CN109142863B - Power system frequency measurement method and system - Google Patents
Power system frequency measurement method and system Download PDFInfo
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- CN109142863B CN109142863B CN201710501870.0A CN201710501870A CN109142863B CN 109142863 B CN109142863 B CN 109142863B CN 201710501870 A CN201710501870 A CN 201710501870A CN 109142863 B CN109142863 B CN 109142863B
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
- G01R23/12—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage by converting frequency into phase shift
Abstract
The invention relates to a method and a system for measuring frequency of an electric power system, wherein the method comprises the steps of firstly carrying out low-pass filtering on a sampling signal of the electric power system to eliminate a high-frequency interference signal in the sampling signal; then, performing sinusoidal Fourier calculation on the obtained low-frequency signal to obtain phasors at three moments with 1/m cycle difference so as to eliminate the influence of low-frequency harmonic waves, wherein m is more than or equal to 3; and finally, obtaining the real-time frequency of the power system according to a phasor frequency measurement method. The invention processes the low-frequency signal of the power system and eliminates the influence of low-frequency harmonic waves by using the sine Fourier, so that the calculated frequency result of the power system is more accurate, compared with the method used in the prior art, the method does not need a large amount of iterative work, and has the advantages of simpler calculation method, reliability, easy popularization and stronger practical application value.
Description
Technical Field
The invention belongs to the technical field of relay protection and control measurement of a power system, and particularly relates to a frequency measurement method and system of the power system.
Background
The concept of "frequency" is derived from classical physical definition of things that change periodically, and is widely used in the electric industry technology because many physical variables in the power system have periodic characteristics. On one hand, the frequency of the power system is used as an index for measuring the quality of the electric energy and needs to be dynamically monitored; on the other hand, as an important state feedback quantity for performing safety and stability control, real-time reconstruction is required. Therefore, accurate frequency measurement has important significance for stable and safe operation of the power system.
The essence of frequency measurement is the problem of dynamic parameter identification of a signal observation model, namely, a real system physical signal is input, and the parameters of a preset model are well estimated by utilizing a signal processing and numerical analysis method. The obtained signal contains fundamental wave with continuously changing frequency, abundant harmonic wave, non-periodic component and noise component. To accurately measure the fundamental frequency, certain hardware (e.g., filters, DSPs, etc.) and corresponding software are required. The algorithm is a core link of frequency measurement, and generally comprises three steps: signal preprocessing, frequency measurement and result reprocessing. The signal preprocessing and result reprocessing are auxiliary calculations, serve for frequency measurement, can optimize measurement performance, and achieve the purpose of practical application.
There are many commonly used frequency measurement methods, for example: zero crossing point frequency measurement, phasor frequency measurement, least square method frequency measurement and the like. When the frequency is deviated and the system waveform is purer, the frequency measurement method can obtain better frequency measurement effect. However, with the large-scale construction of direct current power transmission and new energy, harmonic sources in a power grid are more and more, the situation that a power system contains harmonic waves is more and more common, and the measurement results of the method have errors and even errors in different degrees, so that the research of the anti-harmonic frequency measurement method becomes an urgent problem to be solved.
"power system automation" of 10 d 12/2008 records a paper named "fourier transform-based precise frequency measurement algorithm" by the authors of muulowns and chenchen brocade, and discloses a frequency measurement method based on fourier transform, which uses phasor frequency measurement iteration to improve the harmonic resistance, and although a good effect is obtained, the iterative calculation amount is large, and is not beneficial to practical application.
Disclosure of Invention
The invention aims to provide a frequency measurement method and a frequency measurement system for an electric power system, which are used for solving the problems of large calculation amount and complexity of a harmonic-resistant frequency measurement method in the prior art.
In order to solve the technical problems, the technical scheme of the invention is as follows:
the invention relates to a frequency measurement method of a power system, which comprises the following steps:
1) carrying out low-pass filtering on an original signal of the power system to obtain a low-frequency signal of the power system;
2) performing sine Fourier calculation on the obtained low-frequency signal to obtain phasors at three moments with 1/m cycle difference, wherein m is more than or equal to 3;
3) and obtaining the real-time frequency of the power system by adopting a phasor frequency measurement method according to the obtained phasors at three moments with the difference of 1/m cycle.
Further, a Chebyshev filter is adopted to perform low-pass filtering on the original signal of the power system, so as to obtain a low-frequency signal of the power system.
Further, the power system low frequency signal is subjected to a sine fourier calculation, and the real part and the imaginary part of the obtained phasor are as follows:
wherein, x (N) is the low frequency signal of the power system, N is the sampling number, N is the number of points of one cycle under the sampling rate of the device, coef _ s (i) is the sine filter coefficient of full-cycle Fourier, yc(n) is the real part of the phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system, ysAnd (n) is an imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system.
Further, the real-time frequency of the power system is as follows:
wherein, p is N/m, m is more than or equal to 3, N is a cycle of sampling points, TsIs the sampling interval, yc(n) is the real part of the sine Fourier of the low-frequency signal of the power system at the n moment, ys(n) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n moment, yc(n-p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-p moment, ys(n-p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-p, yc(n-2p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-2p moment, ysAnd (n-2p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-2 p.
The frequency measurement system of the power system comprises a filtering unit and a processing unit connected with the filtering unit, wherein the processing unit comprises a processor;
the filtering unit is used for carrying out low-pass filtering on an original signal of the power system to obtain a low-frequency signal of the power system and transmitting the low-frequency signal of the power system to the processor;
the processor is used for performing sinusoidal Fourier transform on the received low-frequency signal of the power system to obtain phasors at three moments with 1/m cycle difference, and calculating the real-time frequency of the power system according to a phasor frequency measurement method, wherein m is more than or equal to 3.
Further, a Chebyshev filter is adopted to perform low-pass filtering on the original signal of the power system, so as to obtain a low-frequency signal of the power system.
Further, the power system low frequency signal is subjected to a sine fourier calculation, and the real part and the imaginary part of the obtained phasor are as follows:
wherein, x (N) is the low frequency signal of the power system, N is the sampling number, N is the number of points of one cycle under the sampling rate of the device, coef _ s (i) is the sine partial coefficient of full-cycle Fourier, yc(n) is the real part of the phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system, ysAnd (n) is an imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system.
Further, the real-time frequency of the power system is as follows:
wherein, p is N/m, m is more than or equal to 3, N is a cycle of sampling points, TsIs the sampling interval, yc(n) is the real part of the sinusoidal Fourier calculation of the low-frequency signal of the power system at the n moments, ys(n) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n moment, yc(n-p) is n-p moment power system low frequencyReal part of phasor, y, obtained by sinusoidal Fourier calculation of signals(n-p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-p, yc(n-2p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-2p moment, ysAnd (n-2p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-2 p.
The invention has the beneficial effects that:
the invention relates to a method and a system for measuring the frequency of an electric power system, wherein the method comprises the steps of firstly carrying out low-pass filtering on an original signal of the electric power system to eliminate a high-frequency interference signal in the original signal; and then, performing sinusoidal Fourier calculation on the obtained low-frequency signal to eliminate low-frequency harmonic waves in the low-frequency signal to obtain phasors at three moments with 1/m cycle wave difference, and finally, obtaining the real-time frequency of the power system according to a phasor frequency measurement method. The invention processes the low-frequency signal of the power system and eliminates the influence of low-frequency harmonic waves by using the sine Fourier, so that the frequency result of the power system obtained by calculation is more accurate, compared with the method used in the prior art, the method does not need a large amount of iteration work, and has the advantages of simpler calculation method, reliability, easy popularization and stronger practical application value.
Drawings
FIG. 1 is a flow chart of a power system frequency measurement method of the present invention;
FIG. 2 is a graph of the amplitude-frequency characteristics of full-cycle Fourier and sinusoidal Fourier.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail with reference to the accompanying drawings and examples, but the embodiments of the present invention are not limited thereto.
Fig. 1 is a flow chart of a method for measuring frequency of a power system according to the present invention, and the method will be described in detail below.
Firstly, collecting original sampling signal x of power system0(n) using a low pass filter for x0(n) low-pass filtering to eliminate high-frequency interference signal in the original signal of the power system and obtain low-frequency signal of the power systemNumber x (n).
Then, the low-frequency signal x (n) of the power system is subjected to sine Fourier calculation to obtain a real part and an imaginary part of phasor at three moments with 1/m cycle wave difference, wherein m is more than or equal to 3.
And finally, calculating the real-time frequency of the power system according to a phasor frequency measurement method.
The method is further explained below by way of a specific example.
Firstly, a sampled signal of the power system is low-pass filtered by a Chebyshev filter. Adjusting cut-off frequency and attenuation amplitude to obtain filter coefficient, and sampling signal x of power system0And (n) low-pass filtering to obtain a low-frequency signal x (n) of the power system. For example, the sampling frequency is 1200Hz, the passband cut-off frequency of the low-pass filter is 10Hz, the stopband cut-off frequency is 88Hz, the passband maximum ripple attenuation is 1.743dB, the stopband maximum attenuation is 55dB, the order is 26 orders, and the specific coefficients are shown in table 1.
TABLE 1
Then, the obtained low-frequency signal x (n) of the power system is subjected to sine Fourier calculation to obtain phasors at three moments with 1/m cycle difference.
Although the higher harmonic signals can already be eliminated after low-pass filtering, the low-frequency harmonic components in the filter transition band still have a significant effect. The characteristics that the Fourier sine part has better filtering low-order harmonic than full-period Fourier are utilized, and when the frequency offset of the power system is too low, the influence of the harmonic on the frequency measurement precision is weakened. FIG. 2 is a comparison graph of the amplitude-frequency characteristics of full-period Fourier and sinusoidal Fourier, and the comparison analysis of their amplitude-frequency characteristics shows that sinusoidal Fourier has better low-pass filtering characteristics at 50-100 Hz.
1) Electric power system signal model:
x(t)=Asin(ω0t+α)=A[sin(ω0t)cosα+cos(ω0t)sinα] (1)
wherein, the signal amplitude is A, and the initial phase angle is alpha.
2) Multiplying equation (1) by cos (omega)0t) and integrating over a period:
due to sin (ω)0t) and cos (. omega.) of0t) are mutually orthogonal and integrated to 0, yielding:
3) after the derivation of equation (1), sin (ω) is multiplied0t) and integrating over a period:
from the equations (2) and (3), the cosine part of the full-period Fourier of the signal model of the power system can be seenAndare equal.
4) Substitution of the difference for the derivation:
where n is the current sampling number, TsTo sampleInterval, T is the current time, T equals n.TsAnd alpha is the initial phase angle of the power system signal model.
5) Bringing formula (4) into formula (3):
formula (5) is converted to a digital quantity form:
6) the formula of the whole circle Fourier is as follows:
The substitution of the cosine filter part of the full-circled fourier with equation (6) gives:
wherein, x (N) is the signal after low-pass filtering, N is the sampling number, N is the number of points of one cycle under the sampling rate of the device, coef _ s (i) is the sine filter coefficient of full-cycle Fourier, coef _ c (i) is the cosine filter coefficient of full-cycle Fourier, yc(n) is the real part of the power system signal model, ysAnd (n) is an imaginary part of the power system signal model.
And finally, obtaining the real-time frequency of the power system according to a phasor frequency measurement method.
According to three time phasors with a phase difference of 1/m cycle wave obtained by sinusoidal Fourier calculation, calculating the real-time frequency of the power system by using the following formula:
wherein, p is N/m, m is more than or equal to 3, N is a cycle of sampling points, TsIs the sampling interval, yc(n) is the real part of the sinusoidal Fourier calculation of the low-frequency signal of the power system at the n moments, ys(n) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n moment, yc(n-p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-p moment, ys(n-p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-p, yc(n-2p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-2p moment, ysAnd (n-2p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-2 p.
The effect of the frequency measurement method of the power system is verified below. The data in table 2 are obtained by using the method, frequency measurement errors under different frequencies are recorded, and a signal model is as follows:
xsig=A·sin(w·t+phase1)+0.1·A·sin(h·w·t+phase2)
where A is the signal amplitude, w is the signal frequency, h harmonic order, phase1 is the signal phase, and phase2 is the harmonic phase.
In the data in Table 2, phase1 is 0 degrees, phase2 is 60 degrees, and A is the unit value. It can be seen from the table that the frequency measurement accuracy of the invention is in a wide range of 45-55 Hz, and can reach an absolute accuracy of less than 0.01 Hz.
TABLE 2
The frequency measurement system of the power system comprises a filtering unit and a processing unit connected with the filtering unit, wherein the processing unit comprises a processor; the filtering unit is used for carrying out low-pass filtering on the original signal of the power system to obtain a low-frequency signal of the power system and transmitting the low-frequency signal of the power system to the processor; the processor is used for performing sine Fourier calculation on the received low-frequency signals of the power system to obtain phasors at three moments with 1/m cycle difference, and calculating the real-time frequency of the power system according to a phasor frequency measurement method; m is more than or equal to 3.
The system is characterized by realizing the frequency measurement method of the power system. The system will not be described in detail since the description of the above method is sufficiently clear and complete.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (6)
1. A power system frequency measurement method is characterized by comprising the following steps:
1) carrying out low-pass filtering on an original signal of the power system to obtain a low-frequency signal of the power system;
2) performing sine Fourier calculation on the obtained low-frequency signal to obtain phasors at three moments with 1/m cycle difference, wherein m is more than or equal to 3;
3) obtaining the real-time frequency of the power system by adopting a phasor frequency measurement method according to the obtained phasors at three moments with the difference of 1/m cycle; the real-time frequency of the power system is as follows:
wherein, p is N/m, m is more than or equal to 3, N is a cycle of sampling points, TsIs the sampling interval, yc(n) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n moment, ys(n) is the positive of the low-frequency signal of the power system at the n momentImaginary part of phasor obtained by Fourier's calculationc(n-p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-p moment, ys(n-p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-p, yc(n-2p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-2p moment, ysAnd (n-2p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-2 p.
2. The power system frequency measurement method according to claim 1, wherein the low-frequency signal of the power system is obtained by low-pass filtering an original signal of the power system by using a chebyshev filter.
3. The power system frequency measurement method according to claim 1, wherein a sinusoidal fourier calculation is performed on the power system low-frequency signal, and the real part and the imaginary part of the phasor are obtained as follows:
wherein, x (N) is the low frequency signal of the power system, N is the sampling number, N is the number of points of one cycle under the sampling rate of the device, coef _ s (i) is the sine filter coefficient of full-cycle Fourier, yc(n) is the real part of the phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system, ysAnd (n) is an imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system.
4. The frequency measurement system of the power system is characterized by comprising a filtering unit and a processing unit connected with the filtering unit, wherein the processing unit comprises a processor;
the filtering unit is used for carrying out low-pass filtering on an original signal of the power system to obtain a low-frequency signal of the power system and transmitting the low-frequency signal of the power system to the processor;
the processor is used for performing sinusoidal Fourier transform on the received low-frequency signal of the power system to obtain phasors at three moments with 1/m cycle difference, and calculating the real-time frequency of the power system according to a phasor frequency measurement method, wherein m is more than or equal to 3; the real-time frequency of the power system is as follows:
wherein, p is N/m, m is more than or equal to 3, N is a cycle of sampling points, TsIs the sampling interval, yc(n) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n moment, ys(n) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n moment, yc(n-p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-p moment, ys(n-p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-p, yc(n-2p) is the real part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the n-2p moment, ysAnd (n-2p) is the imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system at the time of n-2 p.
5. The frequency measurement system of the power system according to claim 4, wherein the low frequency signal of the power system is obtained by low pass filtering the original signal of the power system with a Chebyshev filter.
6. A frequency measurement system for an electric power system according to claim 4, wherein the low frequency signal of the electric power system is subjected to a Fourier sine calculation, and the real part and the imaginary part of the phasor are obtained by:
wherein, x (N) is the low frequency signal of the power system, N is the sampling sequence number, and N is one of the sampling rate of the deviceThe number of cycle points, coef _ s (i), is the sine filter coefficient of full cycle Fourier, yc(n) is the real part of the phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system, ysAnd (n) is an imaginary part of phasor obtained by the sine Fourier calculation of the low-frequency signal of the power system.
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