CN108717141B - Method and system for measuring electric quantity frequency by using single-phase voltage - Google Patents

Method and system for measuring electric quantity frequency by using single-phase voltage Download PDF

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CN108717141B
CN108717141B CN201810385342.8A CN201810385342A CN108717141B CN 108717141 B CN108717141 B CN 108717141B CN 201810385342 A CN201810385342 A CN 201810385342A CN 108717141 B CN108717141 B CN 108717141B
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frequency
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deviation value
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CN108717141A (en
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冯畅
冯亚东
曹海欧
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Nanjing Hezhi Electric Power Technology Co ltd
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    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention relates to a method and a system for measuring electric quantity frequency by using single-phase voltage, wherein the method comprises the following steps: using three successive intervals ofNCalculating corresponding recursion Fourier phasor according to the sampling data window data of 2 sampling points, and establishing analytic expression with the frequency deviation value as a parameter through the recursion Fourier phasor; calculating to obtain a frequency deviation value by utilizing the inherent geometric position relation among the three recursion Fourier phasors so as to obtain the actual frequency of the signal; wherein the frequency deviation value is the difference between the actual frequency of the signal and the preset frequency of the signal; for the method for measuring the frequency of the single-phase electric quantity by using the recursion Fourier phasor, the influence of a tail term of the Fourier phasor caused by the fact that the sampling frequency is not tracked to the signal frequency can be eliminated, and an accurate frequency measurement result is obtained.

Description

Method and system for measuring electric quantity frequency by using single-phase voltage
Technical Field
The invention relates to a method and a system for measuring the frequency of an electrical quantity by using single-phase voltage.
Background
For an alternating current power system, measurement of frequency, amplitude and phase is a wide and normalized requirement. For the grid-connected operation of the power system, whether the switching-on condition is met is judged according to the fact that the switching-on condition is established on the basis of accurately measuring the frequency, the amplitude and the phase. The accuracy of frequency, amplitude and phase measurement is not good enough, on one hand, a switching-on command of an automatic device can be caused by mistake, and on the other hand, huge impact current is generated to damage on network running equipment; and generating system oscillation to disconnect the power grid. On the other hand, the measurement is less accurate, which may cause the missing of the closing time. The two systems may not be connected to the grid, and the optimal time may be missed, which may result in a large inrush current generated by the subsequent switching-on.
In terms of frequency, its physical nature characterizes the period of the sinusoid signal, which may be affected by harmonics in the signal, channel background noise, and the like. The method for measuring the frequency based on the phase angle change of the recursion Fourier transform phasor is an effective method for overcoming harmonic waves and background noise, but when the sampling frequency is not tracked to the signal frequency, the influence of a tail term exists in the Fourier phasor, so that although a theoretically accurate result can be obtained for the frequency measurement of the three-phase intersection flow, an inherent error exists for the single-phase intersection flow. However, in the power system, there are a lot of situations where single-phase electrical power is connected, such as the connection of line voltage for reclosing in line protection.
Disclosure of Invention
The invention aims to provide a method and a system for measuring the frequency of an electrical quantity by using single-phase voltage, so that the influence of a 'tail term' can be eliminated when the frequency of the single-phase electrical quantity is measured by using a recursion Fourier phasor, and an accurate frequency measurement result is obtained.
In order to solve the above technical problem, the present invention provides a method for measuring a frequency of an electrical quantity by using a single-phase voltage, comprising:
calculating corresponding recursion Fourier phasor by using sampling data window data of continuous three sampling points with N/2 intervals, and establishing analytic expression with a frequency deviation value as a parameter through the recursion Fourier phasor; and
calculating and solving a frequency deviation value by utilizing the inherent geometric position relation among the three recursion Fourier phasors so as to obtain the actual frequency of the signal; wherein
The frequency deviation value is the difference between the actual frequency of the signal and the preset frequency of the signal.
Further, the method for calculating the corresponding recursion Fourier phasor by using the sampling data window data of the continuous three sampling points with the interval of N/2 comprises the following steps:
for single-phase electrical quantities, there are sampled data sequences, i.e.
x0,x1,x2....xN/2,xN/2+1....xN-1,xN,xN+1...x3N/2-1...x2N-1
Selecting x from the sampled data sequence0,x1,x2....xN-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000021
And
selecting x from the sampled data sequenceN/2,xN/2+1....x3N/2-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000022
And
selecting x from the sampled data sequenceN,xN+1...x2N-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000023
Where N is the preset number of samples per cycle, i.e., the data window length of the discrete fourier transform.
Further, the method of calculating the frequency deviation value includes:
setting the frequency deviation value as delta f, and judging the value range of the frequency deviation value delta f; and
and establishing a frequency deviation value delta f calculation formula.
Further, the method for determining the value range of the frequency deviation value Δ f includes:
setting a comparison reference value alpha, then
Figure GDA0001756772820000031
If α >0, Δ f > 0;
if α <0, Δ f < 0.
Further, the formula for calculating the frequency deviation value Δ f, i.e.
Figure GDA0001756772820000032
Wherein
Theta is the phase angle difference of adjacent phasors, and
Figure GDA0001756772820000033
fmeaspresetting a frequency for the signal; and
Figure GDA0001756772820000034
Figure GDA0001756772820000035
Figure GDA0001756772820000036
further, the formula for calculating the actual frequency of the signal, i.e.
freal=fmeas+△f。
In another aspect, the present invention further provides a measurement system, including:
the phasor calculation module is used for calculating and acquiring corresponding recursion Fourier phasor through sampling data window data of continuous three sampling points with the interval of N/2;
the frequency calculation module is used for establishing analytic expression taking the frequency deviation value as a parameter through the recursion Fourier phasor, calculating and solving the frequency deviation value by utilizing the inherent geometric position relation existing among the three successive recursion Fourier phasors, and further obtaining the actual frequency of the signal; wherein the frequency deviation value is the difference between the actual frequency of the signal and the predetermined frequency of the signal.
Further, the sampling data window data of continuous three sampling points with the interval of N/2 are used for calculating corresponding recursion Fourier phasor, namely
For single-phase electric quantity, a sampling data sequence is set:
x0,x1,x2....xN/2,xN/2+1....xN-1,xN,xN+1...x3N/2-1...x2N-1
selecting x from the sampled data sequence0,x1,x2....xN-1And by recursive discrete Fourier transformCalculating to obtain recursive Fourier phasor
Figure GDA0001756772820000041
And
selecting x from the sampled data sequenceN/2,xN/2+1....x3N/2-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000042
And
selecting x from the sampled data sequenceN,xN+1...x2N-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000043
Where N is the preset number of samples per cycle, i.e., the data window length of the discrete fourier transform.
Further, the frequency deviation value is Δ f, and a value range of the frequency deviation value Δ f is determined, that is
Setting a comparison reference value alpha, then
Figure GDA0001756772820000044
If alpha is greater than 0, delta f is greater than 0, if alpha is less than 0, delta f is less than 0, so as to obtain the value range of the frequency deviation value delta f; and
establishing a formula for calculating the frequency deviation value delta f, namely
Is provided with
Figure GDA0001756772820000045
Wherein
Theta is the phase angle of adjacent phasors, and
Figure GDA0001756772820000046
fmeaspresetting a frequency for the signal; and
Figure GDA0001756772820000051
Figure GDA0001756772820000052
Figure GDA0001756772820000053
further, the frequency calculation module is further adapted to obtain the actual frequency of the signal, i.e. freal=fmeas+△f。
The method and the system for measuring the frequency of the electric quantity by using the single-phase voltage have the advantages that the influence of 'tail terms' can be eliminated and an accurate frequency measurement result can be obtained for the single-phase electric quantity by using the recursive Fourier phasor frequency measurement.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a graph of the rotational relationship of the corresponding phasors for the self _ part, conj _ part and recursive calculations in the present invention;
FIG. 2 is a graph of phase angle variation of self _ part with respect to r and Δ f after positive sequence transformation calculation in FIG. 1;
FIG. 3 is a schematic diagram of the recursive discrete Fourier transform in the present invention
Figure GDA0001756772820000054
Obtaining three recursion Fourier phasor relation graphs;
FIG. 4 is a schematic view of a
Figure GDA0001756772820000055
A triangular phasor diagram formed by three phasors;
FIG. 5 is a schematic block diagram of a measurement system of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
Assuming a sine quantity of
Figure GDA0001756772820000061
Where X is the amplitude of the sinusoidal quantity,
Figure GDA0001756772820000062
is the initial phase angle of the sine quantity, frealIs the actual frequency of the signal. Assuming a sampling frequency fsample=N×fmeas,fmeasIs a predetermined frequency (possibly f) of the signal asserted by the measurement proceduremeas=frealAnd may also fmeas≠freal) N is the number of preset samples per cycle and is also the data window length of the discrete fourier transform.
Defining discrete recursive Fourier variations
Figure GDA0001756772820000063
Wherein
Figure GDA0001756772820000064
Is the sampling interval time. Consider Δ f ═ freal-fmeas
The simplified discrete recursive fourier transform becomes:
Figure GDA0001756772820000065
wherein
Figure GDA0001756772820000066
Figure GDA0001756772820000067
And
Figure GDA0001756772820000068
are conjugate with each other, i.e. the two phasors are symmetrical about the real axis X. Definition of
Figure GDA0001756772820000069
Figure GDA00017567728200000610
When Δ f is equal to 0,
Figure GDA00017567728200000611
if the actual frequency of the signal is equal to the preset frequency of the signal, the discrete recursive fourier phasor can accurately reflect the original phasor; otherwise the discrete recursive fourier phasor cannot accurately reflect the original phasor. In the embodiment, self _ part is defined as the present item, and conj _ part is defined as the tail item. The rotating relationship of the corresponding phasors in the case of self _ part, conj _ part, and recursion calculations is shown in FIG. 1.
Referring to fig. 2, the positive sequence transform is defined as:
Figure GDA0001756772820000071
wherein
Figure GDA0001756772820000072
Is the A phase electric quantity phasor,
Figure GDA0001756772820000073
Is the B-phase electric quantity phasor,
Figure GDA0001756772820000074
Is the C-phase electric gas phasor. The ABC three phases are three phases that are electrically in positive order.
Figure GDA0001756772820000075
And in a reverse sequence, the phase angle change of the self _ part is related to r and delta f only, and the delta f can be obtained by utilizing the phase angle change, so that the actual frequency of the signal is obtained.
In the prior art, the tail term (conj _ part) can be filtered out only by using positive sequence transformation calculation for the three-phase intersection flow, but for the single-phase electrical quantity, the change of the phase angle cannot be directly used for measuring the Δ f because the tail term (conj _ part) cannot be eliminated.
Therefore, selection is made in the present embodiment
Figure GDA0001756772820000076
And establishing three recursion Fourier phasors, and calculating and solving a frequency deviation value by utilizing the inherent geometric position relation existing among the three recursion Fourier phasors so as to obtain the actual frequency of the signal.
The specific implementation mode is as follows:
the embodiment provides a method for measuring the frequency of an electrical quantity by using single-phase voltage, which comprises the following steps:
calculating corresponding recursion Fourier phasor by using sampling data window data of continuous three sampling points with N/2 intervals, and establishing analytic expression with a frequency deviation value as a parameter through the recursion Fourier phasor; calculating to obtain a frequency deviation value by utilizing the inherent geometric position relation among the three recursion Fourier phasors so as to obtain the actual frequency of the signal; wherein
The frequency deviation value is the difference between the actual frequency of the signal and the preset frequency of the signal.
In this embodiment, the method for calculating the corresponding recursive fourier phasor by using the sampled data window data of three consecutive sampling points at intervals of N/2 includes:
for single-phase electrical quantities, there are sampled data sequences, i.e.
x0,x1,x2....xN/2,xN/2+1....xN-1,xN,xN+1...x3N/2-1...x2N-1
Selecting x from the sampled data sequence0,x1,x2....xN-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000081
And
selecting x from the sampled data sequenceN/2,xN/2+1....x3N/2-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000082
And
selecting x from the sampled data sequenceN,xN+1...x2N-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000083
Where N is the preset number of samples per cycle, i.e., the data window length of the discrete fourier transform.
Specifically, the method for calculating the frequency deviation value includes: setting the frequency deviation value as delta f, and judging the value range of the frequency deviation value delta f; and establishing a frequency deviation value delta f calculation formula.
The method for judging the value range of the frequency deviation value delta f comprises the following steps: setting a comparison reference value alpha, then
Figure GDA0001756772820000084
If α is>0, then Δ f>0; if α is<0, then Δ f<0。
The formula for calculating the frequency deviation value Δ f, i.e.
Figure GDA0001756772820000085
fmeasPresetting a frequency for the signal; and
Figure GDA0001756772820000086
Figure GDA0001756772820000087
Figure GDA0001756772820000091
the relationship between the three phasors described above, as shown in fig. 3, can be further simplified,
is provided with
Figure GDA0001756772820000092
And
Figure GDA0001756772820000093
to obtain
Figure GDA0001756772820000094
Therefore, it is not only easy to use
Figure GDA0001756772820000095
To be provided with
Figure GDA0001756772820000096
A triangle formed by three phasors is shown in figure 4,
Figure GDA0001756772820000097
Figure GDA0001756772820000098
so as to obtain
Figure GDA0001756772820000099
Further result in
Figure GDA00017567728200000910
Theta is the phase angle difference of adjacent phasors.
The formula for calculating the actual frequency of said signal, i.e.
freal=fmeas+△f。
As shown in fig. 5, the present embodiment further provides a measurement system, including:
the phasor calculation module is used for calculating and acquiring corresponding recursion Fourier phasor through sampling data window data of continuous three sampling points with the interval of N/2;
the frequency calculation module is used for establishing analytic expression taking the frequency deviation value as a parameter through the recursion Fourier phasor, calculating and solving the frequency deviation value by utilizing the inherent geometric position relation existing among the three successive recursion Fourier phasors, and further obtaining the actual frequency of the signal; wherein the frequency deviation value is the difference between the actual frequency of the signal and the predetermined frequency of the signal.
Calculating corresponding recursion Fourier phasor by using sampling data window data with continuous three sampling points with N/2 intervals, namely
For single-phase electric quantity, a sampling data sequence is set:
x0,x1,x2....xN/2,xN/2+1....xN-1,xN,xN+1...x3N/2-1...x2N-1
selecting x from the sampled data sequence0,x1,x2....xN-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000101
And
selecting x from the sampled data sequenceN/2,xN/2+1....x3N/2-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000102
And
selecting x from the sampled data sequenceN,xN+1...x2N-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure GDA0001756772820000103
Wherein N is the preset number of sampling points per cycle for measurement, namely the length of a data window of discrete Fourier transform.
The frequency deviation value is delta f, and the value range of the frequency deviation value delta f is judged, namely
Setting a comparison reference value alpha, then
Figure GDA0001756772820000104
If alpha is greater than 0, delta f is greater than 0, if alpha is less than 0, delta f is less than 0, so as to obtain the value range of the frequency deviation value delta f; and
establishing a formula for calculating the frequency deviation value delta f, namely
Is provided with
Figure GDA0001756772820000105
Wherein
Theta is the phase angle of adjacent phasors, and
Figure GDA0001756772820000111
fmeaspresetting a frequency for the signal; and
Figure GDA0001756772820000112
Figure GDA0001756772820000113
Figure GDA0001756772820000114
the frequency calculation module is adapted to obtain the actual frequency of the signal, i.e. freal=fmeas+△f。
The phasor calculation module and the frequency calculation module in the above embodiment have been described in detail in the method for measuring the frequency of the electrical quantity by using single-phase voltage, and are not described herein again.
The method and the system for measuring the frequency of the electric quantity by using the single-phase voltage can eliminate the influence of a 'tail term' and obtain an accurate frequency measurement result for measuring the frequency of the single-phase electric quantity by using the recursive Fourier phasor.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (2)

1. A method for measuring the frequency of an electrical quantity using a single-phase voltage, comprising:
calculating corresponding recursion Fourier phasor by using sampling data window data of continuous three sampling points with N/2 intervals, and establishing analytic expression with a frequency deviation value as a parameter through the recursion Fourier phasor; and
calculating to obtain a frequency deviation value by utilizing an inherent geometric position relation existing among the three recursion Fourier phasors, wherein the inherent geometric position relation is a triangular relation formed by the three recursion Fourier phasors, and further obtaining the actual frequency of the signal; wherein
The frequency deviation value is the difference between the actual frequency of the signal and the preset frequency of the signal;
the method for calculating the corresponding recursion Fourier phasor by using the sampling data window data of continuous three sampling points with the interval of N/2 comprises the following steps:
for single-phase electrical quantities, there are sampled data sequences, i.e.
x0,x1,x2....xN/2,xN/2+1....xN-1,xN,xN+1...x3N/2-1...x2N-1
Selecting x from the sampled data sequence0,x1,x2....xN-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure FDA0002689516200000011
And
selecting x from the sampled data sequenceN/2,xN/2+1....x3N/2-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure FDA0002689516200000012
And
selecting x from the sampled data sequenceN,xN+1...x2N-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure FDA0002689516200000013
Wherein N is the number of preset sampling points of each cycle wave, namely the length of a data window of discrete Fourier transform;
the method for calculating the frequency deviation value includes:
setting the frequency deviation value as delta f, and judging the value range of the frequency deviation value delta f; and
establishing a calculation formula of a frequency deviation value delta f;
the method for judging the value range of the frequency deviation value delta f comprises the following steps:
setting a comparison reference value alpha, then
Figure FDA0002689516200000021
If alpha is greater than 0, then delta f is greater than 0;
if alpha is less than 0, delta f is less than 0;
the formula for calculating the frequency deviation value Δ f, i.e.
Figure FDA0002689516200000022
Wherein
Theta is the phase angle difference of adjacent phasors, and
Figure FDA0002689516200000023
fmeaspresetting a frequency for the signal; and
Figure FDA0002689516200000024
Figure FDA0002689516200000025
Figure FDA0002689516200000026
the formula for calculating the actual frequency of said signal, i.e.
freal=fmeas+Δf。
2. A measurement system, comprising:
the phasor calculation module is used for calculating and acquiring corresponding recursion Fourier phasor through sampling data window data of continuous three sampling points with the interval of N/2;
the frequency calculation module is used for establishing analytic expression by taking the frequency deviation value as a parameter through the recursion Fourier phasor, calculating and solving the frequency deviation value by utilizing the inherent geometric position relation existing among the three successive recursion Fourier phasors, wherein the inherent geometric position relation is a triangular relation formed by the three recursion Fourier phasors, and further obtaining the actual frequency of the signal;
wherein the frequency deviation value is the difference between the actual frequency of the signal and the preset frequency of the signal;
calculating corresponding recursion Fourier phasor by using sampling data window data with continuous three sampling points with N/2 intervals, namely
For single-phase electric quantity, a sampling data sequence is set:
x0,x1,x2....xN/2,xN/2+1....xN-1,xN,xN+1...x3N/2-1...x2N-1
selecting x from the sampled data sequence0,x1,x2....xN-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure FDA0002689516200000031
And
selecting x from the sampled data sequenceN/2,xN/2+1....x3N/2-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure FDA0002689516200000032
And
selecting x from the sampled data sequenceN,xN+1...x2N-1And calculating by recursive discrete Fourier transform to obtain recursive Fourier phasor
Figure FDA0002689516200000033
Wherein N is the number of preset sampling points of each cycle wave, namely the length of a data window of discrete Fourier transform;
the frequency deviation value is Δ f, and the value range of the frequency deviation value Δ f is determined, that is
Setting a comparison reference value alpha, then
Figure FDA0002689516200000034
If alpha is larger than 0, delta f is larger than 0, if alpha is smaller than 0, delta f is smaller than 0, so as to obtain the value range of the frequency deviation value delta f; and
establishing a formula for calculating the frequency deviation value delta f, namely
Is provided with
Figure FDA0002689516200000035
Wherein
Theta is the phase angle of adjacent phasors, and
Figure FDA0002689516200000036
fmeaspresetting a frequency for the signal; and
Figure FDA0002689516200000041
Figure FDA0002689516200000042
Figure FDA0002689516200000043
the frequency calculation module is further adapted to obtain the actual frequency of the signal, i.e. freal=fmeas+Δf。
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