Characterization of electric field distribution in valve-side casing of 500 kV converter transformer considering AC and DC mixed voltage

The converter transformer, as one of the indispensable core devices in the ultra-high voltage direct current (UHVDC) transmission system, exhibits highly complex electric field distribution characteristics within the valve-side bushing. In-depth research into the electric field distribution characteristics and variation patterns of the valve-side bushing under both alternating current (AC) and direct current (DC) voltage conditions is crucial for ensuring the reliable operation of the transmission system. This study focuses on investigating the electric field distribution of the valve-side bushing under AC and DC voltage excitations. A full-scale finite element model of the valve-side bushing of the converter transformer is constructed using finite element simulation software for modeling and research purposes. The results indicate that the internal electric field distribution of the bushing is generally similar under both AC and DC voltage excitations. However, in the SF6-filled region, a steeper voltage drop is observed under DC excitation compared to AC. The space charges generated in the DC electric field due to field polarization have a significant impact on the distortion of the electric field on the inner and outermost layer electrode plates. These conclusions provide theoretical guidance for the insulation design of the valve-side bushing in converter transformers at the 500 kV voltage level and similar ratings.


Introduction
The location of the converter transformer is in the pivotal position of the DC transmission system, and once a failure occurs, it will cause great losses to the stable operation of the power grid [1][2] .The valveside bushing of the converter transformer, as one of the key components of the converter transformer, plays a role in mechanically supporting as well as improving the insulation of the electric field at the valve-side outlet end of the converter transformer.Converter transformer valve-side bushing working conditions are more complex, harsh operating conditions, because of its simultaneous exposure to AC and DC compound voltage [3] , resulting in frequent failures.Therefore, it is of great significance to explore the electric field distribution law of valve-side casing under mixed AC and DC voltage excitation for fault simulation study and casing insulation design [4] .
The converter transformer works under the DC transmission system, and its valve-side casing is connected to the converter valve.Side casing connected to the converter valve, the valve side casing is subjected to DC voltage and different frequency, phase, amplitude of the AC voltage superimposed by the AC/DC composite voltage [5] .In the related research, Li [6] proposed a strategy to improve the electric field distribution from the perspective of dielectric modification by adding graphene oxide nanoparticles to the epoxy resin, which is the main material of the capacitor core, and completing the dielectric modification by using nanocomposite materials.He et al. [7] established a casing model to explore the influence law of relevant factors such as the length and position of the nonlinear pressureaveraging layer on the electric field distribution of the casing, which reveals the potential application value of nonlinear composites in casing fabrication by systematically analysing and comparing the results of electric field distribution under different parameters.However, most of the existing studies focus on the material structure or separate DC and AC voltages on the casing electric field distribution characteristics of the study, and fail to fully consider the actual operation of the valve-side casing faced with mixed AC and DC voltage excitation, which is alone DC or AC voltage under the electric field distribution of a certain difference, and have an impact on the insulation characteristics.Therefore, it is necessary to study in depth the electric field distribution characteristics of valve-side bushings of UHV converter transformers under mixed AC and DC voltage excitation.
This research paper focuses on the simulation analysis of a converter valve-side casing model.It explores the electric field distribution characteristics of the valve-side casing when subjected to AC and DC voltage excitations.Additionally, it delves into the analysis of the insulating properties of the casing's internal medium.Furthermore, the study investigates the impact of space-charge electric fields formed within the casing on the primary electric field under DC voltage excitation.The research on the AC and DC electric field models of the 500 kV converter transformer's valve-side casing, as presented in this paper, holds significant importance in enhancing the uniformity of electric field distribution, reducing peak electric field values, and improving insulation properties.

Geometric modeling valve-side bushings for converter transformers
In this paper, the 500 kV converter transformer valve-side bushing is selected as the research object, and a simplified simulation model of UHV DC bushing is established.The model consists of components such as a conductive rod, SF6 gas, epoxy resin-impregnated paper capacitor core, insulating jacket, voltage equalising ring, and flange.The study focuses on the electric field distribution inside the casing on the valve side of the converter.In order to simplify the calculation process and improve the calculation speed of the model, as well as to ensure that the overall distribution of the electric field is not affected, the pressure-averaging cover, composite insulating jacket umbrella skirt and flange components outside the casing are simplified accordingly during the process.This simplification is intended to maintain the accuracy and feasibility of the model while reducing the computational complexity.
Figure 1 illustrates the comprehensive finite element model of the converter's valve-side bushing, developed based on detailed technical documentation and model drawings generously provided by the bushing manufacturer.This full-scale model accurately represents the critical components and dimensions of the valve-side bushing.
The total length of the casing is 4620 mm, which encompasses several key components.The conductive tube, measuring 4180 mm, forms the central structural element.Within the insulating oil, an equalization ball with a 120 mm radius is positioned to ensure even field distribution.The valve-side bushing also features a large umbrella skirt, measuring 74.55 mm, and a small umbrella skirt, measuring 49.5 mm, consisting of 26 pairs in total.The capacitor core pole plate is composed of 31 layers, each contributing to the bushing's overall electrical performance.The conductive tube pole plate, extending over a length of 2945 mm, further enhances the electric field distribution within the bushing.The end screen pole plate, spanning 1379 mm, adds to the complex interplay of components.Additionally, the oil end and air end extend over 1525 mm and 3095 mm, respectively, further influencing the electric field dynamics within the bushing.The valve side casing of this converter has a dry composite insulation structure in which the copper conducting tube is surrounded by epoxy resin cardboard.Ten layers of aluminium foil were uniformly selected in the epoxy resin pole plate to improve the radial electric field distribution and to distribute the voltage as uniformly as possible across the capacitor core insulation.In order to improve the insulating properties, the outer sheath was filled with sulfur hexafluoride gas as an insulating medium.In addition, the outer layer of the sleeve is wrapped with a silicone rubber insulating umbrella skirt to prevent creepage effects.In order to meet the requirements of structural strength, the flange of the casing is made of structural steel and the part of the casing below the flange is submerged in transformer oil.This design helps to maintain the stability and durability of the casing.
In terms of material parameter setting, it needs to be selected according to the specific engineering requirements and application environment.These parameters include the dielectric constant of the insulating material, the conductivity, and the properties of the gas-insulating medium.By adopting such a design and material parameter settings, the converter valve-side bushing can provide good insulation performance and electric field distribution uniformity to ensure the safe operation and reliability of the transformer.In addition, it can effectively prevent creepage effects and other insulation faults from occurring, thus improving the insulation level and overall performance of the transformer.Table 1 shows the physical parameters of each material in the finite element model.

Control equations for casing electric field calculations
The method of calculating the electric field distribution in the valve-side bushing of the converter transformer is based on Maxwell's equations that can be solved: 0 The equation of the intrinsic relationship between the field quantities is: where is the material conductivity and is the material dielectric constant.
Neglecting the time effect, the scalar potential φ in the AC and DC electric field of the casing on the valve side of the converter exists in the following equation: The solid insulating medium in the valve side casing of the converter is polarized by the charge under the action of a higher DC electric field, generating a space charge.For the space charge, the following equation exists: When subjected to DC voltage, the valve-side bushing of the converter transformer resides within an electrostatic field, and its electric field distribution is governed by the conduction current, unaffected by the material's dielectric constant.Conversely, in the presence of AC voltage, the valve-side bushing operates within an electric quasi-static field, where the material's dielectric constant becomes the decisive factor shaping the electric field distribution.This distribution can be obtained by solving the Poisson equation: In order to accurately reflect the AC/DC composite voltage condition of the casing to calculate the electric field strength in this case, it is necessary to superimpose the dielectric displacement field with the initially given steady-state conduction field, and then the governing equations of the electric field distribution are as follows: In summary, the following equation can be obtained: ∝  (7)   This equation includes the effects of displacement and conduction currents on the electric field, and problems in transient electric fields can be solved with it.

AC and DC electric field simulation calculation settings
The schematic diagram of each part of the geometric model of the valve-side casing of the converter is shown in Figure 2   For the dissection process of the finite element model, due to the large differences in the sizes of the various parts of the casing, when dissecting small-size regions such as the flange, a smaller mesh size should be used as much as possible to ensure the accurate modeling of the details.When dissecting large-size regions of the outside, such as the outside air of the casing, the mesh size can be appropriately increased in order to reduce the computational complexity.Such a grid dissection strategy helps to maintain the accuracy of the model and the efficiency of the calculation, and provides a useful reference for further academic research.
The geometric model of the converter valve side casing for simulation calculation is dissected into meshes, and different mesh dissecting conditions are set for different solution domains.In the highprecision computational domain, the mesh dissecting of the inner converter valve side casing is set to 6 mm, and in the low-precision computational domain, the mesh dissecting of the outer air of the converter valve side casing is set to 293 mm, to ensure the accuracy and improve the solution efficiency.The final mesh dissecting strategy can help maintain the model accuracy and computational efficiency, and reduce the complexity of calculation for further academic research.The final mesh splitting schematic is shown in Figure 3   High and low potentials are added to the converter valve-side bushing model as shown in Figure 4, where the conductive tube and voltage-averaging sphere are voltage-excited high potentials, while the outermost pole plate, the outer sheath of the pole plate, the transformer tank shell, and the flanges are grounded low potentials.In the AC electric field, the AC voltage with a frequency of 50 Hz continuously charges and discharges the internal electric field of the casing capacitor core on the valve side of the converter, making it difficult to form the electric field of the space charge, only the role of the space charge in the DC field is considered.In order to consider the effect of space charge on the distribution of the DC electric field, five layers are selected as the suspended electrodes for applying space charge in the 31layer pole plate with medium spacing, which is shown schematically in Figure 5.

Characteristics of casing potential distribution on valve side of converter under AC and DC excitation
Based on the finite element electromagnetic simulation calculation software Ansys Maxwell on the above converter valve side casing geometric model and parameter settings for simulation calculations, the valve side casing in the AC excitation and DC excitation potential, electric field strength distribution is obtained as shown in Figures 6 and 7 below.
Obviously, the electric field inside the casing is approximately the same under AC and DC voltages.The high potentials are mainly distributed on the central conducting tube and the equipotential sphere, while the low potentials are distributed on the terminal shielding, the flange and the tank casing, which is consistent with the potential excitation applied in Figure 4.The metal plate of the capacitor chip experienced a radial potential change from high to low in both AC and DC cases.However, there is still some difference in potential distribution between AC and DC, which is especially noticeable in the SF6 region.The potential is significantly higher in the SF6 region at DC compared to AC, especially in the region near the helmeted part at the top of the casing.
Among them, it can be seen that the capacitor core epoxy resin pole plate with the aluminum foil therein improves the electric field distribution between the casing conductive tube and the grounded end screen, which makes the voltage drop more uniform and serves as an insulation.The casing on the valve side of the converter transformer operates under various conditions, including exposure to both AC and DC voltage excitations simultaneously.When subjected to industrial frequency AC voltage, the internal electric field distribution within the valve side casing primarily depends on the dielectric constant of the insulating material.In this case, the electric field is distributed in a capacitive manner.On the other hand, when the valve side casing experiences DC voltage excitation, the electric field distribution is primarily influenced by the conductivity of the insulating medium, resulting in a resistive distribution of the electric field.
In order to analyze in detail the difference in the potential distribution in the SF6 region under AC and DC conditions, a section of the casing along the axial direction as shown in Figure 8 is selected as a straight-line region.Its lower end is connected to the edge of the terminal shielding plate, and its upper end is connected to the helmet-shaped part at the top of the casing.As a result, the potential distribution of SF6 starts from 0 and gradually increases up to 500 kV in both AC and DC cases, making the contrast between AC and DC potential distributions very obvious.
Figure 8 illustrates the potential distribution within the sulfur hexafluoride-filled region in the tail section of the converter's valve-side casing under both AC and DC excitations.It's evident that the voltage drop within the sulfur hexafluoride region is more pronounced when exposed to a DC electric field, while under the influence of an AC field, the voltage dispersion is more extensive.This phenomenon can be attributed to the relationship between potential distribution and material properties.Under AC voltage, potential distribution follows a capacitive pattern and is closely tied to the material's dielectric constant.Sulfur hexafluoride exhibits a relative dielectric constant similar to that of other materials, leading to a more evenly distributed voltage drop within the AC field.
Conversely, under DC voltage, potential distribution is influenced by electrical conductivity.Sulfur hexafluoride possesses extremely low conductivity, resulting in a resistive potential distribution in the DC field.This leads to the concentration of high potential in the upper region of the casing, primarily occupied by sulfur hexafluoride, where the voltage drop is steeper.In the sulfur hexafluoride region, the potential is also concentrated, bearing a more pronounced voltage drop within the AC field.This concentrated potential in the area experiences a steep voltage drop, particularly near the casing's side, resulting in high insulation pressure.

Characteristics of casing field strength distribution at valve side of converter under DC excitation
Figure 9 depicts a cloud diagram illustrating the distribution of electric field strength within the converter's valve-side casing under the influence of DC voltage excitation.When subjected to DC voltage excitation, the concentration of electric field intensity within the casing is primarily observed in the core pole plate of the capacitor and along the periphery of the equalizing sphere.This distribution pattern serves as a reflection of the insulation performance of the internal insulating components, contributing to the enhancement of electric field strength distribution within the casing.Within the core pole plate of the capacitor, the highest electric field strength is found near the innermost pole plate adjacent to the central conductive tube.Furthermore, an extended region of higher electric field strength is observed at the tip of the core pole plate, gradually diminishing in strength as it extends radially outward.

Conclusions
This research explores the electric field distribution characteristics of the 500 kV converter transformer's valve-side casing through simulations involving both AC and DC electric fields.The findings and conclusions derived from these simulations are as follows: (1) In the context of a cylindrical coordinate system, the electric field surrounding the valve-side casing of the converter transformer, when subjected to both AC and DC conditions, exhibits characteristics of an electric quasi-static field.Under AC electric field conditions, the primary influencing factor on the internal electric field distribution is the dielectric constant of the insulating material.This results in an electric field distribution pattern that adheres to a capacitive model.In contrast, when exposed to DC voltage, the main determinant shaping the internal electric field distribution is the conductivity of the insulating medium.In this scenario, the electric field predominantly follows a resistive distribution pattern.(2) Under DC voltage excitation, the voltage drop is steeper in the area filled with sulfur hexafluoride at the end of the casing on the valve side of the converter, and the design of the casing needs to pay attention to the insulating property at the edge of the sulfur hexafluoride sheath under the DC working condition.
The AC and DC electric field model presented for the 500 KV converter transformer's valve-side casing in this study holds theoretical significance in guiding the design of insulation at this voltage level.It plays a pivotal role in enhancing the uniformity of electric field distribution within the casing, diminishing peak electric field values, and bolstering overall insulation performance.Additionally, this research introduces fresh perspectives and methods for further exploration and practical application in relevant fields.

Figure 1 .
Figure 1.Finite element model of the converter transformer valve-side bushing.The valve side casing of this converter has a dry composite insulation structure in which the copper conducting tube is surrounded by epoxy resin cardboard.Ten layers of aluminium foil were uniformly selected in the epoxy resin pole plate to improve the radial electric field distribution and to distribute the voltage as uniformly as possible across the capacitor core insulation.In order to improve the insulating properties, the outer sheath was filled with sulfur hexafluoride gas as an insulating medium.In addition, the outer layer of the sleeve is wrapped with a silicone rubber insulating umbrella skirt to prevent creepage effects.In order to meet the requirements of structural strength, the flange of the casing is made of structural steel and the part of the casing below the flange is submerged in transformer oil.This design helps to maintain the stability and durability of the casing.In terms of material parameter setting, it needs to be selected according to the specific engineering requirements and application environment.These parameters include the dielectric constant of the insulating material, the conductivity, and the properties of the gas-insulating medium.By adopting such a design and material parameter settings, the converter valve-side bushing can provide good insulation performance and electric field distribution uniformity to ensure the safe operation and reliability of the transformer.In addition, it can effectively prevent creepage effects and other insulation faults from occurring, thus improving the insulation level and overall performance of the transformer.Table1shows the physical parameters of each material in the finite element model. below:

Figure 2 .
Figure 2. Detailed structural diagram of plates, flanges, outer sheath and outer insulation umbrella skirt of each layer of rheological valve-side bushing model. below.

Figure 3 .
Figure 3. Model grid division of the internal computing domain (left) and external air computing domain (right) of the valve-side bushing of the converter transformer.

Figure 4 .
Figure 4. Schematic diagram of high and low potentials of valve-side bushing of converter transformer.

Figure 5 .
Figure 5. Schematic diagram of space charge setup on capacitor core plate.

Figure 6 .
Figure 6.Potential distribution of the valve-side bushing of a converter under AC voltage excitation.

Figure 7 .
Figure 7. Potential distribution of the valve-side bushing of a converter under DC voltage excitation.

Figure 8 .
Figure 8. Voltage drop of sulfur hexafluoride under AC and DC voltage excitation.

Figure 9 .
Figure 9. Electric field intensity distribution of the valve-side bushing of a converter transformer under DC voltage excitation.

Table 1 .
Physical parameters of each material in the finite element model.