Calculation method of dynamic hysteresis loop based on r-l type fractional derivative dynamic analytical inverse preisach model

Abstract

The method for calculating the dynamic hysteresis loop of the dynamic analytical inverse Preisach model based on the R-L fractional derivative includes the following steps: establishing an analytical static positive Preisach model considering reversible components; establishing a static analytical inverse Preisach model considering reversible components; constructing a dynamic analytical inverse Preisach model by introducing dynamic eddy current loss components and additional loss components based on loss statistics theory and field separation technology; improving the dynamic eddy current loss components using the R-L fractional derivative; and identifying the parameters of the dynamic eddy current loss components improved by the R-L fractional derivative in the dynamic analytical inverse Preisach model. This invention improves the static analytical positive Preisach model and dynamic loss characteristics, and introduces a parameter identification algorithm to improve the parameter determination method, thereby achieving the goal of accurately simulating the dynamic hysteresis characteristics of ferromagnetic materials.

Description

Technical Field

[0001] This invention relates to the field of hysteresis loop calculation, and in particular to a method for calculating dynamic hysteresis loops based on the dynamic analytical inverse Preisach model using RL-type fractional derivatives. Background Technology

[0002] Accurate electromagnetic transient models are required during the operation of power transformers to ensure their safe and reliable operation. During low-frequency electromagnetic transients, the transformer's saturation characteristics, core losses, and eddy current losses have a significant impact. Therefore, it is necessary to first construct an accurate transformer core model. Thus, establishing an accurate dynamic hysteresis model that considers the nonlinear hysteresis characteristics and dynamic loss characteristics of the core is of great significance for establishing the transformer's electromagnetic transient model.

[0003] For the nonlinear hysteresis characteristics of iron core, a variety of classical models have been established, such as reference [1]: Dong Zhangzhuo, Wu Hong, Shang Teng, Wang Qingliang. Parameter identification of JA hysteresis model of ferromagnetic element [J]. Electrical Application, 2017, 36(09): 22-28. The parameter identification method is used to identify the parameters of the static JA model; reference [2]: Liu Ren, Li Lin. Parameter extraction of Energetic hysteresis model based on simulated annealing and Levenberg-Marquardt hybrid algorithm [J]. Proceedings of the CSEE, 2019, 39(03): 875-884+966. DOI: 10.13334 / j.0258-8013.pcse e.180372. The static Energetic model was identified by a hybrid algorithm of pseudo-annealing and Levenberg-Marquardt; Reference [3]: Zhao Zhigang, Li Xiaoxue, Ji Junan, Wei Le, Wen Tao. Simulation of magnetic properties of electrical steel sheet based on Preisach hysteresis model [J]. High Voltage Engineering, 2019, 45(12):4038-4046.DOI:10.13336 / j.1003-6520.hve.20191125032. The static Preisach model was adopted.

[0004] The above-mentioned classical models are all positive models with magnetic field strength H as input and magnetic flux density B as output. Although such positive models can accurately simulate static hysteresis characteristics, they are usually difficult to use in the establishment of dynamic models and in practical applications. At the same time, in the practical application of ferromagnetic materials, since their working frequency is usually not zero, the static model that only considers nonlinear hysteresis characteristics can no longer accurately describe the dynamic characteristics of transformer cores. It is necessary to introduce dynamic eddy current components and residual loss components to construct an accurate dynamic model of transformer cores. For example, the literature [4]: ​​Bertotti G..Dynamic generalization of the scalar Preisach model of hysteresis[J].IEEE Transactions on Magnetics,1992, 28(5):2599-2601. studied the loss statistics theory, introduced dynamic eddy current loss and additional loss, and constructed a dynamic hysteresis model.

[0005] Traditional loss statistics theory and field separation technology reduce the complexity of loss solution while ensuring calculation accuracy, but they still cannot accurately reflect the correlation characteristics between eddy current components and frequency in the calculation of eddy current components. For example, reference [5]: Kowal Damian et al. Comparison of Iron Loss Models for Electrical Machines With Different Frequency Domain and Time Domain Methods for Excess Loss Prediction[J]. IEEE Transactions on Magnetics,2015,51(1):1-10. It points out the shortcomings of loss statistics theory in terms of frequency correlation characteristics. Reference [6]: Ducharne Benjamin et al. Fractional model of magnetic field penetration into a toroidal soft ferromagnetic sample[J]. International Journal of Dynamics and Control,2018,6(1):89-96. It proposes the RL fractional derivative theory and uses it to improve the dynamic eddy current loss components.

[0006] In summary, although there is considerable research on dynamic core models of transformers both domestically and internationally, most studies are not comprehensive enough and suffer from inaccurate simulation accuracy and large errors. Currently, there is considerable research on simulation methods for the dynamic characteristics of ferromagnetic materials, with progress in various aspects, but there are still shortcomings in the construction of dynamic models and the confirmation of dynamic characteristic parameters. Summary of the Invention

[0007] Based on the traditional static Preisach model, this invention provides a method for calculating the dynamic hysteresis loop of a dynamic analytical inverse Preisach model based on RL-type fractional derivatives. This method first improves the analytical static positive Preisach model by proposing an analytical inverse Preisach model based on the Lorentz function that considers reversible components. Then, based on loss statistics theory and field separation techniques, dynamic eddy current components and additional loss components are introduced, and the expression for the eddy current component is improved using RL fractional derivatives to construct the dynamic analytical inverse Preisach model. Finally, a quantum genetic algorithm is introduced to globally optimize the fractional derivative parameters. Comparison with experimental data shows that this method can effectively and accurately simulate the dynamic hysteresis characteristics of ferromagnetic materials.

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

[0009] The method for calculating the dynamic hysteresis loop of the dynamic analytic inverse Preisach model based on RL-type fractional derivatives includes the following steps:

[0010] Step 1: Establish an analytical static positive Preisach model that considers invertible components;

[0011] Step 2: Establish a static analytic inverse Preisach model considering invertible components;

[0012] Step 3: Based on loss statistics theory and field separation technology, dynamic eddy current loss components and additional loss components are introduced to construct a dynamic analytical inverse Preisach model;

[0013] Step 4: Use the fractional derivative of RL to improve the dynamic eddy current loss components;

[0014] Step 5: Identify the parameters of the dynamic eddy current loss component based on the RL fractional derivative improvement in the dynamic analytical inverse Preisach model.

[0015] In step 1, the analytical static positive Preisach model considering invertible components includes irreversible and invertible components, wherein the expression for the irreversible component is:

[0016] Irreversible component rising branch:

[0017]

[0018] In the formula: H is the magnetic field strength; M(H) is the magnetization; i represents the expression for the rising branch of the irreversible component of the hysteresis loop; A, σ, H d The three parameters are the three basic parameters of the Lorentz function, H. s For saturated magnetic field strength, M s is the saturation magnetization.

[0019] Irreversible component decline branch:

[0020]

[0021] In the formula: d indicates that this formula is the expression for the descending branch of the irreversible component of the hysteresis loop.

[0022] The loren(x,a) function is defined as follows:

[0023]

[0024] In the formula: x and a have no physical meaning; they are parameters of the user-defined Loren function. For example, in the expression for the rising branch of an irreversible component, x represents... a represents 2σ.

[0025] The expression for the invertible component is:

[0026]

[0027] In the formula: B d α and α are the calculation parameters for reversible components, which makes the calculation of reversible components more accurate.

[0028] In step 2, the specific expression of the static parsing inverse Preisach model is as follows:

[0029] The formula for the rising branch of the static analytic inverse Preisach model:

[0030]

[0031] In the formula: H(t) is the magnetic field strength at each moment; H(t+Δt) is the magnetic field strength at the next moment; B(t) is the magnetic flux density at each moment; B(t+Δt) is the magnetic flux density at the next moment; t is the value at each moment; Δt is the change at each moment.

[0032] Static analytical inverse Preisach model descent branch formula:

[0033]

[0034] In step 3, based on the loss separation theory, the total loss W of the ferromagnetic material is decomposed into hysteresis loss W.h Eddy current loss W cl With residual loss W ex :

[0035] W t =W h +W cl +W ex ;

[0036] Based on field separation technology, the total loss W can be further expressed as:

[0037]

[0038] Where: H h (B) represents the hysteresis magnetic field strength corresponding to the hysteresis loss; H cl (B) represents the eddy current magnetic field strength corresponding to eddy current loss; H ex is the residual magnetic field strength corresponding to the residual loss; T is the period.

[0039] The formula for calculating the intensity of an eddy current magnetic field is:

[0040]

[0041] In the formula: d is the thickness of the ferromagnetic material, σ is the electrical conductivity, This is the integral of the magnetic flux density over time.

[0042] The formula for calculating the residual magnetic field strength is:

[0043]

[0044] In the formula: G is a dimensionless number, G = 0.1356, S is the cross-sectional area of ​​the ferromagnetic material, V0 is a statistical coefficient, and λ is a sign function. When dB / dt > 0, λ = 1; when dB / dt < 0, λ = -1.

[0045] Step 3 involves dynamically parsing the inverse Preisach model, including:

[0046] Dynamic analysis of the rising branch of the inverse Preisach model:

[0047]

[0048] Dynamic analysis of the descent branch of the inverse Preisach model:

[0049]

[0050] In step 4, the expression for the fractional derivative of RL is:

[0051]

[0052] In the formula: f(t) is the integrand; t is time; n is a non-integer order, and the range of n is (0,1); Γ(·) is the Euler-Gamma function;

[0053] The improved eddy current loss expression based on fractional derivatives is as follows:

[0054]

[0055] In the formula, denoted by f, which represents the improved eddy current flux density using fractional derivatives; f represents the frequency.

[0056] In step 5, a quantum genetic algorithm is used for parameter identification, as detailed below:

[0057] The quantum genetic algorithm is a probabilistic evolutionary algorithm based on quantum computing and genetic algorithms. This algorithm updates chromosomes with each iteration, bringing them closer to their optimal values. To solve the problem of calculating the optimal fractional derivative parameters ρ and n using the quantum genetic algorithm, an objective function needs to be set. To simplify the objective function for parameter identification and avoid secondary processing of experimental data, this invention directly uses the root mean square error between the calculated value of the improved eddy current loss expression containing the parameters ρ and n and the measured loss value as the objective function of the optimization algorithm. This transforms the problem of identifying the optimal values ​​of the fractional parameters ρ and n into a problem of minimizing the objective function. The objective function expression of the quantum genetic algorithm is:

[0058]

[0059] In the formula, E f W is the root mean square error. cl (i) represents the calculated value from the model; W meas (i) represents the experimental measurement value.

[0060] In step 5, the quantum genetic algorithm includes the following steps:

[0061] Step S5.1: Initialize the population: Randomly generate chromosomes encoded by qubits and form a chromosome encoding matrix under the initialized population. The matrix expression is as follows:

[0062]

[0063] In the formula: represents the population evolving to the j-th chromosome in the g-th generation; m represents the total number of genes in the chromosome. Let be the qubit in the m-th gene of the g-th chromosome, satisfying the normalization condition a. 2 +b 2 =1.

[0064] Step S5.2: Use the collapse function to measure each individual in the initial population once to obtain the corresponding solution set;

[0065] Step S5.3: Based on the objective function, evaluate the fitness of the corresponding solution for each individual in step S5.2, and record the optimal individual and its fitness as the evolution target for the next generation.

[0066] Step S5.4: Iterate through step S5.3 to update and record the individual with the best fitness and its fitness.

[0067] Step S5.5: Determine whether the maximum number of iterations has been reached. If the condition is met, the calculation ends; otherwise, continue to the next step of the operation.

[0068] Step S5.6: Adjust individuals using a quantum rotation gate to achieve chromosomal gene mutation and evolution, thereby obtaining a new population. The update formula for the quantum rotation gate is shown below:

[0069]

[0070] In the formula: θ i Let θ be the rotation angle. i =s(a i ,b i )Δθ i ;s(a i ,b i ) and Δθ i These represent the direction and magnitude of rotation, respectively.

[0071] Step S5.7: Increment the iteration count by 1, then return to step S5.3.

[0072] This invention provides a method for calculating the dynamic hysteresis loop of a dynamic analytical inverse Preisach model based on RL-type fractional derivatives. The technical advantages are as follows:

[0073] 1) In order to accurately construct the electromagnetic transient model of the transformer and accurately simulate the dynamic characteristics of the transformer core, this invention improves the static analytical positive Preisach model and the dynamic loss characteristics, and introduces a parameter identification algorithm to improve the parameter determination method, so as to achieve the purpose of accurately simulating the dynamic hysteresis characteristics of ferromagnetic materials.

[0074] 2) This invention improves the traditional static positive Preisach model into a static analytical inverse Preisach model using the difference method, which is beneficial for constructing dynamic models.

[0075] 3) The method of the present invention is particularly suitable for calculating the magnetic characteristics of the transformer core in the electromagnetic transient model of the transformer, and can accurately calculate the dynamic magnetic characteristics of the transformer core. Attached Figure Description

[0076] Figure 1 This is a flowchart illustrating the dynamic model design of the present invention.

[0077] Figure 2 This is a comparison diagram of the irreversible and reversible components of the static model.

[0078] Figure 3 This is a schematic diagram of the dynamic model.

[0079] Figure 4 Flowchart for identifying parameters of fractional derivatives.

[0080] Figure 5 A comparison chart of calculated and measured values ​​for static models under different magnetic flux densities.

[0081] Figure 6 A graph showing the number of iterations for identifying fractional derivative parameters.

[0082] Figure 7 This is a comparison chart of calculated and measured values ​​for a dynamic model with a maximum magnetic flux density of 0.3T.

[0083] Figure 8 This is a comparison chart of calculated and measured values ​​for a dynamic model with a maximum magnetic flux density of 1.0T.

[0084] Figure 9 This is a comparison chart of calculated and measured values ​​for a dynamic model with a maximum magnetic flux density of 1.4T. Detailed Implementation

[0085] This invention focuses on the hysteresis and dynamic loss characteristics of transformer cores, and constructs a dynamic hysteresis model for transformer cores. The design flow of the dynamic hysteresis loop calculation method based on the RL-type fractional derivative dynamic analytical inverse Preisach model proposed in this invention is as follows: Figure 1 As shown. Includes the following steps:

[0086] Step 1: The Preisach model based on the Lorentz function is an improved version of the classic Preisach model. This model uses the Lorentz function to approximate the Everett distribution function. The distribution function μ(U,V) of the classic Preisach model can be expressed as μ(U,V)P S (U)P S (V), which is the product of the two Lorentz functions, and the analytical expression of the Lorentz function is:

[0087]

[0088] In the formula: H is the magnetic field strength; A, σ, H d Here are the parameters of the Lorentz function. Parameter A can be determined from σ and H. d The calculation formula is as follows:

[0089]

[0090] Where: H s M represents the saturation magnetic field strength. s is the saturation magnetization.

[0091] According to the saturation point of the hysteresis loop of ferromagnetic materials (H) s M s and μ(U,V)=P S (U)P S (-V), from which we can obtain the expressions for the rising and falling segments of the hysteresis loop:

[0092]

[0093]

[0094] Substituting the expressions, we can obtain the formulas for the rising and falling segments of the hysteresis loop, where the formula for the rising segment is:

[0095]

[0096] The formula for the descending segment of the hysteresis loop is:

[0097]

[0098] In the formula, the loren(x,a) function is defined as:

[0099]

[0100] Because both the classic Preisach model and its improved versions rely on rectangular hysteresis loops to describe hysteresis characteristics, they fail to consider the reversible magnetization component during the magnetization process, thus affecting the accuracy of the hysteresis loop simulation. Therefore, to comprehensively describe the magnetization characteristics of ferromagnetic materials, the magnetization process can be divided into two parts: irreversible magnetization and reversible magnetization. The reversible component is then introduced into the Preisach model based on the Lorentz function.

[0101] After introducing a reversible magnetization component, the hysteresis loop should satisfy the condition that the total magnetic flux density B(H) is the sum of the two components:

[0102] B(H)=B irr (H)+B rev (H);

[0103] In the formula: B irr (H) represents the irreversible component; B rev (H) represents the reversible component.

[0104] The total permeability μ(H) follows the same rule, that is, the total permeability is equal to the permeability of the irreversible component μ. irr (H) and reversible component permeability μ rev The sum of (H) is calculated as follows:

[0105] μ(H)=μ irr (H)+μ rev (H)

[0106] Among them, the reversible component permeability μ rev The formula for calculating (H) is:

[0107]

[0108] In the formula: B d α is the parameter for calculating magnetic permeability.

[0109] Through parameter B d The reversible component of the total hysteresis loop can be calculated using formula (11) with α:

[0110]

[0111] By combining irreversible and reversible components, we can obtain an analytical positive Preisach model that considers the reversible components.

[0112] Step 2: Dynamic permeability dB / dH of the static hysteresis loop.

[0113]

[0114] In the formula: μ0 is the free permeability, which has a value of 4π×10⁻⁶. -7 .

[0115] Given the analytical expression for the dynamic permeability dB / dH, the magnetic field strength of ferromagnetic materials can be obtained using the finite difference method. The analytical Preisach model is transformed into its inverse form, and the finite difference method expression is as follows:

[0116]

[0117] In the formula: ΔB is the change in magnetic flux density between two consecutive moments.

[0118] The formula for the rising branch of the static analytic inverse Preisach model:

[0119]

[0120] Static analytical inverse Preisach model descent branch formula:

[0121]

[0122] Step 3: Based on the loss separation theory, decompose the total loss W of the ferromagnetic material into hysteresis loss W0. h Eddy current loss W cl With residual loss W ex :

[0123] W t =W h +W cl +W ex

[0124] Based on field separation technology, the total loss can be further expressed as:

[0125]

[0126] Where: H h H represents the magnetic field component corresponding to hysteresis loss. cl and H ex Let be the frequency-dependent eddy current field and the residual loss field, respectively, expressed as:

[0127]

[0128]

[0129] In the formula: d is the thickness of the ferromagnetic material; σ is the conductivity; G is the dimensionless number, G=0.1356; S is the cross-sectional area of ​​the ferromagnetic material; V0 is the statistical coefficient; λ is the sign function, when dB / dt>0, λ=1; when dB / dt<0, λ=-1.

[0130] Step 4: Both the traditional expressions for eddy current loss and eddy current magnetic field strength contain integer derivatives of the instantaneous magnetic flux density with respect to time. While integer derivatives satisfy the local limit definition, the eddy current magnetic flux density and eddy current loss in ferromagnetic materials exhibit nonlocal, frequency-, and history-dependent processes, making integer derivatives unsuitable for this process. To better account for the frequency dependence of eddy current loss, this invention introduces fractional derivatives to improve the expressions for eddy current loss and eddy current magnetic flux density.

[0131] Fractional derivatives extend the order n of the traditional derivative from integers to non-integer and complex numbers. Currently, commonly used fractional derivative operators include the Grünwald-Letnikov (GL type) and Riemann-Liouville (RL type) fractional derivatives, with the RL type being an improvement and extension of the GL type. Therefore, this invention uses the RL type fractional derivative to improve the traditional formula for calculating eddy current components. The expression for the RL type fractional derivative operator is shown below:

[0132]

[0133] In the formula: n is a non-integer order, and the range of n is (0,1), and Γ(·) is the Euler-Gamma function.

[0134] This allows for improvements to the eddy current field components in traditional loss statistics theory:

[0135]

[0136] In the formula: ρ is the improved eddy current component damping coefficient.

[0137] Under sinusoidal excitation, the calculation formula can be further expressed as:

[0138]

[0139] In the formula: B s This represents the maximum magnetic flux density.

[0140] The improved eddy current loss expression based on fractional derivatives is as follows:

[0141]

[0142] Step 5: The eddy current component calculation model improved based on the fractional derivative of RL faces a key problem: determining the parameters ρ and n. Both parameters ρ and n affect the coercivity of the hysteresis loop corresponding to the eddy current component. Therefore, obtaining the globally optimal values ​​of parameters ρ and n within their range of solutions is crucial for achieving accurate calculation of the dynamic model. To more accurately and quickly identify the optimal values ​​of ρ and n, this invention introduces a quantum genetic algorithm for global optimization.

[0143] The quantum genetic algorithm is a probabilistic evolutionary algorithm based on quantum computing and genetic algorithms. This algorithm updates chromosomes with each iteration, bringing them closer to their optimal values. To solve the problem of calculating the optimal fractional derivative parameters ρ and n using the quantum genetic algorithm, an objective function needs to be set. To simplify the objective function for parameter identification and avoid secondary processing of experimental data, this invention directly uses the root mean square error between the calculated value of the improved eddy current loss expression containing the parameters ρ and n and the measured loss value as the objective function, thus transforming the problem of identifying the optimal values ​​of the fractional parameters ρ and n into a problem of minimizing the objective function. The expression for the objective function is:

[0144]

[0145] In the formula, E f W is the root mean square error. cl This is a theoretically calculated value; W meas This is the measured value of loss.

[0146] The basic steps of the quantum genetic algorithm are as follows:

[0147] 1) Initialize the population. Randomly generate chromosomes encoded by qubits and form a chromosome encoding matrix for the initialized population. The matrix expression is as follows:

[0148]

[0149] In the formula: represents the population evolving to the j-th chromosome in the g-th generation; m represents the total number of genes in the chromosome. Let be the qubit in the m-th gene of the g-th chromosome, satisfying the normalization condition a. 2 +b 2 =1.

[0150] 2) Use the collapse function to measure each individual in the initial population once to obtain the corresponding solution set.

[0151] 3) Based on the objective function, evaluate the fitness of the corresponding solution for each individual in step 2), and record the optimal individual and its fitness as the evolutionary target for the next generation.

[0152] 4) Iterate through step 3) to update the record of the individual with the best fitness and its fitness.

[0153] 5) Determine if the maximum number of iterations has been reached. If the condition is met, the calculation ends; otherwise, continue to the next step of the operation.

[0154] 6) Utilizing quantum rotation gates to adjust individuals, chromosomal gene mutations and evolutions are achieved, thereby obtaining a new population. The update formula for the quantum rotation gate is shown below:

[0155]

[0156] In the formula: θ i Let θ be the rotation angle. i =s(a i ,b i )Δθ i . s(a i ,b i ) and Δθ i These represent the direction and magnitude of rotation, respectively.

[0157] 7) Increment the iteration count by 1 and return to step 3).

[0158] Using the above dynamic model design method, a dynamic analytical inverse Preisach model based on RL-type fractional derivatives was designed. To verify the effectiveness of the model, the calculated values ​​of the model and the experimental measurements were compared for the maximum magnetic flux density of 0.3T, 1.0T and 1.4T, at frequencies of 100Hz / 500Hz / 1000Hz / 2000Hz. The basic parameters of the ultrathin oriented silicon steel monolayer are shown in Table 1.

[0159] Table 1. Sample Parameters of Ultra-Thin Grained Silicon Steel Sheets

[0160]

[0161]

[0162] The parameters of the static models described in Step 1 and Step 2 are shown in Table 2.

[0163] Table 2. Parameter values ​​of static analytical inverse Preisach hysteresis model for different magnetic flux densities.

[0164]

[0165] The calculation results of the static model are as follows Figure 5 As shown. Figure 5 It can be seen that the static model used matches the experimental data measurements and can be used to simulate the static hysteresis loop of ferromagnetic materials.

[0166] In step five, the fractional derivative parameters ρ and n identified using the quantum genetic algorithm are 0.0052 and 0.812, respectively. The parameter identification iteration curve of the quantum genetic algorithm is shown below. Figure 6 As shown. From Figure 6 It can be seen that the root mean square error of the quantum genetic algorithm no longer decreases with the number of iterations after 4 iterations. Therefore, the quantum genetic algorithm has obtained the global optimal value of the identification parameters.

[0167] The final calculation results of the dynamic analytic inverse Preisach model based on RL-type fractional derivatives are as follows: Figure 7 , Figure 8 , Figure 9 As shown. From Figure 7 , Figure 8 , Figure 9 It can be seen that the proposed dynamic analytical inverse Preisach model based on RL-type fractional derivative can accurately simulate the dynamic hysteresis loops of ferromagnetic materials under different magnetic intensities and frequencies. Therefore, this model is an accurate simulation method for the dynamic magnetic properties of ferromagnetic materials.

[0168] The final calculation results and the average relative error calculated from the experimental data are shown in Table 3.

[0169] Table 3. Average relative error of dynamic hysteresis loop under different magnetic flux density and frequency.

[0170]

[0171] As shown in Table 3, the average relative error between the proposed model calculation results and the experimental data is small, indicating that this model is an accurate simulation method for the dynamic magnetic properties of ferromagnetic materials.

[0172] Figure 2 This is a comparison chart of the irreversible and reversible components of the static model. Since the classic Preisach model only considers the irreversible components, from... Figure 2 It can be seen that considering the simulation of the static hysteresis loop by the reversible component is very necessary.

[0173] This invention addresses the low accuracy of transformer electromagnetic transient models by focusing on the hysteresis and dynamic loss characteristics of the transformer core, and constructing a dynamic hysteresis model for the transformer core. First, the traditional static forward Preisach model is improved into a static analytical inverse Preisach model using the finite difference method, which facilitates the construction of the dynamic model. Then, based on field separation technology and fractional derivative theory, the expression for the eddy current component is improved, and a dynamic analytical inverse Preisach hysteresis model is constructed. After parameter identification of the fractional derivative using a quantum genetic algorithm, the globally optimal solution for the model parameters is obtained, achieving accurate simulation of dynamic characteristics by the dynamic model. Finally, the model's computational structure is compared with experimental measurement data. The results show that the maximum average relative error between this dynamic model and the experimental data is 5.857%, verifying the accuracy and effectiveness of the dynamic analytical inverse Preisach model based on RL-type fractional derivatives for calculating dynamic hysteresis loops.

Claims

1. A method for calculating the dynamic hysteresis loop of a dynamic analytic inverse Preisach model based on RL-type fractional derivatives, characterized in that... Includes the following steps: Step 1: Establish an analytical static positive Preisach model that considers invertible components; Step 2: Establish a static analytic inverse Preisach model that considers invertible components; Step 3: Based on loss statistics theory and field separation technology, dynamic eddy current loss components and additional loss components are introduced to construct a dynamic analytical inverse Preisach model; Step 4: Use the fractional derivative of RL to improve the dynamic eddy current loss components; Step 5: Identify the parameters of the dynamic eddy current loss components in the dynamic analytical inverse Preisach model based on the improved RL fractional derivative. In step 1, the analytical static positive Preisach model considering invertible components includes irreversible and invertible components, wherein the expression for the irreversible component is: Irreversible component rising branch: ； In the formula: The magnetic field strength; The magnetization intensity; This formula represents the expression for the rising branch of the irreversible component of the hysteresis loop. , , The three parameters are the three basic parameters of the Lorentz function; This represents the saturation magnetic field strength. The saturation magnetization; Irreversible component decline branch: ； In the formula: This formula represents the expression for the descending branch of the irreversible component of the hysteresis loop; in, The function is defined as: ； In the formula: , This represents the parameters of the custom loren function; In the expression for the rising branch of the irreversible component express , express ; The expression for the invertible component is: ； In the formula: B d Parameters for calculating reversible components; Step 3 involves dynamically parsing the inverse Preisach model, including: Dynamic analysis of the rising branch of the inverse Preisach model: Dynamic analysis of the descent branch of the inverse Preisach model: ； In the formula: The magnetic field strength at each moment; The magnetic field strength at the next moment; Let be the magnetic flux density at each moment; Let be the magnetic flux density at the next moment; For each time step; The change over time; G G is a dimensionless number, G = 0.1356. S For the cross-sectional area of ​​ferromagnetic materials, V 0 is the statistical coefficient, λ is the sign function, when hour, ;when hour, ; In step 4, the expression for the fractional derivative of RL is: In the formula: It is the integrand; t For time; n It is of non-integer order. n The range of values ​​for is (0,1); It is the Euler-Gamma function; The improved eddy current loss expression based on fractional derivatives is as follows: ； In the formula, This represents the improved eddy current flux density using fractional derivatives; Indicates frequency; This represents the magnetic flux density at each moment.

2. The method for calculating the dynamic hysteresis loop of the dynamic analytic inverse Preisach model based on RL-type fractional derivatives according to claim 1, characterized in that: In step 2, the specific expression of the static parsing inverse Preisach model is as follows: The formula for the rising branch of the static analytic inverse Preisach model: In the formula: The magnetic field strength at each moment; The magnetic field strength at the next moment; Let be the magnetic flux density at each moment; Let be the magnetic flux density at the next moment; For each time step; The change over time; Static analytical inverse Preisach model descent branch formula: 。 3. The method for calculating the dynamic hysteresis loop of the dynamic analytic inverse Preisach model based on RL-type fractional derivatives according to claim 1, characterized in that: In step 3, based on the loss separation theory, the total loss of the ferromagnetic material is... W Decomposed into hysteresis loss W h Eddy current loss W cl With residual loss W ex : ； Based on field separation technology, the total loss... W This can be further expressed as: ； In the formula: The hysteresis magnetic field strength corresponds to the hysteresis loss. The eddy current magnetic field strength corresponds to the eddy current loss. The residual magnetic field strength corresponds to the residual loss. For periodicity; The formula for calculating the intensity of an eddy current magnetic field is: ； In the formula: d For the thickness of ferromagnetic materials, For conductivity, This is the integral of the magnetic flux density over time; The formula for calculating the residual magnetic field strength is: ； In the formula: G G is a dimensionless number, G = 0.1356. S For the cross-sectional area of ​​ferromagnetic materials, V 0 is the statistical coefficient, λ is the sign function, when hour, ;when hour, .

4. The method for calculating the dynamic hysteresis loop of the dynamic analytic inverse Preisach model based on RL-type fractional derivatives according to claim 1, characterized in that: In step 5, a quantum genetic algorithm is used for parameter identification, as detailed below: Directly apply the parameters to be optimized and The root mean square error between the calculated value and the measured value of the improved eddy current loss expression is used as the objective function of the optimization algorithm, and then the fractional-order parameters are... and The optimal value identification problem is transformed into an objective function minimization problem. The objective function expression of the quantum genetic algorithm is: ； In the formula, E f The root mean square error; Calculate values ​​for the model; These are experimental measurements.

5. The method for calculating the dynamic hysteresis loop of the dynamic analytic inverse Preisach model based on RL-type fractional derivatives according to claim 4, characterized in that: The quantum genetic algorithm includes the following steps: Step S5.1: Initialize the population: Randomly generate chromosomes encoded by qubits and form a chromosome encoding matrix under the initialized population. The matrix expression is as follows: ； In the formula: For the population to evolve to the first g The generation j One chromosome; m This represents the total number of genes in a chromosome. For the first g generation chromosome m The qubits in each gene satisfy the normalization condition. ; Step S5.2: Use the collapse function to measure each individual in the initial population once to obtain the corresponding solution set; Step S5.3: Evaluate the fitness of the corresponding solution for each individual in step S5.2 based on the objective function, and record the optimal individual and its fitness as the evolution target for the next generation; Step S5.4: Iterate through step S5.3 to update and record the individual with the best fitness and its fitness. Step S5.5: Determine whether the maximum number of iterations has been reached. If the condition is met, the calculation ends; otherwise, continue to the next step of the operation. Step S5.6: Use a quantum rotation gate to adjust individuals, achieving chromosomal gene mutation and evolution, thereby obtaining a new population; the update formula of the quantum rotation gate is shown below: ； In the formula: The rotation angle is... ; and These represent the direction and magnitude of rotation, respectively. Step S5.7: Increment the iteration count by 1, then return to step S5.3.

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