Method for correcting foil winding eddy-current loss formula based on three-dimensional wound core transformer and calculating electromagnetic force of foil winding eddy-current loss formula based on three-dimensional wound core transformer

Abstract

The invention discloses a correction and electromagnetic force calculation method based on a foil winding eddy current loss formula of a three-dimensional wound core transformer. The method comprises the following steps: acquiring parameters of the three-dimensional wound core transformer and a foil winding of the three-dimensional wound core transformer; deriving a current density formula of each layer of conductor of the foil winding; deducing an alternating current resistance coefficient of the foil winding; determining a foil winding alternating current resistance coefficient correction coefficient in the three-dimensional wound core transformer; and calculating the short-circuit electromagnetic force of the foil winding. According to the method, a calculation formula of the eddy current loss of the low-voltage foil winding in the three-dimensional wound core transformer under different frequencies is deduced and corrected, and three correction factors for the three-dimensional wound core transformer, namely a winding correlation coefficient alpha, an iron core correlation coefficient beta and an insulation distance correlation coefficient gamma, are provided; the method for calculating the short-circuit electromagnetic force of the foil winding is determined, and reference is provided for determining the eddy-current loss of the foil winding of the three-dimensional wound core transformer in actual engineering.

Description

Technical Field

[0001] The invention belongs to the field of three-dimensional wound core transformer calculation, and in particular relates to a correction method based on a three-dimensional wound core transformer foil winding eddy current loss formula and an electromagnetic force calculation method thereof. Background Art

[0002] Compared with three-phase flat laminated core transformers, three-dimensional wound core transformers have advantages such as symmetrical magnetic circuits and low vibration and noise. In recent years, they have been widely used in high-rise buildings, subways, and new energy access. Its special three-frame core structure greatly reduces its core loss compared to traditional laminated cores, but at the same time, it causes its central column saturation magnetic density to be small, so it is mostly used in distribution transformers.

[0003] Therefore, in the selection of three-dimensional wound core transformer windings, foil windings play an important role in the field of distribution transformers due to their high degree of mechanization and good winding filling factor. With the continuous improvement of transformer performance indicators, in the field of high-efficiency and energy-saving distribution transformers, especially in the capacity range of 400kVA to 6300kVA, in order to achieve the no-load loss and load loss required by the standard, the use of foil windings for low-voltage windings is almost an inevitable choice.

[0004] Among the load losses of three-dimensional wound core transformers, the eddy current loss of low-voltage foil windings cannot be ignored. However, most current methods use the finite element method to analyze it. At the industrial frequency, only complex two-dimensional or three-dimensional models of the windings can be established for simulation analysis, which greatly increases the time cost.

[0005] Dowell established a one-dimensional electromagnetic field theoretical model of high-frequency transformers in 1966, obtained the AC resistance of copper foil windings, and analytically calculated the eddy current loss of three-dimensional wound core transformer windings. Zhao Bowen and others from Shenyang University of Technology established two-dimensional and three-dimensional finite element models of copper foil windings by using electromagnetic field simulation calculations, and analyzed its current distribution and temperature rise; Zhang Ke and others from Southeast University verified and analyzed the high-frequency transformer winding loss calculation formula proposed by Dowell, proving the correctness of Dowell's formula for calculating transformer winding eddy current loss at high frequencies;

[0006] When a power transformer suddenly short-circuits, a huge short-circuit current will flow through the winding, which will generate a strong leakage magnetic field around the winding. Under the interaction of the two, the transformer winding will be subjected to a short-circuit electromotive force several hundred times the rated value. Therefore, it is very important to conduct relevant research on measures to improve the short-circuit strength of transformers. Therefore, it is particularly important to accurately calculate the short-circuit force of power transformer windings, especially the foil windings commonly used in distribution transformers. Summary of the invention

[0007] The present invention provides a correction method for the eddy current loss formula of the foil winding of a three-dimensional wound core transformer and a method for calculating the electromagnetic force thereof. For the foil winding of the three-dimensional wound core transformer, the correction method for the eddy current loss of the foil winding of the medium and low frequency three-dimensional wound core transformer and the electromagnetic force calculation formula are obtained through the derivation of relevant formulas and specific three-dimensional wound core transformers and winding parameters thereof, which provides support for subsequent engineering applications. The method comprises the following steps:

[0008] Step 1: Obtain the parameters of the three-dimensional wound core transformer and its foil winding;

[0009] According to the actual application scenario, the geometric dimensions of the three-dimensional wound core transformer and its foil winding are obtained, especially the parameters related to the calculation of the foil winding eddy current loss formula, such as the core window height, winding height, winding phase spacing, wound core stack thickness, main air path distance, and the distance between the core column and the inner diameter of the low-voltage winding.

[0010] Step 2: Derive the current density formula of each layer of foil winding conductor;

[0011] According to the relevant parameters obtained in step 1, the Maxwell equations are solved in the eddy current field to obtain the current density of the nth layer conductor of the foil winding, and boundary conditions are imposed on both sides:

[0012]

[0013] Step 3: Derive the AC resistivity of the foil winding;

[0014] According to the current density obtained in step 2, and in Dowell's one-dimensional transformer electromagnetic field theory, the transformer winding height is limited to be equal to the core window height. However, since the winding of a large power transformer is different from that of a small high-frequency transformer, the winding height is generally less than the equivalent core window height, so it can be deduced that N l The expression of AC resistivity of non-overlapping foil winding is:

[0015]

[0016] in:

[0017]

[0018] Where A is the normalized thickness of the copper foil, d is the width of the copper foil conductor, δ is the penetration depth, ρ is the conductor resistivity, μ is the winding magnetic permeability, f is the frequency of the AC current, h is the height of the copper foil conductor, and h core is the core window height.

[0019] Step 4: Determine the correction factor of the AC resistance coefficient of the foil winding in the three-dimensional wound core transformer;

[0020] According to step 3, the AC resistivity of the copper foil winding is composed of two items. The first item explains the influence of the skin effect and is independent of the number of layers. The second item explains the influence of the proximity effect. This item is zero when there is only one layer, and its size increases in a flat manner with the number of layers, indicating that continuous multi-layer winding of copper foil is very likely to produce a large amount of winding losses. If the winding structure does not meet the assumption of one-dimensional magnetic field, the correction factor can be selected to correct step 3 according to the situation. Since the three-dimensional wound core transformer operates under low-frequency conditions, its skin effect is not very significant, and the proximity effect caused by the dense arrangement of conductors accounts for a large proportion of eddy current losses. According to its leakage magnetic field distribution, it can be seen that there is a correlation between the distance between the core column and the inner diameter of the low-voltage winding, the main air path distance, the winding phase distance, and the core's own geometric parameters. Therefore, a correction formula for the eddy current calculation formula of the foil winding of a medium and low-frequency three-dimensional wound core transformer can be derived:

[0021] F′ R =(αf γ +β)·F R

[0022] Among them, F′ R is the final corrected AC resistance coefficient, f is the frequency of the three-dimensional wound core transformer, α, β, and γ are the winding correlation coefficient, core correlation coefficient, and insulation distance correlation coefficient, respectively, and F R is the AC resistivity of foil winding.

[0023] According to the winding, core and insulation distance parameters, the three coefficient calculation formulas can be obtained as follows:

[0024]

[0025] Where, d p is the transformer phase distance, D is the thickness of the three-dimensional wound core, d ch d is the distance between the core column and the inner diameter of the low voltage winding, mc Main airway distance.

[0026] Step 5: Calculate the short-circuit electromagnetic force of the foil winding

[0027] According to steps 1 and 2, when the transformer is powered on, the current in the winding coil interacts with the leakage magnetic field around it, generating electromagnetic force in the winding, also known as electromotive force, which is the product of the current and the magnetic flux density of the leakage magnetic field. According to the Lorentz force formula, let the current density in the copper foil conductor be J z , we can get the radial electromagnetic force on the copper foil conductor as:

[0028] F r =B r n S n J z n2πR n

[0029] The axial electromagnetic force is:

[0030]

[0031] Where S n is the cross-sectional area of ​​the nth copper foil conductor, is the radial leakage flux density of the nth layer conductor, is the axial leakage flux density, is the current density of the nth layer conductor, R n It is the distance from the center of the nth layer conductor to the center line of the core. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 The two-dimensional equivalent diagram of the core of a three-dimensional wound core transformer

[0033] Figure 2 The nth conductor of the foil winding

[0034] Figure 3 The leakage magnetic field and electromagnetic force distribution of foil winding of three-dimensional wound core transformer DETAILED DESCRIPTION

[0035] The specific implementation of the present invention is further described in detail below in conjunction with the drawings and examples.

[0036] The present invention firstly deduces the one-dimensional electromagnetic field theoretical model of high-frequency transformer established by Dowell in 1966, obtains the calculation formula of AC resistance of copper foil winding, then modifies the formula according to the actual geometric parameters of three-dimensional wound core, and finally obtains the calculation formula of short-circuit electromagnetic force of copper foil winding, which includes the following steps:

[0037] Step 1: Obtain the parameters of the three-dimensional wound core transformer and its foil winding

[0038] According to the actual application scenario, the geometric dimensions of the three-dimensional wound core transformer and its foil winding are obtained, especially the parameters related to the calculation of the foil winding eddy current loss formula, such as the core window height, winding height, winding phase spacing, wound core stack thickness, main air path distance, and the distance between the core column and the inner diameter of the low-voltage winding.

[0039] Step 2: Derive the current density formula for each layer of the foil winding conductor

[0040] Dowell's one-dimensional transformer magnetic field theory has the following three assumptions: first, the high-frequency transformer uses a copper foil winding wound parallel to the core column; second, the height of the copper foil winding is equal to the window height, and there is no edge effect at this time; finally, assuming that the magnetic permeability of the core is infinite, the magnetic field strength in the core can be ignored.

[0041] At this time, taking the nth layer conductor of the foil winding as an example, Figure 2 As shown, the Maxwell equations are solved in the eddy current field to obtain the current density, and boundary conditions are imposed on both sides:

[0042]

[0043] Step 3: Derive the AC resistivity of the foil winding;

[0044] According to the current density obtained in step 2, and in Dowell's one-dimensional transformer electromagnetic field theory, the transformer winding height is limited to be equal to the core window height. However, since the winding of a large power transformer is different from that of a small high-frequency transformer, the winding height is generally less than the equivalent core window height, so it can be deduced that N l The expression of AC resistivity of non-overlapping foil winding is:

[0045]

[0046] in:

[0047]

[0048] Where A is the normalized thickness of the copper foil, d is the width of the copper foil conductor, δ is the penetration depth, ρ is the conductor resistivity, μ is the winding magnetic permeability, f is the frequency of the AC current, h is the height of the copper foil conductor, and h core is the core window height.

[0049] Step 4: Determine the AC resistance correction factor for foil windings in three-dimensional wound core transformers

[0050] According to step 3, the AC resistivity of the copper foil winding is composed of two items. The first item explains the influence of the skin effect and is independent of the number of layers. The second item explains the influence of the proximity effect. This item is zero when there is only one layer, and its size increases in a flat manner with the number of layers, indicating that continuous multi-layer winding of copper foil is very likely to produce a large amount of winding losses. If the winding structure does not meet the assumption of one-dimensional magnetic field, the correction factor can be selected to correct step 3 according to the situation. Since the three-dimensional wound core transformer operates under low-frequency conditions, its skin effect is not very significant, and the proximity effect caused by the dense arrangement of conductors accounts for a large proportion of eddy current losses. According to its leakage magnetic field distribution, it can be seen that there is a correlation between the distance between the core column and the inner diameter of the low-voltage winding, the main air path distance, the winding phase distance, and the core's own geometric parameters. Therefore, a correction formula for the eddy current calculation formula of the foil winding of a medium and low-frequency three-dimensional wound core transformer can be derived:

[0051] F′ R =(αf γ +β)·F R

[0052] Among them, F′ R is the final corrected AC resistance coefficient, f is the frequency of the three-dimensional wound core transformer, α, β, and γ are the winding correlation coefficient, core correlation coefficient, and insulation distance correlation coefficient, respectively, and F R is the AC resistivity of foil winding.

[0053] According to the winding, core and insulation distance parameters, the three coefficient calculation formulas can be obtained as follows:

[0054]

[0055] Where, d p is the transformer phase distance, D is the thickness of the three-dimensional wound core, d ch is the distance between the core column and the inner diameter of the low voltage winding, d mc is the main air path distance. Step 5: Calculate the short-circuit electromagnetic force of the foil winding

[0056] According to steps 1 and 2, when the transformer is powered on, the current in the winding coil interacts with the leakage magnetic field around it, generating electromagnetic force in the winding, also known as electromotive force, which is the product of the current and the magnetic flux density of the leakage magnetic field. According to the Lorentz force formula, let the current density in the copper foil conductor be J z , we can get the radial electromagnetic force on the copper foil conductor as:

[0057] F r =B r n S n J z n 2πR n

[0058] The axial electromagnetic force is:

[0059]

[0060] Where S n is the cross-sectional area of ​​the nth copper foil conductor, is the radial leakage flux density of the nth layer conductor, is the axial leakage flux density, is the current density of the nth layer conductor, R n It is the distance from the center of the nth layer conductor to the center line of the core.

[0061] Effects of the Invention

[0062] The present invention derives and corrects the calculation formula for the eddy current loss of the low-voltage foil winding in the three-dimensional wound core transformer at different frequencies, and proposes three correction factors for the three-dimensional wound core transformer: the winding correlation coefficient α, the core correlation coefficient β and the insulation distance correlation coefficient γ, and determines the calculation method of the short-circuit electromagnetic force of the foil winding, which provides a reference for the determination of the eddy current loss of the foil winding of the three-dimensional wound core transformer in actual engineering. It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive, so the present invention includes but is not limited to the embodiments described in the specific embodiments, and any other embodiments derived by those skilled in the art based on the technical solution of the present invention also belong to the scope of protection of the present invention.

Claims

1. A method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof, characterized in that The following steps are involved: Step 1: Obtain the parameters of the three-dimensional wound core transformer and its foil winding; Step 2: Derive the current density formula of each layer of foil winding conductor; Step 3: Derive the AC resistivity of the foil winding; Step 4: Determine the correction factor of the AC resistance coefficient of the foil winding in the three-dimensional wound core transformer; Step 5: Calculate the short-circuit electromagnetic force of the foil winding.

2. According to claim 1, a method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof, characterized in that: In step 1, the core window height is 443 mm, the core stack thickness is 215 mm, the number of turns of the low-voltage foil winding is 24, the low-voltage winding turn spacing is 0.3 mm, the low-voltage winding conductor thickness is 0.9 mm, the winding electrical height is 400 mm, the winding phase distance is 7 mm, and the distance between the low-voltage winding and the core is 5 mm.

3. According to claim 1, a method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof, characterized in that: In step 2, the current density formula of each layer of the foil winding conductor is:

4. According to claim 1, a method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof, characterized in that: In step 3, N l The expression of AC resistivity of non-overlapping foil winding is: in: Where A is the normalized thickness of the copper foil, d is the width of the copper foil conductor, δ is the penetration depth, ρ is the conductor resistivity, μ is the winding magnetic permeability, f is the frequency of the AC current, h is the height of the copper foil conductor, and h core is the core window height.

5. According to claim 1, a method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof, characterized in that: In step 4, a correction formula for the eddy current calculation formula of the foil winding of the medium and low frequency three-dimensional wound core transformer is: F′ R =(αf γ +b)·F R Among them, F′ R is the final corrected AC resistance coefficient, f is the frequency of the three-dimensional wound core transformer, α, β, and γ are the winding correlation coefficient, core correlation coefficient, and insulation distance correlation coefficient, respectively, and F R is the AC resistivity of foil winding. According to the winding, core and insulation distance parameters, the three coefficient calculation formulas can be obtained as follows: Where, d p is the transformer phase distance, D is the thickness of the three-dimensional wound core, d ch d is the distance between the core column and the inner diameter of the low voltage winding, mc Main airway distance.

6. According to claim 1, a method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof, characterized in that: In step 5, the radial electromagnetic force on the copper foil conductor is: F r =B r n S n J z n 2πR n The axial electromagnetic force is: Where S n is the cross-sectional area of ​​the nth copper foil conductor, is the radial leakage flux density of the nth layer conductor, is the axial leakage flux density, is the current density of the nth layer conductor, R n It is the distance from the center of the nth layer conductor to the center line of the core.

7. A method for correcting the eddy current loss formula of foil winding of three-dimensional wound core transformer and calculating the electromagnetic force thereof as described in claims 1-6, characterized in that: The calculation formula for the eddy current loss of the low-voltage foil winding in the three-dimensional wound core transformer at different frequencies was derived and corrected, and the calculation method for the short-circuit electromagnetic force of the foil winding was determined, which provided a reference for determining the eddy current loss of the foil winding of the three-dimensional wound core transformer in actual engineering.

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