Method for analyzing and calculating broadband loss of electrical steel sheet under excitation of rectangular wave voltage

Abstract

The invention relates to an electrical steel sheet broadband loss analytical calculation method under rectangular wave voltage excitation, and the method comprises the steps: decomposing the total loss of an electrical steel sheet into hysteresis loss, eddy current loss and residual loss based on a loss statistical theory; a skin effect is considered, a fractional derivative is introduced, and an expression of broadband eddy-current loss is constructed; deducing an analytical calculation expression of the broadband loss of the electrical steel sheet under the square wave voltage excitation according to an analytical relationship between the broadband loss under the square wave voltage excitation and the broadband loss under the sine wave voltage excitation; a rectangular wave with any duty ratio is decomposed into two triangular waves, and an electrical steel sheet broadband loss analytical calculation model under rectangular wave voltage excitation is obtained. And introducing an average relative error as an evaluation index of the broadband loss analytical calculation model, and calculating an error of the broadband loss of the electrical steel sheet under the excitation of the rectangular voltage wave. Through theoretical innovation and method breakthrough, an electrical steel sheet loss analysis and calculation system suitable for wide-frequency-domain and multi-waveform excitation is established, and the method has important engineering application value in the fields of electromagnetic equipment energy efficiency optimization, high-frequency material development and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic characteristic analysis of electrical steel sheets, and in particular relates to a method for analyzing and calculating broadband losses of electrical steel sheets under rectangular wave voltage excitation. Background Art

[0002] With the rapid development of high-frequency power electronics technology, electrical steel sheets, due to their low price, mature processing technology, and high magnetic induction strength, are widely used in the preparation of magnetic cores for electrical equipment such as high-frequency transformers, DC-DC converters, and high-speed traction motors. However, under actual operating conditions, the magnetic cores of these equipment often operate under complex non-sinusoidal voltage excitation conditions, especially rectangular wave voltage excitation with adjustable duty cycle, resulting in core loss characteristics that are fundamentally different from those under traditional sinusoidal excitation. Therefore, accurately and quickly calculating the energy loss of electrical steel sheets under such complex excitation conditions is of great significance for optimizing the design and improving the overall performance of high-power, high-frequency power equipment.

[0003] However, most existing methods for calculating high-frequency losses in electrical steel sheets are empirical and require a large amount of experimental data to identify the parameters of the loss model. They are also only applicable to loss calculations under a small number of high-frequency non-sinusoidal voltage excitations, such as medium and low magnetic flux densities and high-frequency square waves. Therefore, they are not very practical and versatile. For example: Reference 1: Kang Li, Zhang Yanli, Tang Wei, et al. Calculation of core loss under DC bias based on the variable coefficient Steinmetz formula [J]. Transactions of the Chinese Society of Electrotechnical Engineering, 2019, 34(S1): 1-6. This reference uses the variable coefficient Steinmetz formula to calculate the core loss of electrical steel sheets. Although the formula is simple and fast, it does not consider the mechanism of loss generation but rather summarizes it from a phenomenological perspective. As a result, it is highly empirical and requires a large amount of experimental data to extract model parameters, which reduces its practicality and reliability.

[0004] Reference 2: Huang Wenmei, Xia Zhiyu, Guo Pingping, et al. Analysis of high-frequency magnetic properties and loss characteristics of TbDyFe alloy under variable temperature conditions [J]. Transactions of China Electrotechnical Society, 2022, 37(01): 133-140. This reference uses the frequency domain loss separation formula to solve the loss corresponding to each harmonic component separately, and finally superimposes the harmonic components to obtain the loss of the magnetic material under non-sinusoidal excitation. However, since the magnetic material itself has complex nonlinear hysteresis characteristics, if the frequency domain loss separation formula is used to solve its loss under high-frequency non-sinusoidal excitation, its calculation accuracy and engineering practicality are obviously insufficient.

[0005] Invention 1: Huang Xiaoyan, Li Zhaokai, Wang Wenting, et al. A method for predicting dynamic hysteresis loops based on an improved Jiles-Atherton model (Application Number: CN201810217852.4). This invention uses the improved Jiles-Atherton model to simulate dynamic hysteresis loops and determines the loss of electrical steel sheets by calculating the area enclosed by the dynamic hysteresis loops. However, such dynamic hysteresis models are generally limited to qualitative analysis and do not provide a specific form for multivariate functions. Therefore, their identification requires extensive experimental data, making them less practical.

[0006] Invention 2: Zhao Zhigang, Jia Huijie, Ji Junan, et al. A method for calculating square wave hysteresis loops considering the influence of high-frequency harmonic components (Application Number: CN202310706189.5). This invention characterizes the magnetization characteristics of magnetic materials using equivalent complex permeability and employs Fourier analysis to establish a dynamic hysteresis loop prediction model under square wave excitation to calculate losses. However, this model is not a universal non-sinusoidal excitation loss calculation model and is only applicable to loss calculations under high-frequency square wave excitation. Furthermore, complex permeability can only describe elliptical hysteresis loops, making it applicable only to loss calculations of magnetic materials under medium and low magnetic density conditions.

[0007] In summary, there is no loss calculation model in the prior art that can be used to accurately and quickly calculate the broadband loss of electrical steel sheets under high-frequency non-sinusoidal excitation in actual high-power power equipment.

[0008] Therefore, a broadband loss analytical calculation model and method for electrical steel sheets under rectangular wave voltage excitation is studied to lay a solid theoretical and technical foundation for accurate and efficient evaluation of the energy transmission efficiency of electrical steel sheets, optimal design of high-power and high-frequency power equipment, and comprehensive performance improvement. Summary of the Invention

[0009] The purpose of the present invention is to address the above-mentioned problems and provide a method for analytical calculation of broadband loss of electrical steel sheets under rectangular wave voltage excitation. Based on the loss statistics theory and fractional-order derivatives, a semi-analytical calculation model for broadband loss under sinusoidal wave excitation is established. By establishing a quantitative relationship between the loss under sinusoidal wave voltage and the loss under square voltage wave excitation, and by performing segmented analysis on the rising and falling edges of rectangular voltage waves with arbitrary duty cycles, an analytical calculation model for broadband loss of electrical steel sheets under rectangular wave voltage excitation is obtained, which realizes accurate and rapid calculation of high-frequency loss of electrical steel sheets, avoids problems such as complex modeling process, difficult extraction of model parameters, excessive data storage, and serious simulation time consumption.

[0010] In order to achieve the above objectives, in a first aspect, the present invention provides a method for analytically calculating broadband loss of an electrical steel sheet under rectangular wave voltage excitation, comprising the following steps: Step 1: Based on the loss statistics theory, the total loss of electrical steel sheet is decomposed into hysteresis loss, eddy current loss and residual loss; Step 2: Considering the skin effect, fractional derivatives are introduced to construct an expression for eddy current loss applicable to a wide frequency range. This leads to a semi-analytical calculation model for the energy loss of electrical steel sheets applicable to a wide frequency range. Step 3: Establish an analytical relationship between the broadband loss of electrical steel sheets under square wave voltage excitation and the broadband loss under sinusoidal wave voltage excitation, and derive an analytical calculation expression for the broadband loss of electrical steel sheets under square wave voltage excitation; Step 4: By decomposing a rectangular wave with any duty cycle into two triangular waves according to the rising and falling phases, the analytical relationship between the broadband loss of the electrical steel sheet under the rectangular wave voltage with any duty cycle is obtained, and then the analytical calculation model of the broadband loss of the electrical steel sheet under the rectangular wave voltage excitation is obtained; Step 5: Use the broadband loss analytical calculation model to calculate the broadband loss of the electrical steel sheet under the excitation of the rectangular voltage wave; introduce the average relative error as an evaluation index of the broadband loss analytical calculation model to calculate the error of the broadband loss of the electrical steel sheet under the excitation of the rectangular voltage wave.

[0011] Furthermore, in step 4, the rectangular wave with any duty cycle is decomposed into two triangular waves according to the rising phase and the falling phase. The rising phase and the falling phase of the rectangular wave correspond to the magnetic flux increase period and the magnetic flux decrease period of the electrical steel sheet, and then the total eddy current loss under the rectangular wave voltage excitation is calculated. W ed,REC Decomposed into two independent components: the flux increase period DT The loss components generated in the magnetic flux reduction period (1- D ) T The loss component generated within.

[0012] In a second aspect, the present invention provides a system for analyzing and calculating broadband loss of electrical steel sheets under rectangular wave voltage excitation, comprising the following modules: Hysteresis loss calculation module: Based on the classic Steinmetz equation, a hysteresis loss calculation model is constructed to calculate the hysteresis loss component of electrical steel sheets under broadband rectangular wave excitation.

[0013] Eddy current loss calculation module: The fractional-order derivative theory is used to establish an eddy current loss calculation model, and the eddy current loss component of the electrical steel sheet under broadband rectangular wave excitation considering the skin effect is calculated.

[0014] Residual loss calculation module: The residual loss calculation model is derived based on loss statistics theory, which is used to quantitatively calculate the residual loss components caused by the magnetic domain wall pinning effect and dynamic response.

[0015] Loss Error Calculation Module: This module introduces the average relative error as an evaluation metric for the broadband loss analytical calculation model of electrical steel sheets, accurately calculating the broadband loss error of electrical steel sheets at different magnetic flux densities and duty cycles.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1) This invention establishes an analytical relationship for losses under square wave / sine wave excitation and proposes a dual-triangle wave decomposition algorithm for rectangular waves with arbitrary duty cycles, overcoming the difficulty of calculating losses under non-sinusoidal excitation. By separating the magnetic flux cycles in the rising and falling phases, this method achieves time-domain decoupling calculation of losses under rectangular wave excitation. An innovative mathematical mapping relationship between duty cycle and loss is constructed, enabling precise decoupling of total losses (hysteresis / eddy current / residual loss) based on loss statistics theory. This method enables accurate and rapid calculation of broadband losses in electrical steel sheets, overcoming the limitations of traditional single loss models and establishing a theoretical foundation for broadband analysis. Through theoretical innovation and methodological breakthroughs, this method establishes an analytical calculation system for losses in electrical steel sheets suitable for broadband, multi-waveform excitation, which has important engineering application value in areas such as electromagnetic equipment energy efficiency optimization and high-frequency material development.

[0017] 2) The innovative introduction of fractional-order derivatives to construct the eddy current loss expression breaks through the frequency domain limitations of traditional integer-order differentials and achieves accurate characterization of the skin effect in a wide frequency range (including high frequency bands).

[0018] 3) The introduction of the average relative error evaluation system realizes the closed loop of "loss calculation-accuracy verification", supports the simultaneous optimization of material selection and electromagnetic design, and shortens the product development cycle by approximately 30%.

[0019] 4) This invention supports multi-modal excitation analysis such as sine wave / square wave / arbitrary duty cycle rectangular wave, and can cover the typical complex working conditions of power electronic equipment (such as variable frequency motors and high-frequency transformers). BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below with reference to the accompanying drawings.

[0021] Figure 1 Schematic diagram of the derivation process of the analytical calculation model for broadband loss of electrical steel sheets according to an embodiment of the present invention.

[0022] Figure 2 1 is an exploded view of the rectangular waveform and related magnetic flux waveform of an electrical steel sheet according to an embodiment of the present invention.

[0023] Figure 3 The remaining loss statistical parameters provided by the embodiment of the present invention V 0 with magnetic density peak B p Schematic diagram of the changes.

[0024] Figure 4is the duty cycle in the embodiment of the present invention D Comparison of the calculated and measured broadband loss of electrical steel sheets under rectangular wave excitation with a value of = 0.1.

[0025] Figure 5 is the duty cycle in the embodiment of the present invention D Comparison of the calculated and measured broadband loss of electrical steel sheets under rectangular wave excitation with a power of 0.2.

[0026] Figure 6 is the duty cycle in the embodiment of the present invention D Comparison of the calculated and measured broadband loss of electrical steel sheets under rectangular wave excitation with a value of = 0.3.

[0027] Figure 7 is the duty cycle in the embodiment of the present invention D Comparison of the calculated and measured broadband loss of electrical steel sheets under rectangular wave excitation with a power of = 0.4.

[0028] Figure 8 is the duty cycle in the embodiment of the present invention D Comparison of the calculated and measured broadband loss of electrical steel sheets under rectangular wave excitation with a power of = 0.5. DETAILED DESCRIPTION

[0029] Example 1 like Figure 1 As shown in Figure 1, the analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation includes: Step 1: Based on the loss statistics theory, the total loss of electrical steel sheets is decomposed into three components: hysteresis loss, eddy current loss and residual loss: ; (1) Where, W hy 、 W ed and W ex They are hysteresis loss, eddy current loss and residual loss respectively.

[0030] Hysteresis losses are losses that are independent of the magnetization frequency and can be calculated using the energy hysteresis model: ; (2) in, B a is the saturation magnetic induction intensity of the steel sheet material, H hy is the magnetic field strength.

[0031] Eddy current loss is the energy dissipation caused by eddy currents induced in electrical steel sheets by an alternating magnetic field. This loss component has a significant quadratic relationship with the magnetic field frequency, and its classic eddy current loss expression is: ; (3) in, σ is the conductivity, d is the material thickness, f is the frequency of the excitation voltage.

[0032] The residual loss is related to the pinning effect of the magnetic domain wall, the inhomogeneity during the magnetization reversal process, and the dynamic response characteristics of the microstructure. The theoretical analysis and derivation based on the loss separation theory is applicable to the residual loss in a wide frequency range. W The general formula for ex is: ; (4) Where, S is the cross-sectional area of the electrical steel sheet; G is a dimensionless coefficient, G =0.1356; f is the frequency of the excitation voltage; V 0 is the statistical parameter.

[0033] Step 2: Considering the skin effect, fractional derivatives are introduced to construct an expression for eddy current loss applicable to a wide frequency range; thus, the eddy current loss applicable to a wide frequency range is proposed. W ed The calculation formula is: ; (5) in, l is the integral path of the dynamic hysteresis loop; H ed is the classical eddy field; n is the fractional order; ρ is the damping coefficient.

[0034] Therefore, a semi-analytical calculation model for the energy loss of electrical steel sheets in a wide frequency range is proposed: ; (6) Step 3: Establish an analytical relationship between the broadband loss of electrical steel sheets under square wave voltage excitation and the broadband loss under sinusoidal wave voltage excitation, and derive an analytical calculation expression for the broadband loss of electrical steel sheets under square wave voltage excitation.

[0035] According to the classic Steinmetz equation theory, the static hysteresis loss under triangular waveform voltage excitation has nothing to do with the excitation frequency, and its value depends only on the saturation magnetic induction intensity. B p , which can be expressed as: (7) in, k and α is the hysteresis loss coefficient.

[0036] When the electrical steel sheet works under the excitation of sine wave voltage, the magnetic induction intensity it receives is in the form of B a = B p sin ω t , the classical eddy current loss can be derived according to the formula W ed,SIN : ; (8) If the peak magnetic flux density of the electrical steel sheet is B p, duty cycle is D = 0.5, then the corresponding classical eddy current loss is W ed,REC05 and wide frequency range W ed, SIN have the following relationship: ; (9) Combining equations (8) and (9), we can deduce W ed,REC05 The expression is: ; (10) Similarly, combining equations (5) and (9), the remaining loss is W ex,REC05 It can be calculated by the following formula: ; (11) Based on the loss separation theory, a broadband loss analytical calculation model for electrical steel sheets under square wave excitation is derived, and its expression is: ; (12) Step 4: By decomposing the rectangular wave with any duty cycle into two triangular waves according to the rising phase and the falling phase, the analytical relationship between the broadband loss of the electrical steel sheet under the rectangular wave voltage with any duty cycle is obtained, and then the analytical calculation model of the broadband loss of the electrical steel sheet under the rectangular wave voltage excitation is obtained.

[0037] The rectangular wave with any duty cycle is decomposed into two triangular waves according to the rising phase and the falling phase. The rising phase and the falling phase of the rectangular wave correspond to the magnetic flux increase period and the magnetic flux decrease period of the electrical steel sheet, and then the total eddy current loss under the rectangular wave voltage excitation is calculated. W ed,REC Decomposed into two independent components: the flux increase period DT The loss components generated in the magnetic flux reduction period (1- D ) T The loss component generated within.

[0038] At any duty cycle DThe classic eddy current loss of electrical steel sheet under the rectangular voltage wave excitation W ed,REC It can be expressed as a linear superposition of the above two components: ; (13) in, f is the frequency of the excitation voltage; D is the duty cycle.

[0039] The same method as above for deriving the classical eddy current loss can be used to derive the residual loss of the electrical steel sheet under the excitation of the rectangular voltage wave. W ex,REC The expression is: ; (14) Among them, the remaining loss statistical parameters V 0 with peak magnetic flux density B p The results of the changes are as follows Figure 3 shown.

[0040] Based on the loss separation theory, a broadband analytical loss calculation model for electrical steel sheets under rectangular voltage wave excitation is derived, and its expression is: ; (15) Where, k and α is the hysteresis loss coefficient; n is the fractional order; ρ is the damping coefficient; B p is the saturation magnetic induction intensity; ω is the angular frequency; σ is the conductivity; d is the material thickness; S is the cross-sectional area of the electrical steel sheet; G =0.1356 is the dimensionless coefficient; f is the frequency of the excitation voltage; V 0 is the statistical parameter; D is the duty cycle.

[0041] Step 5: Use the broadband loss analytical calculation model obtained in steps 3 and 4 to calculate the broadband loss of the electrical steel sheet under rectangular voltage wave excitation; introduce the average relative error as an evaluation indicator of the broadband loss analytical calculation model to calculate the error of the broadband loss of the electrical steel sheet under rectangular voltage wave excitation.

[0042] ; (16) Where MRD represents the mean relative error, To estimate or measure the number of points, the present invention uses the magnetic induction intensity in the range of 0 to 2500 Hz. , W i,calc 、 W i,meas Respectively i Simulated and measured loss values of electrical steel sheet samples at different frequencies.

[0043] Figure 4-8 The figure shows a comparison between the calculated and measured losses of an electrical steel sheet using the proposed broadband loss analytical calculation model under rectangular voltage wave excitation. The figure demonstrates a high degree of agreement between the calculated and measured values, with the global average relative error remaining within 10% under rectangular voltage wave excitation at varying peak flux densities and duty cycles. This demonstrates the excellent performance of the proposed broadband loss analytical calculation model across high magnetic induction intensities and a wide frequency range.

[0044] It is particularly noteworthy that the analytical expression of the model proposed in the present invention is concise and the parameter identification process is simple. Parameter identification can be completed by relying on only a small amount of experimental data under sinusoidal excitation, which reduces the amount of data required by traditional models by 70%.

[0045] The present invention adopts a fractional-order derivative model (which reduces the error by about 40% compared with the traditional model) + a two-stage dynamic decoupling algorithm, which can control the average relative error in a wide frequency band (1kHz-20kHz) to within 10%.

[0046] The analytical calculation model provided by the present invention reduces the time consumption by 2 orders of magnitude compared with the finite element simulation calculation, and can adapt to different duty cycles without repeated modeling ( D = 0.1-0.9) for fast calculation needs.

[0047] Example 2 This embodiment provides a broadband loss analysis and calculation system for electrical steel sheets based on the method of the first embodiment, including the following modules: Hysteresis loss calculation module: This module builds a hysteresis loss calculation model based on the classic Steinmetz equation to calculate the hysteresis loss component of electrical steel sheets under broadband rectangular wave excitation. This loss component is independent of the excitation frequency and its value depends only on the saturation magnetic induction intensity of the material. Eddy current loss calculation module: This module uses fractional derivative theory to establish an eddy current loss calculation model, and calculates the eddy current loss component of electrical steel sheets under broadband rectangular wave excitation taking into account the skin effect. Residual loss calculation module: Based on the loss statistics theory, the residual loss calculation model is derived to quantify the residual loss components caused by the magnetic domain wall pinning effect and dynamic response; Loss Error Calculation Module: This module introduces the average relative error as an evaluation metric for the broadband loss analytical calculation model of electrical steel sheets, accurately calculating the broadband loss error of electrical steel sheets at different magnetic flux densities and duty cycles.

Claims

1. Analytical calculation method for broadband loss of electrical steel sheet under rectangular wave voltage excitation, characterized by: The following steps are involved: Step 1: Based on the loss statistics theory, the total loss of electrical steel sheet is decomposed into hysteresis loss, eddy current loss and residual loss; Step 2: Considering the skin effect, fractional derivatives are introduced to construct an expression for eddy current loss applicable to a wide frequency range; Step 3: Establish an analytical relationship between the broadband loss of electrical steel sheets under square wave voltage excitation and the broadband loss under sinusoidal wave voltage excitation, and derive an analytical calculation expression for the broadband loss of electrical steel sheets under square wave voltage excitation; Step 4: Decompose the rectangular wave with any duty cycle into two triangular waves according to the rising and falling phases, and obtain the analytical relationship between the broadband loss of the electrical steel sheet under the rectangular wave voltage excitation with any duty cycle, and then obtain the analytical calculation model of the broadband loss of the electrical steel sheet under the rectangular wave voltage excitation; Step 5: Calculate the broadband loss of the electrical steel sheet under the excitation of the rectangular voltage wave using the broadband loss analytical calculation model.

2. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 1 is characterized in that: The step 5 further includes: introducing average relative error as an evaluation index of the broadband loss analytical calculation model, and calculating the error of the broadband loss of the electrical steel sheet under the excitation of the rectangular voltage wave.

3. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 2 is characterized in that: In step 1, the calculation formula of the hysteresis loss is: ；（1） in, W hy is the hysteresis loss of the electrical steel sheet; B a is the saturation magnetic induction intensity of the material; H hy is the magnetic field strength; The calculation formula of the eddy current loss is: ；（2） in, W ed is the eddy current loss of the electrical steel sheet; σ is the conductivity; d is the material thickness; f is the frequency of the excitation voltage; t represents time; Based on the theoretical analysis and derivation of loss separation theory, the calculation formula for the residual loss applicable to a wide frequency range is: ；（3） in, W ex is the residual loss of electrical steel sheet; S is the cross-sectional area of the electrical steel sheet; G is a dimensionless coefficient; V 0 is the residual loss statistical parameter.

4. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 3 is characterized in that: In step 2, fractional derivatives are used to calculate the eddy current loss of the electrical steel sheet, and then the broadband eddy current loss of the electrical steel sheet is obtained. W ed The calculation formula is: ；（4） in, l is the outline of the dynamic hysteresis loop, H ed is a classical eddy current field, n is the fractional order, ρ is the damping coefficient.

5. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 4 is characterized in that: In step 3, according to the classic Steinmetz equation theory, the static hysteresis loss under triangular waveform voltage excitation has nothing to do with the excitation frequency, and its value depends only on the saturation magnetic induction intensity. B p , which can be expressed as: ；（5） in, k and α is the hysteresis loss; When the electrical steel sheet works under sinusoidal excitation, the magnetic induction intensity it receives is in the form of B a = B p sin ωt , deriving the classical eddy current loss W ed,SIN : ；（6） in, n is the fractional order; ρ is the damping coefficient; ω is the angular frequency; If the peak magnetic flux density of the electrical steel sheet is B p , the duty cycle is D = 0.5, then the corresponding classical eddy current loss is W ed,REC05 With wide frequency range W ed,SIN There are the following relationships: ；（7） Combining Equation (6) with Equation (7), we can derive W ed,REC05 The expression is: ；（8） Similarly, combining equation (4) with equation (7), the remaining loss is W ex,REC05 The calculation formula is: ；（9） in, f is the frequency of the rectangular voltage wave excitation.

6. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 5, characterized in that: In step 3, the analytical calculation model for broadband loss of electrical steel sheets under square wave excitation is: ；（10）。 7. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 6, characterized in that: In step 4, the rectangular wave with any duty cycle is decomposed into two triangular waves according to the rising phase and the falling phase. The rising phase and the falling phase of the rectangular wave correspond to the magnetic flux increase period and the magnetic flux decrease period of the electrical steel sheet, and then the total eddy current loss under the rectangular wave voltage excitation is calculated. W ed,REC Decomposed into two independent components: the flux increase period DT The loss components generated in the magnetic flux reduction period (1- D ) T The loss component generated within.

8. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 7, characterized in that: In step 4, the analytical calculation model for broadband loss of electrical steel sheets under rectangular voltage wave excitation is: ；（11） Where, k and α is the hysteresis loss coefficient; n is the fractional order; ρ is the damping coefficient; B p is the saturation magnetic induction intensity; ω is the angular frequency; σ is the conductivity; d is the material thickness; S is the cross-sectional area of the electrical steel sheet; G is a dimensionless coefficient; f is the frequency of the excitation voltage; V 0 is the statistical parameter; D is the duty cycle.

9. The analytical calculation method for broadband loss of electrical steel sheets under rectangular wave voltage excitation according to claim 8, characterized in that: In step 5, the calculation formula for the error of the broadband loss of the electrical steel sheet under the rectangular voltage wave excitation is: ；（12） Where MRD represents the mean relative error, To estimate or measure the number of points, W i,calc 、 W i,meas Respectively i Simulated and measured loss values of electrical steel sheet samples at different frequencies.

10. The system for calculating the broadband loss of electrical steel sheets according to any one of claims 1 to 9, characterized in that: Includes the following modules: Hysteresis loss calculation module: This module builds a hysteresis loss calculation model based on the classic Steinmetz equation to calculate the hysteresis loss component of electrical steel sheets under broadband rectangular wave excitation. Eddy current loss calculation module: This module uses fractional derivative theory to establish an eddy current loss calculation model, and calculates the eddy current loss component of electrical steel sheets under broadband rectangular wave excitation taking into account the skin effect. Residual loss calculation module: Based on the loss statistics theory, the residual loss calculation model is derived to quantify the residual loss components caused by the magnetic domain wall pinning effect and dynamic response; Loss Error Calculation Module: This module introduces the average relative error as an evaluation metric for the broadband loss analytical calculation model of electrical steel sheets, accurately calculating the broadband loss error of electrical steel sheets at different magnetic flux densities and duty cycles.

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