CN110031677A - Dry-type air-core reactor scene impedance measuring circuit and detection method - Google Patents

Abstract

Dry-type air-core reactor scene impedance measuring circuit and detection method.Since there are also other operating reactance devices to work around tested reactor when detecting at the scene, biggish line-frequency induction electric current can be generated in tested reactor, leading to the electric current for flowing through reactor is the superposition of line-frequency induction electric current and the detection electric current applied.Present invention composition includes: current transformer unit (1), current transformer unit is connect with voltage and current signal acquisition unit (2), voltage and current signal acquisition unit is connect with resitstance voltage divider (3), and resitstance voltage divider is in parallel with tested reactor (4), inductanceL ₃And capacitorC ₁Tested reactor both ends, inductance are connected in parallel on after series connectionL ₃With protective resistanceR ₄Connection, protective resistance are connect with isolating transformer, and isolating transformer is connect with intermediate frequency power supply (5), and tested reactor and surrounding operating reactance device (6) pass through mutual inductanceM ₁₂Connection.The present invention is used for dry-type air-core reactor impedance in-site measurement.

Description

On-site impedance measurement circuit and detection method of dry-type air-core reactor

Technical field:

The invention relates to a dry-type air-core reactor on-site impedance measurement circuit and a detection method.

Background technique:

As the power grid gradually develops in the direction of "large capacity, long distance, ultra-high voltage and ultra-high voltage", it is particularly important to ensure the safe and stable operation of the power grid. Reactors can play the role of compensating reactive power, limiting short-circuit current, filtering high-order harmonics, etc., and are widely used in power grids. The impedance parameter of the reactor is an important index to measure the quality of the reactor, and it is of great significance to effectively measure the impedance of the reactor.

The impedance measurement methods for reactors are mainly DC resistance measurement method and power frequency measurement method. The DC resistance measurement method can only measure the resistance of the reactor, and cannot measure the reactance of the reactor. The power frequency detection method will be affected by the power frequency interference at the test site, so that the measurement signal and the power frequency induction signal have the same frequency, and it is difficult to distinguish the two when they are superimposed together. As a result, this method cannot accurately measure the impedance of the reactor. Therefore, it is very necessary to invent a method to effectively detect the impedance of the reactor.

During on-site detection, since there are other operating reactors around the tested reactor, a large power frequency induced current will be generated in the tested reactor, resulting in the current flowing through the reactor being the power frequency induced current and the applied Superposition of detection currents.

Invention content:

The purpose of the present invention is to provide a dry-type air-core reactor on-site impedance measurement circuit and detection method, which adopts the AC detection signal of an integer multiple frequency of the power frequency, and provides a corresponding detection circuit. The formula for calculating the impedance parameters of the reactor is given by using the harmonic analysis method to eliminate the power frequency interference. And according to the measured impedance parameters to determine whether the reactor is faulty.

The above purpose is achieved through the following technical solutions:

A dry-type air-core reactor field impedance measurement circuit, which comprises: a current transformer unit, the current transformer unit is connected with a voltage and current signal acquisition unit, and the voltage and current signal acquisition unit is connected with a resistance voltage divider , the resistance voltage divider is connected in parallel with the tested reactor, the inductance L3 and the capacitor C1 _are connected in series and connected in parallel at both ends _of the tested reactor, the _inductance L3 is _connected with the protection resistor R4 , so _The protection resistor is connected with the isolation transformer, the isolation transformer is connected with the intermediate frequency power supply, and the tested reactor is connected with the surrounding running reactor through the mutual inductance M12 .

In the dry-type air-core reactor on-site impedance measurement circuit, the surrounding operating reactor includes a resistor R ₁ , the R ₁ is connected in series with the inductor L ₁ , and the resistor R ₁ and the inductor L ₁ are Equivalent resistance and equivalent reactance of the operating reactor.

In the dry-type air-core reactor field impedance measurement circuit, the detected resistance reactor includes a resistance R ₂ , the R ₂ is connected in series with the inductance L ₂ , and the resistance R ₂ and the inductance L ₂ are measured. Equivalent resistance and equivalent reactance of the reactor.

In the dry-type air-core reactor field impedance measurement circuit, the current transformer unit includes an inductance L ₄ , the inductance L ₄ and the capacitor C ₂ are connected in series with the resistor R ₃ in parallel, combined with the current transformer The unit completes the extraction of the reactor current.

A detection method using the dry-type air-core reactor on-site impedance measurement circuit according to claims 1-4, by applying a detection signal of an integer multiple frequency of the processing frequency to the reactor through the intermediate frequency power supply of the detection circuit, and the detection frequency is at the highest frequency with the industrial frequency. Select within the frequency range of 50-400Hz, so that the detection signal and the power frequency interference signal will not be indistinguishable due to the same frequency; it is required that the inductor L ₃ and the capacitor C ₁ form resonance at the power frequency, so that the reactor under test will generate The power frequency induced current will generate a circulating current in the main circuit to ensure that it will not affect the detection power supply;

The current signal collected by the current sensor includes two parts: the detection frequency current and the power frequency induced current, and measures need to be taken to not eliminate the power frequency interference in the collected current;

It is required that the inductor L ₄ and the capacitor C ₂ form a resonance at the power frequency, so that the power frequency signal is short-circuited through the inductor L ₄ and the capacitor C ₂ to eliminate the interference of the power frequency current signal. At the same time, the impedance of the inductor L ₄ and the capacitor C ₂ to the detection signal is required. It is much larger than the resistance R ₃ , so that the detection current signal enters the current acquisition module through the resistance R ₃ ; the voltage at both ends of the reactor is extracted by the resistance voltage divider, and the power frequency interference is eliminated by the harmonic analysis method, and the detection at both ends of the reactor is completed. The voltage signal is extracted, and then the impedance of the reactor can be obtained through the collected voltage and current.

The detection method of the on-site impedance measurement circuit of the dry-type air-core reactor, and the parameter determination method of the detection circuit:

First determine the values of L ₃ and C ₁ , and require that L ₃ and C ₁ and L ₄ and C ₂ have series resonance at the power frequency, then the conditions for power frequency resonance are satisfied:

(3)

The reactor under test applies a detection signal with an integer multiple of the frequency, and its voltage is set to be , whose frequency is n times the power frequency;

M ₂₃ is the mutual inductance between the tested reactor and the LC circuit, In order to apply the detection voltage, the available voltage equation is:

(4)

where is the angular frequency of the applied measurement signal, according to , taking the maximum mutual inductance, solving the above equation can get and They are:

(5)

(6)

Substituting equation (3) into equations (5) and (6) can get:

(7)

(8)

It can be seen from equations (7) and (8) that when the detection signal frequency and the tested reactor are determined, and Both are functions _of L3 , if the reactor under test is required to flow a large measurement current, it is necessary to ensure the positive much smaller than ; then the value of L ₃ that satisfies the condition can be selected according to the above formula, and then the value of C ₁ can be determined by formula (3);

For the current transformer module, L ₄ and C ₂ resonate at the power frequency, and the relationship between the two satisfies the formula (3), then the impedance of L ₄ and C ₂ to the detection current is shown in the following formula:

(9)

If the detection current is required to enter the current acquisition module through R ₃ , the value of Z must be much larger than that of R ₃ (if the value of Z is greater than 50 times the value of R ₃ , it can be considered that the value of Z is much greater than that of R ₃ ). Determine the value of C ₂ that satisfies the condition, and then the value of L ₄ can be determined by formula (3).

The detection method of the dry-type air-core reactor on-site impedance measurement circuit uses the harmonic analysis method to process the collected voltage and current signals of the reactor, and it is necessary to ensure that the sampling period is an integer multiple of the power frequency and the detection signal frequency .

Harmonic analysis method is used to process the collected reactor current signal I and reactor terminal voltage signal V , requiring integration over n fundamental wave cycles, and adjusting the value of n so that nT is an integer multiple of the power frequency cycle; The frequency interference signal is a whole cycle in the nT interval, and its integral value is zero in the nT interval. At this time, the integral result is the calculation result of the applied detection signal, which achieves the purpose of eliminating power frequency interference. The principle is as follows:

Set the current flowing through the reactor of the intermediate frequency measurement power supply as , the voltage drop across the reactor is , the power frequency induced current and voltage on the reactor are respectively and , the current and voltage of the tested reactor are the superposition of the two, then the current flowing through the reactor and the voltage at both ends collected by the transformer are:

(10)

in and Expand with Fourier as:

(11)

(12)

Among them, f ₀ is the fundamental frequency, a _{i 0} is the DC component of V _i , A _ik is the amplitude of the k -th harmonic of V _i , is the initial phase of the k -th harmonic of V _i ; a _{u 0} is the DC component of V _u , A _uk is the amplitude of the k -th harmonic of V _u , is the initial phase of the k -th harmonic of V _u .

In formula (10), and It can be represented by the following expression:

(13)

but and Expand with Fourier as:

(14)

Integrate over n fundamental wave cycles, and it is required to adjust the value of n so that nT is an integer multiple of the power frequency period. It can be seen from the above formula that the power frequency interference signal is an integer period in the nT interval, that is, and The integral value is zero in the nT interval, and only the applied detection signal is left, which achieves the purpose of eliminating power frequency interference. According to the above analysis, the imaginary part a _{i 1} , a _{u 1} and the real part of the two fundamental signals can be obtained b _{i 1} , b _{u 1} are:

(15)

Then the amplitudes of the two groups of fundamental wave signals are:

The initial phases of the fundamental voltage signal and the fundamental current signal are:

Assuming that the ratios of the current transformer module and the resistance divider are n ₁ and n ₂ respectively, the calculation expression of the reactor impedance is obtained through a series of mathematical derivations as follows:

(16)

Beneficial effects:

The present invention can be used for field measurements of reactor impedance. The fault condition of the reactor can be reflected by the measured impedance parameters of the reactor. The study found that when the reactor did not fail, its resistance parameters did not change with the frequency of the applied detection signal. In the event of inter-turn short-circuit and turns deviation faults, the resistance parameters of the reactor will increase with the increase of the detection signal frequency, so whether the reactor is faulty can be judged according to the rate of change of the reactor resistance.

The invention provides a circuit for detecting the resistance parameter of the reactor by adopting the power frequency integer multiple frequency. The harmonic analysis method is used to eliminate the power frequency interference at the measurement site, and the field measurement of the reactor impedance is realized. And the basis for judging the reactor fault according to the measured impedance parameters is given. The problem that the existing reactor impedance measurement method cannot measure the reactance and the measurement result is inaccurate due to the large power frequency interference is well solved.

Description of drawings:

1 is a schematic structural diagram of the present invention.

FIG. 2 is the parallel circuit of the reactor and the LC under the detection signal of the integer multiple of the present invention.

Detailed ways:

Example 1:

A dry-type air-core reactor field impedance measurement circuit, which consists of: a current transformer unit 1, the current transformer unit is connected with a voltage and current signal acquisition unit 2, and the voltage and current signal acquisition unit is divided with a resistor. The resistor ₃ is connected in parallel, the resistance voltage divider is connected in parallel with the tested reactor ₄ , the inductance L3 and the capacitor C1 are connected in series and then connected in parallel at both ends of the tested reactor, the inductance L3 is connected with the protection resistor _{R 4} is connected, the protection resistor is connected with the isolation transformer, the isolation transformer is connected with the intermediate frequency power supply 5, and the tested reactor is connected with the surrounding operating reactor ₆ through the mutual inductance M12 .

Example 2:

According to the dry-type air-core reactor on-site impedance measurement circuit according to Embodiment 1, the surrounding operating reactor includes a resistor R ₁ , the R ₁ is connected in series with the inductor L ₁ , and the resistor R ₁ and the The inductance L1 is the equivalent resistance and equivalent reactance _of the operating reactor.

Example 3:

According to the dry-type air-core reactor on-site impedance measurement circuit according to Embodiment 2, the detected resistance reactor includes a resistor R ₂ , the R ₂ is connected in series with the inductor L ₂ , and the resistor R ₂ and the inductor L ₂ is the equivalent resistance and equivalent reactance of the tested reactor.

Example 4:

According to the dry-type air-core reactor on-site impedance measurement circuit according to Embodiment 3, the current transformer unit includes an inductance L ₄ , and the inductance L ₄ and the capacitor C ₂ are connected in series with the resistance R ₃ in parallel. The current transformer unit completes the extraction of the reactor current.

Example 5:

A detection method using the dry-type air-core reactor on-site impedance measurement circuit according to claims 1-4, by applying a detection signal of an integer multiple frequency of the processing frequency to the reactor through the intermediate frequency power supply of the detection circuit, and the detection frequency is at the highest frequency with the industrial frequency. Select within the frequency range of 50-400Hz, so that the detection signal and the power frequency interference signal will not be indistinguishable due to the same frequency; it is required that the inductor L ₃ and the capacitor C ₁ form resonance at the power frequency, so that the reactor under test will generate The power frequency induced current will generate a circulating current in the main circuit to ensure that it will not affect the detection power supply;

The current signal collected by the current sensor includes two parts: the detection frequency current and the power frequency induced current, and measures need to be taken to not eliminate the power frequency interference in the collected current;

It is required that the inductor L ₄ and the capacitor C ₂ form a resonance at the power frequency, so that the power frequency signal is short-circuited through the inductor L ₄ and the capacitor C ₂ to eliminate the interference of the power frequency current signal. At the same time, the impedance of the inductor L ₄ and the capacitor C ₂ to the detection signal is required. It is much larger than the resistance R ₃ , so that the detection current signal enters the current acquisition module through the resistance R ₃ ; the voltage at both ends of the reactor is extracted by the resistance voltage divider, and the power frequency interference is eliminated by the harmonic analysis method, and the detection at both ends of the reactor is completed. The voltage signal is extracted, and then the impedance of the reactor can be obtained through the collected voltage and current.

In Figure 1, R ₂ and L ₂ are the equivalent resistance and equivalent reactance of the reactor under test; R ₁ and L ₁ are the equivalent resistance and equivalent reactance of the operating reactor; M ₁₂ is between the reactors The mutual inductance of the intermediate frequency power supply is applied to detect the frequency signal; the resistance R ₄ is a protection resistance; L ₃ and C ₁ are connected in series and parallel to both ends of the tested reactor. In the current sensor circuit, L ₄ and C ₂ are connected in series with R ₃ in parallel, combined with the current transformer to complete the extraction of the reactor current. The resistor divider realizes the extraction of the voltage signal across the reactor.

As can be seen from Figure 1, since there is a mutual inductance M ₁₂ between the operating reactor and the reactor under test, the voltage and current in the reactor under test are the common combination of the power frequency induction signal of the reactor and the measurement signal generated by applying the intermediate frequency power supply. When the power frequency signal is induced, the power frequency induced current generated on the tested reactor is short-circuited, and the circuit equation obtained is:

(1)

in and is the current and voltage of the surrounding operating reactor, It is the power frequency induced current generated on the tested reactor. The power frequency induced voltage of the reactor is:

(2)

It is the working current of the normal reactor, which is generally several hundred to several thousand amperes. The power frequency induced voltage on the tested reactor can reach several thousand volts or even higher. Therefore, it is necessary to shield the power frequency interference during on-site testing. .

Example 6:

According to the detection method of the dry-type air-core reactor on-site impedance measurement circuit described in Embodiment 5, the parameter determination method of the detection circuit:

First determine the values of L ₃ and C ₁ , and require that L ₃ and C ₁ and L ₄ and C ₂ have series resonance at the power frequency, then the conditions for power frequency resonance are satisfied:

(3)

The reactor under test applies a detection signal with an integer multiple of the frequency, and its voltage is set to be , whose frequency is n times the power frequency;

M ₂₃ is the mutual inductance between the tested reactor and the LC circuit, In order to apply the detection voltage, the available voltage equation is:

(4)

where is the angular frequency of the applied measurement signal, according to , taking the maximum mutual inductance, solving the above equation can get and They are:

(5)

(6)

Substituting equation (3) into equations (5) and (6) can get:

(7)

(8)

It can be seen from equations (7) and (8) that when the detection signal frequency and the tested reactor are determined, and Both are functions _of L3 , if the reactor under test is required to flow a large measurement current, it is necessary to ensure the positive much smaller than ; then the value of L ₃ that satisfies the condition can be selected according to the above formula, and then the value of C ₁ can be determined by formula (3);

For the current transformer module, L ₄ and C ₂ resonate at the power frequency, and the relationship between the two satisfies the formula (3), then the impedance of L ₄ and C ₂ to the detection current is shown in the following formula:

(9)

If the detection current is required to enter the current acquisition module through R ₃ , the value of Z must be much larger than that of R ₃ (if the value of Z is greater than 50 times the value of R ₃ , it can be considered that the value of Z is much greater than that of R ₃ ). Determine the value of C ₂ that satisfies the condition, and then the value of L ₄ can be determined by formula (3).

Example 7:

According to the detection method of the dry-type air-core reactor on-site impedance measurement circuit described in Embodiment 5, the collected voltage and current signals of the reactor are processed by using the harmonic analysis method, and it is necessary to ensure that the sampling period is the power frequency and the detection signal. Integer multiple of frequency.

Harmonic analysis method is used to process the collected reactor current signal I and reactor terminal voltage signal V , requiring integration over n fundamental wave cycles, and adjusting the value of n so that nT is an integer multiple of the power frequency cycle; The frequency interference signal is a whole cycle in the nT interval, and its integral value is zero in the nT interval. At this time, the integral result is the calculation result of the applied detection signal, which achieves the purpose of eliminating power frequency interference. The principle is as follows:

Set the current flowing through the reactor of the intermediate frequency measurement power supply as , the voltage drop across the reactor is , the power frequency induced current and voltage on the reactor are respectively and , the current and voltage of the tested reactor are the superposition of the two, then the current flowing through the reactor and the voltage at both ends collected by the transformer are:

(10)

in and Expand with Fourier as:

(11)

(12)

Among them, f ₀ is the fundamental frequency, a _{i 0} is the DC component of V _i , A _ik is the amplitude of the k -th harmonic of V _i , is the initial phase of the k -th harmonic of V _i ; a _{u 0} is the DC component of V _u , A _uk is the amplitude of the k -th harmonic of V _u , is the initial phase of the k -th harmonic of V _u .

In formula (10), and It can be represented by the following expression:

(13)

but and Expand with Fourier as:

(14)

Integrate over n fundamental wave cycles, and it is required to adjust the value of n so that nT is an integer multiple of the power frequency period. It can be seen from the above formula that the power frequency interference signal is an integer period in the nT interval, that is, and The integral value is zero in the nT interval, and only the applied detection signal is left, which achieves the purpose of eliminating power frequency interference. According to the above analysis, the imaginary part a _{i 1} , a _{u 1} and the real part of the two fundamental signals can be obtained b _{i 1} , b _{u 1} are:

(15)

Then the amplitudes of the two groups of fundamental wave signals are:

The initial phases of the fundamental voltage signal and the fundamental current signal are:

Assuming that the ratios of the current transformer module and the resistance divider are n ₁ and n ₂ respectively, the calculation expression of the reactor impedance is obtained through a series of mathematical derivations as follows:

(16)

On the basis of the reactance Z measured in the present invention, extracting its real part R is the resistance of the reactor at the detection frequency. Combined with the rated resistance R ₀ of the reactor, the present invention provides the reactor fault judgment basis formula as follows:

(17)

When the reactor is working normally close to 0, when a fault occurs will get bigger, usually When it is greater than 25%, it can be judged that the reactor is faulty. According to the above method, it can be judged whether the reactor is faulty or not.

Claims (7)

1. A dry-type air-core reactor field impedance measurement circuit comprises: the current transformer unit is characterized in that: the current transformer unit is connected with a voltage and current signal acquisition unit, the voltage and current signal acquisition unit is connected with a resistance voltage divider, the resistance voltage divider is connected with a tested reactor in parallel, and an inductorL ₃And a capacitorC ₁After being connected in series, the inductor is connected in parallel at two ends of the measured reactorL ₃And a protective resistorR ₄The protection resistor is connected with the isolation transformerThe isolation transformer is connected with a medium-frequency power supply, and the measured reactor and the surrounding running reactors are mutually inductedM ₁₂And (4) connecting.

2. The dry-type air-core reactor field impedance measurement circuit according to claim 1, characterized in that: the reactor comprises a resistorR ₁The above-mentionedR ₁And an inductorL ₁In series, said resistorR ₁And said inductorL ₁To operate the equivalent resistance and equivalent reactance of the reactor.

3. The dry-type air-core reactor field impedance measurement circuit according to claim 2, characterized in that: the detected resistance reactor comprises a resistorR ₂The above-mentionedR ₂And an inductorL ₂In series, said resistorR ₂And an inductorL ₂The equivalent resistance and the equivalent reactance of the measured reactor.

4. The dry-type air-core reactor field impedance measurement circuit according to claim 3, characterized in that: the current transformer unit comprises an inductorL ₄Said inductorL ₄And a capacitorC ₂After being connected in series with the resistorR ₃And the current transformer units are connected in parallel, and the current of the reactor is extracted by combining the current transformer units.

5. A method of testing a dry air reactor field impedance measurement circuit using the dry air reactor of claims 1-4, comprising: applying a detection signal with power frequency integer times frequency to the reactor through a medium-frequency power supply of the detection circuit, wherein the detection frequency is selected in a frequency range of 50-400Hz closest to the power frequency, so that the detection signal and a power frequency interference signal cannot be distinguished due to the same frequency; required inductanceL ₃And a capacitorC ₁Form resonance at power frequency toThe power frequency induction current generated on the measured reactor generates a circulating current in the main circuit, so that the detection power supply is not influenced;

the current signal collected by the current sensor comprises two parts of detection frequency current and power frequency induced current, and power frequency interference in the collected current is not eliminated by taking measures;

required inductanceL ₄And a capacitorC ₂Forming resonance at power frequency to make power frequency signal pass through inductorL ₄And a capacitorC ₂Short circuit, eliminating power frequency current signal interference and simultaneously requiring inductanceL ₄And a capacitorC ₂The impedance of the detection signal is far larger than that of the resistorR ₃Passing the detection current signal through a resistorR ₃Entering a current acquisition module; the voltage at the two ends of the reactor is extracted through a resistance voltage divider, power frequency interference is eliminated through a harmonic analysis method, extraction of detection voltage signals at the two ends of the reactor is completed, and then the impedance of the reactor can be obtained through the collected voltage and current.

6. The detection method of the dry-type air-core reactor field impedance measurement circuit according to claim 4, characterized in that: the parameter determination method of the detection circuit comprises the following steps:

first, it is determinedL ₃AndC ₁is a value of, a requirementL ₃AndC ₁andL ₄andC ₂series resonance occurs under power frequency, and then the condition of power frequency resonance is satisfied:

(3)

the electric reactor to be tested applies detection signals of integral multiple of power frequency and the voltage is set asAt power frequencynDoubling;

M ₂₃is a measured reactor andLCbetween circuitsThe mutual inductance is generated by the mutual inductance,for applying the detection voltage, the voltage equation can be obtained as follows:

(4)

in which the angular frequency of the applied measuring signal is based onWhen the mutual inductance is maximum, the equation is solved to obtainAndrespectively as follows:

(5)

(6)

by substituting formula (3) for formulae (5) and (6):

(7)

(8)

as can be seen from equations (7) and (8), in the case where the frequency of the detection signal and the electric reactor to be measured are determined,andare all aboutL ₃The function of (1) requires that the measured reactor is passed through a larger measuring current, and then needs to be correctedMuch less than(ii) a Then the ones that satisfy the condition can be selected according to the above formulaL ₃Can be determined by the formula (3)C ₁Taking the value of (A);

in the case of the current transformer module as such,L ₄andC ₂resonance under power frequency, the relation between the two satisfies the formula (3), thenL ₄AndC ₂the impedance to the sense current is given by:

(9)

requiring the passage of a detection currentR ₃Entering the current collection module to satisfyZIs much larger thanR ₃Get itZHas a value of greater thanR ₃50 times the value can be consideredZIs much larger thanR ₃According to the above formula, it can be determined that the condition is satisfiedC ₂The value of (2) can be determined by the formula (3)L ₄The value of (a).

7. The detection method of the dry-type air-core reactor field impedance measurement circuit according to claim 5, characterized in that: processing the acquired voltage and current signals of the reactor by using the harmonic analysis method, and ensuring that the sampling period is integral multiple of the power frequency and the frequency of the detection signal;

reactor current signal acquired by harmonic analysis methodIAnd reactor terminal voltage signalVIs required to be atnThe integration is carried out over a period of one fundamental wave,and require adjustmentnA value of (A) tonTIs an integral multiple of the power frequency period; thus, the power frequency interference signal isnTIn intervals of a full period of timenTThe integral value in the interval is zero, and the integral result is the calculation result of the applied detection signal at the moment, so that the purpose of eliminating power frequency interference is achieved, and the principle is as follows:

if the intermediate frequency measures the current of the power supply flowing through the reactor asThe voltage drop generated across the reactor isThe power frequency induced current and the voltage on the reactor are respectivelyAndand the current and the voltage of the measured reactor are superposed, and the current collected by the mutual inductor and the voltages at the two ends of the current flowing through the reactor are respectively as follows:

(10)

whereinAndwith a Fourier expansion as:

(11)

(12)

wherein,f ₀is the frequency of the fundamental wave and is,a _i0is composed ofV _i The direct-current component of (a) is,A _ik is composed ofV _i Is/are as followskThe magnitude of the sub-harmonics,is composed ofV _i Is/are as followskThe initial phase of the subharmonic;a _u0is composed ofV _u The direct-current component of (a) is,A _uk is composed ofV _u Is/are as followskThe magnitude of the sub-harmonics,is composed ofV _u Is/are as followskThe initial phase of the subharmonic;

in the formula (10), the first and second groups,andcan be expressed by the following expression:

(13)

thenAndwith a Fourier expansion as:

(14)

in thatnIntegration over one fundamental period, and requiring adjustmentnA value of (A) tonTIs the power frequency cycleIntegral multiple of the period, known from the above formula, so that the power frequency interference signal is innTOver a whole period of time, i.e.Andin thatnTThe integral value of the interval is zero, only the applied detection signal is left at the moment, the purpose of eliminating power frequency interference is achieved, and according to the analysis, the imaginary parts of the two fundamental wave signals can be obtaineda _i1、a _u1And real partb _i1、b _u1Comprises the following steps:

(15)

then the amplitudes of the two groups of fundamental wave signals are respectively:

the initial phases of the fundamental voltage signal and the fundamental current signal are respectively as follows:

the proportion of the current transformer module to the resistance voltage divider is respectively set asn ₁Andn ₂then, a calculation expression of the reactor impedance is obtained through a series of mathematical deductions as follows:

(16)。