Finite Element Method Assisted Audible Noise Detection for Overhead Line Conductors Using the Cage Experiment

Abstract

Audible noise (AN) has been the main concern in recent years when considering electromagnetic environmental impact in designing overhead lines (OHLs). Driven by the increased demand of high voltage direct current (HVDC) transmission lines, a novel corona cage experiment is built in association with an acoustic simulation using the finite element method (FEM). The characteristics of the acoustic wave propagation within the testing hall are analyzed using FEM, and the optimized locations for AN detection are determined. On the basis of complying with measurement standards, the location of the measurement is selected to be closer to the sound source and further away from the reflecting surface, to generate more accurate measurement results. In the designated test hall for this paper, the influence of refraction and reflection of sound waves is not obvious. The attenuation of sound waves below 4 kHz is negligible, while for higher frequencies such as 4 kHz and 8 kHz it is significant. Finally, FEM simulation is used to optimize the location for measurement microphones, and further experiments are carried out to verify its accuracy.

1. Introduction

As the voltage level of HVDC transmission lines continues to increase, the electromagnetic environment issues generated by corona discharge on DC transmission lines has become one of the decisive factors in OHL designs [1]. The issue of audible noise (AN) is a significant research focus in relation to the corona effect as concerns about environmental protection grow alongside attention to noise pollution. This problem is increasingly regarded as a constraint on widespread deployment of ultra-high voltage transmission technology because of diverse factors. Noise reduction measures are considered essential to protect the environment of power grids since excessive complaint could result from AN generated from corona discharges [2]. To comply with environmental regulations, it is vital to study the characteristics and mechanism of AN production on HVDC OHLs in order to accurately predict acoustic emission.

AN, as a type of corona effect, is studied using actual operating overhead transmission lines, test line sections, and corona cages. Test line sections and corona cage experiments are commonly used test methods due to their short lead times and low cost when compared to actual lines. The corona cage experiment, in particular, is advantageous due to its low investment costs, controlled test conditions, and short test cycles [3]. As a result, it is an indispensable test device when studying the electromagnetic environment of power transmission lines. Test wires are placed in the center of the corona cage, and unipolar or bipolar wires are used to simulate transmission lines for DC [4,5] and single-phase wires for AC [6,7]. As the distance between the cage wall and the wire is closer than the distance between the line and the ground, a lower voltage is applied to the wire, and the field strength of the wire surface can also reach the surface field strength level of the actual line at a higher voltage level, thus showing the corona characteristics of the transmission line at higher voltage levels. Cage experiments have been well proven to be an effective way to study the environmental impact of transmission lines [8,9,10,11]. Experimental studies of AN generated by corona discharge include both spectral test methods [12] and temporal test methods [13,14]. Most international measurement standards and evaluation indexes for AN from corona discharge are based on spectral characteristics, such as A-weighted sound pressure level and octave characteristics. Consequently, scholars worldwide adopt spectral measurements to study this issue [15]. However, spectral measurements have limitations. It can be challenging to infer waveform information in the temporal mode from spectral measurements for corona noise with broadband characteristics. Temporal measurements provide unprocessed AN waveforms while retaining the detailed characteristics of the acoustic waveform, aiding the study of the mechanism of corona discharge AN [16]. On the other hand, the frequency domain characteristics can be obtained from the temporal signal calculation using signal analysis methods. This makes the temporal measurement of AN more applicable than spectral measurement and is of great importance for the study of corona discharge AN [17]. The measured AN in an outdoor environment has been statistically evaluated and compared in different seasons and weather conditions [18,19,20]. For accurate measurements, AN experiments with corona cages can also be carried out in an anechoic chamber [21,22].

However, the anechoic chamber test for high voltage equipment is always difficult and costly. It is also a feasible method if the interference can be eliminated by using a reasonable test design and subsequent processing. For this reason, this paper designs a detachable indoor corona cage test platform for sound field measurement and optimizes the design of microphone arrangement position using simulation analysis.

This paper is organized as follows. In Section 2, we set up an AN test platform for an HVDC corona cage experiment. In Section 3, we review the test standards of transmission line noise and study the influence of measuring position in a simulation model. A comparison of the simulation results with the experimental results shows that good measurement results can be achieved at the selected measurement positions. We summarize our findings in Section 4.

2. Experiment Setup

2.1. Design of HVDC Corona Cage

2.1.1. Structure of Corona Cage

The cylindrical cage experiment is a proven and effective way to investigate the environmental effects of overhead transmission line conductors. High voltage is applied to the inner conductor while the outer mesh cage is grounded. This arrangement enhances surface electric field strength due to the presence of the cage. Thus, a strong electric field strength on the conductor surface can be achieved at lower voltage levels. For example, by reducing the radius of the cage to 0.75 m, a single-phase power supply of only 150 kV is required to obtain a surface electric field strength similar to that of a conductor of a 400 kV system transmission line. In this paper, a medium-sized detachable corona cage with a frame length of 8 m is designed to enable accurate measurements of the sound field.

The structure of the corona cage is shown Figure 1. The specific design is as follows:

• The required number of intermediate measurement sections is 7 segments; each segment is 0.5 m long, and the total length is 3.5 m;
• The measurement sections can be spliced and dismantled to achieve different lengths of measurement range;
• The metal mesh on the surface of the corona cage is made of stainless steel, and the design requirements for the mesh holes are discussed in detail in Section 2.1.2;
• To facilitate the measurement of electrical parameters on the upper and lower halves of the cage, respectively, each section of the corona cage adopts the upper and lower semi-cylinder structures (see Figure 2 for axial view). The splicing section is made of insulating material to ensure electrical insulation between the upper and lower metal cage structures.

2.1.2. Metal Mesh Design of Corona Cage

The metal mesh of the corona cage plays the role of intercepting free charge and shielding from external interference of electromagnetic waves, so it must have good electrical conductivity. Steel or copper can be considered, and the metal mesh is as dense as possible. However, an overly dense metal mesh will produce a porous sound absorption effect, causing the metal mesh to reflect and scatter the AN generated by the wire.

The degree to which the metal mesh reflects and scatters sound depends on two factors: the diameter of the wire and the porosity, where porosity refers to the proportion of the mesh area occupied in the porous material. When the diameter of the wire is less than one-tenth of the wavelength of sound waves, and the porosity is 0.8 to 0.9, the transmission rate of sound energy can reach 95%; that is, the sound energy reflected and scattered by the metal mesh will be 13 dB smaller than the actual sound energy, and its influence is much smaller than the impact of background noise. The upper limit of the AN frequency range of the corona characteristic test is 20 kHz, and it can be deduced that the diameter of the wire is less than 1.7 mm. Under this wire diameter, it can be calculated that the porosity is 0.84 when the mesh edge length is 20 mm, and the porosity is 0.92 when the mesh edge length is 40 mm. So, the side length of the mesh is set to 20 mm to 40 mm.

2.1.3. Results of Field Intensity Simulation

Currently, the electric field intensity requirements for DC transmission lines vary between countries. According to the Chinese industry standard DL/T 1088-2020 electromagnetic environment parameter limits for ±800 kV UHV DC transmission lines [23], the synthetic field strength limit for ±800 kV DC overhead lines is 25 kV/cm or 30 kV/cm, depending on location. Other voltage levels of DC transmission lines can be implemented using this standard as a reference.

The field intensity of the conductor surface can be calculated using the corona voltage of the wire, with the corona cage cross-section simplified to a coaxial cylinder:

$$E=\frac{U}{r\times \ln \frac{R}{r}}$$

(1)

where U is the corona voltage of the conductor in kV, r is the radius of the conductor in cm, and R is the radius of cage in cm.

By substituting the parameters of the corona cage designed in this paper, the relationship between the field strength of the wire surface and the voltage change is illustrated in Figure 3.

Corona cage experiments can replicate the range of field strength changes experienced by the actual transmission line, making these experiments effective for simulating an actual wire.

2.2. Audible Noise Test Platform

2.2.1. Main Equipment

The time-domain test method is used to study the characteristics of the AN from DC corona discharge. The real-time acquisition and recording of noise signals can obtain the variation pattern of sound pressure signals over time, which is conducive to estimating and effectively removing the influence of background noise.

The sound sensor adopts AWA14423 microphones from AIC to convert the sound signal into an electrical signal. The microphones have an external diameter of 12.7 mm, i.e., 1/2 inch. The nominal sensitivity is 50 mV/Pa. The frequency range is 10 to 20,000 Hz, and the dynamic range is 17 to 140 dB, which meet the use standards of a Class 1 sound level meter. The signal measured using the sensor is amplified by the AWA14604 pre-amplifier and then captured by a data acquisition board for storage. The AWA14604 pre-amplifier has a frequency response of ±0.1 dB in the frequency range of 10 Hz to 20 kHz, a transmission gain of −0.1 dB, and background noise of less than 5 µV. The data acquisition board adopts NI USB-6009, with a vertical resolution of 14 bit and a maximum sampling rate of 48 kSa/s. The maximum frequency of AN is 20 kHz, and the sampling frequency of the data acquisition board meets the requirements of Nyquist’s sampling law.

The components of the AN time-domain measurement system are shown in Figure 4.

2.2.2. Time-Domain Measurement System

The NI USB 6009 data acquisition board is used to acquire the temporal signal of AN, and LabVIEW software is programmed for real-time measurement and storage of AN signals. Figure 5 shows the flow chart of the time-domain measurement system, which can achieve real-time acquisition, display, and storage of the AN signal.

3. Measurement Point Arrangement Based on Sound Field Simulation

3.1. Measurement Standards for Audible Noise

3.1.1. Measuring Instruments

The selection of measuring instruments needs to meet the corresponding test standards:

• According to the requirements of ISO 1996-1:2016 [24], the accuracy of the measuring instrument is Class II, and above the integral sound level meter or noise statistical analyzer, its performance must be in line with the provisions of IEC 61672-1:2013 [25].
• Measuring instruments and acoustic calibrators should be regularly calibrated according to the provisions of the measurement and must hold a valid calibration certificate.
• Measurement before and after the application of sound calibration must include a measuring instrument deviation of not more than 2 dB.

3.1.2. Measuring Requirements

The current OHL AN measurement standards are applicable to short-term manual measurement and long-term automatic measurement of AC/DC line AN. There are clear explanations and corresponding provisions for measurement instruments, measurement methods, and precautions. Some specific measurement requirements are listed below:

• The instrument uses A-weighted sound levels. Equivalent continuous A sound level measurements are expressed in LAeq or simply in Leq (all measurements are Leq values if not stated below) in dB.
• The height of the microphone from the ground should be more than 1.2 m, and it should be aligned with the direction of the noise source in order to measure the maximum value.
• In order to ensure that the microphone remains the same height, it is better to install the instrument on a special stand, and the measuring personnel should be 0.5 m away from the instrument when taking readings.
• The measurement should be carried out under weather conditions without rain and snow and stop when the wind speed reaches 5 m/s (i.e., the wind force is greater than 3) or more.
• The AN from DC transmission lines is greater on sunny days than on rainy days, while the AN from AC transmission lines is greater on rainy days than on sunny days. Thus, measurements can also be made in rainy and snowy weather, which should be stated in the report.

3.1.3. Measuring Position

In ISO 1996-2:2017 “Acoustics—Description, measurement and assessment of environmental noise—Part 2: Determination of environmental noise levels” [26], the measurement of environmental noise is divided into three cases: outdoor measurement, outdoor measurement near buildings, and measurement inside buildings.

Comprehensive relevant standards, site structure of a corona cage test, and requirements for the placement of microphones are summarized as follows:

• 1 m from walls and other reflective surfaces, 1.2 m from the ground, and 1.5 m from windows;
• The microphone is aligned with the direction of the noise source during measurement.

3.2. Sound Field Simulation

This paper aims to determine the optimal location for detecting AN by combining high voltage corona cage experiments with acoustic simulations using the finite element method (FEM) to analyze the propagation characteristics of sound waves in the test hall.

3.2.1. Selection of Physical Field

In this analysis, the equations describing the propagation of sound in fluids are derived from the governing equations for fluid flow (Navier–Stokes equations). Neglecting viscous effects and assuming a lossless and adiabatic flow, a linear isentropic equation of state is used.

Based on these assumptions, the sound field can be described as a variable, namely the pressure p (SI in Pa), and is controlled using the fluctuation equation:

$$\frac{1}{{\rho }_0{c}^2}\frac{{\partial }^{2}p}{\partial t^2}+\nabla \left(-\frac{1}{P_0}\nabla p\right)=0$$

(2)

where t is time (SI in s), ρ₀ is fluid density (SI in kg/m³), and c is the adiabatic speed of sound (SI in m/s).

Acoustic problems typically involve simple harmonic waves, such as sine waves. To solve fluctuation equations in the spectral domain, any signal can be extended to its harmonic component via its Fourier series. The harmonic solution takes the following form:

$$P\left(x,t\right)=p\left(x\right)\sin \left(\omega t\right)$$

(3)

where the spatial p(x) and temporal sin(ωt) components are separated.

A more general representation of pressure can then be derived using complex variables:

$$P\left(x,t\right)=p\left(x\right)e^{i\omega t}$$

(4)

where the actual instantaneous physical value of the pressure is the real part of Equation (4). By employing this pressure field, the transient fluctuation equation reduces to the well-known Helmholtz equation:

$$\nabla ·\left(-\frac{1}{P_0}\nabla p\right)-\frac{{\omega }^2}{{\rho }_0{c}^2}p=0$$

(5)

In the case of a homogeneous medium, a simple solution, using Equation (5), is a plane wave:

$$p=P_0{e}^{i\left(\omega t-k·x\right)}$$

(6)

where P₀ is the wave amplitude (SI in Pa), which moves in the k-direction with an angular frequency of ω and a wave number of k = |k|.

In most practical scenarios, an analytical solution to Equation (5) is unfeasible; solving control equations for acoustic problems through analytical means is only viable for specific scenarios. Therefore, in industrial applications, several physical fields tend to be interconnected, leading to multi-physical field problems that require numerical methods to be resolved accurately.

When using the finite element method (FEM) to solve acoustic problems, the characteristic length scales within the model must be taken into account. The modelling method to be used depends on the frequency under study and in particular on the comparison of the wavelength with the geometric characteristics of the room. For a given room, the Schröder frequency f_s is calculated as Equation (7) to predict the critical frequency between the modal behavior of the room and the high frequency reverberant behavior:

$$f_s=2000\sqrt{\frac{T_{60}}{V}}$$

(7)

where V is the room volume (SI in m³), and T₆₀ reverberation time is the time required to attenuate the sound pressure level generated by the impulse source by 60 dB (SI in s), which can be estimated using Sabine’s formula:

$$T_{60}=\frac{55.3V}{cA}=\frac{55.3V}{c{\displaystyle \sum s_i{\alpha }_i}}$$

(8)

where A is the total absorption (SI in m²) and s_i (SI in m²) and α_i are the surface area and absorption of the i th surface, respectively.

The calculation result’s f_s is about 140 Hz, so the geometric acoustic module was chosen for the simulation analysis, and the simulation model is based on the ray acoustic interface that was established. Ray acoustics is a calculation that tracks acoustic rays as they pass through a room and interact with various surfaces. It can characterize the high frequency acoustic properties of a room and can be used to find its reverberation time, as well as to perform detailed impulse response calculations.

3.2.2. Geometry of the Model

In this model, the acoustic properties of the high voltage test hall at Chongqing University is analyzed. It is a square hall with a volume of 1276.4 m³ and a total surface area of 872.24 m².

The corona cage is in the north-west corner of the test hall, and the sound source is the transmission line in the center of the cage, which generates pulse signals. Under the premise of measuring standards, the microphone is placed in different positions around the corona cage, and the results are compared in order to select the appropriate measuring point.

3.2.3. Parameter Settings

The data are given in the form of octave bands, and the central frequencies of the study range from 125 Hz to 16 kHz. The absorption coefficients of the various surfaces (floor, walls, and windows) shown in

Table 1. Sound absorption coefficients of commonly used building materials.

Material and Its Specifications		Frequency (Hz)
		125	250	500	1000	2000	4000
Concrete wall	Rough	0.36	0.44	0.31	0.29	0.39	0.25
	Painted	0.1	0.05	0.06	0.07	0.09	0.08
	Wooden	0.15	0.11	0.1	0.07	0.06	0.07
Concrete floor	Covered with lacquered cloth, asphalt, rubber, or cork board	0.02	0.03	0.03	0.03	0.03	0.02
	Asphalt topping and wood flooring	0.04	0.04	0.07	0.06	0.06	0.07
Glass	Large pieces of glass	0.18	0.06	0.04	0.03	0.02	0.02
	Regular glass	0.35	0.25	0.18	0.12	0.07	0.04
Marble or terrazzo		0.01	0.01	0.01	0.01	0.02	0.02
Ventilation openings		0.15–0.50

are taken from [27]. In accordance with ISO standards and national standards, the frequency range for the absorption coefficients in the sound absorption test reports is 100 Hz–5 kHz; at higher frequencies the absorption coefficients can be considered to be essentially constant.

The calculation error of impulse response is limited by the number of rays emitted. For each time interval $\mathsf{\Delta }$t of the response, with an expected error of 1 dB, the number of rays should be as follows [28]:

$$N_{rays}={4.34}^2\frac{V}{\pi r^{2}c△t}$$

(9)

where r is the radius of the receiver (SI in m).

3.2.4. Simulation Results

For the 1 kHz band, the local wave front sound pressure level (SPL) after 30 ms propagation is shown in Figure 6a and after 40 ms propagation is shown in Figure 6b. Figure 6c,d shows the propagation at 30 ms for bands with center frequencies of 125 Hz and 8 kHz, respectively. Figure 6a,b visualize the direction of propagation and trajectory of the sound lines. Comparing Figure 6a,c,d, it can be seen that as the frequency of the sound wave increases, the energy decays more rapidly.

A cylindrical measuring surface is designed in the model. The radius of the base of the cylinder is r, and the height is 2 l, where both r and l are 0.6 m. Three cross-sections of the cylinder were selected, and four measurement points were set up on each cross-section, making a total of 12 measurement points. Figure 7 shows the SPL results for the multiple cross-sections, where the locations of the measurement points are marked in black dots.

Table 2. Receiver position and relative sound pressure level.

Point	SPL (p.u.) *	Coordinate—x	Coordinate—y	Coordinate—z	Distance (m)
Sound source	1	xs	ys	zs	0
Receiver 1-1	0.9270	xs-r	ys-l	zs	0.85
Receiver 1-2	0.9267	xs + r	ys-l	zs	0.85
Receiver 1-3	0.9263	xs	ys-l	zs + r	0.85
Receiver 1-4	0.9283	xs	ys-l	zs-r	0.85
Receiver 2-1	0.9304	xs-r	ys	zs	0.60
Receiver 2-2	0.9301	xs + r	ys	zs	0.60
Receiver 2-3	0.9297	xs	ys	zs + r	0.60
Receiver 2-4	0.9320	xs	ys	zs-r	0.60
Receiver 3-1	0.9274	xs-r	ys + l	zs	0.85
Receiver 3-2	0.9271	xs + r	ys + l	zs	0.85
Receiver 3-3	0.9267	xs	ys + l	zs + r	0.85
Receiver 3-4	0.9287	xs	ys + l	zs-r	0.85

* The sound pressure level of the source is used as the reference value.

specifies the relative positions and distances between each receiver and source, as well as the magnitude of the SPL relative to the source.

The results in Table 2 were analyzed to select the appropriate measurement locations. In general, the difference in sound pressure levels between the 12 measurement points was small, with those closer to the source being slightly larger and more effective. The three measurement points, R1-4, 2-4, and 3-4, were less than 1 m from the ground and did not meet the requirements of the measurement criteria; thus, they were first excluded. The corona cage was not placed in the middle of the site due to the constraints of the site layout, but, rather, it was placed in a corner of the test hall. Compared to points R1-2, R2-2, and R3-2, points R1-1, R2-1, and R3-1 are located closer to the wall and are more significantly affected by reflections. Similarly, points R1-3 and R1-2 are more susceptible to reflections from the wall. Of the four remaining locations, R2-2, R2-3, R3-2, and R3-3, R3-2 and R3-3 are a little further away from the sound source. Finally, R2-2 was chosen as the test location for the experiment in terms of simpler wiring and more stable placement of the device.

The acoustic impulse response is the result of the propagation of the excitation source in conjunction with the boundaries of the room. Sound propagation from the shortest path (straight line distance between source and test location) is the first to arrive, and the sound pressure should be maximum. Reflected sound, on the other hand, travels through multiple other paths, losing energy due to air absorption and interface absorption, so that the reflected sound arriving later becomes weaker and weaker. As can be seen from Figure 8, the amplitude of the direct sound is much greater than the reflected sound. Theoretically, the gradual weakening of the reflected sound is permanent. In contrast, the process of sound reflection in this model tends to calm down after 0.5 s.

In the time-domain plot of the impulse response, the direct sound and some of the earliest arrivals of the reflected sound are very easy to recognize. Figure 9 shows the corresponding response results in the frequency domain, with the data smoothed by 1/3 octave. The reflected sound continues to arrive in sequence, sounding smaller and smaller and arriving at similar times, gradually forming an exponential decay that tends to form a typical linear decay trend in the amplitude scale of the logarithmic scale. The energy decay curve (EDC) is obtained by integrating the impulse response and is a method of smoothing out the random fluctuations of IR. Using EDC instead of IR to analyze the decay of sound energy in a room gives more accurate properties (as shown in Figure 10).

The energy attenuation characteristics support the calculation of target room acoustic metrics such as clarity C₈₀; intelligibility D; early decay time EDT; center time t_s; reverberation times T₂₀, T₃₀, T₆₀; and speech transmission index STI (see

Table 3. Objective room acoustic metrics of clarity, definition, and reverberation times of octave band center frequency.

fc (Hz)	D (%)	C80 (dB)	ts (s)	EDT (s)	T20 (s)	T30 (s)	T60 (s)
125	86.294	8.3313	0.050379	0.51577	3.3281	2.7435	1.9597
250	78.508	5.7513	0.098935	2.3352	3.9817	3.7052	2.0153
500	80.858	6.3074	0.101	2.3398	4.1229	3.888	2.0324
1000	85.748	7.8181	0.072317	0.51687	3.9518	2.7528	1.9689
2000	95.912	13.733	0.019843	0.025867	3.9513	2.6353	1.4688
4000	99.019	20.094	0.005748	0.024551	0.2558	2.6408	1.3402
8000	99.523	23.228	0.004619	0.024434	0.25574	0.17081	0.39067

). Reverberation time (RT₆₀ or T₆₀) is an important parameter for evaluating acoustic systems and is defined as the time for the impulse response to drop to 60 dB. However, decay to 60 dB requires a large dynamic range that is often difficult to achieve during experiments; therefore, measurements of 20 dB of decay (T₂₀) or 30 dB of decay (T₃₀) are also used to estimate the decay time to 60 dB.

3.3. Experimental Results

The experimental setup was designed and the experimental environment was set up as described in Section 2. Positive DC corona experiments were carried out, and the actual measured individual impulse response waveforms are shown in Figure 11, where the black curve is the raw unprocessed signal, and the red curve is the smoothed result. The microphone was arranged in the corona cage experiment at positions R2-2 (Figure 11a) and R2-4 (Figure 11b).

To confirm the efficiency of detection point optimization, a comparative experiment was conducted. As displayed in Figure 11b, the temporal waveforms measured at R2-4 present multiple peaks due to the significant influence of the reflection signal, revealing that the folded reflection signal has significant influence and impedes data processing and analysis.

In the actual experiment, the operating transformer was constantly emitting noise, in addition to the random noise from the environment, so the measured signal was much messier than the simulation results. In general, the measured signal has a clear impulse response waveform, and no significant folded reflections are observed, indicating that the location of the measurement points is reasonable and can meet the test requirements.

4. Discussion

Currently, the prediction of audible noise (AN) for DC transmission lines is primarily based on empirical formulas. Empirical formulas used to predict AN in each country rely on conductor parameters, environment, and voltage levels. These formulas, which vary considerably between countries, have limited applicability. The relevant international standard IEC TS 61973:2012/AMD1:2019—Amendment 1—High voltage direct current (HVDC) substation audible noise [29] specifies the maximum allowable values for corona noise. Consequently, designs of high-voltage transmission lines based on empirical formulas may fail to meet the required targets because of differences between conditions defined by formulas and the actual line conditions. Thus, it is crucial to investigate the generation process of AN and its relationship with the corona process, with the first prerequisite being accurate measurement of AN.

Starting with experiments with a DC corona cage built under indoor laboratory conditions, this paper investigates how the design of metal mesh can strike a balance between radio interference and acoustic measurements, and the study outlines designs for a corresponding time-domain test system for DC corona discharge noise. To address the selection of acoustic measurement points, an acoustic field simulation model is built in COMSOL/Multiphysics. A series of simulation results are presented under the radiometric acoustic interface, and the simulation results are used to guide the experiments. The temporal waveforms of the AN generated by the positive DC corona discharge are measured at the selected measurement point locations and compared with the simulation results.

One limitation of this paper, however, is the use of a single-point corona source rather than a full-size conductor in experimental validation. Despite its preliminary character, this study clearly indicates that AN measurement is adequate for subsequent data analysis. Further experiments and measurements using full-scale conductors will be carried out in future studies.

5. Conclusions

This paper describes a laboratory stand for detecting AN induced by DC corona and studies the sound field character of a test hall. This paper presents a method for optimizing the location of detection points for corona discharge AN, effectively achieving accurate measurements of corona discharge audible noise pulses and laying the foundation for analyzing the characteristics of AN. The main conclusions are as follows:

• Corona cage metal mesh with a porosity between 0.8 and 0.9 achieves a good balance between electromagnetic shielding and acoustic measurements.
• Based on the premise of satisfying measurement standards, the test effect is better at locations closer to the sound source and further away from the reflecting surface. The effect of folded reflection is not obvious for the test site in this paper, which is verified using both simulation model and experimental results.
• For the frequency band with a center frequency below 4 kHz, the difference in attenuation speed is not obvious. For the frequency band with a center frequency of 8 kHz and 4 kHz, the attenuation speed is faster, with 8 kHz being particularly obvious, and the difference is considered for processing in the experimental measurement.

At the same time, the simulation model in this paper can also obtain a series of important acoustic characteristic indexes, including reverberation time, etc. It lays the foundation for further optimization of acoustic measurement methods in subsequent DC corona AN experiments.