Research on the dynamic characteristics of electric field distribution of the ± 1100 kV Ultra high voltage converter transformer valve‐side bushing using weakly ionised gas conductance model

National Natural Science Foundation of China, Grant/Award Number: 51807045; The Science and Technology Project of State Grid Corporation of China, Grant/Award Number: SGLNDK00KJJS1900250; National Key Research and Development Program (China), Grant/Award Number: 2017YFB0902702 Abstract Ultra high voltage (UHV) converter transformer valve‐side bushings are the key equipment indirect current (DC) transmission projects, and are subjected to high voltage and large current with large number of harmonics simultaneously. The electric field distribution of converter transformer valve‐side bushings is time‐dependent under DC voltage, polarity reversal voltage and actual voltage waveforms, and the electric and temperature field are coupling with each other in actual operation. The dynamic characteristics of the surface charges and the electric field distribution of China's first � 1100 kV epoxy/paper – SF6 composite insulation converter trans former valve‐side bushing under 2 h DC withstand test voltage and polarity reversal voltage were analysed considering the natural ionisation, drifting, diffusion and recombination processes of positive and negative ions in SF6 gas and air. The time‐dependent electro‐thermal coupling field of the bushing under the actual voltage waveform in one cycle was obtained. The rationality of the simulation method adopted was verified through type tests of the UHV converter transformer valve‐side bushing. The simulation results of the paper can provide a theoretical foundation for the design of converter transformer valve‐ side bushings and it is of great significance to ensure the safe operation of converter stations.


| INTRODUCTION
Converter transformer valve-side bushings are located at the connection position of converter stations and alternating current (AC) line side systems, and are subjected to high voltage, large current and strong mechanical load simultaneously [1]. As the power grid voltage level increasing in China [2], in recent years, China's Yibin, Jinan, and Tianshan converter stations have occurred many explosion failures due to the breakdown of valve-side bushings caused by the distortion of local electric field posing a serious threat to the safety operation of power grid.
To promote the reliability of converter transformer valveside bushings, it is important to investigate the accurate timedependent electric field distribution. The typical time constant ε/σ of epoxy/crepe paper as the main insulation material of converter transformer valve-side bushings in which σ is the conductivity and ε is the permittivity is tens of hours to hundreds of hours which is too long compared to the voltage period of 0.02 s at 50 Hz. The slow interfacial polarisation process at power frequency voltage makes the free charges inside the composite insulation almost zero. Therefore, the AC electric field distribution at power frequency is σ-independent and is a steady process. However, it is a transient process of establishing the electric field when converter transformer valveside bushings are applied to direct current (DC) withstand test voltage, polarity reversal (PR) test voltage or actual operation voltage, and the dynamic characteristics of the charge accumulation process must be considered [3]. Furthermore, converter transformer valve-side bushings simultaneously carry high voltage whose main component is DC voltage and large current with high harmonic components under actual operation condition [4], and the resistivity of epoxy/paper material is varied with temperature. Therefore, to obtain the timedependent electric field of converter transformer valve-side bushings under actual operation working condition, the electrothermal coupling field of converter transformer valve-side bushings needs to be investigated.
To obtain the dynamic characteristics of the surface charge accumulation and the electric field distribution of converter transformer valve-side bushings, the gas conduction processes for SF 6 and air governed by drifting, diffusion, natural ionisation, and recombination of ions need to be considered [5]. However, related researches are rarely reported for the converter transformer valve-side bushing because it has a large size and complicate structure making the governing equations of weakly ionised gas conductance difficult to converge, and most related simulations are applied to gas insulated switchgear / gas insulated line (GIS or GIL) [6][7][8]. Yi Luo et al. [8] simulated the variation process of the basin-type insulator in GIS /GIL under PR voltage, and the generation, diffusion, drift and recombination processes of charge carriers were taken into account. B. Källstrand et al. [9] measured the electric field of a wall bushing with a probe and obtained that the transient DC electric field gets steady at about 10 6 s. However, the resistivity of air was set to be constant when simulating without considering the phenomenon of current saturation in gases. Mengna Sun et al. [1] simulated the PR process of a converter transformer bushing with different PR times. However, it did not consider the ionisation and recombination processes in SF 6 gas and air.
Furthermore, there is almost no literature on the research of the electro-thermal coupling field distribution of converter transformer valve-side bushings under the actual voltage waveform containing multiple harmonics and a certain temperature gradient. Wen Cao et al. [10] proposed a bushing core design method based on the life of materials and obtained the electrothermal field distribution at DC voltage. However, the paper did not consider the electric field distribution of the bushing under actual load condition. Xuandong Liu et al. [11] investigated the electro-thermal coupled field of the � 1100 kV converter valveside bushing under the high DC voltage of 982 kV and the high current condition, and obtained the effect of four factors on the electro-thermal coupled field of the � 1100 kV converter valveside bushing. However, the study did no*t show the variation process of the time-dependent electric field of the converter valve-side bushing under actual voltage waveform.
The dynamic characteristics of the surface charge accumulation and the electric field distribution of China's first � 1100 kV epoxy/paper-SF 6 gas composite insulation converter transformer valve-side bushing under 2 h DC withstand voltage and PR voltage were analysed in consideration of the drifting, diffusion, natural ionisation, and recombination processes of ions in SF 6 and air. The 3D electro-magnetic-thermal-flow coupled field of the bushing was obtained taking the heat conduction, convection and radiation into account. The timedependent electro-thermal coupling field of the bushing under the actual voltage waveform with high harmonic components and the current in temperature rise test was simulated. Finally, the type tests of the bushing were carried out. The study results are hoped to provide theoretical basis for the design and optimisation of converter transformer valve-side bushings.

| SIMULATION METHOD AND FUNDAMENTAL EQUATIONS
The detailed 3D-temperature field simulation method of converter transformer valve-side bushings is shown in our previous paper [12] and the method was not repeated in the paper. The time-dependent electric field simulation method considering the weakly ionised gas conductance model was described in detail in the paper.
The electric field of bushings under pure DC voltage or compound voltage can be regarded as the superposition of the electric field established instantaneously by the applied voltage (including the vacuum static electric field and the induced electric field created by polarised charges, the establishment time of the latter is negligible) and the slowly established electric field by free charges in space. Given the known free charge distribution, any transient electric field can be established based on Poisson equation to establish the relationship between electric field and charge density.
The charge accumulation physical processes of composite insulation systems like converter transformer valve-side bushings can be simulated through three submodules: (1) bulk charge accumulation due to the temperature gradient in solid insulation material volume; (2) charge accumulation in gas volume based on weakly ionised gas conductance model; (3) interface charge accumulation due to the discontinuity of material properties on both sides. The detailed governing equations are described in the following.
The electrostatic field is given by Equation (1) according to the Maxwell equations: The relationship between electric field and body charge based on Gauss's Law is, On the interface, there is, Current continuity equation is shown as Equation (4): where E is the electric field (V/m), φ is the potential in volts, σ is the surface charge density (C/m 2 ), ρ is the bulk charge density (C/m 3 ), ε is the permittivity and J is the current density (A/m 2 ). If the effect of uneven temperature distribution is taken into account, the material's permittivity and conductivity are not constant. Under the temperature gradient condition, the change of permittivity is negligible and can be regarded as constant, but for bulk conductivity, the variation range may span one or two orders of magnitudes. Therefore, due to the uneven distribution of the conductivity, the bulk charges will accumulate inside the solid materials. By combining the Ohm's law and Gauss's law into Equation (4) and assuming a constant permittivity, the transient equation of bulk charge density can be obtained:

| Interface charge accumulation
Studies have shown that there is a slightly conductive surface layer caused by intrinsic or surface states of the dielectric material, the scale of which is much smaller than the material itself, and its thickness is usually several hundred microns or less. Volpov [13] deduced the transient equation of the surface charge density according to the current continuity equation: where J 1n and J 2n are the normal components of current density, J τ is the angential component of current density, n is the normal direction, and τ is the tangential direction.
If the surface tangential current density obeys Ohm's law as well, Equation (7) can be shown as: Equation (7) establishes the relation among the surface charge density, the bilateral current density on interface and the surface tangential electric field. Therefore, Equation (7) can be used as an interface charge boundary condition to solve the interface (surface) charge density. It can be simplified as Equation (8) when the surface conductivity and the thickness were not considered in the paper as follows [13]:

| Weakly ionised gas conductance model
When there are ions, electrons, and other charged particles in the gas, it itself has conductivity. These carriers are usually generated by gas molecules under a strong electric field through impact ionisation or ionisation by high-energy cosmic rays, ultraviolet light, internal earth radiation, X-rays and other radiation [14]. And only the natural ionisation of gas molecules was considered in the paper. During the establishment of the electric field, the positive and negative ions move along the electric field lines under the action of coulomb force. Some of them recombine to form molecules during the movement, and the other finally reach the electrode surface. The movement of the ions that reach the electrode surface in the gas gap forms a current in the weakly ionised gas. In addition, the thermal diffusion movement of the ions under the action of the local concentration difference will also generate current.
Equation (9) gives the expression of the ion current density formed by the migration and diffusion of positive and negative ions in gas. Import Equation (9) into Equation (4), it is given by Equation (10) [15], Here, μ � is the charge mobility (m 2 /(V⋅s), D � is the diffusion coefficient (m 2 /s), dN/dt is the ionisation rate (IP/ [m 3 s]), and k is the combination coefficient (m 3 /s).
The relationship between the recombination rate and the charge mobility of ions is shown in Equation (11) according to [16] as the pressure is greater than 0.29 MPa: The diffusion coefficient for ions is defined by the Einstein equation [17] as: Here, k B is the Boltzmann constant k B ¼ 1.38 � 10 À 23 J/ K, e is the elementary charge e ¼ 1.6 � 10 À 19 C, and T is the temperature K.
The charge mobility μ � , the gas combination rate k and the diffusion coefficient D � of SF 6 gas are inversely proportional to the gas pressure, which is related to the formation of cluster ions at high pressure. The low field ion mobility of SF 6 gas at 0.1 MPa is 0.36 cm 2 /(V⋅s), and the average ionisation rate of SF 6 gas at 0.4 MPa at single-storey house is 32 IP/(cm 3 s) [15]. What's more, the ion mobility in SF 6 gas is varied with pressure as p À 1.25 [18]. So, the recombination and diffusion coefficient of SF 6 gas at 0.35 MPa are 2.7 � 10 À 7 cm 3 /s and 2.1 � 10 À 3 cm 2 /s, respectively, based on Equations (11) and (12), and the ionisation rate of SF 6 gas was set as 32 IP/(cm 3 s) in the paper. The WANG ET AL.
-3 mobility of the small cluster ions in air at standard atmosphere is 1.6 cm 2 /(V⋅s) [19]. According to [20], the ion-ion recombination coefficient which weakly depends on pressure at about 1 atmosphere is varied with ion temperature T i as 2 � 10 À 6 (300/ T i ) 1.5 , so the gas combination coefficient of air was set as 2 � 10 À 6 cm 3 /s in the paper. The ionisation rate of the air was set as 10 IP/(cm 3 s) according to [21]. The detailed simulation parameters for SF 6 and air are shown in Table 1.
It adopts open boundary conditions at interfaces as shown in Equation (13). On the parts of the boundary where fluid flows into the domain, the charge density flows into is 0 (the charges are completely repelled by the electrode with the same polarity). On the remaining parts, where fluid flows out of the domain, the normal component of the ion current density diffusion term is 0 (the charges are completely absorbed by the electrode with the opposite polarity)

| Stabilisation techniques
The underlying finite element discretisation method in COM-SOL Multiphysics is the Galerkin method. When discretising Equation (10) using the Galerkin method, it is well known that the resulting numerical problem becomes unstable for an element Peclet number (Pe) larger than one which is a measure of the relative importance of the convective effects compared to the diffusive effects. A large Péclet number indicates that the convective effects dominate over the diffusive effects.
In general, when the diffusion term exists, the numerical stability of the equation depends mainly on cell resolution. Therefore, increasing the cell density in the corresponding region can significantly improve the numerical oscillation phenomenon; however, the method also causes a large increase of the number of cells making it relatively less viable. In COMSOL, several techniques for handling numerical instabilities without the need for mesh refinement are available. They all have in common that they add terms to the transport equation. These terms introduce numerical diffusion that stabilise the solution including the Isotropic Diffusion, Streamline Diffusion, and Crosswind Diffusion.

| SIMULATION MODEL
In order to meet the requirements of no oil in the valve hall of DC transmission project, in recent years, ultra high voltage (UHV) converter transformer valve-side bushings of China generally adopt the epoxy/crepe paper-SF 6 composite insulation structure as shown in Figure 1. To reduce the temperature of cores, it adopts the double-pipe structure including the current-carrying conductor and the external conductor which is equipotential with the current-carrying conductor and not subjected to current load. The outdoor insulation is a hollow composite insulator, which is mainly composed of epoxy/glass fibre tube and silicon rubber sheath. The main inner insulation is epoxy impregnated paper core which is wrapped around the external conductor with multi-layer coaxial cylindrical aluminium foil plates from the zero-layer plate to the outermost plate, which effectively improves the insulation performance of the bushing. To reduce weight, SF 6 gas with pressure 0.35 MPa is filled inside the bushing. The outlet device at the tail position of core refers to the insulation connection structure between the valve-side winding lead wire and the bushing, and is mainly composed of shielding cover and oil/pressboard. It is closely matched with bushing to form a complex oil-paper barrier insulation system, which subjects severe electrical stress. The � 1100 kV converter transformer valve-side bushing of China is shown in Figure 2 and its technical data are given in Table 2.
To observe the changing law of the surface electric field of the composite insulator more clearly, the sheds of the silicon rubber sheath were omitted when simulating the electric field of the valve-side bushing in the paper as shown in Figure 3.
The electric field simulation model mainly consists of composite insulator (omitting the sheds), epoxy resin/crepe paper composite material (core), SF 6 gas, and the outlet device. As shown in Figure 1, the interface between epoxy/paper core and SF 6 gas is named as interface 1, the interface between SF 6 gas and epoxy/glass fibre tube is named as interface 2 and the interface between core and oil is named as interface 3.
The temperature of transformer oil is kept at 90°C and the temperature of the air environment of converter transformer valve-side bushings is kept at 50°C to get the most severe temperature distribution of converter transformer valve-side bushings when performing the temperature rise test [22], so the temperature of the outlet device was set to be constant with 90°C and the outlet device was neglected when simulating the temperature distribution of the bushing in the paper. The angle between the bushing and the ground was 12°in the simulation which was the same as the orientation of the bushing in the temperature rise test.

| SIMULATION RESULT AND DISCUSSION
To verify the rationality of omitting sheds, the surface electric field of the composite insulator under the 1 h power frequency withstand test voltage of 1495 kV was compared when there were sheds or not. The path was intercepted from the low voltage side to the high voltage side 1 mm away from the surface of the composite insulator as shown in Figure 4. It can be seen from Figure 5 that the surface electric field distribution curve of the composite insulator was a wavy shape before omitting the sheds. The electric field distribution curve after omitting the sheds was relatively smooth. Although the value was different, the changing law of the surface electric field was similar. What's more, the radial electric field of the core was not affected as shown in Figure 6, and the radial path was intercepted from the zero-layer plate to the outermost plate as shown in Figure 4. Therefore, omitting the sheds in the paper was reasonable.

| Time-dependent electric field under the DC voltage
When simulating the transient electric field under 2 h DC withstand test voltage, a step function voltage with amplitude 2060 kV was applied to the bushing. The relative dielectric constant and volume conductivity of solid and transformer oil insulating materials were set to be constant as shown in Table 3, and the influence of the surface conductivity was not considered. The gas simulation parameters are shown in Table 1.
Owing to the time constant of insulation materials is large, it takes a long time when the electric field of valve-side bushings changes from a transient capacitive distribution to a steady resistive distribution at DC voltage. Figure 7 compares the potential distributions of the �1100 kV converter transformer valve-side bushing at 0 s, 10 5 s and 3 � 10 6 s. The interface charge was zero at 0 s, so Equation (2) was Laplace equation form at 0 s. As shown in Figure 7(a), the equi-potential lines were natural transition along the structure of the bushing at 0 s because there was no order difference among the relative dielectric constants of the epoxy/glass tube, the sheath and the gas. The equi-potential lines were almost parallel to the surface when passing through the composite insulator at 3 � 10 6 s shown in Figure 7(b) because there was order of magnitude difference in conductivity among air, SF 6 gas and epoxy/glass tube which led to the large negative charge accumulation on the interface 2 playing a shield effect as shown in Figure 8. And it can be seen that the charge density on the interface 2 which was on the upper part of the outermost plate was negative and was increasing with time. The surface charges almost got steady at 3 � 10 6 s. Figure 9 shows the radial electric field of the epoxy/paper core as time changing from 0 s to 3 � 10 6 s. It can be seen that the radial electric field in the core almost got steady at about 1 � 10 6 s, and the field near the outermost plate which was gradually decreasing was lower than that near the zero-layer plate. What's more, the maximum radial electric field was appearing near the zero-layer plate which was gradually increasing from 10.8 kV/mm at 0 s to 12.9 kV/mm at 3 � 10 6 s. The surface electric field of the composite insulator with time changing is shown in Figure 10. According to the figure, the surface electric field value almost got steady at 3 � 10 6 s with the maximum value of 0.59 kV/mm (resistive distribution). Furthermore, the peak value was 1.10 kV/mm -5 (capacitive distribution) at initial time appearing at the middle position of the sheath which was near the end of the zero-layer plate, and, as time going on, the peak at the middle part of the composite insulator vanished and another peak value at the top of the composite insulator increased until 3 � 10 6 s. According to the IEC/IEEE 65700-19-03 standard, the voltage shall be held for 2 h for the DC applied voltage withstand test after which the voltage shall be reduced to zero within a period not exceeding 1 min. As can be seen from Figures 9 and 10, the electric field distribution of the converter transformer valve-side bushing at 2 h did not reach the stable state. The maximum radial electric field strength of the core was 12.3 kV/mm at 2 h, reaching 95% of the final steady-state value of 12.9 kV/mm. The surface electric field distribution of silicon rubber sheath at 2 h was almost the same as those at 0 s, but the maximum value was higher than the steady value at 3 � 10 6 s and the distribution was different with the steady state. Therefore, as mentioned above, the electric field of the bushing at 2 h under DC voltage is different from the steady electric field distribution.

| Time-dependent electric field under the PR voltage
The PR test voltage of the � 1100 kV converter transformer valve-side bushing is À 1594 kV (120 min)/þ 1594 kV (120 min)/À 1594 kV (90 min) as shown in Figure 11, and the PR process was completed within 2 min. The electric field distribution during the PR process is a superposition of the capacitive electric field distribution and the resistive electric field distribution. Applying the COMSOL Multiphysics Software, the transient process in consideration of the natural ionisation, drifting, diffusion and recombination processes of positive and negative ions in SF 6 gas and air was simulated. The simulation parameters are shown in Tables 1 and 3.
Since the same change law of the electric field distribution during the first and the second PR process, only the first PR process was analysed in detail. During the PR test process, the charges accumulated on the interface 1 increased from 0 s to 7200 s and the maximum charge density was about 1.1 � 10 À 6 C/m 2 as shown in Figure 12. The charge density was almost unchanged when the voltage polarity reversed from 7200 s to 7320 s, because the inversion time (120 s) was much smaller than the discharge time of the surface charges on the interface 1 when the polarity of the excitation voltage was reversed from negative to positive. Then, the charge density gradually F I G U R E 4 Path of the radial electric field of the core and the surface electric field of the composite insulator

F I G U R E 6
The radial electric field strength of epoxy/paper core with and without sheds decreased and the polarity reversed from 7320 s to 14,520 s. What's more, the charge density at 14,520 s when the voltage was 1594 kV was close to zero but not zero. The change law of the charge accumulation on interface 2 as shown in Figure 13 was similar with that on interface 1 because the order of conductivity magnitude of the epoxy/glass tube is almost the same with that of the core. According to Figure 14, the polarity of the charges accumulated on interface 3 for most of the regions was opposite to the voltage polarity and the density was much larger than that on interfaces 1 and 2. Furthermore, the interface charges had a bigger change during the PR process from 7200 to7320 s than that on interfaces 1 and 2. The charge density at 14,520 s when the voltage was 1594 kV was almost the same as the charge density at 7200 s. The reason is that due to the conductivity of the transformer oil is much larger than that of epoxy/crepe paper and epoxy/glass, the time constant of oil is much shorter, and the process of charge accumulation and dissipation is faster.  Figure 15 shows the radial electric field in the core as time going on. The radial electric field gradually transited from the capacitive distribution at 0 s to the resistive distribution with charges accumulating, and the maximum radial electric field was 9.9 kV/mm at 7200 s during the PR test process. The radial electric field value near the zero-layer plate gradually increased and the electric field near the outermost plate gradually decreased which was smaller than that near the zero-layer plate from 0 s to 7200 s. Although the charges on interface 1 were almost unchanged from 7200 s to 7260 s, the voltage polarity reversed at 7200 s and, as the voltage decreasing from 7200 s, the radial electric field strength became lower from 7200 s.

Epoxy
When the voltage polarity was reversed from negative to positive, the radial electric field changed from negative to positive and the radial electric field value near the outermost plate was larger than that near the zero-layer plate. It can be explained as follows: in dielectrics with linear parameters, the electric field at PR voltage can be regarded as the superposition of the resistive electric field E dc before reversing and twice of the capacitive electric field E ac with opposite polarity as shown in Equation (14) [23]. What's more, the DC radial electric field value near the outermost plate was smaller than that near the zero-layer plate at 7200 s at the voltage of À 1594 kV and the AC radial electric field near the outermost plate was larger than that near the zero-layer plate at the voltage of 1594 kV, so during the PR process, the radial electric field value E pr near the outermost plate was larger than the field near the zero-layer plate when the voltage polarity was reversed from negative to positive From the time 7320 s, as the charge accumulation decreasing and then the voltage polarity reversing, the radial electric field near the zero-layer plate gradually increased and the electric field near the outermost plate gradually decreased and transited to the resistive distribution until the time was at 14,520 s.
As shown in Figure 16, the electric field at the core tail position gradually increased from 0 s to 7200 s, then decreased during the voltage PR process from 7200 s to 7320 s and finally increased again when the electric field transited from the capacitance distribution to the resistance distribution. Figure 17 shows the electric field distribution along the oilpaper insulation system at key time points. According to the figure, the electric field inside oil gap was larger than that inside oil/pressboard at initial time because the relative permittivity of oil 2.2 is smaller than that of oil/pressboard 5.3. As the electric field transited from the capacitive distribution at 0 s to the resistive distribution, the electric field strength inside the oil decreased and the electric field increased inside the oil/pressboard because the conductivity of oil is larger than that of oil/ pressboard as shown in Table 1. There was a significant increase of the electric field inside the oil gap and a big decrease inside the oil/pressboard when the voltage completed the reverse process at 7320 s. Then, the electric field gradually transited to the resistive distribution again with time increasing from 7320 s to 14,520 s which was a little smaller than the that at 7200 s due to the accumulated charges during 0 s and 7200 s.
Similarly, the electric field increased significantly inside the oil gap when the voltage reversed from 1594 kV to À 1594 kV at 14,640 s, and the value was a little smaller than the electric field strength at 7320 s. Finally, the electric field gradually transited to a resistive distribution from 14,640 s to 20,040 s and the electric field at 20,040 s was a little smaller than that at 7200 s and 14,520 s. The maximum electric field intensity of the different mediums decreased with an increase of the PR time.
In order to obtain the variation of electric field strength with time changing inside the oil and the oil/pressboard, two key points inside the oil and pressboard, respectively, were chosen to observe and the electric field at the two key points was given as shown in Figure 18. As shown in the figure, the electric field strength inside the oil/pressboard increased from 0 s to 7200 s and reached the maximum value 23 kV/mm at 7200 s. What's more, the maximum electric field strength decreased with an increase of the PR time. The electric field strength inside the oil decreased from 0 s to 7200 s. During the PR process, the electric field strength inside the oil/pressboard gradually decreased and the electric field strength inside the oil had a jump from about 1 kV/mm to 9 kV/mm. Therefore, discharge, breakdown and other discharge accident are likely to occur inside oil gap during the voltage polarity reverse process.

| Time-dependent electro-thermal coupling field under the actual voltage wave-form
Converter transformer valve-side bushings are subjected to high voltage and large current loads simultaneously in actual operation conditions, and the electric and the thermal field are coupling with each other. Therefore, it is important to obtain the time-dependent electric field distribution of the �1100 kV UHV converter transformer valve-side bushing under the actual operating voltage waveform and high current in one cycle 0.02 s. The researched object �1100 kV UHV converter transformer valve-side bushing operates at the Y/Y connection position in the UHV valve hall of Guquan Station, Anhui, China. The black line in Figure 19 shows the actual operating voltage waveform of the bushing.
By performing Fourier transform on the actual voltage waveform, the voltage amplitudes at different frequencies were obtained. For the actual voltage waveform of the converter transformer valve-side bushing, the number of harmonic components can reach infinity. However, considering that the amplitude of the 50 harmonic component was very small, the maximum frequency in the Fourier analysis was 2500 Hz in this paper. The result is shown in Figure 20. It can be seen that the DC component of the Y/Y connection bushing was 975.0 kV, and the voltage peak of the 50 Hz component was 179.0 kV.
Considered that the electricity load and the environment temperature of valve halls at different times are different in actual projects, to get the most serious electric field distribution, the electro-thermal coupling field of the � 1100 kV UHV converter transformer valve-side bushing was simulated under the actual voltage waveform and the current of 5879 A in the F I G U R E 1 5 The radial electric field in the core as time going on F I G U R E 1 6 The variation of the electric field distribution with time at core tail position F I G U R E 1 7 The electric field distribution curves along the oil/ pressboard insulation system at key time points WANG ET AL.
-9 temperature rise test with the oil temperature of 90°C and the air environment temperature of 50°C. The dielectric loss in the epoxy/impregnated paper core was neglected due to the tanδ of the insulation material is low about 0.005 under 50 Hz. The temperature dependent of the conductivity of the epoxy/paper core is given by the following equation: The temperature distribution was obtained as shown in Figure 21 using the 3D electromagnetic-thermal-flow coupled field simulation method described in our previous paper [12]. It can be seen that the higher temperature zone was in the lower part of the bushing, and the temperature gradient inside the conductor and the core was larger. The maximum temperature of the bushing was 137.6°C inside the current-carrying conductor. The maximum temperature of the currentcarrying conductor was 124.4°C appearing at the lower part of the conductor because the temperature of the transformer oil was higher than that of the air side. Due to the air gap between the internal conductor and the external conductor which plays a role of heat insulation, the maximum temperature of the core appearing at the contact position with the external conductor was significantly reduced to 116.0°C, which satisfies the engineering requirements for the temperature value of epoxy insulation materials according to Section 4.8 in IEC 60137:2008. Figure 21(b) shows the flow velocity vector of the SF 6 on the cross section of the bushing with a maximum value of 0.1 m/s. Combined with the actual voltage waveform as shown in Figure 19 and the temperature field distribution as shown in Figure 21, the electro-thermal coupling field was obtained using the simulation method as described in Section 2. The red line and the blue line in Figure 19 are the radial electric field strength of the core near the outermost plate and near the zero-layer plate, respectively. It can be seen that the radial electric field in the core near the outermost plate was higher than that near the zero-layer plate in the actual operation of the valve-side bushing. And the radial electric field in the core reached its maximum value of 7.2 kV/mm at t ¼ 0.0032 s appearing near the outermost plate when the voltage reached  Figure 22(a). Owing to there was a temperature gradient inside the bushing core and the nonlinear variation of the conductivity of epoxy/crepe paper with temperature, the radial electric field near the conductor where temperature was high was lower than that near the flange where temperature was low and the radial electric field of the core reversed compared with the field when there was no temperature gradient inside the core. Figure 22(b) shows the axial electric field in the core at 0.0032 s. The lower axial field strength was higher than the upper axial field strength. What's more, the axial electric field near the outermost plate was larger than that near the zerolayer plate, and the maximum lower axial electric field was F I G U R E 2 1 The thermal-flow coupled field of the valve-side bushing (a) whole temperature, (b) SF 6 velocity, (c) current-carrying conductor temperature, and (d) core temperature F I G U R E 2 2 (a) Radial electric field and (b) axial electric field in the epoxy/paper core WANG ET AL. about 0.5 kV/mm which was below the control value 0.9 kV/ mm. Figure 23 shows the surface electric field distribution curves of the composite insulator at different time points. It can be seen that the maximum surface electric field was appearing at the upper part of the silicon rubber sheath and the distribution was similar with that of the steady electric field at DC voltage as shown in Figure 10 because the main component of the voltage waveform was DC voltage.

| THE TYPE TESTS OF THE ±1100 KV UHV CONVERTER TRANSFORMER VALVE-SIDE BUSHING
The type tests of the � 1100 kV UHV converter transformer valve-side bushing were carried out referred to IEC/IEEE 65700-19-03-2014 'Bushing for DC system' and IEC 60137:2008 'Bushing with AC voltage higher than 1000 kV'. The type test sites of the DC applied voltage withstand test, the PR test and the temperature rise test are shown in Figure 24. The test methods and results for the DC applied voltage withstand test, and PR test items are detailed in Table 4 and the bushing has passed all type tests.
As shown in Figure 24(b), the valve-side bushing was enclosed with an air cover with 16 m long and 2.1 m wide, and the bushing was placed inside the box by means of on-site assembly. The air environment was kept at 50°C, and the oil was kept at 90°C by heaters. After the ambient temperature was stable, the high current generator started working and the 5879 A AC test current was applied to the bushing. The temperature at key points was measured by T-type thermocouples. The test would be end when the temperature at the measuring points did not exceed 1°C within 1 h.
The bushing cannot be damaged when doing the temperature rise test, so T-type thermocouples cannot be installed through holes drilled inside the core and measuring points can only be set at the outside surface of the bushing as shown in Figure 25. As can be seen from Table 5, the maximum difference between the experimental result and the simulation result at measuring points was 7%. The simulation temperature at 4, 5, and 6 points was lower than the test result because the temperature of the air box in the actual temperature rise test cannot be accurately controlled to be uniform 50°C and the position near the heaters had a higher temperature. The simulation temperature at points 7 and 8 was higher than the test result because the seal at the end of the air cover was not tight during the temperature rise test. And the simulation results were closer to the test results in the oil. Overall, although there was a certain error between the test results and the simulation results, the error was small and the simulation method of the 3D temperature field of the bushing in the paper was verified reasonable.

| CONCLUSIONS
The dynamic characteristics of the surface charge accumulation and electric field distribution of China's first � 1100 kV epoxy/paper-SF 6 gas composite insulation converter transformer valve-side bushing under 2 h DC withstand voltage and PR voltage, were analysed, and the electro-thermal coupling field in one cycle under the actual voltage waveform was simulated taking the drifting, diffusion, natural ionisation, and recombination processes of ions in SF 6 and air into account, the main conclusions are as follows: 1. The electric field of the � 1100 kV converter transformer valve-side bushing considering the weakly ionised gas conductance model under the 2 h DC withstand test voltage got steady at about 3 � 10 6 s. The maximum radial electric field changed from 10.8 kV/mm at 0 s to 12.9 kV/ mm at 3 � 10 6 s. The peak value of the surface field of the composite insulator was 1.10 kV/mm at initial time appearing at the middle position of the sheath, and, as time going on, the peak at the middle part of the composite insulator was vanishing and another peak at the top of the composite insulator increased gradually until 3 � 10 6 s 2. During the PR test, the radial electric field of the core near the zero-layer plate gradually increased and the electric field near the outermost plate gradually decreased which was smaller than the value near the zero-layer plate from 0 s to 7200 s. When the voltage polarity reversed from negative to positive, the polarity of the radial electric field changed from negative to positive and the value near the outermost plate was larger than that near the zerolayer plate 3. During the PR test, the electric field strength inside the oil/ pressboard reached the maximum value of 23 kV/mm at 7200 s and dropped during the voltage polarity reverse process. However, the electric field strength inside oil decreased from 0 s to 7200 s, and it had a big jump from about 1 kV/mm to 9 kV/mm during the voltage polarity reverse process. Therefore, discharge, breakdown and other discharge accident are likely to occur inside oil gap during the polarity reverse process F I G U R E 2 3 The surface electric field distribution of the composite insulator 4. Under the actual voltage waveform and the most severe temperature distribution, the radial and axial electric field strength of the core reversed. The radial electric field of the core had the peak value of 7.2 kV/mm and the maximum lower axial electric field strength was about 0.5 kV/mm appearing near the outermost plate at t ¼ 0.0032 s in one cycle 5. The China's first � 1100 kV epoxy/paper-SF 6    -13