Transformer broadband distributed electromagnetic dual model construction method suitable for broadband disturbance analysis

Abstract

The invention discloses a transformer broadband distributed electromagnetic dual model construction method suitable for broadband disturbance analysis. The transformer broadband distributed electromagnetic dual model construction method comprises the following steps of 1) deducing a topological structure of a transformer electromagnetic dual model; 2) performing axial and radial multiple discretization on the iron core and the winding to construct a complete dual model; 3, model parameter identification is carried out, a parameter identification result is input into the complete dual model, and the transformer broadband distributed electromagnetic dual model.The transformer broadband distributed electromagnetic dual model is superior to a traditional broadband model in the aspects of applicable frequency bandwidth and port frequency variation characteristic representation precision.

Description

Technical Field

[0001] This invention relates to the field of transformers, specifically a method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis. Background Technology

[0002] As the core hub of power system energy conversion, the transformer's operating status is crucial to power system safety. In actual operation, transformers are subjected to traditional transient processes, including lightning strikes and switching overvoltages, as well as novel disturbances such as mid-to-high frequency harmonics and broadband oscillations caused by the high proportion of power electronic equipment (wind power / solar power / flexible DC power), with frequencies ranging from several hertz to several megahertz. Under broadband disturbance excitation, the transformer's impedance and transmission characteristics exhibit significant frequency-varying features compared to the power frequency, resulting in complex electromagnetic stress distributions within the transformer that differ significantly from the power frequency, and even posing significant hazards to transformer operation. To reveal the response law of broadband disturbances transmitted through the transformer, it is urgent to construct an accurate broadband electromagnetic model of the transformer. However, traditional broadband models have limited accuracy in characterizing the interactive coupling characteristics of the high-frequency parasitic parameter network inside the transformer, making them unsuitable for the current analysis needs of wider frequency bands.

[0003] Therefore, in order to reveal the response law of broadband disturbances transmitted through transformers, it is urgent to construct an accurate broadband electromagnetic model of transformers to accurately calculate the electromagnetic transient voltage characteristics of transformers, optimize insulation design, and provide a scientific basis for the development of transformers that can withstand broadband disturbances. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, comprising the following steps:

[0005] Step 1) Derive the topology of the electromagnetic dual model of the transformer;

[0006] Step 2) Perform axial and radial multiple discretization on the core and winding to construct a complete dual model;

[0007] Step 3) Identify the model parameters and input the parameter identification results into the complete dual model to construct a broadband distributed electromagnetic dual model of the transformer.

[0008] Furthermore, in step 1), the steps for deriving the topology of the transformer electromagnetic dual model include:

[0009] A distributed magnetic circuit model for a transformer is derived using a multi-discretion strategy involving both axial and radial directions.

[0010] By performing a dual transformation on the distributed magnetic circuit model of the transformer, the topology of the electromagnetic dual model of the transformer is obtained.

[0011] Furthermore, before deriving the distributed magnetic circuit model of the transformer using a multi-discretion strategy involving both axial and radial directions, the following steps are performed:

[0012] The winding is discretized into multiple layers in the radial direction to characterize the non-uniform distribution of its electromagnetic parameters in the radial direction under broadband conditions.

[0013] The change in the interlayer potential difference gradient of the transformer windings with increasing frequency is transformed into a non-uniform distribution.

[0014] The windings are axially discretized to construct a high-frequency parasitic parameter network inside the transformer.

[0015] Furthermore, in step 2), the steps for constructing the complete dual model include:

[0016] Step 2.1) Establish a characterization model of the core frequency variation characteristics, and perform a dual transformation on the characterization model of the core frequency variation characteristics to obtain a dual circuit model of the core.

[0017] Step 2.2) Construct a winding magnetic circuit model and discretize the winding thickness into sub-parts smaller than the characteristic scale of magnetic field change to obtain the winding dual circuit model;

[0018] Step 2.3) Construct a complete dual model including the core dual circuit model and the winding dual circuit model.

[0019] Furthermore, in step 2.1), a Cauer-type equivalent circuit model is used to establish a characterization model for the frequency-varying characteristics of the iron core.

[0020] Furthermore, in step 2.2), a complex permeability model is used to construct a winding magnetic circuit model to characterize the frequency-dependent resistance and inductance characteristics of the conductor.

[0021] Furthermore, in step 3), the parameter identification results include the inductance and resistance parameters in the core and winding circuit model.

[0022] Furthermore, the inductor and resistor parameters in the iron core circuit model are as follows:

[0023] (1)

[0024] Among them l ceq d is the length of the magnetic circuit. i w is the layer thickness. c σ is the core thickness; ceq The conductivity of the iron core material; μ cr ρ is the relative permeability of the core material; μ0 is the permeability of free space. , These are the resistance and inductance parameters in the iron core circuit model.

[0025] Furthermore, the inductor and resistance parameters in the winding circuit model are as follows:

[0026] (2)

[0027] Among them, l weq The height of the equivalent winding conductor cross-section is represented by w; the length of the winding coil is represented by d. n Indicates the thickness of the winding conductor; μ wr σ is the relative permeability of the winding material; weq μ is the electrical conductivity of the winding material; μ0 is the permeability of free space. , These are the resistance and inductance parameters in the winding circuit model.

[0028] Furthermore, in step 3), after constructing the wideband distributed electromagnetic dual model of the transformer, the port impedance and transmission characteristics of the wideband distributed electromagnetic dual model of the transformer are also verified. The verification indicators include the frequency error of the first series resonant point, the frequency error of the second resonant point, and the characterizable frequency band.

[0029] The technical effects of this invention are undeniable. This invention proposes a wideband distributed electromagnetic dual model for transformers suitable for wideband disturbance analysis. Compared with the traditional high-frequency model of transformers, the model of this invention can characterize the radial and axial non-uniform distribution characteristics of current density and magnetic field strength along the surface of the winding and the core to the core under wideband conditions, as well as their interaction characteristics with the distributed capacitor network. It is superior to the traditional wideband model in terms of applicable bandwidth and accuracy of port frequency-varying characteristics. Attached Figure Description

[0030] Figure 1 A flowchart illustrating the construction of a broadband distributed electromagnetic duality model for transformers suitable for broadband disturbance analysis, provided by this invention.

[0031] Figure 2 This is the topology of the transformer broadband distributed electromagnetic duality model of the present invention;

[0032] Figure 3 This is the core dual circuit model in this invention;

[0033] Figure 4 This is the winding dual circuit model in this invention;

[0034] Figure 5 This is the complete single-phase transformer broadband distributed dual circuit model in this invention;

[0035] Figure 6 Comparison curves of port impedance frequency variation characteristics;

[0036] Figure 7 Comparison of frequency conversion curves at the secondary side port. Detailed Implementation

[0037] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0038] Example 1:

[0039] See Figures 1 to 7 A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis includes the following steps:

[0040] Step 1) Derive the topology of the electromagnetic dual model of the transformer;

[0041] Step 2) Perform axial and radial multiple discretization on the core and winding to construct a complete dual model;

[0042] Step 3) Identify the model parameters and input the parameter identification results into the complete dual model to construct a broadband distributed electromagnetic dual model of the transformer.

[0043] Example 2:

[0044] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as in Embodiment 1, further comprising the following steps in step 1) for deriving the topology of the transformer electromagnetic dual model:

[0045] A distributed magnetic circuit model for a transformer is derived using a multi-discretion strategy involving both axial and radial directions.

[0046] By performing a dual transformation on the distributed magnetic circuit model of the transformer, the topology of the electromagnetic dual model of the transformer is obtained.

[0047] Example 3:

[0048] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of Embodiments 1-2, further comprising the following steps before deriving the distributed magnetic circuit model of the transformer using axial and radial multiple discretization strategies:

[0049] The winding is discretized into multiple layers in the radial direction to characterize the non-uniform distribution of its electromagnetic parameters in the radial direction under broadband conditions.

[0050] The change in the interlayer potential difference gradient of the transformer windings with increasing frequency is transformed into a non-uniform distribution.

[0051] The windings are axially discretized to construct a high-frequency parasitic parameter network inside the transformer.

[0052] Example 4:

[0053] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of embodiments 1-3, further comprising the following steps in step 2) for constructing the complete dual model:

[0054] Step 2.1) Establish a characterization model of the core frequency variation characteristics, and perform a dual transformation on the characterization model of the core frequency variation characteristics to obtain a dual circuit model of the core.

[0055] Step 2.2) Construct a winding magnetic circuit model and discretize the winding thickness into sub-parts smaller than the characteristic scale of magnetic field change to obtain the winding dual circuit model;

[0056] Step 2.3) Construct a complete dual model including the core dual circuit model and the winding dual circuit model.

[0057] Example 5:

[0058] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of embodiments 1-4, further wherein, in step 2.1), a Cauer-type equivalent circuit model is used to establish a characterization model of the core frequency-varying characteristics.

[0059] Example 6:

[0060] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of embodiments 1-5, further wherein, in step 2.2), a complex permeability model is used to construct a winding magnetic circuit model to characterize the frequency-varying resistance and inductance characteristics of the conductor.

[0061] Example 7:

[0062] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of embodiments 1-6, further wherein, in step 3), the parameter identification results include the inductance and resistance parameters in the core and winding circuit model.

[0063] Example 8:

[0064] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of embodiments 1-7, further wherein the inductor and resistance parameters in the core circuit model are as follows:

[0065] (1)

[0066] Among them l ceq d is the length of the magnetic circuit. i w is the layer thickness. c σ is the core thickness; ceqThe conductivity of the iron core material; μ cr ρ is the relative permeability of the core material; μ0 is the permeability of free space. , These are the resistance and inductance parameters in the iron core circuit model.

[0067] Example 9:

[0068] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, with the same technical content as any one of embodiments 1-8, further wherein the inductance and resistance parameters in the winding circuit model are as follows:

[0069] (2)

[0070] Among them, l weq The height of the equivalent winding conductor cross-section is represented by w; the length of the winding coil is represented by d. n Indicates the thickness of the winding conductor; μ wr σ is the relative permeability of the winding material; weq μ is the electrical conductivity of the winding material; μ0 is the permeability of free space. , These are the resistance and inductance parameters in the winding circuit model.

[0071] Example 10:

[0072] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis is provided. The technical content is the same as any one of embodiments 1-9. Further, in step 3), after constructing the broadband distributed electromagnetic dual model of the transformer, the port impedance and transmission characteristics of the broadband distributed electromagnetic dual model of the transformer are verified. The verification indicators include the frequency error of the first series resonant point, the frequency error of the second resonant point, and the characterizable frequency band.

[0073] Example 11:

[0074] A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, comprising the following steps:

[0075] S1: Topology Derivation of the Distributed Electromagnetic Duality Model for Transformers. Based on the principle of electromagnetic duality, the electromagnetic dual circuit model of a single-phase transformer is derived. The magnetic field intensity distribution inside the transformer windings is approximately linear at power frequency, but at high frequencies, the magnetic field distribution gradually transitions from approximately linear radially to being distributed only on the surface. Therefore, the radial direction of the windings can be discretized into multiple layers to characterize the non-uniform distribution of electromagnetic parameters along the radial direction over a wide frequency range. The inter-layer potential difference gradient of the transformer windings changes from uniform to non-uniform with increasing frequency, and the proportion of inter-layer capacitance influence increases. Therefore, the winding axis can be discretized to construct a high-frequency parasitic parameter network inside the transformer. The distributed magnetic circuit model of the transformer is derived and dualized as follows: Figure 2The circuit model topology shown.

[0076] S2: Construction of the core and winding circuit model. A Cauer-type equivalent circuit model is used to establish a characterization model of the core's frequency-varying characteristics. Due to the symmetry of the core's magnetic flux distribution and impedance characteristics, a dual transformation is performed on a half-side model and then connected in parallel to obtain the following... Figure 3 The diagram shows a dual-core circuit model. The winding magnetic circuit model uses a complex permeability model to characterize the frequency-dependent resistance and inductance characteristics of the conductor. To characterize the non-uniform distribution of the winding magnetic field along the radial direction, the winding thickness is discretized into sufficiently small sub-parts (i.e., smaller than the characteristic scale of magnetic field variation). The magnetic field is then considered to be evenly distributed in each sub-part, ultimately resulting in the following... Figure 4 The winding dual circuit model shown is shown.

[0077] S3: Parameter Identification. Parameter identification is carried out for the core and winding circuit models constructed in S2. The corresponding resistance and inductance parameters in the core model are given by equation (1), and the corresponding resistance and inductance parameters in the winding model are given by equation (2).

[0078] (1)

[0079] Among them l ceq d is the length of the magnetic circuit. i w is the layer thickness. c σ is the core thickness; ceq The conductivity of the iron core material; μ cr ρ is the relative permeability of the core material; μ0 is the permeability of free space.

[0080] (2)

[0081] Among them, l weq The height of the equivalent winding conductor cross-section is represented by w; the length of the winding coil is represented by d. w Indicates the thickness of the winding conductor; μ wr σ is the relative permeability of the winding material; weq The conductivity of the winding material.

[0082] S4: Complete Model Construction. The model from S2, after parameter identification, is input into the model topology from S1, ultimately resulting in... Figure 5 The transformer broadband distributed electromagnetic dual model is shown.

[0083] S5: Verify the accuracy of the proposed model. A full-scale transformer test was conducted for verification, and the port impedance and transmission characteristics of the π-dual circuit model, the broadband electromagnetic dual model considering eddy current effects, and the broadband distributed electromagnetic dual model of this invention were compared and analyzed. The comparison results are as follows: Figure 6 and Figure 7As shown. Regarding port impedance characteristics, the frequency error at the first series resonant point of the model of this invention is only 2.89%, which is better than the 61.47% of the π dual circuit model. At the higher frequency second resonant point, the error of the model of this invention is smaller than that of the electromagnetic dual model considering eddy current effects. Regarding port transfer characteristics, the model of this invention can characterize the frequency band up to the second resonant point with a frequency error of 9.68%, while neither of the two comparative models can effectively characterize it. Experimental and comparative results show that the transformer broadband distributed electromagnetic dual model proposed in this invention is superior to the traditional broadband model in both applicable bandwidth and accuracy of port frequency-varying characteristic characterization.

Claims

1. A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis, characterized in that, Includes the following steps: Step 1) Derive the topology of the electromagnetic dual model of the transformer; Step 2) Perform axial and radial multiple discretization on the core and winding to construct a complete dual model; Step 3) Identify the model parameters and input the parameter identification results into the complete dual model to construct a broadband distributed electromagnetic dual model of the transformer.

2. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 1, characterized in that, Step 1) involves deriving the topology of the transformer electromagnetic dual model, including: A distributed magnetic circuit model for a transformer is derived using a multi-discretion strategy involving both axial and radial directions. By performing a dual transformation on the distributed magnetic circuit model of the transformer, the topology of the electromagnetic dual model of the transformer is obtained.

3. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 2, characterized in that, Before deriving the distributed magnetic circuit model of the transformer using a multi-discretion strategy involving axial and radial directions, the following steps are performed: The winding is discretized into multiple layers in the radial direction to characterize the non-uniform distribution of its electromagnetic parameters in the radial direction under broadband conditions. The change in the interlayer potential difference gradient of the transformer windings with increasing frequency is transformed into a non-uniform distribution. The windings are axially discretized to construct a high-frequency parasitic parameter network inside the transformer.

4. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 1, characterized in that, In step 2), the steps for constructing the complete dual model include: Step 2.1) Establish a characterization model of the core frequency variation characteristics, and perform a dual transformation on the characterization model of the core frequency variation characteristics to obtain a dual circuit model of the core. Step 2.2) Construct a winding magnetic circuit model and discretize the winding thickness into sub-parts smaller than the characteristic scale of magnetic field change to obtain the winding dual circuit model; Step 2.3) Construct a complete dual model including the core dual circuit model and the winding dual circuit model.

5. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 4, characterized in that, In step 2.1), a Cauer-type equivalent circuit model is used to establish a characterization model of the core frequency-varying characteristics.

6. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 4, characterized in that, In step 2.2), a complex permeability model is used to construct a winding magnetic circuit model to characterize the frequency-dependent resistance and inductance characteristics of the conductor.

7. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 1, characterized in that, In step 3), the parameter identification results include the inductance and resistance parameters in the core and winding circuit model.

8. The method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 7, characterized in that, The inductor and resistor parameters in the iron core circuit model are shown below: ；（1） Among them l ceq d is the length of the magnetic circuit. i w is the layer thickness. c σ is the core thickness; ceq The conductivity of the iron core material; μ cr μ is the relative permeability of the core material; μ0 is the permeability of free space. , These are the resistance and inductance parameters in the iron core circuit model.

9. A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 7, characterized in that, The inductor and resistor parameters in the winding circuit model are shown below: ；（2） Among them, l weq The height of the equivalent winding conductor cross-section is represented by w; the length of the winding coil is represented by d. n Indicates the thickness of the winding conductor; μ wr σ is the relative permeability of the winding material; weq μ is the electrical conductivity of the winding material; μ0 is the permeability of free space. , These are the resistance and inductance parameters in the winding circuit model.

10. A method for constructing a broadband distributed electromagnetic dual model of a transformer suitable for broadband disturbance analysis according to claim 1, characterized in that, In step 3), after constructing the wideband distributed electromagnetic dual model of the transformer, the port impedance and transmission characteristics of the wideband distributed electromagnetic dual model of the transformer are verified. The verification indicators include the frequency error of the first series resonant point, the frequency error of the second resonant point, and the characterizable frequency band.

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