CN107390032A - Line mutual-ground capacitor parameter measurement system and measuring method - Google Patents

Line mutual-ground capacitor parameter measurement system and measuring method Download PDF

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CN107390032A
CN107390032A CN201710545710.6A CN201710545710A CN107390032A CN 107390032 A CN107390032 A CN 107390032A CN 201710545710 A CN201710545710 A CN 201710545710A CN 107390032 A CN107390032 A CN 107390032A
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msub
mrow
msup
mover
omega
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CN107390032B (en
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杨庆
张波
冉佳权
陈嵩
孙健
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Chongqing University
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Chongqing University
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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
    • G01R27/2605—Measuring capacitance

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Abstract

The invention discloses a kind of line mutual-ground capacitor parameter measurement system, including injection transformer and computing module, the primary side of the injection transformer is provided with primary side voltage measurement unit, the secondary side of the injection transformer is provided with input line, the current source in the input line, the secondary side current measuring unit for measuring injection transformer secondary side current and the secondary side voltage measurement unit for measuring injection transformer secondary side voltage, and the current source is used to export the adjustable amplitude current signal in the range of certain frequency；The primary side voltage measurement unit, secondary side current measuring unit and secondary side voltage measurement unit electrically connect with the computing module.The invention also discloses line mutual-ground capacitor measurement method of parameters, the precision of line mutual-ground capacitor parameter measurement can effectively be lifted, have the characteristics that measurement accuracy is high, anti-electromagnetic interference capability is strong, and the security of operating personnel and the practicality of field application can be taken into account.

Description

Line mutual-ground capacitor parameter measurement system and measuring method
Technical field
The invention belongs to the field of measuring technique of inductance or electric capacity, is specifically a kind of line mutual-ground capacitor parameter measurement system System and measuring method.
Background technology
The real-time accurate measurement of circuit on power system direct-to-ground capacitance parameter suppresses for ground-fault over-voltages, reactive-load compensation And fault location has extremely strong practical value.Traditional circuit direct-to-ground capacitance measurement method of parameters can be divided into the direct method of measurement And the indirect method of measurement.The direct method of measurement needs to operate electrical primary loop, security difference and complicated and time consumption.And survey indirectly Amount method mainly includes Biased capacitor method, tuning method and signal injection method.Wherein, Biased capacitor method faces security and real-time The danger for inducing zero sequence loop resonance be present in the problems such as poor, tuning method, and as the signal injection method being most widely used, by The exciting impedance that have ignored injection transformer during its traditional measurement is non-linear and is made open circuit processing, therefore system be present Unite error, and the relative error of measurement result gradually increases away from injection transformer working frequency with Injection Signal frequency. In addition, under power distribution network supply line cable and current supply circuit Complicated Background, system capacitive current increase and instantaneity event Barrier rate rises, therefore the real-time accurate measurement of line mutual-ground capacitor parameter suffers to lifting power distribution network stability and self-healing ability Vital effect.
The content of the invention
In view of this, it is an object of the invention to provide a kind of line mutual-ground capacitor parameter measurement system and measuring method, The precision of line mutual-ground capacitor parameter measurement can be effectively lifted, has the characteristics that measurement accuracy is high, anti-electromagnetic interference capability is strong, And the security of operating personnel and the practicality of field application can be taken into account.
To reach above-mentioned purpose, the present invention provides following technical scheme：
Present invention firstly provides a kind of line mutual-ground capacitor parameter measurement system, including injection transformer and computing mould Block, the primary side of the injection transformer are provided with primary side voltage measurement unit, and the secondary side of the injection transformer is provided with defeated Enter line, the current source in the input line, measured for measuring the secondary side current of injection transformer secondary side current Unit and the secondary side voltage measurement unit for measuring injection transformer secondary side voltage, the current source are used to export necessarily Adjustable amplitude current signal in frequency range；The primary side voltage measurement unit, secondary side current measuring unit and secondary Side voltage measurement unit electrically connects with the computing module.
The invention also provides a kind of line mutual-ground capacitor using line mutual-ground capacitor parameter measurement system as described above Measurement method of parameters, comprise the following steps：
1) the adjustable amplitude current signal of two kinds of different frequencies is exported using the current source, can by the transmission line Amplitude modulation value current signal transfer will be made to stop to the injection transformer positioned at the loop to be measured of the injection transformer primary side Fortune processing；The secondary side current voltage signal and primary side voltage signal of the injection transformer are measured respectively, described in calculating Each component of exciting impedance of injection transformer obtains each component with applying outside with the change and fitting of applied voltage amplitude and frequency The functional relation of voltage magnitude and frequency, finally give the nonlinear characteristic of the injection transformer exciting impedance；
2) loop to be measured is put into operation, injects two kinds not to the injection transformer secondary side using current source Same frequency current signal, the voltage and current signal of the injection port of the injection transformer is measured, according to the frequency of applied voltage Exciting impedance is back-calculated to obtain with amplitude；
3) line mutual-ground capacitor is calculated using the vectorial calculating method of single-frequency or the amplitude calculating method of two kinds of combination of frequencies Parameter.
Further, in the step 1), excitatory resistance R is obtained using curve matchingmWith magnetizing inductance LmIn each frequency section Point ωiFunctional relation under (i=1,2,3 ..., n) between applied voltage amplitude u：
The functional relation is read in into the computing module.
Further, in the step 2), according to the frequencies omega of applied voltagei(i=1,2,3 ..., n) and amplitude ui(i= 1,2,3 ..., n) it is back-calculated to obtain exciting impedance：
Further, line mutual-ground capacitor parameter is calculated using the vectorial calculating method of single-frequency, then：
Wherein, ω is the frequency of applied voltage；For to impedanceImaginary part is taken to handle.
For line-to-ground impedance, and：
Wherein,It is vectorial for injection transformer secondary side current,For injection transformer secondary side voltage vector,For note Enter transformer excitation impedance,It is the known portions in line impedance (because line impedance is compared to line-to-ground impedance It is smaller, therefore unknown portions can be neglected).
Further, line mutual-ground capacitor parameter is calculated using the amplitude calculating method of two kinds of combination of frequencies, then：
Wherein, A=M2Z0 2–2PRMR0–2PXMX0–1；
B=PXM–M2X0, Z0 2=R0 2+ω2L0 2；
PRM=Rm/(Rm 2+Xm 2), PXM=Xm/(Rm 2+Xm 2)；
Due to excitatory resistance RmWith magnetizing inductance LmChange with applied voltage frequency f and change, therefore PRMAnd PXMBe with outside Apply the related coefficients of electric voltage frequency f, when f is determined, RmAnd XmIt is determined that PRMAnd PXMConstant can be regarded as；Z0For line impedance In known portions mould；R0For the resistive component of the known portions in line impedance；X0For the known portions in line impedance Reactive component；ω1And ω2Respectively two kinds different applied voltage frequencies；A1And A2Respectively coefficient A is in ω1And ω2Under Value；B1And B2Respectively coefficient B is in ω1And ω2Under value.
The beneficial effects of the present invention are：
1) measurement accuracy is high, overcomes the non-linear influence to measurement result of injection transformer exciting impedance, improves meter Calculate model；
2) because modified measuring method has taken the influence of the exciting impedance of injection transformer into account, therefore electricity is injected The scope of application of the frequency of stream is wider, and this point is verified by high pressure simulation experiment；
3) it is directed to any kind of injection transformer under voltage class, it is only necessary to when line-to-ground parameter measurement instrument puts into operation The influence that the difference of different type injection transformer is brought to calculating can be eliminated by obtaining its exciting impedance nonlinear characteristic, therefore Relax the model limitation of injection transformer；
4) it is applicable for different grounding modes.
Brief description of the drawings
In order that the purpose of the present invention, technical scheme and beneficial effect are clearer, the present invention provides drawings described below and carried out Explanation：
Fig. 1 is the structural representation of line mutual-ground capacitor parameter measurement system embodiment of the present invention；
Fig. 2 be remove secondary side current voltage measurement unit after line mutual-ground capacitor parameter measurement system structural representation Figure；
Fig. 3 is the equivalent circuit diagram of the line mutual-ground capacitor parameter measurement system of the present embodiment, wherein all parameters are Convert secondary side.
Fig. 4 is 10kV simulated test test loop schematic diagrames.
Embodiment
The invention will be further described with specific embodiment below in conjunction with the accompanying drawings, so that those skilled in the art can be with It is better understood from the present invention and can be practiced, but illustrated embodiment is not as a limitation of the invention.
As shown in figure 1, the structural representation for line mutual-ground capacitor parameter measurement system embodiment of the present invention.The present embodiment Line mutual-ground capacitor parameter measurement system, including injection transformer 4 and computing module 2, the primary side of the injection transformer 4 Provided with primary side voltage measurement unit 7, the secondary side of the injection transformer 4 is provided with input line 3, in input line 3 Current source 1, the secondary side current measuring unit 6 for measuring the secondary side current of injection transformer 4 and for measure inject transformation The secondary side voltage measurement unit 5 of the secondary side voltage of device 4, the current source 1 are used to export the width-adjustable in the range of certain frequency It is worth current signal；The primary side voltage measurement unit 7, secondary side current measuring unit 6 and secondary side voltage measurement unit 5 are equal Electrically connected with the computing module 2.
Current source 1 exports the adjustable amplitude current signal in the range of certain frequency, by transmission line 3 by current signal transfer To injection transformer 4, measured by the secondary side voltage measurement unit 5 and secondary side current that are arranged on injection transformer secondary side The voltage and current signal of injection port (secondary side) is converted into data signal by unit 6, is handled and is obtained accordingly through computing module 2 The voltage x current of frequency, line mutual-ground capacitor is calculated finally by modified computation model.
Specifically, the line mutual-ground capacitor parameter measurement side of the line mutual-ground capacitor parameter measurement system using the present embodiment Method, comprise the following steps：
1) the adjustable amplitude current signal of two kinds of different frequencies is exported using the current source, can by the transmission line Amplitude modulation value current signal transfer will be made to stop to the injection transformer positioned at the loop to be measured of the injection transformer primary side Fortune processing；The secondary side current voltage signal and primary side voltage and current signal of the injection transformer are measured respectively, are calculated Each component of exciting impedance of the injection transformer with applied voltage amplitude and frequency change and be fitted obtain each component with The functional relation of applied voltage amplitude and frequency, finally give the nonlinear characteristic of the injection transformer exciting impedance；
Specifically, in the step 1), stoppage in transit processing is made into loop to be measured, 2 frequency sections are chosen in 0-120Hz Point, the current signal of corresponding frequencies is exported using current source 1, current signal is delivered to injection transformer 4 through transmission line 3, secondary Side voltage measurement unit 5 measures secondary side voltage signal, and secondary side current measuring unit 6 and primary side voltage measurement unit 7 divide Ce Liang not secondary side and primary side current signal；10 equally distributed voltage nodes are chosen in 0-100V, adjust output current Size, it is ensured that at least 10 significant figure strong points under each frequency node, the number of each frequency node is handled using computing module 2 According to using the excitatory resistance R of curve matching acquisitionmWith magnetizing inductance LmIn each frequency node ωi(i=1,2,3 ..., n) under With the functional relation between applied voltage amplitude u：
The functional relation is read in into the computing module.
2) loop to be measured is put into operation, injects two kinds not to the injection transformer secondary side using current source Same frequency current signal, the voltage and current signal of the injection port of the injection transformer is measured, according to the frequency of applied voltage ωi(i=1,2,3 ..., n) and amplitude ui(i=1,2,3 ..., n) it is back-calculated to obtain exciting impedance；
3) line mutual-ground capacitor is calculated using the vectorial calculating method of single-frequency or the amplitude calculating method of two kinds of combination of frequencies Parameter.
Specifically, the present embodiment calculates line mutual-ground capacitor parameter using the vectorial calculating method of single-frequency, then：
Wherein, ω is the frequency of applied voltage；For to impedanceImaginary part is taken to handle.
For line-to-ground impedance, and：
Wherein,It is vectorial for injection transformer secondary side current,For injection transformer secondary side voltage vector,For note Enter transformer excitation impedance,It is the known portions in line impedance (because line impedance is compared to line-to-ground impedance It is smaller, therefore unknown portions can be neglected).
It is, of course, also possible to calculate line mutual-ground capacitor parameter using the amplitude calculating method of two kinds of combination of frequencies, its method is：
Wherein, A=M2Z0 2–2PRMR0–2PXMX0–1；
B=PXM–M2X0, Z0 2=R0 2+ω2L0 2；
PRM=Rm/(Rm 2+Xm 2), PXM=Xm/(Rm 2+Xm 2)；
Due to excitatory resistance RmWith magnetizing inductance LmChange with applied voltage frequency f and change, therefore PRMAnd PXMBe with outside Apply the related coefficients of electric voltage frequency f, when f is determined, RmAnd XmIt is determined that PRMAnd PXMConstant can be regarded as；Z0For line impedance In known portions mould；R0For the resistive component of the known portions in line impedance；X0For the known portions in line impedance Reactive component；ω1And ω2Respectively two kinds different applied voltage frequencies；A1And A2Respectively coefficient A is in ω1And ω2Under Value；B1And B2Respectively coefficient B is in ω1And ω2Under value.
It should be noted that when system neutral is earth-free or through low resistance grounding, injection transformer can elect mother as Line PT, when system neutral is through arc suppression coil, injection transformer can elect bus PT as.
When system neutral is through grounding through arc, the optional isolating transformer for sealing in zero sequence loop is injection transformation Device.Embodiment 1 is one 10kV test platform analog line direct-to-ground capacitance parameters of measurement, by the injection transformation for sealing in zero sequence loop Device injects alien frequencies signal into zero sequence loop, and wiring is as shown in Figure 4.It is single under different capacitances on analogue test platform The result of calculation of the vectorial calculating method of frequency is as shown in table 1；And the result of calculation of the amplitude calculating method of two kinds of combination of frequencies such as table 2 It is shown.When using the vectorial calculating method of single-frequency, injected frequency is recommended in the range of 20Hz~60Hz, now maximum relative Error is 3.77%, when using the amplitude calculating method of two kinds of combination of frequencies, recommend 40Hz＆60Hz and 40Hz＆80Hz both Combination of frequency, now maximum relative error is 2.55%.
The result of calculation of the vectorial calculating method of single-frequency under 1 different capacitances of table
The amplitude result of calculation of the amplitude calculating method of two kinds of combination of frequencies under 2 different capacitances of table
Tested and found by above-mentioned 10kV test platforms, when injected frequency is in the range of 20Hz~60Hz or injected frequency is During both combination of frequencies of 40Hz＆60Hz and 40Hz＆80Hz, it can be met using vectorial calculating method or amplitude calculating method The measurement result of field application.Therefore, the measurement result of the system and method for the present embodiment disclosure satisfy that the demand of field application.
Embodiment described above is only to absolutely prove preferred embodiment that is of the invention and being lifted, protection model of the invention Enclose not limited to this.The equivalent substitute or conversion that those skilled in the art are made on the basis of the present invention, in the present invention Protection domain within.Protection scope of the present invention is defined by claims.

Claims (6)

  1. A kind of 1. line mutual-ground capacitor parameter measurement system, it is characterised in that：Including injection transformer and computing module, the note The primary side for entering transformer is provided with primary side voltage measurement unit, and the secondary side of the injection transformer is provided with input line, installation Current source in the input line, the secondary side current measuring unit for measuring injection transformer secondary side current and it is used for The secondary side voltage measurement unit of injection transformer secondary side voltage is measured, the current source is used to export in the range of certain frequency Adjustable amplitude current signal；The primary side voltage measurement unit, secondary side current measuring unit and secondary side voltage measurement Unit electrically connects with the computing module.
  2. A kind of 2. line mutual-ground capacitor parameter measurement side using line mutual-ground capacitor parameter measurement system as claimed in claim 1 Method, it is characterised in that：Comprise the following steps：
    1) the adjustable amplitude current signal of two kinds of different frequencies is exported using the current source, by the transmission line by width-adjustable It is worth current signal transfer to the injection transformer, will makees positioned at the loop to be measured of the injection transformer primary side at stoppage in transit Reason；The secondary side current voltage signal and primary side voltage signal of the injection transformer are measured respectively, calculate the injection Each component of exciting impedance of transformer obtains each component and applied voltage with the change and fitting of applied voltage amplitude and frequency The functional relation of amplitude and frequency, finally give the nonlinear characteristic of the injection transformer exciting impedance；
    2) loop to be measured is put into operation, injects two kinds of different frequencies to the injection transformer secondary side using current source Rate current signal, the voltage and current signal of the injection port of the injection transformer is measured, according to the frequency and width of applied voltage Value is back-calculated to obtain exciting impedance；
    3) line mutual-ground capacitor parameter is calculated using the vectorial calculating method of single-frequency or the amplitude calculating method of two kinds of combination of frequencies.
  3. 3. line mutual-ground capacitor measurement method of parameters according to claim 2, it is characterised in that：In the step 1), adopt Excitatory resistance R is obtained with curve matchingmWith magnetizing inductance LmIn each frequency node ωiWith applying outside under (i=1,2,3 ..., n) Functional relation between voltage magnitude u：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>&amp;omega;</mi> <mo>=</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>(</mo> <mi>u</mi> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow> <mi>&amp;omega;</mi> <mo>=</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>(</mo> <mi>u</mi> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>
    The functional relation is read in into the computing module.
  4. 4. line mutual-ground capacitor measurement method of parameters according to claim 2, it is characterised in that：In the step 2), root According to the frequencies omega of applied voltagei(i=1,2,3 ..., n) and amplitude ui(i=1,2,3 ..., n) it is back-calculated to obtain exciting impedance：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>m</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>&amp;omega;</mi> <mo>=</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>(</mo> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>L</mi> <mrow> <mi>m</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>g</mi> <mrow> <mi>&amp;omega;</mi> <mo>=</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>(</mo> <msub> <mi>u</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
  5. 5. line mutual-ground capacitor measurement method of parameters according to claim 2, it is characterised in that：Using single-frequency to Gauge algorithm calculates line mutual-ground capacitor parameter, then：
    <mrow> <mi>C</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mi>&amp;omega;</mi> <mi>Im</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>Z</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    Wherein, ω is the frequency of applied voltage；For to impedanceImaginary part is taken to handle.
    For line-to-ground impedance, and：
    <mrow> <msub> <mover> <mi>Z</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> <msub> <mover> <mi>Z</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msub> </mrow> <mrow> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <msub> <mover> <mi>Z</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msub> <mo>-</mo> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> </mrow> </mfrac> <mo>-</mo> <msub> <mover> <mi>Z</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>0</mn> </msub> </mrow>
    Wherein,It is vectorial for injection transformer secondary side current,For injection transformer secondary side voltage vector,Become for injection Depressor exciting impedance,It is the known portions in line impedance (because line impedance is compared to line-to-ground impedanceIt is smaller, Therefore unknown portions can be neglected).
  6. 6. line mutual-ground capacitor measurement method of parameters according to claim 2, it is characterised in that：Utilize two kinds of combination of frequencies Amplitude calculating method calculate line mutual-ground capacitor parameter, then：
    <mrow> <mi>C</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <msup> <msub> <mi>&amp;omega;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <msup> <msub> <mi>M</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <msup> <msub> <mi>&amp;omega;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <msup> <msub> <mi>M</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <msub> <mi>B</mi> <mn>1</mn> </msub> <msub> <mi>&amp;omega;</mi> <mn>1</mn> </msub> <msup> <msub> <mi>&amp;omega;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <msub> <mi>B</mi> <mn>2</mn> </msub> <msup> <msub> <mi>&amp;omega;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <msub> <mi>&amp;omega;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    Wherein, A=M2Z0 2–2PRMR0–2PXMX0–1；
    B=PXM–M2X0, Z0 2=R0 2+ω2L0 2；
    PRM=Rm/(Rm 2+Xm 2), PXM=Xm/(Rm 2+Xm 2)；
    <mrow> <msup> <mi>M</mi> <mn>2</mn> </msup> <mo>=</mo> <mo>|</mo> <mfrac> <mover> <mi>I</mi> <mo>&amp;CenterDot;</mo> </mover> <mover> <mi>U</mi> <mo>&amp;CenterDot;</mo> </mover> </mfrac> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msup> <msub> <mi>R</mi> <mi>m</mi> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>X</mi> <mi>m</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
    Due to excitatory resistance RmWith magnetizing inductance LmChange with applied voltage frequency f and change, therefore PRMAnd PXMIt is with applying electricity outside Coefficient related voltage-frequency rate f, when f is determined, RmAnd XmIt is determined that PRMAnd PXMConstant can be regarded as；Z0For in line impedance The mould of known portions；R0For the resistive component of the known portions in line impedance；X0For the reactance of the known portions in line impedance Component；ω1And ω2Respectively two kinds different applied voltage frequencies；A1And A2Respectively coefficient A is in ω1And ω2Under value；B1 And B2Respectively coefficient B is in ω1And ω2Under value.
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