CN116047163A - Method and device for detecting harmonic waves among power systems - Google Patents

Method and device for detecting harmonic waves among power systems Download PDF

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CN116047163A
CN116047163A CN202310009913.9A CN202310009913A CN116047163A CN 116047163 A CN116047163 A CN 116047163A CN 202310009913 A CN202310009913 A CN 202310009913A CN 116047163 A CN116047163 A CN 116047163A
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phase
full
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harmonic
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樊丽娟
李鸿鑫
安宇
程卓
刘桐雨
舒勤
徐方维
王天行
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Shenzhen Power Supply Bureau Co Ltd
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Abstract

The invention discloses a method and a device for detecting harmonic waves among power systems, wherein the method comprises the following steps: carrying out full-phase data preprocessing on the discrete sampling signals to obtain full-phase data; performing fast Fourier transform on the full-phase data to obtain a full-phase amplitude spectrum and a phase spectrum; combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method; and obtaining constraint conditions based on the obtained inter-harmonic parameters, and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions. The invention can effectively judge the existence of dense spectrums, and has accurate judgment even for dense spectrums with small frequency intervals; the invention can effectively inhibit spectrum leakage, greatly reduce interference caused by spectrum leakage of fundamental waves and harmonic waves to inter-harmonic detection, and also reduce interference between dense spectrum inter-harmonic waves; the invention also has stronger noise immunity.

Description

Method and device for detecting harmonic waves among power systems
Technical Field
The invention belongs to the technical field of power systems, and particularly relates to a method and a device for detecting inter-power-system harmonic waves.
Background
With the increasing application of nonlinear devices in power grids, people have increasingly higher requirements on the stability and reliability of power transmission lines and power systems. However, with the recent strong development of new energy sources such as wind power generation, photovoltaic and the like, and the increasing number of nonlinear loads are connected into a power system, the problems of harmonics and inter-harmonics of the power system become increasingly serious; the safety and stability of the power system are greatly compromised by a large number of harmonics and inter-harmonics.
Currently, methods for detecting harmonics and inter-harmonics in a power grid mainly include a fast fourier transform method (Fast Fourier Transform, FFT), a wavelet transform method, an independent component analysis method (Independent Component Analysis, ICA), a neural network method, and the like. The fast fourier transform method is one of the most widely used and reliable methods, but can cause spectrum leakage and a barrier effect in the case of asynchronous sampling; the wavelet transform method has the advantages that the method can have higher time domain and frequency domain resolution at the same time, but can cause wavelet aliasing and reduce stability; the independent component analysis method often cannot completely separate each component and has larger operand; the neural network-based method requires a large number of training samples and a great amount of computation.
Disclosure of Invention
The technical problem to be solved by the embodiment of the invention is to provide a method and a device for detecting inter-harmonic in an electric power system, so as to accurately reduce the detection error of inter-harmonic parameters under the conditions of lower signal-to-noise ratio and adjacent fundamental waves/harmonics.
In order to solve the above technical problems, the present invention provides a method for detecting an inter-harmonic wave of an electric power system, including:
step A, carrying out full-phase data preprocessing on discrete sampling signals to obtain full-phase data;
step B, FFT transformation is carried out on the full-phase data to obtain a full-phase amplitude spectrum and a phase spectrum;
step C, combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method;
and D, obtaining constraint conditions based on the obtained inter-harmonic parameters, and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions.
Further, the step a specifically includes:
discrete sequences x (N) (n=0, …, N-1) obtained by discrete sampling the original signal, N-1 data in front of x (0) are reserved for weighting, and an n×n matrix is constructed:
x 0 ＝[x(0),x(1),...x(N-1)]
x 1 ＝[x(-1),x(0),...x(N-2)]
......
x N-1 ＝[x(-N+1),x(-N+2),...x(0)]
cyclically shifting each vector to the left with x (0) first, resulting in a new nxn matrix:
x 0 ＝[x(0),x(1)…x(N-1)]
x 1 ′＝[x(0),x(1)…x(-1)]
......
x N-1 ′＝[x(0),x(-N+1)…x(-1)]
all N row vectors of the new N multiplied by N matrix are added and averaged to obtain a full phase data vector:
Figure BDA0004037974220000021
further, the step B specifically includes:
for the sampled N-point discrete single-frequency complex exponential signal x (N), the angular frequency 2 pi f 0 By frequencyBeta times the interval 2 pi/N, gives:
Figure BDA0004037974220000022
wherein ,
Figure BDA0004037974220000023
is the signal initial phase;
the nonwindowed fourier transform spectrum of the sequence { x (n) } is:
Figure BDA0004037974220000024
transformed into:
Figure BDA0004037974220000031
wherein k=0, 1, …, N-1;
based on the shift properties of the discrete fourier transform, x in step a i DFT transform X of (1) i (k) And x i ' DFT transform X i The relationship of' (k) is:
Figure BDA0004037974220000032
from the above, the full phase fourier transform spectrum is obtained:
Figure BDA0004037974220000033
|X ap (k) I is the full phase amplitude spectrum, arg (X ap (k) Is an all-phase spectrum.
Further, the step C specifically includes:
for single frequency signals x respectively 1 (n)、x 2 (n) and the composite signal x (n) are subjected to full-phase FFT (fast Fourier transform) to obtain corresponding amplitude spectrum and phase spectrum;
and obtaining amplitude, phase and frequency parameters of the inter-harmonic by using a full-phase spectral line correction method.
Further, the step D specifically includes:
for complex exponential signals containing multiple frequencies
Figure BDA0004037974220000036
Judging the number of useful frequencies to be M; let the fitting function be
Figure BDA0004037974220000034
Then the sum of squares of the errors is
Figure BDA0004037974220000035
J＝J(a 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) As variable a i 、b i 、c i A parameter (a) for minimizing the sum of squares of errors J according to the principle of least squares 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) I.e. evaluated;
parameter b in fitting function delta (t) i Directly using the frequency value obtained, i.e. b i ＝f 0 (i) Then j=j (a 1 a 2 …a M ,c 1 c 2 …c M ) Simply a i and ci Is a function of (2);
setting inequality constraints
Figure BDA0004037974220000041
The fitting function delta (t) is expressed in linear form
Figure BDA0004037974220000042
wherein ,ahi ＝a i cos(c i ),b hi ＝-a i sin(c i ) The method comprises the steps of carrying out a first treatment on the surface of the The matrix form is as follows: x=fi
Wherein x= [ delta (t) 1 )δ(t 2 )……δ(t N )] T Is an N x 1 dimensional matrix; i= [ a ] h1 b h1 a h2 b h2 ……a hM b hM ] T Is a 2M x 1 dimensional matrix;
Figure BDA0004037974220000043
is an N multiplied by 2M dimensional matrix;
the linear rule of the least square method predicts I
I＝(F T F) -1 F T X
The method comprises the following steps:
Figure BDA0004037974220000044
when the constraint is satisfied, a i and ci The final obtained amplitude and phase values are obtained.
The invention also provides a device for detecting the harmonic wave between the power systems, which comprises:
the preprocessing module is used for preprocessing the full-phase data of the discrete sampling signals to obtain full-phase data;
the Fourier transform module is used for carrying out FFT (fast Fourier transform) on the full-phase data to obtain a full-phase amplitude spectrum and a phase spectrum;
the identification module is used for combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method;
the acquisition module is used for obtaining constraint conditions based on the obtained inter-harmonic parameters and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions.
The implementation of the invention has the following beneficial effects: the invention can effectively judge the existence of dense spectrums, and has accurate judgment even for dense spectrums with small frequency intervals; the invention can effectively inhibit spectrum leakage, thus greatly reducing main lobe interference caused by harmonic wave to inter-harmonic wave detection and reducing interference between dense spectrum inter-harmonic waves; the invention also has stronger noise immunity.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of a method for detecting an inter-power-system harmonic according to an embodiment of the invention.
FIG. 2a is a signal x in an embodiment of the invention 1 (n) amplitude spectrum and phase spectrum, FIG. 2b is a schematic diagram of signal x in an embodiment of the present invention 2 (n) amplitude spectrum and phase spectrum, fig. 2c is a schematic diagram of amplitude spectrum and phase spectrum of signal x (n) in an embodiment of the present invention.
Detailed Description
The following description of embodiments refers to the accompanying drawings, which illustrate specific embodiments in which the invention may be practiced.
In addition to the difficulty of conventional FFTs in identifying dense inter-spectral harmonics and the large errors in inter-harmonic detection of neighboring fundamental/harmonics, noise interference also greatly interferes with the detection of lower amplitude inter-harmonics. Based on this, referring to fig. 1, a first embodiment of the present invention provides a method for detecting an inter-power-system harmonic, including:
step A, carrying out full-phase data preprocessing on the discrete sampling signal x (n) to obtain full-phase data x ap (n)；
Step B, for the full phase data x ap (n) performing fast fourier transform to obtain a full-phase amplitude spectrum and a phase spectrum;
step C, combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method;
and D, obtaining constraint conditions based on the obtained inter-harmonic parameters, and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions.
Specifically, the data is preprocessed in the step A to obtain full-phase data, and then FFT conversion is performed. Assuming that the discrete sequence obtained by performing discrete sampling on the original signal is x (N) (n=0, …, N-1), and N-1 data in front of x (0) is reserved for weighting, an nxn matrix can be constructed as follows:
x 0 ＝[x(0),x(1),...x(N-1)]
x 1 ＝[x(-1),x(0),...x(N-2)] (1)
......
x N-1 ＝[x(-N+1),x(-N+2),...x(0)]
and then circularly shifting each vector to the left to ensure that x (0) is in the first position, so that a new N multiplied by N matrix can be obtained:
x 0 ＝[x(0),x(1)…x(N-1)]
x 1 ′＝[x(0),x(1)…x(-1)] (2)
......
x N-1 ′＝[x(0),x(-N+1)…x(-1)]
all N row vectors of the matrix (2) are added and averaged to obtain a full-phase data vector:
Figure BDA0004037974220000061
and carrying out FFT (fast Fourier transform) on the full-phase data vector to obtain full-phase FFT.
In the step B, for N point discrete single frequency complex exponential signals obtained by sampling:
Figure BDA0004037974220000062
wherein ,f0 Is the signal frequency;
Figure BDA0004037974220000063
for the initial phase of the signal, the angular frequency 2 pi f can be 0 Expressed by beta times of the frequency interval 2 pi/N, to obtain
Figure BDA0004037974220000064
Where β may be a decimal fraction; the nonwindowed fourier transform spectrum of the sequence { x (n) } is:
Figure BDA0004037974220000065
transformed into:
Figure BDA0004037974220000071
where k=0, 1, …, N-1.
Based on the shift property of the discrete Fourier transform (Discrete Fourier Transform, DFT), x in equation (1) i DFT transform X of (1) i (k) And x in formula (2) i ' DFT transform X i The relationship of' (k) is:
Figure BDA0004037974220000072
combining the properties of equations (3), (7), and (8) can yield a full phase fourier transform spectrum:
Figure BDA0004037974220000073
|X ap (k) I is the full phase amplitude spectrum, arg (X) ap (k) I.e. the full phase spectrum.
By comparing the formula (7) and the formula (9), the phase value corresponding to each spectral line of the Fourier transform spectrum is obtained
Figure BDA0004037974220000074
Related to the frequency deviation value (beta-k); and the phase value corresponding to each spectral line of the full-phase Fourier transform spectrum is +.>
Figure BDA0004037974220000075
The true initial phase is irrelevant to the frequency deviation value; this is "phase invariance", which allows phase detection of an all-phase FFT (apFFT) with high accuracy, since it is not affected by spectrum leakage. And the spectral line value of the apFFT is quadratic, so that the side lobe is fast in attenuation, the main lobe is more prominent, and the frequency spectrum leakage can be remarkably reduced.
The step C specifically comprises the following steps:
step C1, dense spectrum identification;
let single frequency signals be respectively
Figure BDA0004037974220000076
The composite signal is x (n) =x 1 (n)+x 2 (N) (n=0, 1, …, N-1); wherein f 1 ＝50.5HZ,f 2 =53 HZ, the number of sampling points n=16, the sampling frequency f s ＝80HZ；
The value of the frequency resolution can be found to be Δf=f s N=5hz, due to, |f 1 -f 2 |＝2.5HZ<Δf, the composite signal x (n) therefore belongs to a dense spectral distribution.
Respectively to x 1 (n)、x 2 And (n) and x (n) are subjected to apFFT conversion to obtain an amplitude spectrum and a phase spectrum, as shown in figure 2. Fig. 2 (a), fig. 2 (b), fig. 2 (c) correspond to the signal x, respectively 1 (n)、x 2 (n) and x (n). It can be seen from the figure that the apFFT phase spectrum of the single frequency signal exhibits significant "flatness". Fig. 2 (c) shows a mixed signal x (n), a peak line value k=10, and the proximity is judgedThe basis of whether dense spectrums exist at the spectral lines 9 and 11 is whether the phase spectrums corresponding to peak spectral line values have flatness or not nearby, and the phase spectrums at the k=9, 10 and 11 positions shown in the figure have extremely large fluctuation, so that the existence of the dense spectrums can be judged. Whereas it is difficult to judge the existence of dense spectrum if the amplitude spectrum is directly observed.
And C2, obtaining amplitude, phase and frequency parameters of the inter-harmonic by using a full-phase spectral line correction method.
Let the peak spectral line be k p From equation (7) and equation (9)
Figure BDA0004037974220000081
Thus there is
Figure BDA0004037974220000082
So line k p Corresponding frequency f 0 Satisfy the following requirements
Figure BDA0004037974220000083
In the case of obtaining the frequency correction value beta, the amplitude A 0 Can be directly obtained from the formula (8), the peak spectral line k p The corresponding spectral line value is
Figure BDA0004037974220000084
Thus (2)
Figure BDA0004037974220000085
Based on the apFFT phase invariance, the peak spectral line k can be directly used p The corresponding phase is taken as the initial phase of the signal
Figure BDA0004037974220000086
In step D, for complex exponential signals containing multiple frequencies
Figure BDA0004037974220000087
The number of useful frequencies can be judged through the steps, and the number is set as M; thus making the fitting function be
Figure BDA0004037974220000091
Then the sum of squares of the errors
Figure BDA0004037974220000092
From this, j=j (a 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) As variable a i 、b i 、c i A parameter (a) for minimizing the sum of squares of errors J according to the principle of least squares 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) I.e. the evaluated value. According to the multivariate differentiation method, a minimum value can be taken when the partial derivative of J on each parameter is 0.
Equation (18) is derived from equations (16) and (17):
Figure BDA0004037974220000093
and holds for k= (1, 2,.. The.m.), solving this linear system of equations can yield estimates of 3M parameters. However, this direct solution to a 3M-ary system of equations is extremely complex and therefore requires simplification. Since the apFFT method already has a very high detection accuracy for frequency, the parameter b in the fitting function delta (t) i The frequency values thus determined can be used directly, i.e. b i ＝f 0 (i) Such that j=j (a 1 a 2 …a M ,c 1 c 2 …c M ) Simply a i and ci Is a function of (2). Considering that the relative error of the detection of amplitude and phase under noise of the apFFT method does not exceed 5%, an inequality constraint condition is set
Figure BDA0004037974220000094
The fitting function delta (t) can be expressed in a linear form
Figure BDA0004037974220000095
wherein ,ahi ＝a i cos(c i ),b hi ＝-a i sin(c i ) Or may be written in a matrix form, such as equation (21):
X＝FI (21)
wherein x= [ delta (t) 1 )δ(t 2 )……δ(t N )] T Is an N x 1 dimensional matrix; i= [ a ] h1 b h1 a h2 b h2 ……a hM b hM ] T Is a 2M x 1 dimensional matrix;
Figure BDA0004037974220000101
is an N x 2M dimensional matrix.
The linear rule of the least square method predicts I
I＝(F T F) -1 F T X (23)
From equations (20) and (21)
Figure BDA0004037974220000102
When constraint (19) is satisfied, a i and ci The final obtained amplitude and phase values are obtained.
For the multi-frequency signal, the mathematical model is very concise, and the model obtained after dense spectrum judgment is also practical, so that the fitting method is further improved from the aspect of constraint conditions under the condition that the sufficient sample size and noise interference are not too strong.
First to a only i Setting constraint on c i No constraint is set; i.e.
Figure BDA0004037974220000103
Obtaining (a) 1 a 2 …a M ) I.e. corrected amplitude, then to c alone i Setting constraints and fitting
Figure BDA0004037974220000104
Obtaining (c) 1 c 2 …c M ) I.e. the corrected phase value.
The invention can accurately reduce the detection error of inter-harmonic parameters under the conditions of lower signal-to-noise ratio and adjacent fundamental waves/harmonic waves through simulation experiments.
Constructing a signal model in matlab as shown in formula (27):
Figure BDA0004037974220000105
the specific parameters of each signal component are shown in table 1, wherein n=0, …, N-1, sampling frequency f s =5120 HZ, according to the IEC detection standard, the frequency resolution should be made 5HZ, so n=1024. The invention is used for detecting the inter-harmonics. And compares the calculation results, calculation errors with other methods as shown in tables 2-7.
TABLE 1 parameters of the components of the signals
Figure BDA0004037974220000111
/>
First restrict only a i I.e.
Figure BDA0004037974220000112
Solving for fitting result a' i Then, the obtained a 'is not taken in' i For only c i Constraint solving, i.e.)>
Figure BDA0004037974220000113
Solving for fitting result c' i 。
The constraint on the phase and the amplitude is respectively relaxed in the fitting process, so that the accuracy is higher. The following tables respectively estimate the inter-harmonic parameters of the signal and obtain the relative error with four algorithms without adding noise and with a signal-to-noise ratio snr=20 dB, e-12 in table 6 being shorthand for the relative errors being of the same order of magnitude. Wherein the method 1 is a common full-phase method, the method 2 is a three-spectral-line interpolation method, the method 3 is a spectral-line equation set method, and the method 4 is a method in the embodiment of the invention
Table 2 inter-harmonic frequency detection relative error contrast (without added noise)
Figure BDA0004037974220000114
Table 3 inter-harmonic frequency detection relative error contrast (snr=20)
Figure BDA0004037974220000115
Table 4 inter-harmonic amplitude detection relative error contrast (without added noise)
Figure BDA0004037974220000116
Table 5 harmonic amplitude detection relative error contrast (snr=20)
Figure BDA0004037974220000121
Table 6 harmonic phase detection relative error contrast (without added noise)
Figure BDA0004037974220000122
Table 7 harmonic phase detection relative error contrast (snr=20)
Figure BDA0004037974220000123
As can be seen from the comparison of tables 2-7, under the condition of no noise, the detection precision of the traditional apFFT method (method 1) on frequency, amplitude and phase is obviously higher than that of a three-spectral-line interpolation method (method 2) and a spectral-line equation set method (method 3), but the detection of amplitude and phase is greatly affected by noise, the method 4 corrects on the basis of the traditional apFFT method, the influence of noise on the detection precision is overcome, and when the signal-to-noise ratio is 20dB, compared with the method 1, the detection relative error of the embodiment on the signal amplitude and phase is improved by about 1-2 orders of magnitude. This shows that, compared with the conventional FFT spectral line method, the apFFT improves the detection accuracy of the signal parameters by suppressing the spectrum leakage, and on the other hand, shows that the correction of the amplitude and the phase on the basis of the apFFT is effective.
Corresponding to the method for detecting inter-power-system harmonics in the first embodiment of the present invention, a second embodiment of the present invention further provides an inter-power-system harmonic detection device, including:
the preprocessing module is used for preprocessing the full-phase data of the discrete sampling signals to obtain full-phase data;
the Fourier transform module is used for carrying out FFT (fast Fourier transform) on the full-phase data to obtain a full-phase amplitude spectrum and a phase spectrum;
the identification module is used for combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method;
the acquisition module is used for obtaining constraint conditions based on the obtained inter-harmonic parameters and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions.
Further, the step B specifically includes:
for the sampled N-point discrete single-frequency complex exponential signal x (N), the angular frequency 2 pi f 0 Expressed as β times the frequency spacing 2 pi/N, yields:
Figure BDA0004037974220000131
wherein ,
Figure BDA0004037974220000135
is the signal initial phase;
the nonwindowed fourier transform spectrum of the sequence { x (n) } is:
Figure BDA0004037974220000132
transformed into:
Figure BDA0004037974220000133
wherein k=0, 1, …, N-1;
based on the shift properties of the discrete fourier transform, x in step a i DFT transform X of (1) i (k) And x i 'DFT transform X' i (k) The relation of (2) is:
Figure BDA0004037974220000134
from the above, the full phase fourier transform spectrum is obtained:
Figure BDA0004037974220000141
|X ap (k) I is the full phase amplitude spectrum, arg (X ap (k) Is an all-phase spectrum.
Further, the step D specifically includes:
for complex exponential signals containing multiple frequencies
Figure BDA0004037974220000142
Judging the number of useful frequencies to be M; let the fitting function be
Figure BDA0004037974220000143
Then the sum of squares of the errors is
Figure BDA0004037974220000144
J＝J(a 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) As variable a i 、b i 、c i A parameter (a) for minimizing the sum of squares of errors J according to the principle of least squares 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) I.e. evaluated;
parameter b in fitting function delta (t) i Directly using the frequency value obtained, i.e. b i ＝f 0 (i) Then j=j (a 1 a 2 …a M ,c 1 c 2 …c M ) Simply a i and ci Is a function of (2);
setting inequality constraints
Figure BDA0004037974220000145
The fitting function delta (t) is expressed in linear form
Figure BDA0004037974220000146
wherein ,ahi ＝a i cos(c i ),b hi ＝-a i sin(c i ) The method comprises the steps of carrying out a first treatment on the surface of the The matrix form is as follows: x=fi
Wherein x= [ delta (t) 1 )δ(t 2 )……δ(t N )] T Is an N x 1 dimensional matrix; i= [ a ] h1 b h1 a h2 b h2 ……a hM b hM ] T Is a 2M x 1 dimensional matrix;
Figure BDA0004037974220000147
is an N multiplied by 2M dimensional matrix;
the linear rule of the least square method predicts I
I＝(F T F) -1 F T X
The method comprises the following steps:
Figure BDA0004037974220000151
when the constraint is satisfied, a i and ci The final obtained amplitude and phase values are obtained.
Further, pair a i Setting constraint on c i No constraint is set; i.e.
Figure BDA0004037974220000152
Obtaining (a) 1 a 2 …a M ) I.e. corrected amplitude, thenIndividual pair c i Setting constraints and fitting:
Figure BDA0004037974220000153
obtaining (c) 1 c 2 …c M ) I.e. the corrected phase value.
For the working principle and process of the present embodiment, please refer to the description of the first embodiment of the present invention, and the description is omitted here.
As can be seen from the above description, compared with the prior art, the invention has the following beneficial effects: the invention can effectively judge the existence of dense spectrums, and has accurate judgment even for dense spectrums with small frequency intervals; the invention can effectively inhibit spectrum leakage, thus greatly reducing main lobe interference caused by harmonic wave to inter-harmonic wave detection and reducing interference between dense spectrum inter-harmonic waves; the invention also has stronger noise immunity.
The foregoing disclosure is illustrative of the present invention and is not to be construed as limiting the scope of the invention, which is defined by the appended claims.

Claims (6)

1. An inter-power-system harmonic detection method, comprising:
step A, carrying out full-phase data preprocessing on discrete sampling signals to obtain full-phase data;
step B, performing fast Fourier transform on the full-phase data to obtain a full-phase amplitude spectrum and a phase spectrum;
step C, combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method;
and D, obtaining constraint conditions based on the obtained inter-harmonic parameters, and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions.
2. The method for detecting inter-power-system harmonics according to claim 1, wherein said step a specifically comprises:
discrete sequences x (N) (n=0, …, N-1) obtained by discrete sampling the original signal, N-1 data in front of x (0) are reserved for weighting, and an n×n matrix is constructed:
x 0 ＝[x(0),x(1),...x(N-1)]
x 1 ＝[x(-1),x(0),...x(N-2)]
......
x N-1 ＝[x(-N+1),x(-N+2),...x(0)]
cyclically shifting each vector to the left with x (0) first, resulting in a new nxn matrix:
x 0 ＝[x(0),x(1)…x(N-1)]
x 1 ′＝[x(0),x(1)…x(-1)]
......
x N-1 ′＝[x(0),x(-N+1)…x(-1)]
all N row vectors of the new N multiplied by N matrix are added and averaged to obtain a full phase data vector:
Figure FDA0004037974210000011
3. the method for detecting inter-power-system harmonics according to claim 1, wherein said step B specifically comprises:
for the sampled N-point discrete single-frequency complex exponential signal x (N), the angular frequency 2 pi f 0 Expressed as β times the frequency spacing 2 pi/N, yields:
Figure FDA0004037974210000012
wherein ,
Figure FDA0004037974210000021
is the signal initial phase;
the nonwindowed fourier transform spectrum of the sequence { x (n) } is:
Figure FDA0004037974210000022
transformed into:
Figure FDA0004037974210000023
wherein k=0, 1, …, N-1;
based on the shift properties of the discrete fourier transform, x in step a i DFT transform X of (1) i (k) And x i 'DFT transform X' i (k) The relation of (2) is:
Figure FDA0004037974210000024
from the above, the full phase fourier transform spectrum is obtained:
Figure FDA0004037974210000025
|X ap (k) I is the full phase amplitude spectrum, arg (X ap (k) Is an all-phase spectrum.
4. The method for detecting inter-power-system harmonics according to claim 1, wherein said step C specifically comprises:
for single frequency signals x respectively 1 (n)、x 2 (n) and the composite signal x (n) are subjected to full-phase FFT (fast Fourier transform) to obtain corresponding amplitude spectrum and phase spectrum;
and obtaining amplitude, phase and frequency parameters of the inter-harmonic by using a full-phase spectral line correction method.
5. The method for detecting inter-power-system harmonics according to claim 1, wherein said step D specifically comprises:
for complex exponential signals containing multiple frequencies
Figure FDA0004037974210000031
Judging the number of useful frequencies to be M; let the fitting function be
Figure FDA0004037974210000032
/>
Then the sum of squares of the errors is
Figure FDA0004037974210000033
J＝J(a 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) As variable a i 、b i 、c i A parameter (a) for minimizing the sum of squares of errors J according to the principle of least squares 1 a 2 …a M ,b 1 b 2 …b M ,c 1 c 2 …c M ) I.e. evaluated;
parameter b in fitting function delta (t) i Directly using the frequency value obtained, i.e. b i ＝f 0 (i) Then j=j (a 1 a 2 …a M ,c 1 c 2 …c M ) Simply a i and ci Is a function of (2);
setting inequality constraints
Figure FDA0004037974210000034
The fitting function delta (t) is expressed in linear form
Figure FDA0004037974210000035
wherein ,ahi ＝a i cos(c i ),b hi ＝-a i sin(c i ) The method comprises the steps of carrying out a first treatment on the surface of the The matrix form is as follows: x=fi;
wherein x= [ delta (t) 1 ) δ(t 2 )……δ(t N )] T Is an N x 1 dimensional matrix; i= [ a ] h1 b h1 a h2 b h2 ……a hM b hM ] T Is a 2M x 1 dimensional matrix;
Figure FDA0004037974210000036
is an N multiplied by 2M dimensional matrix;
the linear rule of the least square method predicts I
I＝(F T F) -1 F T X
The method comprises the following steps:
Figure FDA0004037974210000041
when the constraint is satisfied, a i and ci The final obtained amplitude and phase values are obtained.
6. An inter-power-system harmonic detection apparatus, comprising:
the preprocessing module is used for preprocessing the full-phase data of the discrete sampling signals to obtain full-phase data;
the Fourier transform module is used for carrying out fast Fourier transform on the full-phase data to obtain a full-phase amplitude spectrum and a phase spectrum;
the identification module is used for combining the full-phase amplitude spectrum and the phase spectrum, identifying the existence of dense spectrum and obtaining peak spectral line value, and obtaining inter-harmonic parameters by using a full-phase spectral line correction method;
the acquisition module is used for obtaining constraint conditions based on the obtained inter-harmonic parameters and obtaining accurate values of the inter-harmonic parameters by using a least square fitting method with the constraint conditions.
CN202310009913.9A 2023-01-05 2023-01-05 Method and device for detecting harmonic waves among power systems Pending CN116047163A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116735957A (en) * 2023-06-07 2023-09-12 四川大学 Near-frequency harmonic wave and inter-harmonic wave measuring method and system considering main lobe overlapping interference
CN117607562A (en) * 2023-12-05 2024-02-27 湖南工商大学 Power signal noise level estimation method, device and medium based on phase calibration

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116735957A (en) * 2023-06-07 2023-09-12 四川大学 Near-frequency harmonic wave and inter-harmonic wave measuring method and system considering main lobe overlapping interference
CN116735957B (en) * 2023-06-07 2024-02-27 四川大学 Near-frequency harmonic wave and inter-harmonic wave measuring method and system considering main lobe overlapping interference
CN117607562A (en) * 2023-12-05 2024-02-27 湖南工商大学 Power signal noise level estimation method, device and medium based on phase calibration
CN117607562B (en) * 2023-12-05 2024-05-28 湖南工商大学 Power signal noise level estimation method, device and medium based on phase calibration

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