Method for analyzing performance of amorphous alloy transformer under low-frequency electromagnetic transient

Abstract

This invention relates to a performance analysis method for amorphous alloy transformers under low-frequency electromagnetic transients, belonging to the field of power technology. This invention addresses the problem that existing technologies primarily target silicon steel transformers and lack systematic experimental comparisons. The method first establishes an experimental platform to conduct experiments under three operating conditions: DC bias, ferroresonance, and inrush current, and extracts characteristic data. Secondly, it constructs circuit-magnetic field coupled finite element simulation models for both amorphous alloy and silicon steel transformers, achieving transient joint solution in ANSYS Maxwell. Finally, by comparing simulation and experimental waveforms, combined with core magnetic flux density and loss contour maps, it identifies saturation regions and energy dissipation characteristics, comprehensively evaluating the performance differences between the two types of transformers under transient conditions. This invention achieves accurate evaluation of the multi-dimensional response performance of transformers, providing a theoretical basis for equipment selection and maintenance.

Description

Technical Field

[0001] This invention belongs to the field of power technology and relates to a performance analysis method for amorphous alloy transformers under low-frequency electromagnetic transients. Background Technology

[0002] Amorphous alloy transformers, with their extremely low no-load losses, have become widely used high-efficiency energy-saving devices in power distribution networks. Amorphous alloy materials possess low magnetic anisotropy, high resistivity, and an extremely thin strip structure, making them significantly superior to traditional silicon steel materials in terms of core losses. These material properties enable amorphous alloy transformers to not only occupy an important position in power distribution systems but also demonstrate promising application prospects in renewable energy power generation systems.

[0003] Although the saturation magnetic flux density, operating magnetic flux density, and conventional loss characteristics of amorphous alloys and silicon steel have been extensively studied, these studies have largely focused on rated steady-state operating conditions. In actual transformer operation, various electromagnetic transient shocks are unavoidable, especially low-frequency electromagnetic transient faults closely related to the nonlinear magnetization characteristics of the core material. Low-frequency electromagnetic transients are typically caused by system operation, faults, or disturbances, and are characterized by a wide frequency spectrum and high amplitude. Unlike steady-state operation, these transients force the core operating point into the saturation region. Due to the fundamental differences in saturation characteristics between amorphous alloys and silicon steel, these differences are manifested through macroscopic electrical quantities such as transformer terminal voltage, excitation current, and losses, thus becoming key factors affecting the system's transient response.

[0004] In existing technologies, the analysis methods for transformer performance under low-frequency electromagnetic transients mostly focus on silicon steel transformers, and the conclusions drawn cannot be directly applied to amorphous alloy transformers. Furthermore, existing studies often employ single-condition simulations or simplified equivalent circuit analyses, lacking systematic experimental measurements and comparative analyses for three typical low-frequency electromagnetic transient conditions: DC bias, ferroresonance, and inrush current. This makes it difficult for existing technologies to deeply reveal the performance differences between amorphous alloys and silicon steel materials during transient processes from both the external electrical response and internal core state perspectives. Therefore, there is an urgent need to provide a method that can systematically and accurately analyze the performance of amorphous alloy transformers under typical low-frequency electromagnetic transients, providing a theoretical basis for the engineering application and optimized design of amorphous alloy transformers in complex electromagnetic environments. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for performance analysis of amorphous alloy transformers under low-frequency electromagnetic transients.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A performance analysis method for a typical amorphous alloy transformer under low-frequency electromagnetic transients includes the following steps: S1: Build a low-frequency electromagnetic transient test platform for amorphous alloy transformers and silicon steel transformers. Apply corresponding excitations for three typical low-frequency electromagnetic transient conditions: DC bias, ferroresonance, and inrush current. Measure and extract the excitation current, voltage waveforms, and reactive power characteristic data of the two types of transformers under the three conditions. S2: Construct circuit-magnetic field coupled finite element simulation models of amorphous alloy transformers and silicon steel transformers, measure the geometric dimensions and key parameters of the core and windings of the two types of transformers, establish a three-dimensional finite element model in ANSYS Maxwell, set the nonlinear magnetization curve and loss characteristics of the core material, use the external circuit excitation method to associate the nonlinear inductor element and winding element of the external circuit, and realize the circuit-magnetic field joint solution through the transient solver. S3: Transient simulation is performed based on the circuit-magnetic field coupled finite element simulation model to obtain the response waveforms, core loss waveforms, core magnetic flux density cloud maps, and core loss cloud maps of the two types of transformers under three operating conditions. The simulation waveforms are compared with the experimentally measured waveforms in S1 to verify the accuracy of the model. The distribution of local saturation regions is identified through the core magnetic flux density cloud map, and the loss concentration region is identified through the core loss cloud map. The variation law of the iron loss waveform with the excitation parameters under transient operating conditions is analyzed, and the response characteristics and performance differences of the two types of transformers under typical low-frequency electromagnetic transients are comprehensively evaluated.

[0007] Furthermore, in S1, the excitation method for the DC bias condition is to superimpose an adjustable DC current on the primary side and measure the excitation current and reactive power of the transformer secondary winding under load and no-load conditions under different DC bias conditions. The excitation method for the ferroresonant condition is to form a resonant circuit by connecting a capacitor in series on the excitation side, adjust the system capacitance parameters, measure the transformer terminal voltage waveform, and determine the stability difference. The excitation method for the inrush current condition is to conduct no-load closing tests under different closing angles and record the excitation current waveform, peak value and discontinuity angle.

[0008] Furthermore, in S2, the geometric dimensions of the amorphous alloy transformer and the silicon steel transformer are measured, and non-critical features are simplified. The corresponding external circuit topology and component parameters are determined based on three typical low-frequency electromagnetic transient operating conditions. The component parameters include the DC current amplitude under DC biased magnetization, the series capacitance value under ferromagnetic resonance, and the voltage source closing angle under inrush current. In ANSYS Maxwell, a three-dimensional finite element model is established based on the measured dimensions. The core material is set to amorphous alloy or silicon steel and given corresponding nonlinear magnetization curves and loss characteristics. The winding material is set to copper. The nonlinear inductor in the external circuit is associated with the winding element in the transformer model by using an external circuit excitation method. A transient solver is set to solve the electromagnetic field distribution based on Maxwell's equations to realize the bidirectional coupling and joint solution of the circuit and magnetic field.

[0009] Furthermore, in S3, the simulated excitation current, transformer terminal voltage, and flux linkage response waveforms at the closing moment under DC bias, ferroresonance, and inrush current conditions are extracted and compared with the experimentally measured waveforms in S1; the excitation parameters of the transient condition are changed to obtain the core loss waveforms under different excitations, and the variation law of iron loss with excitation parameters is analyzed; the core magnetic density cloud map in the transient process is extracted to identify the distribution of local saturation regions and the degree of flux linkage offset inside the core, and the core loss cloud map is extracted to identify the loss concentration region and energy dissipation distribution characteristics.

[0010] Furthermore, in S3, under DC bias conditions, the formula is used... Calculate DC flux ,in The magnitude of the DC current superimposed on the DC source. x , y The fitting coefficients of the measured flux linkage-current curve are denoted as . , Angular frequency, This represents the flux linkage amplitude. T For periodicity; through DC magnetic flux ψ DC and incremental inductance Assess the core flux bias and saturation.

[0011] Furthermore, in S3, under the ferromagnetic resonance condition, the nonlinear dynamic characteristics of amorphous alloy transformers and silicon steel transformers are analyzed by phase plane trajectory, Poincaré section and 3D bifurcation diagram, and the stability differences of the two transformers under ferromagnetic resonance are compared. The stability differences include the parameter range of resonance occurrence, voltage amplitude and waveform distortion degree.

[0012] Furthermore, in S3, under the inrush current condition, the closing angle is... ,remanence Calculate the magnetic flux linkage of the transformer core at the instant of energization. By comparing the peak value of inrush current, discontinuity angle and flux linkage deflection recovery time of the two types of transformers, the core saturation degree during transient excitation process is evaluated.

[0013] Furthermore, in step S3, the core loss waveform analysis specifically includes: Under DC bias conditions, the peak core losses of amorphous alloy transformers and silicon steel transformers are compared under different DC bias currents, and the variation law of iron loss with the degree of DC bias is analyzed. Under ferroresonant conditions, the steady-state amplitude of core loss of two transformers with different series capacitance values ​​is compared, and the variation law of core loss with resonance degree is analyzed. Under inrush current conditions, the peak core losses of two types of transformers are compared at different closing angles to analyze the variation law of iron loss with closing angle.

[0014] Furthermore, in S3, by comprehensively comparing the simulation waveforms, analyzing the iron loss waveforms, and identifying the cloud map results, the performance advantages and limitations of amorphous alloy transformers compared to silicon steel transformers under typical low-frequency electromagnetic transients are evaluated. The performance advantages include lower excitation current, reactive power, and core losses, while the limitations include a wider range of ferroresonant generation parameters and a higher resonant voltage amplitude.

[0015] Furthermore, the method combines experimental measurement with simulation analysis to reveal the performance differences between amorphous alloys and silicon steel materials during transient processes from two levels: external electrical response and internal core condition. This provides a basis for equipment selection, condition assessment, and operation and maintenance of amorphous alloy transformers.

[0016] The beneficial effects of this invention are as follows: (1) This invention constructs a complete analysis system covering three typical low-frequency electromagnetic transient conditions: DC bias, ferroresonance, and inrush current. This method breaks through the limitations of existing technologies that only analyze single conditions or specific materials, and comprehensively covers the main low-frequency electromagnetic transient scenarios that amorphous alloy transformers may encounter in actual power grid operation, ensuring the comprehensiveness and systematic nature of performance evaluation.

[0017] (2) This method can not only intuitively obtain the magnetic flux density distribution cloud map and loss evolution law inside the core through the three-dimensional finite element model, and deeply reveal the transient response mechanism of amorphous alloy materials from the electromagnetic field level, but also obtain external electrical response data such as excitation current, harmonic amplitude and reactive power through experiments, thus realizing the accurate evaluation of the multi-dimensional response performance of transformers.

[0018] (3) This method effectively eliminates the errors caused by environmental factors and operating condition fluctuations, and can clearly define the performance advantages and inherent limitations of amorphous alloy materials compared with traditional silicon steel materials under low-frequency electromagnetic transients. It clarifies the differentiated performance of different materials in dealing with transient shocks, and provides a direct basis for the selection and withstand capability assessment of amorphous alloy transformers in engineering applications.

[0019] (4) Through in-depth analysis of the core magnetic density cloud map and loss cloud map, this method can quantify the energy dissipation distribution characteristics of the core under transient impact, thereby guiding the optimization design of transformer structure and improving the reliability and stability of equipment operation in complex electromagnetic environment.

[0020] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of the present invention; Figure 2 shows the measurement results of amorphous alloy and silicon steel transformers under DC bias; Figure 2(a) shows the excitation current waveform under 7 A DC bias; Figure 2(b) shows the peak value variation of excitation current under different DC biases; Figure 2(c) shows the reactive power under different DC biases.

[0022] Figure 3 shows the calculation results of transformer saturation for amorphous alloys and silicon steel under DC bias; Figure 3(a) shows the change in DC flux linkage; Figure 3(b) shows the change in incremental inductance.

[0023] Figure 4 shows the dynamic analysis of amorphous alloy and silicon steel transformers under ferromagnetic resonance; Figure 4(a) shows the phase plane trajectory; Figure 4(b) shows the Poincaré section; Figure 4(c) shows the 3D bifurcation diagram.

[0024] Figure 5 shows the measurement results of amorphous alloy and silicon steel transformers under ferromagnetic resonance; Figure 5(a) shows the resonant voltage waveform under different series capacitors; Figure 5(b) shows the excitation current waveform under different series capacitors; Figure 5(c) shows the waveform of the excitation current under different series capacitors. U AC and C The amplitude of the resonant voltage.

[0025] Figure 6 The measurement results are for amorphous alloy and silicon steel transformers under inrush current. Figure 7 Finite element models of experimental transformers made of amorphous alloy and silicon steel Figure 8 shows the comparison between the finite element simulation response waveforms of amorphous alloy and silicon steel transformers and the experimental waveforms; Figure 8(a) shows the comparison between the excitation current and experimental current waveforms under DC bias of 0 A, 4 A, and 7 A; Figure 8(b) shows the comparison between the ferroresonant voltage and experimental voltage waveforms under capacitors of 10 μF, 20 μF, and 30 μF; Figure 8(c) shows the comparison between the excitation inrush current flux bias and experimental waveforms under closing angles of 0°, 30°, and 60°.

[0026] Figure 9 shows the finite element simulation results of magnetic density cloud diagrams for amorphous alloy and silicon steel transformers; Figure 9(a) shows the magnetic density cloud diagrams under DC bias of 0 A, 4 A, and 7 A; Figure 9(b) shows the ferromagnetic resonance magnetic density cloud diagrams under capacitors of 10 μF, 20 μF, and 30 μF; Figure 9(c) shows the inrush current magnetic density cloud diagrams under closing angles of 0°, 30°, and 60°.

[0027] Figure 10 shows the simulation results of iron loss cloud diagrams for amorphous alloy and silicon steel transformers; Figure 10(a) shows the iron loss cloud diagrams under DC bias of 0 A, 4 A, and 7 A; Figure 10(b) shows the iron loss cloud diagrams under ferromagnetic resonance with capacitors of 10 μF, 20 μF, and 30 μF; Figure 10(c) shows the iron loss cloud diagrams under inrush current with closing angles of 0°, 30°, and 60°.

[0028] Figure 11 shows the simulation and comparison results of iron loss waveforms for amorphous alloy and silicon steel transformers; Figure 11(a) shows the iron loss waveforms under DC bias of 0 A, 4 A, and 7 A; Figure 11(b) shows the iron loss waveforms under ferromagnetic resonance with capacitors of 10 μF, 20 μF, and 30 μF; Figure 11(c) shows the iron loss waveforms under inrush current with closing angles of 0°, 30°, and 60°. Detailed Implementation

[0029] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0030] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0031] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0032] The present invention describes a performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients, such as... Figure 1 As shown, this method mainly includes the following three steps: Part 1: The typical low-frequency electromagnetic transient operating conditions include DC bias, ferroresonance, and inrush current. An experimental platform was built to apply typical transient excitations such as DC bias current, ferroresonance induced by series capacitance, and inrush current at different closing angles to an amorphous alloy transformer. Key characteristic data such as excitation current, voltage waveform, and reactive power were measured under these three operating conditions. Simultaneously, the same experimental method was used to test a silicon steel transformer to obtain response data under the corresponding operating conditions for subsequent comparative analysis.

[0033] Part Two: First, the geometric dimensions of amorphous alloy and silicon steel transformers were measured to obtain key structural parameters of the transformer core and windings, and non-critical features were simplified. Simultaneously, based on three typical low-frequency electromagnetic transient conditions—DC bias, ferroresonance, and inrush current—the corresponding external circuit topology and component parameters were determined. Next, three-dimensional finite element models of the two transformers were established in ANSYS Maxwell software based on the measured dimensions. The core magnetization curve and loss characteristics of the experimental transformers were set, and the transformer winding materials were determined. The simulation adopted an external circuit excitation method, associating the nonlinear inductive components in the external circuit with the winding components in the transformer model, and realizing the circuit through a transient solver. The magnetic field is solved jointly by iterative calculations within each time step to simulate the transient process.

[0034] Part 3: Based on the circuit-magnetic field coupled finite element model established in step S2, transient simulations are performed on amorphous alloy and silicon steel transformers to obtain their response characteristics and evaluate their performance.

[0035] For three typical low-frequency electromagnetic transient conditions—DC bias, ferroresonance, and inrush current—the simulation response waveforms of excitation current, transformer terminal voltage, and flux linkage at closing time are extracted. These simulated waveforms are then compared with the corresponding experimentally measured waveforms from step S1 to verify the accuracy of the simulation model and evaluate the transient response characteristics under different conditions. Simulations are used to obtain the core loss waveforms of amorphous alloy and silicon steel cores during transient processes, studying the variation of core loss with excitation parameters under transient conditions and revealing the dynamic evolution of core loss under different transient conditions.

[0036] The magnetic flux density and loss cloud maps of the iron core during the transient process are extracted. The magnetic flux density cloud map identifies the distribution of local saturation regions within the iron core, determining the degree of flux linkage shift and the saturation range. The loss cloud map identifies areas of concentrated loss, analyzing the energy dissipation distribution characteristics of the iron core under transient impact. Iron loss waveform analysis: The iron loss waveform of the amorphous alloy iron core during the transient process is obtained through simulation. The variation of iron loss with excitation parameters under transient conditions is studied, revealing the dynamic evolution law of iron core loss under different transient conditions.

[0037] 1. Experiments and feature data extraction of typical low-frequency electromagnetic transient conditions.

[0038] The typical low-frequency electromagnetic transient conditions include DC bias, ferroresonance, and inrush current. A transient experimental platform for amorphous alloy and silicon steel transformers was constructed, and corresponding excitations were applied for each of the three conditions: For DC bias, an adjustable DC current was superimposed on the primary side, and the response data of the transformer secondary winding, including excitation current and reactive power, under different DC bias degrees under load and no-load conditions were measured; for ferroresonance, a capacitor was connected in series on the excitation side to form a resonant circuit, and the system capacitance parameters were changed to measure the transformer's response and stability differences under different parameters; for inrush current, no-load closing experiments were conducted at different closing angles, and the waveform, peak value, and discontinuity angle of the excitation current were recorded. Through the above experimental measurements, key characteristic data of amorphous alloy and silicon steel transformers under typical low-frequency electromagnetic transients can be obtained.

[0039] 2. Construction of a Finite Element Simulation Model for Amorphous Alloy Transformer Circuit-Magnetic Field Coupling

[0040] First, the geometric dimensions of the amorphous alloy and silicon steel transformers were measured before modeling, including key parameters of the core and windings, and non-critical features were simplified. Simultaneously, based on three typical low-frequency electromagnetic transient conditions—DC bias, ferroresonance, and inrush current—the corresponding external circuit topology and component parameters were determined, such as the DC current amplitude under DC bias, the series capacitance under ferroresonance, and the voltage source closing angle under inrush current. Then, modeling and solving were performed. A three-dimensional finite element model was established in ANSYS Maxwell based on the measured dimensions. Material properties were set, assigning the nonlinear magnetization curve and loss characteristics of the amorphous alloy and silicon steel core, and copper to the windings. An external circuit excitation method was used to associate the nonlinear inductive components in the circuit with the winding components. Finally, a transient solver was set up to achieve joint solving of the circuit and magnetic field, simulating the transient process through iteration of the circuit and magnetic field within each time step.

[0041] 3. Low-frequency transient response characteristics and performance analysis of amorphous alloy transformers.

[0042] Based on the established circuit-magnetic field coupled finite element model, transient simulations were performed on amorphous alloy and silicon steel transformers to obtain their response characteristics and evaluate their performance. The simulation waveforms and comparative analysis were conducted: For three typical low-frequency electromagnetic transient conditions—DC bias, ferroresonance, and inrush current—the simulated response waveforms of excitation current, transformer terminal voltage, and flux linkage at closing time were extracted. These simulated waveforms were then compared with the corresponding waveforms measured experimentally in step S1 to verify the accuracy of the simulation model and evaluate the transient response characteristics under different conditions. Iron loss waveform analysis was performed: The iron loss waveform of the amorphous alloy core during the transient process was obtained through simulation. The changes in iron loss with transient excitation were studied, revealing the dynamic evolution law of core loss under different transient conditions. Simulation contour map results were analyzed: The core magnetic density contour map and core loss contour map were extracted during the transient process. The magnetic density contour map was used to identify the distribution of local saturation regions inside the core, determining the degree of flux linkage shift and saturation range. The loss contour map was used to identify areas of concentrated loss, analyzing the energy dissipation distribution characteristics of the core under transient impact.

[0043] In specific implementation cases, response data of amorphous alloy and silicon steel transformers were obtained through experiments for three operating conditions: DC bias, ferroresonance, and inrush current, and circuit design was established. Transient simulations were performed using a magnetic field-coupled finite element model. The simulated waveforms were compared with the experimental waveforms, and the performance differences between the two under typical low-frequency electromagnetic transients were evaluated by combining iron loss waveforms and contour plots.

[0044] Step 1: Experiments on typical low-frequency electromagnetic transient conditions and extraction of characteristic data.

[0045] This step involves circuit analysis of typical low-frequency electromagnetic transient conditions and conducting experiments to obtain characteristic data.

[0046] (1) In the DC biased magnetization condition, an adjustable DC current is superimposed on the primary winding of the transformer, causing the transformer core flux linkage to change from the main flux linkage. ψ m Superimposed DC flux ψ DC The iron core enters the deep saturation region, and the excitation current... i One-sided distortion occurs, and reactive power increases. The excitation current and reactive power under different DC bias degrees were measured to analyze the DC bias response characteristics of amorphous alloy and silicon steel transformers. The experimental measurement results are shown in Figure 2.

[0047] Figure 2(a) shows the excitation current waveform under a DC bias of 7 A. Under the same DC injection, the excitation current amplitude of the non-silicon steel transformer is 12.73% and 14.03% lower than that of the amorphous alloy transformer under load and no-load conditions, respectively, and it exhibits more severe distortion. At this time, the core of the silicon steel transformer enters a deeper saturation range, which is manifested as a larger excitation current. Figure 2(b) shows the peak value variation of excitation inrush current under different DC biases. Regardless of whether the secondary winding of the amorphous alloy transformer is under no-load or load, its excitation current is always lower than that of the silicon steel transformer. The fundamental reason for this phenomenon is that DC bias causes a shift in the DC flux linkage, and the core of the silicon steel transformer is more likely to enter a deeper nonlinear saturation region under DC bias. Figure 2(c) shows the reactive power under different DC biases. When the DC bias current is less than 3 A, the core saturation is shallow, and the reactive power of both types of transformers increases approximately linearly. When the DC bias current exceeds 3 A, the core saturation deepens further, and the reactive power exhibits obvious nonlinear characteristics. A comparison of the two types of test transformers shows that the reactive power of the amorphous alloy transformer is consistently lower than that of the silicon steel transformer, indicating that the amorphous alloy transformer exhibits a smaller reactive power demand under DC bias. The most significant difference in reactive power is observed under a 7 A DC bias: under load conditions, the silicon steel transformer is 9.68% higher than the amorphous transformer; under no-load conditions, it is 8.44% higher.

[0048] Based on the excitation current and reactive power data obtained from the above experiments, the DC flux linkage of the iron core under DC bias is further calculated. ψ DC With incremental inductance L cm To evaluate the flux linkage bias and saturation of the transformer under DC bias. ψ DC and L cm The calculation formula is:

[0049]

[0050] in, i DC The magnitude of the DC current superimposed on the DC source. x , y Measured ψ - i The fitting coefficient of the curve; ψ The total flux linkage of the iron core is shown in Figure 3.

[0051] Figure 3(a) shows the DC flux linkage. ψ DC Changes. Within the tested DC bias range, the DC flux linkage of the silicon steel transformer was consistently higher than that of the amorphous alloy transformer, indicating that the flux linkage bias of the amorphous alloy core under DC bias was relatively weak. Figure 3(b) shows the incremental inductance. L cm Changes. Under the same DC bias, the incremental inductance of an amorphous alloy transformer... L cm The fact that the amorphous alloy transformer is consistently higher than that of the silicon steel transformer indicates that the saturation level of the amorphous alloy transformer is shallower, the equivalent inductance of its excitation branch decreases less, and therefore the amplitude of the excitation current is smaller. Furthermore, the distortion and peak characteristics of the current waveform are lower than those of the silicon steel transformer.

[0052] (2) In the ferroresonant condition, a capacitor is connected in series with the primary winding of the transformer. C When the system's inductive resistance X Lm With resistance X C satisfy X Lm = X C At that time, the transformer is excited to a ferroresonant state, and the transformer terminal voltage... u and excitation current i The waveform amplitude increases and the waveform is severely distorted, which affects the stable operation of the transformer. Therefore, the stability of the transformer in the ferroresonant fault is studied through nonlinear dynamic analysis and experimental measurement.

[0053] First, a transformer ferroresonant model was established based on nonlinear dynamics theory. The phase plane trajectory, Poincaré section and bifurcation diagram of the transformer under different series capacitance values ​​were obtained through simulation. The simulation results are shown in Figure 4.

[0054] Figure 4(a) shows the phase plane trajectory, and Figure 4(b) shows the Poincaré cross section. When the series capacitance is 10 μF, 20 μF, and 30 μF, the phase plane trajectory of the amorphous alloy transformer exhibits saturation distortion and multi-turn closed loops, and the Poincaré cross section is a finite number of isolated discrete points. The amorphous alloy transformer is in a periodic resonance state. The phase plane trajectory of the silicon steel transformer is a single coil with closed distortion, and the Poincaré cross section has only one discrete point, which is in a fundamental frequency resonance state. Figure 4(c) shows the 3D bifurcation diagram. Under the same circuit parameter variations, the amorphous alloy transformer exhibits a higher voltage amplitude over a wider parameter range. This indicates that under ferromagnetic resonance, the amorphous alloy transformer, due to its stronger core nonlinearity, satisfies the resonance excitation condition over a wider range of system parameters, and once resonance is established, its voltage amplitude is also higher. In contrast, the silicon steel core, due to its higher saturation magnetic density, relatively flat magnetization curve, and weaker nonlinear effect, has a narrower parameter range for resonance.

[0055] Based on the above nonlinear dynamic simulation analysis, further ferromagnetic resonance experimental measurements were conducted. In the experiment, different capacitors were connected in series on the primary side of the transformer, and the voltage and current responses were recorded to obtain data such as resonant overvoltage. The stability of amorphous alloy and silicon steel transformers under the same circuit parameters was analyzed. The specific experimental results are shown in Figure 5.

[0056] Figure 5(a) shows the measured resonant voltage waveform under different series capacitors, and Figure 5(b) shows the measured excitation current waveform under different series capacitors. Specifically, with a 10 μF capacitor, the silicon steel transformer's voltage is 40.2% higher than that of the amorphous alloy transformer. With 20 μF and 30 μF capacitors, the ferroresonance phenomenon of the silicon steel transformer disappears, while the amorphous alloy transformer remains in a ferroresonant state. The variation law of the excitation current under different series capacitors is consistent with the above voltage results. With a 10 μF capacitor, the excitation current of the silicon steel transformer is 75.4% higher than that of the amorphous alloy transformer. With 20 μF and 30 μF capacitors, the excitation current of the silicon steel transformer decreases significantly. This is because, compared with the silicon steel transformer, the amorphous alloy transformer has a wider capacitance range for ferroresonance due to its lower saturation magnetic flux density, steeper magnetization curve, lower loss, and weaker damping; while the silicon steel transformer, due to its higher saturation magnetic flux density, flatter magnetization curve, and higher loss, can naturally exit resonance under large capacitors, but under specific small capacitors, it can generate higher resonant voltage and current. Figure 5(c) shows the change U AC and CThe figure shows the resonant voltage amplitude. The parameter range for ferroresonance in amorphous alloy transformers is significantly wider than that in silicon steel transformers. However, although the ferroresonance range of silicon steel transformers is smaller, once they enter the resonant state, the peak resonant voltage is higher, the waveform distortion is more severe, and the overall voltage amplitude is significantly higher than that of amorphous alloy transformers.

[0057] (3) Under inrush current conditions, the phase angle of the AC voltage when the transformer is closed is: α Furthermore, transformers may have residual magnetism. ψ r Then, at the instant the transformer core is energized, the magnetic flux linkage of the core... ψ It can be represented as .

[0058] Therefore, the core enters saturation, generating inrush current. To study this operating condition, no-load closing experiments were conducted at different closing angles. The excitation current waveforms, peak values, and discontinuity angles of amorphous alloy and silicon steel transformers were recorded. The experimental results are as follows: Figure 6 As shown. Figure 6 The inrush current waveforms are shown under different closing angles. When the closing angle is 0°, the inrush current of both types of transformers reaches its maximum value, with the peak value of the silicon steel transformer being 29.7% higher than that of the amorphous alloy transformer. When the closing angle is 30°, the peak value of the silicon steel transformer's inrush current is 22.7% higher; and when the closing angle is 60°, the peak value is still 11.8% higher. The results indicate that under the same closing angle, the amorphous alloy transformer core has a lower degree of saturation during transient excitation, resulting in a less significant decrease in excitation inductance and a lower excitation current amplitude. As the closing angle increases, the difference in inrush current between the two types of transformers gradually decreases. Table 1 shows the calculated results of the inrush current discontinuity angle. The discontinuity angle of the silicon steel transformer is significantly higher than that of the amorphous alloy transformer, indicating that during the transient process of inrush current, the intermittent current conduction phenomenon is more pronounced in the silicon steel transformer, while the continuity of current conduction is relatively better in the amorphous alloy transformer. Table 1 Calculation results of transformer discontinuity angle

[0059] Step 2: Construction of a finite element simulation model of amorphous alloy transformer circuit with magnetic field coupling.

[0060] (1) To construct the finite element model of amorphous alloy and silicon steel transformers, the core dimensions of the amorphous alloy and silicon steel transformers used in the actual experiment are as follows: Figure 7 As shown in Table 2, the main structural parameters of the transformer are as follows.

[0061] Table 2 Structural parameters of the experimental transformer

[0062] Based on the principles of three transient operating conditions—DC bias, ferroresonance, and inrush current—the external circuit topology and excitation parameters corresponding to each condition are determined. DC bias: A DC power supply with an output range of 0-7 A is connected to the primary side of the external circuit to simulate the state of the transformer core under different DC biases. Ferroresonance: A capacitor with a capacitance range of 10-40 μF is connected in series on the primary side of the external circuit to excite ferroresonance in transformers with different core materials. Inrush current: An AC voltage source is connected to the primary side of the external circuit, and the initial phase angle of the voltage is controlled by a pulse control circuit when the switch is closed.

[0063] (2) After building the finite element model of the transformer, the material settings of the 3D FEM models of the amorphous alloy transformer and the silicon steel transformer are performed in ANSYS Maxwell software: Core: The core is given the measured nonlinear magnetization BH curve and loss characteristic BP curve of amorphous alloy and silicon steel respectively, so as to accurately reflect the difference in magnetic saturation and loss between the two materials in the transient process. Windings: Both primary and secondary windings are made of copper, and their conductivity is defined.

[0064] After completing the modeling and material property settings, an external circuit excitation method is used to associate the nonlinear inductive elements in the circuit with the winding conductor region in the finite element model, thus establishing the circuit. The coupling relationship of the magnetic field; finally, a transient field solver is set up to realize the circuit. The magnetic field is solved jointly, and the entire transient process is simulated through iterative calculations within each time step.

[0065] Step 3: Low-frequency transient response characteristics and performance analysis of amorphous alloy transformers.

[0066] (1) Finite element simulation and experimental waveform comparison verification Based on the established circuit-magnetic field coupled finite element model, transient simulations were performed on amorphous alloy transformers and silicon steel transformers, respectively. The response waveforms of excitation current, terminal voltage, and closing flux linkage under DC bias, ferroresonance, and inrush current conditions were extracted. To verify the effectiveness of the simulation model, the simulated waveforms were compared and analyzed with the experimentally measured waveforms from step one. Figure 8 shows the comparison results of the simulated and experimental waveforms of the two transformers under typical transient conditions.

[0067] Figure 8(a) shows a comparison of the simulated and experimental excitation current waveforms under DC bias of 0 A, 4 A, and 7 A. Both the simulation and experimental waveforms show that: without DC bias, the excitation current of the amorphous alloy transformer is higher than that of the silicon steel transformer; when the DC bias increases to 4 A, the peak excitation current of the silicon steel transformer begins to be slightly higher than that of the amorphous alloy transformer; when the DC bias reaches 7 A, the excitation current of the silicon steel transformer is significantly higher than that of the amorphous alloy transformer. The current variation law obtained from the finite element simulation under DC bias is consistent with the experimental results. Figure 8(b) shows a comparison of the simulated and experimental ferroresonant voltage waveforms under 10 μF, 20 μF, and 30 μF capacitors. The trend of these waveforms is basically consistent with the experimental results. Under the combined action of the nonlinear excitation inductor and capacitor, both types of transformers exhibit obvious ferroresonant responses. However, the fault waveform characteristics of amorphous alloy and silicon steel transformers differ significantly: the amorphous alloy transformer has a higher peak resonant voltage, more prominent waveform spikes, and greater distortion, indicating that it is more sensitive to ferroresonant resonance; while the resonant voltage waveform of the silicon steel transformer is generally smoother. Although the peak value increases, the distortion is relatively mild, the resonant response is weaker, and the operating state is relatively more stable. Figure 8(c) shows a comparison of the inrush current flux offset and experimental waveforms at closing angles of 0°, 30°, and 60°. As time progresses, under the influence of winding resistance and system damping, the offset component in the flux gradually decays, and the waveform transitions from an asymmetrical state to a steady-state periodic symmetrical state. Simulation results at different closing angles show that the amorphous alloy transformer exhibits smaller flux offsets at closing angles of 0° and 30°, and a more significant offset at 60°, but overall recovers to a symmetrical state relatively quickly. In contrast, the silicon steel transformer recovers more slowly at all closing angles, especially with larger offsets where the decay is less pronounced and the required recovery time is longer. Experimental results also show that the silicon steel transformer exhibits a larger flux offset at the moment of closing, thus displaying a larger inrush current peak value.

[0068] (2) Simulation results of core magnetic density cloud map To further analyze the magnetic flux distribution and saturation characteristics inside the transformer core, Figure 9 presents the simulation results of the core magnetic flux density cloud diagram under DC bias, ferroresonance, and inrush current conditions. By comparing the magnetic flux density distribution of amorphous alloy and silicon steel transformers, local saturation regions and their variation patterns can be identified.

[0069] Figure 9(a) shows the magnetic density cloud diagrams under DC bias of 0 A, 4 A, and 7 A. Without DC bias, the overall magnetic flux density distribution inside the transformer core is relatively uniform, and the core remains in a normal excitation state without significant saturation. When the DC bias increases to 4 A, the high magnetic flux density region begins to expand towards the core column and yoke, and the local saturation phenomenon gradually worsens. When the DC bias is 7 A, most areas of the core of both types of transformers are at a relatively high magnetic flux density level, and the core enters a deeper saturation state. Figure 9(b) shows the ferroresonant magnetic flux density cloud maps for 10 μF, 20 μF, and 30 μF capacitors. As the resonance intensity increases, the magnetic flux density of the amorphous alloy transformer core increases, with some regions approaching or even entering the saturation region. This further enhances the core nonlinearity, making it easier to maintain strong resonant oscillations. In contrast, the overall magnetic flux density of the silicon steel transformer core decreases, with smaller changes in the magnetic flux density cloud map. Its overall core saturation is relatively lower, and the corresponding ferroresonant response is also relatively weaker. Figure 9(c) shows the magnetic flux density cloud diagrams of inrush current under closing angles of 0°, 30°, and 60°. Under the same closing angle, the high magnetic flux density region in the core of the amorphous alloy transformer is relatively small, and the magnetic flux density distribution is more gradual, resulting in a less severe local saturation under the action of inrush current. The core of the silicon steel transformer is more severely saturated, and the distribution range of the high magnetic flux density region is larger. Especially under closing angles of 0° and 30°, the difference between the two types of transformers is more obvious, indicating that a small closing angle is more likely to cause deep core saturation and further amplify the differences in nonlinear magnetization and saturation characteristics of different core materials.

[0070] (3) Simulation results of core loss cloud diagram To analyze the energy dissipation distribution characteristics of the transformer core during transient processes, Figure 10 presents the simulation results of core loss cloud maps under different transient operating conditions.

[0071] Figure 10(a) shows the core loss cloud diagrams under DC bias of 0 A, 4 A, and 7 A. As the DC bias current increases, the local losses of the cores of both types of transformers are significantly aggravated. Comparing the core loss distribution cloud diagrams of amorphous alloy and silicon steel transformers, it can be seen that under 7 A DC bias, the high-loss region of the amorphous alloy transformer is still significantly smaller than that of the silicon steel transformer, and the overall core loss remains at a low level. Figure 10(b) shows the core loss contour plots for ferromagnetic resonance with capacitors of 10 μF, 20 μF, and 30 μF. Under ferromagnetic resonance conditions, the high-loss region of the silicon steel transformer is mainly concentrated in a small area at the core corner, and decreases as the resonance intensity decreases; the core loss of the amorphous alloy transformer gradually increases as the resonance intensity increases, and is mainly concentrated on the outer side of the yoke. Figure 10(c) shows the core loss contour maps of inrush current under closing angles of 0°, 30°, and 60°. Under the same closing conditions, the loss distribution range and concentration of the two types of transformers differ: the high loss area of ​​silicon steel transformers is concentrated in the core column and yoke, while the high loss area of ​​amorphous alloy transformers is mainly in the core column; moreover, silicon steel transformers exhibit a higher overall loss level and a wider high loss distribution area than amorphous alloy transformers at all closing angles.

[0072] (4) Simulation results of core loss waveform To further analyze the dynamic changes of core loss during the transient process, Figure 11 shows the simulation results of core loss waveforms for amorphous alloy and silicon steel transformers under different transient conditions.

[0073] Figure 11(a) shows the iron loss waveforms under DC bias of 0 A, 4 A, and 7 A. Using the peak value of the transient waveform as a comparison: without DC bias, the core loss of the amorphous alloy transformer is 47.6% lower than that of the silicon steel transformer; when the DC bias current increases to 4 A, the difference widens further, with the loss reduction of the amorphous alloy transformer reaching 67.8%; when the DC bias current rises to 7 A, the core loss of the amorphous alloy transformer is 72.5% lower than that of the silicon steel transformer. This demonstrates that as the degree of DC bias increases, the advantage of amorphous alloys in suppressing iron losses becomes increasingly apparent. Figure 11(b) shows the steady-state waveforms of iron loss under ferroresonant capacitances of 10 μF, 20 μF, and 30 μF. When the series capacitances are 10 μF, 20 μF, and 30 μF, respectively, the core loss of the amorphous alloy transformer is reduced by 39.4%, 28.1%, and 8.9% compared to the silicon steel transformer. These data indicate that when ferroresonant capacitance occurs in amorphous alloy and silicon steel transformers, the amorphous alloy core has a significant advantage in reducing losses. As the resonance degree of the amorphous alloy transformer increases, the difference in losses between the two types narrows, but the amorphous alloy still maintains a lower loss level.

[0074] Figure 11(c) shows the iron loss waveforms of inrush current at closing angles of 0°, 30°, and 60°. At a closing angle of 0°, the core loss of the amorphous alloy transformer is 48.3% lower than that of the silicon steel transformer; at 30°, it is 42.2% lower; and at 60°, it is 40.3% lower. Even during the transient moment of inrush current, the iron loss advantage of the amorphous alloy transformer remains significant. While the difference between the two decreases slightly with increasing closing angle, the amorphous alloy consistently maintains a lower loss level.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients, characterized in that: Includes the following steps: S1: Build a low-frequency electromagnetic transient test platform for amorphous alloy transformers and silicon steel transformers. Apply corresponding excitations for three typical low-frequency electromagnetic transient conditions: DC bias, ferroresonance, and inrush current. Measure and extract the excitation current, voltage waveforms, and reactive power characteristic data of the two types of transformers under the three conditions. S2: Construct circuit-magnetic field coupled finite element simulation models of amorphous alloy transformers and silicon steel transformers, measure the geometric dimensions and key parameters of the core and windings of the two types of transformers, establish a three-dimensional finite element model in ANSYS Maxwell, set the nonlinear magnetization curve and loss characteristics of the core material, use the external circuit excitation method to associate the nonlinear inductor element and winding element of the external circuit, and realize the circuit-magnetic field joint solution through the transient solver. S3: Transient simulation is performed based on the circuit-magnetic field coupled finite element simulation model to obtain the response waveforms, core loss waveforms, core magnetic flux density cloud maps, and core loss cloud maps of the two types of transformers under three operating conditions. The simulation waveforms are compared with the experimentally measured waveforms in S1 to verify the accuracy of the model. The distribution of local saturation regions is identified through the core magnetic flux density cloud map, and the loss concentration region is identified through the core loss cloud map. The variation law of the iron loss waveform with the excitation parameters under transient operating conditions is analyzed, and the response characteristics and performance differences of the two types of transformers under typical low-frequency electromagnetic transients are comprehensively evaluated.

2. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S1, the excitation method for DC bias is to superimpose an adjustable DC current on the primary side and measure the excitation current and reactive power of the transformer secondary winding under load and no-load conditions under different DC bias. The excitation method for the ferroresonant condition is to form a resonant circuit by connecting a capacitor in series on the excitation side, adjust the system capacitance parameters, measure the transformer terminal voltage waveform, and determine the stability difference. The excitation method for the inrush current condition is to conduct no-load closing tests under different closing angles and record the excitation current waveform, peak value and discontinuity angle.

3. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S2, the geometric dimensions of the amorphous alloy transformer and the silicon steel transformer are measured, and non-critical features are simplified. The corresponding external circuit topology and component parameters are determined based on three typical low-frequency electromagnetic transient operating conditions. The component parameters include the DC current amplitude under DC biased magnetization, the series capacitance value under ferromagnetic resonance, and the voltage source closing angle under inrush current. In ANSYS Maxwell, a three-dimensional finite element model is established based on the measured dimensions. The core material is set to amorphous alloy or silicon steel and given corresponding nonlinear magnetization curves and loss characteristics. The winding material is set to copper. The nonlinear inductor in the external circuit is associated with the winding element in the transformer model by using an external circuit excitation method. A transient solver is set to solve the electromagnetic field distribution based on Maxwell's equations to realize the bidirectional coupling and joint solution of the circuit and magnetic field.

4. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In step S3, the simulated excitation current, transformer terminal voltage, and flux linkage response waveforms at the closing moment under DC bias, ferroresonance, and inrush current conditions are extracted and compared with the experimentally measured waveforms in step S1. The excitation parameters of the transient conditions are changed to obtain the core loss waveforms under different excitations, and the variation law of iron loss with excitation parameters is analyzed. The core magnetic density cloud map in the transient process is extracted to identify the distribution of local saturation regions and the degree of flux linkage offset inside the core, and the core loss cloud map is extracted to identify the loss concentration region and energy dissipation distribution characteristics.

5. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S3, under DC bias conditions, the formula is used... Calculate DC flux ,in The magnitude of the DC current superimposed on the DC source. x , y The fitting coefficients of the measured flux linkage-current curve are denoted as . , Angular frequency, This represents the flux linkage amplitude. T For periodicity; through DC magnetic flux ψ DC and incremental inductance Assess the core flux bias and saturation.

6. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S3, under the ferromagnetic resonance condition, the nonlinear dynamic characteristics of amorphous alloy transformers and silicon steel transformers are analyzed by phase plane trajectory, Poincaré section and 3D bifurcation diagram. The stability differences of the two transformers under ferromagnetic resonance are compared. The stability differences include the parameter range of resonance occurrence, voltage amplitude and waveform distortion degree.

7. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S3, under the inrush current condition, the closing angle is... ,remanence Calculate the magnetic flux linkage of the transformer core at the instant of energization. By comparing the peak value of inrush current, discontinuity angle and flux linkage deflection recovery time of the two types of transformers, the core saturation degree during transient excitation process is evaluated.

8. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S3, the core loss waveform analysis specifically includes: Under DC bias conditions, the peak core losses of amorphous alloy transformers and silicon steel transformers are compared under different DC bias currents, and the variation law of iron loss with the degree of DC bias is analyzed. Under ferroresonant conditions, the steady-state amplitude of core loss of two transformers with different series capacitance values ​​is compared, and the variation law of core loss with resonance degree is analyzed. Under inrush current conditions, the peak core losses of two types of transformers are compared at different closing angles to analyze the variation law of iron loss with closing angle.

9. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: In S3, the performance advantages and limitations of amorphous alloy transformers compared with silicon steel transformers under typical low-frequency electromagnetic transients are evaluated by comprehensively comparing simulation waveforms, analyzing iron loss waveforms, and identifying cloud maps. The performance advantages include lower excitation current, reactive power, and core loss, while the limitations include a wider range of ferroresonant generation parameters and a higher resonant voltage amplitude.

10. The performance analysis method for amorphous alloy transformers under typical low-frequency electromagnetic transients according to claim 1, characterized in that: The method combines experimental measurement and simulation analysis to reveal the performance differences between amorphous alloys and silicon steel materials during transient processes from two levels: external electrical response and internal core condition. This provides a basis for equipment selection, condition assessment, and operation and maintenance of amorphous alloy transformers.

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