4.2. Adaptive Security Early Warning Algorithm
For different voltage levels of high-voltage DC live equipment, such as ±500 kV and ±800 kV, the early warning device can identify different voltage levels of live equipment, and the electric field sensor adjusts the range and sensitivity dynamically, which bases on the voltage level recognized by the microprocessor to meet the measurement requirements. The voltage level identification and related logic processing are performed by obtaining electric field sensing data and performing filtering processing and data fusion. In addition, a corresponding voltage level identification algorithm needs to be designed.
The electric field strength value increases exponentially when approaching high-voltage DC charged equipment. The gradient of the electric field strength changes to the maximum when the safety distance is reached [
25,
26,
27]. The safety distance is different for different voltage levels. That is, the position of the electric field change gradient is distinguished. The electric field strength gradient
can be expressed by the change of the electric field
with time.
In this paper, ±500 kV and ±800 kV HVDC transmission lines are taken as examples to analyze the calculation of their spatial electric field strength and the variation of the electric field strength gradient. The electric field strength is generated by the electric charge of the transmission line [
23,
24,
25]. The calculation of the electric field strength is divided into two steps, as:
- (1)
Calculate the equivalent charge on a unit length DC transmission line using the Maxwell coefficient method;
- (2)
Calculate the strength of the electric field generated by the electric charge according to the mirror image method.
Assuming that the HVDC transmission line is an infinitely long straight wire and parallel to the ground. The equivalent charge of the transmission line is solved by the mirror method as shown in
Figure 12.
Solving the equivalent charge on the transmission line which bases on the following matrix equation.
where,
is the operating voltage of the transmission line to ground, kV;
is the Maxwell potential coefficient, m/F;
is the equivalent charge of the transmission line, C/m.
According to equation (11) and (12), the Maxwell potential coefficient can be obtained.
where,
is the dielectric constant of vacuum;
is the height of transmission line a from the ground, m;
is the equivalent radius of transmission line a, cm.
is the distance between the positive polarity power line a and the negative polarity power line b, m.
is the distance from the positive polarity power line a to the mirror negative power line b’, m.
The equivalent charge of the transmission line and its mirrored transmission line can be obtained according to Equation (10), and the magnitude and direction of the electric field can be calculated. The electric field component in the horizontal X direction is equation (13).
where,
is the equivalent charge of power line a;
is the coordinate of power line a; the total number of power lines and mirror power lines is
n = 4.
Similarly, the electric field component in the vertical Y direction as Equation (14).
The magnitude and direction of the electric field strength along the transmission line can be obtained as in Equation (15):
The electric field strength gradient
can be calculated from the above:
In summary, the method for calculating the electric field variation gradient of DC transmission lines is theoretically derived. It lays the theoretical foundation for the electric field distribution simulation calculation and electric field gradient change analysis of DC transmission lines with different voltage levels.
A two-dimensional calculation model was established according to the actual DC transmission line, and the COMSOL software was used to simulate the spatial electric field distribution of the ±500 kV and ±800 kV DC transmission lines. The two-dimensional calculation model simplifies the actual scene and ignores the influence of metal fittings such as transmission towers and insulator strings [
28]. It is assumed that the transmission line is a wireless, long, straight wire parallel to the horizontal ground. The vertical height of the line is the vertical distance from the ground to the lowest position of the arc. The two-dimensional calculation model is shown in
Figure 13.
This paper analyzed the ±800 kV DC transmission line. According to its actual operating parameters, the height of the transmission line from the ground is
H = 18 m and the distance between the positive and negative transmission lines is
Lab = 22 m. The XOY plane perpendicular to the transmission line is used as the calculation surface. The spatial potential contour of the ±800 kV DC transmission line is shown in
Figure 14.
It can be seen from
Figure 14 that the spatial potential of the ±800 kV DC transmission line is symmetrically distributed and the electric field distribution is also symmetrically distributed. The left side is a positive transmission line and the right is a negative transmission line.
Because the simulation is based on actual operating parameters, the distance between the positive and negative transmission lines is relatively long. This was in order to observe the changes of the electric field intensity in the space around the DC transmission line more closely. The cloud diagram of the distribution of the electric field in the space around the positive transmission line is taken as shown in the
Figure 15.
It can be seen from
Figure 15 that the center position is a direct current transmission line and the electric field strength is attenuated from the inside to the outside, and the change of the electric field can be clearly seen. The electric fields at the two positions marked by the purple wire-frames in the picture are significantly distorted. The electric field distribution is distorted due to the simulation calculation of the grid corners.
The vertical electric field distributions of ±500 kV and ±800 kV bipolar DC transmission lines calculated by COMSOL software are shown in
Figure 16.
The horizontal electric field distributions of ±500 kV and ±800 kV bipolar DC transmission lines calculated by COMSOL software are shown in
Figure 17.
As it can be seen from
Figure 16 and
Figure 17 that the green curve represents a ±500 kV electric field distribution curve and the blue curve represents a ±800 kV electric field distribution curve. Meanwhile, with vertical height or horizontal distance, the voltage level is higher and the electric field strength is greater. This trend becomes more distinct as it approaches the high-voltage source until it is near the safe distance which can be used as a reference for safe distance warning.
Generally, the value of the electric field strength near the safety distance is selected and obtained through multiple measurements and statistics. Calculating the electric field intensity gradient value or the unit distance change rate
of the electric field. Different voltage levels of DC charged equipment are distinguished by gradient values of different electric field strengths. However, this algorithm is susceptible to the speed of human movement, and the influences can be eliminated by Karlman filtering [
29,
30]. Based on the above principles, the design flow of the adaptive security early warning algorithm is shown in
Figure 18.
If in the DC converter station, the early warning electric field strength can be automatically calculated according to the ground reference electric field strength, and the state judgment can be made based on the height change information. It is not necessary to distinguish the voltage level to achieve accurate early warning.
4.3. Early Warning Device Field Test
In order to verify the actual reliability of the high-voltage DC electric field adaptive safety early warning device. An onsite working condition test was selected in a ±500 kV DC converter station. The early warning device test site is shown in
Figure 19.
At the +500 kV pole-one outlet position of the DC converter station, the early-warning device measured the space electric field strength at that location to be 5.8 kV/m, and the space electric field strength at the location was about 5.5 kV/m through simulation calculations. The simulation values and actual measurements. The values differ by 0.3 kV/m. The measured electric field strength is basically consistent with the simulation results of the field conditions which indicates that the electric field sensor used in the early warning device has good reliability. It can provide a reliable electric field value for the early warning device and ensure accurate alarm prompts.
The warning device will give an alarm when the safety warning device is
d0 = 7.1 m from the ±500 kV live equipment. This is the minimum safe distance
d1 = 6.8 m corresponding to the ±500 kV DC live equipment stipulated in the “Power Safe Working Rules and Power Lines” in
Table 5. The difference between the two safety distances is 0.3 m, which is used as the safety distance redundancy [
30]. The early warning requirements have been met, and there are no omissions and false alarms which indicating that the early warning device meets the requirements.
In order to further verify the reliability of this high-voltage DC electric field adaptive safety early warning device. Four simulation of early warning test experiments of +500 kV, −500 kV, +800 kV and −800 kV were performed, and the high-voltage simulation test platform is shown in
Figure 20.
Using the early-warning device developed in this article to simulate early-warning tests on four different voltage levels. It can accurately reflect the changing trend of the electric field in the space around the DC charged equipment. The test results are shown in
Table 6 as:
Comparing
Table 5 and
Table 6, it can be known that the safety distance of the early warning device for the warning test of ±500 kV voltage level is greater than 6.8 m, and the safety distance for the warning test of ±800 kV voltage level is greater than 10.1 m. In addition, in the early warning test of the −500 kV and +800 kV voltage levels, the safety alarm distance is very close to the value specified in
Table 5, which shows that the early warning device accurately reports the alarm, and there are no false alarms [
31].