Experimental Analysis of Third Harmonic on Zero Line Heating Influence Based on COMSOL

In the study of zero-line heating fire hazard caused by the third harmonic, the harmonic content in a high harmonic incidence place is measured, and an indoor physical experiment platform is built as well. Based on the experimental platform, the third harmonic heating experiment on zero lines is carried out with different wire diameters. The heating pattern of zero lines under different working conditions is obtained, which could provide a certain experimental basis for electrical fire prevention in public places. Based on the COMSOL multi-physical field coupling simulation software, the third harmonic heating model of zero line is established, and the curve of temperature distribution gradient and zero line temperature is obtained. The comparison between simulation results and experimental results verifies the accuracy of the simulation model. It provides a theoretical method for a reasonable selection of zero-line diameter, arrangement of zero line layout, and prevention of electrical fire.


Introduction
With the development of electronic technology and the increase of a large number of nonlinear loads, the waveform of the power system is seriously distorted.The large-scale use of high-intensity gas discharge lamps, LED lamps, and fluorescent lamps has resulted in a large number of harmonic currents [1][2] .Among them, the 3rd harmonic and its multiple harmonics will be superimposed on the centerline in a zero sequence feature, resulting in excessive neutral current and fire hazards.
Better power quality can reduce line network loss and prolong the service life of electrical equipment [3][4][5] .However, harmonics in the power grid cannot be eliminated, and can only be suppressed by compensation equipment and compensation strategies [6][7] .
In this paper, the measurement is carried out for places with a high frequency of 3rd harmonic generation.Based on the experimental platform, the 3rd harmonic heating experiment is carried out for zero lines with different wire diameters, and the actual temperature change of zero lines with different wire diameters is obtained.Based on COMSOL, the physical model of the influence of the third harmonic on the temperature rise of the zero line is established, and the rule of the influence of harmonic current on the heating of the wire is obtained.The accuracy of the model is verified by comparing it with the experimental data.It has theoretical guidance and aids further research on zeroline fire prevention under different working conditions.

Basic Theory
Any wave function can be Fourier decomposed into several signals with different frequencies： Where M is the highest harmonic frequency of the signal; A m is fundamental or harmonic amplitude; m is the harmonic frequency; φ m is the initial phase of fundamental wave or harmonic wave.
As shown in Fig. 1, for an ideal three-phase symmetrical system, the phase difference of the fundamental three-phase current is 120° in turn, and the resultant current on the zero line is 0. However, in practice, the third harmonic current content of fluorescent lamp electronic ballast and other equipment is as high as 80%~90%, and the third harmonic in zero sequence characteristics, which will be superimposed on the zero line, could result in high temperature and causing a fire.

Field Testing
The A-phase currents of medical types of equipment in different hospitals were monitored.The results are shown in  Due to the large-scale use of LED lighting in football fields, the third harmonic generated cannot be offset on the zero lines due to the phase relationship, so the third harmonic on the zero line accounts for the highest proportion.Because of the large number of power electronic components in the medical equipment of the hospital, the waveform distortion rate of the power grid is very large, mainly including the 3rd, 5th, 7th, and 9th harmonics.Among them, the 3rd and 9th harmonics are very likely to overlap on the zero line.If they are not treated, it probably leads to an overload of the zero line, which may lead to an electrical fire.

Experimental Equipment
The indoor experimental device is shown in Figure 2, which is mainly composed of the power supply system, adjustable load, temperature measurement system, and monitoring system.The power supply system is Shenghong HG200A pure power supply; The adjustable load is HG200A harmonic current generator; the temperature measurement system adopts HIOKI-LR8431 10-channel temperature collector; the monitoring system monitors the voltage and current of the line, and the model is HIOKI-PQ3198.Experiments were carried out on 1.5 square, 2.5 square, 4 square, and 6 square copper conductors respectively.The effective value of the third harmonic current on the zero line was changed by adjusting the load, and the temperature at the measuring point was recorded.

Experimental Results
The rated currents of different conductors are shown in Table 5, and experiments are carried out on the 3rd harmonic under load, rated current, and overload of zero lines of different sections.The experimental results are shown in Fig. 3     For the 1.5 square neutral line, when the effective value of the third harmonic current reaches the rated value, the overall temperature of the neutral line is stable at about 40 ℃, and the terminal has no obvious temperature rise due to the large contact surface and strongly rated current carrying capacity.When the value of the third harmonic current reaches 1.5 times the rated current carrying capacity, the temperature rise of the zero line is obvious.
However, due to the influence of experimental errors such as the contact between the thermocouple and wire, the temperature difference between the four temperature measuring points on the zero line is large.After 340s of experiments, the average temperature is stabilized at about 75℃.At this time, the insulation skin of the zero line has begun to soften, and there must be a large fire hazard during longterm operation.
For 2.5 square and 4 square neutral lines, when the third harmonic current reaches 2.5 times and 2.7 times the rated value respectively, the neutral line emits obvious white smoke, and the insulation skin on the wire is burnt and falls off.As shown in Fig. 7, it can be seen that when the harmonic distortion rate of electrical equipment is high and is not treated, a large number of 3rd harmonic currents will stack on the zero line, resulting in zero-line overload, heating, burning, and even fire.

Simulation Model
Because there may be some accidental factors and measurement errors in the experiments, in order to further analyze the temperature distribution of the zero line and its surroundings, so as to effectively prevent fire, a third harmonic heating model of the zero lines is established based on COMSOL.

Model Equation
The electric field model is described by the following set of equations: Where J labels the current density, E is the electric field, Q j,v is charge density, while e 0 and e r are permittivity of vacuum and relative permittivity.
The flow field equations are described by the following set of equations: where F is volume force.The velocity field, pressure, density, and dynamic viscosity are denoted by u, p, ρ, and μ respectively.The discharge heat source in the heat equation is implemented by: Where the density, heat capacity at constant stress, temperature, and velocity vector are denoted by ρ, C p , T, and u respectively, while k B , q, J, E, and Q rad represent the stefan-boltzmann constant, electronic charge, current density, electric field, and volumetric net radiation loss.

Simulation Experiment
In order to reduce the amount of calculation, a two-dimensional axisymmetric model is established as shown in Fig. 8.The neutral line is a 1.5 square copper conductor with a length of 5m.The insulation is made of polyethylene.The neutral line is placed in the air with an initial ambient temperature of 25 ℃.The upper end of the zero line is connected to the third harmonic current source, the effective value of the current is consistent with the experimental value of the 1.5 square zero line, the lower end of the zero line is grounded and the electric potential is 0.

Results of Simulation
The temperature distribution of the 1.5 square line obtained by simulation is shown in Fig. 9.In the simulation, the temperature on the bare conductor of the zero line tends to be the same, but it is different in the real experiment.The main reasons for the experimental difference include poor contact between the thermocouple and the conductor, increased heat dissipation due to the contact between the thermocouple and the conductor, and errors in the equipment itself.It can be seen from the figure that when the third harmonic current is applied at the beginning, the temperature rise of the air at the bare conductor is obviously faster than that of the insulation skin because of the better fluidity.With the continuous heating of the conductor, the air temperature near the bare conductor tends to be consistent with the insulation skin.According to the simulation results, the temperature curve of the inner part of the conductor and the insulation sheath with time is shown in Fig. 10.With the continuous application of the current, the temperature of the internal conductor is significantly higher than that of the insulation skin, and the temperature difference between the two is expanding.The comparison between the simulation results and the experimental results is shown in   As the laying mode and rated current carrying capacity of the neutral line are different in different power lines, based on this simulation model, the heating analysis can be carried out for the neutral line under specific working conditions to quantify the fire risk safety level of the neutral line.

Conclusion
The field measurement of the harmonic components of distribution lines in typical public places shows that when the load contains large-scale power electronic components, the distribution network lines contain higher harmonics of the third order, which are easily superimposed on the zero line, leading to an overload of the zero line.
Based on experiment and simulation, the influence of the third harmonic on the heating of the neutral line is studied.The results show that the third harmonic is easy to cause the zero line overload and there is a great safety hazard potential.It is necessary to carry out further research based on simulation and experiment to explore the heating effects of different laying methods of conductors on the zero line, so as to provide a theoretical basis for a reasonable selection of zero line diameter, arrangement of zero line layout and prevention of building fires.

Figure 1 .
Figure 1.Schematic diagram of zero line synthetic current.

Figure 2 .
Figure 2. Schematic diagram of the experimental system.During the experiment, temperature monitoring is conducted at five typical points on the zero line, where Point a is the terminal, and Point b, Point c, Point d, Point e are the measuring points 1m apart from Point a on the zero line.The temperature sensors on Point a, Point c and Point e are in direct

Figure 3 .
Figure 3. Temperature curve of 1.5 square zero line.

Figure 4 .
Figure 4. Temperature curve of 2.5 square zero line.

Figure 5 .
Figure 5. Temperature curve of 4 square zero line.

Figure 6 .
Figure 6.Temperature curve of 6 square zero line.

Figure 7 .
Figure 7.The insulating skin is burnt and falls off.

Figure 9 .
Figure 9. Temperature distribution of zero line.
Fig. 11.It can be seen from the figure that although the experimental results have large fluctuations, they still have a large degree of coincidence with the simulation results, and the average values of different measurement points are roughly consistent with the simulation results, which demonstrates the accuracy of the simulation model laterally.

Figure 10 .
Figure 10.Temperature curve of zero line.Figure11.Comparison of temperature rise between simulation and experiment.

Figure 11 .
Figure 10.Temperature curve of zero line.Figure11.Comparison of temperature rise between simulation and experiment.

Table 1 .
Measurement of the harmonic value of a football field (LED lighting) in city B.

Table 2 .
Distribution of A-phase current harmonic content of CT machines in 5 hospitals in city S.

Table 3
. Distribution of A-phase current harmonic content of X-ray machines in 3 hospitals in city S.

Table 4 .
Distribution of A-phase current harmonic content of gastrointestinal projector in 2 hospitals in city H.