A calculation method for the short-circuit withstand capability of transformer windings

Abstract

The present invention belongs to the technical field of transformer winding coils, and in particular relates to a method for calculating the short-circuit resistance of transformer winding coils. The method includes the following aspects: calculation of coil annular stress; calculation of coil axial bending stress; calculation of coil radial bending stress; and calculation of force synthesis, which synthesizes the three forces (the coil annular stress, the coil axial bending stress, and the coil radial bending stress) to calculate the resultant force. The present invention provides a method for calculating the short-circuit resistance of transformer winding coils. This method considers factors such as the forces acting on the coil in all directions, the bending deformation of two adjacent coil pads, and the bending deformation of two adjacent coil struts. This method addresses the shortcomings of traditional methods, which simplify the model and do not consider the forces acting on the pads, and provides a more accurate calculation method.

Description

Technical Field

[0001] The invention belongs to the technical field of transformer winding coils, and in particular relates to a method for calculating the short-circuit resistance of transformer winding coils. Background Art

[0002] The stable operation of transformers is crucial for ensuring the normal and efficient operation of power systems. However, if a short-circuit fault occurs during operation, the short-circuit current flowing through the windings can reach dozens of times the rated current. This high current induces electromagnetic forces in the windings, subjecting components such as the transformer coils and conductors to electromagnetic shocks. This electromagnetic force can cause axial instability in the coils, potentially leading to transformer damage. Therefore, accurate calculation methods for the short-circuit withstand capability of transformer windings help understand the transformer's tolerance and provide timely protection for components with poor short-circuit withstand capability to prevent secondary damage.

[0003] The existing calculation method for short-circuit withstand capacity is too simple. It regards the entire coil as a model and does not consider the impact of internal impact on the coil and the force on the pad. Under the action of impact force, the compression displacement of the end coil of the winding is the largest, and the main force-bearing area is the location of the pad. The limitations of the existing calculation method reduce the accuracy of the calculation results, affecting the judgment of the transformer's short-circuit withstand capacity.

[0004] To this end, the present invention provides a method for calculating the short-circuit resistance of transformer windings. Summary of the Invention

[0005] In order to solve or improve the problem that the limitations of existing calculation methods reduce the accuracy of calculation results and affect the judgment of the transformer's short-circuit withstand capacity, the present invention provides a method for calculating the short-circuit withstand capacity of transformer winding coils. The specific technical solution is as follows:

[0006] The present invention provides a method for calculating the short-circuit resistance of transformer winding coils, including the following aspects:

[0007] Calculate the coil annular stress;

[0008] Calculate the axial bending stress of the wire cake;

[0009] Calculate the radial bending stress of the wire cake;

[0010] The three forces of coil annular stress calculation, coil axial bending stress calculation and coil radial bending stress are synthesized to obtain the resultant force

[0011] Preferably, the coil annular stress is the axial tension exerted on the inner and outer coils under the action of the magnetic field. The calculation equation of the coil annular stress is as follows:

[0012]

[0013] Where, F h is the annular stress of the coil, F1 is the axial force per unit length of a single wire of the coil, D l is the diameter of a single wire in the coil.

[0014] Preferably, the calculation equation for the axial force per unit length of a single wire of the coil is as follows:

[0015] F1=B z icosα

[0016] Where F1 is the axial force per unit length of a single wire of the coil, B z is the axial magnetic induction intensity uniformly distributed around the coil, i is the short-circuit current flowing through a single coil of the coil, and α is the angle between the axial force F1 and the axial direction.

[0017] Preferably, the calculation equation for the axial magnetic induction intensity of the magnetic field uniformly distributed around the coil is as follows:

[0018]

[0019] Where B z is the axial magnetic induction intensity uniformly distributed around the coil, N1 is the number of phase turns, ρ is the Rockwell coefficient, h is the height of the winding reactance, and the supporting role of the winding spacers, stays, and core is taken into account.

[0020] Preferably, the axial bending stress of the coil is the stress generated between the coils when the coils are subjected to the axial electromagnetic force. The calculation equation for the axial bending stress of the coil is as follows:

[0021]

[0022] Where, F Z is the axial bending stress of the coil, q and p are the axial and radial dimensions of the coil wire respectively, M Z is the torque when the coil is subjected to force.

[0023] Preferably, the calculation equation of the torque when the coil is subjected to force is as follows:

[0024]

[0025] Where l is the coil length of the two pads, and F1 is the axial force per unit length of a single conductor of the coil.

[0026] Preferably, the calculation formula for the coil length of the two pads is as follows:

[0027]

[0028] Where M jis the torque of the coil, D1 is the coil diameter, n1 is the number of pads, k d is the pad width, k f is the gap width.

[0029] Preferably, the radial bending stress of the coil is the bending stress that the coil is subjected to under the action of the radial electromagnetic force, and the calculation equation is as follows:

[0030]

[0031] Where, F j is the radial bending stress of the wire cake, M j The torque acting on the coil, q and p are the axial and radial dimensions of the coil wire respectively.

[0032] Preferably, the calculation equation for the torque of the wire cake is as follows:

[0033]

[0034] Where F2 is the radial force per unit length of a single conductor of the coil, and l1 is the length of the coil between the two supports.

[0035] The calculation formula for the length of the coil between the two struts is as follows:

[0036]

[0037] Where D1 is the coil diameter, n2 is the number of stays, k c is the pad width, k f is the gap width.

[0038] Preferably, the calculation equation for the radial force per unit length of a single wire of the coil is as follows:

[0039] F2=B z isinα;

[0040] Where F2 is the radial force per unit length of a single wire of the coil, B z is the axial magnetic induction intensity uniformly distributed around the coil, i is the short-circuit current flowing through the coil, and α is the angle between the axial force and the axial direction.

[0041] The beneficial effects of the present invention are as follows: the present invention provides a method for calculating the short-circuit resistance of a transformer winding coil, which takes into account factors such as forces in all directions of the coil, bending deformation of two adjacent pads of the coil, and bending deformation of two adjacent struts of the coil, thereby solving the shortcomings of the traditional method of simplifying the model and not considering the forces on the pads, and the calculation method is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0043] Figure 2 is a uniform distribution diagram of the magnetic field;

[0044] Figure 3 It is a composite diagram of forces. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0046] It will be understood that when used in this specification and the appended claims, the terms “comprises” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0047] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0048] It should be further understood that the term "and / or" used in the present description and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0049] In order to solve the problem that the limitations of the existing calculation method reduce the accuracy of the calculation results and affect the judgment of the transformer's short-circuit withstand capacity, the following method is proposed: Figure 1 The calculation method of the short-circuit withstand capability of a transformer winding coil shown in the figure includes the following aspects:

[0050] Calculation of coil annular stress;

[0051] Calculation of axial bending stress of wire cake;

[0052] Calculation of radial bending stress of wire cake;

[0053] The force synthesis calculation combines the coil annular stress calculation, the wire cake axial bending stress calculation, and the wire cake radial bending stress to calculate the resultant force.

[0054] As a specific embodiment of the present invention, a method for calculating the annular stress of a coil is provided. When a short-circuit current passes through, the magnetic field is evenly distributed around the coil, such as Figure 2 , the coil annular stress F can be calculated h for:

[0055]

[0056] In formula (1), F1 is the axial force per unit length of a single wire of the coil, D l is the wire diameter. Under the action of the magnetic field, the inner and outer coils are subjected to axial tension, resulting in annular stress in the coils. In formula (1), the axial force F1 per unit length of a single wire in the coil can be calculated by the following formula (2):

[0057] F1=B z icosα (2)

[0058] In formula (2), B z is the axial magnetic induction intensity uniformly distributed around the coil, i is the short-circuit current flowing through the coil, and α is the angle between the axial force F1 and the axial direction.

[0059]

[0060] In formula (3), N1 is the number of phase turns, ρ is the Rockwell coefficient, and h is the height of the winding reactance, taking into account the supporting role of the winding spacers, stays, and core.

[0061] As a specific embodiment of the present invention, the coils are subjected to axial electromagnetic forces, which generate axial bending stress between the coils, causing the spacer to bend. Under the impact of the force, the coil end compression displacement is the largest, and the main stress area is where the spacer is located. The torque of the coil when the force is applied is:

[0062]

[0063] In formula (4), l is the length of the coils between the two pads, which can be calculated by the following formula (5):

[0064]

[0065] In formula (5), D1 is the coil diameter, n1 is the number of pads, k d is the pad width, k f is the gap width. The axial bending stress F of the wire cake can be obtained Z for:

[0066]

[0067] In equation (6), q and p are the axial and radial dimensions of the coil conductor.

[0068] As a specific embodiment of the present invention, the coil is subjected to bending stress under the action of radial electromagnetic force, causing the coil between the struts to bend and deform. At this time, the torque on the coil is:

[0069]

[0070] In formula (7), l1 is the length of the coil between the two stays, and the radial force per unit length of a single conductor of the coil is F2.

[0071] The length l1 of the coil between the two struts can be calculated by the following formula (8):

[0072]

[0073] In formula (8), D1 is the coil diameter, n2 is the number of stays, k c is the pad width, k f is the gap width. The radial force F2 per unit length of a single coil conductor can be calculated using the following formula (9):

[0074] F2=B z isinα (9)

[0075] The radial bending stress F of the wire cake can be obtained j for:

[0076]

[0077] As a specific embodiment of the present invention, the coil annular stress calculation method, the coil axial bending stress calculation method, and the coil radial bending stress calculation method are synthesized. Figure 3 , first calculate the axial bending stress F of the wire cake Z and radial bending stress F j synthesis

[0078]

[0079] Then Coil annular stress synthesis

[0080]

[0081] In the central region of the coil, the magnetic field lines are approximately parallel to the axial direction. This axial magnetic field exerts a radial force on the coil current. The axial magnetic induction intensity is greatest in the central region of the coil, and therefore the radial force acting on it is greatest there. From the central region to the coil ends, the axial component of the magnetic field decreases while the radial component increases, reaching its maximum at the coil ends. The radial component of the magnetic field exerts an axial force on the coil current. The axial force exerted by the radial magnetic field on the coil current at the upper and lower ends of the inner and outer coils is directed in the direction of the coil's height compression. The axial force exerted on each coil of the coil is proportional to the amplitude component of the magnetic field. Therefore, the coil at the end of the coil is subjected to the largest axial force, and the coil in the middle of the coil is subjected to the smallest axial force. However, when the coil at the end of the coil is subjected to axial compression, this force will be "transmitted" to the adjacent coil through the inter-coil pad. Therefore, the coil and wire at the position of the inter-coil pad are subjected to the accumulated axial force through "transfer". The qualitative analysis of this force approximately shows that the maximum value is located in the middle of the coil, that is, the inter-coil pad in the middle of the coil and the coils and wires on both sides of the pad are subjected to the largest accumulated axial force.

[0082] Those skilled in the art will appreciate that the units of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition of each example has been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0083] In the embodiments provided in the present application, it should be understood that the division of units is merely a logical function division, and there may be other division methods in actual implementation, for example, multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored, etc.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and description of the present invention.

Claims

1. A method for calculating the short-circuit resistance of transformer winding coils, characterized in that: Including the following aspects: Calculate the coil annular stress; the coil annular stress is the axial tension exerted on the inner and outer coils under the action of the magnetic field. The calculation equation for the coil annular stress is as follows: ； Where, F h is the annular stress of the coil, F1 is the axial force per unit length of a single wire of the coil, D l is the diameter of a single wire of the coil; Calculate the axial bending stress of the coil; the axial bending stress of the coil is the stress generated between the coils when the coils are subjected to the axial electromagnetic force. The calculation equation for the axial bending stress of the coil is as follows: ； Where, F Z is the axial bending stress of the coil, q and p are the axial and radial dimensions of the coil wire respectively, M Z is the moment when the coil is subjected to axial force; Calculate the radial bending stress of the coil; the radial bending stress of the coil is the bending stress of the coil under the action of the radial electromagnetic force. The calculation equation is as follows: ； Where, F j is the radial bending stress of the wire cake, M j is the moment of radial force on the coil, q and p are the axial and radial dimensions of the coil conductor respectively; The three forces of the coil annular stress calculation, the wire cake axial bending stress calculation, and the wire cake radial bending stress are synthesized to obtain a resultant force.

2. The method for calculating the short-circuit withstand capability of a transformer winding according to claim 1, wherein: The calculation equation for the axial force per unit length of a single wire of the coil is as follows: ； Where F1 is the axial force per unit length of a single wire of the coil, B z is the axial magnetic induction intensity uniformly distributed around the coil, i is the short-circuit current flowing through a single coil of the coil, and α is the angle between the axial force F1 and the axial direction.

3. The method for calculating the short-circuit withstand capability of a transformer winding according to claim 2, wherein: The calculation equation for the axial magnetic induction intensity of the magnetic field uniformly distributed around the coil is as follows: ； Where B z is the axial magnetic induction intensity uniformly distributed around the coil, N1 is the number of phase turns, ρ is the Rockwell coefficient, h is the height of the winding reactance, and the supporting role of the winding spacers, stays, and core is taken into account.

4. The method for calculating the short-circuit withstand capability of a transformer winding according to claim 1, wherein: The calculation equation for the torque when the coil is subjected to force is as follows: ； Where M Z is the moment when the coil is subjected to axial force, l is the length of the coil between the two pads, and F1 is the axial force per unit length of a single conductor of the coil.

5. The method for calculating the short-circuit resistance of transformer windings according to claim 4, characterized in that: The calculation formula for the coil length of the two pads is as follows: ； Where, l is the coil length of the two pads, D1 is the coil diameter, n1 is the number of pads, k d is the pad width, k f is the gap width.

6. The method for calculating the short-circuit withstand capability of a transformer winding according to claim 1, wherein: The calculation equation for the torque of the coil is as follows: Where M j is the torque of the coil acting radially, F2 is the radial force per unit length of a single conductor of the coil, and l1 is the length of the coil between the two stays; The calculation formula for the length of the coil between the two struts is as follows: ； Where l1 is the length of the coil between the two stays, D1 is the coil diameter, n2 is the number of stays, k d is the pad width, k f is the gap width.

7. The method for calculating the short-circuit withstand capability of a transformer winding according to claim 6, characterized in that: The calculation equation for the radial force per unit length of a single wire of the coil is as follows: ； Where F2 is the radial force per unit length of a single wire of the coil, B z is the axial magnetic induction intensity uniformly distributed around the coil, i is the short-circuit current flowing through the coil, and α is the angle between the axial force and the axial direction.

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