CN116299138A - Sub-nanosecond impulse response characteristic detection method of 10kV voltage transformer - Google Patents
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Abstract
The invention discloses a method for detecting sub-nanosecond impulse response characteristics of a 10kV voltage transformer, which comprises the steps of establishing an improved pi-type equivalent model according to frequency variation characteristics of core complex permeability and core loss of the 10kV voltage transformer; the improved vector matching method is adopted to fit an admittance parameter matrix, the admittance matrix of the linear region of the improved pi-type equivalent model is subtracted at different frequency points, a broadband model is built, the frequency-dependent characteristics of iron loss and magnetic conductivity are brought into the building process of the model, the frequency-dependent characteristics of iron loss and magnetic conductivity are further overlapped with the broadband model, the using frequency of the model is improved, the frequency-dependent characteristics of iron loss and magnetic conductivity under subnanosecond pulse excitation are obvious, the using frequency of the black box model of the existing transformer equipment is improved, an energy transmission path between two secondary is obtained by utilizing the built internal equivalent circuit model, the vulnerability assessment of the 10kV voltage transformer under high-altitude nuclear electromagnetic pulse injection can be used as a reference from the angle of the energy transmission path, and the accuracy of a detection result is improved.
Description
Technical Field
The invention belongs to the technical field of power system simulation and analysis, and particularly relates to a sub-nanosecond impulse response characteristic detection method of a 10kV voltage transformer.
Background
In the field of power distribution, 10kV voltage transformers are widely used in switch cabinets of power distribution switchboards. Compared with a power transmission line, the 10kV line has the characteristics of low voltage level and dense distribution, and is more threatened by high-altitude nuclear electromagnetic pulse. Since electromagnetic pulses injected through a 10kV line will be coupled to the comprehensive measurement protection device of the voltage transformer itself and the secondary side in the cabinet, it is necessary to build an equivalent voltage transformer model to evaluate the threat level faced by the voltage transformer itself and the secondary side. This is of great importance for power system simulation and analysis.
Traditional transformer equipment modeling methods such as a matrix expression model, a saturated transformer element model and a topological structure-based model can simulate and calculate some nonlinear transient processes, but can only be used for transient calculation under the conditions of power frequency, medium frequency and low frequency. The frequency range of lightning overvoltage in the power system is generally 0.1-2 MHz, which is far beyond the application range of the model. Due to the high frequency nature of these overvoltages, conventional models of transformer-like devices are clearly unable to meet the requirements of simulation calculations.
At present, modeling research on transformer equipment is based on construction of a broadband model and is divided into an internal equivalent circuit model and a black box model. The internal equivalent circuit model establishes an equivalent circuit model according to a specific structure in the equipment, and reflects a specific wave process in the equipment. The black box model equivalent the device as a black box, does not study the specific energy transmission process inside the device, and only studies the port characteristics of the device according to the transfer function and the driving point function of the device. In the existing researches in the electric field, the effectiveness of the models is verified only in the frequency range of the operating wave and the lightning wave, and the frequency-dependent effect of the core loss and the change relation of the magnetic permeability with the frequency in the magnetic spectrum are not considered. These factors will significantly affect the transfer characteristics of the voltage transformer in the frequency range of the high-altitude nuclear electromagnetic pulse (sub-nanosecond front), and thus affect the effectiveness of the broadband model.
Disclosure of Invention
The invention aims to provide a method for detecting the sub-nanosecond impulse response characteristic of a 10kV voltage transformer, which overcomes the defects of the prior art and realizes the accurate equivalence of the port characteristic and the internal wave process of the 10kV voltage transformer under the sub-nanosecond leading-edge pulse.
A sub-nanosecond impulse response characteristic detection method of a 10kV voltage transformer comprises the following steps:
s1, establishing an improved pi-type equivalent model according to the frequency-dependent characteristics of the core complex permeability and the core loss of a 10kV voltage transformer;
s2, fitting an admittance parameter matrix by adopting an improved vector matching method, subtracting the admittance matrix of the linear region of the improved pi-type equivalent model under different frequency points, and establishing a broadband model;
s3, constructing an internal equivalent circuit model of the 10kV voltage transformer by using a multi-conductor transmission line model, and solving a wave process in the transformer by using the internal equivalent circuit model;
and S4, solving the port characteristic of the 10kV voltage transformer by adopting a broadband model and an improved pi-type equivalent model, and combining the wave process inside the transformer obtained by solving to obtain an energy transmission path between the first and second steps.
Preferably, the core complex permeability of the 10kV voltage transformer core at high frequency is measured using a tunable rectangular waveguide resonant cavity.
Preferably, the iron core is placed at an electric field wave node in the rectangular cavity, the change of the resonant frequency and the Q value before and after the iron core is placed is measured, and the complex permeability of the iron core is calculated; the complex permeability of the core at low frequencies is approximately obtained by a vector network analyzer.
Preferably, the primary side of the voltage transformer measures current using a high frequency current loop. The secondary side of the voltage transformer is output to an oscilloscope through an attenuator, and the obtained voltage and current discrete data are multiplied under different frequencies, accumulated and averaged to obtain the frequency-dependent characteristic of the core loss.
Preferably, the exciting resistance and the exciting reactance are calculated by using the core loss and the core complex permeability which change along with the frequency, and the improved classical pi-type equivalent model of the 10kV voltage transformer is obtained by combining the nonlinear characteristic of the exciting reactance considered in the classical pi-type equivalent model.
Preferably, the output end of a pulse source capable of generating sub-nanosecond leading edge pulses is connected to the primary side of a 10kV voltage transformer, electromagnetic pulses are injected into the voltage transformer, fast Fourier transformation is carried out on a secondary voltage waveform, then an improved vector matching method is used for fitting a frequency domain curve, and meanwhile, the improved vector matching method is used for adding port passive constraint conditions into the vector matching method, so that a transfer function fitting polynomial of the 10kV voltage transformer under the high altitude nuclear electromagnetic pulse frequency spectrum is obtained.
Preferably, a scattering parameter matrix of the 10kV voltage transformer is converted into an admittance parameter matrix, an improved vector matching method is adopted to fit the admittance parameter matrix, then transfer function fitting polynomials obtained by using a pulse source are used for supplementing and correcting, the admittance parameter matrix after correction is subtracted from the admittance matrix of the linear region of the improved pi-type equivalent model under different frequency points, and a broadband model is established.
Preferably, the broadband model and the improved pi-type equivalent model are overlapped to form the 10kV voltage transformer black box model based on the subnanosecond impulse response characteristic.
Preferably, the electrical parameters of the winding structure are extracted by adopting a finite element method, excitation pulses are decomposed into superposition of sine quantities by utilizing fast Fourier transformation, then winding voltage distribution is obtained by solving a transmission line equation in the form of phasors under sinusoidal excitation of each frequency, and the result is superposed to obtain total voltage distribution under a time domain.
Preferably, the internal equivalent circuit model of the total 10kV voltage transformer is as follows:
in the method, in the process of the invention,
the direction of the electromagnetic energy is the propagation direction of electromagnetic energy at any point in the 10kV voltage transformer at any time.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a method for detecting sub-nanosecond impulse response characteristics of a 10kV voltage transformer, which is used for establishing an improved pi-type equivalent model according to the frequency-dependent characteristics of core complex permeability and core loss of the 10kV voltage transformer; the improved vector matching method is adopted to fit an admittance parameter matrix, the admittance matrix of the linear region of the improved pi-type equivalent model is subtracted at different frequency points, a broadband model is built, the frequency-dependent characteristics of iron loss and magnetic conductivity are brought into the building process of the model, the frequency-dependent characteristics of iron loss and magnetic conductivity are further overlapped with the broadband model, the using frequency of the model is improved, the frequency-dependent characteristics of iron loss and magnetic conductivity under subnanosecond pulse excitation are obvious, the using frequency of the black box model of the existing transformer equipment is improved, an energy transmission path between two secondary is obtained by utilizing the built internal equivalent circuit model, the vulnerability assessment of the 10kV voltage transformer under high-altitude nuclear electromagnetic pulse injection can be used as a reference from the angle of the energy transmission path, and the accuracy of a detection result is improved.
The invention uses a subnanosecond pulse source as a transmission characteristic of a 10V voltage transformer obtained by excitation to correct a frequency response curve obtained by a vector network analyzer, and further combines the frequency variation characteristics of core loss and magnetic permeability to obtain an improved black box model, so that the simulation precision in the frequency range from power frequency to thunder and lightning wave is higher.
Drawings
Fig. 1 is a flowchart of a modeling method of a 10kV voltage transformer in an embodiment of the invention.
FIG. 2 is a diagram of a pi-type equivalent model in an embodiment of the invention.
FIG. 3 is a flow chart of an improved pi-type equivalent model of the invention.
In the figure: 1-excitation resistor; 2-exciting inductance; 3-second time leakage inductance.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
As shown in FIG. 1, the method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer comprises a black box model and an internal equivalent circuit model, wherein the black box model is used for solving the port characteristic of the 10kV voltage transformer, and the internal equivalent circuit model is used for solving the wave process in the transformer. The black box model includes a broadband model and a modified pi-type equivalent model as shown in fig. 3. Improved pi-type equivalent model: based on the classical pi-type equivalent model, the frequency-dependent characteristics of core loss and core complex permeability are brought into the establishment process of the classical pi-type equivalent model, and the improved pi-type equivalent model is obtained by superposition with a broadband model, so that the use frequency of the classical pi-type equivalent model is improved. The internal equivalent circuit model solves a frequency domain telegraph equation, and combines the space-time distribution of the electromagnetic field in the transformer to obtain a secondary energy transmission path.
The invention provides a method for detecting sub-nanosecond impulse response characteristics of a 10kV voltage transformer, which is completed through the following steps:
establishing a classical pi-type equivalent model of the 10kV voltage transformer, wherein the classical pi-type equivalent model comprises an excitation resistor 1, an excitation inductor 2 and a secondary leakage inductance 3 as shown in figure 2;
the existing T model and gamma model have physical defects, namely that the saturation degree of each part is consistent when the iron core is deeply saturated, which is not in accordance with the actual situation.
The parameters of the classical pi-type equivalent model comprise leakage inductance L between a primary winding and a secondary winding by adopting the classical pi-type equivalent model k Primary side excitation inductance L m1 Secondary side excitation inductance L m2 Primary winding resistor R k1 Secondary side winding resistor R k2 Primary side exciting resistor R m1 And a secondary side excitation resistor R m2 。
Winding resistance and winding leakage inductance were determined by short circuit test:
wherein I is k The high-voltage side current is equal to the high-voltage side rated current; u (U) k High-side voltage, p, when high-side current reaches rated current k Short circuit power when the high-side current reaches rated current. The primary winding resistor and the secondary winding resistor are distributed proportionally according to the resistance value measured under the direct current; z is Z k Represents winding drain impedance; r is R k Represents a winding resistor; x is X k Representing leakage reactance.
The exciting reactance and exciting resistance of the transformer under the power frequency are measured by an open circuit test:
in U 1N And I 0 P is the modulus of phasors 0 Is no-load loss; z is Z m Is a modulus of impedance, R m Is the excitation resistance X m Is the excitation reactance.
The exciting windings are distributed evenly; and then, generating alternating current-direct current excitation by using a signal generator and a power amplifier, and acting on a voltage transformer to deeply saturate the voltage transformer. By measuring excitation characteristics of a plurality of saturation points; the nonlinear inductor is used as an excitation inductor of the voltage transformer at the power frequency. The distribution of the excitation curve in the two excitation branches is obtained by iteration, the proportion of the currents of the two excitation branches can be obtained according to the shunt relation, and the sum of the currents of the two excitation branches is the fundamental frequency current of the primary side of the deep saturation test. Therefore, the recursion relation of the magnetic linkage, namely the magnetic linkage current curve, is obtained by knowing the current of the two excitation branches. The initial value of the exciting branch current is half of the linear region current. The initial flux linkage of both branches being that of the linear region, i.e
i k1 (j)+i k2 (j)＝i k (j)
Wherein: psi phi type k1 (j) Is the jth data point of the primary side flux linkage, ψ k1 (j-1) is the j-1 th data point of the primary side flux linkage, L m1 (j) For the primary side excitation inductance i calculated in the jth iteration k1 (j) J data point i being the primary side excitation current k1 (j-1) is the j-1 data point of the primary side excitation current, ψ k2 (j) Is the jth data point of the secondary side flux linkage, ψ k2 (j-1) is the j-1 th data point of the secondary side flux linkage, L m2 (j) For the secondary side excitation inductance i calculated in the j-th iteration k2 (j) The j-th data point, i of the secondary side exciting current k2 (j-1) is the j-1 th data point, i of the secondary side excitation current k (j) The j data point of the fundamental frequency current at the primary side of the deep saturation test; l (L) k Is leakage inductance between the primary winding and the secondary winding.
After the flux linkage current curve is obtained, flux linkage data under different currents are imported into a type 96 hysteresis nonlinear inductance model of ATP-EMTP, so that excitation inductances of two branches can be equivalently achieved.
Measuring the winding resistance and winding leakage inductance through a short circuit test; the excitation reactance and excitation resistance (linear region) of the transformer at power frequency were measured by an open circuit test. The method comprises the steps of generating alternating current and direct current excitation by using a signal generator and a power amplifier, acting on a voltage transformer to enable the voltage transformer to be deeply saturated, and measuring excitation characteristics of a plurality of saturation points to adopt nonlinear inductance as excitation inductance of the voltage transformer under power frequency; the expression of the classical pi-type equivalent model is as follows:
wherein I is 1 For primary side current, U 1 For primary side voltage, I 2 Is the secondary side current, U 2 Is the secondary side voltage, Y a Is 1 in classical pi-type equivalent modelAdmittance parameter matrix of 0kV voltage transformer, namely
Wherein Y is 11 And Y 22 For driving point admittance, Y 12 And Y 21 Is the transfer admittance; the driving point admittance and transfer admittance expressions are as follows:
wherein L is k L is leakage inductance between the primary winding and the secondary winding m1 And L m2 The primary side excitation inductance and the secondary side excitation inductance are respectively, the excitation inductance is nonlinear inductance, and different excitation currents i are different m Corresponding to different excitation inductances, R k1 And R is k2 R is a primary winding resistor and a secondary winding resistor respectively m1 And R is m2 The primary side excitation resistance and the secondary side excitation resistance are respectively, and the secondary side parameters are all calculated to the primary side.
S2, measuring the complex permeability of the 10kV voltage transformer iron core at high frequency by using a frequency-adjustable rectangular waveguide resonant cavity;
and placing the iron core into an electric field wave node in the rectangular cavity, measuring the change of the resonant frequency and the Q value before and after the iron core is placed, and calculating the complex permeability of the iron core.
The complex permeability of the iron core at low frequency is approximately obtained by a vector network analyzer;
measurement of real part mu 'of complex permeability using rectangular waveguide resonant cavity' r And imaginary part mu' r The expression of (2) is:
wherein f is resonant frequency, Q is quality factor, subscript 0 represents a parameter in a cavity state, and subscript s represents a resonant parameter of a resonant cavity after the iron core is placed; v (V) 0 Is the volume of the resonant cavity; v (V) s Is the volume of the material to be measured.
S3, constructing a high-frequency core loss measurement platform:
the measuring platform is composed of a signal generator and a power amplifier, and generates sine wave currents I with different frequencies m The method comprises the steps of carrying out a first treatment on the surface of the The power amplifier is connected with a 10kV voltage transformer. The primary side of the voltage transformer measures current using a high frequency current loop. The secondary side of the voltage transformer is output to an oscilloscope through an attenuator. And multiplying the obtained voltage and current discrete data at different frequency points, accumulating and then averaging to obtain the frequency-dependent characteristic of the core loss. The expression of core loss is:
p Fe (ω) is core loss, n represents the number of data points tested, i j (omega) the jth sample value of the secondary current at frequency omega, u j (ω) represents the jth sample value of the voltage data (converted to the primary side) at the frequency ω, ω being the test frequency and j being the jth sample point.
S4, calculating excitation resistance and excitation reactance by using core loss and core complex permeability which consider frequency-dependent characteristics, and combining the nonlinear characteristics of the excitation reactance considered in the classical pi-type equivalent model to obtain an improved classical pi-type equivalent model of the 10kV voltage transformer;
in the improved classical pi-type equivalent model, the expression of the excitation resistance and the excitation reactance are respectively as follows:
X m1 ＝2πfL m1 (i m1 ，ω)
X m2 ＝2πfL m2 (i m2 ，ω)
wherein A is the cross-sectional area of the core, l is the length of the magnetic circuit, i m Is excitation current; p is p Fe For core loss, I m X is the total exciting current m1 X is the excitation reactance of the primary side m2 The secondary side excitation reactance.
L m (i m ω) is a nonlinear inductance controlled by both excitation current and frequency, expressed as follows:
μ(i m1 ) Is the magnetic permeability of the primary side excitation branch, mu (i m2 ) The two parameters are the magnetic permeability of the secondary side excitation branch measured in the classical pi-type equivalent model, and only the saturation phenomenon caused by excitation current is considered; μ' (100 pi) is the core complex permeability at the high frequency measured in step s2, considering only the saturation phenomenon caused by the frequency, and ignoring the influence of the exciting current.
Substituting the expressions of exciting resistance and exciting inductance into admittance matrix Y of classical pi-type equivalent model a In the improved pi-type equivalent model admittance matrix Y b The improved pi-type equivalent model is solved in the frequency domain.
S5, connecting the output end of a pulse source capable of generating sub-nanosecond leading edge pulses to the primary side of a 10kV voltage transformer, and injecting electromagnetic pulses into the voltage transformer; the primary side voltage is measured using a voltage divider; the secondary side voltage is output to an oscilloscope through an attenuator and a coaxial cable with a shielding layer, so that a primary side voltage waveform and a secondary side voltage waveform are obtained.
S6, performing fast Fourier transform on the primary side voltage waveform and the secondary side voltage waveform, and then fitting a frequency domain curve by using an improved vector matching method.
The fast fourier transform is a fast algorithm of the discrete fourier transform, and the discrete fourier transform is divided into two parts by symmetry first: one part is an odd term and one part is an even term.
A(x)＝(a 0 +a 2 x 2 +...+a n-2 x n-2 )+x(a 1 +a 3 x 2 +...+a n-1 x n-2 )
Wherein a is n The coefficient of the discrete Fourier series is expressed by A (x) under a single frequency point, x is a base number, a natural constant e is often taken in the discrete Fourier transform, and n is the number of time domain sample points.
Simplifying to obtain
A(x)＝A 1 (x 2 )+xA 2 (x 2 )
And then using the properties of the unit root to derive: the expression of the discrete fourier transform at each frequency bin is obtained by summing n complex numbers differing by 2 pi/n.
The first half of the sequence is traced back each time, iterating to n=1, using the relation of the two equations, recursively dividing.
The improved vector matching method adds the port passive constraint condition into the vector matching method, so that a transfer function fitting polynomial of the 10kV voltage transformer under the high-altitude nuclear electromagnetic pulse frequency spectrum is obtained.
The process of vector matching is as follows:
let the fitting polynomial of the transfer function be:
wherein s represents complex frequency, a m Is pole, r m For the remainder, N is the fitting order, d is a constant term, and e is the fitting polynomial coefficient of the first order.
The pole determination is obtained by solving the least squares problem:
σ(s)f(s)＝p(s)
where d is a constant term of the vector matching expression,
for an estimate of d that matches a constant term in the function, σ(s) is the use of the initial pole q m The constructed matching function is a vector matching expression of the transfer function of the transformer to be found f(s), and p(s) is the vector matching at the initial pole q m The following match value.
The simultaneous addition of the equality constraint prevents zero solution from occurring:
in the method, in the process of the invention,
vector matching residue estimate, re is a function of the real part, N s Vector matching frequency point total number s k For complex frequency, q m Is the pole of vector matching.
S7, measuring a scattering parameter matrix of the 10kV voltage transformer by using a vector network analyzer, converting the scattering parameter matrix into an admittance parameter matrix, and fitting the admittance parameter matrix Y by using an improved vector matching method:
then the transfer function fitting polynomial obtained by using impulse response method is supplemented and corrected, namely
Where f (jω) is the transfer admittance calculated using the impulse response method.
Subtracting the admittance matrix of the linear region of the improved pi-type equivalent model from the corrected admittance parameter matrix at different frequency points to establish a broadband model; admittance matrix Y of broadband model c The expression of (2) is:
Y c (ω)＝Y(ω)-Y b (ω)| linear region
The broadband model and the improved pi-type equivalent model are overlapped to form a 10kV voltage transformer black box model based on subnanosecond impulse response characteristics; the expression of the black box model is:
s8, constructing an internal equivalent circuit model of the 10kV voltage transformer by using a multi-conductor transmission line model. The black box model is used for solving port characteristics of the 10kV voltage transformer, and the internal equivalent circuit model is used for solving a wave process in the 10kV voltage transformer.
And extracting the electrical parameters of the winding structure by adopting a finite element method. Namely a resistance R per unit length, an inductance L per unit length, a conductance G per unit length and a capacitance C per unit length.
The telegraph equation describing the voltage-current relationship of the multi-conductor transmission line in the time domain is:
where R is the resistance per unit length of the transmission line, G is the conductance per unit length of the transmission line, i is the current value on the transmission line, and u is the voltage value on the transmission line.
The telegram equation under the frequency domain is:
in the method, in the process of the invention,
and->
The voltage and current of the transmission line in the frequency domain at Z, Z being the characteristic impedance and Y being the characteristic admittance, respectively.
The boundary condition is that the voltage and the current of the end of the ith line are respectively equal to the voltage and the current of the head end of the (i+1) th line, the head end of the first line is excited by the head end of the first line, and the end of the nth line is grounded.
In the solving aspect, excitation pulse is decomposed into superposition of sine quantities by utilizing fast Fourier transform, and the decomposed frequency point is k cj J=0, 1,2,..n-1, complex sequence x [ j ]]Sampling frequency f s If the sequence length is N, the decomposition result of the excitation pulse is:
where U is the excitation pulse.
The corresponding frequencies:
in the solving aspect, excitation pulses are decomposed into superposition of sine quantities by utilizing fast Fourier transformation, then winding voltage distribution is obtained by solving a transmission line equation in the form of phasors under sinusoidal excitation of each frequency, and the result is superposed to obtain total voltage distribution under a time domain.
Wherein A is j1 And A j2 For the undetermined coefficients, the characteristic impedance is determined by the boundary conditions:
the decay constant α and the phase constant β are determined by the following equations:
and superposing the results to obtain the total voltage distribution in the time domain:
s9, combining winding voltage distribution obtained by a multi-conductor transmission line model and space-time distribution E (x, y, z, t) and H (x, y, z, t) of an electromagnetic field in the 10kV voltage transformer obtained by finite element analysis to obtain a secondary energy transmission path of the 10kV voltage transformer under high-altitude nuclear electromagnetic pulse injection.
The internal equivalent circuit model of the total 10kV voltage transformer is as follows:
in the method, in the process of the invention,
the direction of the electromagnetic energy is the propagation direction of electromagnetic energy at any point in the 10kV voltage transformer at any time.
The sub-nanosecond impulse response characteristic model of the total 10kV voltage transformer is as follows:
according to the invention, the port characteristic of the 10kV voltage transformer is solved by using the black box model, the wave process inside the transformer is solved by using the internal equivalent circuit model, the use frequency of the existing model is improved to be within the frequency spectrum range of the high-altitude nuclear electromagnetic pulse, and the accurate equivalence of the port characteristic of the 10kV voltage transformer and the internal wave process under the subnanosecond leading-edge pulse is realized.
According to the invention, the frequency-dependent characteristics of core loss and magnetic permeability are combined with a classical pi-type equivalent model, so that an improved nonlinear model is obtained, and the use frequency of the black box model of the traditional transformer equipment is improved due to the fact that the frequency-dependent characteristics of the core loss and the magnetic permeability are obvious under subnanosecond pulse excitation compared with lightning impulse waves.
The built internal equivalent circuit model obtains an energy transmission path between two secondary, and can be used as a reference for evaluating the vulnerability of the 10kV voltage transformer under the injection of high-altitude nuclear electromagnetic pulse from the angle of the energy transmission path.
The invention uses a subnanosecond pulse source as a transmission characteristic of a 10V voltage transformer obtained by excitation to correct a frequency response curve obtained by a vector network analyzer, and further combines the frequency variation characteristics of core loss and magnetic permeability to obtain an improved black box model. The existing model does not consider the frequency-dependent characteristics of core loss and magnetic conductivity, so that the simulation precision of the improved black box model in the frequency range from power frequency to thunder and lightning wave frequency is higher.
Claims (10)
1. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer is characterized by comprising the following steps of:
s1, establishing an improved pi-type equivalent model according to the frequency-dependent characteristics of the core complex permeability and the core loss of a 10kV voltage transformer;
s2, fitting an admittance parameter matrix by adopting an improved vector matching method, subtracting the admittance matrix of the linear region of the improved pi-type equivalent model under different frequency points, and establishing a broadband model;
s3, constructing an internal equivalent circuit model of the 10kV voltage transformer by using a multi-conductor transmission line model, and solving a wave process in the transformer by using the internal equivalent circuit model;
and S4, solving the port characteristic of the 10kV voltage transformer by adopting a broadband model and an improved pi-type equivalent model, and combining the wave process inside the transformer obtained by solving to obtain an energy transmission path between the first and second steps.
2. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer according to claim 1, wherein the core complex permeability of the 10kV voltage transformer core at high frequency is measured by using a tunable rectangular waveguide resonant cavity.
3. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer according to claim 2, wherein the iron core is placed at an electric field wave node in a rectangular cavity, the change of the resonant frequency and the Q value before and after the iron core is placed is measured, and the complex permeability of the iron core is calculated; the complex permeability of the core at low frequencies is approximately obtained by a vector network analyzer.
4. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer according to claim 2, wherein the primary side of the voltage transformer uses a high-frequency current loop to measure current; the secondary side of the voltage transformer is output to an oscilloscope through an attenuator, and the obtained voltage and current discrete data are multiplied under different frequencies, accumulated and averaged to obtain the frequency-dependent characteristic of the core loss.
5. The method for detecting the subnanosecond impulse response characteristic of the 10kV voltage transformer according to claim 4, wherein the excitation resistance and the excitation reactance are calculated by using the core loss and the core complex permeability which change along with the frequency, and the improved classical pi-type equivalent model of the 10kV voltage transformer is obtained by combining the nonlinear characteristic of the excitation reactance considered in the classical pi-type equivalent model.
6. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer according to claim 1, wherein an output end of a pulse source capable of generating sub-nanosecond leading-edge pulses is connected to a primary side of the 10kV voltage transformer, electromagnetic pulses are injected into the voltage transformer to perform fast Fourier transform on a secondary voltage waveform, then an improved vector matching method is used for fitting a frequency domain curve, and meanwhile port passive constraint conditions are added into the vector matching method by the aid of the improved vector matching method, so that a transfer function fitting polynomial of the 10kV voltage transformer under a high-altitude nuclear electromagnetic pulse frequency spectrum is obtained.
7. The method for detecting the subnanosecond impulse response characteristic of the 10kV voltage transformer according to claim 6, wherein a scattering parameter matrix of the 10kV voltage transformer is converted into an admittance parameter matrix, the admittance parameter matrix is fitted by adopting an improved vector matching method, then transfer function fitting polynomials obtained by using a pulse source are used for supplementing and correcting, and the admittance parameter matrix after correction is subtracted by an improved pi-type equivalent model linear area admittance matrix under different frequency points, so that a broadband model is established.
8. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer according to claim 7, wherein the broadband model and the improved pi-type equivalent model are overlapped to form a 10kV voltage transformer black box model based on the sub-nanosecond impulse response characteristic.
9. The method for detecting the subnanosecond impulse response characteristic of the 10kV voltage transformer according to claim 1, wherein the electrical parameters of a winding structure are extracted by adopting a finite element method, excitation pulses are decomposed into superposition of sine quantities by utilizing fast Fourier transformation, winding voltage distribution is obtained by solving a transmission line equation in the form of phasors under sinusoidal excitation of each frequency, and the result is superposed to obtain total voltage distribution in a time domain.
10. The method for detecting the sub-nanosecond impulse response characteristic of the 10kV voltage transformer according to claim 1, wherein the total internal equivalent circuit model of the 10kV voltage transformer is as follows:
in the method, in the process of the invention,
the direction of the electromagnetic energy is the propagation direction of electromagnetic energy at any point in the 10kV voltage transformer at any time.
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