Calculation Method of Short-Circuit Impedance of Multi-Winding Transformer

Abstract

The present invention belongs to the field of power electronics technology and relates to a method for calculating the short-circuit impedance of a multi-winding transformer. The multi-winding transformer includes a primary winding P and n, where n ≥ 2, secondary windings. Given the rated voltage, rated current, and number of turns of each winding in the multi-winding transformer, the specific steps for calculating the short-circuit impedance are as follows: Step 1: Based on the ampere-turn balance principle, the number of turns of each of the secondary windings S2 to Sn is respectively equivalent to the number of turns of the secondary winding S1; Step 2: Treating the n secondary windings as a single secondary winding S to obtain the number of turns of the secondary winding S; Step 3: Based on the ampere-turn balance principle, the multi-winding transformer is equivalent to a two-winding transformer, and the short-circuit impedance is calculated as for a two-winding transformer. The present invention can simplify the short-circuit impedance testing steps of the multi-winding transformer and improve the test accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of power electronics and relates to a transformer, in particular to a method for calculating the short-circuit impedance of a multi-winding transformer, which is used for testing the short-circuit impedance of the transformer. Background Art

[0002] Transformer short-circuit impedance, also known as transformer impedance voltage, is a standard value expressed as a percentage, indicating the internal impedance of the transformer. Short-circuit impedance is a key technical indicator of transformers, crucial for the stability of power supply systems and the quality of power supplied to loads. Transformer short-circuit impedance is a crucial indicator for determining whether transformer windings are deformed and is a common method for calculating transformer capacity in engineering applications.

[0003] The short-circuit impedance test of a multi-winding transformer is a relatively complex problem. Figure 1 ) as an example, where winding 1 is low voltage, winding 2 is medium voltage, and winding 3 is high voltage, or winding 1 is medium voltage, winding 2 is low voltage, and winding 3 is high voltage. Usually, when designing, manufacturing, and shipping a transformer, only the short-circuit impedance when one of the windings is unloaded and the other two windings are treated as a two-winding transformer is given, that is, the short-circuit impedance U of winding 1 and winding 2 of a three-phase transformer. kx12 (%), short-circuit impedance U of three-phase transformer winding 1 and winding 3 kx13 (%), short-circuit impedance U of three-phase transformer winding 2 and winding 3 kx23 (%), respectively according to the formula The calculation is as follows:

[0004]

[0005]

[0006] Where f is the frequency; e t is the potential per turn of the winding, unit: V / turn; I1 W1 is the rated ampere-turns of winding 1; ρ 12 is the Rockwell coefficient of winding 1 and winding 2, ρ 13 is the Rockwell coefficient of winding 1 and winding 3, ρ 23 is the Rockwell coefficient of winding 2 and winding 3, K 12 is the additional reactance coefficient of winding 1 and winding 2, K 13 is the additional reactance coefficient of winding 1 and winding 3, K 23 is the additional reactance coefficient of winding 2 and winding 3, H k12 is the average reactance height of winding 1 and winding 2, H k13 is the average reactance height of winding 1 and winding 3, H k23is the average reactance height of winding 2 and winding 3, a1 is the radial thickness between bare wires of winding 1, a2 is the radial thickness between bare wires of winding 2, a3 is the radial thickness between bare wires of winding 3, r1 is the average radius of winding 1, r2 is the average radius of winding 2, r3 is the average radius of winding 3, a 12 is the width of the oil channel between the bare wires of winding 1 and winding 2, a 13 is the width of the oil channel between the bare wires of winding 1 and winding 3, a 23 is the width of the oil channel between the bare wires of winding 2 and winding 3, r 12 is the average radius of the oil passage between winding 1 and winding 2, r 13 is the average radius of the oil passage between winding 1 and winding 3, r 23 is the average radius of the oil channel between winding 2 and winding 3.

[0007] If the capacities of the three windings are unequal, the short-circuit impedance between the corresponding two windings must be converted to 100% capacity, which makes this test method very complicated. It should be noted that the more windings there are, the more complicated the test method becomes, and the transformer short-circuit impedance test accuracy is reduced. Summary of the Invention

[0008] The present invention addresses the above-mentioned problems in the prior art such as the complexity of short-circuit impedance testing of multi-winding transformers, and provides a method for calculating the short-circuit impedance of a multi-winding transformer, which can simplify the short-circuit impedance testing steps of the multi-winding transformer and improve the accuracy of the test.

[0009] To achieve the above object, the present invention provides a method for calculating the short-circuit impedance of a multi-winding transformer, wherein the multi-winding transformer includes a primary winding P and n, where n ≥ 2, secondary windings. The rated voltage, rated current, and number of turns of each winding in the multi-winding transformer are known, wherein the rated current of the primary winding P is I and the number of turns is W, the rated current of the secondary winding S1 is I1 and the number of turns is w1, the rated current of the secondary winding S2 is I2 and the number of turns is w2, ..., and the rated current of the secondary winding Sn is In and the number of turns is wn. The specific steps for calculating the short-circuit impedance of the multi-winding transformer are as follows:

[0010] Step 1: According to the ampere-turn balance principle, the number of turns of the secondary windings S2 to Sn is equivalent to the number of turns of the secondary winding S1;

[0011] Step 2: Take n secondary windings as a secondary winding S and obtain the number of turns of the secondary winding S;

[0012] Step 3: Following the process of steps 1 and 2, based on the ampere-turn balance principle, the multi-winding transformer is equivalent to a two-winding transformer, and the short-circuit impedance is calculated according to the two-winding transformer.

[0013] Preferably, in step 1, the number of turns of the secondary windings S2 to Sn is equivalent to the number of turns of the secondary winding S1 according to formula (1), and formula (1) is expressed as:

[0014] wn'*I1=wn*In (1)

[0015] From formula (1), we can obtain wn'=wn*In / I1.

[0016] Preferably, in step 2, the number of turns of the secondary winding S is:

[0017] w=w1+w2'+...+wn'=w1+w2*I2 / I1+...+wn*In / I1 (2).

[0018] Preferably, in step 3, the short-circuit impedance of the dual-winding transformer is calculated using formula (3), which is expressed as:

[0019]

[0020] Where U kx is the short-circuit impedance of the multi-winding transformer; f is the frequency; e t is the potential per turn, unit: V / turn; IW is the rated ampere-turns of the primary winding P; ρ PS is the Rockwell coefficient of the primary winding P and the secondary winding S, R2 is the outer radius of the primary winding P, unit: cm; R1 is the inner radius of the secondary winding S, unit: cm; H is the magnetic field strength; K PS is the additional impedance coefficient of the primary winding P and the secondary winding S, h x H is the height of the area occupied by unbalanced ampere-turns, unit: cm; k is the reactance height of the winding with the higher axial dimension between the primary winding P and the secondary winding S, in cm; λ is the total width of the leakage magnetic field, K k is the coefficient; H kPS is the average reactance height of the primary winding P and the secondary winding S;

[0021] When there is no axial air passage between the inner and outer windings of each winding, ΣD is calculated using the following formula: Among them, a P is the radial thickness between bare wires of the primary winding P; r P is the average radius of the primary winding P, a S is the radial thickness between bare wires of the secondary winding S; r S is the average radius of the secondary winding S, a PS The width of the oil channel between the primary winding P and the secondary winding S bare wire; r PS is the average radius of the oil channel between the primary winding P and the secondary winding S;

[0022] When there is an axial air passage between the inner and outer windings of each winding, ΣD is calculated using the following formula: Among them, a P ' is the radial thickness between bare wires of the primary winding P, a P " is the radial thickness between bare wires of the primary winding P and the outer winding, a S ' is the radial thickness between bare wires of the secondary winding S, a S " is the radial thickness between bare wires of the secondary winding S, a PP is the oil channel width between the bare wires of the primary winding P; a SS is the oil channel width between the bare wires of the secondary winding S; r PP is the average radius of the oil channel in the primary winding P; r SS is the average radius of the oil channel in the secondary winding S; W' is the total number of turns of the primary winding P when it is tapped; w' is the total number of turns of the secondary winding S when it is tapped.

[0023] Compared with the prior art, the advantages and positive effects of the present invention are:

[0024] The short-circuit impedance calculation method of the multi-winding transformer of the present invention treats multiple secondary windings of the multi-winding transformer as equivalent to one secondary winding according to the ampere-turn balance principle, and then calculates the short-circuit impedance of the multi-winding transformer according to the short-circuit impedance calculation method of a double-winding transformer. The calculation is simplified and the calculation accuracy is high. The difficult problem of simple calculation of the multi-winding transformer is solved, the calculation efficiency of the short-circuit impedance of the multi-winding transformer is improved, and the short-circuit impedance test steps of the multi-winding transformer are simplified, thereby improving the test accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic diagram of the structure of the windings in a three-winding transformer;

[0026] Figure 2 A schematic diagram of the windings of the multi-winding transformer of the present invention;

[0027] Figure 3 This is a winding diagram of the multi-winding transformer of the present invention after being equivalent to a double-winding transformer;

[0028] Figure 4 This is a schematic structural diagram of the windings in a double-winding transformer (when there is no air passage between the inner and outer windings) after the multi-winding transformer according to the present invention is equivalent;

[0029] Figure 5 This is a schematic structural diagram of the windings in a double-winding transformer (when there is an air passage between the inner and outer windings of the windings) after the multi-winding transformer of the present invention is equivalent;

[0030] Figure 6Schematic diagram of the windings of the three-winding transformer according to embodiment 1 of the present invention;

[0031] Figure 7 Schematic diagram of the windings of the four-winding transformer according to embodiment 2 of the present invention;

[0032] Figures 8a-8b Schematic diagram of the area occupied by unbalanced ampere-turns according to an embodiment of the present invention.

[0033] In the figure, 1, winding 1, 2, winding 2, 3, winding 3, 4, magnetic core, 5, primary winding P, 6, secondary winding S, 7, inner winding P' of primary winding P, 8, outer winding P", of primary winding P, 9, inner winding S' of secondary winding S, 10, outer winding S", of secondary winding S. DETAILED DESCRIPTION

[0034] The present invention is described in detail below by way of exemplary embodiments, but it should be understood that elements, structures, and features of one embodiment may be beneficially combined in other embodiments without further description.

[0035] The present invention provides a method for calculating the short-circuit impedance of a multi-winding transformer. Figure 2 The multi-winding transformer includes a primary winding P and n, where n≥2, secondary windings. The rated voltage, rated current, and number of turns of each winding in the multi-winding transformer are known. The rated current of the primary winding P is I, and the number of turns is W. The rated current of the secondary winding S1 is I1, and the number of turns is w1. The rated current of the secondary winding S2 is I2, and the number of turns is w2, .... The rated current of the secondary winding Sn is In, and the number of turns is wn. The specific steps for calculating the short-circuit impedance of the multi-winding transformer are:

[0036] Step 1: Based on the ampere-turn balance principle, the number of turns of the secondary windings S2 to Sn is equivalent to the number of turns of the secondary winding S1 according to formula (1). Formula (1) is expressed as:

[0037] wn'*I1=wn*In (1)

[0038] From formula (1), we can obtain wn'=wn*In / I1.

[0039] Step 2: Treat n secondary windings as a secondary winding S. The number of turns of the secondary winding S is:

[0040] w=w1+w2'+...+wn'=w1+w2*I2 / I1+...+wn*In / I1 (2).

[0041] Step 3: According to the process of step 1 and step 2, based on the ampere-turn balance principle, the multi-winding transformer is equivalent to a double-winding transformer (see Figure 3 ), the short-circuit impedance of the double-winding transformer is calculated using formula (3), which is expressed as:

[0042]

[0043] Where U kx is the short-circuit impedance of the multi-winding transformer; f is the frequency; e t is the potential per turn, unit: V / turn; IW is the rated ampere-turns of the primary winding P. ρ PS is the Rockwell coefficient of the primary winding P and the secondary winding S, R2 is the outer radius of the primary winding P (to the bare wire), unit: cm. R1 is the inner radius of the secondary winding S (to the bare wire), unit: cm. H is the magnetic field strength. K PS is the additional impedance coefficient of the primary winding P and the secondary winding S, h x is the height of the area occupied by the unbalanced ampere-turns (see Figure 8a 、 8b ,exist Figure 8a In, h x =h x1 +h x2 ), unit: cm; H k is the reactance height of the winding with the higher axial dimension between the primary winding P and the secondary winding S, in cm; λ is the total width of the leakage magnetic field, K k is the coefficient. kPS is the average reactance height of the primary winding P and the secondary winding S.

[0044] In a specific embodiment of the present invention, when there is no axial air passage between the inner and outer windings of each winding (see Figure 4 ), ΣD is calculated by the following formula: Among them, a P is the radial thickness between bare wires of the primary winding P; r P is the average radius of the primary winding P, a S is the radial thickness between bare wires of the secondary winding S; r S is the average radius of the secondary winding S, a PS The width of the oil channel between the primary winding P and the secondary winding S bare wire; r PS It is the average radius of the oil channel between the primary winding P and the secondary winding S.

[0045] In another embodiment of the present invention, when there is an axial air passage between the inner and outer windings of each winding (see Figure 5 ), the inner winding of the primary winding P is P', the outer winding of the primary winding P is P", the inner winding of the secondary winding S is S', and the outer winding of the secondary winding S is S", and ΣD is calculated by the following formula:

[0046]

[0047] Among them, a P ' is the radial thickness between bare wires of the inner winding P' of the primary winding P, a P " is the radial thickness between bare wires of the outer winding P" of the primary winding P, a S ' is the radial thickness between bare wires of winding S' in secondary winding S, a S " is the radial thickness between bare wires of secondary winding S and outer winding S", a PP is the oil channel width between the bare wires of the primary winding P; a SS is the oil channel width between the bare wires of the secondary winding S; r PP is the average radius of the oil channel in the primary winding P; r SS is the average radius of the oil channel in the secondary winding S; W' is the total number of turns of the primary winding P when it is tapped; w' is the total number of turns of the secondary winding S when it is tapped.

[0048] The method for calculating the short-circuit impedance of the multi-winding transformer will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] Example 1: This example provides a method for calculating the short-circuit impedance of a three-winding transformer. Figure 5 The three-winding transformer includes a primary winding P and two secondary windings, namely secondary winding S1 and secondary winding S2. The rated voltage, rated current and number of turns of each winding in the three-winding transformer are known. Among them, the rated current of the primary winding P is I and the number of turns is W, the rated current of the secondary winding S1 is I1 and the number of turns is w1, and the rated current of the secondary winding S2 is I2 and the number of turns is w2. The specific steps for calculating the short-circuit impedance of the multi-winding transformer are:

[0050] Step 1: Based on the ampere-turn balance principle, the number of turns of the secondary winding S2 is equivalent to the number of turns w2' of the secondary winding S1 according to the following formula;

[0051] w2'*I1=w2*I2

[0052] Then we can get w2'=w2*I2 / I1;

[0053] Step 2: Combine the two secondary windings into one secondary winding S. The number of turns of the secondary winding S is:

[0054] w=w1+w2′=w1+w2*I2 / I1

[0055] Step 3: Following the process of steps 1 and 2, based on the ampere-turn balance principle, the three-winding transformer is equivalent to a two-winding transformer. The short-circuit impedance is calculated according to formula (3) based on the two-winding transformer. Formula (3) is expressed as:

[0056]

[0057] Where U kx is the short-circuit impedance of the three-winding transformer (in this embodiment); f is the frequency; e t is the potential per turn, unit: V / turn; IW is the rated ampere-turns of the primary winding P. ρ PS is the Rockwell coefficient of the primary winding P and the secondary winding S, R2 is the outer radius of the primary winding P (to the bare wire), unit: cm. R1 is the inner radius of the secondary winding S (to the bare wire), unit: cm. H is the magnetic field strength. K PS is the additional impedance coefficient of the primary winding P and the secondary winding S, h x is the height of the area occupied by the unbalanced ampere-turns (see Figure 8a 、 8b ,exist Figure 8a In, h x =h x1 +h x2 ), unit: cm; H k is the reactance height of the winding with the higher axial dimension between the primary winding P and the secondary winding S, in cm; λ is the total width of the leakage magnetic field, K k is the coefficient. kPS is the average reactance height of the primary winding P and the secondary winding S.

[0058] When there is no axial airway between the inner and outer windings of each winding (see Figure 4 ), ΣD is calculated by the following formula: Among them, a P is the radial thickness between bare wires of the primary winding P; r P is the average radius of the primary winding P, a S is the radial thickness between bare wires of the secondary winding S; r S is the average radius of the secondary winding S, a PS The width of the oil channel between the primary winding P and the secondary winding S bare wire; r PS It is the average radius of the oil channel between the primary winding P and the secondary winding S.

[0059] When there is an axial airway between the inner and outer windings of each winding (see Figure 5 ), the inner winding of the primary winding P is P', the outer winding of the primary winding P is P", the inner winding of the secondary winding S is S', and the outer winding of the secondary winding S is S", and ΣD is calculated by the following formula:

[0060]

[0061] Among them, a P' is the radial thickness between bare wires of the inner winding P' of the primary winding P, a P " is the radial thickness between bare wires of the outer winding P" of the primary winding P, a S ' is the radial thickness between bare wires of winding S' in secondary winding S, a S " is the radial thickness between bare wires of secondary winding S and outer winding S", a PP is the oil channel width between the bare wires of the primary winding P; a SS is the oil channel width between the bare wires of the secondary winding S; r PP is the average radius of the oil channel in the primary winding P; r SS is the average radius of the oil channel in the secondary winding S; W' is the total number of turns of the primary winding P when it is tapped; w' is the total number of turns of the secondary winding S when it is tapped.

[0062] It should be noted that in the ΣD calculation formula, the values ​​of various parameters are known values ​​after the three-winding transformer product is finalized.

[0063] The actual short-circuit impedance of the three-winding transformer is 4.0%, and the short-circuit impedance calculated using the calculation method described in this embodiment is 4.1%. It can be seen that the calculation method described in this embodiment can effectively calculate the short-circuit impedance of the three-winding transformer with high accuracy.

[0064] Example 2: This example provides a method for calculating the short-circuit impedance of a four-winding transformer. Figure 6 The four-winding transformer includes a primary winding P and three secondary windings, namely secondary winding S1, secondary winding S2, and secondary winding S3. The rated voltage, rated current, and number of turns of each winding in the multi-winding transformer are known. Among them, the rated current of the primary winding P is I and the number of turns is W, the rated current of the secondary winding S1 is I1 and the number of turns is w1, the rated current of the secondary winding S2 is I2 and the number of turns is w2, and the rated current of the secondary winding S3 is I3 and the number of turns is w3. The specific steps for calculating the short-circuit impedance of the four-winding transformer are:

[0065] Step 1: Based on the ampere-turn balance principle, the turns of the secondary windings S2 and S3 are equivalent to the turns of the secondary winding S1 according to formula (1). Formula (1) is expressed as:

[0066] wn'*I1=wn*In (1)

[0067] From formula (1), we get wn'=wn*In / I1;

[0068] The secondary winding S2 is equivalent to the secondary winding S1 with a number of turns w2′=w2*I2 / I1, and the secondary winding S3 is equivalent to the secondary winding S3 with a number of turns w3′=w3*I3 / I1.

[0069] Step 2: Combine the three secondary windings into one secondary winding S. The number of turns of the secondary winding S is:

[0070] w=w1+w2'+w3'=w1+w2*I2 / I1+w3*I3 / I1

[0071] Step 3: Following the process of steps 1 and 2, based on the ampere-turn balance principle, the four-level winding transformer is equivalent to a double-winding transformer. The short-circuit impedance is calculated according to formula (3) based on the double-winding transformer. Formula (3) is expressed as:

[0072]

[0073] Where U kx is the short-circuit impedance of the four-winding transformer (in this embodiment); f is the frequency; e t is the potential per turn, unit: V / turn; IW is the rated ampere-turns of the primary winding P. ρ PS is the Rockwell coefficient of the primary winding P and the secondary winding S, R2 is the outer radius of the primary winding P (to the bare wire), unit: cm. R1 is the inner radius of the secondary winding S (to the bare wire), unit: cm. H is the magnetic field strength. K PS is the additional impedance coefficient of the primary winding P and the secondary winding S, h x is the height of the area occupied by the unbalanced ampere-turns (see Figure 8a 、 8b ,exist Figure 8a In, h x =h x1 +h x2 ), unit: cm; H k is the reactance height of the winding with the higher axial dimension between the primary winding P and the secondary winding S, in cm; λ is the total width of the leakage magnetic field, K k is the coefficient. kPS is the average reactance height of the primary winding P and the secondary winding S.

[0074] When there is no axial airway between the inner and outer windings of each winding (see Figure 4 ), ΣD is calculated by the following formula: Among them, a P is the radial thickness between bare wires of the primary winding P; r P is the average radius of the primary winding P, a S is the radial thickness between bare wires of the secondary winding S; r S is the average radius of the secondary winding S, a PS The width of the oil channel between the primary winding P and the secondary winding S bare wire; r PSis the average radius of the oil passage between the primary winding P and the secondary winding S. When there is an axial air passage between the inner and outer windings of each winding (see Figure 5 ), the inner winding of the primary winding P is P', the outer winding of the primary winding P is P", the inner winding of the secondary winding S is S', and the outer winding of the secondary winding S is S", and ΣD is calculated by the following formula:

[0075]

[0076] Among them, a P ' is the radial thickness between bare wires of the inner winding P' of the primary winding P, a P " is the radial thickness between bare wires of the outer winding P" of the primary winding P, a S ' is the radial thickness between bare wires of winding S' in secondary winding S, a S " is the radial thickness between bare wires of secondary winding S and outer winding S", a PP is the oil channel width between the bare wires of the primary winding P; a SS is the oil channel width between the bare wires of the secondary winding S; r PP is the average radius of the oil channel in the primary winding P; r SS is the average radius of the oil channel in the secondary winding S; W' is the total number of turns of the primary winding P when it is tapped; w' is the total number of turns of the secondary winding S when it is tapped.

[0077] It should be noted that in the ΣD calculation formula, the values ​​of various parameters are known values ​​after the four-winding transformer product is finalized.

[0078] The actual short-circuit impedance of the four-winding transformer is 3.6%, and the short-circuit impedance calculated using the calculation method described in this embodiment is 3.8%. It can be seen that the calculation method described in this embodiment can effectively calculate the short-circuit impedance of the four-winding transformer with high accuracy.

[0079] The above embodiments are used to explain the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for calculating the short-circuit impedance of a multi-winding transformer, characterized in that: The multi-winding transformer includes a primary winding P and n, n≥2 secondary windings. The rated voltage, rated current, and number of turns of each winding in the multi-winding transformer are known. The rated current of the primary winding P is I and the number of turns is W; the rated current of the secondary winding S1 is I1 and the number of turns is w1; the rated current of the secondary winding S2 is I2 and the number of turns is w2, ...; the rated current of the secondary winding Sn is In and the number of turns is wn. The specific steps for calculating the short-circuit impedance of the multi-winding transformer are: Step 1: According to the ampere-turn balance principle, the number of turns of the secondary windings S2 to Sn is equivalent to the number of turns of the secondary winding S1; Step 2: Take n secondary windings as a secondary winding S and obtain the number of turns of the secondary winding S; Step 3: Following the process of steps 1 and 2, based on the ampere-turn balance principle, the multi-winding transformer is equivalent to a two-winding transformer, and the short-circuit impedance is calculated according to the two-winding transformer.

2. The method for calculating the short-circuit impedance of a multi-winding transformer according to claim 1, wherein: In step 1, the number of turns of the secondary windings S2 to Sn is equivalent to the number of turns of the secondary winding S1 according to formula (1). Formula (1) is expressed as: wn'*I1=wn*In (1) From formula (1), we can obtain wn'=wn*In / I1.

3. The method for calculating the short-circuit impedance of a multi-winding transformer according to claim 2, wherein: In step 2, the number of turns of the secondary winding S is: w=w1+w2'+...+wn'=w1+w2*I2 / I1+...+wn*In / I1 (2).

4. The method for calculating the short-circuit impedance of a multi-winding transformer according to claim 3, wherein: In step 3, the short-circuit impedance of the double-winding transformer is calculated using formula (3), which is expressed as: Where U kx is the short-circuit impedance of the multi-winding transformer; f is the frequency; e t is the potential per turn, unit: V / turn; IW is the rated ampere-turns of the primary winding P; ρ PS is the Rockwell coefficient of the primary winding P and the secondary winding S, R2 is the outer radius of the primary winding P, unit: cm; R1 is the inner radius of the secondary winding S, unit: cm; H is the magnetic field strength; K PS is the additional impedance coefficient of the primary winding P and the secondary winding S, h x H is the height of the area occupied by unbalanced ampere-turns, unit: cm; k is the reactance height of the winding with the higher axial dimension between the primary winding P and the secondary winding S, in cm; λ is the total width of the leakage magnetic field, K k is the coefficient; H kPS is the average reactance height of the primary winding P and the secondary winding S; When there is no axial air passage between the inner and outer windings of each winding, ΣD is calculated using the following formula: Among them, a P is the radial thickness between bare wires of the primary winding P; r P is the average radius of the primary winding P, a S is the radial thickness between bare wires of the secondary winding S; r S is the average radius of the secondary winding S, a PS The width of the oil channel between the primary winding P and the secondary winding S bare wire; r PS is the average radius of the oil channel between the primary winding P and the secondary winding S; When there is an axial air passage between the inner and outer windings of each winding, ΣD is calculated using the following formula: Among them, a P ' is the radial thickness between bare wires of the primary winding P, a P " is the radial thickness between bare wires of the primary winding P and the outer winding, a S ' is the radial thickness between bare wires of the secondary winding S, a S " is the radial thickness between bare wires of the secondary winding S, a PP is the oil channel width between the bare wires of the primary winding P; a SS is the oil channel width between the bare wires of the secondary winding S; r PP is the average radius of the oil channel in the primary winding P; r SS is the average radius of the oil channel in the secondary winding S; W' is the total number of turns of the primary winding P when it is tapped; w' is the total number of turns of the secondary winding S when it is tapped.

5. The method for calculating the short-circuit impedance of a multi-winding transformer according to any one of claims 1 to 4, wherein: The multi-winding transformer is a three-winding transformer, which includes a primary winding P and two secondary windings. The rated voltage, rated current and number of turns of each winding in the three-winding transformer are known, wherein the rated current of the primary winding P is I and the number of turns is W, the rated current of the secondary winding S1 is I1 and the number of turns is w1, and the rated current of the secondary winding S2 is I2 and the number of turns is w2.

6. The method for calculating the short-circuit impedance of a multi-winding transformer according to any one of claims 1 to 4, wherein: The multi-winding transformer is a four-winding transformer, which includes a primary winding P and three secondary windings. The rated voltage, rated current and number of turns of each winding in the four-winding transformer are known. Among them, the rated current of the primary winding P is I, and the number of turns is W; the rated current of the secondary winding S1 is I1, and the number of turns is w1; the rated current of the secondary winding S2 is I2, and the number of turns is w2; the rated current of the secondary winding S3 is I3, and the number of turns is w3.

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