CN107271773B - Rapid detection method for harmonic waves of power system - Google Patents
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Abstract
The invention discloses a method for quickly detecting harmonic waves of an electric power system, in particular to a method for quickly detecting phases and amplitudes of signals with different frequencies in the harmonic waves of the electric power system, which comprises the following steps: (1) sampling points with at least twice of harmonic number are collected by taking twice of the highest frequency multiplication as a sampling rate; (2) constructing a sine signal and a cosine signal corresponding to each harmonic frequency; (3) calculating harmonic detection parameters by fitting coefficients before each sine item and each cosine item; (4) and combining coefficients before the sine term and the cosine term with the same frequency to obtain the amplitude and the phase of each frequency harmonic. Compared with the prior art, the method has the advantages that the required data volume is small, and the result can be calculated only by data of half the length of the fundamental frequency signal; compared with the FFT (fast Fourier transform) method, the method can avoid the problem of frequency leakage; and can be compatible with a certain degree of clutter interference.
Description
Technical Field
The invention relates to the field of digital signal processing, in particular to a method for quickly detecting harmonic waves of a power system.
Background
In recent years, the requirements of people on the quality of electric energy are higher and higher, but factors causing the problem of the quality of electric energy are also increasing, wherein one of the factors is mainly represented by harmonics and inter-harmonics in an electric power system, the harmonic problem poses a potential threat to the safety, stability and economic operation of the electric power system, and the harm to electric power equipment is particularly serious, so that the research on the harmonics of the electric power system is particularly important, and the detection of the harmonics of the electric power system is the primary task of the research.
Fast Fourier Transform (FFT) is the most commonly used harmonic detection method, and this method needs to collect all data in at least one complete period of fundamental frequency to obtain correct result, and the FFT algorithm has the problem of energy leakage, resulting in large difference between the calculated harmonic amplitude of each frequency and the actual amplitude, and in addition, the FFT algorithm has a complex calculation process, and cannot realize real-time analysis.
Therefore, it is desirable to provide a new fast detection method for harmonic in power system to solve the above problems.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for quickly detecting harmonic waves of an electric power system, wherein harmonic wave detection can be realized only by acquiring half-period sampling data.
In order to solve the technical problems, the invention adopts a technical scheme that: the method for rapidly detecting the harmonic waves of the power system comprises the following steps:
sampling points with the number of at least two times of harmonic waves are collected by taking the frequency of at least two times of the highest frequency multiplication as the sampling rate;
constructing a sine signal and a cosine signal corresponding to each harmonic frequency;
calculating harmonic detection parameters by fitting coefficients before each sine item and each cosine item;
and combining coefficients before the sine term and the cosine term with the same frequency to obtain the amplitude and the phase of each frequency harmonic.
In a preferred embodiment of the present invention, the method of calculating the harmonic detection parameters comprises a least squares method.
Further, the method for rapidly detecting the harmonic of the power system specifically comprises the following steps:
(1) constructing a harmonic signal mixing model: the fundamental frequency is F, the maximum harmonic frequency is N times of the fundamental frequency, namely NF, so the collected sampling signal X is
Wherein, an(n＝1，...，N)，bnN is a coefficient before a sine term and a cosine term corresponding to the N times of fundamental frequency harmonic, namely a harmonic detection parameter, and Sn and Pn are the amplitude and the phase of the N times of harmonic;
(2) calculating harmonic detection parameters:
s2.1: acquiring a signal of 0.01 second at the frequency of 2NF, recording the signal as x, setting the length of the x as M, and calculating a sampling interval d;
s2.2: an M-row 2N-column matrix A is constructed as follows
Wherein A ismnIs an element of the m-th row and n-th column in the matrix A, [ alpha ], [ alpha]Represents a ceiling operation;
s2.3: constructing M line vectors B
Bi＝xi
Wherein B isiThe element in row i of vector B is represented and xi represents the magnitude of the sample point i of signal x.
S2.4: calculating a vector W using the following formula;
W＝(ATA)-1(ATB)
s2.5: a is calculated by the following formulan(n＝1，...，N)，bn(n＝1，...，N)，
an＝W(2n-1)
bn＝W(2n)
Where W (n) denotes the nth element in the vector W.
(3) Using a calculated in step (2)j，bjThe amplitude S of the frequency multiplication harmonic of j is calculated according to the following formulajAnd phase Pj。
Pj＝a tan 2(bj,aj)
The invention has the beneficial effects that: compared with the existing harmonic detection method, the harmonic detection method has the advantages that the data demand is small, the harmonic detection can be realized only by acquiring data with half the length of the fundamental frequency signal, the problem of frequency leakage does not exist, and the difference between the calculated harmonic amplitude of each frequency and the actual amplitude is small; the calculation method is simple, has certain compatibility with interference signals, can be used for real-time detection of harmonic waves of the power system, and is suitable for wide popularization and application.
Drawings
Fig. 1 is a flow chart of a method for rapidly detecting harmonics in an electrical power system according to a preferred embodiment of the present invention.
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the invention easier to understand by those skilled in the art, and thus will clearly and clearly define the scope of the invention.
Referring to fig. 1, an embodiment of the present invention includes:
a method for rapidly detecting harmonic waves of a power system comprises the following steps:
1) the method comprises the steps of collecting sampling points with the frequency of at least two times of the highest frequency multiplication as the sampling rate, collecting data of half period time length of a fundamental frequency signal if the signal noise intensity is 1% of the original signal intensity, and collecting signal data of more than half period time length if the signal noise intensity is higher than 1% so as to increase the stability of the sampled data;
2) constructing a sine signal and a cosine signal corresponding to each harmonic frequency;
3) calculating harmonic detection parameters by fitting coefficients before each sine item and each cosine item, preferably, the fitting method adopts a least square method;
4) and combining coefficients before the sine term and the cosine term with the same frequency to obtain the amplitude and the phase of each frequency harmonic.
Further, the method for rapidly detecting the harmonic waves of the power system comprises the following specific steps:
(1) constructing a harmonic signal mixing model: the fundamental frequency is F, the maximum harmonic frequency is N times of the fundamental frequency, namely NF, so the collected sampling signal X is
Wherein, an(n＝1，...，N)，bnN is a coefficient before a sine term and a cosine term corresponding to the N times of fundamental frequency harmonic, namely a harmonic detection parameter, and Sn and Pn are the amplitude and the phase of the N times of harmonic;
(2) calculating harmonic detection parameters:
s2.1: acquiring a signal of 0.01 second at the frequency of 2NF, recording the signal as x, setting the length of the x as M, and calculating a sampling interval d;
s2.2: an M-row 2N-column matrix A is constructed as follows
Wherein A ismnIs an element of the m-th row and n-th column in the matrix A, [ alpha ], [ alpha]Represents a ceiling operation;
s2.3: constructing M line vectors B
Bi＝xi
Wherein B isiThe element in row i of vector B is represented and xi represents the magnitude of the sample point i of signal x.
S2.4: calculating a vector W using the following formula;
W＝(ATA)-1(ATB)
s2.5: a is calculated by the following formulan(n＝1，...，N)，bn(n＝1，...，N)，
an＝W(2n-1)
bn＝W(2n)
Where W (n) denotes the nth element in the vector W.
(3) Using a calculated in step (2)j，bjThe amplitude S of the frequency multiplication harmonic of j is calculated according to the following formulajAnd phase Pj。
Pj＝a tan 2(bj,aj)
Taking a harmonic signal with a fundamental frequency of 50Hz as an example, assuming that the signal has harmonics with two frequencies of 50Hz and 100Hz, a harmonic signal mixed model constructed by the harmonic signal mixed model has four sine terms and cosine terms, and when fitting sine and cosine term coefficients, only 4 groups of data are needed to ensure a certain unique solution of an equation. Therefore, the harmonic detection result can be obtained only by acquiring data of 4 sampling points. When the sampling rate is 1000Hz, the sampling period is 1ms, so the time required for acquiring data of 4 sampling points is (4-1) × 1ms ═ 3ms, which is much shorter than one period length (10ms) of 100 Hz. It can therefore be seen that the length of time to acquire a desired sample point is shorter as the sampling rate is higher.
Compared with the prior art, the method has the advantages that the required data volume is small, the harmonic detection can be realized only by data with the length of one half of the fundamental frequency signal, the problem of frequency leakage does not exist, and the difference between the calculated harmonic amplitude of each frequency and the actual amplitude is small; the calculation method is simple, has certain compatibility with interference signals, can be used for real-time detection of harmonic waves of the power system, and is suitable for wide popularization and application.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (2)
1. A method for rapidly detecting harmonic waves of an electric power system is characterized in that,
sampling points with the number of at least two times of harmonic waves are collected by taking the frequency of at least two times of the highest frequency multiplication as the sampling rate;
constructing a sine signal and a cosine signal corresponding to each harmonic frequency;
calculating harmonic detection parameters by fitting coefficients before each sine item and each cosine item;
combining coefficients before the sine item and the cosine item with the same frequency to obtain the amplitude and the phase of each frequency harmonic; the method comprises the following specific steps:
(1) constructing a harmonic signal mixing model: the fundamental frequency is F, the maximum harmonic frequency is N times of the fundamental frequency, namely NF, so the collected sampling signal X is
Wherein, an(n＝1，...，N)，bnN is a coefficient before a sine term and a cosine term corresponding to the N times of fundamental frequency harmonic, namely a harmonic detection parameter, and Sn and Pn are the amplitude and the phase of the N times of harmonic;
(2) calculating harmonic detection parameters:
s2.1: collecting signals of at least 2N sampling points at the lowest frequency of 2NF, recording the signals as x, setting the length of the x as M, and calculating a sampling interval d;
s2.2: constructing an M-row 2N-column matrix A, wherein the construction method comprises the following steps:
wherein A ismnIs an element of the m-th row and n-th column in the matrix A, [ alpha ], [ alpha]Represents a ceiling operation;
s2.3: constructing M line vectors B
Bi＝xi
Wherein B isiRepresents the element of the ith row in vector B, and xi represents the amplitude of the ith sample point in signal x;
s2.4: calculating a vector W using the following formula;
W＝(ATA)-1(ATB)
s2.5: a is calculated by the following formulan(n＝1，...，N)，bn(n＝1，...，N)，
an＝W(2n-1)
bn＝W(2n)
Where W (n) represents the nth element in the vector W;
(3) using a calculated in step (2)j，bjThe amplitude S of the frequency multiplication harmonic of j is calculated according to the following formulajAnd phase Pj：
2. The method of claim 1, wherein the calculation of the harmonic detection parameters comprises a least squares method.
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| CN101915874B (en) * | 2010-07-20 | 2013-01-09 | 北海市深蓝科技发展有限责任公司 | Harmonic wave detection method based on Fourier transformation |
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| CN103197141A (en) * | 2013-03-21 | 2013-07-10 | 广东电网公司电力科学研究院 | Method of measuring electrical power system signal frequency and harmonic wave parameters |
| CN103926462B (en) * | 2014-04-28 | 2017-02-01 | 东南大学 | Rapid harmonic wave analyzing method and device of power system |
| CN104459318B (en) * | 2014-11-13 | 2017-06-16 | 广东电网有限责任公司电力科学研究院 | The measuring method and system of electric harmonic |
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| JP2015219189A (en) * | 2014-05-20 | 2015-12-07 | 一般財団法人電力中央研究所 | Harmonic wave estimation device, harmonic wave estimation method and harmonic wave estimation program |
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