Experimental Study on the Discharge Characteristics of a Dripping ‘Rod–Plane’ Air Gap at High Altitude Under DC Voltages

Abstract

High-voltage transmission and substation projects at high altitudes are pivotal in realizing the objective of universal electricity access. However, the reduced air density at elevated heights facilitates the formation and propagation of discharges, posing more stringent challenges to the external insulation of these projects compared to their counterparts in plains areas. Furthermore, considering the influence of meteorological conditions such as rainfall, it is imperative to conduct comprehensive experimental studies on the insulation properties of air gaps to inform the design and maintenance of engineered external insulation. This paper presents the results of rod–plane gap discharge tests conducted under dripping conditions at an actual high-altitude location of 2500 m. The employed test methodology effectively simulates the impact of rainfall on the insulation characteristics of the gap. Based on the experimental findings, a detailed analysis is conducted on the effects of gap distance, dripping flow rate, and conductivity on the gap breakdown voltage. Additionally, the discharge paths and underlying mechanisms under water-dripping conditions on rod electrodes are briefly discussed. The acquired data and conclusions contribute to a deeper understanding of the mechanisms governing rainfall effects on gap discharges and provide valuable insights for the design of external insulation in high-altitude HVDC transmission projects.

1. Introduction

The expansion of the power grid is a direct response to the growing demand for electrical energy driven by socio-economic development, thereby diversifying the operating environment for transmission and substation projects. To achieve greater grid interconnection and address the issue of uneven resource distribution, transmission projects will inevitably encounter high-altitude environments [1]. A crucial foundation for designing external insulation dimensions is the test results of air gap discharges. However, consistent research has demonstrated that the air gap breakdown voltage is lower at high altitudes compared to sea level, due to reduced air density and increased ultraviolet radiation [2]. Furthermore, the breakdown voltage at varying altitudes reveals a significant decline with ascending altitude. This necessitates specific design considerations for external insulation in high-altitude transmission and substation projects.

Research on the discharge characteristics of air gaps at high altitudes has been an active area of study in recent years, driven by the increasing need for reliable power transmission in these regions. Studies have delved into the fundamental principles of gas discharge, exploring how parameters like voltage form, electric field uniformity, and gap distance impact breakdown voltage [3,4,5,6]. For instance, there are studies that have demonstrated the linear relationship between breakdown voltage and gap distance for rod–plane configurations under DC voltage conditions [7,8,9]. However, most existing data and breakdown voltage curves primarily reflect the influence of individual factors, neglecting the complex interactions observed in real-world scenarios.

Rainfall profoundly affects the insulation properties of air gaps. Water droplets have the potential to reduce the effective gap distance and distort the electric field distribution, thereby lowering the breakdown voltage and altering the discharge pathways. A seminal research paper from Tsinghua University delved into the impact of droplet size and distribution on the breakdown voltage of air gaps in humid conditions, underscoring the pivotal role of droplet morphology in the initiation and progression of discharges [10]. Nevertheless, a comprehensive understanding of the precise mechanisms and influencing factors is yet to be fully realized. Presently, research pertaining to the breakdown characteristics of air gaps under rainfall conditions is relatively scarce. The existence of raindrops inevitably modifies the electric field distribution within the gap. Owing to the complexity inherent in long air gap discharges, the development of models capable of precisely calculating the breakdown voltage and forecasting the discharge path presents a significant challenge. The breakdown characteristics of air gaps under rainfall conditions is a multifaceted domain that integrates electrical engineering, fluid dynamics, and materials science. Ongoing and future research efforts are essential to enhance the understanding of these complex phenomena and to improve the reliability and safety of high-voltage systems operating in adverse weather conditions.

To cater to the requirements of engineering design, the problem of altitude correction for air gap breakdown voltage has been a subject of considerable interest [11,12,13]. By conducting discharge experiments across diverse insulation configurations and under varying voltage conditions, the impact of altitude on the breakdown voltage can be ascertained, leading to the development of a parametric design methodology for air gap clearance in high-altitude regions. Furthermore, in such high-altitude environments, concerns pertaining to the electromagnetic compatibility (EMC) of transmission lines and the influence of specific ambient conditions on the discharge characteristics of air gaps have been documented in publications [14,15,16].

Despite the progress made, several gaps in knowledge persist. Firstly, a comprehensive understanding of the discharge mechanism under high-altitude rainfall conditions is lacking. Secondly, a reliable method for correcting breakdown voltage considering the combined effects of rainfall and altitude is yet to be developed. Finally, further research is needed to investigate the impact of rainfall on air gap discharge characteristics in a more detailed manner, providing a solid foundation for the design of effective external insulation for high-altitude power-transmission systems.

In this study, water dripping from rod electrodes is employed to simulate the rod–plane air gap under rainy conditions, and DC breakdown tests are conducted at a significant altitude of 2500 m. The influence of various factors, including gap spacing, water conductivity, and dripping rate, on the breakdown voltage is thoroughly investigated. Given that the type testing of high-voltage equipment often requires execution in humid environments, the findings presented in this paper offer valuable insights that can serve as a reference for such tests. Furthermore, these results provide essential support for the design of external insulation in high-altitude HVDC transmission projects.

2. Test Setup

The test platform employed in this study is depicted in Figure 1, with Figure 2 providing a detailed physical illustration. The DC power supply utilized features a rated voltage of ±600 kV and a rated current of ±500 mA. The primary circuit of this power supply comprises a single-sided voltage-doubling configuration, incorporating a coupling capacitance of 300 pF. The rod–plane electrode arrangement facilitates the generation of a highly inhomogeneous electric field. The rod electrode measures 1.5 m in length, while the plane electrode spans an area of 3 m by 3 m.

This investigation explored three distinct gap distances: 0.4 m, 0.8 m, and 1.2 m. The determination of the gap distances was predicated upon the following three considerations: Firstly, it is recognized that the breakdown voltage for a 1.2 m gap under standard conditions is approximately 450 kV. In light of the fact that the maximum output voltage of the test power supply is 600 kV, and in an effort to mitigate the risk of power supply malfunction, the laboratory stipulates that the maximum breakdown voltage during discharge testing should be maintained at around 70% of the maximum output voltage. Consequently, a 1.2 m gap was elected as the maximum distance for the present experimental investigation. Secondly, it is understood that smaller gap distances are associated with lower breakdown voltages, which can lead to substantial discrepancies in the measured breakdown voltage values as recorded by the experimental system. To ascertain the breakdown voltage with the highest degree of accuracy, a 0.4 m gap was designated as the minimum distance for the current test. Thirdly, experiments were also undertaken at a 0.8 m gap distance to enable a more exhaustive and comparative analysis.

The rod–plane gap represents a classic example of a highly non-uniform electric field configuration. When comparing gaps of equal distance, the rod–plane gap exhibits a lower breakdown voltage than other configurations such as rod–rod or sphere–plane, thereby attracting significant attention in both engineering design and operational maintenance. Moreover, at equivalent voltage levels, the rod–plane gap is more susceptible to discharge initiation and progression, which simplifies the investigation into the effects of various factors on the breakdown path. Consequently, this study focuses exclusively on conducting breakdown tests for the rod–plane gap, without extending the experiments to other gap structures.

The difference between this test and the conventional rod-plane gap discharge test arrangement is that a water drip device is installed on the rod electrodes to simulate the situation during rainfall. Different water droplet patterns can be simulated at the tapered end of the rod electrode for heavy and light rain by adjusting the control valve. In this work, the results of the tests at two different flow rates (the flow rate of the water droplets falling from the rod electrode) were used for comparative analyses, which are 0.12 mL/s (individual drops at the tapered end of the rod electrode) and 1.2 mL/s (continuous stream at the tapered end of the rod electrode), respectively. The choice of flow rate was governed by two primary considerations: Firstly, the control valve (in Figure 1) employed in the experiments possesses a restricted adjustment range. Secondly, the principal aim of this test is to examine the effects of water droplets on the gap. Notably, the droplet morphology at the rod electrode differs significantly between flow rates of 0.12 mL/s and 1.2 mL/s, effectively mirroring the distinction in gap behavior under light rain versus heavy rain conditions. The dimensions of the tapered end of the rod electrode and water droplet morphology at different flow rates are shown in Figure 3.

It is crucial to highlight that the air gap discharge tests conducted in this research adhere strictly to the procedural guidelines as meticulously outlined in the relevant standard. However, it is important to acknowledge that the methodology utilized for simulating water droplets (rainfall) deviates from the wet testing protocols prescribed in both the IEC (IEC 60060 [17]) and IEEE standards (IEEE Std 4 [18]).

By adding NaCl to the water, the electrical conductivity of the simulated droplets can be conveniently altered. In this test, three distinct levels of water conductivity were selected for the trials, namely 80 µS/cm, 24 mS/cm, and 55 mS/cm. The conductivity of rainwater in the western region of China typically falls within the range of 60–100 µS/cm. The water with a conductivity of 80 µS/cm, achieved through filtration, represents a scenario where no electrolytes are added to the water. The conductivity level of 24 mS/cm is indicative of precipitation that may be encountered under salt fog conditions or in environments with severe air pollution, reflecting the complex interactions between atmospheric contaminants and rainfall. Meanwhile, the 55 mS/cm conductivity level is deliberately chosen to investigate the potential saturation effect at high conductivity levels, thereby providing insights into the impact of conductivity on relevant physical processes.

Because of the polarity effect under the highly inhomogeneous electric field, the polarity of the power supply output voltage during the test is set to positive. Once the electrodes have been positioned, the control valve is adjusted to allow the rod electrodes to drip at the specified flow rate and the voltage is then increased at a rate of 5 kV/s until the gap breaks and the value of the breakdown voltage is recorded. In this work, 10 breakdowns were performed under each test condition and the average value was taken as the valid data.

The temperature and humidity conditions in the laboratory were maintained at a temperature of T = 20 ± 0.2 °C and a relative humidity of HR = 65 ± 1% during the tests. The actual altitude of the test chamber is 2500 m and the air pressure during the test is 81.53 kPa.

3. Results

To ascertain the discharge characteristics of the gap under a specified structure, several critical factors are considered: the distance between the two electrodes (i.e., the gap distance), the dielectric properties of the gap (such as temperature and conductivity), and the type of voltage applied across the gap. In this study, a positive polarity DC voltage is applied to the gap, with temperature and humidity meticulously maintained at constant levels throughout the testing process. Consequently, the investigation focuses on the impact of the drip flow rate, conductivity, and gap distance on the breakdown voltage, particularly in the presence of a drip at the rod electrode. Indeed, when a water droplet descends from the rod electrode, the medium between the two electrodes transitions from a single-phase state to a mixed-phase environment comprising liquid droplets and air.

3.1. Breakdown Voltages at Different Gap Distances

Based on the theory of gas discharge and the outcomes of numerous air gap discharge tests, it has been established that the breakdown voltage and gap distance exhibit a roughly linear relationship within a 10 m gap distance under DC voltage, with the average breakdown field strength for rod–plane gaps being approximately 4.5 kV/cm [19]. In the present study, the variation curves of breakdown voltage with respect to gap distance are presented in Figure 4. These curves were obtained under conditions where the flow rate of water dripping from the rod electrode was maintained at 0.12 mL/s and the conductivity of the simulated rainwater was 55 mS/cm. The solid line in Figure 4 illustrates the trend of linear fitting, whereas the dashed line depicts the trend of the actual experimental results.

According to the results in Figure 4, the linear correlation coefficient R ≈ 0.9991 for this experiment, indicating that there is basically a linear relationship between breakdown voltage and gap distance. This linear relationship appears to be independent of the water dripping on the rod electrode. In fact, when both the drip rate and the conductivity of the water were changed, the linear relationship remained. For instance, based on the analysis of the test results, it was found that the linear correlation coefficient between the breakdown voltage and the gap distance is approximately 0.9999 when the drip flow rate is 1.2 mL/s and the water conductivity is 24 mS/cm.

3.2. Breakdown Voltages at Different Drip Flow Rates

To compare the varying conditions under light and heavy rain, the breakdown voltages (U_b) of the rod–plane gap were tested at drip flow rates (FR) of 0.12 mL/s and 1.2 mL/s across three distinct gap distances. The results, along with the standard deviations (S_D) of the test outcomes, are presented in

Table 1. Comparison of breakdown voltages at different drip flow rates.

Gap Distance	Ub (kV) Without Dirpping	FR = 0.12 mL/s		FR = 1.2 mL/s		Difference in Breakdown Voltage
		Ub (kV)	SD	Ub (kV)	SD
0.4 m	146.9	137	2.43	134.4	1.05	1.90%
0.8 m	286.7	267.7	4.66	262.4	7.43	1.98%
1.2 m	445.2	436.5	2.26	423.4	5.11	3.00%

. Additionally, the breakdown voltages recorded without dripping are included for comparative purposes.

The results presented in Table 1 illustrate that the breakdown voltage is influenced by the drip rate when water droplets are present at the rod electrode. As the drip flow rate at the rod electrode increased from 0.12 mL/s to 1.2 mL/s, the breakdown voltage of the gap exhibited an average decrease of approximately 2.29% across three different gap distance conditions. Furthermore, the impact of the drip flow rate on the breakdown voltage seems to intensify with the increase in gap distance. It is important to highlight that the conductivity of the water utilized for the tests in Table 1 was approximately 80 μS/cm.

3.3. Breakdown Voltages at Different Conductivity Values

In order to determine the effect of the conductivity of the dripping water on the breakdown voltage of the gap, this paper compares the breakdown voltages of the rod electrode dripping water at three different gap distances at a flow rate of 1.2 mL/s with a conductivity of 24 mS/cm and 55 mS/cm, respectively, which is shown in

Table 2. Comparison of breakdown voltages at different conductivities.

Gap Distance	Conductivity = 24 mS/cm		Conductivity = 55 mS/cm		Difference in Breakdown Voltage
	Ub (kV)	SD	Ub (kV)	SD
0.4 m	137.9	3.71	132.8	2.25	3.70%
0.8 m	263.8	0.14	258	8.70	2.19%
1.2 m	404.9	6.36	390.3	0.42	3.61%

.

The data in Table 2 indicate that as the conductivity of the drip water rises from 24 mS/cm to 55 mS/cm, the gap breakdown voltage decreases for all three distinct distances, with the reduction ranging between 2% and 4%. However, when considering the test results from Table 1, which were obtained at a conductivity of 80 μS/cm and a consistent flow rate of 1.2 mL/s, it is evident that an increase in conductivity does not invariably lead to a decrease in breakdown voltage, particularly for gap distances of 0.4 m or 0.8 m. For larger gap distances, as evidenced by the results in this paper for a gap distance of 1.2 m, the gap breakdown voltage exhibits a marked downward trend with increasing conductivity of the dripping water at the rod electrode, as illustrated in Figure 5. A potential explanation for this phenomenon is presented and discussed in the subsequent section.

4. Discussion

4.1. Discussion on the Effects of the Altitude

The effect of altitude on the gap breakdown voltage is first discussed as the tests in this paper were carried out at an actual altitude of 2500 m. According to the recommendations given in the IEC standard (IEC 60071-2 [20]), the correction factor K_a is based on the dependence of the atmospheric pressure on the altitude and can be calculated from equation:

$$K_a=e^{m({\displaystyle \frac{H}{8150}})}$$

(1)

where H is the altitude above the sea level (in meters) and the value of m is 1.0 for air clearances. Thus, K_a is approximately 1.3 for an altitude of 2500 m. However, considering the structure of the electrodes used and the actual situation of the test in this paper, we choose K_a = 1.2 to consistent with the test results in this paper. Consequently, the breakdown voltage of the 1.2 m gap is approximately 450 kV at 2500 m area under normal conditions, excluding the effect of altitude. A comparison of this value with the test results in Table 1 and Table 2 shows that the breakdown voltage of the gap is reduced in the presence of dripping water at the rod electrode (a reduction of 3% to 13.27%). This reduction is attributed to both the shortening of the air gap by the water droplets and the distortion of the electric field, which facilitate discharge development.

4.2. Discussion of the Discharge Path

A set of typical gap discharge breakdown instantaneous images obtained at three different gap distances for a rod electrode drop rate of 1.2 mL/s are shown in Figure 6. For the detailed visualization of the complete discharge processes under three varying inter-electrode spacing conditions, please consult the Supplementary Materials labeled as Video S1, Video S2 and Video S3.

Figure 6 illustrates that in the presence of dripping at the rod electrode, two distinct breakdown paths emerge across the gap. The primary discharge path initiates at the tip of the rod electrode, while a secondary breakdown path may develop at the point of water droplets formation, situated above the electrode’s tip. Owing to the installation of the counterweight, the actual rod electrode used in the tests presented in this paper is not perfectly perpendicular to the plane containing the plane electrode. Consequently, when a water droplet falls, its trajectory exhibits an inclination relative to the extension line aligned with the tip of the rod electrode. This scenario is depicted in Figure 7. Simultaneously, under ideal conditions, the water-storage bottle mounted on the rod electrode is designed to be connected via a flexible hose, directing the water to drip precisely from the electrode’s tip. Nonetheless, in practical terms, leakage may occur at the junction between the hose and the storage bottle, potentially causing dripping to happen above the electrode’s tip. This phenomenon further elucidates the emergence of the second breakdown path across the gap, as depicted in Figure 6. In real-world power engineering scenarios, raindrops during precipitation can descend from various positions, not necessarily at the point of minimum electrical distance, yet still pose a risk of insulation failure.

The presence of multiple discharge paths increases the likelihood of breakdown, leading to a lower breakdown voltage compared to dry conditions. In a real engineering operating environment, the presence of unavoidable wind on rainy days will make the droplets at the high field strength electrodes dripping randomly, so the situation in this paper’s test is closer to reality. In addition, this makes the prediction of the breakdown voltage of the air gap in a rainy environment more uncertain.

To confirm whether the discharge path would be affected by the electric field distribution on the surface of the plane electrode, in this paper a tapered electrode was placed at X cm (Separate tests were carried out for cases X = 20 and X = 30) from the intersection of the vertical line from the tapered end of the rod electrode and the plane electrode to verify whether the breakdown point would fall on this tip electrode. The test results show that the breakdown point does not fall on the tip electrode, as shown in Figure 8, i.e., the path of the discharge is not affected by the electric field distribution of the plane electrode.

This work still has some imperfections. In order to better understand the effect of rainfall on the insulation characteristics of the gaps, and even to explore the correction of the gap breakdown voltage under the combined effect of rainfall and altitude, more work is needed in the future, particularly on the coupled simulation analysis of the electrical and flow fields.

4.3. Discussion of the Breakdown Mechanism

The discharge mechanism of long air gaps under highly non-uniform electric fields encompasses theories such as corona discharge and streamer propagation [21,22]. To date, several physical models have been developed to describe the discharge phenomena in simple air gaps [23,24]. Nevertheless, owing to the inherent complexity of discharge processes, accurately determining the breakdown voltage across the gap presents a significant challenge. In the context of this study, the long gap discharge does not occur within a pure gaseous medium; the presence of water droplets influences both the initiation and progression of the discharge, thereby adding a layer of complexity to the underlying mechanism.

Consequently, it is imperative to incorporate pertinent hydrodynamic theories to elucidate the interrelation between the morphological transformations of water droplets and the progression of the discharge. Furthermore, an explanation is required for the influence of conductivity on the breakdown voltage, as evidenced by the test results presented in Section 3.3. The charge and ion concentration are pivotal to the discharge development. As the conductivity of the water droplets contacting the rod electrode rises, the concentration of charges and ions participating in the discharge reaction inevitably escalates, thereby facilitating the discharge process and consequently lowering the gap’s breakdown voltage.

In our subsequent research, the mechanism of the water droplet effect on gap discharge is worthy of further investigation. And the new method of designing the external insulation parameters of HVDC, taking into account the combined influence of rainfall and altitude, needs to be considered.

5. Conclusions

Comprehending the discharge characteristics of air gaps within complex environments is imperative for the selection of appropriate insulation dimensions and for the assurance of reliability and safety in transmission projects. This study elucidates the variation of breakdown voltage under diverse dripping conditions and gap distances, as well as the influences of various factors on the breakdown voltage, through meticulously conducted discharge tests on a dripping rod–plane air clearance at a high-altitude location. The following conclusions have been derived:

• The presence of water droplets on rod electrodes results in a reduction of the breakdown voltage. Notably, the variation in conductivity exhibits a more pronounced effect on the breakdown voltage for extended gaps compared to shorter gaps.
• When dripping is initiated at the rod electrode, both the drip flow rate and conductivity exert significant influence on the breakdown voltage of the rod–plane gap. An elevation in the flow rate results in a decrement in the breakdown voltage, with the experimental data presented in this paper demonstrating a reduction range of 2–4%.
• A pronounced linear relationship has been identified between the gap breakdown voltage and the gap distance in the presence of dripping water on rod electrodes. This finding necessitates further corroboration through extensive large-scale studies, and a comprehensive examination of the influence of rainfall on the discharge mechanism is warranted.

It is envisioned that this research will contribute essential data and knowledge, thereby serving as a foundational reference for the design of external insulation in high-altitude HVDC transmission and substation projects.