Temperature‐dependent adaptive conductivity coating for surface charge release and electric field control under electro‐thermal coupling field

Abstract

Surface charge accumulation is the potential criminal for surface insulation failure on spacers under direct current (DC) voltages. The existence of thermal gradient posing the difficulty of surface charge regulation. This study proposes a temperature‐dependent adaptive conductivity coating technique for surppressing surface charge accumulation under electro‐thermal coupling field. A two‐dimensional axis‐symmetrical simulation model regrading surface charge computation is established. The effects of thermal gradients and coating conductivity on surface charge and electric field distribution are investigated. The results show that the thermal gradient increases the bulk conductive current, therefore aggravating surface charge accumulation. The effects of the coating condcutivity on surface charge and electric field contains three stages. The lower coating conductivity leads to aggravated homo‐polarity charge accumulation. By increasing the coating conductivity, the surface charge and electric field are significantly suppressed at the obtained optimal conductivity, where the bulk and surface conductive current reach a balance stage. Continuously increasing the coating conductivity results in aggravated hetero‐polarity charges. Besides, the increase of thermal gradient to an appropriate extent contributes to the further suppression of surface charge on coated spacers. It is hoped that this study could provide some references for designing highly reliable DC GIL under electro‐thermal coupling field.

INTRODUCTION

High voltage direct current (HVDC) transmission strategies have provided the solutions for conveying power energy of large capacity over long distances [1]. Gas-insulated transmission lines (GIL) have attracted great attention due to its low cost, high efficiency, and environmental friendliness [2]. In GIL, spacers are key components serving as mechanical support and electrical insulation. The spacers and the surrounded gas which may be SF₆ gas or other environmental friendly gas mixtures constitute the insulation system in GIL [3, 4]. The resulted gas–solid interface becomes the most vulnerable link in the compound insulation system. The long-term DC excitation enables the spacer surface to accumulate plenty of charges, which may distort the surface electric field and then destroy the safety of the gas–solid interface insulation [5]. The proper surface modification strategies are necessary for releasing surface charges and guarding the reliability of gas–solid interface insulation.

In recent years, gas–solid interface charge regulation becomes continuously hot research spot [6, 7]. Numerous surface modification methods are proposed to improve surface charge and electric field distribution [8, 9]. In terms of suppressing charge injection, the Cr₂O₃ coating method or doping thermal resistance particles with epoxy resin spacers was proposed [10]. In terms of accelerating charge dissipation, surface fluorination, surface plasma treatment, and surface highly conductive coating were proposed [11–13]. These methods aimed at increasing surface conductivity to realise the fast dissipation of surface charges. Among these methods, the concept of surface conductivity graded spacer was proposed by Du et al, the surface conductivity of which is gradiently distributed from high voltage to grounded electrode [14, 15], attracting widespread interests in the field. This kind of conductivity distribution can improve surface charge and electric field distribution, and moreover no excessive surface leakage current is introduced. Besides that, the physical characteristics of the spacer bulk will not be changed. Accordingly, the surface conductivity graded spacer has wide application perspective.

In fact, when DC GIL is put into service, the large current along the central high-voltage electrode will generate Joule heat, which enables the spacer surface to form a temperature gradient distribution [16]. The existence of thermal gradient on spacer surface will promote the migration of surface charge, then increase the amount of surface charges and ultimately decrease surface insulation strength [17, 18]. However, the surface charge and electric field regulation under the thermal gradient field is less paid attention to, which still needs the systematic and deep investigation.

In this study, we propose a novel surface charge and electric field regulation method called temperature-dependent adaptive conductivity coating, aiming at releasing surface charge and improving surface electric field distribution under electro-thermal coupling field. A multi-physical field simulation model considering the coupling of electric field and thermal field is established. The surface charge and electric field distribution with different temperature-dependent surface conductivities are obtained. The regulation mechanism of temperature-dependent conductivity adaptive coating on surface charge and electric field are revealed. The optimal coating conductivity distribution is also obtained from the simulation results. We hope that this investigation could provide some guidance as well as inspire novel ideas for the optimal design of DC GIL.

SIMULATION MODEL UNDER ELECTRO-THERMAL COUPLING FIELD

Model description

In this study, a two-dimensional axis-symmetric calculation model for calculating surface charge and electric field distribution is built [19], as shown in Figure 1. The high voltage (HV) and grounded (GND) electrode are aluminium. The spacer is epoxy-based materials, which is surrounded by SF₆ gas of 0.4 MPa.

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The mathematics-physics equations of surface charge accumulation

The surface charge accumulation process has been investigated for many years. A commonsense has been reached that three kinds of conduction current contribute to surface charge accumulation, namely the spacer bulk conductive current, the spacer surface conductive current and the surrounded gas bulk conductive current [20]. The dynamic variation of surface charge density is dependent on these three kinds of current, as displayed in Equation (1). 1 $$\frac{\partial \sigma }{\partial t}={J}_{\mathrm{sn}}-{J}_{\mathrm{s}{\uptau }}-{J}_{\mathrm{gn}}$$ where σ is the surface charge density, C/m². J_sn, J_gn, J_sτ are the normal current density from spacer bulk, from gas bulk and the current density along spacer surface, A/m².

The above three kinds of conduction current are decided by the corresponding conductivities. As for spacer side, the bulk and surface conductive current are dependent on bulk and surface conductivity respectively. The correlation can be described by Equations (2) and (3). 2 $${J}_{\mathrm{s}\mathrm{n}}={\gamma }_{\mathrm{s}\mathrm{v}}{E}_{\mathrm{s}\mathrm{n}}$$ 3 $${J}_{\mathrm{s}{\uptau }}=\nabla \cdot \left({\gamma }_{\mathrm{s}{\uptau }}{E}_{{\uptau }}\right)$$ where γ_sv, γ_sτ are the conductivity of spacer bulk and surface respectively. E_sn, E_τ are the normal and tangential electric field of spacer side.

Experimental researches reveal that the spacer bulk conductivity is dependent upon the temperature [21], as expressed by Equation (4). 4 $${\gamma }_{\mathrm{v}\mathrm{i}}=A{\mathrm{e}}^{-\tfrac{B}{T}}$$ where A and B are the constant related to the materials. T refers to the temperature along the spacer.

As for the gas side, the bulk conductive current is dependent on the gas conductivity, which can be described as the following Equation (5). 5 $${J}_{\mathrm{g}\mathrm{n}}=e{E}_{\mathrm{g}\mathrm{n}}\left({n}^{+}{b}^{+}+{n}^{-}{b}^{-}\right)-e\nabla \left({D}^{+}{n}^{+}+{D}^{-}{n}^{-}\right)$$ where e is the quantity of element charge, 1.6 × 10⁻¹⁹ C. E_gn is the normal electric field of gas side, V/m. n⁺, n⁻ are the concentration of positive and negative charges correspondingly, m⁻³. b⁺, b⁻ are the mobility rate of positive and negative charges correspondingly, cm²·(V·s)⁻¹. D⁺, D⁻ are the diffusion rate of positive and negative charges correspondingly, m²/s.

The concentrations of positive and negative charges are closely related to its microscopic behaviour, including the generation, recombination, migration, and diffusion process [22]. The variation of charged particle concentration can be characterised by the following Equation (6). 6 $$\left\{\begin{array}{@{}l@{}}\frac{\partial {n}^{+}}{\partial t}=\frac{\partial {n}_{\mathrm{I}\mathrm{P}}}{\partial t}-{k}_{r}{n}^{+}{n}^{-}-\nabla \cdot \left({n}^{+}{b}^{+}E\right)+{D}^{+}{\nabla }^{2}{n}^{+}\\ \frac{\partial {n}^{-}}{\partial t}=\frac{\partial {n}_{\mathrm{I}\mathrm{P}}}{\partial t}-{k}_{r}{n}^{+}{n}^{-}+\nabla \cdot \left({n}^{-}{b}^{-}E\right)+{D}^{-}{\nabla }^{2}{n}^{-}\end{array}\right.$$ where n_IP is the initially generated ion pairs by natural ionisation, cm⁻³. k_r is the recombination rate of the positive and negative charges.

The diffusion coefficient of the positive and negative charges can be characterised by the Einstein Equation (7). 7 $${D}^{+}={D}^{-}={b}^{+/-}\frac{{k}_{\mathrm{B}}{T}_{\mathrm{g}}}{e}$$ where k_B is the Boltzmann constant, 1.38 × 10⁻²³ J/K. T_g is the gas temperature, K.

The electric field are determined by the Maxwell Equation (8). The relation between potential distribution φ and charged particle concentration are described by the Possion's Equation (9). 8 $$E=-\nabla \varphi $$ 9 $${\nabla }^{2}\varphi =-\frac{e\left({n}^{+}-{n}^{-}\right)}{{\varepsilon }_{\mathrm{g}}}$$ where E is the electric field. ε_g is the relative permittivity of the surrounded gas.

In this study, it is assumed that the ion pairs by natural ionisation are the only sources of initial surface charges. During the simulation, no extra partial discharge happens.

The boundary condition is set as follows. A 500 kV/−500 kV DC is applied to the HV electrode, and the enclosure is grounded.

For the boundary that the electric current outflows, if the charged particle is of positive polarity, the Dirichlet boundary conditions are applicable, as presented in Equation (10). While the charged particle is of negative polarity, the Newman boundary conditions are applicable, as presented in Equation (11). 10 $${n}^{+}=0$$ 11 $$\nabla {n}^{-}=0$$

For the boundary that the electric current inflows, if the charged particle is of negative polarity, the Dirichlet boundary conditions are applicable, as presented in Equation (12). While the charged particle is of positive polarity, the Newman boundary conditions are applicable, as presented in Equation (13). 12 $${n}^{-}=0$$ 13 $$\nabla {n}^{+}=0$$

Thermal field

In DC GIL, when large current flows through the bus bar, the Joule heat is generated. Then the heat transfers through spacers and surrounded gas, ultimately forming thermal gradient on spacers along radial direction from HV to GND electrode [23]. The heat transfer process satisfies the Fourier law, as expressed in Equation (14). 14 $$\left\{\begin{array}{@{}l@{}}\rho C\frac{\partial T}{\partial t}+\rho Cu\nabla T+\nabla q=Q\\ q=-k\nabla T\end{array}\right.$$ where ρ is the density of the materials, kg·m⁻³. C is the heat capacity at constant pressure, J·(kg·K)⁻¹. T is the temperature, K. u is the velocity of the fluid. q is the heat flux, W·m⁻². Q is the quantity of the heat, W·m⁻². k is the heat conductive coefficient, W·(m·K)⁻¹.

In GIL, the materials involve spacers, surrounded gas and metallic electrodes. The heat mainly depends on the heat conduction, radiation and convection to transfer among these materials. During this simulation, all these three heat transfer ways are considered to model the actual situation.

The heat conduction primarily happens between solid materials, that is, the electrodes and the spacers. The formation of heat conduction results from the difference in temperature of different locations. The heat transfer is determined by the heat conductive coefficient, as described in Equation (15). 15 $$\frac{k}{r}\cdot \frac{\partial }{\partial r}\left(r\frac{\partial T}{\partial r}\right)+k\frac{{\partial }^{2}T}{\partial {z}^{2}}+Q=0$$ where r and z represent the direction of the space location.

The heat convection results from the relative movement of the particles in the fluid aroused by the inhomogeneous distribution of fluid density. In GIL, the convection includes two classes, the one between HV electrode, spacers and the internal gas, the other one between GND electrode and the external atmospheric air. In order to simplify the calculation process, the natural convection is regarded for both external and internal convection. The convection process in GIL satisfies the Newton cooling law, as presented in Equation (16). 16 $$\left\{\begin{array}{@{}l@{}}q=h{\Delta }T\\ \Phi =Ah{\Delta }T\end{array}\right.$$ where h refers to the convection coefficient. ∆T is the temperature difference on fluid or solid material surface. Ф is the generated heat quantity per second by the heat source of per unit volume, W·s⁻¹·m⁻³. A is the surface area, m².

The heat radiation happens due to the temperature of the materials higher than absolute zero degree. In GIL, the heat radiation occurs between the HV electrode and the adjacent gas, the spacers and the adjacent gas, the grounded electrode and the external atmospheric air. The heat radiation can be expressed by Stefan-Boltzmann law, as presented in Equation (17). 17 $$\Phi =\varepsilon A\sigma \left({T}_{1}^{4}-{T}_{2}^{4}\right)$$ where ε is the surface radiation rate. σ is a constant. T₁ refers to the surface temperature of materials that radiate heat while T₂ refers to the surface temperature of materials that absorb heat.

The initial temperature is set as 293.15 K. The heat sources originate from the Joule loss generated by load current. The gas pressure of SF₆ is set as 0.4 MPa.

The related parameters for simulation

During the simulation, the related parameters are from measurement or other publications [16, 24], which is presented in the following Table 1.

TABLE 1 Related parameters for involved materials

Attribute	Aluminium (for HV and GND electrode)	SF6	Epoxy-based spacer	Unit
Heat capacity of constant pressure	900	665.18	1500	J/(kg·K)
Thermal conduction coefficient	43.2	0.012	0.2	W/(m·K)
Relative permittivity	104	1	4.95
Density	2700	26.08	1200	kg/m3
Surface radiation rate	For HV electrode: 0.05	/	0.8
For GND electrode: 0.15
Dynamic viscosity	/	1.42 × 10−5	/	Pa·s
Specific heat ratio	/	1.33	/

Concept of the temperature-dependent adaptive conductivity coated spacers

The temperature distribution in DC GIL and along spacer upper surface is displayed in Figure 2. It can be seen that the temperature is uniformly distributed inside the GIL, where the highest temperature locates near HV electrode while the lowest temperature is near GND electrode. The temperature along the spacer in radial direction presents a descending distribution from HV and GND electrode. That is to say, a thermal gradient distribution is formed on the spacer. Based on the thermal gradient distribution, we propose a novel surface charge regulation method under DC electric field and thermal gradient field - a temperature-dependent adaptive conductivity coating. It refers to that the conductivity of the deposited coating presents a positive correlation with temperature. According to Equation (4), for most dielectrics, the conductivity exhibits exponential relation with the temperature. The higher temperature brings about higher conductivity, and vice versa. In consequence, a highly conductive coating can be deposited on spacer surface. The thermal gradient distribution on spacer surface enables the conductivity of the coating to exhibit a continuously gradient distribution. As is known, in DC system the electric field distribution is negatively proportional to the conductivity distribution of the involved materials [25]. A higher conductivity corresponds to a lower electric field. Therefore, the temperature-dependent adaptive conductivity coated spacers can realise the adaptive regulation of electric field distribution.

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In the following, the key point is to obtain the optimal temperature-dependent conductivity distribution of the coating, with the goal of less surface charge accumulation and lower surface electric field. The change in conductivity can be realised by changing the high conductive filler contents in the coating.

According to Equation (4), when the thermal gradient is determined, the conductivity distribution is dependent on the parameters A and B which are closely related to the material itself. Here, the parameters A is taken as 12.3 S/m [14]. For the temperature-dependent adaptive conductivity coating, by optimising the parameters A and B, the coating conductivity distribution can be optimised. For simplifying the calculation process, only parameter B is changed during the simulation.

RESULTS AND DISCUSSIONS

Surface charge distribution under electro-thermal coupling field

In this investigation, the dynamic surface charge accumulation process is calculated. After about 10⁴ s, surface charge accumulation reaches a steady state. In the following, the steady surface charge and electric field distribution are presented.

Under different thermal gradient excitation, charge distribution at steady stage on spacer upper surface under 500 kV/−500 kV DC voltages is presented in Figure 3. When the temperature on HV electrode increases from 323 to 383 K, the accumulated surface charges exhibit an increasing trend on spacers. The polarity of accumulated charges keeps unchanged, which is the same as that of applied DC excitation. It indicates that the increase of thermal gradient will definitely contribute the accumulation of surface charges.

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From Figure 3, with the rise of thermal gradients, surface charge density increases as a whole. It is hard to observe the migration of surface charges when raising the temperature of HV electrode. It indicates that the accumulation of surface charge originates from the contribution of spacer bulk conductive current. The increase of thermal gradient promotes the overall bulk conductive current, contributing to the increase in surface charge density.

Surface charges and electric field distribution on temperature-dependent adaptive conductivity coated spacers

The surface charge distribution on temperature-dependent adaptive conductivity coated spacers are calculated. The thermal gradient distribution on spacers is presented in Figure 2. The temperature-dependent conductivity is varied by changing the parameters B. The selection of parameters B is presented in Table 2.

TABLE 2 Different values of parameter B

Label	B1	B2	B3	B4	B5	B6
Parameter B (K−1)	10,800	10,600	10,500	10,400	10,200	10,000

Different selections of B correspond to different conductivity distributions of the coating on spacers, as presented in Figure 4. It can be seen that the existence of thermal gradient results in the continuous conductivity gradient distribution on spacer surface, where the conductivity decreases gradually from HV to GND electrode. The larger B brings about the lower conductivity. When the parameter B changes from 10,800 to 10,000, the conductivity of the coating near HV electrode decreases from 2 × 10⁻¹² to 3 × 10⁻¹³ S/m while that near GND electrode decreases from 3 × 10⁻¹⁴ to 1.5 × 10⁻¹⁵ S/m.

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The surface charge distribution patterns on spacers with different temperature-dependent adaptive conductivity coatings at steady stage under 500/−500 kV are presented in Figure 5. Different coating conductivities bring about significant distinctions in surface charge patterns on spacer surface. In general, the surface charge patterns with the variation of parameter B can be classified into three stages. The first stage is characterised by homo-polarity charges domination. At this stage, the value of parameter B is B₁, B₂, B₃. With the decrease of parameter B, the accumulated homo-polarity charges on spacer surface decrease obviously no matter what the polarity of applied excitation is. When the value of parameter B increases to B₄, nearly no charges accumulate on spacer surface except for the location at 0–40 mm, which forms the second stage. The third stage is characterised by hetero-polarity charges domination at 40–160 mm. With the decrease of parameter B, the accumulated hetero-polarity charges on spacer surface increase obviously. The reason for the formation of these three stages mainly lies in that the variation of coating conductivity enables the transition of surface charge dominant mechanism. The polarity of dominant surface charges is determined by the relative value between the surface conductivity and bulk conductivity. With the increase of coating conductivity, both homo-charges and hetero-charges increase due to the increased surface leakage current. The hetero-charges migrate towards the HV electrode and neutralise with the homo-charges supplied by bulk leakage current, especially at 40–160 mm. The homo-charges are mainly remained at 0–40 mm, some of which are neutralised by these hetero-charges. With the increase of coating conductivity, the supplied hetero-charges dominate at 40–160 mm. While the supplied homo-charges are restricted at 0–40 mm due to the decreased charge mobility towards GND electrode.

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A common consensus has been reached that surface charge accumulation originates from three ways, including the current from solid bulk side, solid surface side, and the gas side. According to Equation (1), the growth rate of surface charge density is determined by the relative value of these three kinds of current. In this investigation, the current from gas side is constant and only the current from solid side and surface side varies with the thermal gradient and the parameter B. Accordingly, surface charge accumulation is mainly determined by solid surface conductivity and bulk conductivity. When the parameter B is B₄, these three kinds of current distribution on spacer surface are presented in Figure 6. According to the combination of these three kinds of current density (corresponding to $$\partial \sigma /\partial t$$), under 500 kV DC application, $$\partial \sigma /\partial t$$ is almost below zero; under −500 kV DC application, $$\partial \sigma /\partial t$$ is nearly above zero. It illustrates that surface charge density decreases significantly at B₄. Besides, it can be seen that the solid surface current density J_sτ is larger than both the bulk current density J_sn and the gas current density J_gn. And the surface charge distribution profile is similar to that of J_sτ, which shows that surface charge accumulation process is dominated by solid surface conductivity.

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In order further illustrate the contribution of surface and bulk conductivity on surface charge accumulation, the surface charge distribution along spacer radial direction is presented in Figure 7. Here, surface charge accumulation process at 0–40 mm and 40–160 mm are discussed separately since the variation in charge polarity is different in these two regions.

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At 0–40 mm, surface charges are still homo-polarity no matter how high the coating conductivity. At this location, when the coating conductivity is at a low level, such as at B₁, B₂, or B₃, it is still the bulk conductivity dominates surface charge accumulation (the First stage). The charges mainly rely on the normal electric field to accumulate on spacer surface. When the coating conductivity increases to a high level, such as at B₄, B₅ and B₆, both bulk and surface conductivity dominate surface charge accumulation at 0–40 mm (the Second and Third stage). The accumulated charges originate from surface and bulk leakage current. With the increase of coating conductivity, surface leakage current increases synchronously, resulting in the increase in homo-charges and hetero-charges on spacer surface [26]. With the help of surface tangential electric field, homo-charges move towards the HV electrode while hetero-charges move towards the GND electrode. The tangential electric field is high near the HV electrode, and then decreases towards the GND electrode, as presented in Figure 7. Meanwhile, the temperature on spacer surface decreases by about 30 K at 40–160 mm compared with that near HV electrode. As reported in ref. [27], the charge mobility is closely related to the electric field and the temperature. Higher electric field and temperature bring about higher charge mobility. Combining the distribution of electric field and temperature gradient on spacer surface, the homo-charges moves slowly towards the GND electrode, most of which remain near the HV electrode. The hetero-charges moves slowly at 160–40 mm, then faster at 40–0 mm towards the HV electrode. The homo-charges supplied by surface and bulk leakage current will be neutralised by some hetero-charges supplied by surface leakage current, ultimately still leaving homo-charges remained at 0–40 mm.

At 40–160 mm, it can be seen that surface charge distribution profile differs obviously at the first stage and the third stage. At the first stage, surface charge accumulation is dominated by spacer bulk conductivity. The charge distribution profile is mainly determined by the normal electric field. When the coating conductivity increases from B₁ to B₂ or B₃, the supplied homo-charges and hetero-charges also increase. Most homo-charges remain near the HV electrode and it is hard for them to enter the region at 40–160 mm. While the hetero-charges migrate from GND to HV electrode and then neutralise with some of the homo-charges. From HV to GND electrode, a decreasing trend for surface charge distribution is observed, which corresponds to the vertical electric field distribution. The dominate charges are still homo-polarity. Thus it is still the bulk conductivity dominates surface charge accumulation process at this stage. At the third stage, surface charge accumulation is dominated by spacer surface conductivity. The charge distribution is mainly determined by the tangential electric field. A decreasing trend for surface charge distribution from GND to HV electrode is found, which is in accordance with the variation in charge mobility caused by tangential electric field. At this stage, the coating conductivity increases to a high level, leading to an obvious increase in surface leakage current. Similarly, the homo-charges and hetero-charges supplied by surface leakage current migrate towards the GND and HV electrode with the help of surface tangential electric field respectively. The homo-charges scarcely enter into the region at 40–160 mm due to the low charge mobility. The hetero-charges can migrate along 160–40 mm and neutralise with the homo-charges supplied by bulk leakage current. The dominate charges are still hetero-polarity. Thus it is the surface conductivity dominates surface charge accumulation process at this stage.

In order to further understand surface charge accumulation process on temperature-dependent adaptive conductivity coated spacers, a simple schematic diagram is established, as presented in Figure 8. In fact, for untreated spacers, the solid surface current is lower than solid bulk current. Surface charge accumulation process is dominated by solid bulk conductivity, as similar to charge distribution patterns at B₁, B₂, and B₃ in Figure 5. The accumulated surface charges are mainly homo-polarity, as shown in Figure 8a. With the increase in coating conductivity, the surface charge supplied by surface conduction current gradually increases, bringing about the increase in both the homo-charges and hetero-charges. The homo-charges mainly remain near HV electrode (0–40 mm) due to the decreased charge mobility towards GND electrode. The hetero-charges move fast especially towards HV electrode, and then neutralise with some of the homo-charges. Accordingly, with the decrease in parameter B, the accumulated surface charges decrease synchronously (40–160 mm). At B₃∼B₄, the supplied hetero-charges increase and almost neutralise with all homo-charges supplied by bulk conductive current, which results in almost a charge-free surface at 40–160 mm, as shown in Figure 8b. Continuously decreasing the parameter B, the supplied hetero-charges by surface conductivity plays a dominant role at 40–160 mm, leading to gradually increased surface charge density with hetero-polarity, as shown in Figure 8c. That is to say, the regulation effect of temperature-dependent adaptive conductivity coating on surface charges is realised by increasing surface conduction current to compensate bulk conduction current. When these two kinds of current reach a balance, a charge-free spacer surface is achieved.

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The surface electric field distribution at steady stage is also calculated, as displayed in Figure 9. The variation law in surface electric field with different parameters B can be divided into third stages, including the first stage where the parameter B is higher than B₄, the second stage where the parameter B is around B₄ and the third stage where the parameter B is lower than B₄. At the first stage, increasing the parameter B brings about a little change in surface electric field. When the parameter B reaches B₄, surface electric field is significantly lowered. The maximum electric field is reduced by about 34%. At the second stage, decreasing the parameter B leads to a dramatic increase in surface electric field. When the parameter B reduces to B₆, the surface electric field almost increases to the level at first stage. It illustrates that the excessively increased coating conductivity is detrimental to the homogenisation of surface electric field distribution.

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The surface electric field distribution is dependent on both the coating conductivity and the surface charge distribution. In DC system, the electric field distribution is reversely proportional to the conductivity of involved materials, where the higher conductivity contributes to lower electric field. The existence of homo-polarity charges near HV electrode suppress the electric field thereby but enhanced the electric field between these charges and the GND electrode, forming the electric field distribution at the first stage. At B₄, both the decreased surface charge density and the increased coating conductivity contributes to the significant suppression of surface electric field, forming the electric field distribution at the second stage. At the third stage, the accumulated surface charges turn into hetero-polarity, which greatly enhanced the electric field on spacer surface. In consequence, continuously increasing the coating conductivity at this stage results in enhanced surface electric field distribution.

Surface charge and electric field distribution on temperature-dependent adaptive conductivity coated spacers under different thermal gradients

In GIL, the changes in load would result in the variation in Joule heat, and afterwards affect the temperature on HV electrode, which forms a different thermal gradient distribution. In order to verify the performance of temperature-dependent adaptive conductivity coating in the situation of fluctuations in temperature, the effects of thermal gradient on surface charge and electric field behaviour on this novel spacer are investigated. Four kinds of thermal gradient distribution are considered when the temperature of HV electrode is 323, 343, 363, 383 K. The surface charge and electric field distribution on temperature-dependent adaptive conductivity coated spacers along radial direction at B₄ is calculated and presented in Figure 10. The temperature-dependent adaptive conductivity coating always has a decent effect for suppressing surface charge accumulation from 323 to 363 K. Moreover, the increase in the temperature on HV electrode contributes to lowering surface charge accumulation and also the electric field on spacers. The regulating effect is a little different for different thermal gradients. From 323 to 363 K, surface charge density continuously decreases, and the electric field is also gradually lowered. From 363 to 383 K, surface charge density is a little increased compared with that at 363 K, but still lower than that at 343 K. It shows that excessively increased coating conductivity will weaken the effect of the coating.

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By comparing Figures 3 and 10, surface charge behaves in an opposite manner under the effects of thermal gradient. For untreated spacers, the rise of thermal gradient results in aggravated surface charge accumulation. While for temperature-dependent adaptive conductivity coated spacers, appropriately raising the thermal gradient restricts the surface charge accumulation and mitigate the distorted surface electric field. This is the outstanding advantage of the temperature-dependent adaptive conductivity coating.

Superiority of the proposed temperature-dependent adaptive conductivity coated spacers

This study proposes a novel surface charge and electric field control technique named temperature-dependent adaptive conductivity coating, aiming at suppressing surface charge accumulation under electro-thermal coupling field. From the results in Sections 3.2 and 3.3, the optimal coating conductivity distribution that the parameter B is around B₄ under 500 kV/−500 kV is obtained. Both the accumulated charges and the resulted electric field achieve an optimal distribution at around B₄. The proposed novel method has two aspects of advantages compared with present research. Firstly, this kind of coating can form a continuously graded conductivity distribution from HV to GND electrode under the effect of thermal gradient, which is superior to the discontinuously graded conductivity coating that brings about the surface electric field distortion point [28]. Secondly, different from the electric field-dependent adaptive conductivity coating by SiC/epoxy or ZnO/epoxy composites, the conductivity of these coating is only greatly influenced by the thermal gradient not the electric field. Actually, during the operation of DC GIL, the spacers may suffer electric field generated by various types of over-voltages. As a result, the conductivity of electric field-dependent adaptive conductivity coating may be increased significantly, which poses hazardous effect on spacer surface insulation strength [29]. However, the variation of thermal gradient is limited during the operation of DC GIL. Accordingly, the temperature-dependent adaptive conductivity coating is capable of resisting the adverse effect of the electric field-dependent adaptive conductivity coating when facing over-voltages. And fortunately, the temperature-dependent adaptive conductivity coating still owns the excellent surface charge and electric field suppression performance even if suffering the fluctuation of thermal gradient. Above all, the temperature-dependent adaptive conductivity coating has more prominent prospect for industrialised application perspective on GIL spacers.

CONCLUSIONS

This study proposes a temperature-dependent adaptive conductivity coating for suppressing surface charge accumulation and lowering surface electric field on GIL spacers under electro-thermal coupling field. The following conclusions are summarised:

• (1)

  The existence of thermal gradient field on DC GIL aggravates surface charge accumulation on spacers. The increased surface charges are on account of the increased bulk conductive current induced by thermal gradient.

• (2)

  The conductivity of the proposed coating presents a continuously gradient distribution from HV to GND electrode under the excitation of thermal gradient, which is beneficial to mitigating surface charge accumulation and lowing surface electric field. With the increase of the coating conductivity, surface charge dominant mechanism changes gradually from bulk conductivity to surface conductivity. When the supplied bulk conductive current and surface conductive current reach a balance stage, the most optimal suppression effect for surface charge accumulation and surface electric field is achieved, where the parameter B is around B₄ in this study.

• (3)

  The increase in thermal gradient will not destroy the performance of temperature-dependent adaptive conductivity coating suppressing surface charges and lowering surface electric field. An appropriately increased thermal gradient contributes to the further suppression of surface charge accumulation and decrease of surface electric field, which is opposite to the results on the untreated spacers.

ACKNOWLEDGEMENTS

This work is financially supported by the Science and Technology Project of Electric Power Research Institute of State Grid Anhui Electric Power Co., Ltd. (No. SGAHDK00NYJS2200056), National Natural Science Foundation of China (No. 52107143).

CONFLICT OF INTEREST

The authors declare no potential conflict of interests.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

Shu, Y.B., Chen, W.J.: Research and application of UHV power transmission in China. High Volt. 3(1), 1–13 (2018). [DOI: https://dx.doi.org/10.1049/hve.2018.0003]