High-frequency transformer electromagnetic model modeling method based on magnetic conductance-capacitance analogy method

Abstract

The modeling method of the high-frequency transformer electromagnetic model based on the magnetic conductance-capacitance analogy method comprises the following steps: according to the magnetic force line direction of the transformer, the magnetic field of the transformer is divided into multiple magnetic path sections, and a magnetic conductance is used for equivalent for each magnetic path section; the magnetic field of the transformer is divided into two parts of core magnetic field and leakage magnetic field, and the leakage magnetic field of the transformer is divided into a winding copper conductor area and an air area without copper conductor; the Preisach magnetic hysteresis model considering reversible components is used for the core magnetic path section to simulate the magnetic hysteresis effect of the core; the Foster equivalent circuit is used for the equivalent of the winding copper conductor area; the leakage magnetic conductance of the air leakage area without copper conductor is calculated; and the transformer rotor-magnetic conductance model is established. The method can be applied to the high-frequency transformer electromagnetic transient modeling and accurate characteristic evaluation, can more accurately simulate the magnetic hysteresis effect of the core, and is more in line with the real core magnetization physical process.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic modeling and characteristic evaluation of high-frequency transformers, and specifically relates to a modeling method for electromagnetic models of high-frequency transformers based on the permeability-capacitance analogy method. Background Technology

[0002] Power electronic transformers (PETs) are widely used in large-scale DC power source interconnection systems, megawatt-level DC voltage conversion, and DC power grids. Their core component is the high-frequency transformer, which plays a crucial role in electromagnetic isolation, energy transmission, and voltage transformation. Due to the influence of ferromagnetic materials, the electromagnetic model of a transformer exhibits strong nonlinear characteristics, manifesting as hysteresis. The frequency range of high-frequency transformers is mostly from several hundred Hz to several hundred kHz; however, as the frequency increases, parameters such as leakage inductance and AC resistance are affected by the skin effect and proximity effect, exhibiting frequency-varying effects. Therefore, establishing an accurate electromagnetic model of a transformer to accurately simulate hysteresis characteristics and frequency-varying leakage inductance, frequency-varying AC resistance, and other parameters is of great significance for providing data support for transformer protection.

[0003] There are three main existing methods for transformer modeling: the coupled inductance model, the reluctance-resistance analogy, and the permeability-capacitance analogy. The coupled inductance model was proposed by Rabins in the 1950s and subsequently refined by Fergestad et al. This method links the magnetic circuit parameters with the circuit parameters through dual transformation, using inductors and ideal transformers to represent the magnetic components. While widely used, the coupled inductance model cannot be applied to non-planar models and cannot reflect the geometry of the core.

[0004] The magnetoresistive-resistance analogy method compares magnetoresistive resistance to resistance, magnetomotive force to voltage, and magnetic flux to current, using the flow of current to simulate the flow of magnetic flux. This method achieves the connection between the external circuit and the magnetic circuit. Although this method is widely accepted, the energy dissipation characteristics of resistance and the energy storage characteristics of magnetoresistive resistance are contradictory.

[0005] To address the aforementioned issues, Carpenter and Butenbach proposed the permeability-capacitance analogy, which compares permeability to capacitance, magnetomotive force to voltage, and the rate of change of magnetic flux to current. The energy storage properties of capacitance correspond to those of permeability, thus overcoming the problem of unclear energy relationships in the reluctance-resistance analogy.

[0006] Hamill, based on the permeability-capacitance analogy, proposed a gyrator-capacitor model for the iron core, equating the winding to an LC gyrator and replacing the core permeability with a capacitor. He also pointed out that it is feasible to use a nonlinear capacitor to simulate the nonlinear characteristics of the iron core. Building upon Hamill's work, Min Luo et al. established a gyrator-permeability model for transformers using the permeability-capacitance analogy. Instead of using a nonlinear capacitor, they constructed a magnetic circuit model using nonlinear permeability in the magnetic domain. Min Luo solved for the optimal values ​​of each leakage permeability through experiments and control algorithms. However, the numerical value of the leakage permeability is not necessarily related to the leakage flux during transformer operation, making it impossible to accurately simulate the flux of each leakage part. Furthermore, Min Luo did not consider the frequency-varying effects of high-frequency transformers. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a high-frequency transformer electromagnetic modeling method based on the permeability-capacitance analogy. This method can be applied to the electromagnetic transient modeling and accurate characteristic evaluation of high-frequency transformers, and can more accurately simulate the hysteresis effect of the iron core, while also being more consistent with the actual iron core magnetization physical process.

[0008] The technical solution adopted in this invention is as follows:

[0009] The electromagnetic modeling method for high-frequency transformers based on the permeability-capacitance analogy includes the following steps:

[0010] Step 1: Based on the direction of the transformer's magnetic field lines, divide the transformer's magnetic field into multiple magnetic circuit segments, and use a magnetic permeability to represent each magnetic circuit segment;

[0011] Step 2: Divide the transformer's magnetic field into two main parts: the core magnetic field and the leakage magnetic field. Then, divide the transformer's leakage magnetic field into the winding copper conductor region and the air region without copper conductors.

[0012] Step 3: The Preisach hysteresis model considering reversible components is used to simulate the hysteresis effect of the iron core in the core magnetic circuit section.

[0013] Step 4: Use the Foster equivalent circuit to perform equivalent calculations on the copper conductor region of the winding, and calculate the leakage magnetic energy and eddy current loss of the copper conductor region of the winding at different frequencies.

[0014] Step 5: Calculate the leakage permeability of the air leakage region that does not contain copper conductors;

[0015] Step 6: Based on the magnetic permeability-capacitance analogy, establish the transformer rotary-magnetic permeability model.

[0016] In step 3, considering the analytical Preisach hysteresis model of reversible components, the total magnetic flux density is decomposed into reversible magnetization components and irreversible magnetization components, as calculated below:

[0017] B cmb (H)=B irr (H)+B rev (H);

[0018] In the formula: B cmb (H) represents the total magnetic flux density; B irr (H) represents the irreversible magnetization component; B rev (H) is the reversible magnetization component.

[0019] Total permeability μ cmb (H) equals the irreversible component permeability μ irr (H) and reversible component permeability μ rev The sum of (H) is calculated as follows:

[0020] μ cmb (H)=μ irr (H)+μ rev (H);

[0021] The permeability of the irreversible component of the descending branch is shown below:

[0022]

[0023] Where: H S H represents the magnetic field strength at the point where the ascending and descending branches meet; H is the magnetic field strength. s >H>-H s ;

[0024] A, σ, H d is the Lorentz function parameter; μ0 is the permeability in vacuum.

[0025] The permeability of the irreversible component of the rising branch is shown below:

[0026]

[0027] Reversible component permeability μ rev The formula for calculating (H) is:

[0028]

[0029] In the formula: B d α is the parameter for calculating magnetic permeability; B rev It is a reversible magnetization component.

[0030] The initial magnetization curve, where permeability is the slope of the initial magnetization curve, is calculated as follows:

[0031]

[0032] In the formula: B satμ is the saturation magnetic flux density. sat ρ is the permeability of the iron core when it is close to saturation; a is the free coefficient.

[0033] In step 4, a second-order series Foster equivalent circuit is used to characterize the frequency-varying effects of winding leakage inductance and AC resistance. The equivalent impedance expression of this second-order series Foster equivalent circuit is:

[0034]

[0035] In the formula: R0 is the DC resistance of the winding; R1, R2, L1, L2 are parameters to be determined; ω is the angular frequency; j is the imaginary number.

[0036] In step 5, finite element numerical calculation is used to extract the energy of the leakage magnetic region and the average magnetic flux flowing through the leakage magnetic region, and the leakage magnetic permeability is calculated using the following formula:

[0037]

[0038] In the formula: φ is the magnetic flux; W is the leakage magnetic energy stored in the air leakage magnetic region; B and H are the magnetic flux density and magnetic field strength, respectively; P is the magnetic permeability; V is the volume of the leakage magnetic region; and S is the cross-sectional area of ​​the leakage magnetic region.

[0039] In step 6, a transformer rotator-magnetic permeability model is established, as follows:

[0040] Voltage v and current i on the gyroscope circuit side and the rate of change of magnetic flux on the gyroscope magnetic circuit side The magnetomotive force F satisfies the following relationship:

[0041]

[0042]

[0043] In the formula: N is the number of turns in the winding; F is the magnetomotive force generated by the winding; φ is the magnetic flux;

[0044] rate of change of magnetic flux The expression is as follows:

[0045]

[0046] Combining φ=B·A, Ampere's circuital law F=H·l, and the magnetic permeability calculation formula p=μ(H)A / l, where B is the magnetic field density.

[0047] rate of change of magnetic flux Represented as:

[0048]

[0049] In the formula: A is the cross-sectional area of ​​the iron core; l is the magnetic circuit length; μ(H) is the dynamic permeability, which is calculated from the HB curve of the iron core.

[0050] This invention provides a high-frequency transformer electromagnetic modeling method based on the permeability-capacitance analogy, with the following technical advantages:

[0051] 1) The advantage of step 1 of the present invention is that the magnetic field of the transformer is complex. Especially when considering the leakage magnetic field, it is difficult to accurately simulate the actual magnetic circuit of the transformer using a single magnetic circuit model. Therefore, it is necessary to divide the complex magnetic circuit and perform separate equivalents on each part in order to simulate the actual magnetic circuit of the transformer.

[0052] 2) The advantage of step 2 of this invention is that it models magnetic circuit segments with different characteristics separately to achieve accurate simulation of the transformer. The magnetic circuit is divided into a ferromagnetic material part (core) and a part without ferromagnetic material (leakage flux). Due to the nonlinear characteristics of ferromagnetic materials, the core magnetic circuit segment exhibits hysteresis, which manifests as a nonlinear relationship between magnetic flux density and magnetic field strength. Therefore, a nonlinear model is needed to represent it. The leakage flux part does not contain ferromagnetic material, but due to the skin effect and proximity effect of the winding, the leakage flux and AC resistance in the copper conductor region of the winding have frequency-varying effects, while the leakage flux in the air does not have frequency-varying effects. Therefore, the leakage flux region is divided into the copper conductor region of the winding and the leakage flux region in the air.

[0053] 3) The advantage of step 3 of this invention is that the hysteresis phenomenon of ferromagnetic materials is usually described by hysteresis models. Currently available hysteresis models mainly include the JA model, the Energetic model, and the Preisach model. However, the JA and Energetic models are computationally complex and have difficulty in parameter identification, leading to slow computation when applied to power electronic systems. The Preisach model, on the other hand, is widely used in hysteresis modeling of ferromagnetic materials due to its simple computation. Furthermore, the Preisach model, which considers reversible components, can more accurately simulate the hysteresis loop of ferromagnetic materials. Therefore, this invention uses the Preisach model, which considers reversible components, to simulate the hysteresis effect of the iron core.

[0054] 4) The advantage of step 4 of this invention is that the frequency-varying effects of winding leakage inductance and AC resistance are usually characterized using the Cauer equivalent circuit or the Foster equivalent circuit. Both equivalent circuits share the same principle, but the Foster equivalent circuit parameter calculation is simpler in terms of computational complexity. Furthermore, the Foster equivalent circuit has both series and parallel forms; the series form's impedance expression is more intuitive from the perspective of the circuit's equivalent impedance expression. Therefore, this invention selects the series Foster equivalent circuit to characterize the frequency-varying effects of the winding.

[0055] 5) The advantage of step 5 of the present invention is that: since the shape of the leakage magnetic field of the transformer is difficult to determine, the magnetic permeability cannot be calculated according to the definition formula of magnetic permeability. Therefore, finite element numerical calculation can be adopted to extract the energy of the leakage magnetic field region and the average magnetic flux flowing through the leakage magnetic field region to calculate the leakage magnetic permeability. This method has the advantages of simple calculation, fast calculation speed and high accuracy.

[0056] 6) The advantage of step 6 of this invention is that there are three main existing transformer modeling methods: coupled inductance model, magnetoresistive-resistance analogy, and permeability-capacitance analogy. Although the coupled inductance model is widely used, it cannot be applied to non-planar models and cannot reflect the geometry of the core. The magnetoresistive-resistance analogy connects the external circuit and the magnetic circuit. Although this method is widely accepted, the energy dissipation characteristics of resistance and the energy storage characteristics of magnetoresistive resistance contradict each other. The permeability-capacitance analogy compares permeability to capacitance, magnetomotive force to voltage, and the rate of change of magnetic flux to current. The energy storage properties of capacitance and permeability correspond to each other, overcoming the problem of unclear energy relationships in the magnetoresistive-resistance analogy.

[0057] 7) The method of the present invention can be applied to electromagnetic modeling and accurate evaluation of characteristics of high-frequency transformers. The rotator-magnetic permeability model of the transformer can directly reflect the geometric shape, nonlinear properties and other characteristics of the iron core without converting the complex magnetic circuit into an electrical circuit. It realizes the direct transfer of energy in the magnetic circuit and the electrical circuit, and avoids the confusion of energy relationship in the traditional resistance-magnetic reluctance analogy method. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the modeling process of the present invention.

[0059] Figure 2 This is a gyroscope-magnetic permeability model diagram of a transformer.

[0060] Figure 3 This is a diagram showing the magnetic field distribution of a transformer.

[0061] Figure 4 This is a magnetic circuit model diagram of a core-type transformer.

[0062] Figure 5 This is a module diagram of a core magnetic circuit section containing irreversible components.

[0063] Figure 6 This is a schematic diagram illustrating the implementation process of the Preisach model.

[0064] Figure 7 The circuit diagram is used to verify the hysteresis model.

[0065] Figure 8 The graph shows the experimental and simulated values ​​of the hysteresis loop of the nanocrystalline composite.

[0066] Figure 9 This is a model diagram of a high-frequency transformer.

[0067] Figure 10 This is a diagram showing the magnetic circuit segment division of a transformer.

[0068] Figure 11 This is a magnetic flux density cloud map of a transformer.

[0069] Figure 12 This is a diagram showing the distribution of leakage magnetic energy in a transformer.

[0070] Figure 13 This is the equivalent circuit diagram of a second-order series Foster circuit.

[0071] Figure 14 This is a contour map of eddy current losses in the copper conductor region.

[0072] Figure 15 This is a graph showing the equivalent inductance and equivalent resistance values ​​of the copper conductor region of the winding in the finite element method.

[0073] Figure 16 This is a gyroscope-magnetic permeability model diagram of a core-type transformer.

[0074] Figure 17 This is the circuit diagram for the short-circuit experiment of the transformer model.

[0075] Figure 18 This is a graph showing the inductance and resistance values ​​referred to the primary side. Detailed Implementation

[0076] This invention proposes a method for establishing electromagnetic modeling and parameter extraction of high-frequency transformers based on the permeability-capacitance analogy, as follows: Figure 1 As shown, the magnetic circuit distribution of the transformer was analyzed using the finite element method. Based on the direction of the magnetic field lines, the magnetic field was divided into multiple magnetic circuit segments, and a magnetic circuit model of the transformer was established. The core magnetic circuit segment was simulated using the Preisach model considering reversible components to simulate the hysteresis effect of ferromagnetic materials. The frequency-varying inductance and AC resistance of the winding copper conductor region were extracted using Maxwell eddy current fields. The winding copper conductor region was equivalently represented using the Foster equivalent circuit. The leakage magnetic permeability of the air leakage magnetic region without copper conductors was calculated using the finite element method. Finally, a gyrator-magnetic permeability model of the core transformer was established based on the permeability-capacitance analogy. The following steps were included:

[0077] Step 1: Based on the direction of the transformer's magnetic field lines, divide the transformer's magnetic field into multiple magnetic circuit segments;

[0078] In step one, when establishing the gyrator-permeability model of the transformer based on the magnetic conductivity-capacitance analogy, it is necessary to establish the lumped magnetic circuit model of the transformer, using permeability to simulate the main magnetic flux and leakage flux in the transformer core. To establish the transformer's magnetic circuit model, the transformer's magnetic field distribution needs to be analyzed. Based on Maxwell finite element simulation... Figure 3 The magnetic field distribution diagram of the core transformer prototype under secondary short-circuit conditions with a short-circuit current of 1A is given. The main magnetic flux is formed in the core region, and leakage magnetic flux is formed between the winding and the core, between the winding and the yoke, and between the windings.

[0079] Based on the direction of the transformer's magnetic field lines, the transformer's magnetic field is divided into multiple magnetic circuit segments, and it is assumed that the magnetic flux within each magnetic circuit segment is uniformly distributed. Specifically:

[0080] A transformer short-circuit experiment simulation was conducted using Maxwell finite element method to obtain the transformer's magnetic field distribution. Based on the transformer's magnetic field distribution and the orientation of the magnetic field lines (horizontal and vertical directions), the magnetic field was segmented. (See...) Figure 3 and Figure 4 .

[0081] Each magnetic circuit segment is equivalent to a single magnetic permeability. Specifically:

[0082] according to Figure 3 The magnetic field distribution and magnetic field lines of a transformer are divided into multiple magnetic circuit segments. Each magnetic circuit segment is then represented by an equivalent magnetic permeability, such as... Figure 4 As shown. For the magnetic circuit section of the iron core, a nonlinear iron core is used for equivalent representation, the specific method of which is described in detail in step 3. For the magnetic circuit section with leakage flux in the air, a linear permeability is used for equivalent representation, the specific method of which is described in detail in step 4. For the leakage flux region of the winding, a Foster equivalent circuit is used for modeling, the specific method of which is described in detail in step 5.

[0083] The transformer's magnetic field is divided into two main parts: the core magnetic field and the leakage magnetic field. Considering the frequency-varying effect of the windings under high-frequency conditions, this effect mainly affects the magnetic field magnitude in the copper conductor region of the windings. Outside the conductor region, such as between windings or between the windings and the yoke, the frequency-varying effect is negligible. Therefore, the transformer's leakage magnetic field is divided into the copper conductor region of the windings and the air region (without copper conductors).

[0084] Among them, the core magnetic field is divided into 22 magnetic circuit segments C1-C2. 22 The leakage magnetic field of a transformer is divided into a copper conductor region and an air region without copper conductors. The copper conductor region is divided into four magnetic circuit segments D1-D4, and the air region without copper conductors is divided into thirteen magnetic circuit segments (P1-P...). 13 ).Depend on Figure 2It can be seen that a transverse magnetic field parallel to the upper yoke flux exists at the winding end, and a vertical magnetic field parallel to the side yoke flux exists on both sides of the winding. Since the core-type transformer has an axisymmetric structure, based on the electromagnetic simulation results and the principle of magnetic field segmentation, a half-circuit model of the core-type transformer can be drawn, as shown below. Figure 3 As shown. Step 2: Establish a core magnetic circuit module based on the analytical Preisach model considering reversible components; details are as follows:

[0085] The analytical Preisach hysteresis model, considering reversible components, decomposes the total magnetic flux density into reversible and irreversible magnetization components, as shown in the following formula:

[0086] B cmb (H)=B irr (H)+B rev (H)

[0087] In the formula: B irr (H) represents the irreversible magnetization component; B rev (H) is the reversible magnetization component.

[0088] Total permeability μ cmb (H) equals the irreversible component permeability μ irr (H) and reversible component permeability μ rev The sum of (H) is calculated as follows:

[0089] μ cmb (H)=μ irr (H)+μ rev (H)

[0090] The permeability of the irreversible component of the descending branch is shown below:

[0091]

[0092] Where: H S Let A, σ, and H be the magnetic field strengths at the point where the ascending and descending branches meet. d These are the parameters of the Lorentz function.

[0093] The permeability of the irreversible component of the rising branch is shown below:

[0094]

[0095] Reversible component permeability μ rev The formula for calculating (H) is:

[0096]

[0097] In the formula: B d α is the parameter for calculating magnetic permeability.

[0098] The initial magnetization curve, where permeability is the slope of the initial magnetization curve, is calculated as follows:

[0099]

[0100] In the formula: B sat μ is the saturation magnetic flux density. sat ρ is the permeability of the iron core when it is close to saturation; a is the free coefficient. These three parameters can be solved by the initial magnetization curve.

[0101] In PLECS, the variable core module can adjust the permeability in real time according to the input signal, thereby realizing the nonlinear characteristics of the core. For example... Figure 5 As shown: At time t1, the magnetomotive force F(t1) between the two terminals of the dynamic permeability is divided by the magnetic circuit length l to obtain the time-varying magnetic field strength H(t1). H(t1) is used as the input to the C-Script module, which outputs the permeability μ(H). The permeability μ(H) multiplied by A / l is used as the permeability input to the variable permeability module. Since the permeability value has been calculated, the second input dp / dt of the variable core can be set to zero. The third input signal is the magnetic flux φ.

[0102] Figure 6 The implementation process of the Preisach model is shown: Assume t1 = 0 is the starting point of the simulation, corresponding to the origin of the BH coordinate system (point 1). As the excitation current i in the circuit increases, the magnetic field strength H gradually increases, and the magnetic flux density B rises along the initial magnetization curve. The curve between points 1 and 3 is the initial magnetization curve, and the permeability is the slope of the initial magnetization curve.

[0103] At time t3 (point 3), it can be determined according to... The sign change is used to detect this point. After the current reaches its peak, it gradually decreases, the magnetic field strength H begins to decrease, and the magnetic flux density B changes along the descending branch of the hysteresis loop between points 3 and 5. At this time, H... S The magnetic field strength corresponding to point 3, and the permeability are calculated as follows:

[0104] μ cmb (H)=μ irr d (H)+μ rev (H);

[0105] When the turning point of the descending branch is reached (point 5), As the value changes from negative to positive, H begins to increase. S The magnetic flux density B is updated, changing along the rising branch of the hysteresis loop (e.g., at position 6), at which point the permeability is calculated as:

[0106] μ cmb (H)=μ irri (H)+μ rev (H);

[0107] The limiting hysteresis loop of a nanocrystalline composite standard sample was measured using a TD8210 soft magnetic DC measurement system. The parameters of the reversible and irreversible magnetization components were determined using a global optimization particle swarm optimization method: A = 181.19, σ = 1.3676, and H... d =1.6574, B d =0.5073, α=10, and the irreversible component permeability μ irr (H) and reversible component permeability μ rev (H) Substitute Figure 5 The modules for reversible and irreversible components. Figure 7 To verify the circuit of the hysteresis model, a voltage excitation was applied to one end of the hysteresis core module, and the other end was left open. R1 was the internal resistance of the voltage source, set to 0.1Ω. The magnetic field strength H and magnetic induction intensity B in the combined hysteresis core model were extracted, and the HB curve was plotted. Figure 8 To compare the experimentally measured HB curve with the simulation results, by Figure 8 As can be seen, the simulation results are in good agreement with the experimental results.

[0108] Step 3: Determining the equivalent permeability parameters of the air leakage magnetic field region:

[0109] In step three Figure 9 and Figure 10 The three-dimensional model of the core transformer prototype and the division of magnetic circuit sections are shown. The geometric dimensions of each magnetic circuit section are listed in Table 1. The transformer core material is a nanocrystalline alloy, with a rated power of 10 kVA, a rated frequency of 5 kHz, a rated voltage of 540 V, a primary-to-secondary turns ratio of 40:40, and both primary and secondary windings are rectangular flat copper wires with a thickness of 1 mm, a width of 4 mm, a turn spacing of 0.1 mm, and a layer spacing of 0.5 mm. The cross-sectional area Sc of the transformer is 880 mm². 2 .

[0110] Table 1 Dimensions of each magnetic circuit segment

[0111]

[0112] Because the magnetic field distribution in the leakage region of a transformer is uneven, it is difficult to accurately define the shape of the magnetic circuit passing through the air, and the leakage permeability cannot be calculated using the definition formula for magnetic permeability. Therefore, finite element numerical calculation can be used to extract the energy in the leakage region and the average magnetic flux flowing through the leakage region, and the leakage permeability can be calculated using the following formula:

[0113]

[0114] To calculate leakage energy and magnetic flux, a three-dimensional model of the transformer was built using Maxwell's algorithm. Figure 11 and Figure 12 The magnetic flux density distribution cloud map and leakage flux energy density cloud map of the transformer under short-circuit test are given respectively. Multiple cross sections are selected in each leakage flux magnetic circuit segment to calculate the average magnetic flux of the magnetic circuit segment. Then, the volume integral of the magnetic field energy density of each magnetic circuit segment is used to obtain the leakage flux energy to calculate the magnetic permeability. The results are shown in Table 2.

[0115] Table 2 Equivalent magnetic permeability of each magnetic circuit segment (unit: H)

[0116]

[0117] Step 4: Determining the equivalent model and parameters for the copper conductor region:

[0118] In step four, the frequency-varying effects of winding leakage inductance and AC resistance are characterized using the Foster equivalent circuit. Figure 13 This is a schematic diagram of a second-order series Foster circuit. The frequency-varying effects of winding leakage inductance and AC resistance are characterized using a second-order series Foster equivalent circuit. The equivalent impedance expression for this Foster equivalent circuit is:

[0119]

[0120] In the formula: R0 is the DC resistance of the winding; R1, R2, L1, and L2 are parameters to be determined.

[0121] The leakage magnetic energy and eddy current loss in the copper conductor region of the winding can be calculated using the Maxwell eddy current solver at different frequencies. Figure 14 The eddy current loss contour plot for copper conductors is shown below; the leakage magnetic energy contour plot is also shown below. Figure 12 .

[0122] The equivalent inductance and AC resistance of the copper conductor region of the winding referred to the primary side at different frequencies can be calculated using the energy method. After obtaining the calculation results, the undetermined parameters are fitted using the equivalent impedance expression. The calculated values ​​are: R1 = 15.4Ω, R2 = 1.17Ω, L1 = 9.25 × 10⁻⁶. -6 H, L2 = 1.73 × 10 -5 H, the finite element simulation results and fitting results are as follows: Figure 15 As shown.

[0123] Step 5: Establish the transformer rotator-magnetic permeability model;

[0124] Establish Figure 2 The transformer rotary-magnetic permeability model shown is as follows:

[0125] The voltage (V) and current (i) on the gyroscope circuit side and the rate of change of magnetic flux on the gyroscope magnetic circuit side. The magnetomotive force (F) satisfies the following relationship:

[0126]

[0127]

[0128] In the formula: v and i are the voltage and current on the circuit side; N is the number of turns of the winding; F is the magnetomotive force generated by the winding; φ is the magnetic flux.

[0129] Current through magnetic permeability The expression is as follows:

[0130]

[0131] Combining φ=B·A, Ampere's circuital law F=H·l, and the magnetic permeability calculation formula p=μ(H)A / l, the magnetic conductivity current... It can be represented as:

[0132]

[0133] In the formula: A is the cross-sectional area of ​​the iron core; l is the magnetic circuit length. μ(H) is the dynamic permeability, which can be calculated from the HB curve of the iron core, thereby introducing the saturation and hysteresis effects of the iron core.

[0134] Therefore, based on the established variable permeability model of the iron core, the Foster equivalent circuit model of the copper conductor region of the winding, and the leakage magnetic permeability model in air without copper conductors, a rotator-permeability model of the core transformer can be established, such as... Figure 16 As shown.

[0135] To verify the accuracy of the model's inductance parameters, a short-circuit test was performed. In PLECS, an excitation voltage with an amplitude of 1V and a frequency of 1kHz-100kHz was applied to the primary side of the transformer, while the secondary side was short-circuited, obtaining the waveforms of the primary voltage u and the short-circuit current i. Inputting these voltage and current waveforms into the discrete Fourier transform module in PLECS yields the amplitude and phase of the voltage and current at the fundamental frequency, thus providing the phase voltage. and phase current according to The leakage inductance and resistance referred to the primary winding at the fundamental frequency are calculated, such as... Figure 17 As shown.

[0136] The leakage inductance and AC resistance of a high-frequency transformer test model were measured using an Agilent 4294A high-precision impedance analyzer. During measurement, the fixture was connected to the primary winding, and the secondary winding was short-circuited. The measurement frequency range was 1kHz-100kHz. The obtained resistance and inductance are those referred to the primary winding. Figure 18The experimentally measured leakage inductance and AC resistance values ​​are displayed alongside the simulated values. Compared to the experimental values, the average error in the simulation for leakage inductance is only 2.44%, and the average error for AC resistance is 9.55%, which effectively verifies the correctness of the model parameters.

[0137] This invention is based on an analytical Preisach model considering reversible components and the permeability-capacitance analogy. It utilizes the underlying modules and programming language of the power electronics simulation software PLECS to establish an analytical Preisach model based on the Lorentz distribution function, with magnetic field strength H as input and magnetic flux density B as output. The permeability analogy to capacitance enables a direct connection between the magnetic circuit and the electrical circuit, eliminating the need to convert the complex magnetic circuit into an electrical circuit. The permeability-capacitance analogy directly reflects the geometry and nonlinear properties of the iron core. The energy storage characteristics of permeability correspond to those of capacitance, enabling direct energy transfer between the magnetic circuit and the electrical circuit, avoiding the confusion of energy relationships inherent in the traditional resistance-magnetic reluctance analogy.

Claims

1. A high-frequency transformer electromagnetic modeling method based on the permeability-capacitance analogy, characterized in that... Includes the following steps: Step 1: Based on the direction of the transformer's magnetic field lines, divide the transformer's magnetic field into multiple magnetic circuit segments, and use a magnetic permeability to represent each magnetic circuit segment; Step 2: Divide the transformer's magnetic field into two main parts: the core magnetic field and the leakage magnetic field. Then, divide the transformer's leakage magnetic field into the winding copper conductor region and the air region without copper conductors. Step 3: The Preisach hysteresis model considering reversible components is used to simulate the hysteresis effect of the iron core in the magnetic circuit section. Step 4: Use the Foster equivalent circuit to perform equivalent calculations on the copper conductor region of the winding, and calculate the leakage magnetic energy and eddy current loss of the copper conductor region of the winding at different frequencies; Step 5: Calculate the leakage permeability of the air leakage region that does not contain copper conductors; Step 6: Establish the transformer rotator-magnetic permeability model; In step 3, the Preisach hysteresis model considering reversible components decomposes the total magnetic flux density into reversible magnetization components and irreversible magnetization components, as calculated below: ； In the formula: The total magnetic flux density; This is an irreversible magnetization component; It is a reversible magnetization component; Total permeability Equal to the irreversible component permeability and reversible component permeability The sum is calculated as follows: ； The permeability of the irreversible component of the descending branch is shown below: ； In the formula: H S The magnetic field strength at the moment of the boundary between the rising and falling branches; The magnetic field strength; ; A , σ , H d These are the parameters of the Lorentz function; is the magnetic permeability in vacuum; The permeability of the irreversible component of the rising branch is shown below: ； Reversible component permeability The calculation formula is: ； In the formula: B d , α These are parameters for calculating magnetic permeability; It is a reversible magnetization component; The initial magnetization curve, where permeability is the slope of the initial magnetization curve, is calculated as follows: ； In the formula: The saturation magnetic flux density; The permeability of the iron core when it is close to saturation; For the free coefficient; B Magnetic flux density; In step 4, a second-order series Foster equivalent circuit is used to characterize the frequency-varying effects of winding leakage inductance and AC resistance. In step 5, finite element numerical calculation is used to extract the energy of the leakage magnetic field region and the average magnetic flux flowing through the leakage magnetic field region. In step 6, a transformer rotary-magnetic permeability model is established based on the magnetic permeability-capacitance analogy.

2. The high-frequency transformer electromagnetic modeling method based on the permeability-capacitance analogy as described in claim 1, characterized in that: In step 4, a second-order series Foster equivalent circuit is used to characterize the frequency-varying effects of winding leakage inductance and AC resistance. The equivalent impedance expression of this second-order series Foster equivalent circuit is: ； In the formula: R 0 represents the DC resistance of the winding; R 1. R 2. L 1. L 2 is a parameter to be determined; Angular frequency; It is the symbol for imaginary numbers.

3. The high-frequency transformer electromagnetic modeling method based on the permeability-capacitance analogy as described in claim 1, characterized in that: In step 5, finite element numerical calculation is used to extract the energy of the leakage magnetic region and the average magnetic flux flowing through the leakage magnetic region, and the leakage magnetic permeability is calculated using the following formula: ； In the formula: For magnetic flux; W The leakage magnetic energy stored in the air leakage magnetic region; B and H These are magnetic flux density and magnetic field strength, respectively. P It has magnetic permeability; V The volume of the leakage magnetic field region; S This represents the cross-sectional area of ​​the magnetic leakage region.

4. The high-frequency transformer electromagnetic modeling method based on the permeability-capacitance analogy as described in claim 1, characterized in that: In step 6, a transformer rotary-magnetic permeability model is established based on the magnetic permeability-capacitance analogy, as follows: Voltage on the gyroscope circuit side v Current i The rate of change of magnetic flux on the magnetic circuit side of the gyroscope Magnetomotive force F The following relationship must be satisfied: ； ； In the formula: N This refers to the number of turns in the winding. F The magnetomotive force generated by the winding; For magnetic flux; rate of change of magnetic flux The expression is as follows: ； Combination Ampere's circuital law Magnetic permeability calculation formula ; rate of change of magnetic flux Represented as: ； In the formula: A Let be the cross-sectional area of ​​the iron core; l This is the length of the magnetic circuit; For dynamic permeability, Through iron will HB The curve was calculated.

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