KR20160116525A - Method for determining parameter of Randless Equivalent Circuit - Google Patents

Method for determining parameter of Randless Equivalent Circuit Download PDF

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KR20160116525A
KR20160116525A KR1020150044364A KR20150044364A KR20160116525A KR 20160116525 A KR20160116525 A KR 20160116525A KR 1020150044364 A KR1020150044364 A KR 1020150044364A KR 20150044364 A KR20150044364 A KR 20150044364A KR 20160116525 A KR20160116525 A KR 20160116525A
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frequency
complex impedance
equivalent circuit
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measured
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KR101691290B1 (en
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김효성
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공주대학교 산학협력단
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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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • 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
    • G01R27/16—Measuring impedance of element or network through which a current is passing from another source, e.g. cable, power line
    • G01R31/3662—

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Abstract

Provided is a parameter determining method of a Randles equivalent circuit. The parameter determining method of a Randles equivalent circuit according to an embodiment of the present invention comprises: a step of determining a first input frequency and a second input frequency, which respectively display a negative number and a positive number of an imaginary number part of a complex impedance measured for a target, by using a phase angle of a complex impedance and a property graph of frequencies; a first calculation step for calculating series resistance of the Randles equivalent circuit based on a first complex impedance and a second complex impedance measured for each of two frequencies smaller than the first input frequency by a predetermined ratio; a second calculation step for calculating the bottom frequency in which the size of a real number part and the size of an imaginary number part become the same in a target complex impedance based on the calculated series resistance, and for calculating parallel resistance and capacitance of the Randles equivalent circuit based on a third complex impedance measured for the target in the bottom frequency; and a third calculation step for calculating a zero-point frequency in which a phase angle of the complex impedance converges to 90 degrees based on a fourth complex impedance measured in the second input frequency, and for calculating series inductance of the Randles equivalent circuit based on the zero-point frequency.

Description

[0001] The present invention relates to a method of determining a parameter of a Randless Equivalent Circuit

The present invention relates to a method of determining parameters of a LANDEL equivalent circuit.

Generally, a method of measuring the impedance of a measurement object is to apply an external power source having a specific frequency to measure both voltage and current of the measurement object, and to calculate the impedance using the measured voltage and current. At this time, when the measurement object includes an inductance or a capacitance component other than the resistance, the complex impedance consisting of the real part and the imaginary part is calculated. Here, since the impedance changes depending on the frequency of the inductance and the capacitance, the measurement object is replaced with an equivalent circuit, and a power source having the reference frequencies is applied to extract the parameters of the equivalent circuit to measure the complex impedance of the measurement object.

When an object to be measured is represented by an equivalent circuit in this way, it is determined in consideration of the characteristics of the object to be measured. For example, when impedance of the battery is measured nondestructively or live wire insulation resistance is measured by a sinusoidal method, do.

In general, a LANDEL equivalent circuit consists of a series inductance L s , a series resistance R t , a parallel resistance R ins , and a capacitance C e . The measurement of the impedance of the object to be measured by using the LAN-equivalent circuit is performed by extracting these parameters.

However, in order to effectively extract the parameters of the LAN-equivalent circuit, it is necessary to apply the zero frequency (f 0 ) and the bottom frequency (f π / 4 ) representing the characteristics of the LANEL equivalent circuit. However, It is cumbersome and time consuming.

Accordingly, there is a demand for a parameter extraction method capable of performing parameter extraction of the LANDEL equivalent circuit at a high speed by linking the determination of the frequency of the power source applied to extract the parameters of the LANDEL equivalent circuit and the parameter calculation through the determined frequency.

KR 2007-0097623 A

In order to solve the problems of the prior art as described above, one embodiment of the present invention is a method of determining a parameter of a LANDEL equivalent circuit capable of easily extracting a parameter of a LANDEL equivalent circuit used for measuring an impedance of a measurement object at a high speed .

According to an aspect of the present invention for solving the above problems, there is provided a method of determining a parameter of a LANDEL equivalent circuit for measuring an impedance of an object to be electrically analyzed. The parameter determination method of the LANDEL equivalent circuit determines a first input frequency representing a negative number of imaginary parts of the complex impedance measured for the object and a second input frequency representing a positive number using a characteristic graph of the phase angle and the frequency of the complex impedance step; A first calculation step of calculating a series resistance of the Randel equivalent circuit based on the first complex impedance and the second complex impedance measured for the object at each of two frequencies smaller than the first input frequency by a certain ratio; Calculating a bottom frequency at which the phase angle of the complex impedance of the object is 45 degrees based on the calculated series resistance and calculating a parallel resistance of the Randel equivalent circuit based on the third complex impedance measured for the object at the bottom frequency and A second calculation step of calculating a capacitance; And a controller for calculating a zero point frequency at which the phase angle of the complex impedance converges at 90 degrees based on the fourth complex impedance measured at the second input frequency and calculating a serial inductance of the RANEL equivalent circuit based on the zero point frequency 3 calculation step.

In one embodiment, the determining comprises: determining whether the imaginary part of the complex impedance measured for the object at any frequency is negative; A second step of reducing the imaginary number by a predetermined ratio if the imaginary number is not negative; And a third step of remeasuring the object with respect to the reduced frequency, wherein the first to third steps can be repeated until the imaginary number of the complex impedance measured for the object becomes negative have.

In one embodiment, the determining comprises: determining whether the imaginary number of the complex impedance measured for the object at any frequency is positive; A fifth step of increasing the imaginary number by a predetermined ratio if the imaginary number is not negative; And a sixth step of remeasuring the object with respect to the reduced frequency, wherein the fourth to sixth steps can be repeated until the imaginary number of the measured complex impedance of the object becomes positive have.

In one embodiment, the measurement frequency of the second complex impedance may be smaller than the measurement frequency of the first complex impedance by a certain ratio.

In one embodiment, the first calculating step calculates the series resistance (Rt) by the following equation,

Figure pat00001

Here, f 1, Z re1, and Z im1 is each of the first and the complex impedance measurement frequency, the real part and the imaginary part of, f 2, Z re2, and Z im2 each said second measured frequency of the complex impedance, the real Can be negative and imaginary parts.

In one embodiment, the second calculating step

Figure pat00002
And
Figure pat00003
The floor frequency f ? / 4 can be calculated.

In one embodiment, the second calculating step calculates the parallel resistance (R ins ) by the following equation,

Figure pat00004

Where Z re and Z im may be the real and imaginary parts of the impedance measured at the bottom frequency, respectively.

In one embodiment, the second calculating step

Figure pat00005
The capacitance C e can be calculated.

In one embodiment, the third calculation step may be performed while measuring the complex impedance with the initial value of the current frequency f k as the second input frequency

Figure pat00006
The frequency (f k +1 ) at which the phase angle of the complex impedance converges at 90 degrees is determined as the zero point frequency (f 0 )

here,

Figure pat00007
And
Figure pat00008
Is a real part and an imaginary part of the complex impedance measured for the object at the current frequency f k , and K can be a convergence factor obtained by the Newton-Rhapson numerical analysis method.

In one embodiment, the third calculation step may be performed while measuring the complex impedance with the initial value of the current frequency f k as the second input frequency

Figure pat00009
The frequency (f k +1 ) at which the phase angle of the complex impedance converges at 90 degrees is determined as the zero point frequency (f 0 )

here,

Figure pat00010
And
Figure pat00011
Is a real part and an imaginary part of the complex impedance measured for the object at the current frequency f k , and K can be a convergence factor obtained by the Newton-Rhapson numerical analysis method.

In one embodiment, the third calculating step

Figure pat00012
So that the series inductance can be calculated.

The method of determining the parameters of the LAN-Led Equivalent Circuit according to an embodiment of the present invention includes determining the frequency of the complex impedance | tan | It is possible to search the frequency suitable for the measurement by using the characteristic graph, and to extract the parameter of the LANDEL equivalent circuit easily at a high speed according to the detected frequency, so that the parameter extraction time can be reduced.

Further, the parameter determination method of the LANDEL equivalent circuit of the present invention is characterized in that the frequency- The zero point frequency (f 0 ) and the bottom frequency (f π / 4 ), which characterize the LANDEL equivalent circuit, can be easily determined by repeated search according to the characteristic graph, and the accuracy of parameter extraction can be improved.

1 is a circuit diagram showing a LANDEL equivalent circuit.
2 is a diagram showing a complex impedance-frequency spectrum locus of a LANDEL equivalent circuit on a complex plane.
Fig. 3 is a diagram showing a complex impedance-frequency spectrum trajectory of a circuit excluding the series resistance (R t ) on the complex plane in the LANDEL equivalent circuit of Fig.
Figs. 4 and 5 show the frequency-tan? Relationship of the complex impedance according to the frequency when the series inductance L s of the Randel-equivalent circuit is increased by 10 times by 0.47 [mH], 4.7 [mH], and 47 [mH] Fig.
Figs. 6 and 7 show the frequency-tan? Relationship of the complex impedance according to the frequency when the capacitance C e of the LANDel equivalent circuit is increased 10 times by 5 [uF], 50 [uF], and 500 [uF] FIG.
Figures 8 and 9 show the capacitance (C e ) of the Randel- In the vicinity of the zero point frequency, the frequency-tan? Relation of the complex impedance according to the frequency when the series inductance (L s ) is increased by 10 times, respectively.
10 is a diagram showing the nature of a right triangle in contact with a circle to explain a principle of measuring the parallel resistance (R ins ) of the LANDEL equivalent circuit.
11 is a view for explaining a parallel resistance (R ins ) measurement algorithm of the LANDEL equivalent circuit using the nature of the semicircle shown in FIG.
12 is a view for explaining a capacitance (C e) measurement algorithms Randles equivalent circuit.
13 is a diagram showing a spectrum locus concept for explaining an appropriate measurement frequency estimation algorithm of the LANDEL equivalent circuit.
FIG. 14 is a diagram showing a result of a complex impedance frequency spectrum simulation of a LANDEL equivalent circuit under specific conditions. FIG.
Figs. 15 and 16 are diagrams showing tan?, Which is the slope of the imaginary part and imaginary part, in the complex impedance frequency spectrum of the LANDEL equivalent circuit.
17 is a diagram for explaining an appropriate measurement frequency estimation algorithm in a linear section of the frequency-tan? Characteristic of the LANDEL equivalent circuit.
18 is a frequency corresponding to the capacitance (C e) the value of the equivalent circuit of Randall - | shows a characteristic graph of | tanφ.
19 is a graph showing the relationship between the frequency - | tan? | In the range of 1.8 ° <? <89.8 ° shown in FIG. The graph is a log-scale graph of the characteristics.
20 is a diagram showing an impedance-frequency spectrum around the LC resonance frequency of the LANDEL equivalent circuit.
FIG. 21 is a flowchart illustrating a method of determining parameters of a LANDEL equivalent circuit according to an embodiment of the present invention.
FIG. 22 is a graph showing the relationship between the frequency of the LAN-LAN equivalent circuit represented by the log-log scale according to the capacitance C e - Fig.
23 is a flowchart showing a negative imaginary part frequency search method of FIG.
FIG. 24 is a diagram for explaining a frequency search algorithm of the parameter determination method of the LANDe equivalent circuit according to an embodiment of the present invention.
25 is a flowchart showing a method of calculating the series resistance (R t ) in FIG.
26 is a flowchart showing a method of calculating the parallel resistance (R ins ) and the capacitance (C e ) in FIG.
FIG. 27 is a flowchart showing a positive imaginary part frequency search method of FIG.
FIG. 28 is a flowchart showing a method of calculating the zero point frequency and the series inductance (L s ) of FIG.
29 is a schematic configuration diagram of a parameter determination system of a LANDEL equivalent circuit according to an embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings, which will be readily apparent to those skilled in the art to which the present invention pertains. The present invention may be embodied in many different forms and is not limited to the embodiments described herein. In order to clearly illustrate the present invention, parts not related to the description are omitted, and the same or similar components are denoted by the same reference numerals throughout the specification.

The present invention relates to a method for determining a parameter of a LANDEL equivalent circuit used when measuring the internal impedance of a battery in a non-destructive manner or measuring a live insulation resistance of a sinusoidal method.

The present invention can calculate a series resistance, a parallel resistance, a capacitance, and a series inductance forming a LANDEL equivalent circuit based on a phase angle (| tan? |) Of a complex impedance with respect to a LANDEL equivalent circuit and a frequency characteristic graph.

On the other hand, the characteristic curve of the frequency - | tan? | Of the complex impedance has a linear negative slope in a frequency section smaller than a zero point and a nonlinearity in a frequency section larger than a zero point based on a zero- And has an increasing positive slope.

The present invention proposes a method of determining the zero frequency and the bottom frequency in order to calculate the main parameters of the LANDEL equivalent circuit using the characteristics of the complex impedance of - tan | At this time, the series inductance (L s ) and capacitance (C e ) can be obtained automatically by knowing the zero frequency (f 0 ) and the bottom frequency (f π / 4 ). Here, the zero frequency f 0 is a case where the phase angle φ of the complex impedance is 90 ° and the bottom frequency f π / 4 is the case where the phase angle φ of the complex impedance is 45 °.

Hereinafter, the theoretical background of the present invention will be described first, and then a method for determining parameters of the LAND equivalent circuit according to an embodiment of the present invention will be described.

1, the LANDEL equivalent circuit includes a series resistance component R t , a parallel resistance component R ins , and a capacitance C e , and the inductance L s is a parasitic inductance of the circuit or a low frequency band Corresponds to the sum of the inductances for the pass filter. Here, for the measurement of non-destructive resistance or impedance, a battery or a power line may be assumed as a LANDEL equivalent circuit as shown in FIG.

The following analytical techniques can be applied to characterize the LANDEL equivalent circuit.

Complex  Impedance-frequency spectrum analysis

The characteristics of the LANDEL equivalent circuit can be found by interpreting the frequency characteristics of the LANDEL equivalent circuit impedance to the sinusoidal voltage. The following Equation 1 shows a process of calculating the complex impedance value of the LANDEL equivalent circuit shown in FIG.

[Formula 1]

Figure pat00013

Figure pat00014

Figure pat00015

When the impedance value according to the frequency of the LANDEL equivalent circuit is expressed in a complex plane, a semicircular frequency spectrum trajectory as shown in FIG. 2 is formed.

2, the complex impedance value of Randall equivalent circuit is the R t points to move to the left along the locus of a semicircle, as the very low-frequency access to the right jeomin semicircular trajectory R t + R ins and the frequency increases And when the frequency increases infinitely, it increases infinitely along the vertical line of the imaginary axis. The following equations 2, 3 and 4 show the complex impedance value of the LANDEL equivalent circuit at the main frequency.

[Formula 2]

Figure pat00016
when,
Figure pat00017

[Formula 3]

Figure pat00018
when,
Figure pat00019

[Formula 4]

Figure pat00020
when,
Figure pat00021

Randall complex impedance of Randall equivalent circuits other than the series resistance (R t), as shown, in Figure 3 except for the series resistance (R t) in the Randall equivalent circuit of Figure 1 in order to systematically analyze the equivalent circuit, the frequency spectrum The locus is a semicircle whose diameter is the parallel resistance value (R ins ).

The angle (phase angle?) Of a line segment passing through an arbitrary complex impedance coordinate having a semicircle locus at the origin shown in FIG. 3 can be defined by the following equation (5).

[Formula 5]

Figure pat00022

Typical values of the phase angle phi according to the applied frequency are expressed by the following equations (6) to (8). Where f 0 is the zero frequency and f π / 4 is the floor frequency.

[Formula 6]

Figure pat00023
when,
Figure pat00024

[Equation 7]

Figure pat00025
when,
Figure pat00026

[Equation 8]

Figure pat00027
when,
Figure pat00028

Serial Inductance s )on  The frequency- tan φ characteristics

The frequency-tan? Relationship of the complex impedance according to the frequency when the series inductance (L s ) of the LANDEL equivalent circuit is increased by 10 times by 0.47 [mH], 4.7 [mH], and 47 [mH] do.

As shown in FIG. 4, it can be seen that the imaginary number of impedances at a frequency inversely proportional to the square root of the series inductance (L s ) shifts from a negative value to a positive value. The frequency at which the imaginary number of the complex impedance is at the boundary between the negative value and the positive value (that is, when the imaginary part is zero) is defined as a zero frequency (f 0 )

Figure pat00029
.

Capacitance e )on  The frequency- tan φ characteristics

The frequency-tan? Relationship of the complex impedance according to the frequency is shown in Figs. 6 and 7 when the capacitance (C e ) of the LANDEL equivalent circuit is increased by 10 times by 5 [uF], 50 [uF], and 500 [uF] .

As shown in FIG. 6, it can be seen that the value of the imaginary impedance component is zero in a frequency band that is inversely proportional to the square root of the capacitance C e . This is because the zero point frequency (f 0 ), which is the frequency when the imaginary part of the complex impedance is on the boundary line between the negative value and the positive value

Figure pat00030
.

Figures 8 and 9 show the capacitance (C e ) of the Randel- And the frequency-tan? Relation of the complex impedance according to the frequency when the series inductance (L s ) is increased by 10 times, respectively, in the vicinity of the zero point frequency (f 0 ). For convenience, the frequency axis is used as the logarithmic scale to observe the position of the zero point frequency according to the parameter value.

Parallel Resistance ( R ins ) Measurement algorithm

The parallel resistance (R ins ) measurement of the LANDEL equivalent circuit utilizes the semicircular nature of the impedance trace of the LANDEL equivalent circuit.

In FIG. 10, when the straight line EF is a line segment passing through the center of the circle, the angle at which the line segment DE and the line segment DF meet at an arbitrary point D located in the circle arc is always perpendicular. Therefore, it can be seen that the triangle formed by point D, point E, and point F is a right triangle with a hypotenuse of the diameter of the circle. This means that the triangle formed by any one point of the diameter and the locus of the circle is always a right triangle in contact with the circle.

11 is a view for explaining a parallel resistance (R ins ) measurement algorithm of the LANDEL equivalent circuit using the nature of the semicircle shown in FIG. In order to facilitate understanding, the semicircle existing on the complex plane is moved parallel to the real axis and placed at the origin, and the real part and the imaginary part of the complex impedance at an arbitrary frequency (f a ) In other words,

Figure pat00031
,
Figure pat00032
).

The size (distance) of the parallel resistor (R ins ) is equal to the length of the hypotenuse of a right triangle that is tangent to a semicircle. The following equations (9) and (10) describe the angle between the hypotenuse and the base of a right triangle intersecting with a semicircle. Using the equations (9) and (10), the measurement algorithm for the parallel resistor (R ins ) is derived.

[Equation 9]

Figure pat00033

[Equation 10]

Figure pat00034

[Equation 11]

Figure pat00035

Capacitance ( C e ) Measurement algorithm

The measurement of the capacitance (C e ) of the Randel equivalent circuit also utilizes the semicircular nature of the complex impedance trajectory of the Randel equivalent circuit. In the case of the measurement of the parallel resistance (R ins ) of the Randel-equivalent circuit, the distance (magnitude) of the complex impedance present in the semicircle's locus is an important measurement element but the measurement of the capacitance (C e ) The complex impedance and the slope of the origin are important measurement factors.

In Figure 12, the coordinates of the complex impedance in the trajectory of the semicircle are (

Figure pat00036
,
Figure pat00037
), And the angle between the coordinate and the origin is the same as the angle φ between the base of the right triangle and the hypotenuse. At this time, the slope of the coordinate and the origin means tan ?. The following Expression 12 shows impedance analysis of tan?.

[Equation 12]

Figure pat00038

Figure pat00039
(only,
Figure pat00040
)

Equation (12) implies that the slope between the impedance coordinate in the semicircle's trajectory and the origin of the complex plane is dependent on the parallel resistance, the measurement frequency, and the capacitance. The equation (12) is summarized with respect to the capacitance, and a capacitance ( Ce ) measurement algorithm as shown in the following Equation 13 is derived.

[Formula 13]

Figure pat00041

The capacitance value of Equation 13 indicates that it is dependent on the parallel resistance (R ins ), which means that the parallel resistance (R ins ) measurement should precede the capacitance measurement.

Optimum measuring frequency estimation algorithm

13 is a diagram showing a spectrum locus concept for explaining an appropriate measurement frequency estimation algorithm of the LANDEL equivalent circuit. In the above description, the parallel resistance (R ins ) and the capacitance (C e ) of the LANDEL equivalent circuit were measured using impedance according to frequency. In this case, the angle of the complex impedance and the origin, φ, is in the range of 0 to 90 °. At the point indicating the right end of the semicircle locus, φ has a value of 0, φ has 45 °. Also, φ at the origin has 90 °.

Considering that the real part of the impedance and the imaginary part have the same value, the value of φ for measuring the parallel resistance (R ins ) and the capacitance (C e ) is preferably 45 °. However, it is not necessary to set the frequency to be 45 ° exactly, and it should be possible to measure within an appropriate error range if it is adjusted to approximately 45 ° ± 15 °. However, in the case of < 45 DEG, the frequency becomes unnecessarily small and the measuring time may take a long time. Therefore, it is preferable to determine the frequency so that? Is approximately 45 to 60 degrees. If φ> 60 °, the real part of the impedance and the imaginary part become very small, and the impedance analysis is not easy.

13 shows an impedance spectrum portion in which? Is in a range of 45 to 60 in green to indicate an appropriate measurement frequency band, and an impedance spectrum portion in which? Is in a range of 60 to 90 is displayed in red to indicate that it is an inadequate measurement frequency band have. At the bottom frequency (f 0 ), which is the optimal measurement frequency, φ is 45 °, making it easiest to measure the parallel resistance (R ins ) and capacitance (C e ) of the Lane Equivalent Circuit, where the real part of the complex impedance and the imaginary part The size

Figure pat00042
. The following example illustrates a suitable measurement frequency tracking algorithm as a simulation example.

FIG. 14 is a diagram showing a result of a complex impedance frequency spectrum simulation of a LANDEL equivalent circuit under specific conditions. FIG. In particular, the simulation results of Fig. 14 is executed under the condition of 4.7 mH inductance (L s), the 50 ㎌ capacitance (C e), the series resistance (R t) and a parallel resistance of 100 ㏀ of 270 ㏀ (R ins) of .

As a result of the simulation results shown in FIG. 14, it can be confirmed that the complex impedance spectrum of the LANDEL equivalent circuit has a semicircular shape as the frequency changes as described above.

In the complex impedance frequency spectrum, the slope tan? Of the real part and the imaginary part can be expressed by the following Equation 14, and the characteristics as shown in Figs. 15 and 16 are shown as the frequency changes.

[Equation 14]

Figure pat00043

The graph of the frequency-tan phi shown in FIG. 15 is nonlinear as a whole, but the range of the frequency of 0.001 to 100 Hz shows a nearly linear characteristic as shown in FIG. FIG. 16 is an enlarged view of the frequency range of 0.001 to 100 Hz in FIG. 15, and Table 1 below shows numerical values of the change of tan? According to the change of the interval of 0.001 to 100 Hz.

Frequency (f) tanφ φ (degree) 0.001 -0.03141 -1.7994 ° 0.002 -0.06283 -3.5952 ° 0.004 -0.09424 -5.3840 ° 0.008 -0.15707 -8.9270 ° 0.01 -0.3141 -17.440 ° 0.02 -0.6283 -32.141 DEG 0.32 -1.0053 -45.152 ° 0.04 -1.5707 -57.518 ° 0.08 -2.1991 -65.547 ° 0.1 -3.141 -72.343 DEG One -31.41 -88.176 [deg.] 10 -313.8 -89.817 ° 100 -2850.1 -89.97 [deg.]

As can be seen in FIG. 16 and Table 1, at a frequency range of 0.001 to 100 Hz, tan? Changes substantially linearly with respect to frequency, which corresponds to a range of 1.8 to 90 degrees in terms of angle, 0.03 to 3,000. In the linear section of the frequency-tan φ characteristic, Equation (13) is summarized for tan φ.

[Formula 15]

Figure pat00044

Therefore, the frequency estimation method as shown in FIG. 17 is possible in a linear region of the frequency-tan? Characteristic of the LANDEL equivalent circuit.

17 is a diagram for explaining an appropriate measurement frequency estimation algorithm in a linear section of the frequency-tan? Characteristic of the LANDEL equivalent circuit.

First, according to a sinusoidal type having an arbitrary test frequency f 1 | measures | tanφ 1. In this case, the magnitude of | tan? 1 | can be calculated as shown in Equation 16 below.

[Formula 16]

Figure pat00045

[pi] Next, we calculate | tan? aim | for the target phase angle. In this case, the magnitude of | tan? Aim | can be calculated as shown in Equation 17 below.

[Formula 17]

Figure pat00046

17, the ratio of | tan? | To the frequency f is the same, so that the target frequency of the complex impedance having the desired | tan | have.

[Formula 18]

Figure pat00047

For example, the bottom frequency f π / 4 of the complex impedance of the Lane's equivalent circuit with φ = 45 ° can be estimated as follows:

[Formula 19]

Figure pat00048

(R ins ) of the LANE equivalent circuit by applying the real part (Z re ) and the imaginary part (Z im ) of the complex impedance measured in the corresponding frequency band to the above-described equations (111) and (13) And the capacitance can be calculated.

18 is a frequency corresponding to the capacitance (C e) the value of the equivalent circuit of Randall - | shows a characteristic graph of | tanφ. Referring to FIG. 18, the frequency - | tan? The characteristic is nonlinear as a whole, but it exhibits a linear characteristic in a certain interval (for example, in the range of 8 ° <φ <89.8 °).

19 is a graph showing the relationship between the frequency - | tan? | In the range of 1.8 ° <? <89.8 ° shown in FIG. Is a graph showing the characteristics on a log scale. In Fig. 16, the slope of the frequency-tan? Characteristic changing linearly is negative, while the frequency-tan | The reason why the slope of the characteristic is positive is because the log scale conversion can not take a negative value due to the characteristics of the log, and therefore, tan | Therefore, Fig. 19 is opposite in direction to Fig. 16, but the changing characteristics are substantially the same. 19, the frequency - | tan? It can be seen that the characteristic graph is substantially linear. Also, as the value of capacitance (C e ) increases, It can be confirmed that the measurement frequency band having a value is inversely proportional.

Series resistance R t ) Measurement algorithm

The tan ratio of the complex impedance phase angle (φ) to the frequency of the LAND equivalent circuit measured around the appropriate frequency band is constant. In other words, the following equation (20) holds.

[Formula 20]

Figure pat00049

The series resistance R t can be measured according to the following Equation 21 and Equation 22 according to Equation 20. [

[Formula 21]

Figure pat00050

[Formula 22]

Figure pat00051

Serial inductance ( L s ) Measurement algorithm

The inductance component of the Randall equivalent circuit and the imaginary value of the complex impedance measured at the zero point frequency f o of the capacitance component become zero and the complex impedance at the zero point frequency f o becomes the value of the series resistance R t .

20 is a diagram showing an impedance-frequency spectrum around the LC resonance frequency of the LANDEL equivalent circuit. Referring to FIG. 20, the frequency-tan? Characteristic of a Lange equivalent circuit at a zero point frequency (f o ) with respect to a given series inductance (L s ) shows a monotonic increase characteristic as shown in FIGS. 8 and 9. Therefore, the zero point frequency f o can be found by the following method. That is, a new measurement frequency band (f k +1 ) is set according to the following equation (23) according to the real part and the imaginary part of the complex impedance measured in an arbitrary frequency band (f k ).

[Equation 23]

Figure pat00052

In Equation 23,

Figure pat00053
Is the real part of the currently measured complex impedance,
Figure pat00054
Is the imaginary part of the currently measured complex impedance, and K is the convergence coefficient obtained by the Newton-Raphson method.

By repeating Equation 23, the zero point frequency f o can be found.

Or the real part of the complex impedance near the zero point frequency (f o )

Figure pat00055
The zero point frequency can be found by the following equation (24).

[Equation 24]

Figure pat00056

In Equation 24,

Figure pat00057
Is the imaginary part of the currently measured complex impedance, and K is the convergence coefficient obtained by the Newton-Raphson method.

When the zero point frequency f o is found according to the above equation (23) or (24), the value of the series inductance (L s ) can be obtained by the following equation (25).

[Formula 25]

Figure pat00058

According to the above-described algorithm, the present invention provides a method that can more easily determine the parameters of the LANDEL equivalent circuit.

FIG. 21 is a flowchart illustrating a method of determining parameters of a LANDEL equivalent circuit according to an embodiment of the present invention.

A method 100 for determining a parameter of a LAND equivalent circuit according to an embodiment of the present invention includes a step S101 of searching for a frequency at which the measured complex impedance has a negative imaginary part, calculating a parallel resistor (R ins) and capacitance (C e) on the basis of the complex impedance measured at the step (S102), the bottom frequency (f π / 4) for calculating a series resistance (R t) on the basis of the complex impedance step (S103), consists of calculating a zero frequency step (S104), and the zero point frequency series inductance (L s) based on a (f 0) for searching a (f 0).

In order to more clearly explain the method of determining the parameters of the LANE equivalent circuit according to the embodiment of the present invention, Let's look at the characteristics in more detail.

Figure 22 is a capacitance (C e), if a value 10-fold different settings, log in the entire frequency domain of the frequency Randles equivalent circuit representation of a logarithmic scale - | tanφ | Fig.

22, the characteristic curve 1 indicated by blue is the largest value of the capacitance C e , and the characteristic curve 2 indicated by green is 10 times smaller than the characteristic curve 1, The characteristic curve 3 is the case where the value of the capacitance C e is the smallest and is 100 times smaller than the characteristic curve 1. In Fig. 22, the frequency band in which the characteristic curve in each case falls vertically is the zero point frequency (f o ).

For convenience, the zero point frequencies of the characteristic curves (1) to (3) are expressed as (f o1 ), (f o2 ) and (f o3 ), respectively. In Fig. 22, the magnitude of the zero point frequency for each characteristic curve is

Figure pat00059
, Which is proportional to the reciprocal of the square root of the value of the capacitance C e .

In each characteristic curve, the value of tanφ in the frequency domain smaller than the zero point frequency is negative, but the value of | tanφ | taking the absolute value is a positive number. In other words, the value of the characteristic curve located to the left of the zero point frequency (f o1 ), (f o2 ), (f o3 ) of each characteristic curve is actually negative. Therefore, in the frequency range sufficiently lower than the zero point frequency of each characteristic curve by 10 times or less, The slope of the characteristic curve is linear and has a negative value.

 Also, in the frequency range higher than the zero point frequency of each characteristic curve, The slope of the characteristic curve is nonlinear but has a monotonic increasing positive slope.

When? is 45 °, tan? = -1, and the bottom frequency at this time is

Figure pat00060
. The bottom frequency in the characteristic curve (1) in Fig. 22 is
Figure pat00061
, And the floor frequency in the characteristic curve (2) is
Figure pat00062
, And the bottom frequency in the characteristic curve 3 is
Figure pat00063
, It can be seen that the frequency is inversely proportional to the value of the capacitance C e , It can be seen that the slope of the characteristic curve is completely linear.

Here, it is very important to know the zero frequency (f o ) and the bottom frequency (f π / 4 ) in order to determine the parameters of the LANDEL equivalent circuit. This is because, when the parallel resistance value (R ins ) is known by knowing the zero frequency and the bottom frequency, the inductance (L s ) value and the capacitance (C e ) value can be automatically calculated.

21, the parameter determination method 100 of the LANDEL equivalent circuit of the embodiment of the present invention first calculates the imaginary number of the complex impedance measured for the object using the phase angle and frequency characteristic graph of the complex impedance, It is possible to determine a first input frequency indicating an additional negative number (step S101). In this case, by applying the bi-sectional search concept to the entire frequency band, the frequency band having a negative imaginary part in the frequency-tan? Characteristic graph can be searched as follows.

As shown in Fig. 23, the complex impedance can be measured for an object to be measured at an arbitrary initial set frequency, and the imaginary part (Z im ) of the measured complex impedance can be calculated (step S210).

Next, it can be determined whether the measured imaginary part (Z im ) of the complex impedance is negative (step S211). In this case, the imaginary part (Z im ) of the complex impedance may be a positive number or a negative number according to the frequency-tan? Characteristic graph.

FIG. 24 is a diagram for explaining a frequency search algorithm of the parameter determination method of the LANDe equivalent circuit according to an embodiment of the present invention.

For example, in the characteristic graph (1) shown in green in FIG. 24, the value of the imaginary part (Z im ) is positive, and in the case of the characteristic graphs (2) and (3) (Z im ) is negative.

If it is determined in step S211 that the value of the imaginary part ( Zim ) of the complex impedance measured at an arbitrary initial set frequency is negative, the process proceeds to step S213 in FIG. 25. If it is determined that the imaginary part is negative, enough (e.g., 10 times) reduction (step S212), the measurement and the imaginary part of the complex impedance of the step S210 to the step S211 returns to step S210 imaginary part (Z im) the input frequency constant rate positive values of Negative judgment is performed.

In this case, steps S210 to S212 can be repeatedly performed until the measured imaginary part (Z im ) of the complex impedance becomes negative.

Referring again to FIG. 21, a first complex impedance Z 1 and a second complex impedance Z 1 are measured for an object at two frequencies smaller than a first input frequency by a predetermined ratio, The series resistance R t of the circuit can be calculated (step S102).

25, the first complex impedance Z 1 is measured at a frequency f 1 that is smaller than the negative imaginary part frequency found in step S101 by a predetermined ratio (for example, 1/10) , The real part Z re1 and the imaginary part Z im1 of the first complex impedance Z 1 can be calculated (step S213).

Next, the second complex impedance Z 2 is measured at a further reduced frequency f 2 (for example, 1/10), and the real part Z re2 of the second complex impedance Z 2 and the imaginary part Quot ; Zim2 &quot; (step S214).

Next, the series resistance value R t can be calculated according to the following equation (26) (step S215).

[Equation 26]

Figure pat00064

Here, f 1, Z re1, and Z im1 is each of the first and the complex impedance measurement frequency, the real part and the imaginary part of, f 2, Z re2, and Z im2 each said second measured frequency of the complex impedance, the real Partial and imaginary parts.

Referring again to FIG. 21, a floor frequency f ? / 4 having a phase angle of 45 degrees of the complex impedance of the object is calculated based on the calculated series resistance R t , and the floor frequency f ? The parallel resistance (R ins ) and capacitance (C e ) of the LANDe equivalent circuit can be calculated based on the third complex impedance measured for the object (step S102).

Referring to Figure 26 to describe in more detail, first, the second measurement frequency (f 2) of the complex impedance in step S214, the real part (Z re2), and the imaginary part (Z im2) a series resistor (R t) calculated with Can be applied to the following equations (27) and (28) to calculate the floor frequency f ? / 4 (step S216).

[Equation 27]

Figure pat00065
And

[Equation 28]

Figure pat00066

Next, the real impedance Zre and the imaginary impedance Z im can be calculated by measuring the complex impedance at the bottom frequency f / 4 (step S217).

Next, the real part (Z re ) and the imaginary part (Z im ) of the complex impedance measured at the bottom frequency (f ? / 4 ) and the value of the series resistance (R t ) ins ) (step S218).

[Equation 29]

Figure pat00067

Next, the capacitance C e at the bottom frequency f ? / 4 can be calculated by the following equation (30) (step S219).

[Formula 30]

Figure pat00068

Next, a characteristic graph of the phase angle and the frequency of the complex impedance may be used to determine a second input frequency representing the imaginary number of the measured complex impedance to the object, in order to search for the zero point frequency. In this case, applying the bi-directional search concept to the entire frequency band, the frequency band having a positive imaginary part in the frequency-tan? Characteristic graph can be searched as follows.

As shown in FIG. 27, the complex impedance can be measured at an arbitrary initial frequency to calculate the value of the imaginary part (Z im ) of the complex impedance (step S220).

Next, it can be determined whether the measured imaginary part (Z im ) of the complex impedance is positive (step S221). In this case, the imaginary part (Z im ) of the complex impedance may be a positive number or a negative number according to the frequency-tan? Characteristic graph.

If it is determined in step S221 that the value of the imaginary part Z im of the complex impedance measured at an arbitrary initial frequency is positive, the process proceeds to step S223 in FIG. 28, , The input frequency is increased by a predetermined ratio (for example, 10 times) when the imaginary part (Z im ) of the complex impedance is negative (step S222), and the process returns to step S220 to return to step S220 The complex impedance is measured and the imaginary part is judged.

At this time, steps S220 to S222 may be repeated until the imaginary part (Z im ) of the measured complex impedance becomes positive.

Referring again to FIG. 21, a zero point frequency (f 0 ) at which the phase angle of the complex impedance converges at 90 degrees based on the fourth complex impedance measured at the second input frequency, where the imaginary number of the complex impedance measured for the object represents a positive number, (Step S104), and the serial inductance L s of the LANDEL equivalent circuit can be calculated based on the zero point frequency f 0 (step S105).

28, first, the zero point frequency f 0 can be calculated based on the complex impedance measured at the frequency at which the complex impedance has a positive imaginary part as a result of the determination at step S221 (step S223).

At this time, while the initial value of the current frequency f k is measured as the second input frequency with the complex impedance of the positive imaginary part and the complex impedance is measured, the frequency at which the phase angle of the complex impedance converges to 90 according to the following expression f k +1 ) can be calculated as the zero point frequency (f 0 ).

[Formula 31]

Figure pat00069

here,

Figure pat00070
And
Figure pat00071
Is the real part and imaginary part of the complex impedance measured for the object at the current frequency (f k ), and K is the convergence coefficient obtained by the Newton-Raphson method.

Alternatively, the frequency (f k +1 ) at which the phase angle of the complex impedance converges to 90 can be calculated as the zero point frequency (f 0 ) by applying the following Expression 32 instead of Expression 31.

[Formula 32]

Figure pat00072

Next, the series inductance L s can be calculated by applying the zero point frequency f 0 and the capacitance C e as described above to the following Expression 33 (Step S225).

[Equation 33]

Figure pat00073

Such methods may be implemented by a parameter determination system of a LAN-like equivalent circuit as described below, and in particular, a software program that performs these steps, in which case these programs may be stored on a computer- Stored or transmitted by a computer data signal coupled with a carrier wave in a transmission medium or a communication network.

At this time, the computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer system is stored. For example, ROM, RAM, CD-ROM, DVD-ROM, DVD- , A floppy disk, a hard disk, an optical data storage device, or the like.

Hereinafter, a parameter determination system of the LANDs equivalent circuit according to the embodiment of the present invention will be described with reference to FIG.

The parameter determination system 300 of the LANDEL equivalent circuit includes a sine wave voltage source 310, a sine wave current source 320, a voltage sensing unit 330, a current sensing unit 340, and a control unit 350.

The sine wave voltage source 310 generates a reference voltage according to the frequency designated by the controller 350 and supplies the reference voltage to the sine wave current source 320.

The sinusoidal current source 320 generates a current according to the voltage supplied from the sinusoidal voltage source 310 and applies the generated current to the measurement target. At this time, the object to be measured can be analyzed by the Randall equivalent circuit comprising a series inductance (L s), the series resistance (R t), the parallel resistor (R ins), and capacitance (C e) as shown in Figure 29 .

The voltage sensing unit 330 may measure the voltage across both ends of the measurement target, that is, the LANDEL equivalent circuit, and supply the voltage to the control unit 350.

The current sensing unit 340 may measure the total current of the object to be measured, that is, the LANDel equivalent circuit, and supply the measured current to the controller 350.

The controller 350 can determine the frequency of the voltage or current generated in the sinusoidal voltage source 310 and the sinusoidal current source 320 applied to the LANDEL equivalent circuit in order to measure the impedance of the measurement object.

The control unit 350 may measure the complex impedance of the measurement object according to the voltage and current of the measurement object sensed through the voltage sensing unit 330 and the current sensing unit 340. At this time, the control unit 350 can calculate the parameters of the LANDEL equivalent circuit based on the complex impedance of the measurement object and the frequency of the applied signal according to the method described above.

More specifically, the control unit 350 searches for a frequency having a positive imaginary part or a negative imaginary part of the measured complex impedance as a zero frequency (f 0 ), a floor frequency (f π / 4 ) The sine wave voltage source 310 and the sine wave current source 320 can be controlled to generate a signal of the sine wave voltage source 310 and the sine wave current source 320, respectively. At this time, the control unit 350 may measure the complex impedance of the LANDel equivalent circuit by measuring the voltage and current across the LAND equivalent circuit through the voltage sensing unit 330 and the current sensing unit 340. [ Here, the controller 350 may calculate the real part and the imaginary part of the measured complex impedance.

Based on the frequency and the imaginary part of the measured complex impedance, the controller 350 calculates a series inductance L s , a series resistance (L s ) R t ), a parallel resistor (R ins ), and a capacitance (C e ).

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

300: Parameter determination system of the LANDEL equivalent circuit
310: Sine wave voltage source 320: Sine wave current source
330: Voltage sensing unit 340: Current sensing unit
350:

Claims (11)

A method for determining a parameter of a LANDEL equivalent circuit for measuring an impedance of an object to be electrically analyzed,
Determining a second input frequency representing a first input frequency and a positive number representing an imaginary number of imaginary additions of the complex impedance measured for the object using a characteristic graph of the phase angle and the frequency of the complex impedance;
A first calculation step of calculating a series resistance of the Randel equivalent circuit based on the first complex impedance and the second complex impedance measured for the object at each of two frequencies smaller than the first input frequency by a certain ratio;
Calculating a bottom frequency at which the phase angle of the complex impedance of the object is 45 degrees based on the calculated series resistance and calculating a parallel resistance of the Randel equivalent circuit based on the third complex impedance measured for the object at the bottom frequency and A second calculation step of calculating a capacitance; And
Calculating a zero point frequency at which the phase angle of the complex impedance converges at 90 degrees based on the fourth complex impedance measured at the second input frequency, and calculating a serial inductance of the LAND equivalent circuit based on the zero point frequency, Calculating a parameter of a LAN-like equivalent circuit including a calculation step. The method according to claim 1,
The step of determining
A first step of determining whether an imaginary part of the complex impedance measured for the object at an arbitrary frequency is negative;
A second step of reducing the imaginary number by a predetermined ratio if the imaginary number is not negative; And
And a third step of remeasuring the object for the reduced frequency,
And repeating the first to third steps until the imaginary part of the complex impedance measured for the object becomes negative. The method according to claim 1,
The step of determining
A fourth step of determining whether an imaginary number of the complex impedance measured for the object at an arbitrary frequency is positive;
A fifth step of increasing the imaginary number by a predetermined ratio if the imaginary number is not negative; And
And a sixth step of remeasuring the object for the reduced frequency,
And repeating the fourth to sixth steps until the imaginary number of the complex impedance measured for the object becomes a positive number. The method according to claim 1,
Wherein the measurement frequency of the second complex impedance is smaller than the measurement frequency of the first complex impedance by a predetermined ratio. 5. The method of claim 4,
Wherein the first calculating step calculates the series resistance (Rt) by the following equation,
Figure pat00074

Here, f 1, Z re1, and Z im1 is each of the first and the complex impedance measurement frequency, the real part and the imaginary part of, f 2, Z re2, and Z im2 each said second measured frequency of the complex impedance, the real A method for determining parameters of an equivalent circuit and an imaginary part of an equivalent circuit of a LAN. 6. The method of claim 5,
The second calculating step
Figure pat00075
And
Figure pat00076
To calculate the floor frequency (f ? / 4 ). The method according to claim 6,
The second calculating step calculates the parallel resistance (R ins ) according to the following equation,
Figure pat00077

Where Zre and Zim are the real and imaginary parts of the impedance measured at the bottom frequency, respectively. 8. The method of claim 7,
The second calculating step
Figure pat00078
To calculate the capacitance (C e ) by means of the capacitance (C e ). 9. The method of claim 8,
The third calculation step may be performed while measuring the complex impedance with the initial value of the current frequency f k as the second input frequency
Figure pat00079
The frequency (f k +1 ) at which the phase angle of the complex impedance converges at 90 degrees is determined as the zero point frequency (f 0 )
here,
Figure pat00080
And
Figure pat00081
Is a real part and an imaginary part of the complex impedance measured for the object at the current frequency (f k ), and K is a convergence coefficient obtained by a Newton-Raphson numerical analysis method. 9. The method of claim 8,
The third calculation step may be performed while measuring the complex impedance with the initial value of the current frequency f k as the second input frequency
Figure pat00082
The frequency (f k +1 ) at which the phase angle of the complex impedance converges at 90 degrees is determined as the zero point frequency (f 0 )
here,
Figure pat00083
And
Figure pat00084
Is a real part and an imaginary part of the complex impedance measured for the object at the current frequency (f k ), and K is a convergence coefficient obtained by a Newton-Raphson numerical analysis method. 11. The method according to claim 9 or 10,
The third calculating step
Figure pat00085
To calculate the series inductance.
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Citations (5)

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Publication number Priority date Publication date Assignee Title
US20050021254A1 (en) * 2003-07-25 2005-01-27 James G. Biddle Co. Method and apparatus for determining the complex impedance of an electrical component
KR20070097623A (en) 2006-03-28 2007-10-05 (주) 원아테크 Apparatus for measuring internal resistance of electrochemical power source and method of the same
KR20110047497A (en) * 2009-10-30 2011-05-09 숭실대학교산학협력단 Method for generating state-of-charge standard information of secondary battery and method for estimating state-of-charge of secondary battery using state-of-charge standard information
KR101406546B1 (en) * 2013-05-30 2014-06-11 공주대학교 산학협력단 Sinusoidal insulation monitoring apparatus having operation frequency setting function
KR101407864B1 (en) * 2013-05-30 2014-06-16 공주대학교 산학협력단 Impedance calculation appratus and sinusoidal insulation monitoring apparatus comprising the voltage sensing

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050021254A1 (en) * 2003-07-25 2005-01-27 James G. Biddle Co. Method and apparatus for determining the complex impedance of an electrical component
KR20070097623A (en) 2006-03-28 2007-10-05 (주) 원아테크 Apparatus for measuring internal resistance of electrochemical power source and method of the same
KR20110047497A (en) * 2009-10-30 2011-05-09 숭실대학교산학협력단 Method for generating state-of-charge standard information of secondary battery and method for estimating state-of-charge of secondary battery using state-of-charge standard information
KR101406546B1 (en) * 2013-05-30 2014-06-11 공주대학교 산학협력단 Sinusoidal insulation monitoring apparatus having operation frequency setting function
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