A method for calculating the distributed capacitance of a multi-layer winding of a high-frequency transformer

Abstract

The application provides a calculation method of a high-frequency transformer multi-layer winding distributed capacitance, comprising the following steps: step 1, dividing the total distributed capacitance of the high-frequency transformer multi-layer winding into three parts, i.e. the primary winding interlayer capacitance, the secondary winding interlayer capacitance and the primary-secondary winding interlayer capacitance; step 2, establishing the interlayer capacitance calculation model of the primary winding and the secondary winding respectively according to the actual winding mode; step 3, establishing the interturn capacitance calculation model of the winding by using the tangent function path; step 4, establishing the inter-winding capacitance calculation model by equivalently taking the directly opposite area of the two windings as a parallel plate capacitor; and step 5, establishing the three-capacitance winding model, equivalently taking the calculated three part capacitance values, and obtaining the total distributed capacitance. The application comprehensively considers the influence of the winding mode on the interlayer potential distribution and the actual path of the interturn electric field, and realizes the systematic calculation of the distributed capacitance through the three-capacitance equivalent model, thereby effectively improving the calculation accuracy.

Description

Technical Field

[0001] This invention relates to the field of high-frequency transformer technology, and in particular to a method for calculating the distributed capacitance of multilayer windings in a high-frequency transformer. Background Technology

[0002] With the rapid development of power electronic devices such as switching power supplies and solid-state transformers towards higher frequencies and smaller sizes, high-frequency transformers, as core components, have seen their operating frequencies increase from tens of kilohertz to megahertz levels. Under high-frequency operating conditions, due to their compact structure, the distributed capacitance within and between the windings has an increasingly significant impact on circuit performance. Distributed capacitance not only causes high-frequency oscillations and electromagnetic interference but also alters the soft-switching characteristics of the converter and reduces power transmission efficiency. Therefore, accurate calculation of the distributed capacitance of high-frequency transformers during the circuit design phase is of significant engineering importance for optimizing winding structure and predicting parasitic parameter effects in the circuit.

[0003] The distributed capacitance of high-frequency transformer windings includes inter-turn capacitance, inter-layer capacitance, and inter-secondary winding capacitance. There are two main methods for extracting distributed capacitance: finite element method (FEM) numerical simulation and analytical calculation. The FEM solves for the capacitance matrix by establishing a two-dimensional or three-dimensional electromagnetic field model. It can account for edge effects and complex geometries, and has high calculation accuracy, but the modeling process is cumbersome and requires significant computational resources. Analytical calculation, based on electrostatic field theory, simplifies or equivalences the winding structure for estimation. It is fast and convenient for engineering applications.

[0004] However, existing analytical calculation methods still have some shortcomings: most methods do not fully consider the influence of the actual winding method on the interlayer potential distribution when calculating interlayer capacitance, resulting in a large deviation between the calculated results and the measured values. Furthermore, they lack a systematic capacitance equivalent model that uniformly accounts for interlayer, inter-turn, and primary-secondary capacitances at the winding ports. Therefore, further analysis and research are needed on the distributed capacitance of high-frequency transformers with different winding methods for multi-layer windings. Summary of the Invention

[0005] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a method for calculating the distributed capacitance of multilayer windings of high-frequency transformers, so as to solve the technical problems of insufficient calculation accuracy, failure to distinguish the differences in winding processes, and lack of a unified equivalent model in existing analytical methods.

[0006] To solve the above-mentioned technical problems, the present invention provides a method for calculating the distributed capacitance of multilayer windings of a high-frequency transformer, comprising the following steps: Step 1: Divide the total distributed capacitance of the multilayer winding of the high-frequency transformer into three parts: the interlayer capacitance of the primary and secondary windings, the inter-turn capacitance of the primary and secondary windings, and the inter-winding capacitance between the primary and secondary windings. Step 2: Based on whether the actual winding method is U-shaped or Z-shaped, analyze the potential distribution between adjacent layers, and use the electric field energy integration method to establish the interlayer capacitance calculation model of the primary and secondary windings respectively. Step 3: Establish a calculation model for the inter-turn capacitance of the winding using the tangent function path; Step 4: Equivalently represent the area where the two windings face each other as a parallel plate capacitor to establish a capacitance calculation model between the windings; Step 5: Establish a three-capacitor winding model. Equivalently convert the three partial capacitance values ​​calculated by the inter-layer capacitance calculation model, the inter-turn capacitance calculation model, and the inter-winding capacitance calculation model to obtain the total distributed capacitance of the multi-layer winding of the high-frequency transformer.

[0007] Furthermore, the calculation models for the interlayer capacitance of the primary and secondary windings are the same, as are the calculation models for the inter-turn capacitance of the primary and secondary windings.

[0008] Furthermore, in step 2, when the winding method between the winding layers is a U-shaped winding, the interlayer capacitance calculation model includes the following calculation steps: Calculate the interlayer voltage based on the structure of the U-shaped winding. The calculation formula is: ; Calculating the electric field energy between adjacent layers when using the U-shaped winding method The calculation formula is: ; Calculating the electric field energy of the entire winding when using a U-shaped winding The calculation formula is: ; Calculate the interlayer capacitance of U-shaped windings The calculation formula is: ; In the formula The voltage across the winding is The height of the winding, This refers to the number of winding layers. This represents the distance between adjacent winding layers. The average turn length of the winding, denoted as the relative permittivity of the material, x is a variable representing the length of a single-layer winding, represents the electric field strength, and dv represents a volume element.

[0009] Furthermore, in step 2, when the winding method between the winding layers is a Z-shaped winding, the interlayer capacitance calculation model includes the following calculation steps: Calculate the interlayer voltage based on the Z-shaped winding structure. The calculation formula is: ; Calculating the electric field energy between adjacent layers when using Z-shaped winding The calculation formula is: ; Calculating the electric field energy of the entire winding when using Z-shaped winding The calculation formula is: ; Calculate the interlayer capacitance of Z-type winding The calculation formula is: ; In the formula The voltage across the winding is The height of the winding, This refers to the number of winding layers. This represents the distance between adjacent winding layers. The average turn length of the winding, The relative permittivity of the material is . x Let be a variable representing the length of a single layer of winding. Let dv be the electric field strength, and dv be the volume element.

[0010] Furthermore, in step 3, the calculation model for the inter-turn capacitance of the winding includes the following calculation steps: Treating adjacent conductor turns as cylindrical, considering only the influence of the electric field between adjacent conductors and neglecting the electric field effect at the conductor edges, and assuming that the conductor surfaces are equipotential surfaces, assuming that the electric field lines between two circular conductors originate from the conductor surfaces, traverse the inter-turn region with tangent functions, and reach the surfaces of adjacent conductors, then the inter-turn electric field lines can be expressed as follows: ; In the formula Let be the position and angle of the electric field lines on the circumference of the circular conductor. express electric field lines at that location, The distance between the centers of two adjacent conductors. The outer diameter of the winding conductor. This is the inner diameter of the winding conductor; Inter-turn capacitance can be considered as consisting of the capacitance of the insulating layer and the capacitance of the air gap between the conductors connected in series: ; The inter-turn capacitance between adjacent conductors is: ; In the formula, For inter-turn capacitance of conductors, It is an insulating layer capacitor. For air gap capacitance, The vacuum permittivity, The relative permittivity of the material is . This represents the distance between adjacent winding layers. This represents the average turn length of the winding.

[0011] Furthermore, in step 4, the inter-winding capacitance calculation model includes the following calculation steps: The two windings of the transformer are equivalent to the two plates of a parallel-plate capacitor, and the capacitance between the primary and secondary windings is... The calculation formula is: ; in, The vacuum permittivity, The distance between the windings. For winding thickness, The relative permittivity of the material is . This represents the average turn length of the winding.

[0012] Furthermore, in the three-capacitor winding model described in step 5, the primary distributed capacitance is denoted as... The secondary distributed capacitance is denoted as The capacitance between the primary and secondary windings is denoted as ,in , satisfy ; ; In the formula, This refers to the number of turns in a single-layer winding. This refers to the interlayer capacitance of the primary winding. This refers to the interlayer capacitance of the secondary winding. This refers to the inter-turn capacitance of the primary winding. This refers to the inter-turn capacitance of the secondary winding. The voltage across the winding is The height of the winding, This refers to the number of winding layers. This represents the distance between adjacent winding layers. The average turn length of the winding, The relative permittivity of the material Beneficial effects of this invention: (1) The calculation method for distributed capacitance of multilayer windings of high-frequency transformers proposed in this invention improves the accuracy of distributed parameter calculation by taking into account the winding method. (2) The three-capacitor equivalent model established by the present invention enables the capacitors of each part to be combined in an orderly manner, which can be better applied to circuit simulation. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to an embodiment of the present invention. Figure 2 This is a diagram showing the U-shaped winding structure and interlayer potential distribution according to an embodiment of the present invention; Figure 3 This is a diagram showing the Z-shaped winding structure and interlayer potential distribution according to an embodiment of the present invention; Figure 4 This is a diagram showing the electric field path distribution between conductor turns in an embodiment of the present invention. Figure 5 This is the equivalent model of three capacitors in an embodiment of the present invention; Figure 6 This is a structural diagram of a transformer according to an embodiment of the present invention. Detailed Implementation

[0014] The present invention will now be described in further detail with reference to the accompanying drawings and specific examples.

[0015] Implementation example: combined with appendix Figure 1 A method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer includes the following steps.

[0016] Step 1: Based on the winding structure of the high-frequency transformer, the total distributed capacitance is divided into three parts: the interlayer capacitance between the primary and secondary windings, the inter-turn capacitance between the primary and secondary windings, and the inter-winding capacitance between the primary and secondary windings. Interlayer capacitance between primary and secondary windings refers to the capacitance between different layers of the same winding; interturn capacitance between primary and secondary windings refers to the capacitance between two adjacent turns of the same layer of the same winding; inter-primary and secondary winding capacitance refers to the capacitance between the entire primary winding and the entire secondary winding.

[0017] In one embodiment, the primary winding and secondary winding of the high-frequency transformer are set to be the same, so the interlayer capacitance and interturn capacitance of the primary winding are the same as those of the secondary winding.

[0018] Step 2: For the interlayer capacitance of the winding, depending on whether the actual winding method is U-shaped or Z-shaped, analyze the potential distribution between adjacent layers, and use the electric field energy integration method to establish the interlayer capacitance calculation model of the primary and secondary windings respectively. First, calculate the interlayer capacitance. Figure 5 For example, if the transformer winding is U-shaped, then it can be based on... Figure 2 The interlayer voltage between adjacent layers and the electric field energy of the entire winding are calculated using the U-shaped winding structure and the interlayer potential distribution diagram, and then the interlayer capacitance is obtained, as shown in the following formula: Calculate the interlayer voltage based on the structure of the U-shaped winding. The calculation formula is: ; Calculating the electric field energy between adjacent layers when using the U-shaped winding method The calculation formula is: ; Calculating the electric field energy of the entire winding when using a U-shaped winding The calculation formula is: ; Calculate the interlayer capacitance of U-shaped windings The calculation formula is: ; In the formula The voltage across the winding is The height of the winding shown in the figure. This refers to the number of winding layers. This represents the distance between adjacent winding layers. The average turn length of the primary / secondary winding. The relative permittivity of the material is . x Let be a variable representing the length of a single layer of winding. Let dv be the electric field strength, and dv be the volume element.

[0019] Step 3: For the inter-turn capacitance of the winding, a calculation model for the inter-turn capacitance of the winding is established using the tangent function path; Then calculate the inter-turn capacitance. Figure 3 and Figure 5 Taking the given parameters as an example, we consider adjacent conductor turns as cylindrical, only considering the influence of the electric field between adjacent conductors, ignoring the electric field effect at the conductor edges, and assuming that the conductor surface is an equipotential surface. Assuming that the electric field lines between the two circular conductors originate from the conductor surface, travel along the trajectory of the tangent function through the inter-turn region to reach the surface of the adjacent conductors, then the inter-turn electric field lines are expressed as follows:

[0020] In the formula Let be the position and angle of the electric field lines on the circumference of the circular conductor. express electric field lines at that location, The distance between the centers of two adjacent conductors. The outer diameter of the winding conductor. This is the inner diameter of the winding conductor; Inter-turn capacitance can be considered as consisting of the capacitance of the insulating layer and the capacitance of the air gap between the conductors connected in series: ; Then, the calculations above will be used to... Substituting other parameters into the following formula yields the inter-turn capacitance between adjacent conductors. for: ; In the formula, For inter-turn capacitance of conductors, It is an insulating layer capacitor. For air gap capacitance, The vacuum permittivity, The relative permittivity of the material is . The average turn length of the winding, This represents the maximum value of the position angle of the electric field lines. express The differential, express The differential, express The differential, express The differential.

[0021] The inter-turn capacitance of a multi-layer winding can be calculated using the above formula.

[0022] Step 4: For the capacitance between the primary and secondary windings, the area directly opposite the two windings is equivalent to a parallel plate capacitor to establish a capacitance calculation model between the windings. Finally, calculate the inter-winding capacitance. Based on... Figure 5 The transformer structure shown represents the two windings of a parallel-plate capacitor as equivalent to the two plates of the capacitor. The distributed capacitance between the windings can then be calculated using the following formula: ; Step 5: Establish a three-capacitor winding model, and make equivalent use of the capacitance values ​​of each part calculated in Steps 2 to 4 to finally obtain the distributed capacitance of the multi-layer winding of the high-frequency transformer.

[0023] The calculation models for the inter-layer capacitance and the inter-turn capacitance of the primary and secondary windings are the same. That is, the inter-layer capacitance and inter-turn capacitance of the primary and secondary windings are calculated according to steps 2 and 3 above. The winding parameters such as winding height and number of winding layers in the above formulas are parameters for the corresponding windings. Specifically, when calculating the inter-layer capacitance and inter-turn capacitance of the primary winding, the winding height and number of winding layers in the above formulas are parameters for the primary winding; similarly, when calculating the inter-layer capacitance and inter-turn capacitance of the secondary winding, the winding height and number of winding layers in the above formulas are parameters for the secondary winding. If the configurations of the primary and secondary windings are completely identical, the calculated capacitance values ​​will also be the same.

[0024] The primary winding interlayer capacitance calculated using the above method is denoted as . The interlayer capacitance of the secondary winding calculated according to the above method is denoted as... The inter-turn capacitance of the primary winding calculated using the above method is denoted as... The inter-turn capacitance of the secondary winding calculated using the above method is denoted as... .

[0025] according to Figure 4 The three-capacitor equivalent model shown is obtained by substituting the capacitance values ​​calculated in steps 2 to 4 into the following formula to obtain the lumped distributed capacitance of the primary / secondary side.

[0026] ; ; In one embodiment, the transformer parameters are shown in Table 1.

[0027] Table 1 ; The distributed capacitance of the example transformer was measured using an LCR bridge, and the calculated theoretical value was compared with the measured value. The results are shown in Table 2. Table 2 shows that the relative error of each capacitance component is less than 5%, indicating high calculation accuracy.

[0028] Table 2 ; The above embodiments are merely preferred implementations of the present invention and do not constitute any limitation on the scope of protection of the present invention. The scope of protection of the present invention is determined by the technical solutions defined in the claims of this application, including equivalent substitutions of the technical features recorded in the claims; all equivalent substitutions and partial improvements made within the spirit and inventive concept of the present invention fall within the scope of protection of the present invention.

Claims

1. A method for calculating the distributed capacitance of a multilayer winding in a high-frequency transformer, characterized in that, Including the following steps: Step 1: Divide the total distributed capacitance of the multilayer winding of the high-frequency transformer into three parts: the interlayer capacitance of the primary and secondary windings, the inter-turn capacitance of the primary and secondary windings, and the inter-winding capacitance between the primary and secondary windings. Step 2: Based on whether the actual winding method is U-shaped or Z-shaped, analyze the potential distribution between adjacent layers, and use the electric field energy integration method to establish the interlayer capacitance calculation model of the primary and secondary windings respectively. Step 3: Establish a calculation model for the inter-turn capacitance of the winding using the tangent function path; Step 4: Equivalently represent the area where the two windings face each other as a parallel plate capacitor to establish a capacitance calculation model between the windings; Step 5: Establish a three-capacitor winding model. Equivalently convert the three partial capacitance values ​​calculated by the inter-layer capacitance calculation model, the inter-turn capacitance calculation model, and the inter-winding capacitance calculation model to obtain the total distributed capacitance of the multi-layer winding of the high-frequency transformer.

2. The method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to claim 1, characterized in that, The calculation models for the interlayer capacitance of the primary and secondary windings are the same, as are the calculation models for the interturn capacitance of the primary and secondary windings.

3. The method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to claim 1, characterized in that, In step 2, when the winding method between winding layers is U-shaped, the interlayer capacitance calculation model includes the following calculation steps: Calculate the interlayer voltage based on the structure of the U-shaped winding. The calculation formula is: ； Calculating the electric field energy between adjacent layers when using the U-shaped winding method The calculation formula is: ； Calculating the electric field energy of the entire winding when using a U-shaped winding The calculation formula is: ； Calculate the interlayer capacitance of U-shaped windings The calculation formula is: ； In the formula The voltage across the winding is The height of the winding, This refers to the number of winding layers. This represents the distance between adjacent winding layers. The average turn length of the winding, The relative permittivity of the material is . x Let be a variable representing the length of a single layer of winding. Let dv be the electric field strength, and dv be the volume element.

4. The method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to claim 1, characterized in that, In step 2, when the winding method between winding layers is Z-shaped, the interlayer capacitance calculation model includes the following calculation steps: Calculate the interlayer voltage based on the Z-shaped winding structure. The calculation formula is: ； Calculating the interlayer electric field energy when using Z-shaped winding The calculation formula is: ； Calculating the electric field energy of the entire winding when using Z-shaped winding The calculation formula is: ； Calculate the interlayer capacitance of Z-type winding The calculation formula is: ； In the formula The voltage across the winding is The height of the winding, This refers to the number of winding layers. This represents the distance between adjacent winding layers. The average turn length of the winding, The relative permittivity of the material is . x Let be a variable representing the length of a single layer of winding. Let dv be the electric field strength, and dv be the volume element.

5. The method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to claim 1, characterized in that, In step 3, the calculation model for the inter-turn capacitance of the winding includes the following calculation steps: Treating adjacent conductor turns as cylindrical, considering only the influence of the electric field between adjacent conductors and neglecting the electric field effect at the conductor edges, and assuming that the conductor surfaces are equipotential surfaces, assuming that the electric field lines between two circular conductors originate from the conductor surfaces, traverse the inter-turn region with tangent functions, and reach the surfaces of adjacent conductors, then the inter-turn electric field lines can be expressed as follows: ； In the formula Let be the position and angle of the electric field lines on the circumference of the circular conductor. express electric field lines at that location, The distance between the centers of two adjacent conductors. The outer diameter of the winding conductor. This is the inner diameter of the winding conductor; Inter-turn capacitance can be considered as consisting of the capacitance of the insulating layer and the capacitance of the air gap between the conductors connected in series: ； The inter-turn capacitance between adjacent conductors is: ； In the formula, For inter-turn capacitance of conductors, It is an insulating layer capacitor. For air gap capacitance, The vacuum permittivity, The relative permittivity of the material is . The average turn length of the winding, express The differential, express The differential, express The differential, express The differential.

6. The method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to claim 1, characterized in that, In step 4, the inter-winding capacitance calculation model includes the following calculation steps: The two windings of the transformer are equivalent to the two plates of a parallel-plate capacitor, and the capacitance between the primary and secondary windings is... The calculation formula is: ； in, The vacuum permittivity, The distance between the windings. For winding thickness, The relative permittivity of the material is . This represents the average turn length of the winding.

7. The method for calculating the distributed capacitance of a multilayer winding of a high-frequency transformer according to claim 1, characterized in that, In the three-capacitor winding model described in step 5, the primary distributed capacitance is denoted as... The secondary distributed capacitance is denoted as The capacitance between the primary and secondary windings is denoted as ,in , satisfy ； ； In the formula, The number of turns in a single-layer winding. This refers to the interlayer capacitance of the primary winding. This refers to the interlayer capacitance of the secondary winding. This refers to the inter-turn capacitance of the primary winding. This refers to the inter-turn capacitance of the secondary winding. The voltage across the winding is The height of the winding, This refers to the number of winding layers. The average turn length of the winding, is the relative permittivity of the material.

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