Parasitic energy capacitance analysis method of transformer air gap and related device

Abstract

The invention discloses a parasitic energy capacitance analysis method for a transformer air gap and a related device, and the method comprises the steps: applying the same voltage excitation to the two sides of a primary winding and a secondary winding of a transformer, and enabling the voltage excitation to be in positive and negative symmetry with respect to the center line of the transformer; solving the Laplacian equation by taking the boundary voltage of a single air gap on a central magnetic column of the transformer as a boundary condition to obtain the potential of any position in the air gap; calculating the electric field intensity of the air gap according to the potential, and calculating the electric field energy of the air gap according to the electric field intensity; and calculating the parasitic capacitance of the air gap according to the electric field energy so as to design the transformer. The method solves the problems that the parasitic capacitance of the air gap part is not considered in the prior art, and the air gap capacitance of different sizes and structures cannot be accurately predicted, so that the design of reducing the parasitic capacitance of the transformer is not facilitated.

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 the transformer works under high power or high voltage conditions, the magnetic flux density in the core will increase significantly. By setting an air gap in the core, the magnetic resistance can be effectively increased, the magnetic permeability of the core can be reduced, and the magnetic flux density can be changed in a higher range, so as to achieve the anti-saturation performance of the core under a larger current, thereby allowing more energy to be stored. However, when the air gap is too large, it may cause the introduction of electromagnetic interference and increase the loss, thereby reducing the working efficiency of the magnetic component. Due to the high electric field strength inside the air gap in the transformer, the air gap stores non-negligible electric field energy, thereby forming parasitic capacitance related to the air gap. The parasitic capacitance of the transformer in the high-frequency circuit may act as a feedback path, or combine with the stray inductance to form a resonant circuit, resulting in parasitic oscillation, thereby causing electromagnetic interference, reducing the stability of the converter, limiting the operating frequency of the converter, and affecting the efficiency and power density of the switching power supply. Since parasitic parameters affect the waveform quality and voltage oscillation of the power electronic transformer, and thus affect the overall system transmission characteristics, it is necessary to model such parasitic parameters more accurately.

[0004] At present, the research on winding-related capacitance in magnetic components such as transformers and inductors has been relatively mature at home and abroad, but there is less research on core and air gap related capacitance. The existing transformer capacitance modeling focuses on the capacitance between windings and the capacitance between windings and cores, without considering the parasitic capacitance of the air gap part, 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. Summary of the invention

[0005] The present invention provides a method for analyzing the parasitic energy capacitance of a transformer air gap and a related device, which are used to solve the problem that the prior art 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 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 neutral line of the transformer;

[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 the design of the transformer.

[0011] Optionally, 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:

[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, constructing and solving the boundary voltage equations on the left and right sides of the air gap according to the voltage linear distribution law, and obtaining 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 the bottom circle as the origin, the axial direction as the z-axis direction, and the radial direction as the r-axis direction;

[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 boundary voltage of the air gap is obtained by taking the upper and lower boundary voltages as the opposite exponential distribution law.

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

[0020] Among them, the electric field strength calculation formula includes:

[0021] ;

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

[0023] Based on the electric field energy calculation formula of the air gap, the electric field energy of the air gap is calculated according to the electric field strength;

[0024] Wherein, 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] Based on a parasitic capacitance calculation formula, the parasitic capacitance of the air gap is calculated according to the electric field energy;

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

[0029] ;

[0030] In the formula, 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, used for 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 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 calculation 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 the design of the transformer.

[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, constructing and solving the boundary voltage equations on the left and right sides of the air gap according to the voltage linear distribution law, and obtaining 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 the bottom circle as the origin, the axial direction as the z-axis direction, and the radial direction as the r-axis direction;

[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 boundary voltage of the air gap is obtained by taking the upper and lower boundary voltages as the opposite exponential distribution law.

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

[0044] Based on an electric field strength calculation formula, the electric field strength of the air gap is calculated according to the electric potential;

[0045] Among them, the electric field strength calculation formula includes:

[0046] ;

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

[0048] Based on the electric field energy calculation formula of the air gap, the electric field energy of the air gap is calculated according to the electric field strength;

[0049] Wherein, 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] Based on a parasitic capacitance calculation formula, the parasitic capacitance of the air gap is calculated according to the electric field energy;

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

[0054] ;

[0055] In the formula, 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 parasitic energy capacitance analysis device 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 used 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] 1) In the traditional research on parasitic capacitance of transformers, the focus is on the capacitance related to the winding, and the research on the capacitance inside the magnetic core is limited. The purpose of opening an air gap in the magnetic core of the transformer is to improve the anti-saturation performance of the magnetic core, while ignoring the parasitic capacitance introduced by the air gap and the interference caused by it. The present invention provides a method for analytically calculating the capacitance of the air gap according to its structure, and incorporating the capacitance of the air gap into the modeling of the parasitic parameters of the transformer.

[0062] 2) In the existing research on cylindrical nickel-zinc ferrite cores, an analytical model of core energy capacitance was proposed based on the electric field boundary value problem, but it did not take into account that the air gaps distributed in the core may also store a considerable amount of electric field energy, and the corresponding capacitance cannot be ignored. The present invention can derive the boundary potential conditions of the air gap in the core in combination with the potential distribution law in the transformer, and solve its stored energy and capacitance on the basis of solving the air gap boundary value problem, 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative labor.

[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 plane finite element model of a DC transformer with a central magnetic column and an air gap provided in an embodiment of the present invention;

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

[0067] Figure 4 A relationship diagram between the potential distribution of the core internal boundary path 1 (AD) and the 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 variation of the boundary voltage 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 two-dimensional plane of the air gap as the coordinate origin provided in the embodiment of the present invention;

[0070] Figure 7 is 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 A schematic diagram of processing and fitting data by using the Curve Fitting Tool tool of MATLAB software provided in an embodiment of the present invention;

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

[0073] Fig.10 The present invention is a flowchart of a parasitic energy capacitance analysis system for a transformer air gap provided in 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 creative work are within the scope of protection of the present invention.

[0075] See also Figure 1 , a parasitic energy capacitance analysis method 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 neutral line of the transformer.

[0077] Step 102: 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.

[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 the design of the transformer.

[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 the bottom circle as the origin, the axial direction as the z-axis direction, and the radial direction as the r-axis direction;

[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 boundary voltage of the air gap is obtained by taking the upper and lower boundary voltages as the opposite exponential distribution law.

[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] Among them, the electric field strength calculation formula includes:

[0090] ;

[0091] In the formula, , are the electric field strengths in the r and z directions, respectively, 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] In the formula, 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 scheme is described. Figure 2 This is a two-dimensional plane finite element model of a DC transformer with an air gap in the central magnetic column. The magnetic core is made of ferrite material, the side lengths of the rectangular vacuum domain inside the magnetic core are l1 and l2 respectively, and the air gap length is l g The primary and secondary windings are evenly wound on both sides of the magnetic core with the same number of turns, which 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 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 magnetic core is related to the voltage excitation applied to the winding part. Figure 4 Point A is the origin. Figure 5The graphs of boundary voltage variation along path 1 and path 2 show that the voltages of the two paths maintain a linear distribution along the direction shown. Since the air gap length is relatively small, it can be approximately considered that the voltage at the air gap boundary varies according to the voltage distribution law of the core boundary. Since the voltages applied to the primary and secondary windings are the same, the boundary voltage distribution of the cores on both sides of the transformer is exactly the same.

[0102] The following takes 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] By 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, from the above voltage linear distribution law, it can be known that the boundary voltage equations on the left and right sides of the air gap are:

[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 for the cases of 40, 20, 10, and 5 respectively Figure 6 The lower boundary potential U of the air gap is 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 by using the Curve Fitting Tool of MATLAB software, as follows Figure 8 As shown, the fitting empirical formula for the lower boundary voltage of the air gap is 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 to the electric field boundary value problem is to use boundary conditions (2) (3) to solve the Laplace equation (1) 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 problems 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 the first-order homogeneous boundary conditions of the Bessel function, the general solution of 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 is calculated 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 value of the capacitor converted to the primary and secondary sides is the same. The calculation process of all the above analytical solutions can be implemented in a computer through MATLAB programming. The program flow chart is shown below Fig. 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 for storing 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 the same linear distribution, and the upper and lower boundary voltages are 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, and 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 Fig.10 , a parasitic energy capacitance analysis system of a transformer air gap provided in an embodiment of the present invention comprises:

[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 neutral line of the transformer.

[0131] The first calculation unit 202 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.

[0132] The second calculation unit 203 is used 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.

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

[0134] Furthermore, an embodiment of the present invention also provides a parasitic energy capacitance analysis device of 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 used 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, a computer-readable storage medium is provided in an embodiment of the present invention, and 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 above method embodiment.

[0138] Those skilled in the art can 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 only schematic, for example, the division of units is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

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

[0141] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0142] If the integrated unit is implemented in the form of 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, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[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 the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. 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 embodiments of the present invention.

Claims

1. A parasitic energy capacitance analysis method 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 neutral line of the transformer; 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; The parasitic capacitance of the air gap is calculated according to the electric field energy, so as to be used for the design of the transformer.

2. The parasitic energy capacitance analysis method of transformer air gap according to claim 1, characterized in that: 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, constructing and solving the boundary voltage equations on the left and right sides of the air gap according to the voltage linear distribution law, and obtaining 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 the bottom circle as the origin, the axial direction as the z-axis direction, and the radial direction as the r-axis direction; 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 boundary voltage of the air gap is obtained by taking the upper and lower boundary voltages as the opposite exponential distribution law.

3. The parasitic energy capacitance analysis method of transformer air gap according to claim 1, characterized in that: The step of 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, comprises: Based on an electric field strength calculation formula, the electric field strength of the air gap is calculated according to the electric potential; Among them, the electric field strength calculation formula includes: ； In the formula, , are the electric field strengths in the r and z directions, respectively, is the gradient of the electric potential at any position in the air gap; Based on the electric field energy calculation formula of the air gap, the electric field energy of the air gap is calculated according to the electric field strength; Wherein, 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).

4. The parasitic energy capacitance analysis method of 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: Based on a parasitic capacitance calculation formula, the parasitic capacitance of the air gap is calculated according to the electric field energy; Wherein, the parasitic capacitance calculation formula is: ； In the formula, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

5. A parasitic energy capacitance analysis system for a transformer air gap, characterized in that: include: An excitation unit, 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 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 calculation 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; 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 the design of the transformer.

6. The parasitic energy capacitance analysis system of transformer air gap according to claim 5, characterized in that: 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, constructing and solving the boundary voltage equations on the left and right sides of the air gap according to the voltage linear distribution law, and obtaining 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 the bottom circle as the origin, the axial direction as the z-axis direction, and the radial direction as the r-axis direction; 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 boundary voltage of the air gap is obtained by taking the upper and lower boundary voltages as the opposite exponential distribution law.

7. The parasitic energy capacitance analysis system of transformer air gap according to claim 5, characterized in that: The second computing unit is specifically configured to: Based on an electric field strength calculation formula, the electric field strength of the air gap is calculated according to the electric potential; Among them, the electric field strength calculation formula includes: ； In the formula, , are the electric field strengths in the r and z directions, respectively, is the gradient of the electric potential at any position in the air gap; Based on the electric field energy calculation formula of the air gap, the electric field energy of the air gap is calculated according to the electric field strength; Wherein, 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).

8. The parasitic energy capacitance analysis system of transformer air gap according to claim 5, characterized in that: The third computing unit is specifically used for: Based on a parasitic capacitance calculation formula, the parasitic capacitance of the air gap is calculated according to the electric field energy; Wherein, the parasitic capacitance calculation formula is: ； In the formula, is the electric field energy of the air gap, and △U is the voltage difference between the primary and secondary windings of the transformer.

9. A parasitic energy capacitance analysis device for a transformer air gap, characterized in that: The device comprises a processor and a memory: The memory is used to store program code and transmit the program code to the processor; The processor is used to execute the parasitic energy capacitance analysis method of the transformer air gap according to any one of claims 1-4 according to the instructions in the program code.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium is used to store program codes, and the program codes are used to execute the parasitic energy capacitance analysis method of the transformer air gap according to any one of claims 1 to 4.

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