Method and system for calculating electric field of circular arc region of capacitor element

Abstract

The application provides a method and system for calculating the electric field of a circular arc region of a capacitor element, comprising the following steps: step 1, constructing a capacitor element model; step 2, setting different reduction factors, reducing the size of the capacitor element model by using the reduction factors to obtain a plurality of capacitor element reduction models; step 3, performing finite element calculation on each capacitor element reduction model to obtain a set of calculation results of the electric field of the circular arc region corresponding to each capacitor element reduction model; step 4, fitting each set of calculation results of the electric field of the circular arc region and the corresponding reduction factor to obtain a display relationship; and step 5, calculating the electric field intensity of the circular arc region corresponding to the capacitor element model by using the obtained display relationship. The application has the advantages of saving cost and obtaining the electric field intensity of the entire region.

Description

Technical Field

[0001] This invention belongs to the field of power capacitors, and specifically relates to a method and system for calculating the electric field in the arc region of a capacitor element. Background Technology

[0002] Capacitor elements are the basic structural units in power capacitors, and a reasonable electric field intensity distribution within them is crucial for the functional realization and safe operation of power capacitors in the system.

[0003] Due to manufacturing processes, the formed capacitor element will have a semi-cylindrical region on each side, generally called the arc region. Since the electric field intensity often concentrates in the arc region, it can lead to breakdown. Therefore, this region becomes the weak point of the capacitor element. Accurately obtaining the electric field intensity distribution in the arc region is crucial for preventing capacitor element breakdown and maintaining the safe operation of the capacitor.

[0004] Currently, the electric field intensity in a circular arc region is mainly obtained through actual measurement or simulation calculation. However, the actual measurement method has the following drawbacks: 1) high cost; 2) only a very limited number of observation points can be obtained; 3) it is difficult to conduct electric field tests during operation. Simulation calculation can circumvent these problems. There are two main existing simulation calculation methods:

[0005] The first method is to use a correction factor to calculate the electric field value of the arc region by adding a correction factor to the electric field of the parallel stretched region of the capacitor element; the second method is to directly perform finite element calculations using a full-size three-dimensional model of the capacitor element. The first method has accuracy issues, and the selection of the correction factor often relies on experience. For the second method, since there is a thin film structure inside the capacitor element, the size is very different from the overall size, which requires a lot of computing resources and sometimes even makes the calculation impossible. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for calculating the electric field in the arc region of a capacitor element, which solves the problems of low accuracy and excessive computational resource consumption in existing methods for calculating the electric field in the arc region of a capacitor element.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] This invention provides a method for calculating the electric field in the arc region of a capacitor element, comprising the following steps:

[0009] Step 1: Construct a capacitor element model;

[0010] Step 2: Set different scaling factors and use these factors to reduce the size of the capacitor element model to obtain multiple scaled-down capacitor element models.

[0011] Step 3: Perform finite element calculations on each reduced model of capacitor element to obtain the calculation results of a set of electric fields in the circular arc region corresponding to each reduced model of capacitor element.

[0012] Step 4: Fit the calculated electric field results of each group of circular arc regions with the corresponding reduction factor to obtain the display relationship;

[0013] Step 5: Calculate the electric field strength of the arc region corresponding to the capacitor element model using the obtained display relationship.

[0014] Preferably, in step 1, a capacitor element model is constructed using finite element modeling.

[0015] Preferably, in step 2, different scaling factors are set, and the size of the capacitor element model is reduced using these scaling factors to obtain multiple reduced capacitor element models. Specifically, the method is as follows:

[0016] Set a scaling factor, and use the scaling factor to proportionally reduce the size of the constructed capacitor element model in the x and y directions to obtain the reduced capacitor element model corresponding to each scaling factor.

[0017] Preferably, when reducing the size of the capacitor element model using a reduction factor, the size of the capacitor element model is reduced in the z-direction.

[0018] Preferably, the dimension of the reduced capacitor element model in the z-direction is one-tenth of the dimension of the capacitor element model in the z-direction.

[0019] Preferably, in step 4, the calculation results of the electric field of each group of circular arc regions are fitted with the corresponding reduction factor using the least squares method to obtain the display relationship.

[0020] Preferably, in step 5, the electric field strength of the arc region corresponding to the capacitor element model is calculated using the obtained explicit relationship. Specifically, the method is to set the reduction factor η = 1 and calculate the electric field strength corresponding to the capacitor element model in combination with the explicit relationship.

[0021] The present invention also provides a system for calculating the electric field in the arc region of a capacitor element, comprising:

[0022] Model building unit, used to build capacitor element models;

[0023] The model reduction unit is used to set different reduction factors, and the size of the capacitor element model is reduced by the reduction factor to obtain multiple reduced capacitor element models;

[0024] The fitting unit is used to perform finite element calculations on each reduced model of capacitor element, and obtain the calculation results of a set of electric fields in the arc region corresponding to each reduced model of capacitor element.

[0025] The calculated electric field results for each group of circular arc regions are then fitted with the corresponding reduction factor to obtain the display relationship;

[0026] The electric field strength calculation unit is used to calculate the electric field strength of the arc region corresponding to the capacitor element model using the obtained display relationship.

[0027] Compared with the prior art, the beneficial effects of the present invention are:

[0028] This invention provides a method for calculating the electric field in the arc region of a capacitor element. Compared to existing methods that multiply the electric field strength of a parallel stretched region by a correction factor to obtain the electric field strength in the arc region, the method of this invention considers the complete structure of the capacitor element and has the advantage of higher accuracy. Compared to existing methods that use a full-size model for finite element calculation, this invention reduces the entire model structure for calculation, which has the advantages of low computational resource consumption and high computational efficiency. Compared to methods that obtain the electric field strength distribution by actual measurement inside the capacitor element, the method of this invention has the advantages of cost savings and the ability to obtain the electric field strength of the entire region. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the overall structure of an existing capacitor;

[0030] Figure 2 This is a schematic diagram of the equivalent forming process of a capacitor element;

[0031] Figure 3 This is a schematic diagram of the capacitor element model structure described in this invention;

[0032] Figure 4 This is an electric field distribution diagram of the transition region between the outer edge of the arc region and the parallel stretching region of the present invention. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings.

[0034] like Figure 1 As shown, the capacitor element is made by winding two aluminum foils as positive and negative electrodes and a polypropylene film as the inter-electrode dielectric.

[0035] Specifically, first, multiple layers of alternating aluminum foil and polypropylene film are rolled into a cylindrical shape, and then flattened to obtain a capacitor element;

[0036] Next, multiple capacitor elements are stacked together and welded according to the designed series and parallel connections to finally form a capacitor core with a specific capacitance value.

[0037] Finally, the capacitor core is inserted into a steel casing and benzyltoluene is injected to form the complete capacitor.

[0038] The equivalent forming process of capacitor elements is as follows: Figure 2 As shown, it can be seen that the repetition Figure 2 The equivalent winding process shown ultimately results in a cylindrical layered region on both sides of the capacitor element.

[0039] In practice, a capacitor element typically consists of 80 to 100 layers of polypropylene film and aluminum foil. The thickness of a single polypropylene film is approximately 12 micrometers, and the thickness of a single aluminum foil is approximately 5 micrometers. The overall size of the capacitor element at its largest point is approximately 400 millimeters. Building a complete three-dimensional finite element model of a capacitor element requires approximately 10... 15 The related calculations for each tetrahedron are obviously a very large amount of computation.

[0040] Therefore, this embodiment scales down the original capacitor element model by a certain proportion, including reducing its size and the number of polypropylene film and aluminum foil layers, resulting in a series of scaled-down models. Using the electric field strength of the arc region obtained from these scaled-down models, the corresponding electric field strength in the actual model is calculated.

[0041] Specifically, the present invention provides a method for calculating the electric field in the arc region of a capacitor element, comprising the following steps:

[0042] Step 1: Construct a capacitor element model using finite element modeling, as shown in the figure below. Figure 3 As shown;

[0043] Step 2, the capacitor element model obtained in Step 1 is then... Figure 3 The dimensions are reduced proportionally in the x and y directions, with a reduction factor of η, where η is a real number less than 1; at the same time, the amount of polypropylene film and aluminum foil is reduced to a certain quantity in the z direction.

[0044] Step 3: Set different values ​​of the reduction factor η to obtain the corresponding capacitor element reduction model;

[0045] Step 4: Perform finite element calculations on the reduced model of the capacitor element corresponding to a certain reduction factor to obtain the calculation results of a set of electric fields in the circular arc region corresponding to the reduced model of the capacitor element.

[0046] Step 5: Using the calculated results of the electric field of several sets of circular arc regions and the corresponding reduction factor η values ​​as data points, the explicit relationship between the circular arc region and the reduction factor η is obtained by fitting with the least squares method.

[0047] Step 6: Calculate the electric field of the arc region corresponding to the capacitor element model using the obtained explicit relationship.

[0048] By setting the reduction factor η = 1 and combining it with explicit relationships, the electric field strength corresponding to the capacitor element model is calculated.

[0049] The present invention also provides a system for calculating the electric field in the arc region of a capacitor element, comprising:

[0050] Model building unit, used to build capacitor element models;

[0051] The model reduction unit is used to set different reduction factors, and the size of the capacitor element model is reduced by the reduction factor to obtain multiple reduced capacitor element models;

[0052] The fitting unit is used to perform finite element calculations on each reduced model of capacitor element, and obtain the calculation results of a set of electric fields in the arc region corresponding to each reduced model of capacitor element.

[0053] The calculated electric field results for each group of circular arc regions are then fitted with the corresponding reduction factor to obtain the display relationship;

[0054] The electric field strength calculation unit is used to calculate the electric field strength of the arc region corresponding to the capacitor element model using the obtained display relationship.

[0055] Example

[0056] The reduction factor η is set to take values ​​of 0.005, 0.004, 0.0025, and 0.0015.

[0057] The amount of polypropylene film and aluminum foil in the z-direction is reduced to 1 / 10 of the original amount;

[0058] The electric field calculation results for the circular arc region are obtained based on the least squares method and the basic electric field equations.

[0059] Based on the principle that the value of electric field strength is the negative gradient of electric potential, the following relationship can be given between the electric field strength of the original model and the electric field strength of the scaled model:

[0060]

[0061] Among them, E extra E represents the electric field strength corresponding to the model of the capacitor element to be determined; x-red E y-red and Ez-red These represent the x-axis, y-axis, and z-axis components of the electric field strength in the reduced model of the capacitor element, respectively.

[0062] Due to E extra Since it is a fixed value, the relationship between the electric field strength and the value of η can be derived from equation (1):

[0063]

[0064] Among them, E sp This represents the electric field value of a certain arc region on the reduced model of each capacitor element, where α and β are parameters to be determined.

[0065] The specific methods for calculating α and β are as follows:

[0066] The applied voltage to the capacitor element is 2kV, and the original dimensions of the capacitor element model are shown in Table 1:

[0067] Table 1 Original dimensions of the capacitor element model

[0068]

[0069] By setting the reduction factor η, the electric field intensity at the midpoint of the arc region on the reduced capacitor element model was calculated, as shown in Table 2.

[0070] Table 2

[0071]

[0072]

[0073] Based on the parameters in Table 2 and the least squares method, the optimal values ​​of the parameters α and β are obtained, i.e., α and β are 0.0018MV. 2 / m 2 . and 2682.11MV 2 / m 2 .

[0074] This leads to the explicit relationship between the arc region and the reduction factor η:

[0075]

[0076] The electric field strength corresponding to the capacitor element model is calculated based on this relationship, i.e.:

[0077] Setting the reduction factor η to 1, the electric field strength at the midpoint of the arc region in the capacitor element model is 51.789 MV / m, which has only a 6% error compared to the theoretical value of 55.6 MV / m.

[0078] According to the method of this embodiment, in Figure 4 The electric field distribution within 200 micrometers of the transition region between the outer edge of the circular arc region and the parallel stretching region is given, which is consistent with the measured results.

[0079] In terms of computational runtime, the method in this embodiment takes a total of 29 minutes and 35 seconds to compute each scaled-down model, while the computation time for the full-size model is approximately 20 hours, demonstrating the efficiency of the method proposed in this embodiment.

[0080] The above-described embodiments are only used to illustrate the technical solutions of this embodiment, and are not intended to limit it. Although this embodiment has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of this embodiment, and should all be included within the protection scope of this embodiment.

Claims

1. A method for calculating the electric field in the arc region of a capacitor element, characterized in that, Includes the following steps: Step 1: Construct a capacitor element model; Step 2: Set different scaling factors and use these factors to reduce the size of the capacitor element model to obtain multiple scaled-down capacitor element models. Step 3: Perform finite element calculations on each reduced model of capacitor element to obtain the calculation results of a set of electric fields in the circular arc region corresponding to each reduced model of capacitor element. Step 4: Fit the calculated electric field results of each group of circular arc regions with the corresponding reduction factor to obtain the display relationship; Step 5: Calculate the electric field strength of the arc region corresponding to the capacitor element model using the obtained display relationship; In step 2, different scaling factors are set, and the size of the capacitor element model is reduced using these scaling factors to obtain multiple reduced capacitor element models. The specific method is as follows: Set a scaling factor, and use the scaling factor to scale down the x and y directions of the constructed capacitor element model proportionally to obtain the reduced capacitor element model corresponding to each scaling factor; When reducing the size of a capacitor element model using a scaling factor, the size of the capacitor element model is reduced in the z-direction. The dimension of the reduced model of the capacitor element in the z-direction is one-tenth of the dimension of the model of the capacitor element in the z-direction; In step 4, the least squares method is used to fit the calculated electric field of each group of circular arc regions with the corresponding reduction factor to obtain the display relationship; In step 5, the electric field strength of the arc region corresponding to the capacitor element model is calculated using the obtained explicit relationship. The specific method is: set the reduction factor η=1, and calculate the electric field strength corresponding to the capacitor element model in combination with the explicit relationship.

2. The method for calculating the electric field in the arc region of a capacitor element according to claim 1, characterized in that, In step 1, the capacitor element model is constructed using finite element modeling.

3. A system for calculating the electric field in the arc region of a capacitor element, characterized in that, The method based on claim 1 includes: Model building unit, used to build capacitor element models; The model reduction unit is used to set different reduction factors, and the size of the capacitor element model is reduced by the reduction factor to obtain multiple reduced capacitor element models; The fitting unit is used to perform finite element calculations on each reduced model of capacitor element, and obtain the calculation results of a set of electric fields in the arc region corresponding to each reduced model of capacitor element. The calculated electric field results for each group of circular arc regions are then fitted with the corresponding reduction factor to obtain the display relationship; The electric field strength calculation unit is used to calculate the electric field strength of the arc region corresponding to the capacitor element model using the obtained display relationship.

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