CN108828318B - Method for extracting parasitic capacitance of cascaded isolation transformer - Google Patents

Method for extracting parasitic capacitance of cascaded isolation transformer Download PDF

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CN108828318B
CN108828318B CN201810160014.8A CN201810160014A CN108828318B CN 108828318 B CN108828318 B CN 108828318B CN 201810160014 A CN201810160014 A CN 201810160014A CN 108828318 B CN108828318 B CN 108828318B
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isolation transformer
impedance
circuit
cascade
frequency
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CN108828318A (en
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李盈
崔翔
齐磊
东野忠昊
李鸿达
刘远
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North China Electric Power University
Global Energy Interconnection Research Institute
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Global Energy Interconnection Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
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Abstract

The invention belongs to the technical field of high-frequency transformer modeling, and particularly relates to a method for extracting parasitic capacitance of a cascade isolation transformer, which comprises the following steps: constructing an equivalent circuit model of a single isolation transformer based on a low-frequency magnetic effect and a high-frequency capacitance effect of the isolation transformer; the model of the cascade connection of the n isolation transformers is equivalent to a chain circuit to calculate the port impedance function of the cascade isolation transformer; establishing a relational expression of port impedance resonant frequency and circuit parameters of the cascade isolation transformer according to zero-pole analysis; and testing by using an impedance analyzer to obtain the port open-circuit impedance resonance frequency of the cascade isolation transformer and the input end impedance of the cascade isolation transformer under the conditions of open circuit and short circuit of the output end at low frequency, respectively calculating the excitation inductance and the leakage inductance, and calculating the parasitic capacitance of the isolation transformer. The invention can conveniently and effectively extract the parasitic capacitance in the transformer without internal structure data, and is beneficial to researching the broadband characteristic and parasitic parameter effect of the two-port network of the cascaded transformer.

Description

Method for extracting parasitic capacitance of cascaded isolation transformer
Technical Field
The invention belongs to the technical field of high-frequency transformer modeling, and particularly relates to a method for extracting parasitic capacitance of a cascade type isolation transformer.
Background
The energy supply system of the hybrid high-voltage direct-current circuit breaker is composed of a cascade isolation transformer and an energy taking magnetic ring. The high-voltage direct-current circuit breaker is directly connected with hundreds of kilovolts of high potential, an energy supply system of the high-voltage direct-current circuit breaker is tested in high voltage withstand to the ground, commercial power is cascaded to the high-potential direct-current circuit breaker through a plurality of isolation transformers due to the requirement of high potential isolation, and only an input port of a first isolation transformer and an output port of a last isolation transformer are connected with the outside after the cascade isolation transformers are subjected to insulation pouring and integrated packaging.
Energy supplyThe distance between the loop cable and the main branch and the transfer branch of the circuit breaker is very close, mutual inductance between the loops cannot be ignored, and when the circuit breaker acts, the circuit breaker turns off dozens of kiloamperes of current within a few ms, according to the principle that
Figure BDA0001582664030000011
It is known that a large overvoltage will be induced in the supply loop. And the load of the energy supply system is directly connected with the high-voltage direct-current overhead line, so that lightning overvoltage and various operation overvoltages are easily introduced into an energy supply loop. In order to analyze the reliability of an energy supply system under the condition of overvoltage, a model capable of accurately reflecting the broadband characteristic of the cascade isolation transformer needs to be established.
At present, a parasitic capacitance extraction method based on external measurement is mature for a single transformer, but no research is provided on external characteristic analysis and parasitic capacitance extraction methods of two-port networks cascaded by a plurality of transformers.
Disclosure of Invention
In view of the above technical problems, the present invention provides a method for extracting parasitic capacitance of a cascaded isolation transformer, comprising:
step 1, constructing an equivalent circuit model of a single isolation transformer based on a low-frequency magnetic effect and a high-frequency capacitance effect of the isolation transformer;
step 2, the model of the cascade connection of the n isolation transformers is equivalent to a chain circuit, and port impedance functions of the cascade isolation transformers are calculated according to a chain circuit transmission matrix;
step 3, constructing a relational expression of the port impedance resonant frequency of the cascade isolation transformer and the circuit parameters of the single isolation transformer according to the zero-pole analysis of the port impedance function of the cascade isolation transformer;
step 4, testing by using an impedance analyzer to obtain a port open-circuit impedance curve of the cascade isolation transformer, and obtaining the resonant frequency of the port open-circuit impedance;
step 5, testing by using an impedance analyzer to obtain input end impedance of the cascade isolation transformer under the conditions of open circuit and short circuit of the output end at low frequency, and respectively calculating to obtain excitation inductance and leakage inductance of the isolation transformer;
and 6, calculating the parasitic capacitance of the isolation transformer according to the port open-circuit impedance resonance frequency, the excitation inductance and the leakage inductance.
The single isolation transformer equivalent circuit model comprises: excitation inductance L of windingmLeakage inductance L of the windingsReduced to the winding resistance R of the primary sidesCore loss equivalent resistance R of isolation transformermSelf-capacitance C between winding turns1Mutual capacitance C between the primary winding and the secondary winding2。
The cascaded isolation transformer port impedance function comprises:
Figure BDA0001582664030000021
Figure BDA0001582664030000022
wherein Z isocFor the input impedance, Z, of the cascade isolation transformer when the output is opencFor the characteristic impedance, Z, of each isolating transformer0Is the open circuit impedance of a single isolating transformer, ZkThe short-circuit impedance of a single isolation transformer is N, the number of the single isolation transformers contained in the cascade isolation transformer is N, j is an imaginary number unit, and gamma is the propagation coefficient of each isolation transformer.
The relation between the port impedance resonance frequency of the cascade isolation transformer and the circuit parameter of the single isolation transformer comprises the following steps:
Figure BDA0001582664030000031
Figure BDA0001582664030000032
ωn＝2πfn
wherein, ω isn+1For the n +1 parallel point frequency correspondenceAngular velocity of (a) ([ omega ])nFor the angular velocity corresponding to the nth series resonance point frequency, the intermediate variable L1＝2LmMiddle variable L2＝Ls，fnThe number is the nth parallel or series resonance point, N is the serial number of the isolation transformer, and N is the number of the single isolation transformers contained in the cascade isolation transformer.
Input end impedance Z under the condition that the output end is open circuit at low frequencyoThe expression is as follows:
Figure BDA0001582664030000033
input end impedance Z under the condition of short circuit of output end at low frequencysThe expression is as follows:
Zs＝N(jωLs+Rs)
ω is the angular frequency.
The invention has the beneficial effects that: the invention can conveniently and effectively extract the parasitic capacitance in the single isolation transformer without internal structure data only by external test of the two-port network of the n cascade transformers, and is beneficial to researching the broadband characteristic and parasitic parameter effect of the two-port network of the cascade transformer.
Drawings
FIG. 1 is an equivalent model schematic diagram of a single isolation transformer
FIG. 2 is a schematic diagram of an equivalent model of a cascaded isolation transformer
FIG. 3 is a graph of the impedance function of a two-port network of 5 cascaded transformers
Detailed Description
The embodiments are described in detail below with reference to the accompanying drawings.
The transformation ratio of the isolation transformer is 1: 1, the primary and secondary windings are uniformly and densely wound on the annular magnetic core, and a single transformer model can be regarded as an equivalent circuit which is symmetrical left and right, and up and down, as shown in fig. 1; in the cascade isolation transformer, the distance between the transformers is far enough, mutual inductance between the transformers can be ignored, therefore, the cascade models of the n transformers are directly connected with the models of the n figure 1 to form a chain circuit, as shown in figure 2, the parameter of the model is extracted, namely the parameter of a single isolation transformer of the model is required to be extracted.
Constructing a circuit model of the isolation transformer shown in fig. 1, wherein the model considers the low-frequency magnetic effect and the high-frequency capacitance effect of the isolation transformer and can reflect the broadband characteristic of the isolation transformer, and the meaning of each parameter is as follows: l ismExcitation inductance for the winding, LsIs the leakage inductance of the winding, RsTo be reduced to the winding resistance of the primary side. RmCore loss equivalent resistance, C, for isolating transformers1Is the self-capacitance between turns of the winding, C2Is the mutual capacitance between the primary winding and the secondary winding.
In this embodiment, the extraction of the capacitance of the single isolation transformer shown in fig. 1 is realized by testing the port impedance of the cascaded isolation transformer shown in fig. 2. The specific method comprises the following steps:
step 1, calculating the relation between the impedance resonance frequency of a port of a cascade isolation transformer and the circuit parameters of a single isolation transformer.
Firstly, a model of the cascade isolation transformer is equivalent to a chain circuit, and a port impedance function of the cascade isolation transformer is calculated according to a transmission matrix of the chain circuit.
For a two-port chain circuit formed by cascading N identical symmetrical circuits, the impedance of an input end is equal to
Figure BDA0001582664030000041
Wherein the content of the first and second substances,
Figure BDA0001582664030000042
Z0is the open circuit impedance of the subunit circuit, ZkIs the short circuit impedance of the subunit circuit.
Secondly, obtaining the relation between the resonant frequency of the port impedance and the circuit parameters of the single isolation transformer according to the zero-pole analysis of the port impedance function.
The parallel resonance point of the open input impedance is the pole of the open impedance function,
Figure BDA0001582664030000051
Figure BDA0001582664030000052
the series resonance point of the open input impedance is the zero point of the open impedance function,
Figure BDA0001582664030000053
then
Figure BDA0001582664030000054
Considering that the resistance hardly affects the resonant frequency of the transformer, neglecting damping, the open-circuit impedance resonant frequency of the two-port network of fig. 2 has the following relationship with the individual transformer circuit parameters of fig. 1:
Figure BDA0001582664030000055
Figure BDA0001582664030000056
ωn＝2πfn
fnis the nth parallel/series resonance point frequency
Because only two capacitance parameters to be solved are arranged in the transformer, only the first two resonance points are needed, namely the first parallel resonance point and the first series resonance point.
According to formula (6), when N is 1 or N is N, there are
Figure BDA0001582664030000057
So when n is equal to 1, there are
ω1p 2L1C1-1＝0 (9)
According to formula (7), when n is 1, there are
Figure BDA0001582664030000058
ω1pIs the 1 st parallel resonance point, ω1sIs the 1 st series resonance point
The open-circuit and short-circuit impedance resonance conditions of the two-port network of the 5 cascaded isolation transformers are shown in fig. 3, wherein the peak value in the curve is a parallel resonance point, and the valley value is a series resonance point.
Step 2: and acquiring the port open-circuit impedance resonant frequency of the cascade isolation transformer.
And (3) opening the output end of the two-port network of the cascade isolation transformer, measuring the impedance of the input end by using an impedance analyzer, and setting the sweep frequency range as the lower limit and the upper limit of the impedance analyzer. The resonant point frequency thereof is acquired.
And step 3: calculating the excitation inductance LmAnd leakage inductance Ls。
Firstly, the output end of the cascade isolation transformer is opened, and an impedance analyzer is used for testing the impedance Z of the input end under the condition of low frequencyoThe range of the frequency sweep is set to be 50Hz-100 Hz. According to input terminal impedance ZoCalculating excitation inductance L of isolation transformerm. Input terminal impedance ZoThe expression of (a) is:
Figure BDA0001582664030000061
secondly, the output end of the cascade isolation transformer is short-circuited, and the impedance Z of the input end under the condition of low frequency is tested by an impedance analyzersThe range of the frequency sweep is set to be 50Hz-100 Hz. According to input terminal impedance ZsCalculating leakage inductance L of isolation transformers. Input terminal impedance ZsThe expression of (a) is:
Zs＝N(jωLs+Rs) (12)
where n is the number of cascaded isolation transformers and ω is the angular frequency.
And 4, step 4: excitation inductance L according to open-circuit impedance resonance frequencymAnd leakage inductance LsAnd calculating the parasitic capacitance of the isolation transformer.
The parasitic capacitance in this embodiment comprises the self-capacitance C of the winding1And a mutual capacitance C between the primary winding and the secondary winding2The capacitance parameter is calculated according to the equations (9) and (10).
In this embodiment, a 5-stage cascade isolation transformer for a ± 500kV high-voltage dc circuit breaker energy supply system is described, and a 1 st parallel resonant frequency and a 1 st series resonant frequency are obtained by measurement with an impedance analyzer. The capacitance C can be obtained according to the formulas (8) and (9)1And C2The value of (c).
The present invention is not limited to the above embodiments, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. A method for extracting parasitic capacitance of a cascade isolation transformer is characterized by comprising the following steps:
step 1, constructing an equivalent circuit model of a single isolation transformer based on a low-frequency magnetic effect and a high-frequency capacitance effect of the isolation transformer;
step 2, the model of the cascade connection of the n isolation transformers is equivalent to a chain circuit, and port impedance functions of the cascade isolation transformers are calculated according to a chain circuit transmission matrix;
step 3, constructing a relational expression of the port impedance resonant frequency of the cascade isolation transformer and the circuit parameters of the single isolation transformer according to the zero-pole analysis of the port impedance function of the cascade isolation transformer;
step 4, testing by using an impedance analyzer to obtain a port open-circuit impedance curve of the cascade isolation transformer, and obtaining the resonant frequency of the port open-circuit impedance;
step 5, testing by using an impedance analyzer to obtain input end impedance of the cascade isolation transformer under the conditions of open circuit and short circuit of the output end at low frequency, and respectively calculating to obtain excitation inductance and leakage inductance of the isolation transformer;
step 6, calculating the parasitic capacitance of the isolation transformer according to the port open-circuit impedance resonance frequency, the excitation inductance and the leakage inductance;
the single isolation transformer equivalent circuit model comprises: excitation inductance L of windingmLeakage inductance L of the windingsReduced to the winding resistance R of the primary sidesCore loss equivalent resistance R of isolation transformermSelf-capacitance C between winding turns1Mutual capacitance C between the primary winding and the secondary winding2；
The cascaded isolation transformer port impedance function comprises:
Figure FDA0002774628870000011
Figure FDA0002774628870000012
wherein Z isocFor the input impedance, Z, of the cascade isolation transformer when the output is opencFor the characteristic impedance, Z, of each isolating transformer0Is the open circuit impedance of a single isolating transformer, ZkThe short-circuit impedance of a single isolation transformer is obtained, N is the number of the single isolation transformers contained in the cascade isolation transformer, j is an imaginary number unit, and gamma is the propagation coefficient of each isolation transformer;
the relation between the port impedance resonance frequency of the cascade isolation transformer and the circuit parameter of the single isolation transformer comprises the following steps:
Figure FDA0002774628870000021
Figure FDA0002774628870000022
ωn＝2πfn
wherein, ω isn+1Angular velocity, ω, corresponding to the n +1 th parallel point frequencynFor the angular velocity corresponding to the nth series resonance point frequency, the intermediate variable L1＝2LmMiddle variable L2＝Ls，fnThe number is the nth parallel or series resonance point, N is the serial number of the isolation transformer, and N is the number of the single isolation transformers contained in the cascade isolation transformer.
2. Method according to claim 1, characterized in that the input impedance Z in the case of an open circuit at the output is the input impedanceoThe expression is as follows:
Figure FDA0002774628870000023
input impedance Z in case of short circuit of the outputsThe expression is as follows:
Zs＝N(jωLs+Rs)
ω is the angular frequency.
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