CN111879996A - Transient overvoltage back-calculation method based on electromagnetic voltage transformer - Google Patents
Transient overvoltage back-calculation method based on electromagnetic voltage transformer Download PDFInfo
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Abstract
The invention discloses a transient overvoltage back-calculation method based on an electromagnetic voltage transformer, which mainly comprises the following steps: 1) establishing an electromagnetic dual pi model of the voltage transformer; 2) carrying out an open circuit test on the voltage transformer electromagnetic dual pi model; 3) carrying out short circuit test on the voltage transformer electromagnetic dual pi model; 4) establishing an excitation curve when two excitation branches are deeply saturated; 5) the single-valued magnetization curves when the two excitation branches are not saturated and the excitation curves when the two excitation branches are deeply saturated are combined, so that the saturation characteristic of the iron core of the voltage transformer is represented; 6) and monitoring secondary side overvoltage of the voltage transformer in real time, and performing inversion calculation according to kirchhoff voltage and current law and volt-ampere relation of each element in the PT electromagnetic dual pi model to obtain time sequence waveform data of the primary side overvoltage. The transient overvoltage detection method can accurately measure the transient overvoltage in the power system through the secondary distortion voltage of the mutual inductor and the mutual inductor model, and can reflect the time sequence evolution process of a real overvoltage accident.
Description
Technical Field
The invention relates to the power technology, in particular to a low-frequency or high-amplitude transient overvoltage back-calculation method based on an electromagnetic voltage transformer.
Background
The overvoltage is an important expression form of the electromagnetic transient process of the power grid, has important influence on the insulation reliability of electrical equipment, the insulation coordination of a system, relay protection and operation control, and is one of important factors threatening the safe and reliable operation of the power grid. The overvoltage research always runs through the important stages of power transmission and distribution equipment and system safety of a power system: the overvoltage is an important basis for insulation matching design and verification, is an important factor for tracing accidents in operation and evaluating and maintaining insulation risks of equipment, and is an important reference for equipment retirement decision. The power system has a series of overvoltage protection measures such as a lightning rod, a lightning conductor, a lightning arrester, lightning protection grounding and the like, but the overvoltage phenomenon still happens occasionally and causes a series of accidents such as breakdown, discharge, flashover, explosion and the like of electrical equipment. The online overvoltage monitoring can realize online capture and real-time analysis of overvoltage waveforms, and provide real first-hand data for inversion, treatment and numerical simulation research of overvoltage accidents.
The voltage transformer is a main device for acquiring overvoltage signals of a power system, a core electromagnetic induction unit of the voltage transformer is an iron core, and intrinsic physical defects exist when overvoltage (overvoltage full-wave data) with wide-width and wide-frequency characteristics is monitored: high amplitude overvoltage can cause iron core saturation, which leads to serious distortion of secondary side voltage waveform; the dynamic magnetization process of the iron core of the voltage transformer has frequency dependence characteristics, so that the effective sensing frequency of the voltage transformer does not exceed 500Hz, and the fundamental problem of limiting overvoltage full-wave monitoring is solved. In view of establishing a wideband model of a voltage transformer, a method for truly restoring a primary side voltage waveform is proposed, and certain research results are obtained, such as the following two methods:
1) and establishing an overvoltage inversion calculation model according to the secondary side voltage signal of the voltage transformer and the broadband transmission characteristic of the secondary side voltage signal. The broadband transmission characteristic is obtained by measuring with a vector network analyzer, the excitation signal is small, the network function is linear, and the saturation nonlinear effect of the iron core is not considered.
2) A traditional T-shaped equivalent circuit of the voltage transformer is connected with a black box model in parallel to establish a broadband nonlinear parallel extended model of the voltage transformer, the saturation effect of an iron core can be considered, but the T model has inherent physical defects when the deep saturation of the iron core is simulated, and has larger errors when the low-frequency or high-amplitude transient process is simulated.
Disclosure of Invention
The invention aims to provide a low-frequency or high-amplitude transient overvoltage back-calculation method based on an electromagnetic voltage transformer so as to improve the perception capability of the voltage transformer for low-frequency transient voltage. The method for back-calculating the transient overvoltage with low frequency or high amplitude based on the electromagnetic voltage transformer mainly comprises the following steps:
1) and establishing a voltage transformer electromagnetic dual pi model considering a geometric physical structure based on a transformer electromagnetic dual model and a winding and iron core electromagnetic coupling mechanism. The primary winding of the voltage transformer is equivalent to an ideal transformer I, and the secondary winding of the voltage transformer is equivalent to an ideal transformer II. The voltage transformer electromagnetic dual pi model is provided with two excitation branches which are respectively marked as an excitation branch I and an excitation branch II. The capacitance among the primary winding and the secondary winding in the voltage transformer electromagnetic dual pi model and the capacitance on the secondary side of the voltage transformer can be ignored when the working characteristics of low-frequency or high-amplitude transient voltage are researched.
2) Performing standard open circuit test on the voltage transformer electromagnetic dual pi model to determine the excitation resistance R of two excitation branches of the electromagnetic dual pi modelm1、Rm2And respectively establishing single-valued magnetization curves when the two excitation branches are not saturated.
3) Performing short circuit test on the voltage transformer electromagnetic dual pi model to determine leakage inductance L of the electromagnetic dual pi modelsAnd a winding resistance RsThe numerical value of (c). Measuring the winding DC resistance and comparing the winding resistance R with the winding DC resistancesDistributed to two sides of the electromagnetic dual pi model of the voltage transformer, namely, the winding resistance of the primary side of the voltage transformer is set as Rs1The winding resistance of the secondary side is Rs2。
4) AC/DC hybrid power supply as excitation sourceTesting the excitation inductance of the iron core of the voltage transformer under different saturation degrees, considering the difference of the excitation characteristics of the excitation branches at different ports of the voltage transformer, proposing a port excitation curve distribution method based on a circuit model, and respectively obtaining the deep saturation inductance L of the two excitation branches according to a distribution principlem1_sAnd a deeply saturated inductance Lm2_s. And converting the deep saturation inductances of the two excitation branches into data points of a deep saturation section of the excitation curve, and establishing the excitation curve when the two excitation branches are deeply saturated. The alternating current-direct current hybrid power supply comprises a function generator and a power amplifier. The function generator generates excitation pulses, and the excitation pulses are amplified by the power amplifier and then sent to the voltage transformer.
When the voltage transformer works in a non-saturation region, two excitation inductances of the pi model are far larger than leakage inductance, the influence of the leakage inductance can be ignored, and the method for distributing the port excitation inductances comprises the following steps: the magnetic flux and the excitation resistance are equally distributed to the two excitation branches.
The magnetic flux, the current and the resistance of the two excitation curves respectively satisfy the following formula:
ψ1＝ψ2＝ψ (1)
Rm1＝Rm2＝2Rm(3)
in the formula, ψ represents a magnetic flux. i represents a current, RmRepresenting the resistance. The subscript 1 denotes the excitation branch I. The subscript 2 indicates the excitation branch II.
When the voltage transformer works in a saturation region, the deep saturation inductors L of the two excitation curvesm1_sAnd a deeply saturated inductance Lm2_sThe allocations are as follows:
where n is a secondary-side discrete data number, and n is 1,2, 3, and … …. Psis1(n)、ψs2And (n) respectively represent nth discrete magnetic flux data of two excitation curves. i.e. is1(n)、is2And (n) respectively represent nth discrete current data of the two excitation curves.
Wherein, the currents of the two excitation curves respectively satisfy the following formula:
is1(n)+is2(n)＝is(n) (7)
in the formula isAnd (n) is nth discrete total current data of the two excitation curves.
5) And the saturation characteristic of the iron core of the voltage transformer is represented by combining a single-value magnetization curve when the two excitation branches are not saturated and an excitation curve when the two excitation branches are deeply saturated.
6) And deducing to obtain a discrete inversion algorithm based on an inverse calculation circuit model based on kirchhoff voltage, current law and volt-ampere characteristics of an electromagnetic element in a PT electromagnetic dual pi model, monitoring voltage data of a secondary side of the voltage transformer in real time, and performing inversion calculation to obtain time sequence waveform data of primary side overvoltage.
The main steps of back-calculating the time sequence waveform data of the primary side overvoltage are as follows:
6.1) setting the number of turns of a primary side coil and the number of turns of a secondary side coil of the voltage transformer to satisfy the following formula according to the transformation characteristic and the isolation characteristic of the voltage transformer:
in the formula, N1: n represents the transformation characteristic of the voltage transformer, k is the transformation ratio of the electromagnetic voltage transformer, and the value of k depends on the turn ratio of the primary side winding and the secondary side winding. N: n is a radical of2The isolation characteristic of the electromagnetic voltage transformer is represented.
6.2) Voltage interaction when Low-frequency or high-amplitude transient overvoltages act on PTThe sensor works in a saturated or deep saturated state, and the current i flowing through the exciting inductorLm1And iLm2And the magnetic flux of the excitation inductor has nonlinear characteristics, namely the following nonlinear functions are satisfied:
iLm1＝fLm1(ψ1)。iLm2＝fLm2(ψ2) (9)
in the formula (f)Lm1(ψ1)、fLm2(ψ2) Respectively representing the magnetic flux ψ about the excitation branch I1And with respect to the excitation branch II magnetic flux ψ2Is a non-linear function of (a).
Wherein, the excitation inductance Lm2The cross-link magnetic flux ψ satisfies the following equation:
in the formula u3Exciting inductance L for secondary side excitation branch of voltage transformerm2The voltage across. Δ t is the nth discrete voltage data u3(n) and (n-1) th discrete voltage data u3(n-1) time difference.
6.3) calculating the secondary side excitation branch voltage u3Namely:
in the formula u2Is the secondary side voltage of the voltage transformer.
6.4) leakage inductance LsThe leakage inductance voltage is calculated by the volt-ampere characteristic, and the method mainly comprises the following steps:
6.4.1) establishing the leakage-inductance voltage uLsI.e.:
in the formula iRm1To flow through the exciting resistor Rm1The current of (2).
6.4.2) converting the continuous integral function (12) into a differential algebraic equation, namely:
in the formula iLs(n) is a flow leakage inductance LsThe nth discrete current data.
6.4.3) solving the formula (13) to obtain the leakage inductance voltage uLs。
6.5) calculating the primary side excitation branch voltage u5Namely:
6.6) calculating the primary side current i of the voltage transformerRs1Namely:
6.8) calculating the Primary Port Voltage u1Namely:
u1＝u5+iRs1·Rs1(16)
in the overvoltage reverse calculation process, when the secondary-side overvoltage waveform is known, time-series waveform data of the primary-side overvoltage is obtained by sequentially reversing from the secondary side to the primary side according to kirchhoff's voltage-current law and the voltage-current relationship of each element.
The technical effect of the invention is undoubtedly that the characterization accuracy of the gradient saturation characteristic of the iron core of the electromagnetic voltage transformer has a large influence on the error of the voltage back calculation, and the accurate characterization of the gradient saturation region of the excitation curve is the premise of realizing the accurate back calculation, and compared with the existing overvoltage on-line monitoring technology, the low-frequency or high-amplitude transient overvoltage back calculation method of the electromagnetic voltage transformer provided by the invention has the following advantages: the electrical connection mode of the existing primary side equipment is not changed, any non-standard primary equipment is not introduced, only a secondary side acquisition device and a storage device are added on the basis of the existing voltage transformer, and the cost is low; the method can accurately measure the transient overvoltage with low frequency or high amplitude caused by the nonlinearity of the iron core in the power system, and can reflect the time sequence evolution process of a real overvoltage accident.
The algorithm provided by the invention restores the true waveform of the primary side, greatly reduces the maximum error, can not add any non-standard primary equipment, and greatly improves the accurate measurement and perception capability of the PT (voltage transformer) on the low-frequency transient voltage.
Drawings
FIG. 1 is a structural diagram of an electromagnetic voltage transformer;
FIG. 2 is an electromagnetic dual schematic diagram I;
FIG. 3 is an electromagnetic dual schematic diagram II;
FIG. 4 is a schematic circuit diagram of an electromagnetic voltage transformer with iron cores in mind;
FIG. 5 is a low-frequency or high-amplitude transient overvoltage back-calculation model of the electromagnetic voltage transformer;
FIG. 6 shows hysteresis loops and basic magnetization curves at different voltages obtained by an open circuit test;
FIG. 7 is a deep saturation test platform of an electromagnetic voltage transformer;
FIG. 8 is a fitting curve of two excitation branches of a pi model of an electromagnetic voltage transformer;
FIG. 9 is a waveform of the measured and back-calculated high-amplitude high-frequency resonant voltage of the voltage transformer;
FIG. 10 is a graph of measured and back-calculated waveforms of high amplitude transient voltages of the voltage transformer;
FIG. 11 is a comparison of inverse voltage spectra of a voltage transformer;
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 5, a method for back-calculating a low-frequency or high-amplitude transient overvoltage based on an electromagnetic voltage transformer mainly includes the following steps:
1) referring to fig. 2 to 4, a voltage transformer electromagnetic pair pi model considering a geometric physical structure is established based on a transformer electromagnetic pair model and a winding and iron core electromagnetic coupling mechanism. In FIG. 2, F1、F2For energizing the power supply, 1,2 denote the excitation branch I and the excitation branch II, respectively. In FIG. 3, i1、i2Respectively as a deeply saturated inductor Lm1And a deeply saturated inductance Lm2Of the current source. The primary winding of the voltage transformer is equivalent to an ideal transformer I, and the secondary winding of the voltage transformer is equivalent to an ideal transformer II. The voltage transformer electromagnetic dual pi model is provided with two excitation branches which are respectively marked as an excitation branch I and an excitation branch II. Aiming at the back calculation research of the low-frequency or high-amplitude transient voltage of the electromagnetic voltage transformer, the influence of stray capacitance can be ignored during modeling.
2) Performing open circuit test on the voltage transformer electromagnetic dual pi model to determine the excitation resistance R of two excitation branches of the electromagnetic dual pi modelm1And an excitation resistor Rm2And respectively establishing single-valued magnetization curves when the two excitation branches are not saturated.
3) Performing short circuit test on the voltage transformer electromagnetic dual pi model to determine leakage inductance L of the electromagnetic dual pi modelsAnd a winding resistance RsThe numerical value of (c). Measuring the winding DC resistance and comparing the winding resistance R with the winding DC resistancesDistributed to two sides of the electromagnetic dual pi model of the voltage transformer, namely, the winding resistance of the primary side of the voltage transformer is set as Rs1The winding resistance of the secondary side is Rs2。
4) The AC-DC hybrid power supply is used as an excitation source, the excitation inductance of the iron core of the voltage transformer under different saturation degrees is tested, and the deep saturation inductance L of the two excitation branches is obtained according to the distribution principlem1_sAnd a deeply saturated inductance Lm2_s. And converting the deep saturation inductances of the two excitation branches into data points of a deep saturation section of the excitation curve, and establishing the excitation curve when the two excitation branches are deeply saturated. The AC/DC hybrid power supply comprises a function generator anda power amplifier. The function generator generates excitation pulses, and the excitation pulses are amplified by the power amplifier and then sent to the voltage transformer. When the voltage transformer works in a non-saturation region, the method for distributing the port excitation inductance comprises the following steps: the magnetic flux and the excitation resistance are equally distributed to the two excitation branches.
The magnetic flux, the current and the resistance of the two excitation curves respectively satisfy the following formula:
ψ1＝ψ2＝ψ (1)
Rm1＝Rm2＝2Rm(3)
in the formula, ψ represents a magnetic flux. i represents a current, RmRepresenting the resistance. The subscript 1 denotes the excitation branch I. The subscript 2 indicates the excitation branch II.
When the voltage transformer works in a saturation region, the deep saturation inductors L of the two excitation curvesm1_sAnd a deeply saturated inductance Lm2_sThe allocations are as follows:
where n is the secondary-side discrete voltage data number, and n is 1,2, 3, … …. Psis1(n)、ψs2And (n) respectively represent nth discrete magnetic flux data of two excitation curves. i.e. is1(n)、is2And (n) respectively represent nth discrete current data of the two excitation curves.
Wherein, the currents of the two excitation curves respectively satisfy the following formula:
is1(n)+is2(n)＝is(n) (7)
in the formula isAnd (n) is nth discrete total current data of the two excitation curves.
5) And the saturation characteristic of the iron core of the voltage transformer is represented by combining a single-value magnetization curve when the two excitation branches are not saturated and an excitation curve when the two excitation branches are deeply saturated.
6) And deducing to obtain a discrete inversion algorithm based on an inverse calculation circuit model based on kirchhoff voltage, current law and volt-ampere characteristics of an electromagnetic element in a PT electromagnetic dual pi model, monitoring voltage data of a secondary side of the voltage transformer in real time, and performing inversion calculation to obtain time sequence waveform data of primary side overvoltage. .
The main steps of back-calculating the time sequence waveform data of the primary side overvoltage are as follows:
6.1) setting the number of turns of a primary side coil and the number of turns of a secondary side coil of the voltage transformer to satisfy the following formula according to the transformation characteristic and the isolation characteristic of the voltage transformer:
in the formula, N1: n represents the transformation characteristic of the voltage transformer, and N is the transformation ratio of the electromagnetic voltage transformer, and the value of the transformation ratio depends on the turn ratio of the primary side winding to the secondary side winding. N: n is a radical of2The isolation characteristic of the electromagnetic voltage transformer is represented.
6.2) when transient overvoltage with low frequency or high amplitude acts on PT, the voltage transformer works in a saturated or deep saturated state, and current i flowing through the excitation inductor at the momentLm1And iLm2And the magnetic flux of the excitation inductor has nonlinear characteristics, namely the following nonlinear functions are satisfied:
iLm1＝fLm1(ψ1)。iLm2＝fLm2(ψ2) (9)
in the formula (f)Lm1(ψ1)、fLm2(ψ2) Respectively representing the magnetic flux ψ about the excitation branch I1And with respect to the excitation branch II magnetic flux ψ2Is a non-linear function of (a).
Wherein, the excitation inductance Lm2The cross-link magnetic flux ψ satisfies the following equation:
in the formula u3Exciting inductance L for secondary side excitation branch of voltage transformerm2The voltage across. Δ t is the nth discrete voltage data u3(n) and (n-1) th discrete voltage data u3(n-1) time difference.
6.3) calculating the secondary side excitation branch voltage u3Namely:
6.4) leakage inductance LsThe leakage inductance voltage is calculated by the volt-ampere characteristic, and the method mainly comprises the following steps:
6.4.1) establishing the leakage-inductance voltage uLsI.e.:
in the formula iRm1To flow through the exciting resistor Rm1The current of (2).
6.4.2) converting the continuous integral function (12) into a differential algebraic equation, namely:
in the formula iLs(n) is a flow leakage inductance LsThe nth discrete current data.
6.4.3) solving the formula (13) to obtain the leakage inductance voltage uLs。
6.5) calculating the primary side excitation branch voltage u5Namely:
6.6) calculating the electric powerPrimary side current i of voltage transformerRs1Namely:
6.8) calculating the Primary Port Voltage u1Namely:
u1＝u5+iRs1·Rs1(16)
example 2:
referring to fig. 6 to 11, the experiment based on the transient overvoltage back-calculation method of the electromagnetic voltage transformer mainly includes the following steps:
1) modeling: a10 kV single-phase electromagnetic voltage transformer is used as a research object for modeling, the model number is JDZ10(G) -10B3, the capacity is 15VA, and the iron core material is 10JNEX900 non-oriented silicon steel.
2) Open circuit test: in order to obtain a single-valued hysteresis-free magnetization curve of the iron core, a plurality of sets of open circuit tests were performed, and the voltage applied to the secondary side of a PT (potential transformer) was gradually increased from 0.1 pu. Because the PT rated working point is low and the rated capacity is 15VA, the maximum voltage of the open circuit test is applied to 1.4pu in combination with the laboratory conditions, the test data is shown in Table 1, the corresponding hysteresis loop and the single value magnetization curve are shown in FIG. 4, and the excitation resistance of the voltage transformer is 1237.7 ohms. Analysis shows that when the voltage U is 141.4V, the peak current is 0.822A, which is 5 to 6 times the PT secondary side rated current (0.15A), and the saturation degree of the core is high.
TABLE 1 single-valued magnetization curve data of electromagnetic voltage transformer
3) Short-circuit test: the secondary side (1a-1b side) of the voltage transformer is shorted and a voltage is applied to the primary side. The voltage was gradually increased to bring the current to the nominal value (0.15A), and the voltage and current were measured and recorded. And (3) calculating the obtained winding resistance and leakage inductance parameters: obtaining leakage inductance Ls1.96mH, winding resistance Rs0.6756 omega, the DC resistance R of the primary and secondary windings of the test transformerdc1＝2.2677kΩ，Rdc2When the resistance of the primary side winding and the resistance of the secondary side winding of the electromagnetic dual pi model are calculated to be 0.3945 omega, respectively: r's1＝0.25Ω，Rs2＝0.43Ω。
4) Deep saturation test: a voltage transformer deep saturation inductance test platform is built, as shown in fig. 5, a function generator generates direct current voltage with alternating current coupling signals, and a power amplifier is used for providing enough power supply capacity. After the deep saturation inductances of the two excitation branches of the voltage transformer electromagnetic dual pi model are measured, the two excitation branches are converted into data on a deep saturation excitation curve, and the result is shown in table 2. In combination with the excitation curves obtained by the open circuit test, two excitation curves considering deep saturation are obtained, as shown in fig. 8.
Table 2 data distribution results at different saturation states
5) According to the data, a reverse calculation program of the transient overvoltage based on the electromagnetic voltage transformer is written in Matlab, and the reverse calculation verification of the frequency division ferromagnetic resonance overvoltage is carried out. A frequency division ferromagnetic resonance test platform of an electromagnetic voltage transformer is built, a frequency division ferromagnetic resonance overvoltage is generated on the primary side of the transformer, a response waveform is obtained by measuring on the secondary side of the transformer, and according to the transient overvoltage back-calculation method provided in embodiment 1, the voltage waveform on the secondary side of the voltage transformer is back-calculated to the primary side, and the result is shown in fig. 9 and 10. From the comparison of the back-calculated waveforms, the distorted portion of the PT secondary side voltage is restored to a higher degree.
The inverse result relative error can be expressed as:
wherein: u shape′1The voltage, V, is back-calculated for the primary side obtained by the method herein. U shape1Is the primary true voltage value, V. ErThe relative error of the voltage with respect to the true voltage is calculated back.
To back-calculate the overall error of the waveform, N is the amount of data collected by the PT port. N is 0,1,2, … … N.
TABLE 3 inverse and normalized Voltage error comparison
Fourier decomposition is carried out on back-calculated voltage, primary real voltage and secondary reduced voltage in a power frequency overvoltage test of the electromagnetic voltage transformer, and main harmonic components in discrete voltage data are shown in figure 11.
As can be seen from the error analysis in table 3 and the spectrum analysis in fig. 10, the overall back calculation error of the back-calculated voltage calculated by the back calculation algorithm based on the electromagnetic voltage transformer proposed herein is only 4.6%, and the maximum error is reduced from 65.64% to 9%, which significantly improves the sensing level of the transient voltage of the voltage transformer. In addition, as can be known from spectrum analysis, more higher harmonics exist in the reduced voltage, and the harmonic components of the back-calculated voltage are basically consistent with those of the real voltage, so that the back-calculated voltage can be proved to be capable of obtaining the primary side real voltage data more accurately.
Claims (5)
1. The transient overvoltage back-calculation method based on the electromagnetic voltage transformer is characterized by mainly comprising the following steps of:
1) and establishing a voltage transformer electromagnetic dual pi model considering a geometric physical structure based on the voltage transformer electromagnetic dual model and a winding and iron core electromagnetic coupling mechanism. Wherein, the primary winding of the voltage transformer is equivalent to an ideal transformer I, and the secondary winding is equivalent to an ideal transformer II; the voltage transformer electromagnetic dual pi model is provided with two excitation branches which are respectively marked as an excitation branch I and an excitation branch II;
2) performing open circuit test on the voltage transformer electromagnetic dual pi model to determine the excitation resistance R of two excitation branches of the electromagnetic dual pi modelm1、Rm2Respectively establishing single-valued magnetization curves when the two excitation branches are not saturated based on a trapezoidal integration method;
3) performing short circuit test on the voltage transformer electromagnetic dual pi model to determine leakage inductance L of the electromagnetic dual pi modelsAnd a winding resistance RsThe value of (d); measuring the winding DC resistance and comparing the winding resistance R with the winding DC resistancesDistributed to two sides of the electromagnetic dual pi model of the voltage transformer, namely, the winding resistance of the primary side of the voltage transformer is set as Rs1The winding resistance of the secondary side is Rs2；
4) Exciting and testing the excitation inductance of the iron core of the voltage transformer under different saturation degrees by taking an alternating-current and direct-current hybrid power supply as an excitation source; distributing port excitation inductance according to parameters of two excitation branch circuits of a voltage transformer pi model and a voltage transformer pi model circuit structure to obtain deep saturation inductance L of the two excitation branch circuitsm1And a deeply saturated inductance Lm2(ii) a Converting the deep saturation inductances of the two excitation branches into data points of a deep saturation section of an excitation curve, and establishing the excitation curves when the two excitation branches are deeply saturated;
5) the single-valued magnetization curves when the two excitation branches are not saturated and the excitation curves when the two excitation branches are deeply saturated are combined, so that the saturation characteristic of the iron core of the voltage transformer is represented;
6) and deducing to obtain a discrete inversion algorithm based on an inverse calculation circuit model based on kirchhoff voltage, current law and volt-ampere characteristics of an electromagnetic element in a PT electromagnetic dual pi model, monitoring voltage data of a secondary side of the voltage transformer in real time, and performing inversion calculation to obtain time sequence waveform data of primary side overvoltage.
2. The electromagnetic voltage transformer-based transient overvoltage back-calculation method according to claim 1 or 2, wherein when the voltage transformer works in an unsaturated region, two excitation inductances of the pi model are far larger than a leakage inductance, and the leakage inductance influence is not counted, and the method for distributing the port excitation inductances comprises the following steps: the magnetic flux and the excitation resistance are evenly distributed to two excitation branches;
the magnetic flux, the current and the resistance of the two excitation curves respectively satisfy the following formula:
ψ1＝ψ2＝ψ (1)
Rm1＝Rm2＝2Rm(3)
in the formula, ψ represents a magnetic flux; i represents a current, RmRepresents a resistance; subscript 1 denotes an excitation branch I; the subscript 2 indicates the excitation branch II.
3. The electromagnetic voltage transformer-based transient overvoltage back-calculation method as claimed in claim 1, wherein when the voltage transformer is operated in a saturation region, the deeply saturated inductances L of the two excitation curvesm1_sAnd a deeply saturated inductance Lm2_sThe allocations are as follows:
in the formula, #s1(n)、ψs2(n) respectively representing nth discrete magnetic flux data of the two excitation curves; i.e. is1(n)、is2(n) respectively representing nth discrete current data of the two excitation curves;
the currents of the two excitation curves respectively satisfy the following formula:
is1(n)+is2(n)＝is(n) (7)
in the formula, n isA secondary-side discrete data number, n is 1,2, 3, … …; i.e. isAnd (n) is nth discrete total current data of the two excitation curves.
4. The method for back-calculating the transient overvoltage based on the electromagnetic voltage transformer as claimed in claim 1, wherein the step of back-calculating the time-series waveform data of the primary-side overvoltage comprises the following steps:
1) according to the transformation characteristic and the isolation characteristic of the voltage transformer, the number of turns of a primary side coil and the number of turns of a secondary side coil of the voltage transformer are set to satisfy the following formula:
in the formula, N1: n represents the transformation characteristic of the electromagnetic voltage transformer, k is the transformation ratio of the voltage transformer, and the value of k depends on the turn ratio of a primary side winding and a secondary side winding; n: n is a radical of2The isolation characteristic of the electromagnetic voltage transformer is represented;
2) when low-frequency or high-amplitude transient overvoltage acts on PT, the voltage transformer works in a saturated or deep saturated state, and current i flowing through the excitation inductor at the momentLm1And iLm2And the magnetic flux of the excitation inductor has nonlinear characteristics, namely the following nonlinear functions are satisfied:
iLm1＝fLm1(ψ1)；iLm2＝fLm2(ψ2) (9)
in the formula (f)Lm1(ψ1)、fLm2(ψ2) Respectively representing the magnetic flux ψ about the excitation branch I1And with respect to the excitation branch II magnetic flux ψ2A non-linear function of (d);
wherein, the excitation inductance Lm2Of the cross-link magnetic flux psi2(n) satisfies the following formula:
in the formula u3Is a secondary of a voltage transformerSide excitation branch excitation inductance Lm2Voltage at two ends; Δ t is the nth discrete voltage data u3(n) and (n-1) th discrete voltage data u3(n-1) time difference therebetween;
3) calculating secondary side excitation branch voltage u3Namely:
in the formula u2Is the secondary side voltage of the voltage transformer;
4) by leakage inductance LsThe leakage inductance voltage is calculated by the volt-ampere characteristic, and the method mainly comprises the following steps:
4.1) establishing the leakage-inductance voltage uLsI.e.:
in the formula iRm1To flow through the exciting resistor Rm1The current of (a);
4.2) converting the continuous integral function (12) into a differential algebraic equation, namely:
in the formula iLs(n) is a flow leakage inductance LsThe nth discrete current data;
4.3) calculating the formula (13) to obtain the leakage inductance voltage uLs；
5) Calculating primary side excitation branch voltage u5Namely:
6) calculating primary side current i of voltage transformerRs1Namely:
7) calculating a primary side port voltage u1Namely:
u1＝u5+iRs1·Rs1(16)。
5. the transient overvoltage back-calculation method based on the electromagnetic voltage transformer according to claim 1, wherein: the transient overvoltage back-calculation method based on the electromagnetic voltage transformer is used for restoring the primary side real waveform.
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