CN116911090A - High-frequency transformer electromagnetic model modeling method based on magnetic conduction-capacitance analogy method - Google Patents
High-frequency transformer electromagnetic model modeling method based on magnetic conduction-capacitance analogy method Download PDFInfo
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Abstract
The modeling method of the electromagnetic model of the high-frequency transformer based on the magnetic conduction-capacitance analogy method comprises the following steps: dividing a magnetic field of the transformer into a plurality of magnetic path sections according to the trend of magnetic lines of the transformer, and carrying out equivalence on each magnetic path section by using one magnetic guide; dividing the magnetic field of the transformer into two parts, namely an iron core magnetic field and a leakage magnetic field, and dividing the leakage magnetic field of the transformer into a winding copper conductor area and an air area without copper conductors; the core magnetic circuit section adopts a Preisach hysteresis model considering reversible components to simulate the hysteresis effect of the core; adopting a Foster equivalent circuit to perform equivalent on the winding copper conductor region; calculating the flux leakage conductance of the air flux leakage area without the copper conductor; and establishing a transformer gyrator-magnetic conduction model. The method can be applied to electromagnetic transient modeling and accurate characteristic evaluation of the high-frequency transformer, can more accurately simulate the hysteresis effect of the iron core, and is more in line with the actual physical process of iron core magnetization.
Description
Technical Field
The invention belongs to the field of electromagnetic modeling and characteristic evaluation of high-frequency transformers, and particularly relates to a high-frequency transformer electromagnetic model modeling method based on a magnetic conduction-capacitance analogy method.
Background
Power Electronic Transformers (PET) have been widely used in large-scale dc source interconnection systems, megawatt dc voltage conversion, and dc power grids, and their core components are high frequency transformers, which serve as electromagnetic isolation, energy transmission, and voltage conversion. The electromagnetic model of the transformer has very strong nonlinear characteristics due to the influence of ferromagnetic materials, and shows hysteresis characteristics. The frequency range of the high-frequency transformer is mostly different from hundreds of Hz to hundreds of kHz, however, as the frequency is increased, parameters such as leakage inductance, alternating current resistance and the like are affected by skin effect and proximity effect, and the high-frequency transformer has a frequency-dependent effect. Therefore, an accurate electromagnetic model of the transformer is established, parameters such as hysteresis characteristics, frequency-dependent leakage inductance, frequency-dependent alternating current resistance and the like are accurately simulated, and the method has great significance in providing data support for transformer protection.
The existing transformer modeling methods mainly comprise three methods: coupling inductance model, magneto-resistive analogy, magneto-conductive-capacitive analogy. The coupling inductance model is proposed by Rabins in the fifty of the last century, and then the model is perfected by Fergustad et al, the method links the magnetic circuit parameters with the circuit parameters through a dual transformation method by the magnetic circuit part of the transformer, and the magnetic elements are equivalent by elements such as an inductance, an ideal transformer and the like. The coupled inductance model, although widely used, cannot be applied to a non-planar model and cannot reflect the geometry of the core.
The magneto-resistance analogy method is to analogize magneto-resistance to resistance, magnetomotive force to voltage, magnetic flux to current and flow of magnetic flux to simulate the flow of magnetic flux, and the method realizes the connection between an external circuit and a magnetic circuit, and although the method is generally accepted, the energy consumption characteristic of the resistance and the energy storage characteristic of the magneto-resistance are mutually contradictory.
In order to solve the above problems, carpenter and Butenbach propose a flux-capacitance analogy method, which is to convert the flux into capacitance, the magnetomotive force is still similar to voltage, the change rate of magnetic flux is similar to current, and the energy storage property of the capacitance corresponds to the energy storage property of the flux, so as to overcome the problem of unclear energy relation in the magneto-resistance analogy method.
Hamill is based on flux-capacitance analogy, and a gyrator-capacitance model of an iron core is proposed, the winding is equivalent to an L-C gyrator, the flux of the iron core is replaced by a capacitance, and it is feasible to simulate the nonlinear characteristics of the iron core by a nonlinear capacitance. The Min Luo and other students use magnetic conduction-capacitance analogy to build a gyrator-magnetic conduction model of the transformer on the basis of Hamill, and the magnetic domain part does not use nonlinear capacitance but uses nonlinear magnetic conduction to build a magnetic circuit model. The Min Luo solves the optimal value of each magnetic flux leakage flux guide through experiments and control algorithms, but the numerical value of the magnetic flux leakage flux guide is not necessarily related to the magnetic flux leakage in the working process of the transformer, the magnetic flux of each magnetic flux leakage part cannot be accurately simulated, and the Min Luo does not consider the frequency-dependent effect of the high-frequency transformer.
Disclosure of Invention
In order to solve the technical problems, the invention provides a high-frequency transformer electromagnetic model modeling method based on a magnetic conduction-capacitance analogy method, which can be applied to electromagnetic transient modeling and accurate characteristic evaluation of a high-frequency transformer, can more accurately simulate hysteresis effect of an iron core, and is more in line with a real iron core magnetization physical process.
The technical scheme adopted by the invention is as follows:
the modeling method of the electromagnetic model of the high-frequency transformer based on the magnetic conduction-capacitance analogy method comprises the following steps:
step 1: dividing a magnetic field of the transformer into a plurality of magnetic path sections according to the trend of magnetic lines of the transformer, and carrying out equivalence on each magnetic path section by using one magnetic guide;
step 2: dividing the magnetic field of the transformer into two parts, namely an iron core magnetic field and a leakage magnetic field, and dividing the leakage magnetic field of the transformer into a winding copper conductor area and an air area without copper conductors;
step 3: the core magnetic circuit section adopts a Preisach hysteresis model considering reversible components to simulate the hysteresis effect of the core;
step 4: the Foster equivalent circuit is adopted to perform equivalent on the winding copper conductor area, and leakage energy and eddy current loss of the winding copper conductor area under different frequencies are calculated;
step 5: calculating the flux leakage conductance of the air flux leakage area without the copper conductor;
step 6: and establishing a transformer gyrator-magnetic conductance model according to the magnetic conductance-capacitance analogy method.
In the step 3, the total magnetic flux density is decomposed into a reversible magnetization component and an irreversible magnetization component by considering an analytical Preisach hysteresis model of the reversible component, and the calculation formula is as follows:
B cmb (H)＝B irr (H)+B rev (H)；
wherein: b (B) cmb (H) Is the total magnetic flux density; b (B) irr (H) Is an irreversible magnetization component; b (B) rev (H) Is a reversible magnetization component.
Total magnetic permeability mu cmb (H) Equal to the irreversible component permeability mu irr (H) And reversible component permeability mu rev (H) The sum is calculated as follows:
μ cmb (H)＝μ irr (H)+μ rev (H)；
the irreversible component permeability of the descending branch is as follows:
wherein: h S The magnetic field intensity at the moment of the boundary point of the ascending branch and the descending branch is as follows; h is the magnetic field strength; h s >H>-H s ；
A、σ、H d Is a Lorentz function parameter; mu (mu) 0 Is the permeability in vacuum.
The irreversible component permeability of the ascending branch is as follows:
reversible component permeability mu rev (H) The calculation formula is as follows:
wherein: b (B) d Alpha is a magnetic permeability calculation parameter; b (B) rev Is a reversible magnetization component.
The initial magnetization curve, the magnetic permeability is the slope of the initial magnetization curve, and the calculation formula is as follows:
wherein: b (B) sat Is the saturation magnetic flux density; mu (mu) sat The magnetic permeability of the iron core is close to saturation; a is a free coefficient.
In the step 4, a second-order series Foster equivalent circuit is adopted to represent the frequency-dependent effect of the winding leakage inductance and the alternating current resistance, and the second-order series Foster equivalent circuit equivalent impedance expression is as follows:
wherein: r is R 0 The direct current resistance of the winding; r is R 1 、R 2 、L 1 、L 2 Is a pending parameter; omega is the angular frequency; j is an imaginary symbol.
In the step 5, finite element numerical calculation is adopted to extract the energy of the magnetic leakage area and the average magnetic flux flowing through the magnetic leakage area, and the flux leakage is calculated by the following formula:
wherein: phi is magnetic flux; w is leakage magnetic energy stored in the air leakage magnetic area; b and H are magnetic flux density and magnetic field strength, respectively; p is the magnetic flux guide; v is the volume of the magnetic leakage area; s is the sectional area of the magnetic leakage area.
In the step 6, a transformer gyrator-magnetic conduction model is established, and the method specifically comprises the following steps:
voltage v and current i on the gyrator circuit side and rate of change of magnetic flux on the gyrator magnetic circuit sideMagnetomotive force F satisfies the following relationship:
wherein: n is the number of turns of the winding; f is magnetomotive force generated by the winding; phi is magnetic flux;
rate of magnetic flux changeThe expression is as follows:
and B is the magnetic field density in combination with phi=b·a, ampere loop law f=h·l, and the flux-guide calculation formula p=μ (H) a/l.
Rate of magnetic flux changeExpressed as:
wherein: a is the cross-sectional area of the iron core; l is the magnetic path length; mu (H) is dynamic magnetic permeability and is calculated by the H-B curve of the iron core.
The invention discloses a high-frequency transformer electromagnetic model modeling method based on a magnetic conduction-capacitance analogy method, which has the following technical effects:
1) The step 1 of the invention has the advantages that: the magnetic field of the transformer is complex, and particularly under the condition of considering the leakage magnetic field, the actual magnetic circuit of the transformer is difficult to accurately simulate by using a single magnetic circuit model, so that the complex magnetic circuit is required to be divided, and each part is independently and equivalently used, so that the actual magnetic circuit of the transformer can be simulated.
2) The step 2 of the invention has the advantages that: the magnetic circuit sections with different characteristics are respectively modeled to realize accurate simulation of the transformer. The magnetic circuit part is divided into a ferromagnetic material part (iron core) and does not contain the ferromagnetic material part (magnetic leakage), and the magnetic path part of the iron core has hysteresis effect due to the nonlinear characteristics of the ferromagnetic material and shows a nonlinear relation of magnetic density changing along with the intensity of a magnetic field, so that a nonlinear model needs to be established to be equivalent to the nonlinear relation. The magnetic leakage part does not contain ferromagnetic materials, but the magnetic leakage and alternating current resistance of the winding copper conductor area have a frequency-dependent effect due to the skin effect and the proximity effect of the winding, and the magnetic leakage in the air does not have a frequency-dependent effect, so that the magnetic leakage area is divided into the winding copper conductor area and the magnetic leakage area in the air.
3) The step 3 of the invention has the advantages that: the hysteresis phenomenon of the ferromagnetic material is generally described by using a hysteresis model, and the existing hysteresis model mainly comprises a J-A model, an energy model, a Preisach model and the like, because the J-A model and the energy model are complex in calculation and large in parameter identification difficulty, the hysteresis model is applied to a power electronic system and has the problems of slow calculation and the like, and the Preisach model is widely applied to the hysteresis modeling of the ferromagnetic material due to simple calculation. The Preisach model considering the reversible component can be used for realizing the accurate simulation of the hysteresis loop of the ferromagnetic material, so that the hysteresis effect of the iron core is simulated by adopting the Preisach model considering the reversible component.
4) The step 4 of the invention has the advantages that: the frequency-dependent effects of winding leakage inductance and ac resistance are typically characterized using a Cauer equivalent circuit or a Foster equivalent circuit. The two equivalent circuit principles are the same, and the Foster equivalent circuit parameters are simpler and more convenient to calculate from the aspect of complexity of calculation. In addition, the Foster equivalent circuit is provided with two forms of series connection and parallel connection, and the impedance expression of the series connection form is more visual from the viewpoint of the equivalent impedance expression of the circuit. Therefore, the invention selects a series Foster equivalent circuit to represent the frequency-dependent effect of the winding.
5) The step 5 of the invention has the advantages that: because the shape of the transformer air leakage magnetic field is difficult to determine and the flux guide can not be calculated according to a flux guide definition formula, finite element numerical calculation can be adopted to extract the energy of a magnetic leakage area and the average magnetic flux flowing through the magnetic leakage area to calculate the flux guide.
6) The step 6 of the invention has the advantages that: the existing transformer modeling method mainly comprises three methods, namely a coupling inductance model, a magneto-resistance analog method and a magnetic conduction-capacitance analog method. The coupled inductance model, although widely used, cannot be applied to a non-planar model and cannot reflect the geometry of the core. The magneto-resistance analogy method realizes the connection between an external circuit and a magnetic circuit, although the method is generally accepted, the energy consumption characteristic of the resistor and the energy storage characteristic of the magneto-resistance are contradictory, the magneto-conductivity-capacitance analogy method can be used for analogize the magneto-conductivity into a capacitor, the magnetomotive force is still analogized into a voltage, the change rate of the magneto-flux is analogized into a current, the energy storage characteristic of the capacitor and the energy storage characteristic of the magneto-conductivity are mutually corresponding, and the problem of unclear energy relation existing in the magneto-resistance analogy method is solved.
7) The method can be applied to electromagnetic modeling and characteristic accurate evaluation of a high-frequency transformer, a gyrator-magnetic conduction model of the transformer can directly reflect the characteristics of the geometric shape, the nonlinear property and the like of the iron core without converting a complex magnetic circuit into a circuit, the direct transfer of energy in the magnetic circuit and the circuit is realized, and the confusion of the energy relation of the traditional resistance-magnetic resistance analogy method is avoided.
Drawings
FIG. 1 is a schematic diagram of a modeling flow of the present invention.
Fig. 2 is a gyrator-flux guide model diagram of a transformer.
Fig. 3 is a diagram of a transformer magnetic field profile.
Fig. 4 is a diagram of a core transformer magnetic circuit model.
Fig. 5 is a block diagram of a core magnetic circuit segment containing irreversible components.
FIG. 6 is a schematic diagram of the implementation process of the Preisach model.
Fig. 7 is a hysteresis model verification circuit diagram.
FIG. 8 is a graph of experimental and simulated values of nanocrystalline hysteresis loops.
Fig. 9 is a diagram of a high frequency transformer model.
Fig. 10 is a sectional view of a magnetic circuit section of a transformer.
Fig. 11 is a magnetic dense cloud of a transformer.
Fig. 12 is a leakage energy distribution diagram of a transformer.
Fig. 13 is a second order series Foster equivalent circuit diagram.
Fig. 14 is a cloud of copper conductor area eddy current loss.
Fig. 15 is a graph of equivalent inductance versus equivalent resistance for a copper conductor region of a finite element method winding.
Fig. 16 is a gyrator-flux guide model diagram of a cardioid transformer.
Fig. 17 is a short-circuit experimental circuit diagram of a transformer model.
Fig. 18 is a graph showing inductance and resistance values calculated on the primary side.
Detailed Description
The invention provides a high-frequency transformer electromagnetic modeling and parameter extraction method based on a magnetic conduction-capacitance analogy method, and the establishment idea of the method is shown in figure 1. The magnetic circuit distribution of the transformer is analyzed by a finite element method, a magnetic field is divided into a plurality of magnetic path sections according to the trend of magnetic lines, and a magnetic circuit model of the transformer is established; the magnetic circuit section of the iron core adopts a Preisach model considering reversible components to simulate hysteresis effect of ferromagnetic materials; the winding copper conductor area extracts a frequency-dependent inductance and a frequency-dependent alternating current resistance by using a Maxwell vortex field; the copper conductor area of the winding is equivalently conducted by combining a Foster equivalent circuit; and calculating magnetic flux leakage flux guide according to a finite element method in an air magnetic flux leakage area without the copper conductor, and finally establishing a gyrator-magnetic flux guide model of the core transformer according to a magnetic flux guide-capacitance analogy method. The method comprises the following steps:
step one: dividing a magnetic field of the transformer into a plurality of magnetic sections according to the trend of magnetic lines of the transformer;
in the first step, when a gyrator-flux guide model of the transformer is established based on the flux guide capacitance analogy method, a lumped magnetic circuit model of the transformer needs to be established, and the flux guide is used for simulating main magnetic flux and leakage magnetic flux in a core of the transformer. In order to build a magnetic circuit model of a transformer, it is necessary to analyze the magnetic field distribution of the transformer. Based on Maxwell finite element simulation, fig. 3 shows a magnetic field distribution diagram of a core transformer prototype under a secondary side short circuit condition, and the short circuit current is 1A. The core region forms a main magnetic flux, and a leakage magnetic flux is formed between the winding and the core, between the winding and the yoke, and between the winding and the winding.
According to the trend of magnetic lines of force of the transformer, the magnetic field of the transformer is divided into a plurality of magnetic sections, and the magnetic fluxes in the magnetic sections are considered to be uniformly distributed, specifically:
and (3) carrying out short-circuit experimental simulation on the transformer through Maxwell finite elements to obtain the magnetic field distribution of the transformer, and carrying out sectional treatment on the magnetic field according to the magnetic field distribution of the transformer and the trend of magnetic lines (horizontal and vertical directions), wherein the magnetic field is shown in fig. 3 and 4.
For each magnetic circuit segment an equivalent is made with one flux guide. The method specifically comprises the following steps:
according to the magnetic field distribution and the trend of magnetic lines of force of the transformer in fig. 3, the transformer is divided into a plurality of magnetic path sections, and each magnetic path section is equivalently conducted by using a magnetic flux guide, as shown in fig. 4. The method comprises the steps of carrying out equivalence on a magnetic circuit section of an iron core by using a nonlinear iron core, specifically describing the method in detail in the step 3, carrying out equivalence on a magnetic leakage magnetic circuit section of air by using linear magnetic conductance, specifically describing the method in detail in the step 4, modeling a magnetic leakage area of a winding by using a Foster equivalent circuit, and specifically describing the method in detail in the step 5.
The magnetic field of the transformer is divided into two parts, namely an iron core magnetic field and a leakage magnetic field. Considering the frequency-dependent effect of the winding under the high-frequency condition, the frequency-dependent effect mainly influences the magnetic field of the copper conductor area of the winding, and the frequency-dependent effect is smaller and negligible for the outside of the conductor area, such as between the windings and the iron yoke. Accordingly, the leakage field of the transformer is divided into a winding copper conductor region and an air region free of copper conductors.
Wherein: the iron core magnetic field is divided into 22 magnetic circuit sections C 1 -C 22 The leakage magnetic field of the transformer is divided into a winding copper conductor area and an air area without copper conductors, and the winding copper conductor area is divided into 4 magnetic path sections D 1 -D 4 The air region free of copper conductors is divided into 13 magnetic sections (P 1 -P 13 ). As can be seen from fig. 2, there is a transverse magnetic field parallel to the upper yoke magnetic flux at the winding end, and there is a vertical magnetic field parallel to the side yoke magnetic flux at the left and right sides of the winding, and as the core-type transformer is in an axisymmetric structure, a half magnetic circuit model diagram of the core-type transformer can be drawn according to electromagnetic simulation results and a magnetic field segmentation principle, as shown in fig. 3. Step two: establishing an iron core magnetic circuit section module based on an analytical Preisach model considering reversible components; the method comprises the following steps:
the analytical Preisach hysteresis model of the reversible component is considered to decompose the total magnetic flux density into a reversible magnetization component and an irreversible magnetization component, and the calculation formula is as follows:
B cmb (H)＝B irr (H)+B rev (H)
wherein: b (B) irr (H) Is an irreversible magnetization component; b (B) rev (H) Is a reversible magnetization component.
Total magnetic permeability mu cmb (H) EtcPermeability mu in irreversible component irr (H) And reversible component permeability mu rev (H) The sum is calculated as follows:
μ cmb (H)＝μ irr (H)+μ rev (H)
the irreversible component permeability of the descending branch is as follows:
wherein: h S The magnetic field intensity at the boundary point of the ascending branch and the descending branch is A, sigma and H d Is a lorentz function parameter.
The irreversible component permeability of the ascending branch is as follows:
reversible component permeability mu rev (H) The calculation formula is as follows:
wherein: b (B) d Alpha is the magnetic permeability calculation parameter.
The initial magnetization curve, the magnetic permeability is the slope of the initial magnetization curve, and the calculation formula is as follows:
wherein: b (B) sat Is the saturation magnetic flux density; mu (mu) sat The magnetic permeability of the iron core is close to saturation; a is the free coefficient, and these 3 parameters can be solved by the initial magnetization curve.
In PLECS, the variable iron core module can adjust the magnetic permeability in real time according to an input signal, so that the nonlinear characteristic of the iron core is realized. As shown in fig. 5: at t 1 Time of day, dynamic flux guide two endsMagnetomotive force F (t) between the children 1 ) Dividing by the magnetic path length l to obtain the time-varying magnetic field strength H (t 1 ). Will H (t) 1 ) As the input quantity of the C-Script module, magnetic permeability mu (H) is output, and the magnetic permeability mu (H) multiplied by A/l is input to the variable magnetic permeability module as magnetic permeability. Since the value of permeability is calculated, the second input dp/dt input of the variable pellet can be set to zero. The third input signal is the magnetic flux phi.
Fig. 6 shows the implementation process of the Preisach model: let t be 1 =0 is the start point of the simulation, corresponding to the origin position (point 1) of the B-H coordinate system. When the exciting 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 point 1 and point 3 is the initial magnetization curve and the permeability is the slope of the initial magnetization curve.
At t 3 Time (point 3) can be based onThe sign change of (c) is detected. The current gradually decreases after reaching the peak value, the magnetic field strength H begins to decrease, the magnetic flux density B changes along the hysteresis loop between the point 3 and the point 5, and H S For the magnetic field strength corresponding to point 3, the permeability is calculated as:
μ cmb (H)＝μ irr d (H)+μ rev (H)；
when the down leg flip point is reached (point 5),from negative to positive, H begins to increase, H S Updated, the magnetic flux density B changes along the hysteresis loop rising branch (e.g., at position 6), at which time the permeability is calculated as:
μ cmb (H)＝μ irr i (H)+μ rev (H)；
the TD8210 soft magnetic direct current measurement system is used for measuring the limit hysteresis loop of the nano-crystalline standard sample, and parameters of the reversible magnetization component and the irreversible magnetization component are respectively A= 181.19, sigma= 1.3676 and H determined by a global optimizing particle swarm method d ＝1.6574、B d = 0.5073, α=10, and will not be reversible in component permeability μ irr (H) And reversible component permeability mu rev (H) Substituting the reversible and irreversible component modules of fig. 5. FIG. 7 is a circuit for verifying hysteresis model, wherein voltage excitation is applied to one end of a hysteresis core module, and the other end is opened, R 1 The internal resistance of the voltage source is set to be 0.1 omega, the magnetic field intensity H and the magnetic induction intensity B in the combined hysteresis core model are extracted, and an H-B curve is drawn. Fig. 8 is a comparison of the H-B curve measured experimentally and the simulation result, and as can be seen from fig. 8, the simulation result substantially coincides with the experimental result.
Step three: determination of equivalent magnetic permeability parameters of an air magnetic leakage area:
in the third step, fig. 9 and 10 show the three-dimensional model of the prototype of the cardioid transformer and the division of the magnetic circuit segments, and the geometric dimensions of each magnetic circuit segment are listed in table 1. The transformer core material is nanocrystalline alloy, the rated power is 10 kV.A, the rated frequency is 5kHz, the rated voltage is 540V, and the turns ratio of the primary side and the secondary side is 40:40, the primary and secondary windings are rectangular flat copper wires, the thickness of the windings is 1mm, the width is 4mm, the inter-turn distance of the windings is 0.1mm, the inter-layer distance is 0.5mm, and the cross section area Sc of the transformer is 880mm 2 。
Table 1 size diagram of each magnetic circuit segment
Because the magnetic field distribution of the transformer magnetic leakage area is uneven, the shape of a magnetic circuit passing through air is difficult to be accurately defined, and the flux leakage can not be calculated by using a flux guiding definition formula. Therefore, finite element numerical calculation can be adopted to extract the energy of the magnetic leakage area and the average magnetic flux flowing through the magnetic leakage area, and the flux leakage conductance can be calculated by the following formula:
in order to calculate leakage magnetic energy and magnetic flux, a three-dimensional model of the transformer is built in Maxwell, a magnetic density distribution cloud image and a leakage magnetic energy density cloud image of the transformer under a short circuit test are respectively shown in fig. 11 and 12, a plurality of sections are selected from each divided leakage magnetic circuit section, the average magnetic flux of the magnetic circuit sections is calculated, and the magnetic field energy density of each magnetic circuit section is subjected to volume integration to obtain the leakage magnetic energy calculation flux guide, and the result is shown in table 2:
TABLE 2 equivalent permeabilities of magnetic circuit segments (unit: H)
Step four: determination of equivalent model and parameters of copper conductor region:
in the fourth step, the frequency-dependent effect of the winding leakage inductance and the alternating current resistance is represented by adopting a Foster equivalent circuit. Fig. 13 is a schematic diagram of a second order series Foster circuit. The frequency-dependent effect of the winding leakage inductance and the alternating current resistance is represented by adopting a second-order serial Foster equivalent circuit, and the equivalent impedance expression of the Foster equivalent circuit is as follows:
wherein: r is R 0 The direct current resistance of the winding; r is R 1 、R 2 、L 1 、L 2 Is a pending parameter.
According to the Maxwell vortex field solver, the leakage energy and the eddy current loss of the copper conductor area of the winding under different frequencies can be calculated, and fig. 14 is a copper conductor eddy current loss cloud chart, and the leakage energy cloud chart is shown in fig. 12.
The equivalent inductance and the alternating current resistance converted to the primary side of the winding copper conductor area under different frequencies can be calculated by an energy method. And fitting out undetermined parameters according to the equivalent impedance expression after the calculation result is obtained. Calculated, R 1 ＝15.4Ω、R 2 ＝1.17Ω、L 1 ＝9.25×10 -6 H、L 2 ＝1.73×10 -5 The results of the finite element simulation calculation and the fitting result are shown in fig. 15.
Step five: establishing a transformer gyrator-magnetic conduction model;
the transformer gyrator-flux guide model shown in fig. 2 is built, specifically as follows:
rate of change of voltage (v), current (i) and magnetic flux on gyrator circuit side and gyrator magnetic circuit sideMagnetomotive force (F) satisfies the following relationship:
wherein: v and i are the voltage and current at the circuit side; n is the number of turns of the winding; f is magnetomotive force generated by the winding; phi is magnetic flux.
Current through flux guideThe expression is as follows:
combined with phi=b·a, ampere loop law f=h·l, flux-guide calculation formula p=μ (H) a/l, flux-guide currentCan be expressed as:
wherein: a is the cross-sectional area of the iron core; l is the magnetic path length. Mu (H) is dynamic magnetic permeability, and can be calculated through an H-B curve of the iron core, so that saturation and hysteresis effect of the iron core can be introduced.
Thus, a gyrator-flux guide model of the core type transformer can be built according to the built variable magnetic guide model of the iron core, the Foster equivalent circuit model of the winding copper conductor region and the magnetic leakage flux guide model of the copper-free conductor in the air, as shown in fig. 16.
In order to verify the accuracy of the inductance parameters of the model, a short circuit test is performed on the model. In PLECS, exciting voltage with the voltage amplitude of 1V and the frequency of 1kHz-100kHz is introduced to the primary side of the transformer, and the secondary side is short-circuited, so that the waveforms of the primary side voltage u and the short-circuit current i are obtained. The voltage and current waveforms are input into a discrete Fourier transformer module in PLECS, so that the amplitude and the phase of the voltage and the current under the fundamental wave frequency can be obtained, and further the phase voltage is obtainedSum phase current->According to->The leakage inductance and resistance, which are converted to the primary winding at the fundamental frequency, are calculated as shown in fig. 17.
The leakage inductance and the alternating current resistance of the high-frequency transformer test model are measured by adopting an Agilent4294A high-precision impedance analyzer, a clamp is connected to a primary winding during measurement, a secondary winding is short-circuited, and the frequency range of measurement is 1kHz-100kHz. The resulting resistance and inductance are the resistance and inductance that are calculated to the primary side, and fig. 18 shows the leakage inductance, ac resistance and simulation values that were experimentally measured. Compared with the experimental value, the average error of leakage inductance in the simulation is only 2.44%, the average error of alternating current resistance is 9.55%, and the correctness of the model parameters is well verified.
The invention establishes an analytical Preisach model based on a Lorentz distribution function by taking magnetic field intensity H as input and magnetic flux density B as output by adopting a power electronic simulation software PLECS bottom layer module and language programming program based on an analytical Preisach model taking reversible components into consideration and a flux-capacitance analogy method. The magnetic flux guide is analogous to a capacitor, and realizes direct connection of a magnetic circuit and a circuit without converting a complex magnetic circuit into a circuit. The magnetic conduction-capacitance analogy method can directly reflect the characteristics of the geometric shape, the nonlinear property and the like of the iron core. The energy storage characteristic of the magnetic guide corresponds to the energy storage characteristic of the capacitor, so that the direct transfer of energy in the magnetic circuit and the circuit is realized, and the confusion of the energy relation of the traditional resistance-magnetic resistance analog method is avoided.
Claims (5)
1. The modeling method of the electromagnetic model of the high-frequency transformer based on the magnetic conduction-capacitance analogy method is characterized by comprising the following steps of:
step 1: dividing a magnetic field of the transformer into a plurality of magnetic path sections according to the trend of magnetic lines of the transformer, and carrying out equivalence on each magnetic path section by using one magnetic guide;
step 2: dividing the magnetic field of the transformer into two parts, namely an iron core magnetic field and a leakage magnetic field, and dividing the leakage magnetic field of the transformer into a winding copper conductor area and an air area without copper conductors;
step 3: the core magnetic circuit section adopts a Preisach hysteresis model considering reversible components to simulate the hysteresis effect of the core;
step 4: the Foster equivalent circuit is adopted to perform equivalent on the winding copper conductor area, and leakage energy and eddy current loss of the winding copper conductor area under different frequencies are calculated;
step 5: calculating the flux leakage conductance of the air flux leakage area without the copper conductor;
step 6: and establishing a transformer gyrator-magnetic conduction model.
2. The method for modeling the electromagnetic model of the high-frequency transformer based on the flux-guide-capacitance analogy method according to claim 1, wherein the method comprises the following steps of: in the step 3, the total magnetic flux density is decomposed into a reversible magnetization component and an irreversible magnetization component by considering an analytical Preisach hysteresis model of the reversible component, and the calculation formula is as follows:
B cmb (H)＝B irr (H)+B rev (H)；
wherein: b (B) cmb (H) Is the total magnetic flux density; b (B) irr (H) Is an irreversible magnetization component; b (B) rev (H) Is a reversible magnetization component;
total magnetic permeability mu cmb (H) Equal to the irreversible component permeability mu irr (H) And reversible component permeability mu rev (H) The sum is calculated as follows:
μ cmb (H)＝μ irr (H)+μ rev (H)；
the irreversible component permeability of the descending branch is as follows:
wherein: h S The magnetic field intensity at the moment of the boundary point of the ascending branch and the descending branch is as follows; h is the magnetic field strength; h s >H>-H s ；
A、σ、H d Is a Lorentz function parameter; mu (mu) 0 Is the permeability in vacuum;
the irreversible component permeability of the ascending branch is as follows:
reversible component permeability mu rev (H) The calculation formula is as follows:
wherein: b (B) d Alpha is a magnetic permeability calculation parameter; b (B) rev Is a reversible magnetization component;
the initial magnetization curve, the magnetic permeability is the slope of the initial magnetization curve, and the calculation formula is as follows:
wherein: b (B) sat Is the saturation magnetic flux density; mu (mu) sat The magnetic permeability of the iron core is close to saturation; a is a free coefficient.
3. The method for modeling the electromagnetic model of the high-frequency transformer based on the flux-guide-capacitance analogy method according to claim 1, wherein the method comprises the following steps of: in the step 4, a second-order series Foster equivalent circuit is adopted to represent the frequency-dependent effect of the winding leakage inductance and the alternating current resistance, and the second-order series Foster equivalent circuit equivalent impedance expression is as follows:
wherein: r is R 0 The direct current resistance of the winding; r is R 1 、R 2 、L 1 、L 2 Is a pending parameter; omega is the angular frequency; j is an imaginary symbol.
4. The method for modeling the electromagnetic model of the high-frequency transformer based on the flux-guide-capacitance analogy method according to claim 1, wherein the method comprises the following steps of: in the step 5, finite element numerical calculation is adopted to extract the energy of the magnetic leakage area and the average magnetic flux flowing through the magnetic leakage area, and the flux leakage is calculated by the following formula:
wherein: phi is magnetic flux; w is leakage magnetic energy stored in the air leakage magnetic area; b and H are magnetic flux density and magnetic field strength, respectively; p is the magnetic flux guide; v is the volume of the magnetic leakage area; s is the sectional area of the magnetic leakage area.
5. The method for modeling the electromagnetic model of the high-frequency transformer based on the flux-guide-capacitance analogy method according to claim 1, wherein the method comprises the following steps of: in the step 6, a transformer gyrator-magnetic conductance model is established according to a magnetic conductance-capacitance analogy method, and the method specifically comprises the following steps:
voltage v and current i on the gyrator circuit side and rate of change of magnetic flux on the gyrator magnetic circuit sideMagnetomotive force F satisfies the following relationship:
wherein: n is the number of turns of the winding; f is magnetomotive force generated by the winding; phi is magnetic flux;
rate of magnetic flux changeThe expression is as follows:
combining phi=b·a, ampere loop law f=h·l, and a flux-guide calculation formula p=μ (H) a/l, B being magnetic field density;
rate of magnetic flux changeExpressed as:
wherein: a is the cross-sectional area of the iron core; l is the magnetic path length; mu (H) is dynamic magnetic permeability and is calculated by the H-B curve of the iron core.
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