CN113239649B - Modeling method of transformer - Google Patents

Modeling method of transformer Download PDF

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CN113239649B
CN113239649B CN202110545211.3A CN202110545211A CN113239649B CN 113239649 B CN113239649 B CN 113239649B CN 202110545211 A CN202110545211 A CN 202110545211A CN 113239649 B CN113239649 B CN 113239649B
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transformer
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CN113239649A (en
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王顺亮
周俊杰
马俊鹏
杨雨石
陈相
刘天琪
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Sichuan University
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Abstract

The invention discloses a transformer modeling method, which comprises the following steps: s1: establishing a static J-A model; s2: obtaining an initial transformer model according to the static J-A model; s3: carrying out parameter identification on correct model parameters of the J-A model by adopting an optimization algorithm to obtain complete parameters of the static J-A model; s4: and inputting the complete parameters of the static J-A model into the initial transformer model to obtain a final transformer model. The transformer modeling method disclosed by the invention can accurately calculate the harmonic current while accurately describing the excitation characteristics of the transformer.

Description

Modeling method of transformer
Technical Field
The invention relates to the technical field of transformers, in particular to a modeling method of a transformer.
Background
In order to obtain larger magnetic permeability, many devices in the power system have a structure of an iron core, and most of the iron cores are made of ferromagnetic materials, including hard magnetic materials and soft magnetic materials. Besides the characteristic of higher magnetic permeability, the ferromagnetic material inevitably has hysteresis and saturation phenomena, and the hysteresis phenomenon is that the change of the magnetic flux density B in a hysteresis loop lags behind H; saturation is a phenomenon in which the magnetic flux density B is hardly changed by increasing the external magnetic field H to a certain extent and then continuously increasing H. In the electromagnetic transient simulation software of the power system or related documents commonly used at present, the modeling of hysteresis and saturation characteristics of a key device of the power system, namely a transformer, has defects, if hysteresis is not considered, a single-value curve is used for replacing, so that calculation can be simplified, but the simulation precision of the power system is reduced; in addition, even if a transformer model based on a J-A model is embedded, the J-A model has some problems, so that the excitation characteristics of the transformer cannot be correctly described and the harmonic current cannot be correctly calculated.
The Jiles-Atherton (J-a) model is a widely used hysteresis modeling theory that describes hysteresis deep into the physical essence. The J-A model describes the relationship of magnetic flux density B and magnetic field strength H during magnetization based on the relationship of magnetic domain theory and energy conservation. The J-A model formula is a group of differential equations, the first differential equation is established, the first energy conservation, the correct expression of each variable, the first derivation and the like are needed, however, many researches at present have more or less errors in using the J-A model, and although the corresponding model can be established by the formula, the formula does not conform to the physical rule, is unfavorable for expansion and subsequent research, and has misleading effect for readers.
Disclosure of Invention
The invention aims to provide a modeling method of a transformer, which aims to solve the problems that the existing transformer model cannot accurately describe the excitation characteristics and cannot accurately calculate harmonic current.
The technical scheme for solving the technical problems is as follows:
the invention provides a modeling method of a transformer, which comprises the following steps:
s1: establishing a static J-A model;
s2: obtaining an initial transformer model according to the static J-A model;
s3: carrying out parameter identification on correct model parameters of the J-A model by adopting an optimization algorithm to obtain complete parameters of the static J-A model;
s4: and inputting the complete parameters of the static J-A model into the initial transformer model to obtain a final transformer model.
Optionally, in the step S1, establishing a static J-a model includes:
s11: according to the conservation relation of magnetic domain movement energy, a differential model of magnetization intensity M and magnetic field intensity H is obtained;
s12: according to the differential model, a differential expression model of the hysteresis-free magnetization intensity to the magnetic field intensity is obtained;
s13: and obtaining a static J-A model according to the differential expression model of the hysteresis free magnetization intensity to the magnetic field intensity.
Alternatively, the magnetic domain motion energy conservation relationship includes a first magnetic domain motion energy conservation and a second magnetic domain motion energy conservation;
the first magnetic domain motion energy conservation is:
Figure BDA0003073272010000021
the second magnetic domain motion energy conservation is:
Figure BDA0003073272010000022
or is:
Figure BDA0003073272010000031
wherein mu 0 Is vacuum magnetic permeability, M is magnetization intensity, H e For effective magnetic field strength, M irr For irreversible magnetization, δ represents the magnetization direction, δ=sign (dM/dH), and k is a parameter representing the hysteresis strength.
Optionally, in the step S1, a differential model of the magnetization M and the magnetic field strength H is:
Figure BDA0003073272010000032
wherein c is a parameter reflecting the elastic displacement movement of magnetic domains, M is magnetization intensity, H is magnetic field intensity, delta is magnetization direction, k is a parameter representing the magnetic hysteresis strength, and alpha is a parameter reflecting the association degree between magnetic domains.
Optionally, in the step S2, a differential expression model of the hysteresis-free magnetization versus the magnetic field strength is:
Figure BDA0003073272010000033
wherein M is s Is saturation magnetization, alpha is a non-hysteresis magnetization curve shape parameter, k is a parameter representing hysteresis strength, c is a parameter reflecting magnetic domain elastic displacement motion,
Figure BDA0003073272010000034
μ 0 is vacuum magnetic permeability, M is magnetization intensity, H is external magnetic field intensity, M an Is hysteresis-free magnetization.
Alternatively, the initial transformer model is obtained by writing custom elements in PSCAD/EMTDC; and/or
In the step S4, the final transformer model is obtained by writing custom elements in the PSCAD/EMTDC.
Optionally, writing the custom element in the PSCAD includes:
the nonlinear inductance of the transformer is written in PSCAD, specifically:
I km (t)＝I km (t-Δt)+Δt/(2L)[u k (t-Δt)-u m (t-Δt)]
wherein I is km (t) is the current value at the present time, I km (t-Deltat) is the current value at the previous time, u k And u m The voltage at two ends of the nonlinear inductance element is L, and the calculating method is as follows:
Figure BDA0003073272010000041
where N is the number of turns, S is the cross-sectional area, l is the equivalent magnetic path length, Δb and Δh are the amounts of change in magnetic flux density and magnetic field strength.
Optionally, in the step S3, the parameters M of the J-A model are calculated s And carrying out parameter identification on alpha, a, k and c.
Optionally, in the step S3, the optimization algorithm is: a genetic algorithm; and/or a particle swarm algorithm; and/or simulated annealing algorithms; and/or a random frog-leaping algorithm.
Optionally, after the step S4, the modeling method of the transformer further includes:
s5: changing relevant parameters of an excitation branch established by the static J-A model, keeping other data unchanged, and inputting the initial transformer model to obtain a final transformer model, wherein the final transformer model comprises a first final transformer model and a second final transformer model;
s6: comparing the first final transformer model with the second final transformer model to obtain a comparison result;
s7: and determining the actual meaning of the correct model of the static J-A model according to the comparison result.
The invention has the following beneficial effects:
1. the invention discovers and summarizes errors and defects of a J-A model in the current research, carries out first deduction on a model formula from a basic principle, and provides a differential equation of the first J-A model, thereby being beneficial to deeper research and theoretical analysis in the field of subsequent hysteresis modeling.
2. The invention adopts various intelligent optimization algorithms to identify the parameters of the J-A model, establishes hysteresis inductance based on the corrected J-A model in PSCAD/EMTDC, and accurately simulates the characteristic of the excitation branch of the transformer.
3. The invention respectively adopts the correct and error J-A models to establish the excitation branch models of the transformer, compares and demonstrates the change condition of the harmonic component and the total harmonic distortion rate of excitation current and the hysteresis loop of the direct current magnetic flux generated by the transformer established by adopting the correct and error J-A models, points out the adverse effect on modeling caused by using the error J-A models, and has reference value in the fields of hysteresis characteristic modeling, relay protection, power system stability analysis and the like.
Drawings
FIG. 1 is a flowchart of a modeling method of a transformer according to an embodiment of the present invention;
FIG. 2 is a partial flow chart of step S1 in FIG. 1;
FIG. 3 is another flowchart of a modeling method of a transformer according to an embodiment of the present invention;
FIG. 4 is a diagram showing the deflection of magnetic domains under an external magnetic field;
FIG. 5 is a schematic diagram of hysteresis loops and energy loss partitions of ferromagnetic material;
FIG. 6 shows hysteresis loop fitting results obtained by different optimization algorithms;
FIG. 7 is a fitness rise curve fitted by different optimization algorithms;
FIG. 8 is a comparison of saturated hysteresis loops obtained for correct and incorrect models;
FIG. 9 is a comparison of irreversible magnetization components from correct and incorrect models;
FIG. 10 is a comparison of the reversible magnetization components obtained for the correct and incorrect models;
FIG. 11 is a graph showing the comparison of the excitation current of the unbiased transformer obtained by the correct and incorrect models;
FIG. 12 is a graph showing the comparison of the excitation current of the transformer when the DC flux obtained by the correct and incorrect models is 0.15T;
FIG. 13 is a graph showing the comparison of the excitation current of the transformer when the DC flux obtained by the correct and incorrect models is 0.3T;
FIG. 14 is a comparison of unbiased hysteresis loops obtained for correct and incorrect models;
FIG. 15 is a comparison of hysteresis loops for a DC flux of 0.15T for a correct and incorrect model;
FIG. 16 is a comparison of hysteresis loops for a DC flux of 0.3T for a correct and incorrect model;
FIG. 17 is a graph showing the variation of the excitation current subharmonics with bias magnetic quantity for the correct and incorrect models;
FIG. 18 is a graph showing the total harmonic distortion of the excitation current obtained by the correct and incorrect models as a function of bias magnetic quantity;
FIG. 19 is a graph showing the variation of excitation current with bias magnetic quantity for correct and incorrect models;
fig. 20 is a comparison of the hysteresis loop obtained for the correct and incorrect models as a function of bias magnetic quantity.
Detailed Description
The principles and features of the present invention are described below with reference to the drawings, the examples are illustrated for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.
Examples
The technical scheme for solving the technical problems is as follows:
referring to fig. 1, the present invention provides a modeling method of a transformer, the modeling method of the transformer comprising the steps of:
s1: establishing a static J-A model;
s2: obtaining an initial transformer model according to the static J-A model;
s3: carrying out parameter identification on correct model parameters of the J-A model by adopting an optimization algorithm to obtain complete parameters of the static J-A model;
s4: and inputting the complete parameters of the static J-A model into the initial transformer model to obtain a final transformer model.
The invention has the following beneficial effects:
1. the invention discovers and summarizes errors and defects of a J-A model in the current research, carries out first deduction on a model formula from a basic principle, and provides a differential equation of the first J-A model, thereby being beneficial to deeper research and theoretical analysis in the field of subsequent hysteresis modeling.
2. The invention adopts various intelligent optimization algorithms to identify the parameters of the J-A model, establishes hysteresis inductance based on the corrected J-A model in PSCAD/EMTDC, and accurately simulates the characteristic of the excitation branch of the transformer.
3. The invention respectively adopts the correct and error J-A models to establish the excitation branch models of the transformer, compares and demonstrates the change condition of the harmonic component and the total harmonic distortion rate of excitation current and the hysteresis loop of the direct current magnetic flux generated by the transformer established by adopting the correct and error J-A models, points out the adverse effect on modeling caused by using the error J-A models, and has reference value in the fields of hysteresis characteristic modeling, relay protection, power system stability analysis and the like.
Optionally, in the step S1, referring to fig. 2, establishing the static J-a model includes:
s11: according to the conservation relation of magnetic domain movement energy, a differential model of magnetization intensity M and magnetic field intensity H is obtained;
s12: from the differential model, a differential expression model of the hysteresis-free magnetization versus the magnetic field strength (i.e., M an -H differential expression model, supra);
s13: and obtaining a static J-A model according to the differential expression model of the hysteresis free magnetization intensity to the magnetic field intensity.
Alternatively, the magnetic domain motion energy conservation relationship includes a first magnetic domain motion energy conservation and a second magnetic domain motion energy conservation;
the first magnetic domain motion energy conservation is:
Figure BDA0003073272010000071
the second magnetic domain motion energy conservation is:
Figure BDA0003073272010000072
or is:
Figure BDA0003073272010000073
wherein mu 0 Is vacuum magnetic permeability, M is magnetization intensity, H e For effective magnetic field strength, M irr For irreversible magnetization, δ represents the magnetization direction, δ=sign (dM/dH), and k is a parameter representing the hysteresis strength. Here, according to the machine model selection, it is determined that the first magnetic domain movement energy conservation equation is the correct magnetic domain movement energy conservation equation, and the second magnetic domain movement energy conservation equation is the wrong magnetic domain movement energy conservation equation, whereby the following model is established according to the correct magnetic domain movement energy conservation equation.
Optionally, in the step S1, a differential model of the magnetization M and the magnetic field strength H is:
Figure BDA0003073272010000081
wherein c is a parameter reflecting the elastic displacement movement of magnetic domains, M is magnetization intensity, H is magnetic field intensity, delta is magnetization direction, k is a parameter representing the magnetic hysteresis strength, and alpha is a parameter reflecting the association degree between magnetic domains.
Optionally, in the step S2, a differential expression model of the hysteresis-free magnetization versus the magnetic field strength is:
Figure BDA0003073272010000082
wherein M is s Is saturation magnetization, alpha is a non-hysteresis magnetization curve shape parameter, k is a parameter representing hysteresis strength, c is a parameter reflecting magnetic domain elastic displacement motion,
Figure BDA0003073272010000083
μ 0 is vacuum magnetic permeability, M is magnetization intensity, H is external magnetic field intensity, M an Is hysteresis-free magnetization.
Alternatively, the initial transformer model is obtained by writing custom elements in PSCAD/EMTDC; and/or
In the step S4, the final transformer model is obtained by writing custom elements in the PSCAD/EMTDC.
Optionally, writing the custom element in the PSCAD includes:
the nonlinear inductance of the transformer is written in PSCAD, specifically:
I km (t)＝I km (t-Δt)+Δt/(2L)[u k (t-Δt)-u m (t-Δt)]
wherein I is km (t) is the current value at the present time, I km (t-Deltat) is the current value at the previous time, u k And u m Is the voltage across the nonlinear inductive elementL is a nonlinear inductance value, and the calculation method comprises the following steps:
Figure BDA0003073272010000091
where N is the number of turns, S is the cross-sectional area, l is the equivalent magnetic path length, Δb and Δh are the amounts of change in magnetic flux density and magnetic field strength.
Optionally, in the step S3, the optimization algorithm is: a genetic algorithm; and/or a particle swarm algorithm; and/or simulated annealing algorithms; and/or a random frog-leaping algorithm.
Optionally, after the step S4, referring to fig. 3, the modeling method of the transformer further includes:
s5: changing relevant parameters of an excitation branch established by the static J-A model, keeping other data unchanged, and inputting the initial transformer model to obtain a final transformer model, wherein the final transformer model comprises a first final transformer model and a second final transformer model; here, the first final transformer model is obtained by the above-described first domain movement energy conservation scheme, and the second final transformer is obtained by the above-described second domain movement energy conservation scheme, and since the first domain movement energy conservation scheme is the correct domain movement energy conservation scheme and the second domain movement energy conservation scheme is the wrong domain movement energy conservation scheme, the obtained first final transformer model is the correct final transformer model and the second final transformer model is the wrong final transformer model.
S6: comparing the first final transformer model with the second final transformer model to obtain a comparison result;
s7: and determining the actual meaning of the correct model of the static J-A model according to the comparison result.
FIG. 4 is a schematic diagram illustrating the deflection of magnetic domains under the action of an external magnetic field, which is the basis of the J-A model. As shown in fig. 5, in the ferromagnetic material, when the external magnetic field is relatively small (linear region) during magnetization, reversible elastic displacement of the domain wall occurs; when the external magnetic field is larger (saturation region), the inelastic displacement and magnetic moment rotation process of the irreversible magnetic domain wall occurs, when the external magnetic field is reduced to 0, the magnetic flux is not 0, after the external magnetic field disappears, the irreversible movement of the magnetic domain wall is restored, the irreversible movement part of the magnetic domain wall and the rotating magnetic moment cannot be fully restored, and a reverse magnetic field is needed to be applied to restore the irreversible movement part, and the consumed energy of the reverse magnetic field is equal to the heat generated by hysteresis loss caused by irreversible magnetization. The area of the hysteresis loop is proportional to the hysteresis loss, so that the hysteresis loops obtained by different conservation of energy must have different areas (shapes).
In the invention, firstly, an M-H differential model of a correct model of a J-A model is deduced, and the method is concretely as follows:
conservation of energy for first domain motion:
Figure BDA0003073272010000101
mu in the middle 0 Is vacuum magnetic permeability, M is magnetization intensity, H e For effective magnetic field strength, M irr For irreversible magnetization, δ represents the magnetization direction, δ=sign (dM/dH), and k is a parameter representing the hysteresis strength. The physical meaning is that the actual magnetostatic energy in the magnetization process of the ferromagnetic material is equal to the hysteresis-free magnetization energy minus the energy consumed by the irreversible magnetization,
however, many studies have adopted the energy conservation equation:
Figure BDA0003073272010000102
or is:
Figure BDA0003073272010000103
it is clear that these two expressions do not correspond to physical meanings, constituting a second expression. In addition to errors in energy conservation, many documents confuse many variables in J-A in the derivation of model formulas.
Thus, the energy conservation of the first domain motion results from:
Figure BDA0003073272010000104
this can be achieved by:
Figure BDA0003073272010000105
Figure BDA0003073272010000106
finally, the following steps are obtained:
Figure BDA0003073272010000111
wherein c is a parameter reflecting the elastic displacement movement of magnetic domains, alpha is a parameter reflecting the degree of association between magnetic domains, H e =h+αm is the effective magnetic field strength, M irr Is irreversible magnetization intensity.
M from which the correct model is derived an -H differential expression model process:
the above is the first M an Expression from which dM can be found an dH and not be able to find dM an /dH e The first derivation according to the above equation is:
Figure BDA0003073272010000112
thus:
Figure BDA0003073272010000113
in the above formula: m is M s Is saturated magnetization intensity, alpha is hysteresis-free magnetization curve shapeThe parameter k is the parameter representing the magnetic hysteresis strength, c is the parameter reflecting the elastic displacement motion of the magnetic domain,
Figure BDA0003073272010000114
μ 0 is vacuum magnetic permeability, M is magnetization intensity, H is external magnetic field intensity, M an Is hysteresis-free magnetization.
Secondly, adopting an optimization algorithm to perform model parameter M s And (3) carrying out parameter identification on alpha, a, k and c, wherein the optimization algorithm comprises a genetic algorithm, a particle swarm algorithm, a simulated annealing algorithm, a random frog-leaping algorithm and a cuckoo optimization algorithm, different algorithms are adopted for simulation, and a group of parameters with the best optimization result are selected as parameters used for the next modeling according to the simulation results of the various algorithms.
The optimization algorithms are all stochastic optimization algorithms, and the adoption of the algorithms is the simplest method because the objective function fitted on the hysteresis loop based on the JA model has no analytical expression and is a nonlinear multidimensional space optimization problem.
The optimization target expression is:
Figure BDA0003073272010000121
in the method, in the process of the invention,
Figure BDA0003073272010000122
normalizing the ordinate of the target curve sample point, b m And normalizing the processed ordinate for the optimized curve sample point. After normalization, the ordinate range is [ -1,1]Thus, the maximum value of the distance between N sample points is +.>
Figure BDA0003073272010000123
The distance between the two corresponding sample points is taken as a reference value. When the target curve is closest to the optimization curve, the function value reaches the maximum, and the best set of parameters is output through continuous iteration.
J-A model parameter identification
Giving a hysteresis loop, adopting different optimization algorithms to perform hysteresis loop fitting to obtain corresponding J-A model parameters, wherein the optimized objective function is the distance between two curves:
Figure BDA0003073272010000124
wherein d is the objective function value,
Figure BDA0003073272010000125
for a sample point on the sample curve, (H) m ,B m ) To optimize the sampling points on the curve.
As can be seen from fig. 6 and 7, the optimization results of the respective algorithms have a certain error, and the optimization result parameters of the Genetic Algorithm (GA) having the highest fitting degree are adopted.
Furthermore, the transformer models considering saturation and hysteresis are respectively built according to the correct and incorrect models, and the important point is to compare the characteristics of the excitation branches built by the correct and incorrect J-A models, so that the excitation branch voltage is taken as an input quantity, the excitation current is taken as an output quantity, the excitation resistance, leakage inductance and winding resistance of the transformer are not considered, and only the excitation characteristics are considered. The current is deduced from the voltage by adopting an inverse J-A model, and the specific process is as follows:
collecting the voltage U at two ends of an excitation branch, and calculating excitation current I according to the following steps:
Figure BDA0003073272010000126
Figure BDA0003073272010000127
dB＝B n+1 -B n
I n+1 ＝H n+1 ·l/N
Figure BDA0003073272010000131
Figure BDA0003073272010000132
M n+1 ＝M n +dM
in the above formula: b (B) n+1 For the magnetic induction intensity of the next moment, B n For the magnetic induction intensity at this moment, H n+1 For the magnetic field strength at the next moment, M n+1 For the magnetization at the next moment, M n For the magnetization at this moment, I n+1 For the current at the next moment, S is the equivalent cross-sectional area of the iron core, l is the equivalent length of the magnetic circuit of the iron core, and N is the number of turns of the primary winding of the transformer. Then, the PSCAD custom electrical interfaces CCIN and GGIN are used for connecting the model into a circuit, and the usage rules are as follows: the reactance capacitance of all lumped parameters is represented as a resistive parallel current source, which represents the current at the previous moment. The calculation process is as follows:
Figure BDA0003073272010000133
in the above formula: i km (t) is the current value at the present time, I km (t-Deltat) is the current value at the previous time, u k And u m The voltage at two ends of the nonlinear inductance element is L, and the calculating method is as follows:
Figure BDA0003073272010000134
in the above formula, N is the number of turns, S is the sectional area, l is the equivalent magnetic path length, and Δb and Δh are the amounts of change in magnetic flux density and magnetic field strength.
The saturation hysteresis loop generated when the external magnetic field in the simulation process is large is extracted, compared with the magnetic field generated by the external magnetic field in the simulation process, the magnetization irreversible component is shown in fig. 9, the reversible component is shown in fig. 10, and the components are different. Establishing a corresponding excitation branch model according to the model, applying symmetrical alternating voltage, and positioning a working point at the knee of a saturation hysteresis loop, wherein the obtained excitation current pair is shown in fig. 11, applying 0.15T direct current flux, the obtained excitation current waveform pair is shown in fig. 12, and applying 0.3T direct current flux, and the obtained excitation current waveform pair is shown in fig. 13; hysteresis loop pairs corresponding to the above three conditions are shown in fig. 14, 15, and 16, respectively.
Finally, under the same working condition and under the condition that other parameters are the same except that excitation branches established by the J-A models are different, harmonic components of excitation currents generated by the two transformer models, the change condition of total harmonic distortion along with direct current magnetic flux and the change condition of hysteresis loops are compared, and adverse effects on modeling caused by using the J-A model based on error deduction are pointed out.
The direct current magnetic flux is gradually increased from 0 to the core depth saturation, the obtained exciting current is 2 to 7 times of harmonic wave change conditions are shown in fig. 17, the total harmonic distortion rate change conditions are shown in fig. 18, and the total harmonic distortion rate is larger than that of the correct model when the subharmonic content of the error model is found. The excitation current variation is shown in fig. 19, and the hysteresis loop variation is shown in fig. 20.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (8)

1. A method of modeling a transformer, the method comprising the steps of:
s1: establishing a static J-A model;
s2: obtaining an initial transformer model according to the static J-A model;
s3: carrying out parameter identification on correct model parameters of the J-A model by adopting an optimization algorithm to obtain complete parameters of the static J-A model;
s4: inputting the complete parameters of the static J-A model into the initial transformer model to obtain a final transformer model; in the step S1, the static J-A model is established by:
s11: according to the conservation relation of magnetic domain movement energy, a differential model of magnetization intensity M and magnetic field intensity H is obtained;
s12: according to the differential model, a differential expression model of the hysteresis-free magnetization intensity to the magnetic field intensity is obtained;
s13: obtaining a static J-A model according to the differential expression model of the hysteresis free magnetization intensity to the magnetic field intensity; in the step S12, the differential expression model of the hysteresis-free magnetization to the magnetic field strength is:
Figure FDA0004070141950000011
wherein M is s The saturation magnetization, alpha is a parameter reflecting the degree of association between magnetic domains, a is a parameter of a shape of a non-hysteresis magnetization curve, k is a parameter representing the strength of hysteresis, c is a parameter reflecting the elastic displacement movement of the magnetic domains,
Figure FDA0004070141950000012
μ 0 is vacuum magnetic permeability, M is magnetization intensity, H is external magnetic field intensity, M an Is hysteresis-free magnetization.
2. The modeling method of a transformer according to claim 1, wherein in the step S11, the magnetic domain movement energy conservation relation includes a first magnetic domain movement energy conservation formula and a second magnetic domain movement energy conservation formula;
the first magnetic domain motion energy conservation is:
Figure FDA0004070141950000021
the second magnetic domain motion energy conservation is:
Figure FDA0004070141950000022
or is:
Figure FDA0004070141950000023
wherein mu 0 Is vacuum magnetic permeability, M is magnetization intensity, H e For effective magnetic field strength, M irr For irreversible magnetization, δ represents magnetization direction, δ=sign (dM/dH), k is a parameter representing hysteresis strength, M an Is hysteresis-free magnetization.
3. The modeling method of a transformer according to claim 1, wherein in the step S11, the differential model of the magnetization M and the magnetic field H is:
Figure FDA0004070141950000024
wherein c is a parameter reflecting the elastic displacement movement of magnetic domains, M is magnetization intensity, H is magnetic field intensity, delta is magnetization direction, k is a parameter representing the magnetic hysteresis intensity, alpha is a parameter reflecting the association degree between magnetic domains, M an Is hysteresis-free magnetization.
4. The method according to claim 1, wherein in step S2, the initial transformer model is obtained by writing custom elements in PSCAD/EMTDC; and/or
In the step S4, the final transformer model is obtained by writing custom elements in the PSCAD/EMTDC.
5. The method of modeling a transformer as claimed in claim 4, wherein said writing custom elements in the PSCAD comprises:
the nonlinear inductance of the transformer is written in PSCAD, specifically:
I km (t)＝I km (t-Δt)+Δt/(2L)[u k (t-Δt)-u m (t-Δt)]
wherein I is km (t) is the current value at the present time, I km (t-Deltat) is the current value at the previous time, u k And u m The voltage at two ends of the nonlinear inductance element is respectively, L is the nonlinear inductance value, and the calculation method is as follows:
Figure FDA0004070141950000031
wherein N is the number of turns, S is the sectional area, l is the equivalent magnetic path length, and DeltaB and DeltaH are the variation of the magnetic flux density and the magnetic field intensity respectively.
6. The modeling method of a transformer according to claim 1, wherein in the step S3, the parameter M of the J-a model is calculated s And carrying out parameter identification on alpha, a, k and c.
7. The method of modeling a transformer according to claim 6, wherein in the step S3, the optimization algorithm is:
a genetic algorithm; and/or a particle swarm algorithm; and/or simulated annealing algorithms; and/or a random frog-leaping algorithm; and/or a cuckoo optimization algorithm.
8. The method of modeling a transformer according to any of claims 1-7, further comprising, after step S4:
s5: changing relevant parameters of an excitation branch established by the static J-A model, keeping other data unchanged, and inputting the initial transformer model to obtain a final transformer model, wherein the final transformer model comprises a first final transformer model and a second final transformer model;
s6: comparing the first final transformer model with the second final transformer model to obtain a comparison result;
s7: and determining the actual meaning of the correct model of the static J-A model according to the comparison result.
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