A parasitic energy capacitance analysis method of transformer air gap and related device

Abstract

The present invention discloses a method for analyzing the parasitic energy capacitance of a transformer air gap and a related device. The method comprises: applying the same voltage excitation to both sides of the primary and secondary windings of the transformer, with the voltage excitation being positively and negatively symmetrical about the transformer's centerline; solving the Laplace equation using the boundary voltage of a single air gap on the transformer's central magnetic pole as a boundary condition to obtain the electric potential at any position within the air gap; calculating the electric field strength of the air gap based on the electric potential, and calculating the electric field energy of the air gap based on the electric field strength; and calculating the parasitic capacitance of the air gap based on the electric field energy, thereby providing a basis for transformer design. The present invention addresses the problem that prior art techniques fail to consider the parasitic capacitance of the air gap and cannot accurately predict the capacitance of air gaps of different sizes and structures, which hinders the design of transformers that reduce parasitic capacitance.

Description

Technical Field

[0001] The present invention relates to the technical field of transformer design, and in particular to a parasitic energy capacitance analysis method of a transformer air gap and a related device. Background Art

[0002] In high-power applications, in order to achieve key functions such as power transmission, voltage conversion, electrical isolation and bidirectional energy flow, power electronic transformers have gradually become a research hotspot. They can replace the original huge industrial frequency transformers and have broad application prospects in locomotive traction, smart grids and new energy grid connection.

[0003] When a transformer operates at high power or high voltage, the magnetic flux density in the core increases significantly. Introducing an air gap in the core effectively increases magnetic resistance and reduces the core's permeability, allowing the flux density to vary over a wider range. This improves the core's resistance to saturation at higher currents, allowing for greater energy storage. However, excessively large air gaps can introduce electromagnetic interference (EMI), increase losses, and reduce the efficiency of the magnetic component. Due to the high electric field strength within the air gap in a transformer, significant electric field energy is stored within the gap, resulting in gap-related parasitic capacitance. In high-frequency circuits, the transformer's parasitic capacitance can act as a feedback path or, combined with stray inductance, form a resonant circuit, leading to parasitic oscillations. This can cause electromagnetic interference, reduce converter stability, limit the converter's operating frequency, and impact the efficiency and power density of the switching power supply. Because parasitic parameters affect the waveform quality and voltage oscillations of power electronic transformers, and thus the overall system transmission characteristics, accurate modeling of these parasitic parameters is essential.

[0004] While research on winding-related capacitance in magnetic components such as transformers and inductors is relatively mature, research on core- and air gap-related capacitance is less extensive. Existing transformer capacitance modeling focuses on the capacitance between windings and between the windings and the core, without considering the parasitic capacitance of the air gap. Furthermore, air gap capacitance cannot be accurately predicted for various sizes and structures, hindering transformer design efforts to minimize parasitic capacitance. Summary of the Invention

[0005] The present invention provides a method and related device for analyzing the parasitic energy capacitance of a transformer air gap, which is used to solve the problem that the existing technology does not take the parasitic capacitance of the air gap part into consideration and cannot accurately predict the air gap capacitance of different sizes and structures, which is not conducive to the design of reducing the parasitic capacitance of the transformer.

[0006] In view of this, a first aspect of the present invention provides a method for analyzing the parasitic energy capacitance of a transformer air gap, the method comprising:

[0007] Applying the same voltage excitation to both sides of the primary and secondary windings of the transformer, and the voltage excitation is positively and negatively symmetrical about the transformer neutral line;

[0008] The Laplace equation is solved with the boundary voltage of a single air gap on the central magnetic column of the transformer as the boundary condition to obtain the potential at any position in the air gap.

[0009] Calculating the electric field strength of the air gap according to the electric potential, and calculating the electric field energy of the air gap according to the electric field strength;

[0010] The parasitic capacitance of the air gap is calculated according to the electric field energy, so as to be used for designing the transformer.

[0011] Optionally, solving the Laplace equation using the boundary voltage of a single air gap on the central magnetic column of the transformer as a boundary condition to obtain the potential at any position in the air gap includes:

[0012] The Laplace equation is solved with the boundary voltages on the left and right sides of a single air gap on the central magnetic column of the transformer and the upper and lower boundary voltages of the air gap as boundary conditions to obtain the potential at any position in the air gap.

[0013] The process of solving the boundary voltages on the left and right sides of the air gap includes:

[0014] Assuming that the voltage difference between the primary and secondary windings of the transformer is △U, the boundary voltage equations on the left and right sides of the air gap are constructed and solved according to the voltage linear distribution law to obtain the boundary voltages on the left and right sides of the air gap;

[0015] The process of solving the upper and lower boundary voltages of the air gap includes:

[0016] For the cylindrical air gap, a two-dimensional plane coordinate system is established with the center of its bottom surface as the origin, the axial direction as the z-axis, and the radial direction as the r-axis.

[0017] In the transformer, the air gap radius is set to r0 and the air gap length is set to l g , set the air gap structure ratio to the ratio of radius to length r0 / l g , obtain the ratio r0 / l at different air gap structures g The lower boundary potential U L The relationship curve between (r) and radial position r is normalized to obtain the lower boundary potential U of the air gap. L (r) and the preset voltage U at point A A The ratio of r to l g The relationship curve of the ratio is processed and fitted to obtain the empirical formula for fitting the lower boundary voltage of the air gap and solve it to obtain the lower boundary voltage of the air gap, and the upper and lower boundary voltages are distributed according to the opposite exponential law to obtain the upper boundary voltage of the air gap.

[0018] Optionally, calculating the electric field strength of the air gap according to the electric potential, and calculating the electric field energy of the air gap according to the electric field strength, includes:

[0019] Calculating the electric field strength of the air gap according to the electric potential based on an electric field strength calculation formula;

[0020] The electric field strength calculation formula includes:

[0021] ;

[0022] Where, 、 are the electric field strengths in the r and z directions, is the gradient of the electric potential at any position in the air gap;

[0023] Calculating the electric field energy of the air gap according to the electric field strength based on the electric field energy calculation formula of the air gap;

[0024] The calculation formula of the electric field energy of the air gap is: ;

[0025] Where ε0 is the dielectric constant in vacuum, ε r is the relative dielectric constant of the air gap medium, r0 is the air gap radius, l g is the air gap length, is E(r, z).

[0026] Optionally, calculating the parasitic capacitance of the air gap according to the electric field energy includes:

[0027] Calculating the parasitic capacitance of the air gap according to the electric field energy based on a parasitic capacitance calculation formula;

[0028] Wherein, the parasitic capacitance calculation formula is:

[0029] ;

[0030] Where, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

[0031] A second aspect of the present invention provides a parasitic energy capacitance analysis system for a transformer air gap, the system comprising:

[0032] An excitation unit, configured to apply the same voltage excitation to both sides of the primary and secondary windings of the transformer, wherein the voltage excitation is positively and negatively symmetrical about the neutral line of the transformer;

[0033] The first calculation unit is used to solve the Laplace equation with the boundary voltage of a single air gap on the central magnetic column of the transformer as the boundary condition to obtain the potential at any position in the air gap;

[0034] a second calculating unit, configured to calculate the electric field strength of the air gap according to the electric potential, and calculate the electric field energy of the air gap according to the electric field strength;

[0035] The third calculation unit is used to calculate the parasitic capacitance of the air gap according to the electric field energy, so as to be used for transformer design.

[0036] Optionally, the first computing unit is specifically configured to:

[0037] The Laplace equation is solved with the boundary voltages on the left and right sides of a single air gap on the central magnetic column of the transformer and the upper and lower boundary voltages of the air gap as boundary conditions to obtain the potential at any position in the air gap.

[0038] The process of solving the boundary voltages on the left and right sides of the air gap includes:

[0039] Assuming that the voltage difference between the primary and secondary windings of the transformer is △U, the boundary voltage equations on the left and right sides of the air gap are constructed and solved according to the voltage linear distribution law to obtain the boundary voltages on the left and right sides of the air gap;

[0040] The process of solving the upper and lower boundary voltages of the air gap includes:

[0041] For the cylindrical air gap, a two-dimensional plane coordinate system is established with the center of its bottom surface as the origin, the axial direction as the z-axis, and the radial direction as the r-axis.

[0042] In the transformer, the air gap radius is set to r0 and the air gap length is set to l g , set the air gap structure ratio to the ratio of radius to length r0 / l g , obtain the ratio r0 / l at different air gap structures g The lower boundary potential U L The relationship curve between (r) and radial position r is normalized to obtain the lower boundary potential U of the air gap. L (r) and the preset voltage U at point A A The ratio of r to l g The relationship curve of the ratio is processed and fitted to obtain the empirical formula for fitting the lower boundary voltage of the air gap and solve it to obtain the lower boundary voltage of the air gap, and the upper and lower boundary voltages are distributed according to the opposite exponential law to obtain the upper boundary voltage of the air gap.

[0043] Optionally, the second computing unit is specifically configured to:

[0044] Calculating the electric field strength of the air gap according to the electric potential based on an electric field strength calculation formula;

[0045] The electric field strength calculation formula includes:

[0046] ;

[0047] Where, 、 are the electric field strengths in the r and z directions, is the gradient of the electric potential at any position in the air gap;

[0048] Calculating the electric field energy of the air gap according to the electric field strength based on the electric field energy calculation formula of the air gap;

[0049] The calculation formula of the electric field energy of the air gap is: ;

[0050] Where ε0 is the dielectric constant in vacuum, ε r is the relative dielectric constant of the air gap medium, r0 is the air gap radius, l g is the air gap length, is E(r, z).

[0051] Optionally, the third computing unit is specifically configured to:

[0052] Calculating the parasitic capacitance of the air gap according to the electric field energy based on a parasitic capacitance calculation formula;

[0053] Wherein, the parasitic capacitance calculation formula is:

[0054] ;

[0055] Where, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

[0056] A third aspect of the present invention provides a device for analyzing parasitic energy capacitance of a transformer air gap, the device comprising a processor and a memory:

[0057] The memory is used to store program code and transmit the program code to the processor;

[0058] The processor is configured to execute the steps of the parasitic energy capacitance analysis method of the transformer air gap as described in the first aspect according to the instructions in the program code.

[0059] A fourth aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium is used to store program code, and the program code is used to execute the parasitic energy capacitance analysis method of the transformer air gap described in the first aspect.

[0060] It can be seen from the above technical solutions that the present invention has the following advantages:

[0061] Traditional research on transformer parasitic capacitance focuses on winding-related capacitance, with limited attention paid to capacitance within the core. Air gaps in transformer cores are designed to improve the core's resistance to saturation, but the parasitic capacitance introduced by the air gap and the resulting interference are largely ignored. This paper provides a method for analytically calculating the capacitance of an air gap based on its structure, incorporating the capacitance of the air gap into the modeling of transformer parasitic parameters.

[0062] 2) Existing research on cylindrical nickel-zinc ferrite cores has proposed an analytical model for core energy capacitance based on the electric field boundary value problem. However, this model fails to consider that the air gaps distributed within the core may also store significant electric field energy, resulting in a non-negligible corresponding capacitance. This invention, based on the potential distribution patterns within the transformer, derives the boundary potential conditions for the air gaps within the core. By solving the boundary value problem for the air gaps, this method can determine their stored energy and capacitance, providing a reference for the design of power electronic transformers in high-power circuits. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0064] Figure 1 A schematic flow chart of a method for analyzing parasitic energy capacitance of a transformer air gap provided in an embodiment of the present invention;

[0065] Figure 2 A two-dimensional finite element model of a DC transformer with an air gap in the central magnetic column provided in an embodiment of the present invention;

[0066] Figure 3 The potential distribution and electric field intensity distribution diagram of the transformer obtained through finite element simulation provided in the embodiment of the present invention;

[0067] Figure 4 A diagram showing the relationship between the potential distribution of the core internal boundary path 1 (AD) and path 2 (ABCD) and the voltage excitation applied to the winding part provided in an embodiment of the present invention;

[0068] Figure 5 A graph showing the boundary voltage variation along path 1 and path 2 provided in an embodiment of the present invention;

[0069] Figure 6The ROZ plane coordinate system is established with the midpoint of the lower boundary of the air gap two-dimensional plane as the coordinate origin provided in the embodiment of the present invention;

[0070] Figure 7 The boundary potential U provided in the embodiment of the present invention L (r) and the voltage U at point A A The ratio of r0 to l g The relationship curve of the ratio;

[0071] Figure 8 Schematic diagram of data processing and fitting using the Curve Fitting Tool of MATLAB software provided in an embodiment of the present invention;

[0072] Figure 9 This is a flow chart of the parasitic energy capacitance analysis method of the transformer air gap provided in an embodiment of the present invention implemented in a computer through MATLAB programming;

[0073] Figure 10 The present invention provides a flow chart of a parasitic energy capacitance analysis system for a transformer air gap according to an embodiment of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, features, and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0075] See also Figure 1 , a method for analyzing the parasitic energy capacitance of a transformer air gap provided in an embodiment of the present invention includes:

[0076] Step 101: Apply the same voltage excitation to both sides of the primary and secondary windings of the transformer, and the voltage excitation is positively and negatively symmetrical about the transformer neutral line.

[0077] Step 102: Solve the Laplace equation using the boundary voltage of a single air gap on the central magnetic column of the transformer as a boundary condition to obtain the electric potential at any position in the air gap.

[0078] Step 103: Calculate the electric field strength of the air gap according to the electric potential, and calculate the electric field energy of the air gap according to the electric field strength.

[0079] Step 104: Calculate the parasitic capacitance of the air gap according to the electric field energy, so as to be used for transformer design.

[0080] In one embodiment, step 102 includes:

[0081] The Laplace equation is solved with the boundary voltages on the left and right sides of a single air gap on the central magnetic column of the transformer and the upper and lower boundary voltages of the air gap as boundary conditions to obtain the potential at any position in the air gap.

[0082] The process of solving the boundary voltages on the left and right sides of the air gap includes:

[0083] Assuming that the voltage difference between the primary and secondary windings of the transformer is △U, the boundary voltage equations on the left and right sides of the air gap are constructed and solved according to the voltage linear distribution law to obtain the boundary voltages on the left and right sides of the air gap;

[0084] The process of solving the upper and lower boundary voltages of the air gap includes:

[0085] For the cylindrical air gap, a two-dimensional plane coordinate system is established with the center of its bottom surface as the origin, the axial direction as the z-axis, and the radial direction as the r-axis.

[0086] In the transformer, the air gap radius is set to r0 and the air gap length is set to l g , set the air gap structure ratio to the ratio of radius to length r0 / l g , obtain the ratio r0 / l at different air gap structures g The lower boundary potential U L The relationship curve between (r) and radial position r is normalized to obtain the lower boundary potential U of the air gap. L (r) and the preset voltage U at point A A The ratio of r to l g The relationship curve of the ratio is processed and fitted to obtain the empirical formula for fitting the lower boundary voltage of the air gap and solve it to obtain the lower boundary voltage of the air gap, and the upper and lower boundary voltages are distributed according to the opposite exponential law to obtain the upper boundary voltage of the air gap.

[0087] In one embodiment, step 103 includes:

[0088] Based on the electric field strength calculation formula, the electric field strength of the air gap is calculated according to the electric potential;

[0089] The electric field strength calculation formula includes:

[0090] ;

[0091] Where, 、 are the electric field strengths in the r and z directions, is the gradient of the electric potential at any position in the air gap;

[0092] Based on the calculation formula of the electric field energy of the air gap, the electric field energy of the air gap is calculated according to the electric field strength;

[0093] Among them, the calculation formula of the electric field energy of the air gap is: ;

[0094] Where ε0 is the dielectric constant in vacuum, ε r is the relative dielectric constant of the air gap medium, r0 is the air gap radius, l g is the air gap length, is E(r, z), which is the electric field strength at any coordinate (r, z) in the air gap.

[0095] In one embodiment, step 104 includes:

[0096] Based on the parasitic capacitance calculation formula, the parasitic capacitance of the air gap is calculated according to the electric field energy;

[0097] Among them, the parasitic capacitance calculation formula is:

[0098] ;

[0099] Where, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

[0100] The following is a principle description of the parasitic energy capacitance analysis method of the transformer air gap provided by the present invention:

[0101] The following reference Figure 2 The transformer structure of this solution is described. Figure 2 This is a two-dimensional finite element model of a DC transformer with a central magnetic column and an air gap. The magnetic core is made of ferrite material, the side lengths of the rectangular vacuum region inside the magnetic core are l1 and l2, and the air gap length is l g The primary and secondary windings are evenly wound on both sides of the core with the same number of turns, and they mainly play an isolation role in high-power circuits. The same linear voltage excitation (-10~10V) is applied to both sides of the primary and secondary windings. The potential distribution and electric field strength distribution of the transformer are obtained through finite element simulation as follows Figure 3 、 Figure 4 As shown. Figure 3 It can be seen that the electric field intensity in the air gap is higher and a larger amount of electric field energy is stored. Figure 4 It can be seen that the potential distribution of the inner boundary path 1 (AD) and path 2 (ABCD) of the core is related to the voltage excitation applied to the winding part. Figure 4 Point A is the origin, Figure 5The graphs below show the boundary voltage variation along paths 1 and 2. The voltage distribution along both paths follows a linear pattern. Because the air gap is relatively small, the voltage at the gap boundary can be roughly assumed to follow the voltage distribution at the core boundary. Because the primary and secondary windings are applied with the same voltage, the boundary voltage distribution on both sides of the transformer core is identical.

[0102] The following uses the cylindrical air gap in the central magnetic column as an example to introduce the method for solving the parasitic capacitance of the air gap part.

[0103] like Figure 6 As shown, the ROZ plane coordinate system is established with the midpoint of the lower boundary of the air gap two-dimensional plane as the coordinate origin, where the air gap radius is r0 and the length is l g Since there is no free charge distribution in the air gap field, the next problem is to solve the Laplace equation for the air gap potential distribution:

[0104] (1)

[0105] Using the electric potential, the present invention can calculate the electric field energy and capacitance of the air gap. Assuming that the voltage difference between the primary and secondary windings is △U, the voltage equations at the left and right boundaries of the air gap can be obtained from the above voltage linear distribution law:

[0106] (2)

[0107] In the transformer, the air gap radius r0 is set to a fixed value, and the air gap length l is changed. g , to change its size structure, in different air gap structure ratio r0 / l g Simulation results are 40, 20, 10, and 5 respectively. Figure 6 The lower boundary potential U of the air gap shown L (r) and the voltage U at point A A The ratio of r0 to l g The relationship curve of the ratio is as follows Figure 7 The data is processed and fitted using the Curve Fitting Tool in MATLAB software, as shown below. Figure 8 As shown, the fitting empirical formula for the lower boundary voltage of the air gap is obtained as follows:

[0108] (3)

[0109] The potential at point A can be obtained from the voltage linear distribution relationship:

[0110] (4)

[0111] The root mean square error of the fitting curve is RMSE = 0.01553, and the fitting effect is excellent. Since the voltage excitation is symmetrically distributed between positive and negative, the voltage at the upper boundary of the air gap is -U L (r). For air gaps of different sizes and structures, the electric field distribution can be scaled to r0 / l g The unit air gap structure with the same ratio. The solution of the electric field boundary value problem is to solve the Laplace equation (1) using the boundary conditions (2) (3) to obtain the voltage distribution φ (r, z) in the air gap. The solution process is as follows:

[0112] make , transform the boundary conditions and problem into:

[0113] (5)

[0114] in, . Next we will solve the function , since the potential distribution equations on the left and right boundaries of the air gap are first-kind homogeneous boundary conditions of the Bessel function, the general solution to this problem is:

[0115] (6)

[0116] Where J0 and J1 are Bessel functions of the first kind, with orders of 0 and 2 respectively, and x n (0) is the nth positive zero point of J1, A0, B0, A n , B n is the coefficient of the corresponding term in the above formula. The coefficient is solved as follows:

[0117] (7)

[0118] therefore The final solution of φ(r,z) can be obtained by the above mathematical analytical method:

[0119] (8)

[0120] After finding the electric potential, the electric field strength in the r and z directions can be found by the following formula:

[0121] (9)

[0122] The electric field energy of the air gap W g for:

[0123] (10)

[0124] Where ε0 is the dielectric constant in vacuum, which is 8.854×10 -12 , ε ris the relative dielectric constant of the air gap medium, which is taken as 1. The parasitic capacitance C of the air gap g for:

[0125] (11)

[0126] Since the voltage difference between the primary and secondary windings is the same, the capacitance converted to the primary and secondary sides is the same. All the above analytical solutions can be implemented in a computer through MATLAB programming. The program flow chart is shown below. Figure 9 .

[0127] The embodiment of the present invention provides a method for analyzing the parasitic energy capacitance of a transformer air gap. 1) Based on the analytical method of the electric field boundary value problem, the boundary voltage of a single air gap on the central magnetic column of the transformer is used as the boundary condition to solve the Laplace equation, obtain the electric potential and field strength at any position in the air gap, and then calculate the electric field energy, and then solve the parasitic capacitance of the air gap part used to store energy. 2) During the analytical calculation, the same voltage excitation is applied to the primary and secondary windings of the transformer, and the excitation is positively and negatively symmetrical about the center line of the transformer, ensuring that the left and right boundary voltages in the two-dimensional air gap plane model are of the same linear distribution, and the upper and lower boundary voltages are of opposite exponential distributions. The present invention is applicable to columnar air gaps of different sizes in transformers, and can quickly predict the corresponding parasitic capacitance based on the structure of the air gap in the transformer, providing a reference for the design of reducing transformer parasitic parameters in power electronic high-power circuits.

[0128] The above is a parasitic energy capacitance analysis method of a transformer air gap provided in an embodiment of the present invention. The following is a parasitic energy capacitance analysis system of a transformer air gap provided in an embodiment of the present invention.

[0129] See also Figure 10 , a parasitic energy capacitance analysis system of a transformer air gap provided in an embodiment of the present invention includes:

[0130] The excitation unit 201 is used to apply the same voltage excitation to both sides of the primary and secondary windings of the transformer, and the voltage excitation is positively and negatively symmetrical about the transformer neutral line.

[0131] The first calculation unit 202 is configured to solve the Laplace equation using the boundary voltage of a single air gap on the central magnetic column of the transformer as a boundary condition to obtain the potential at any position in the air gap.

[0132] The second calculation unit 203 is configured to calculate the electric field intensity of the air gap according to the electric potential, and calculate the electric field energy of the air gap according to the electric field intensity.

[0133] The third calculation unit 204 is configured to calculate the parasitic capacitance of the air gap according to the electric field energy, so as to be used for transformer design.

[0134] Furthermore, an embodiment of the present invention also provides a parasitic energy capacitance analysis device for a transformer air gap, the device comprising a processor and a memory:

[0135] The memory is used to store program code and transmit the program code to the processor;

[0136] The processor is configured to execute the steps of the parasitic energy capacitance analysis method of the transformer air gap as described in the above method embodiment according to the instructions in the program code.

[0137] Furthermore, an embodiment of the present invention also provides a computer-readable storage medium, which is used to store program code, and the program code is used to execute the parasitic energy capacitance analysis method of the transformer air gap described in the above method embodiment.

[0138] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0139] In the several embodiments provided by the present invention, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0140] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0141] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0142] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the various embodiments of the method of the present invention. The aforementioned storage medium includes various media that can store program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0143] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for analyzing the parasitic energy capacitance of a transformer air gap, characterized in that: include: Applying the same voltage excitation to both sides of the primary and secondary windings of the transformer, and the voltage excitation is positively and negatively symmetrical about the transformer neutral line; The Laplace equation is solved with the boundary voltage of a single air gap on the central magnetic column of the transformer as the boundary condition to obtain the potential at any position in the air gap. Calculating the electric field strength of the air gap according to the electric potential, and calculating the electric field energy of the air gap according to the electric field strength; Calculating the parasitic capacitance of the air gap according to the electric field energy, thereby using it for transformer design; The method of solving the Laplace equation with the boundary voltage of a single air gap on the central magnetic column of the transformer as the boundary condition to obtain the potential at any position in the air gap includes: The Laplace equation is solved with the boundary voltages on the left and right sides of a single air gap on the central magnetic column of the transformer and the upper and lower boundary voltages of the air gap as boundary conditions to obtain the potential at any position in the air gap. The process of solving the boundary voltages on the left and right sides of the air gap includes: Assuming that the voltage difference between the primary and secondary windings of the transformer is △U, the boundary voltage equations on the left and right sides of the air gap are constructed and solved according to the voltage linear distribution law to obtain the boundary voltages on the left and right sides of the air gap; The process of solving the upper and lower boundary voltages of the air gap includes: For the cylindrical air gap, a two-dimensional plane coordinate system is established with the center of its bottom surface as the origin, the axial direction as the z-axis, and the radial direction as the r-axis. In the transformer, the air gap radius is set to r0 and the air gap length is set to l g , set the air gap structure ratio to the ratio of radius to length r0 / l g , obtain the ratio r0 / l at different air gap structures g The lower boundary potential U L The relationship curve between (r) and radial position r is normalized to obtain the lower boundary potential U of the air gap. L (r) and the preset voltage U at point A A The ratio of r0 to l g The relationship curve of the ratio is processed and fitted to obtain the empirical formula for fitting the lower boundary voltage of the air gap and solve it to obtain the lower boundary voltage of the air gap, and the upper and lower boundary voltages are distributed according to the opposite exponential law to obtain the upper boundary voltage of the air gap.

2. The parasitic energy capacitance analysis method of the transformer air gap according to claim 1, characterized in that: Calculating the electric field intensity of the air gap according to the electric potential, and calculating the electric field energy of the air gap according to the electric field intensity, comprises: Calculating the electric field strength of the air gap according to the electric potential based on an electric field strength calculation formula; The electric field strength calculation formula includes: ； Where, 、 are the electric field strengths in the r and z directions, is the gradient of the electric potential at any position in the air gap; Calculating the electric field energy of the air gap according to the electric field strength based on the electric field energy calculation formula of the air gap; The calculation formula of the electric field energy of the air gap is: ; Where ε0 is the dielectric constant in vacuum, ε r is the relative dielectric constant of the air gap medium, r0 is the air gap radius, l g is the air gap length, is E(r, z), which is the electric field strength at any coordinate (r, z) in the air gap.

3. The parasitic energy capacitance analysis method of the transformer air gap according to claim 1, characterized in that: Calculating the parasitic capacitance of the air gap according to the electric field energy includes: Calculating the parasitic capacitance of the air gap according to the electric field energy based on a parasitic capacitance calculation formula; Wherein, the parasitic capacitance calculation formula is: ； Where, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

4. A parasitic energy capacitance analysis system for a transformer air gap, characterized in that: include: An excitation unit, configured to apply the same voltage excitation to both sides of the primary and secondary windings of the transformer, wherein the voltage excitation is positively and negatively symmetrical about the neutral line of the transformer; The first calculation unit is used to solve the Laplace equation with the boundary voltage of a single air gap on the central magnetic column of the transformer as the boundary condition to obtain the potential at any position in the air gap; a second calculating unit, configured to calculate the electric field strength of the air gap according to the electric potential, and calculate the electric field energy of the air gap according to the electric field strength; a third calculation unit, configured to calculate the parasitic capacitance of the air gap according to the electric field energy, so as to be used for transformer design; The first computing unit is specifically configured to: The Laplace equation is solved with the boundary voltages on the left and right sides of a single air gap on the central magnetic column of the transformer and the upper and lower boundary voltages of the air gap as boundary conditions to obtain the potential at any position in the air gap. The process of solving the boundary voltages on the left and right sides of the air gap includes: Assuming that the voltage difference between the primary and secondary windings of the transformer is △U, the boundary voltage equations on the left and right sides of the air gap are constructed and solved according to the voltage linear distribution law to obtain the boundary voltages on the left and right sides of the air gap; The process of solving the upper and lower boundary voltages of the air gap includes: For the cylindrical air gap, a two-dimensional plane coordinate system is established with the center of its bottom surface as the origin, the axial direction as the z-axis, and the radial direction as the r-axis. In the transformer, the air gap radius is set to r0 and the air gap length is set to l g , set the air gap structure ratio to the ratio of radius to length r0 / l g , obtain the ratio r0 / l at different air gap structures g The lower boundary potential U L The relationship curve between (r) and radial position r is normalized to obtain the lower boundary potential U of the air gap. L (r) and the preset voltage U at point A A The ratio of r0 to l g The relationship curve of the ratio is processed and fitted to obtain the empirical formula for fitting the lower boundary voltage of the air gap and solve it to obtain the lower boundary voltage of the air gap, and the upper and lower boundary voltages are distributed according to the opposite exponential law to obtain the upper boundary voltage of the air gap.

5. The parasitic energy capacitance analysis system of the transformer air gap according to claim 4, characterized in that: The second computing unit is specifically configured to: Calculating the electric field strength of the air gap according to the electric potential based on an electric field strength calculation formula; The electric field strength calculation formula includes: ； Where, 、 are the electric field strengths in the r and z directions, is the gradient of the electric potential at any position in the air gap; Calculating the electric field energy of the air gap according to the electric field strength based on the electric field energy calculation formula of the air gap; The calculation formula of the electric field energy of the air gap is: ; Where ε0 is the dielectric constant in vacuum, ε r is the relative dielectric constant of the air gap medium, r0 is the air gap radius, l g is the air gap length, is E(r, z), which is the electric field strength at any coordinate (r, z) in the air gap.

6. The parasitic energy capacitance analysis system of the transformer air gap according to claim 4, characterized in that: The third computing unit is specifically configured to: Calculating the parasitic capacitance of the air gap according to the electric field energy based on a parasitic capacitance calculation formula; Wherein, the parasitic capacitance calculation formula is: ； Where, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

7. A parasitic energy capacitance analysis device for a transformer air gap, characterized in that: The device includes a processor and a memory: The memory is used to store program code and transmit the program code to the processor; The processor is configured to execute the parasitic energy capacitance analysis method of the transformer air gap according to any one of claims 1 to 3 according to the instructions in the program code.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium is used to store program code, and the program code is used to execute the parasitic energy capacitance analysis method of the transformer air gap according to any one of claims 1 to 3.

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