Hilbert Fractal Antenna for Abnormal Discharge Detection of Transmission Equipment

The safe and stable operation of the power system can ensure people’s basic electricity needs. It also plays an important role in energy security and economic development and can contribute to environmental protection and energy conservation. If there are problems in the power system, it will not only affect people’s normal life and work but also lead to power loss or waste, thereby exacerbating the impact on the environment. With the long-term operation of transmission equipment, insulation devices are aging, leading to frequent abnormal discharges and affecting the safety and stability of the power system. Therefore, timely detection and troubleshooting are necessary. When abnormal discharge occurs in transmission equipment, it will radiate radio frequency (RF) electromagnetic waves, which are mainly concentrated between 200 MHz and 300 MHz. RF antennas that can capture signals in this frequency band can be used for detection to determine whether abnormal discharge has occurred. This article uses the Hilbert fractal antenna as the research object to analyze the impact of different orders on antenna performance and optimizes the different feeding point positions of the antenna. Finally, the antenna structure for detecting abnormal discharge is obtained. By making an actual antenna and conducting experimental analysis, the discharge detection function of the designed antenna is verified.


Introduction
With the rapid development of the social economy, the demand for electricity in various industries is also increasing day by day, and with the operation of the power system, abnormal discharge phenomena will inevitably occur.The electrochemical corrosion caused by abnormal discharge may accelerate the aging and even damage of power equipment.In addition, abnormal discharge is also a precursor to some defects and faults in the equipment [1].Abnormal discharge of transmission equipment consumes electrical energy and is an important component that cannot be ignored in various energy losses during the transmission process.The corrosive gas generated by discharge can also corrode the surface of the wire, reducing its service life.If abnormal discharge frequently occurs on line towers, it can also accelerate the aging of insulators, especially those with composite material shells [2].In addition, the pulse current and high-frequency pulse electromagnetic waves generated during abnormal discharge can also interfere with radio and high-frequency communication, affecting public utilities and the lives of surrounding residents.Therefore, it is of great engineering and social significance to be able to detect abnormal discharges in a timely and rapid manner and reasonably suppress them.
In the study of abnormal discharge in transmission equipment, based on the generation of radio frequency electromagnetic waves during discharge, the frequency range of electromagnetic waves is mainly concentrated between 200 MHz and 300 MHz.Therefore, discharge detection can be achieved through radio frequency antennas [3].The Hilbert fractal antenna is a microstrip antenna based on the shape of Hilbert fractal geometry, which is a research hotspot [4][5].The main characteristics of the Hilbert fractal antenna are its very wide frequency band and small size.Due to its shape based on fractal geometry, it can achieve larger electrical lengths and generate very complex electromagnetic field distributions, making its frequency response smoother and able to operate over a wider frequency range [6][7].In addition, the Hilbert fractal antenna also has good directionality and impedance-matching performance.This article conducts relevant research on Hilbert fractal antennas, designs an antenna structure for detecting abnormal discharge, and verifies the detection function of the antenna through experiments.

The Structure of Hilbert Fractal Antennas
1 order 2 order 3 order 4 order Figure 1.Structure of Hilbert fractal antennas with different orders The core structure of the Hilbert fractal antenna is the Hilbert fractal curve.The Hilbert fractal curve is a curve with self-similarity, which changes with the increase of order.As shown in Figure 1, the Hilbert fractal curve of orders 1 to 4 is continuous and has strict self-similarity.With the increase of fractal order, the Hilbert fractal curve gradually fills from one-dimensional space to two-dimensional space through self-similarity iteration.The fractal dimension of the curve increases with the increase of fractal order [8].The dimension can be obtained from the following equation.(1) in this equation, n is the order of the Hilbert fractal antenna, and D is the dimension.As the order changes, the value of dimension D approaches 2 infinitely, and the range of values for dimension D is [1,2).The size of dimension D characterizes the utilization of space occupied by the fractal curve.According to the Hilbert fractal curve, a fractal antenna can be constructed using a planar antenna structure, which has the characteristics of small size and easy impedance matching.Figure 2

Simulation Analysis of Hilbert Fractal Antenna
Hilbert fractal antenna, due to its small size and lightweight, can enable unmanned aerial vehicles to enter power transmission equipment for close-range discharge detection.The detection frequency band for abnormal discharge of transmission equipment is 200 MHz-300 MHz.Considering the need for miniaturization of the antenna, the size of the antenna is limited to 15 cm×15 cm; the dielectric base layer is made of FR4 material with a thickness of 1.6 mm.Generally speaking, the return loss value of the detection antenna should be less than -10 dB within the detection frequency band.However, due to the miniaturization of the Hilbert fractal antenna, drones can be used for close-range detection of the detection area when in use.That is, if the signal can be detected within 5 meters, the return loss value should be set to be less than -5 dB.
The simulation analysis adopts the finite element method and establishes a Hilbert fractal antenna model based on the antenna structure and size design requirements.When the order n of the Hilbert antenna is larger, the space occupation rate is larger, and the antenna performance is better.Considering the limitations of the actual size of the antenna, excessive fractal order can increase the difficulty of antenna wiring.Therefore, a fourth-order is adopted for the antenna order, as shown in Figure 3.By simulating the position of antenna feed points and the unit length of wires, the influence of different parameters on antenna performance is analyzed.Starting from the left entrance of the antenna and ending at the right exit, a set of simulations were conducted every 9 mm.Through comprehensive analysis of the simulation results of each point, the lowest point and the bandwidth below -5 dB were selected (49, -41).In order to further select the most advantageous point, with (49, -41) as the center, the simulation continued at ten points with a length of 1 mm from x=46 to 55. Comparing the simulation data, it was found that the maximum bandwidth of point (50, -41) in the 200-300 MHz frequency band was 19.8 MHz, while the minimum value of point (50, -41) was -40.5874 dB, which was smaller than the minimum value of point (51, -41).Overall, This article selects (50, -41) as the feed point for the antenna.
By changing the length of the wire, the initial simulation design was l=4.5 mm, and the length of a single segment of wire was 2 l, that is, the initial length of a single segment of wire was 9 mm.This article will simulate the length from l=4.1 mm in units of 1 mm to l=4.7 mm, and the simulation results are shown in Table 1 When other parameters are fixed and l changes, only when l=4.5 mm, both the bandwidth and the lowest point are the optimal results.Therefore, this article will choose l=4.5 mm, which is a singlesegment wire length of 9 mm, as the final design parameter for l.
Based on simulation optimization, the final result of the Hilbert antenna is determined to be a 4-order antenna with (50, -41) as the feeding position and a single wire length of 9 mm.The return loss and radiation pattern of the antenna are shown in Figures 4 and 5.  4, it can be concluded that in the 200-300 MHz frequency band, the bandwidth less than -5 dB is 21.9 MHz, and the minimum return loss is -34.2171dB.There are three resonance points in this frequency band.Figure 5 shows that the axial Hilbert antenna has the largest radiant intensity in the Z axis, and the simulation results show that there are fewer side lobes.Hence, its power loss is small, and the designed antenna has good directivity, which can preliminarily meet the requirements of abnormal discharge directional detection.

Experimental Analysis of Hibert Fractal Antenna
The designed antenna structure is processed into a physical antenna, and a discharge detection experimental platform is built, as shown in Figure 6. Figure 6.Experimental platform for antenna detection After connecting the oscilloscope with the Hilbert fractal antenna through a coaxial cable, the oscilloscope is set to single mode.A discharge pulse generator is used to simulate abnormal discharge phenomena, and the discharge pulse generator switch is pressed.The oscilloscope records the timedomain waveform of discharge and analyzes the waveform of discharge in the frequency domain.The representative discharge waveform is shown in Figure 7, with the yellow curve representing the time domain discharge waveform and the red curve representing the frequency domain discharge waveform.It can be seen that the designed 4-order Hilbert fractal antenna can achieve abnormal discharge detection.In order to determine the discharge detection distance, further experiments were conducted on the antenna discharge detection distance.The distance between the discharge pulse generator and the antenna is changed, starting from 0 meter and testing every 1 meter until the waveform cannot be detected by the oscilloscope.The distance at this point is the detection distance of the designed fractal antenna.The recording line chart of detection distance and signal amplitude is shown in Figure 8.
Finally, when the distance is 8 m, the oscilloscope cannot detect the waveform of abnormal discharge.It is determined that the maximum detection distance of the antenna designed in this article is 8 m, and the strength of the detection signal of the detection antenna decreases with the increase of distance.

Conclusion
This article conducts research on the Hilbert fractal antenna to achieve abnormal discharge detection in transmission equipment.Through simulation research, the impact of different feeding positions and wire lengths on antenna performance was analyzed.Based on the simulation results, the optimal feeding position and wire length were selected to determine the final antenna structure.The antenna is made into a physical object, and through experimental analysis, it is determined that it can achieve discharge detection.Through antenna detection distance testing, it is determined that the antenna can capture discharge signals within 8 meters, providing a basis for using drone-mounted antennas for close-range detection in the future.
is a schematic diagram of a planar antenna.

Figure 2 .
Figure 2. Structure of planar antenna

Figure 7 .Figure 8 .
Figure 7.Typical discharge waveforms in time and frequency domains

Table 1 .
. Simulation results from different variables