Power transformer grading ring field intensity optimization design method used at different altitudes

Abstract

The invention relates to a field intensity optimization design method for a grading ring of a power transformer at different altitudes, and belongs to the technical field of high voltage and insulation. According to the method, firstly, a parameter dynamic correction model of relative air density changing along with the altitude is constructed according to the relation of temperature and air pressure changing along with the altitude, then a grading ring corona inception field intensity calculation model based on an improved PEEK formula is established, and the grading ring corona inception field intensity is calculated according to the parameter dynamic correction model and the grading ring corona inception field intensity calculation model. Performing simulation design on the three-dimensional electric field of the transformer, and extracting spatial distribution of electric field intensity on the surface of the grading ring; and finally, carrying out grading ring electric field optimization design based on curvature radius optimization. According to the method, the influence of the air density changing along with the altitude, the corona starting mechanism and the overall electric field distribution characteristic of the transformer are comprehensively considered, and fine selection of the field intensity optimization control size parameters of the grading ring of the extra-high voltage transformer is achieved.

Description

Technical Field

[0001] This invention belongs to the field of high voltage and insulation technology, and relates to the design of external insulation structure of power transformers under different altitude backgrounds, and particularly to a method for optimizing the design of field strength of equalizing rings of power transformers under different altitudes. Background Technology

[0002] With the large-scale construction of ultra-high voltage (UHV) power transmission and transformation projects and the continuous increase in the voltage levels of large power transformers, the electrical stress on their external insulation structures has increased significantly. Problems such as local over-electric fields, corona discharge, and insulation aging have become increasingly prominent, becoming one of the important factors restricting the safe and stable operation of power transmission systems. In particular, compared with the same operating voltage and structural conditions in plain areas, the air density is lower in high-altitude, low-pressure areas, leading to a significant decrease in gas insulation strength and making transformers more susceptible to corona and flashover discharge faults. Therefore, conducting research on the optimized design of the external insulation structure of UHV and extra-high voltage power transformers is crucial.

[0003] Equalizing rings are typically installed at the connection between the transformer bushing and the tank to improve the electric field distribution at the end, reduce electric field distortion and tip effects, thereby improving the electrical strength and operational reliability of the external insulation. Equalizing rings are generally three-dimensional ring-shaped fittings, and their surface electric field distribution is closely related not only to the ring's own geometric parameters such as ring diameter, tube diameter, and installation height, but also to the combined influence of the surrounding layout and operating environment conditions. Therefore, the local electric field strength on the surface of the equalizing ring at different altitudes is difficult to accurately predict using simple empirical formulas.

[0004] In current engineering design practices, the selection of equipotential ring dimensions largely relies on empirical data and limited type test results. A common approach is to first determine the initial dimensions based on empirical structures in plains areas, and then adjust them according to altitude, converting them for voltage levels and creepage distances. While this method can meet the needs of some local projects, it mostly only provides discretization coefficients for a few typical altitude points, making it difficult to cover the continuous altitude range of 0–5000 m. Furthermore, simple empirical correction formulas cannot accurately reflect the actual electric field level in local high-field areas, making it difficult to quantitatively determine the design margin.

[0005] Regarding the impact of altitude, conventional methods typically employ relative air density or air pressure conversion to perform simple linear corrections to the electric field calculation results or the corona initiation field strength threshold. However, this approach often treats altitude as a static correction factor, failing to systematically incorporate changes in air density into the corona initiation mechanism and electric field distribution calculations. This makes it difficult to simultaneously meet the consistent design requirements of transformers with different voltage levels and structural forms across the entire altitude range. Furthermore, for three-dimensional fittings such as equalizing rings, the curvature differences at different locations on the surface are significant, making field strength control in local high-field regions particularly critical. Traditional methods struggle to accurately reflect this spatial non-uniformity.

[0006] In summary, existing transformer equalizing ring design methods generally suffer from problems such as inconsistent design standards and insufficiently accurate field strength verification under high-altitude ultra-high voltage and complex three-dimensional structural conditions. Therefore, there is an urgent need for an equalizing ring field strength optimization design method that can comprehensively consider changes in altitude environment, to guide the optimized design of the external insulation structure of ultra-high voltage transformers in different altitude regions. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a method for optimizing the field strength of the equalizing ring of power transformers at different altitudes. Targeting the external insulation design requirements of UHV transformers in the entire altitude range of 0–5000m, this method is based on a dynamic correction model of air density, uses the improved Peek formula as the core for calculating the halo field strength of the equalizing ring, and combines three-dimensional electric field finite element simulation and curvature radius optimization strategy to form a set of equalizing ring size optimization process that can directly guide engineering applications.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A method for optimizing the field strength of voltage equipotential rings in power transformers at different altitudes, comprising the following steps: S1. Based on the temperature and air density under standard sea level conditions, introduce the vertical temperature lapse rate, and construct a parameter dynamic correction model for relative air density as a function of altitude according to the relationship model between temperature and air density and altitude. S2. Introduce the calculation methods of principal curvature and Gaussian curvature of the annular section, and establish a calculation model of the halo field strength of the equal pressure ring based on the improved PEEK formula; S3. Based on the dynamic correction model of the parameters and the calculation model of the corona induction field strength of the equalizing ring, the three-dimensional electric field of the transformer is simulated and designed, and the spatial distribution of the electric field strength on the surface of the equalizing ring is extracted. S4. Using the inner and outer diameters and equivalent radius of curvature of the equalizing ring as design variables, the maximum electric field strength on the surface of the equalizing ring obtained from three-dimensional simulation as the evaluation index, and the target electric field strength not exceeding the safety margin coefficient of the halo field strength as the optimization objective, the electric field optimization design of the equalizing ring is carried out based on the optimization of the radius of curvature.

[0009] Furthermore, in step S1, the relationship between temperature and altitude is represented by the following model:

[0010] In the formula, Altitude Sea level reference temperature This represents the vertical temperature lapse rate. The relationship between air pressure and altitude can be represented by the following model:

[0011] In the formula, For reference air density at sea level, Standard gravitational acceleration, Let be the gas constant for dry air; from this, a dynamic correction model for the relative air density as a function of altitude is obtained. .

[0012] Furthermore, in step S2, a method for calculating the principal curvature and Gaussian curvature of the annular cross-section is introduced to uniformly map the inner and outer diameters of the equalizing ring to an equivalent radius of curvature, and to use the Gaussian curvature ( Using the electrode curvature parameter in the Peek formula, an improved Peek formula suitable for toroidal fittings is constructed, which is expressed as:

[0013] In the formula, and For polynomial parameters; The roughness coefficient reflects the surface condition of the equalizing ring fitting; This represents the relative air density at the current altitude. Let be the radius of curvature of the equalizing ring.

[0014] Furthermore, the radius of curvature of the equalizing ring is calculated as follows:

[0015] In the formula, and These are the curvatures corresponding to the inner and outer diameters of the equalizing ring, respectively, and they are calculated as follows:

[0016]

[0017] In the formula, and These are the inner and outer diameters of the equalizing ring, respectively.

[0018] Furthermore, in step S3, the three-dimensional electric field simulation model of the transformer established during the simulation process includes the transformer tank, bushings, equalizing rings, oil conservator, and leads. It can realistically reflect the geometric dimensions and layout of the equipment on site. During the simulation, the corresponding rated voltage or test voltage is applied to the ends of the high voltage, medium voltage and low voltage windings. The enclosure and neutral point are grounded, and an environmental boundary is set around the perimeter and zero potential is applied to simulate infinity. During the simulation, based on the dynamic correction model of air density, the relative permittivity of air is automatically adjusted according to the target altitude to realize the dynamic simulation of the electric field distribution around the transformer under different altitude environments.

[0019] Furthermore, in step S3, based on the established three-dimensional electric field simulation model of the transformer, the spatial distribution of the electric field intensity on the surface of the equalizing ring is obtained, including at least extracting the maximum field intensity value at the lower edge of the outer side of the ring, to provide electric field response data for subsequent size optimization.

[0020] Furthermore, in step S4, the constraint range of the design variables for the inner and outer diameters and equivalent curvature of the equalizing ring is expressed as follows:

[0021] In the formula, Used to adjust the constraint range; The evaluation method, which uses the maximum electric field intensity on the surface of the equalizing ring obtained from three-dimensional simulation as the evaluation index, is as follows:

[0022] In the formula, This represents the maximum electric field intensity on the surface of the equalizing ring obtained from the three-dimensional simulation. altitude The uniform pressure ring below generates a strong halo field. By iteratively adjusting the combination of inner and outer diameters, the corresponding maximum electric field strength value is obtained by repeatedly calling the three-dimensional electric field simulation model and comparing it with the halo field strength: if the maximum electric field strength is less than a certain proportion of the halo field strength, the combination is recorded as a feasible solution; if it is not satisfied, the geometric parameters are adjusted and the iteration continues. After multiple rounds of optimization, the recommended size of the equalizing ring is selected based on the required structural dimensions, material usage, and installation conditions, under the premise of satisfying the field strength constraint. This achieves field strength optimization design of the equalizing ring for a given transformer model and operating altitude.

[0023] Furthermore, in step S4, the optimization process specifically involves: 1) Determine the altitude and environmental conditions, and then apply the improved PEEK formula for that altitude; 2) Given Range and inner / outer diameter constraints; and determine the initial... and inner and outer diameter; 3) Determine the boundary conditions for transformer electric field simulation; 4) Calculate the maximum electric field intensity on the surface of the equalizing ring; 5) Judgment Is it true? If so, record it. If the inner and outer diameters are combined, proceed to step 6); otherwise, proceed directly to step 6). 6) Determine if the inner and outer diameter combinations have been traversed. If yes, proceed to step 7; otherwise, proceed to step 8. 7) Determine if traversal is required If yes, proceed to step 10; if no, proceed to step 9. 8) Replace the inner and outer diameter groups and return to step 4) to recalculate the maximum electric field strength on the surface of the equalizing ring; 9) Replacement And return to step 4) to recalculate the maximum electric field strength on the surface of the equalizing ring; 10) Obtain The minimum value was determined, and the optimal size of the equalizing ring was finally determined.

[0024] The beneficial effects of this invention are as follows: This invention integrates full-altitude air density correction, improved Peek halo field strength calculation, three-dimensional electric field simulation, and curvature radius optimization, and proposes a unified design process that covers the entire altitude range of 0 to 5000m and can be directly applied in engineering.

[0025] This invention introduces parameters such as the equivalent curvature and Gaussian curvature of the equalizing ring, comprehensively considering the influence of air density variations with altitude, the corona initiation mechanism, and the overall electric field distribution characteristics of the transformer. This enables precise selection of the dimensional parameters for optimizing the control of the electric field strength of the equalizing ring in ultra-high voltage transformers. This improves the accuracy of predicting the corona initiation electric field strength of thick-walled, high-curvature annular fittings, overcoming the limitations of traditional empirical formulas and point-based correction methods.

[0026] Furthermore, this invention can provide standard equalizing ring field strength and structural optimization technology for UHV transformers in different regions and at different voltage levels, which helps to improve the design efficiency and reliability of external insulation, reduce the risk of corona discharge and insulation failure, and provide technical support for the safe and reliable operation of UHV power transmission and transformation projects in high-altitude and complex environments.

[0027] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the overall process of the transformer equalization ring field strength optimization design method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the halo field strength-radius of curvature fitting curves at different altitudes according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the basic model of the three-dimensional electric field simulation model of the transformer according to an embodiment of the present invention, wherein, Figure 3 (a) is the overall model of the three-dimensional electric field simulation of the transformer. Figure 3 (b) is a partial enlarged view of the high-voltage side bushing and equalizing ring; Figure 4 This is a schematic diagram illustrating the size optimization process of the three-dimensional electric field simulation model of the transformer in an embodiment of the present invention; Figure 5 This is an example diagram showing the electric field simulation results of an ultra-high voltage transformer according to an embodiment of the present invention. Figure 5 (a) is an embodiment of the present invention when =95cm, Cloud map of the overall electric field distribution of a 1000 kV UHV transformer at a radius of 190 cm. Figure 5 (b) is an embodiment of the present invention when =95cm, Cloud map of the overall electric field distribution of the equalizing ring on the high-voltage side of a 1000 kV UHV transformer at a height of 190 cm. Detailed Implementation The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0029] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0030] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0031] Please see Figures 1-5This is a method for optimizing the field strength of the equalizing ring of power transformers at different altitudes.

[0032] Example This embodiment details the specific process of a method for optimizing the field strength of an equalizing loop in a power transformer at different altitudes. The overall steps are as follows: Figure 1 As shown, it includes: S1. Establish a parameter correction model for all altitude working conditions: First, considering the variation characteristics of meteorological parameters along the 0–5000 m altitude gradient, a quantitative relationship between altitude and gas density was established with reference to the 1976 standard atmospheric model. Using temperature and air density under standard sea-level conditions as a benchmark, a temperature vertical lapse rate was introduced to establish a model of temperature variation with altitude, as shown in Equation 1. Then, a model of air density variation with altitude was constructed by combining the temperature dynamic correction model, as shown in Equation 2. This yielded a dynamic correction model of relative air density variation with altitude, as shown in Equation 3.

[0033]

[0034] In the formula, The altitude is 0~5000m in this embodiment; For the sea level reference temperature, this embodiment uses 288.15K; The vertical temperature lapse rate is 0.0065 in this embodiment; For reference air density at sea level, this embodiment uses 1.225 kg / m³. 3 ; Standard gravitational acceleration, Let be the gas constant of dry air; in this embodiment, we take . 287.05 J / (kg·K), then calculate .

[0035] In this model, the air density correction coefficient under the corresponding operating conditions can be calculated by inputting the altitude of the operating location, and further coupled to the calculation of dielectric parameters and corona field strength to achieve unified correction for a continuous altitude range of 0 to 5000 m.

[0036] S2: Calculation of the halo field strength of the equalizing ring based on the improved PEEK formula: The traditional Peek formula is mainly designed for thin cylindrical conductors and is obtained by fitting under the condition of small radius of curvature and near two-dimensional structure. When directly applied to thick-walled three-dimensional equalizing ring structure, it cannot accurately reflect the comprehensive curvature characteristics of the ring section in different directions, resulting in a large error in the prediction of the halo field strength.

[0037] This invention introduces a method for calculating the principal curvature and Gaussian curvature of an annular cross-section, uniformly mapping the inner and outer diameters of the equalizing ring to an equivalent radius of curvature, and utilizing Gaussian curvature (… To replace the electrode curvature parameter in the traditional Peek formula, an improved Peek formula suitable for ring fittings is constructed, as shown in Equation 7. This formula, while retaining the original empirical formula structure, recalibrates the polynomial coefficients and considers factors such as fitting surface roughness, outdoor operating environment, and overload conditions, providing an analytical expression for the corona induction field strength of the equalizing ring under different altitude conditions.

[0038]

[0039]

[0040]

[0041] in, and These are the inner and outer diameters of the equalizing ring, respectively, in cm; and The corresponding curvature; Let be the radius of curvature of the equalizing ring; The halo field strength of the equalizing ring fitting at the current altitude is kV / cm; and For polynomial parameters; The roughness coefficient (0-1) is used to reflect the surface condition of the equalizing ring fitting. In this embodiment, it is taken as 0.7, taking into account the outdoor operating environment of the transformer and the overload ratio.

[0042] By conducting corona induction tests and numerical simulations on equalizing rings under various altitude conditions, the maximum surface electric field of equalizing rings with different combinations of inner and outer diameters was statistically analyzed and fitted with the corona induction electric field corresponding to the measured corona induction voltage. Figure 2 As shown, the polynomial parameters in the improved Peek formula are obtained, making the formula more applicable to a wide range of curvature radii and all altitude conditions.

[0043] S3: Constructing a three-dimensional electric field simulation model of a transformer: After obtaining the calculation model of the corona induction field strength of the equalizing ring, this invention further establishes a three-dimensional electric field simulation model of the external insulation system of the ultra-high voltage transformer, such as... Figure 3 As shown, Figure 3 (a) is the overall model of the three-dimensional electric field simulation of the transformer. Figure 3 (b) is a partial enlarged view of the high-voltage side bushing and equalizing ring. This model includes key components such as the transformer tank, bushing, equalizing ring, oil conservator, and leads, and accurately reflects the geometric dimensions and layout of the equipment on site.

[0044] In the simulation, the high-voltage, medium-voltage, and low-voltage windings are subjected to their respective rated or test voltage conditions. The transformer housing and neutral point are grounded, and a suitable environmental boundary is set around the perimeter, with zero potential applied to simulate infinity. By embedding the air density correction model established in the first step into the material parameter setting module, the simulation software can automatically adjust parameters such as the relative permittivity of air according to the target altitude, achieving dynamic simulation of the electric field distribution around the transformer under different altitude environments. Based on this three-dimensional electric field model, the spatial distribution of the electric field intensity on the surface of the equalizing ring can be obtained. The maximum field strength value of the most corona-prone areas, such as the lower edge of the outer side of the ring, is extracted, providing accurate electric field response data for subsequent dimensional optimization.

[0045] S4: Electric field optimization design of the equalizing ring based on radius of curvature optimization: After determining the voltage level and operating altitude of the target transformer, this invention first uses the improved Peek formula to calculate the corona induction field strength of the equalizing ring under the altitude conditions, and selects the constraint range of the inner and outer diameters of the equalizing ring based on engineering experience to ensure that the structural strength and installation conditions meet the requirements.

[0046] Subsequently, the inner and outer diameters and equivalent radius of curvature of the equalizing ring were used as design variables (constraint formulas are shown in Equations 8 and 9), the maximum field strength on the surface of the equalizing ring obtained from three-dimensional simulation was used as the evaluation index (as shown in Equation 10), and the optimization objective was to ensure that the target field strength does not exceed the safety margin coefficient of the halo field strength.

[0047]

[0048] In the formula, N is used to adjust the constraint range. In actual engineering, N can be changed according to specific requirements. In this embodiment, it is taken as 5. This represents the maximum electric field intensity on the surface of the equalizing ring obtained from the three-dimensional simulation. altitude The uniform pressure ring below generates a strong field.

[0049] By iteratively adjusting the combination of inner and outer diameters, the corresponding maximum electric field strength value is obtained by repeatedly calling the three-dimensional electric field simulation model and comparing it with the halo field strength. If the maximum electric field strength is less than a certain proportion of the halo field strength, the combination is recorded as a feasible solution; if it is not satisfied, the geometric parameters are adjusted and the iteration continues.

[0050] After multiple rounds of optimization, a parameter combination that is moderate in structural size, reasonable in material usage, and friendly in installation conditions, while satisfying the field strength constraint, was selected as the recommended size for the equipotential ring. This achieves field strength optimization design of the equipotential ring for a given transformer model and operating altitude. The optimization solution process is as follows: Figure 4 As shown, it specifically includes: 1) Determine the altitude and environmental conditions, and then apply the improved PEEK formula for that altitude; 2) Given Range and inner / outer diameter constraints; and determine the initial... and inner and outer diameter; 3) Determine the boundary conditions for transformer electric field simulation; 4) Calculate the maximum electric field intensity on the surface of the equalizing ring; 5) Judgment Is it true? If so, record it. If the inner and outer diameters are combined, proceed to step 6); otherwise, proceed directly to step 6). 6) Determine if the inner and outer diameter combinations have been traversed. If yes, proceed to step 7; otherwise, proceed to step 8. 7) Determine if traversal is required If yes, proceed to step 10; if no, proceed to step 9. 8) Replace the inner and outer diameter groups and return to step 4) to recalculate the maximum electric field strength on the surface of the equalizing ring; 9) Replacement And return to step 4) to recalculate the maximum electric field strength on the surface of the equalizing ring; 10) Obtain The minimum value was determined, and the optimal size of the equalizing ring was finally determined.

[0051] Compared with traditional empirical selection methods, the optimization process of this invention has clear criteria and repeatability, which facilitates engineering promotion and application.

[0052] Example 2 In this embodiment, to verify the effectiveness of the method of the present invention, a 1000 kV UHV transformer of type ODFPS-1000000 / 1000 is used as the object, and an operating environment at an altitude of 2000 m is selected as a typical working condition for calculation analysis. Based on literature review and relevant experimental data, the coefficients are calibrated by combining the improved Peek formula, and the expression for the halo field strength under the condition of 2000 m altitude is obtained (11):

[0053] According to the method of this invention, the air density correction coefficient at an altitude of 2000 m is first calculated using a full-altitude parameter correction model, and then introduced into the simulation of corona initiation field strength and electric field to achieve unified modeling of the thin air at high altitudes. Subsequently, a complete three-dimensional electric field model of the transformer is established. Considering structural details such as the tank, bushing, and equalizing ring, the rated voltage condition is applied and the electric field is solved to obtain the surface electric field distribution under the traditional equalizing ring size scheme. The results show that there is a significant local over-electric field at the lower outer edge of the equalizing ring in the original scheme, with the maximum field strength approaching or slightly exceeding the corona initiation field strength limit calculated using the traditional Peek formula, indicating a certain risk of corona discharge.

[0054] Based on this, using the inner and outer diameters of the equalizing ring as design variables, a curvature radius optimization strategy was employed to adjust the ring's dimensions. Through multiple rounds of iterative calculations, when the equivalent curvature parameter was approximately 136.1, the optimal dimensional parameters were found to be an inner diameter of 95 cm and an outer diameter of 190 cm. Figure 5 As shown, where, Figure 5 (a) is an embodiment of the present invention when =95cm, Cloud map of the overall electric field distribution of a 1000 kV UHV transformer at a radius of 190 cm. Figure 5 (b) is an embodiment of the present invention when =95cm, At 190cm, the overall electric field distribution cloud map of the equalizing ring on the high-voltage side of the 1000 kV UHV transformer shows that the maximum electric field strength on the surface of the equalizing ring is optimized to about 7.27 kV / cm, which is much lower than the corona initiation electric field strength of about 12.98 kV / cm calculated under the same altitude conditions, forming a significant safety margin.

[0055] The recommended dimensions obtained by this invention can serve as an important reference and verification basis for the design of equalizing ring structures of similar transformers in 1000 kV and 2000 m altitude power transmission projects, providing technical support for the long-term safe operation of UHV transformers in high-altitude areas.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the field strength of voltage equalization loops in power transformers at different altitudes, characterized in that: The method includes the following steps: S1. Based on the temperature and air density under standard sea level conditions, introduce the vertical temperature lapse rate, and construct a parameter dynamic correction model for relative air density as a function of altitude according to the relationship model between temperature and air density and altitude. S2. Introduce the calculation methods of principal curvature and Gaussian curvature of the annular section, and establish a calculation model of the halo field strength of the equal pressure ring based on the improved PEEK formula; S3. Based on the dynamic correction model of the parameters and the calculation model of the corona induction field strength of the equalizing ring, the three-dimensional electric field of the transformer is simulated and designed, and the spatial distribution of the electric field strength on the surface of the equalizing ring is extracted. S4. Using the inner and outer diameters and equivalent radius of curvature of the equalizing ring as design variables, the maximum electric field strength on the surface of the equalizing ring obtained from three-dimensional simulation as the evaluation index, and the target electric field strength not exceeding the safety margin coefficient of the halo field strength as the optimization objective, the electric field optimization design of the equalizing ring is carried out based on the optimization of the radius of curvature.

2. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 1, characterized in that: In step S1, the relationship between temperature and altitude is represented by the following model: In the formula, Altitude Sea level reference temperature This represents the vertical temperature lapse rate. The relationship between air density and altitude can be represented by the following model: In the formula, For reference air density at sea level, Standard gravitational acceleration, Let be the gas constant for dry air; from this, a dynamic correction model for the relative air density as a function of altitude is obtained. .

3. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 2, characterized in that: In step S2, a method for calculating the principal curvature and Gaussian curvature of the annular cross-section is introduced to uniformly map the inner and outer diameters of the equalizing ring to an equivalent radius of curvature, and to use Gaussian curvature ( Using the electrode curvature parameter in the Peek formula, an improved Peek formula suitable for toroidal fittings is constructed, which is expressed as: In the formula, and For polynomial parameters; The roughness coefficient reflects the surface condition of the equalizing ring fitting; This represents the relative air density at the current altitude. Let be the radius of curvature of the equalizing ring.

4. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 3, characterized in that: The radius of curvature of the equalizing ring is calculated as follows: In the formula, and The curvatures corresponding to the inner and outer diameters of the equalizing ring are respectively, and their calculation method is as follows: In the formula, and These are the inner and outer diameters of the equalizing ring, respectively.

5. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 3, characterized in that: In step S3, the three-dimensional electric field simulation model of the transformer established during the simulation process includes the transformer tank, bushings, equalizing rings, oil conservator, and leads. It can realistically reflect the geometric dimensions and layout of the equipment on site. During the simulation, the corresponding rated voltage or test voltage is applied to the ends of the high voltage, medium voltage and low voltage windings. The enclosure and neutral point are grounded, and an environmental boundary is set around the perimeter and zero potential is applied to simulate infinity. During the simulation, based on the dynamic correction model of air density, the relative permittivity of air is automatically adjusted according to the target altitude to realize the dynamic simulation of the electric field distribution around the transformer under different altitude environments.

6. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 5, characterized in that: In step S3, based on the established three-dimensional electric field simulation model of the transformer, the spatial distribution of the electric field intensity on the surface of the equalizing ring is obtained, including at least extracting the maximum field intensity value at the lower edge of the outer side of the ring, to provide electric field response data for subsequent size optimization.

7. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 6, characterized in that: In step S4, the constraint range of the design variables for the inner and outer diameters and equivalent curvature of the equalizing ring is expressed as follows: In the formula, Used to adjust the constraint range; The evaluation method, which uses the maximum electric field intensity on the surface of the equalizing ring obtained from three-dimensional simulation as the evaluation index, is as follows: In the formula, This represents the maximum electric field intensity on the surface of the equalizing ring obtained from the three-dimensional simulation. Altitude The equalizing ring below generates a strong halo field. By iteratively adjusting the combination of inner and outer diameters, the corresponding maximum electric field strength value is obtained by repeatedly calling the three-dimensional electric field simulation model and comparing it with the halo field strength: if the maximum electric field strength is less than the halo field strength by a certain proportion, the combination is recorded as a feasible solution; if it is not satisfied, the geometric parameters are adjusted and the iteration continues. After multiple rounds of optimization, the recommended size of the equalizing ring is selected based on the required structural dimensions, material usage, and installation conditions, under the premise of satisfying the field strength constraint. This achieves field strength optimization design of the equalizing ring for a given transformer model and operating altitude.

8. The method for optimizing the field strength of the voltage equalization loop of a power transformer at different altitudes according to claim 7, characterized in that: In step S4, the optimization process is as follows: 1) Determine the altitude and environmental conditions, and then apply the improved PEEK formula for that altitude; 2) Given Range and inner / outer diameter constraints; and determine the initial... and inner and outer diameter; 3) Determine the boundary conditions for transformer electric field simulation; 4) Calculate the maximum electric field intensity on the surface of the equalizing ring; 5) Judgment Is it true? If so, record it. If the inner and outer diameters are combined, proceed to step 6); otherwise, proceed directly to step 6). 6) Determine if the inner and outer diameter combinations have been traversed. If yes, proceed to step 7; otherwise, proceed to step 8. 7) Determine if traversal is required If yes, proceed to step 10; if no, proceed to step 9. 8) Replace the inner and outer diameter groups and return to step 4) to recalculate the maximum electric field strength on the surface of the equalizing ring; 9) Replacement And return to step 4) to recalculate the maximum electric field strength on the surface of the equalizing ring; 10) Obtain The minimum value was determined, and the optimal size of the equalizing ring was finally determined.

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