Electromagnetic radiation of power line communication system outdoors

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Electromagnetic radiation of power line communication system outdoors [Copy link]

Outdoor radiated
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1 Introduction
PLC networks were first developed in suburban areas. In low-voltage distribution networks, buried cables are increasingly used. The advantage is that the power grid can be protected from lightning strikes and noise, while also maintaining a beautiful external environment.
This paper will focus on the electromagnetic radiation of PLC signals (frequency 1~30MHz) injected into low-voltage underground cables. It explains why common-mode propagation is chosen instead of differential mode, or both, to characterize electromagnetic radiation. An initial model is proposed to discuss all propagation phenomena in the common-mode mode and the nature of the ground. Some simulations are performed based on antenna theory and verified by some experiments. From the obtained results, the polarization and attenuation of the propagating wave, the wavelength in the ground compared with free space, and the energy exchange between the cable and the ground are known.
2 Initial model of low-voltage (LV) buried cable

Figure 1 shows the structure of the HN33S33 buried cable. As can be seen from the figure, HN33S33 has no symmetry plane. And its shielding steel belt is electrically connected to the neutral line. Under
normal conditions, the signal is differentially injected between the neutral line and the phase line. The differential mode propagation established is not the only consideration. The steel strip can be considered as a shield, which can block the radiation from differential signal injection.
In the low-voltage distribution network, the neutral line is connected to the ground through an electrical connection, so that the PLC signal circulates in the second loop formed by the ground. Therefore, it can be assumed that most of the radiation comes from common-mode propagation only. Another factor, although less important than the electrical connection, is the asymmetric effect related to the user's terminal load. Asymmetry also affects the radiation. One example of evidence is that the radiation from the asymmetric digital subscriber line (ADSL) network that has no electrical contact with the ground is disturbed by common-mode propagation due to the asymmetric terminal load.
Considering that the PLC signal circulates in the second loop formed by the ground, it is assumed that the system composed of the low-voltage buried cable and the ground is compared to a coaxial cable: the core is the integral cable and the shell (shield) is the ground. In this way, the core is assumed to be a perfect conductor and the ground has dielectric loss characteristics. The core is separated from the shield by CRP insulation material. The core radius is selected as 13mm, the CRP thickness is 2mm, and the shielding radius is about 10m. 13mm corresponds to the equivalent cable radius value defined by the steel belt: 10m is related to the air penetration depth δg in the ground. When the frequency range is 1~30MHz, the air penetration depth can be calculated using formula (1):

In the formula, μ0=4π×10-7H/m, which is the vacuum magnetic permeability;
ω=2πf, which is the angular frequency;
δg=10-3s/m, which is the electrical conductivity of general soil.
Substituting the numbers into formula (1), when f=1MHz, δg≈6.35m can be obtained. This is the reason why the ground shielding radius is selected as 10m.
Figure 2 shows the cross-sectional view and side view of the common mode coaxial cable.

3 Simulation based on antenna theory
The common mode electromagnetic radiation of low voltage cables is simulated using the NEC4 code. NEC4 is also based on antenna theory like NEC2. The main difference between NEC2 and NEC4 is the medium in which the radiation structure is embedded. With NEC4, it is assumed that the entire medium is not a vacuum but a lossy material, whose properties are represented by relative permittivity and finite conductivity or dielectric loss angle. The losses are calculated using the strict Sommerfeld integral or Fresnel reflection coefficient approximation. The simulation in this paper uses the strict Sommerfeld integral.
When thin wires are assumed, it is suspected that the assumptions made with NEC4 are exactly the same as those of NEC2. In fact, for a model structure with thin wires, it can be assumed that each thin wire represents a radius whose value is much smaller than the wavelength of the signal propagating in the structure. As a model structure, it must be discretized into many neat blocks. Let the number of discrete levels be δ and the wavelength of the injected signal in free space be λo. Then all far-field and near-field electromagnetic calculations are correct only when (2) is satisfied:

where α is the weighting coefficient, and its typical value is between 10 and 20.
Two different schemes are considered for the radiation simulation of the 100m long low-voltage buried cable shown in Figure 2 using NEC4. One is that the cable is buried at a depth of 10m and the ground around the cable is uncertain. The first is that the cable is buried at a depth of 80cm, which is also the typical value in actual situations. The soil in the two cases is different: the soil in the first case is very wet; the soil in the second case is normal.
In all simulations, a monochromatic signal generator is used to emit a signal of size Eocos (2πfot), where Eo=5V, fo [1MHz…30HMz]. An internal impedance of 100Ω is added to the generator. The electromagnetic field and its amplitude are calculated one by one to simulate the radiation power and the injection power. For each simulation, the selected observation point at the electromagnetic field and the study frequency must be clearly defined.

3.1 Radiation of the cable in the uncertain ground

The model in Figure 3 is first used for simulation. The generator and its internal impedance are placed between X=-49m and X=-48.75m, and the terminal load is inserted between X=-48.75m and X=-49m. The ground is considered to be an uncertain medium. Figure 4 shows the electric field at 1MHz and 30MHz obtained from the observation line (OL). The observation line is written in Cartesian coordinate form according to equation (3), and its unit is m. The polarization of the power field is studied at the spatial position ρ1 (10m, 0, -10m) at the same frequency. Consider the case where the soil is very wet. Table 1 lists the soil characteristics. Figure 5 shows the results.
OL1={(x, y, z) R31-60≤x≤60, y=0, z=-10} (3)

It can be clearly seen from Figure 4 that the radio wave is a non-transverse (TE) propagation mode. The transverse propagation formula indicates that at each propagation axis point, the resulting electric field is orthogonal to the propagation direction, so the x component is far less than the other two components. The observation shows that the radio wave is a non-transverse propagation mode, which also proves that the calculation using rigorous antenna theory is correct.
There are two additional reasons for studying the polarization of radio waves. First, through the two-dimensional expression of polarization, it can be assumed that the y component of the electric field can be ignored compared to the other two components. This is confirmed by the definition of the observation line (OL1) with y=0m. Second, the influence of frequency and observation point on the elliptical polarization of the electric field can be seen. There is a big difference between the elliptical geometric characteristics of 1MHz and 30MHz.
The attenuation of the radio wave in the ground is determined by the three spatial direction components of the electric field at 1MHz and 30MHz. The soil is still very wet. For a 100m long cable, the average attenuation AE at two typical frequencies of 1MHz and 30MHz is calculated from the obtained electric field. The results are listed in Table 2. It is easy to see that the attenuation of radio waves is very sensitive to frequency changes. The higher the frequency, the greater the attenuation.

Interestingly, the wavelength of the injected signal in the ground can be obtained from Figure 4. The visible oscillations on the two terminal lines are a good indication of the existence of standing waves. An important physical property of this phenomenon is that the distance between the two maximum oscillations is equal to half the wavelength in the medium, where the medium is the ground. Therefore, by measuring this distance, the value of the wavelength of the PLC signal in the ground can be obtained, and the velocity coefficient can be derived. For simulation, the observation surface is set at a depth of 10m. In this way, most of the propagation phenomena occur in the insulating material in the center of the structure. Therefore, by examining the situation of the two lower terminal lines at a given frequency, the wavelength values of the PLC signal in the insulating material and in the ground can be obtained. Referring to Figure 4, assume that the wavelengths in the insulating material and in the ground are λi and λg, respectively. According to Figure 4, when the frequency is 30MHz, it can be obtained that λi≈6m and λg≈2m. In a vacuum, the wavelength λ0 should be 10m. It can be obtained that the velocity factors in the insulating material and in the ground are

and respectively

.
The complex index η of the lossy medium is introduced. It can be represented by the relative dielectric constant εr and the conductivity σ. Its definition is as shown in formula (4). The velocity factor θ can be expressed as a function of η through the relationship θ=|η|. Table 3 compares the velocity factors obtained by simulation and calculated according to formula (4).

Finally, the power transfer between the buried cable and the ground is estimated and the results are listed in Table 4. In contrast to the attenuation of radio waves, the efficiency factor is independent of frequency, since most of the radiation is in the ground.

3.2 Determined radiation of the cable in the ground

This section discusses the same coaxial model as before, with a burial depth of 80 cm. This is the actual depth. Since this situation is more representative of the actual working conditions, a more complete simulation result is presented with an explanation. Figure 6 shows the structural model simulated with the NEC4 code. It is obvious that the only difference from the previous model is the burial depth: here it is 80 cm, and previously it was 10 m. The generator and its internal impedance are still placed between X = -49 m and X = -48.75 m, and the terminal load is still inserted between X = -49 m and X = -48.75 m. The observation line OL2 corresponds to (5), and its unit is m:
OL2={(x, y, z) R31-70≤x≤70, y=2, z=5} (5)

For this observation line, the electromagnetic field distribution at three typical frequencies of 4MHz, 10MHz and 17MHz is calculated again. The results are shown in Figures 7 and 8 respectively.

Table 5 lists the radiation power of the simulation model. It can be seen from Table 5 that the ratio of radiation power to input power decreases with increasing frequency. This result is likely to be wrong in differential mode propagation between cables. In fact, the injection studied here is only common mode. In the power budget, the nonlinear characteristics of the ground play a key role, so the ratio of radiation power to input power decreases with increasing frequency. It should also be noted that, contrary to the previous simulation, the efficiency varies greatly with frequency. The main reason is that the burial depth here is less than the underground penetration depth. Finally

, Table 6 gives the average electromagnetic field and magnetic field attenuation AE and AH calculated according to the observation line of formula (5). It can be seen that the attenuation is related to the frequency. In addition, the attenuation of the magnetic field is about 3 dB greater than that of the electric field.

4 Experimental verification
A 100 m long HN33S33 cable was buried in the suburbs and excited by a monochromatic signal generator. The location was chosen so that there would be no parasitic coupling with other cables and pipelines (long-distance communication cables, water pipes, cables, etc.). The signal was injected between the neutral line and the metal conductor (1 m long, as shown in Figure 9) to stimulate common mode propagation. A 100 Ω resistive load was placed at the other end of the cable. The HFH2Z1 rod antenna (or HFH2Z2 loop antenna) was connected to an HP4395A spectrum analyzer to measure the vertical component of the electric field (or magnetic field).
The ML measurement line defined by equation (6) was used for measurement to compare the simulation results with the experimental data.
ML = {(x, y, z) R3 | 5m ≤ x ≤ 90 m, y = 0 m, z = 1.4 m} (6)

Figure 10 shows the comparison of the simulation and experimental results of the vertical component of the electric field when the injection power is 16 dB. As can be seen from Figure 10, the maximum difference between the simulation data and the experimental data is 5 dB. The difference is partly due to the way the signal is injected through the cable. In order to match the cable impedance, a coupling device is added to the generator injection port. The coupling device is composed of adjustable inductors and capacitors, and the impedance is not completely matched.

Reference
IEEE Int Symp EMC, 2001 D3-A2-02

Author: Translated by Yang Renfu, edited by Shuiyu

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