature, acquisition experiments were done many times, taking a thermostatic plate as the test object. The actual temperature of the thermostatic plate was measured by a thermometer at the same time. The data are shown in
Table 5 below.
Table 5 shows that the maximum relative error of the test results is 2.54%, which can meet the requirement of accuracy value as 1 °C.
4.4. Application of Monitoring System
The online monitoring system has been installed in Nan’an Power Supply Bureau of Chongqing for trial operation. The highest temperature of cable trench is obtained by simulation analysis. Temperature sensors are arranged at the highest temperature to obtain the highest temperature inside the cable trench, so as to ensure that the overall temperature of cable trench does not exceed the specified value. The two temperature measurement points represented by node 1 and node 2 are located nearby the cable connector and the body of cable conductor, respectively. The distance between the two points is ~20 m. The sampling frequency of the system is every 20 s, and the response time of the infrared thermometer is 100 ms. If extremely high temperature or thick smoke occurs in the cable trench, the monitoring system will send an alarm message timely. If the cable trench runs normally, the monitoring system will send status information, including temperature and air conditions, to the mobile phone almost every 6 h and store them as historical data. On-site photos of the monitoring system are shown in
Figure 11a–c. Information sent by GPRS are shown in
Figure 12 and also listed in
Table 6.
Because the cable trench environment is relatively closed, the main determinants of temperature are load conditions and the surrounding environment of the cable.
Table 6 shows that the temperature value of both node 1 and node 2 is only a little bit bigger than 10 °C at ambient temperature, which indicates that the cable works normal with quite small load current. Meanwhile, the temperature of the cable joint is slightly lower than that of the cable skin. The reason may be that the package is thicker at the cable joint. The temperature of cable skin varies within the normal range, and the temperature distribution versus time is not uniform, but has certain regularity, which is consistent with the various load. In general, the monitoring system runs well and the data transmission works reliably.