Wideband modeling method of electromagnetic voltage transformer considering core nonlinear saturation

Abstract

The present application belongs to the field of power system measurement and simulation, and relates to a wide-band modeling method of electromagnetic voltage transformer considering core nonlinear saturation, which comprises the following steps: regarding the electromagnetic voltage transformer as a two-port network, obtaining its wide-band scattering parameters through sweep frequency measurement, converting the scattering parameters into an admittance parameter matrix, solving the stray capacitance value of the electromagnetic voltage transformer based on the mapping relationship between the admittance parameter and the stray capacitance, and folding the secondary side resistance and inductance to the primary side according to the ideal transformer ratio to construct a wide-band linear network model; constructing a core nonlinear module by measuring the loss power and no-load current under different voltages through no-load test; and coupling the wide-band linear network model and the core nonlinear module. The method has the advantages of precise coupling of wide-band parameters and core nonlinear saturation characteristics, high extraction accuracy of stray capacitance, high accuracy of core nonlinear modeling, clear model structure, high calculation efficiency, strong universality and wide application range.

Description

Technical Field

[0001] This invention relates to the field of power system measurement and simulation technology, and in particular to a broadband modeling method for electromagnetic voltage transformers that considers core nonlinear saturation. Background Technology

[0002] In traditional power systems, the modeling of electromagnetic voltage transformers (PTs) is mostly designed for power frequency or lower frequency harmonic signals, which can meet the measurement requirements under normal operating conditions. However, in the wide-frequency operating environment of new power systems, the electromagnetic characteristics of the transformers exhibit more complex changes, among which the nonlinear saturation characteristics of the core become a key factor affecting the modeling accuracy. As the core component of the PT, when encountering transient impacts or other conditions that cause the flux density to exceed the saturation magnetic induction intensity, the core will enter the nonlinear region, the permeability will drop sharply, and the excitation current will increase exponentially, leading to problems such as output waveform distortion and decreased dynamic response capability, directly affecting the reliability of measurement results. At the same time, the stray capacitance and winding distribution parameters of the PT itself will interact with the nonlinear saturation characteristics of the core over a wide frequency range, further increasing the complexity of modeling.

[0003] Existing broadband modeling techniques for power PTs have significant limitations. Firstly, traditional modeling methods often treat the core as a linear magnetic permeability element, neglecting the nonlinear saturation characteristics of the core's permeability with flux linkage density. This approach only ensures modeling accuracy under power frequency or small-signal excitation scenarios. When broadband signals such as transient overvoltages or high-frequency harmonics impact the system, the core enters the saturation region, and the model cannot accurately represent the rapid changes in excitation current and the distortion of the output waveform, leading to significant deviations between simulation results and actual equipment operating characteristics. Secondly, existing broadband modeling schemes often consider high-frequency characteristics such as winding distributed parameters and stray capacitance in isolation, failing to establish a coupling relationship model between the two. However, within a broadband range, there is a significant interaction between winding distributed parameters and the nonlinear saturation characteristics of the core. This lack of coupling makes it difficult for existing models to achieve accurate full-band coverage from DC and power frequency to high-frequency transients. Third, although some improved modeling methods have introduced the nonlinear characteristics of the iron core, they mostly adopt simplified processing methods such as piecewise linearization, which fail to accurately fit the actual magnetization curve of the iron core. The adaptability and versatility of the model are insufficient, making it difficult to adapt to the broadband modeling needs of PTs with different materials and structures.

[0004] Therefore, there is an urgent need in this field for a modeling method that can accurately couple the broadband parameters of the PT with the nonlinear saturation characteristics of the iron core, so as to achieve accurate characterization of the electromagnetic characteristics across the entire frequency band and provide reliable support for power system-related analysis, simulation and equipment optimization. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation, employing the following technical solution, including the following steps: S1. The electromagnetic voltage transformer is regarded as a two-port network. Its wideband scattering parameters are obtained by frequency sweep measurement. The scattering parameters are converted into an admittance parameter matrix. Based on the mapping relationship between admittance parameters and stray capacitance, the stray capacitance value of the electromagnetic voltage transformer is solved. The secondary side resistance and inductance are converted to the primary side according to the ideal transformer ratio to construct a wideband linear network model. S2, by measuring the power loss and no-load current under different voltages through no-load tests, the voltage-current characteristic curve of the nonlinear resistor is solved by using a piecewise linearization method combined with the phase angle synergy relationship. Based on the parity constraint of the flux linkage nonlinear resistor current and the nonlinear inductor current, the flux linkage-current characteristic curve of the nonlinear inductor is solved by piecewise linearization and a quadratic equation, and the core nonlinear module is constructed. S3, the wideband linear network model is coupled with the iron core nonlinear module, and the iron core nonlinear module is formed by connecting nonlinear resistors and nonlinear inductors in parallel, replacing the linear excitation branch in the traditional model, and embedded in the wideband linear network topology to form a complete wideband equivalent circuit model of electromagnetic voltage transformer.

[0006] Preferably, the measurement of the broadband scattering parameters in step S1 specifically includes: Connect the primary winding of the electromagnetic voltage transformer to port 1 of the network analyzer, and connect the secondary winding to port 2 of the network analyzer. Set the frequency sweep parameters of the network analyzer to a frequency sweep range of 10Hz to 1MHz; The excitation level of the input signal is 10% of the rated voltage of the electromagnetic voltage transformer, and the scattering parameters are measured respectively. , , , .

[0007] Preferably, the step of converting the scattering parameters into an admittance parameter matrix in step S1 specifically includes: Convert the scattering parameters into a transmission parameter matrix: ,in, To transmit the four elements of the parameter matrix, To match the reference impedance; Convert the transfer parameters into an admittance parameter matrix: ,in, , , , These are the four elements of the admittance parameter matrix.

[0008] Preferably, the step S1 of solving for the stray capacitance value based on the mapping relationship between admittance parameters and stray capacitance specifically includes: Establish a system of equations: ,in, Angular frequency, The imaginary unit, This refers to the stray capacitance of the primary winding to ground. This refers to the stray capacitance of the secondary winding to ground. This refers to the stray capacitance between the primary and secondary windings. By solving the above system of equations, the stray capacitance of the primary winding to ground can be calculated. Secondary winding to ground stray capacitance Stray capacitance between primary and secondary windings The specific value.

[0009] Preferably, the step of solving the voltage-current characteristic curve of the nonlinear resistor in step S2 specifically includes: The effective values ​​of different voltages were measured through no-load tests. Power loss Calculate the peak voltage magnetic flux peak ; Piecewise linearization of the voltage-current characteristic curve is performed for the first... Within the segment, the instantaneous value of the nonlinear resistive current With instantaneous voltage value They satisfy a linear relationship; According to the definition of power The integration interval is segmented according to the phase angle, where the phase angle is... Establish information about the unknown peak current. linear equation of one variable; Solving this linear equation in one variable yields the peak current. The peak current under each state is calculated sequentially, and the discrete data points are connected to obtain the voltage-current characteristic curve of the nonlinear resistor.

[0010] Preferably, the step of solving the flux linkage-current characteristic curve of the nonlinear inductor in step S2 specifically includes: The effective values ​​of different voltages were measured through no-load tests. RMS value of no-load current Calculate the peak flux linkage ; The flux linkage-current characteristic curve is linearized piecewise. For the first... Within the segment, the instantaneous value of the nonlinear inductor current With the instantaneous value of magnetic flux They satisfy a linear relationship; According to the definition of the effective value of current ,use Even function To constrain the parity of odd functions, the integration interval is simplified to... ; The integration interval is segmented according to the phase angle, where the phase angle is... By combining the voltage-current characteristic curve of the nonlinear resistor, an equation is established regarding the unknown peak current. The quadratic equation of ; Solving this quadratic equation yields the peak current. The peak current under each state is calculated sequentially, and the discrete data points are connected to obtain the flux linkage-current characteristic curve of the nonlinear inductor.

[0011] Preferably, the coupling step between the broadband linear network model and the core nonlinear module in step S3 specifically includes: A nonlinear resistor and a nonlinear inductor are connected in parallel to form a nonlinear core module, which is then connected in parallel to the primary excitation branch of an ideal current transformer. The voltage-current characteristic curve of the nonlinear resistor module is used to characterize the loss characteristics of the core, and the flux linkage-current characteristic curve of the nonlinear inductor module is used to characterize the nonlinear saturation characteristics of the core.

[0012] Preferably, in step S1, the secondary-side resistance and inductance are converted to the primary side according to the ideal transformer ratio, using the following conversion formula: ,in, For secondary side resistance, It is the secondary inductor. This represents the ideal turns ratio for an electromagnetic voltage transformer. This is the equivalent value of the secondary resistance converted to the primary side. This is the equivalent value of the secondary inductance converted to the primary side.

[0013] Preferably, the broadband linear network topology in step S3 includes: An ideal current transformer has a primary winding-to-ground stray capacitance connected in parallel on its primary side. A stray capacitor between the primary and secondary windings is connected in parallel between the primary and secondary sides. Parallel connection of secondary winding to ground on the secondary side and the converted secondary resistance and inductor Connected in series to the secondary side branch.

[0014] Preferably, the voltage range of the no-load test in step S2 is set from 10% to 120% of the rated voltage of the electromagnetic voltage transformer, and the measurement points are distributed at logarithmic intervals according to the voltage values ​​to ensure coverage of the linear region, transition region and saturation region of the core.

[0015] Compared with the prior art, the present invention has the following main advantages: (1) It has accurate coupling of wideband parameters and core nonlinear saturation characteristics: By organically combining the extraction of wideband linear network parameters with the modeling of core nonlinear characteristics, a coupling correlation model of core nonlinear saturation characteristics and winding wideband parameters is established, which overcomes the defect of the separation between linear and nonlinear models in the existing technology and realizes accurate characterization of the full-band electromagnetic characteristics of PT from DC, power frequency to high-frequency harmonics and transient waves.

[0016] (2) High accuracy of stray capacitance extraction: The stray capacitance solution method based on scattering parameter measurement and admittance parameter mapping is adopted. By utilizing the physical law that stray capacitance dominates admittance characteristics at high frequencies, the accurate inversion extraction of stray capacitance is realized, avoiding the complex electromagnetic field calculation in traditional methods and improving the accuracy and efficiency of parameter identification.

[0017] (3) High accuracy of nonlinear modeling of iron core: The nonlinear resistance voltage-current characteristic curve is solved by combining piecewise linearization with phase angle synergy, and the nonlinear inductor flux-current characteristic curve is solved by combining the parity constraint of flux linkage and current with a quadratic equation. This achieves accurate fitting of the actual magnetization curve of the iron core and overcomes the accuracy loss caused by the traditional piecewise linearization simplification process.

[0018] (4) Clear model structure and high computational efficiency: The model structure realizes the decoupling and synergy of linear and nonlinear networks. Through reasonable model simplification and parameter identification strategies, it takes into account both modeling accuracy and computational efficiency. The model is suitable for large-scale simulation scenarios such as power system harmonic analysis and transient fault simulation.

[0019] (5) Strong versatility and wide range of applications: It does not depend on specific PT structure and material parameters, and can adapt to the broadband modeling needs of PTs with different materials and structures. It has strong versatility and engineering application value. Attached Figure Description

[0020] To more clearly illustrate the solutions in this invention, the accompanying drawings used in the description of the embodiments of this invention will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0021] Figure 1This is a flowchart of an embodiment of the electromagnetic voltage transformer broadband modeling method considering core nonlinear saturation of the present invention; Figure 2 This is a schematic diagram of a two-port network used in the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention. Figure 3 This is a schematic diagram of the equivalent circuit model of an electromagnetic voltage transformer constructed in the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention. Figure 4 A flowchart illustrating another embodiment of the electromagnetic voltage transformer broadband modeling method considering core nonlinear saturation of the present invention; Figure 5(a) is a graph of the nonlinear voltage-current UI characteristic curve of the core of the electromagnetic voltage transformer in the wideband modeling method of the electromagnetic voltage transformer considering the nonlinear saturation of the core in this invention. Figure 5(b) is a graph of the nonlinear flux linkage-current ψ-I characteristic curve of the electromagnetic voltage transformer core in the wideband modeling method of the electromagnetic voltage transformer considering the nonlinear saturation of the core in this invention. Figure 6 This is a schematic diagram of the wideband equivalent circuit model of an electromagnetic voltage transformer constructed in simulation software using the wideband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention. Figure 7 This is a schematic diagram of the scattering parameter test wiring used in the wideband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention. Detailed Implementation

[0022] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used herein in the specification is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings are used to distinguish different objects and not to describe a particular order.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0025] It should be noted that the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation provided in the embodiments of the present invention is generally executed by a server / terminal device, and correspondingly, the broadband modeling device for electromagnetic voltage transformers considering core nonlinear saturation is generally set in the server / terminal device.

[0026] It should be understood that the number of terminal devices, networks, and servers is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be used.

[0027] Example 1 Please refer to Figure 1 The flowchart illustrates an embodiment of the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to the present invention. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation includes the following steps: Step S1: Treat the electromagnetic voltage transformer as a two-port network, obtain its broadband scattering parameters by frequency sweep measurement, convert the scattering parameters into an admittance parameter matrix, solve the stray capacitance value of the electromagnetic voltage transformer based on the mapping relationship between admittance parameters and stray capacitance, and convert the secondary side resistance and inductance to the primary side according to the ideal transformer ratio to construct a broadband linear network model.

[0028] In this embodiment, the electronic device (e.g., a server / terminal device) on which the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation operates can receive broadband modeling requests for electromagnetic voltage transformers considering core nonlinear saturation via wired or wireless connections. It should be noted that the aforementioned wireless connection methods may include, but are not limited to, 3G / 4G / 5G connections, WiFi connections, Bluetooth connections, WiMAX connections, Zigbee connections, UWB (ultrawideband) connections, and other currently known or future-developed wireless connection methods.

[0029] The broadband network scattering parameters of electromagnetic voltage transformers can be measured using the black box method.

[0030] In this embodiment, step S1 may specifically include the following steps: S11, measures the broadband scattering parameters of the electromagnetic voltage transformer.

[0031] Connect the primary winding of the electromagnetic voltage transformer to port 1 of the network analyzer, and the secondary winding to port 2 of the network analyzer. Ensure the grounding terminal of the electromagnetic voltage transformer is reliably grounded. Set the sweep parameters of the network analyzer, with a frequency sweep range of 10Hz to 1MHz, dividing the sweep points into logarithmic intervals. Set the excitation level of the input signal to 10% of the rated voltage of the electromagnetic voltage transformer. Measure the scattering parameters using the network analyzer. , , , .

[0032] S12 performs the conversion of scattering parameters into transport parameters and admittance parameters.

[0033] The scattering parameters are converted into a transmission parameter matrix for a two-port network using the following formula: .

[0034] in: — The four elements of the transmission parameter matrix are dimensionless; — Scattering parameters, dimensionless; — Matching reference impedance, in ohms (Ω), typically 50Ω or 75Ω. In this embodiment, the network analyzer uses a matching reference impedance. . Figure 2 This is a schematic diagram of a two-port network used in the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention.

[0035] The transmission parameter matrix describes the relationship between the input voltage and current and the output voltage and current of a two-port network, and is the basis for subsequent conversion into admittance parameters.

[0036] The transfer parameters are further converted into an admittance parameter matrix using the following formula: .in: — The four elements of the admittance parameter matrix, in Siemens (S), represent the input self-admittance, reverse transfer admittance, forward transfer admittance, and output self-admittance, respectively. — The four elements of the transmission parameter matrix are dimensionless.

[0037] The admittance parameter matrix can intuitively reflect the relationship between the port current and port voltage of a two-port network, which facilitates the subsequent establishment of a mapping relationship with the parameters of circuit elements.

[0038] S13, Solving for stray capacitance based on admittance parameter mapping.

[0039] The admittance parameter matrix of an electromagnetic voltage transformer contains four independent parameters. , , , .in, and Solving for the stray capacitance of the primary winding to ground Stray capacitance between primary and secondary windings ; and Solving for the stray capacitance of the associated secondary winding to ground Stray capacitance between primary and secondary windings .

[0040] Based on the relationship between admittance parameters and stray capacitance, the following system of equations is established: .

[0041] in: — The four elements of the admittance parameter matrix, in Siemens (S); —Imaginary unit, dimensionless; — Angular frequency, measured in radians per second (rad / s); — Stray capacitance of primary winding to ground, in farads (F); — Secondary winding to ground stray capacitance, in farads (F); — Stray capacitance between primary and secondary windings, measured in farads (F).

[0042] By solving the above system of equations, we can calculate... , , The specific values ​​of the three stray capacitances are given. The advantage of this mapping solution method is that it utilizes the physical law that stray capacitance dominates admittance characteristics at high frequencies to achieve accurate inversion extraction of stray capacitances, avoiding the complex electromagnetic field calculations in traditional methods.

[0043] S14, perform the conversion of secondary side parameters to primary side.

[0044] The resistance on the secondary side of the electromagnetic voltage transformer and inductor Based on the transformation ratio of an ideal current transformer, the conversion formula applied to the primary side is as follows: .in: — The equivalent value of the secondary resistance converted to the primary side, in ohms (Ω); — Equivalent value of secondary inductance converted to primary side, in Henry (H); — Secondary resistance, in ohms (Ω); — Secondary inductance, measured in Henry (H); — The ideal turns ratio of an electromagnetic voltage transformer, dimensionless. , The number of turns in a primary winding. This refers to the number of turns in the secondary winding.

[0045] The purpose of this conversion step is to uniformly reduce the secondary side parameters to the primary side, which facilitates the establishment of a unified equivalent circuit model and simplifies subsequent circuit analysis and simulation calculations.

[0046] The purpose of step S1 is to measure and extract the parameters of the broadband linear network.

[0047] Step S2: Measure the power loss and no-load current under different voltages through no-load tests. Use a piecewise linearization method combined with the phase angle synergy to solve the voltage-current characteristic curve of the nonlinear resistor. Based on the parity constraint of the flux linkage nonlinear resistor current and the nonlinear inductor current, solve the flux linkage-current characteristic curve of the nonlinear inductor through piecewise linearization and a quadratic equation to construct the core nonlinear module.

[0048] In this embodiment, step S2 may specifically include the following steps: S21, Obtain the nonlinear resistor voltage-current characteristic curve.

[0049] The voltage across the nonlinear resistor varies with the rate of change of magnetic flux. Neglecting the DC component, the effective voltage across the nonlinear resistor and the peak magnetic flux have the following relationship: .in: — The effective value of the experimental voltage, in volts (V); — The angular frequency of the experimental voltage, in radians per second (rad / s); — Peak flux linkage, in Weber (Wb).

[0050] The voltage values ​​at each point on the nonlinear resistor voltage-current characteristic curve are the peak values ​​of the experimental voltages. .in: — No. A voltage peak value, in volts (V). — No. The effective value of the experimental voltage is expressed in volts (V).

[0051] By performing piecewise linearization on the power loss, the peak current flowing through the nonlinear resistor is obtained. The first point of the voltage-current characteristic curve is then... As the origin, the second point If it lies above the linear segment, then It can be directly derived from the following formula: .in: — The effective value of the nonlinear resistance current corresponding to the first point, in amperes (A); — The power loss corresponding to the first point is expressed in watts (W). — The effective value of the voltage corresponding to the first point, in volts (V).

[0052] Before the result is obtained Peak current Under the premise of finding the first Peak current The voltage-current characteristic curve is moved from the first point. To the point common Piecewise linearization of points Section. For the first of these... Within this segment, voltage and current exhibit a linear relationship: .in: — Instantaneous value of nonlinear resistive current, in amperes (A); — Instantaneous value of voltage across the nonlinear resistor, in volts (V); subscript — indicates the first Each segmented interval is dimensionless. — No. Peak current at the end and beginning of the segment, in amperes (A). — No. The peak voltage at the end and beginning of the segment, in volts (V).

[0053] According to the definition of power, power loss The relationship with voltage and current is as follows: .in: — No. The power loss corresponding to each voltage peak is expressed in watts (W). — Instantaneous voltage value, in volts (V); — Instantaneous current value, in amperes (A); —Phase angle, in radians (rad); Pi (π) is dimensionless.

[0054] As the phase angle gradually increases from 0 to At that time, voltage and current All values ​​gradually decrease from their peak value to 0, therefore the integration interval can be segmented: .in: — Phase angle, in radians (rad), calculated using the following formula: , ; — No. A voltage peak value, in volts (V). — No. A voltage peak value, measured in volts (V).

[0055] This expression describes the relationship between the phase angle and voltage. Increase, voltage As the resistance gradually decreases, the voltage-current characteristic curve of the corresponding nonlinear resistor changes from the first... The state transitions to the first... A momentary state.

[0056] when , When, only As the unknown variable, the above integral equation is simplified to obtain the following... A linear equation in one variable. Solving this equation will yield the corresponding... Value. Following this method, calculate the value for each state sequentially. By connecting these discrete voltage and current data points, the desired nonlinear resistor voltage-current characteristic curve can be obtained.

[0057] The advantage of this method is that by introducing phase angle coordination and piecewise linearization, it achieves accurate conversion from loss power measurement data to nonlinear resistance voltage-current characteristics, thus avoiding complex electromagnetic field numerical calculations.

[0058] S22, obtain the nonlinear inductor flux linkage-current characteristic curve.

[0059] The flux linkage-current characteristic curve of a nonlinear inductor consists of the peak current and peak flux linkage of the nonlinear inductor under no-load test, and their corresponding relationship is expressed as follows: .in: — Instantaneous flux linkage, in Weber (Wb); — RMS voltage value, in volts (V); — Angular frequency, measured in radians per second (rad / s); — The DC component in the flux linkage, measured in Weber (Wb).

[0060] When there is no DC component, the above equation simplifies to: .in: — Peak flux linkage, in Weber (Wb); — RMS voltage value, in volts (V); — Angular frequency, measured in radians per second (rad / s).

[0061] Take the first point of the flux linkage-current characteristic curve The origin, the second point It is obtained from the no-load current and the nonlinear resistive current: .in: — The effective value of the nonlinear inductor current corresponding to the first point, in amperes (A); — The effective value of the no-load current corresponding to the first point, in amperes (A); — The effective value of the nonlinear resistance current corresponding to the first point, in amperes (A).

[0062] In the already obtained Under the premise of finding the first Peak current The flux linkage-current characteristic curve is changed from the first point. To the point common Piecewise linearization of points Section. For the first of these... Within the segment, the magnetic flux linkage and current exhibit a linear relationship: .in: — Instantaneous value of nonlinear inductor current, in amperes (A); — Instantaneous flux linkage value, in Weber (Wb); subscript — indicates the first Each segmented interval is dimensionless. — No. Peak current at the end and beginning of the segment, in amperes (A). — No. The peak flux linkage at the end and beginning of the segment, in Weber (Wb).

[0063] According to the definition of the effective value of current, the effective value of no-load current. satisfy: .in: — No. The effective value of the no-load current corresponding to each voltage peak is expressed in amperes (A). — Instantaneous value of nonlinear resistive current, in amperes (A); — Instantaneous value of nonlinear inductor current, in amperes (A); — Phase angle, in radians (rad); Pi (π) is dimensionless.

[0064] Current With voltage Change, in The waveform within the range of variation is The even function of . In contrast, current With magnetic chain Change, in The waveform within the range of variation is The odd function. Based on this parity constraint, we can obtain: ; .

[0065] Substituting the above relationship into the definition of the effective value of current, we get: .

[0066] Furthermore, by utilizing the voltage-current characteristic curve of the nonlinear resistor, the integration interval is segmented: .in: — Phase angle, in radians (rad), calculated using the following formula: , ; — No. A voltage peak value, in volts (V). — No. A voltage peak value, measured in volts (V).

[0067] This expression characterizes the relationship between the phase angle and the magnetic flux linkage: as the phase angle... Gradually increase, iron core magnetic flux As the flux linkage-current characteristic curve of the nonlinear inductor increases synchronously, it changes from the first... The state transitions to the first state. A momentary state.

[0068] when , When the above piecewise integral equation is combined with the expression for the nonlinear resistor voltage-current characteristic curve, the result containing only... This is a quadratic equation with one variable representing the unknown. By solving this quadratic equation, the equation corresponding to the current working condition can be accurately obtained. Numerical value.

[0069] In practice, 8-12 measurement points can be set at logarithmic intervals based on the voltage values ​​during the no-load test to ensure coverage of the core's linear region (10%-80% of rated voltage), transition region (80%-100% of rated voltage), and saturation region (100%-120% of rated voltage). For 35kV voltage-level PTs, the number of turns in the winding is greater, and the stray capacitance high-frequency characteristics are more pronounced; therefore, the frequency sweep range is extended to 2MHz to cover high-frequency transient characteristics.

[0070] The advantage of this method is that by utilizing the parity constraints of magnetic flux and current, the parameter extraction problem of nonlinear inductors is transformed into a univariate quadratic equation that can be solved analytically, avoiding complex iterative calculations and improving the accuracy and efficiency of parameter identification.

[0071] The purpose of step S2 is to construct the voltage-current characteristic curves of the nonlinear resistor and the flux linkage-current characteristic curves of the nonlinear inductor respectively, thereby completing the modeling of the nonlinear characteristics of the iron core.

[0072] Step S3: Couple the broadband linear network model with the iron core nonlinear module, and form the iron core nonlinear module by connecting nonlinear resistors and nonlinear inductors in parallel. Replace the linear excitation branch in the traditional model and embed it into the broadband linear network topology to form a complete broadband equivalent circuit model of electromagnetic voltage transformer.

[0073] In this embodiment, step S3 may specifically include the following steps: S31, construct a broadband linear network topology.

[0074] Based on the primary winding-to-ground stray capacitance obtained in step S1 Secondary winding to ground stray capacitance Stray capacitance between primary and secondary windings And the secondary resistance referred to the primary side. and inductor A basic topology for a broadband linear equivalent circuit of an electromagnetic voltage transformer is constructed. This linear network topology is centered around an ideal transformer, with the primary winding-to-ground stray capacitance connected in parallel on its primary side. A stray capacitor between the primary and secondary windings is connected in parallel between the primary and secondary sides. Parallel connection of secondary winding to ground on the secondary side and the converted secondary resistance and inductor Connected in series to the secondary side branch.

[0075] S32, embedded iron core nonlinear module.

[0076] The core nonlinear characteristic module constructed in step S2 is used as the core of the equivalent circuit and embedded in the linear network topology. Referring to the modeling concept of the transformer T-type equivalent circuit, the nonlinear resistor and nonlinear inductor are connected in parallel to form the core nonlinear module, replacing the linear excitation branch in the traditional model.

[0077] The nonlinear resistor module uses the voltage-current characteristic curve obtained in step S21 to characterize the loss characteristics of the iron core, including eddy current loss and hysteresis loss; the nonlinear inductor module uses the flux linkage-current characteristic curve obtained in step S22 to characterize the nonlinear saturation characteristics of the iron core.

[0078] S33, perform model integration and verification.

[0079] A nonlinear module with an iron core is connected in parallel to the primary excitation branch of an ideal current transformer to form a complete coupled model with a broadband linear network. A complete broadband equivalent circuit model of the electromagnetic voltage transformer is built using simulation software (such as MATLAB / Simulink). The excitation signal under actual operating conditions is input to verify the model's output response under power frequency, harmonic, and transient conditions. The model's accuracy is confirmed by comparing it with measured data.

[0080] Figure 3 This is a schematic diagram of the equivalent circuit model of an electromagnetic voltage transformer constructed in the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention. In the figure, - Stray capacitance to ground of primary winding; - Secondary winding to ground stray capacitance; - Stray capacitance between primary and secondary windings; - Primary side resistance converted to the primary side; - The secondary resistance referred to the primary side; - The primary-side inductance converted to the primary side; - The secondary inductance is referred to the primary side. The resistance and inductance of the secondary side of the current transformer are referred to the primary side of the current transformer according to the turns ratio of an ideal current transformer. The iron core is added to the network to form a linear network, resulting in the following... Figure 3 The PT equivalent circuit model is shown.

[0081] The purpose of step S3 is to complete the construction of the broadband equivalent circuit model.

[0082] The beneficial effects of implementing this embodiment are: (1) It has accurate coupling of wideband parameters and core nonlinear saturation characteristics: By organically combining the extraction of wideband linear network parameters with the modeling of core nonlinear characteristics, a coupling correlation model of core nonlinear saturation characteristics and winding wideband parameters is established, which overcomes the defect of the separation between linear and nonlinear models in the existing technology and realizes accurate characterization of the full-band electromagnetic characteristics of PT from DC, power frequency to high-frequency harmonics and transient waves.

[0083] (2) High accuracy of stray capacitance extraction: The stray capacitance solution method based on scattering parameter measurement and admittance parameter mapping is adopted. By utilizing the physical law that stray capacitance dominates admittance characteristics at high frequencies, the accurate inversion extraction of stray capacitance is realized, avoiding the complex electromagnetic field calculation in traditional methods and improving the accuracy and efficiency of parameter identification.

[0084] (3) High accuracy of nonlinear modeling of iron core: The nonlinear resistance voltage-current characteristic curve is solved by combining piecewise linearization with phase angle synergy, and the nonlinear inductor flux-current characteristic curve is solved by combining the parity constraint of flux linkage and current with a quadratic equation. This achieves accurate fitting of the actual magnetization curve of the iron core and overcomes the accuracy loss caused by the traditional piecewise linearization simplification process.

[0085] (4) Clear model structure and high computational efficiency: The model structure realizes the decoupling and synergy of linear and nonlinear networks. Through reasonable model simplification and parameter identification strategies, it takes into account both modeling accuracy and computational efficiency. The model is suitable for large-scale simulation scenarios such as power system harmonic analysis and transient fault simulation.

[0086] (5) Strong versatility and wide range of applications: It does not depend on specific PT structure and material parameters, and can adapt to the broadband modeling needs of PTs with different materials and structures. It has strong versatility and engineering application value.

[0087] This invention can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0088] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing related hardware through computer-readable instructions. These computer-readable instructions can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods. The aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, optical disk, or read-only memory (ROM), or random access memory (RAM).

[0089] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0090] Example 2 Please refer to Figure 4 The flowchart illustrates another embodiment of the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to the present invention. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation includes the following steps: Step 1: Obtain the parameters of the broadband linear network.

[0091] In practice, step 1 includes the following steps: Step 1.1: Perform a sweep frequency measurement to obtain S-parameters.

[0092] This step involves performing frequency sweep measurements on the primary and secondary ports of the PT using a network analyzer to obtain its scattering parameters (S-parameters) over a wide frequency range. S-parameters reflect the relationship between the incident and reflected waves of the PT under high-frequency signals and are key parameters describing the characteristics of high-frequency networks. By sweeping the frequency band from low to high frequencies, the electromagnetic response of the PT at different frequencies can be comprehensively captured, providing realistic and continuous frequency domain data support for subsequent modeling. The advantages of this method are its simplicity and high accuracy, especially its suitability for the high-frequency band, avoiding the cumbersome analytical calculations in traditional modeling.

[0093] Step 1.2: Parameter conversion S-parameters -> Y-parameters.

[0094] While S-parameters are easy to measure, they are not convenient for directly constructing equivalent circuits. This step uses mathematical transformation to convert the S-parameters into an admittance parameter matrix (Y-parameters). Y-parameters can more intuitively describe the relationship between port voltage and current, making them suitable for subsequent circuit model construction. This transformation preserves the accuracy of the S-parameters across the entire frequency band and provides a foundation for the inversion of stray capacitance, serving as a crucial bridge connecting measured data and model parameters.

[0095] Step 1.3: Inversely deduce stray capacitance based on Y parameters.

[0096] The characteristics of a power PT at high frequencies are mainly affected by stray capacitances, including primary-to-ground capacitance, secondary-to-ground capacitance, and capacitance between the primary and secondary windings. This step utilizes the mapping relationship between the Y-parameters and these stray capacitances to deduce the values ​​of three key capacitances analytically or numerically. This process achieves a precise mapping from macroscopic network characteristics to microscopic physical parameters, avoiding errors caused by empirical estimations and providing accurate electrical parameters for the construction of broadband linear networks.

[0097] Step 1.4: Convert to the primary side according to the ratio.

[0098] In broadband modeling, the secondary side parameters of a current transformer (PT), such as resistance and inductance, need to work in conjunction with the primary side. This step, based on the turns ratio of an ideal current transformer, converts the secondary side parameters to the primary side, forming a unified equivalent circuit structure. This conversion method ensures the consistency of the model's electrical characteristics with the actual PT, laying the foundation for the subsequent embedding of nonlinear modules, while also simplifying the model structure and improving simulation efficiency.

[0099] Step 2: Extract the nonlinear characteristics of the iron core.

[0100] In practice, step 2 includes the following steps: Step 2.11: Calculate the flux linkage Ψ and the no-load current.

[0101] The no-load current under different voltages was obtained through no-load tests, and the peak flux linkage of the iron core was calculated accordingly. The flux linkage exhibits an integral relationship with voltage and is a core variable describing the saturation state of the iron core. This step provides fundamental data for subsequent modeling of nonlinear inductors, ensuring that the model reflects the magnetization characteristics of the iron core under different excitation conditions.

[0102] Step 2.12: Construct parity constraints for iR and iL.

[0103] Under AC excitation, the nonlinear resistive current (iR) and the nonlinear inductor current (iL) exhibit even and odd function characteristics in their waveforms, respectively. This step utilizes this parity constraint to decompose the excitation current into loss and magnetization components, providing a theoretical basis for decoupling and modeling these components, and improving the accuracy and rationality of nonlinear characteristic extraction.

[0104] Step 2.13: Calculate the nonlinear inductor current.

[0105] Based on the relationship between magnetic flux and current, and combined with a piecewise linearization method, a quadratic equation in univariate iL is constructed and solved. This process takes into account the nonlinear characteristics of the iron core magnetization curve, avoids the simplification of the magnetization curve in traditional methods, and enables the model to accurately reflect the saturation behavior of the iron core under wideband, large-signal excitation.

[0106] Step 2.14: Plot the nonlinear inductance Ψ-I curve.

[0107] Connecting the calculated flux linkage and current data points forms a complete Ψ-I characteristic curve. This curve is the core nonlinear element describing the magnetization characteristics of the iron core and directly determines the model's performance under saturation conditions. Its accuracy directly affects the simulation accuracy of the PT under complex conditions such as harmonics and transients.

[0108] In addition, step 2 also includes the following steps: Step 2.21: Measure the power loss under no-load conditions.

[0109] The power loss under different voltages was measured through no-load tests. This loss is mainly caused by the hysteresis and eddy currents of the iron core. The power loss is a key input for nonlinear resistance modeling, determining the amplitude and variation of the loss component in the excitation branch.

[0110] Step 2.22: Power-based and piecewise linearization.

[0111] By correlating power loss with peak voltage, a piecewise linearization method is used to construct the voltage-current (UI) characteristic curve of the nonlinear resistor. Piecewise linearization can accurately fit the nonlinear changes in core losses while ensuring computational efficiency, thus improving the model's adaptability over a wide voltage range.

[0112] Step 2.23: Calculate the nonlinear resistor current.

[0113] By utilizing the relationship between power balance and phase angle, an equation for iR is established and solved to obtain the current values ​​under different voltage peak values. This process fully considers the nonlinear characteristics of core losses as a function of excitation voltage, ensuring that the nonlinear resistor module can accurately reflect the core loss behavior under saturation.

[0114] Step 2.24: Plot the nonlinear resistance UI curve.

[0115] This step is essentially the plotting of the nonlinear resistance UI curve, used to characterize the core loss characteristics. It is then used in conjunction with the nonlinear inductor module to form a complete nonlinear excitation branch for the core, providing achievable nonlinear component characteristics for subsequent model embedding.

[0116] Step 3: Construct the PT broadband nonlinear model.

[0117] In practice, step 3 includes the following steps: Step 3.1: Build the basic linear network topology.

[0118] Based on the stray capacitance and the converted winding parameters obtained in step 1, a linear equivalent circuit topology for the PT is constructed. This topology encompasses the distributed parameter characteristics of the PT at high frequencies and serves as the basic framework of the broadband model, ensuring that the impedance characteristics of the model are consistent with those of the physical device across the entire frequency band.

[0119] Step 3.2: Embed the nonlinear module.

[0120] A nonlinear core module, consisting of a nonlinear resistor and a nonlinear inductor connected in parallel, replaces the linear excitation branch in the traditional model. This structure achieves decoupling and synergy between the linear network and the nonlinear characteristics, retaining the high-frequency characteristics of the broadband network while introducing the nonlinear behavior of core saturation. This is the core innovation of the model structure in this embodiment.

[0121] Step 3.3: Assign a nonlinear characteristic curve.

[0122] The UI and Ψ-I curves extracted in step 2 are assigned to the nonlinear resistor and nonlinear inductor modules, respectively, giving the model realistic electromagnetic characteristics of the iron core. This process ensures that the model's response under different excitation conditions is highly consistent with that of the actual device, improving the reliability of the simulation.

[0123] Step 3.4: Form the PT broadband equivalent model.

[0124] By integrating linear networks with nonlinear modules, a complete PT broadband equivalent circuit model is formed. This model can accurately simulate the electromagnetic characteristics across the entire frequency band, from DC and power frequency to high-frequency harmonics and transient waves. It is suitable for various application scenarios such as harmonic analysis, transient simulation, and equipment optimization, and has good engineering practical value.

[0125] Example 3 This embodiment is based on Embodiment 1, using a machine with a rated voltage of Using an electromagnetic voltage transformer as the implementation object, the effectiveness and practicality of the modeling method of this invention are verified. (Transformation ratio) (Assuming the rated phase voltage on the secondary side is 0.1kV). The method in this embodiment specifically includes the following steps: 1. Measurement and extraction of parameters for broadband linear networks.

[0126] Figure 7 This is a schematic diagram of the scattering parameter test wiring used in the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation of the present invention. Figure 7 As shown, when obtaining the broadband scattering parameters of the PT, the primary winding of the electromagnetic voltage transformer is connected to port 1 of the network analyzer, and the secondary winding is connected to port 2 of the network analyzer. The grounding terminal of the electromagnetic voltage transformer is reliably grounded. The sweep parameters of the network analyzer are set, with the frequency sweep range set to 10Hz to 1MHz, and the sweep points divided at logarithmic intervals. The excitation level of the input signal is set to 10% of the rated voltage of the electromagnetic voltage transformer. The scattering parameters are then measured using the network analyzer. , , , .

[0127] Using the conversion formula in step S12 of Example 1, the measured scattering parameters are converted into a transmission parameter matrix and an admittance parameter matrix. Based on the mapping relationship between the admittance parameter and stray capacitance, the primary winding-to-ground capacitance is calculated. Secondary winding to ground capacitance and the capacitance between the primary and secondary windings The values ​​of are as follows. In this embodiment, the extracted stray capacitance parameters are shown in Table 1: Table 1

[0128] According to the ideal transformation ratio of electromagnetic voltage transformer That is, the ratio The secondary-side resistance and inductance are then referred to the primary side. After referencing, the secondary-side resistance... Equivalent resistance referred to the primary side Secondary inductor Equivalent inductance referred to the primary side Complete the construction of the broadband linear network model.

[0129] 2. Modeling of nonlinear characteristics of iron core.

[0130] An unloaded test was conducted on the electromagnetic voltage transformer. Sinusoidal voltages of varying effective values ​​were applied, gradually increasing from 10% to 120% of the rated voltage. The corresponding unloaded current and power loss were measured. Under the assumption of no DC component, the peak voltage was calculated from the effective voltage value. Using the piecewise linearization of power loss and the phase angle correlation formula in step S21 of Example 1, the peak current corresponding to each voltage peak of the nonlinear resistor was obtained, and a complete voltage-current characteristic curve was plotted.

[0131] Based on the relationship between the peak flux linkage and the effective voltage value, and utilizing the parity constraint relationship between the nonlinear resistive current and the nonlinear inductor current in step S22 of Example 1, the flux linkage-current characteristic curve of the nonlinear inductor is obtained through piecewise linearization and solving a quadratic equation. In this example, the constructed core nonlinear characteristic curves are shown in Figures 5(a) and 5(b), where Figure 5(a) is the core nonlinear voltage-current UI characteristic curve of the electromagnetic voltage transformer in the broadband modeling method of the electromagnetic voltage transformer considering core nonlinear saturation of the present invention; Figure 5(b) is the core nonlinear flux linkage-current ψ-I characteristic curve of the electromagnetic voltage transformer in the broadband modeling method of the electromagnetic voltage transformer considering core nonlinear saturation of the present invention.

[0132] 3. Construction of wideband equivalent circuit model.

[0133] Based on the scattering parameters and converted admittance and reduced parameters obtained by frequency sweep measurement using a network analyzer in step 1, a basic topology for the broadband linear equivalent circuit of the electromagnetic voltage transformer is constructed. The core nonlinear characteristic module constructed in step 2 is used as the core of the equivalent circuit. A nonlinear core module composed of parallel nonlinear resistors and nonlinear inductors replaces the linear excitation branch in the traditional model and is embedded in the linear network topology.

[0134] The nonlinear resistor module uses a voltage-current characteristic curve obtained by piecewise linearization to characterize the loss characteristics of the iron core; the nonlinear inductor module uses a flux linkage-current characteristic curve constructed based on parity constraints and piecewise linearization to characterize the nonlinear saturation characteristics of the iron core.

[0135] The final complete equivalent circuit model of the electromagnetic voltage transformer is as follows: Figure 6 As shown, Figure 6 This diagram illustrates the broadband equivalent circuit model of an electromagnetic voltage transformer constructed in simulation software using the broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation, as described in this invention. This model can simultaneously characterize the influence of broadband distributed parameters and the nonlinear saturation characteristics of the core, achieving accurate simulation of electromagnetic characteristics across the entire frequency range from power frequency to high-frequency transients.

[0136] 4. Model validation.

[0137] The constructed wideband equivalent circuit model of the electromagnetic voltage transformer was implemented in the MATLAB / Simulink simulation platform. The rated power frequency voltage, the composite voltage containing multiple harmonics, and the impulse waveform of the simulated transient overvoltage were applied respectively, and the output response of the model was recorded.

[0138] Under power frequency conditions, the output voltage amplitude error is ≤2% and the phase error is ≤1°; under harmonic conditions (2nd-50th harmonics), the waveform distortion rate error is ≤3%; under transient conditions, the peak impulse voltage error is ≤5% and the rise time / fall time error is ≤10%.

[0139] The simulation results were compared with the measured waveforms, and the two remained highly consistent under power frequency, harmonic, and transient conditions, verifying the accuracy and effectiveness of the modeling method of the present invention.

[0140] Example 4 This embodiment uses another unit with a rated voltage as... Using an electromagnetic voltage transformer as the implementation object, the modeling steps in Example 2 are repeated. The difference from Example 2 is that, due to the different voltage levels, the stray capacitance parameters and core nonlinear characteristics are different.

[0141] In the broadband linear network parameter measurement and extraction step, the scanning frequency range was adjusted to 10Hz to 2MHz to cover the characteristics of a higher frequency band. Through measurement and calculation, the primary winding-to-ground capacitance of the 35kV PT was extracted. Secondary winding to ground capacitance Inter-winding capacitance .

[0142] In the modeling step of the nonlinear characteristics of the iron core, the voltage range of the no-load test is adjusted to be from 10% to 110% of the rated voltage to avoid over-saturation of the iron core. Using the same piecewise linearization method and parity constraint method as in Example 2, the voltage-current characteristic curves of the nonlinear resistor and the flux linkage-current characteristic curves of the nonlinear inductor are constructed respectively.

[0143] In the broadband equivalent circuit model construction step, the above parameters are substituted into the model to form a broadband equivalent circuit model applicable to 35kV PT. The model verification results show that the model can accurately reflect the electromagnetic characteristics of the PT in the frequency range from power frequency to 100kHz, further proving the universality and applicability of the method of the present invention for PTs of different voltage levels and different structures.

[0144] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0145] Obviously, the embodiments described above are merely some embodiments of the present invention, not all embodiments. The accompanying drawings show preferred embodiments of the present invention, but do not limit the patent scope of the present invention. The present invention can be implemented in many different forms; rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the patent protection scope of this invention.

Claims

1. A broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation, characterized in that, Includes the following steps: S1. The electromagnetic voltage transformer is regarded as a two-port network. Its wideband scattering parameters are obtained by frequency sweep measurement. The scattering parameters are converted into an admittance parameter matrix. Based on the mapping relationship between admittance parameters and stray capacitance, the stray capacitance value of the electromagnetic voltage transformer is solved. The secondary side resistance and inductance are converted to the primary side according to the ideal transformer ratio to construct a wideband linear network model. S2, by measuring the power loss and no-load current under different voltages through no-load tests, the voltage-current characteristic curve of the nonlinear resistor is solved by using a piecewise linearization method combined with the phase angle synergy relationship. Based on the parity constraint of the flux linkage nonlinear resistor current and the nonlinear inductor current, the flux linkage-current characteristic curve of the nonlinear inductor is solved by piecewise linearization and a quadratic equation, and the core nonlinear module is constructed. S3, the wideband linear network model is coupled with the iron core nonlinear module, and the iron core nonlinear module is formed by connecting nonlinear resistors and nonlinear inductors in parallel, replacing the linear excitation branch in the traditional model, and embedded in the wideband linear network topology to form a complete wideband equivalent circuit model of electromagnetic voltage transformer.

2. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 1, characterized in that, The measurement of broadband scattering parameters in step S1 specifically includes: Connect the primary winding of the electromagnetic voltage transformer to port 1 of the network analyzer, and connect the secondary winding to port 2 of the network analyzer. Set the frequency sweep parameters of the network analyzer to a frequency sweep range of 10Hz to 1MHz; The excitation level of the input signal is 10% of the rated voltage of the electromagnetic voltage transformer, and the scattering parameters are measured respectively. , , , .

3. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 2, characterized in that, The step of converting the scattering parameters into an admittance parameter matrix as described in step S1 specifically includes: Convert the scattering parameters into a transport parameter matrix: ,in, To transmit the four elements of the parameter matrix, To match the reference impedance; Convert the transfer parameters into an admittance parameter matrix: ,in, , , , These are the four elements of the admittance parameter matrix.

4. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 3, characterized in that, The step S1, which involves solving for the stray capacitance value based on the mapping relationship between admittance parameters and stray capacitance, specifically includes: Establish a system of equations: ,in, Angular frequency, The imaginary unit, This refers to the stray capacitance of the primary winding to ground. This refers to the stray capacitance of the secondary winding to ground. This refers to the stray capacitance between the primary and secondary windings. By solving the above system of equations, the stray capacitance of the primary winding to ground can be calculated. Secondary winding to ground stray capacitance Stray capacitance between primary and secondary windings The specific value.

5. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 1, characterized in that, The step of solving the voltage-current characteristic curve of the nonlinear resistor in step S2 specifically includes: The effective values ​​of different voltages were measured through no-load tests. Power loss Calculate the peak voltage magnetic flux peak ; Piecewise linearization of the voltage-current characteristic curve is performed for the first... Within the segment, the instantaneous value of the nonlinear resistive current With instantaneous voltage value They satisfy a linear relationship; According to the definition of power The integration interval is segmented according to the phase angle, where the phase angle is... Establish information about the unknown peak current. linear equation of one variable; Solving this linear equation in one variable yields the peak current. The peak current under each state is calculated sequentially, and the discrete data points are connected to obtain the voltage-current characteristic curve of the nonlinear resistor.

6. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 1, characterized in that, The step of solving the flux linkage-current characteristic curve of the nonlinear inductor in step S2 specifically includes: The effective values ​​of different voltages were measured through no-load tests. RMS value of no-load current Calculate the peak flux linkage ; The flux linkage-current characteristic curve is linearized piecewise. For the first... Within the segment, the instantaneous value of the nonlinear inductor current With the instantaneous value of magnetic flux They satisfy a linear relationship; According to the definition of the effective value of current ,use Even function To constrain the parity of odd functions, the integration interval is simplified to... ; The integration interval is segmented according to the phase angle, where the phase angle is... By combining the voltage-current characteristic curve of the nonlinear resistor, an equation is established regarding the unknown peak current. The quadratic equation of ; Solving this quadratic equation yields the peak current. The peak current under each state is calculated sequentially, and the discrete data points are connected to obtain the flux linkage-current characteristic curve of the nonlinear inductor.

7. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 1, characterized in that, The coupling steps between the broadband linear network model and the core nonlinear module described in step S3 specifically include: A nonlinear resistor and a nonlinear inductor are connected in parallel to form a nonlinear core module, which is then connected in parallel to the primary excitation branch of an ideal current transformer. The voltage-current characteristic curve of the nonlinear resistor module is used to characterize the loss characteristics of the core, and the flux linkage-current characteristic curve of the nonlinear inductor module is used to characterize the nonlinear saturation characteristics of the core.

8. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 1, characterized in that, In step S1, the secondary-side resistance and inductance are converted to the primary side according to the ideal transformer ratio, using the following conversion formula: ,in, For secondary side resistance, It is the secondary inductor. This represents the ideal turns ratio for an electromagnetic voltage transformer. This is the equivalent value of the secondary resistance converted to the primary side. This is the equivalent value of the secondary inductance converted to the primary side.

9. The broadband modeling method for electromagnetic voltage transformers considering core nonlinear saturation according to claim 1, characterized in that, The broadband linear network topology mentioned in step S3 includes: An ideal current transformer has a primary winding-to-ground stray capacitance connected in parallel on its primary side. A stray capacitor between the primary and secondary windings is connected in parallel between the primary and secondary sides. Parallel connection of secondary winding to ground on the secondary side and the converted secondary resistance and inductor Connected in series to the secondary side branch.

10. A broadband modeling device for electromagnetic voltage transformers considering core nonlinear saturation, characterized in that, The voltage range of the no-load test in step S2 is set from 10% to 120% of the rated voltage of the electromagnetic voltage transformer. The measurement points are distributed at logarithmic intervals according to the voltage values ​​to ensure coverage of the linear region, transition region and saturation region of the core.

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