CN112630527A - Distortion signal electric quantity measuring method based on empirical wavelet transform - Google Patents
Distortion signal electric quantity measuring method based on empirical wavelet transform Download PDFInfo
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Abstract
The invention discloses a distortion signal electric quantity measuring method based on empirical wavelet, which comprises the steps of firstly collecting original voltage signals and current signals in a power grid as signals to be observed; performing empirical wavelet transform on a signal to be observed, specifically: firstly, carrying out self-adaptive spectrum division on a signal to be observed, and dividing the signal to be observed into different modes; then, performing empirical wavelet transform on each mode to decompose a signal to be observed; and extracting a fundamental wave signal and a distortion signal of a signal to be observed from the empirical wavelet transform decomposition result, and further obtaining the active power P. The problems that in the existing electric quantity metering technology, wavelet base and decomposition layer number selection is needed in wavelet transformation, adaptive detection cannot be achieved due to poor adaptive capacity, frequency aliasing phenomenon exists in wavelet decomposition, and the principle of inaccurate Heisenberg measurement is adopted are solved.
Description
Technical Field
The invention belongs to the technical field of electric quantity metering automation, and relates to a distortion signal electric quantity metering method based on empirical wavelets.
Background
The occupancy rate of various nonlinear loads such as induction heating furnaces, electric locomotives, power electronic switching equipment, electrochemical industrial equipment and the like in modern power systems is rapidly increased, the increase of the loads causes the asymmetry degree of power supply voltage to be intensified, the volatility to be more and more serious, a large amount of harmonic signals are generated, the power quality of a power grid is more and more deteriorated, and the distortion of the power grid signals is serious. Besides fundamental wave, the voltage and current signals are also doped with a large number of quasi-periodic, time-varying and non-stable distortion signals, which seriously affect the quality of electric energy of other users and also provide new requirements for the functions of the traditional electric quantity metering mode and the metering instrument. At present, most of metering schemes used by the power grid only meter the fundamental wave and the electric energy generated by the fundamental wave, and in fact, the fundamental wave signal and the distortion signal also have electric energy exchange. At present, no unified distortion signal electric quantity metering standard exists at home and abroad, so that punishment measures for nonlinear load users are lost, and huge economic loss is caused to a power grid. The research and the improvement of the theory and the method for measuring the electric quantity of the non-stationary distortion signal of the power grid are the problems to be solved urgently at present.
Most of time-frequency analysis tools used by the existing electric quantity metering equipment are Fast Fourier Transform (FFT), the FFT has good frequency domain resolution capability on steady-state signals, but the problems of side lobe, frequency spectrum leakage and the like are exposed in the analysis on power grid distortion signals, and the time-frequency analysis tools are difficult to adapt to the current complex power system distortion signals. At present, distortion signal detection has attracted wide interest of scholars at home and abroad, although short-time Fourier transform (STFT) can analyze distortion signals by combining time domain and frequency domain information, once a window function is selected, the time-frequency resolution capability is fixed, and the detection precision is limited. Although Wavelet Transform (WT) solves the problem of fixed STFT time-frequency resolution, the wavelet basis and the number of decomposition layers need to be specifically selected according to the actual scene. The S transform has good time-frequency analysis capability and noise resistance as STFT and WT extensions, but is constrained by the Heisenberg inaccurate measurement principle as STFT. The Hilbert-Huang transform (HHT) has strong self-adaptation capability, is not restricted by a Heisenberg inaccuracy measuring principle, does not have nonlinear cross terms, but still has a modal aliasing phenomenon, and the divergence phenomenon occurs at two ends of a data sequence, so that the Hilbert-Huang transform (HHT) is difficult to apply to practice.
A new signal analysis method, namely Empirical Wavelet Transform (EWT), is proposed by Gilles in France scholars in 2013, is developed in the theoretical framework of Empirical Mode Decomposition (EMD) and Wavelet transform, has high operation efficiency, is widely applied to the fields of engineering signal analysis, fault diagnosis and the like, and achieves good effects. The wavelet transform is used for carrying out electric quantity measurement on distortion signals, the selection of wavelet bases and the number of decomposition layers is needed, and the self-adaptive capacity is poor. In Korea camphan, Shenshuin, Xiaotao, Yao Li, Penghe, Song Brigjie, distorted signal electric quantity measurement based on morphological wavelets [ J ] electric measurement and instrument, 2016,53(10):44-51, the electric quantity measurement of nonlinear signals based on morphological wavelets is proposed, but frequency aliasing phenomenon among various frequency bands may exist, and adaptive detection cannot be realized. An improved S transformation and a rapid S transformation algorithm based on binary sampling have stronger time-frequency analysis capability but are still limited by a Heisberg inaccurate measurement principle are proposed to research on a Shiqiang, Tang quest, Song Peng, Zyongwang and nonlinear load electricity measurement method [ J ]. electron measurement and instrument study 2018, 32(04): 181-.
Disclosure of Invention
The invention aims to provide a distortion signal electric quantity measuring method based on empirical wavelet transform, which aims to solve the problems that the electric quantity measurement of distortion signals in the wavelet transform in the prior art needs to be poor in self-adaptive capacity when wavelet bases and decomposition layer numbers are selected, and the electric quantity measurement of distortion signals in the prior art has the frequency aliasing phenomenon among frequency bands, cannot realize self-adaptive detection and is subject to the Heisenberg inaccurate measurement principle.
In order to solve the technical problems, the technical scheme adopted by the invention is a distortion signal electricity metering method based on empirical wavelets, which comprises the following specific steps:
step S1: collecting original voltage signals and current signals in a power grid as signals to be observed;
step S2: performing empirical wavelet transform on a signal to be observed, specifically:
firstly, carrying out self-adaptive frequency spectrum division on a signal to be observed, and dividing the signal to be observed into different modes; then, performing empirical wavelet transform on each mode to decompose a signal to be observed;
step S3: and extracting a fundamental wave signal and a distortion signal of a signal to be observed from the empirical wavelet transform decomposition result, and further obtaining the active power P.
Further, the step S2 of adaptively dividing the frequency spectrum specifically includes: firstly, determining the number of signals N to be observed; then, the boundary omega of the divided spectrum is determinednWhere n is the nth spectral boundary around each ωnDefine a transition section TnWidth of 2 munIn which μn＝γωnAnd gamma is a coefficient.
Further, the step S2 of performing empirical wavelet transform on each modality specifically includes:
step S2.1: from the determined spectral boundary ωnConstruction of empirical wavelet psin(omega) mathematical models and empirical scales
A mathematical model;
step S2.2: and performing empirical wavelet transform and inverse transform.
Further, said empirical wavelet ψnThe (ω) mathematical model is:
said empirical measure
The mathematical model is as follows:
wherein the content of the first and second substances,
let the intermediate variable
Then
Further, the specific steps of performing empirical wavelet transform and inverse transform are as follows:
step S2.2.1: the original signal f (t) is compared with the empirical scale
Performing inner product processing to obtain approximate coefficient
Comprises the following steps:
the original signal f (t) is compared with the empirical wavelet psin(t) performing inner product processing to obtain detail coefficient
Comprises the following steps:
wherein the content of the first and second substances,
is a scale of experience
Complex conjugation of (a);
for empirical wavelets psin(t) complex conjugation;
fourier transform of the original signal f (t);
is a scale of experience
Fourier transform of (1);
for empirical wavelets psin(t) Fourier transform; f-1[.]F (tau) is an original signal at the time of tau for inverse Fourier transform;
step S2.2.2: reconstructing an original signal, and decomposing the original signal into a mathematical model of the sum of amplitude modulation and frequency modulation components:
wherein "+" is convolution processing;
indicating an empirical scale, #n(t) represents an empirical wavelet;
representing empirical dimensions
Fourier transform of (1);
representing empirical wavelet psin(t) Fourier transform;
representing approximation coefficients
The fourier transform of (a) the signal,
showing detail coefficients
Fourier transform of (1); f-1[.]Is an inverse fourier transform.
Further, the empirical mode f obtained by decomposing the AM and FM componentsk(t) is:
then
Wherein the content of the first and second substances,
in order to approximate the coefficients of the coefficients,
is the kth single component detail coefficient; n represents the total number of single components; psik(t) is the kth single-component empirical wavelet;
is an empirical scale.
Further, the active power P in the step S3 is the power P generated by the fundamental voltage current signal1(t) power p generated by the action of fundamental voltage signal and distorted current signal1s(t) power p generated by the action of the distorted voltage signal and the fundamental current signals1(t), power p generated by distorted voltage signal and current signalss(t) composition.
Further, the number of the signals N to be observed and the boundary omega of the divided frequency spectrum are determinednThe method specifically comprises the following steps: maximum amplitude sequence of signal frequency spectrum according to amplitude
Performing descending arrangement processing, wherein M is the total number of the maximum amplitude values of the signal frequency spectrum, and i is the serial number of the maximum amplitude values of the signal frequency spectrum after descending arrangement processing; and set a threshold value of M theretoM+α(M1-MM) The range is adjustable, wherein the alpha epsilon (0, 1) represents the relative amplitude ratio; in the arranged sequence, marking the maximum values larger than the threshold value as main maximum values, wherein the number of the main maximum values is the number N of the signals to be observed; then, the boundary omega of the divided spectrum is determinedn. The frequency omega corresponding to two adjacent main maxima in the frequency spectrumnAnd Ωn+1The midpoint of (a) is the boundary omega of the divided spectrumnWhere N-1, 2, …, N-1, denotes the nth spectral boundary; omega0＝0，ωN＝π。
The invention has the beneficial effects that: the invention provides a power grid distortion signal electric quantity measuring method based on empirical wavelet transform, which can realize self-adaptive decomposition and analysis of common distortion signals of a power grid by using the empirical wavelet transform, can carry out self-adaptive decomposition according to a spectrogram without setting decomposition layer number, accurately decomposes fundamental wave signals and subharmonic signals, and obviously lightens the mode aliasing phenomenon of the wavelet transform; meanwhile, the time domain positioning precision is high, the starting time and the ending time of a distortion signal can be accurately positioned, and a fundamental wave signal and the distortion signal can be accurately reconstructed, so that accurate electric quantity metering can be carried out. The method not only reduces the metering error of the traditional wavelet transform and lightens the end point effect of the wavelet transform, but also keeps the advantage of simultaneous localization of the wavelet transform time frequency.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flow chart of distortion signal electricity metering.
Fig. 2 is a graph of empirical mode decomposition results of a stable distortion voltage signal.
Fig. 3 is a graph of empirical mode decomposition results of a stable distortion current signal.
Fig. 4 is a graph of the wavelet 5-level decomposition result of the stabilized distortion voltage signal Daubechies 40.
Fig. 5 is a graph of the wavelet 5-layer decomposition result of the stable distortion current signal Daubechies 40.
Fig. 6 is a graph comparing a reconstructed fundamental voltage signal, a reconstructed distorted voltage signal and an original signal of a stabilized distorted voltage signal.
Fig. 7 is a graph comparing a reconstructed fundamental current signal, a reconstructed distortion current signal and an original signal of a stabilized distortion current signal.
Fig. 8 is a graph of empirical wavelet transform decomposition adaptive spectral partitioning of a stable distorted voltage signal.
Fig. 9 is an empirical wavelet transform decomposition adaptive spectral partitioning diagram of a stable distortion current signal.
Fig. 10 is an exploded view of empirical wavelet transform distortion voltage for each mode.
Fig. 11 is an exploded view of empirical wavelet transform distortion current for each mode.
Fig. 12 is a graph comparing a stabilized distorted voltage signal reconstructed voltage fundamental wave signal with an original voltage fundamental wave signal.
Fig. 13 is a graph comparing a reconstructed voltage distortion signal of a stabilized distorted voltage signal with an original voltage distortion signal.
Fig. 14 is a graph comparing a stabilized distorted current signal reconstructed current fundamental signal with an original current fundamental signal.
Fig. 15 is a graph comparing a reconstructed current distortion signal of a stabilized distortion current signal with an original current distortion signal.
Fig. 16 is an exploded view of the time varying distortion voltage empirical mode distortion voltage.
Fig. 17 is an empirical mode distortion current exploded view of a time varying distortion current.
Fig. 18 is a graph of a time varying distortion voltage signal Daubechies40 wavelet 5-layer decomposition result.
Fig. 19 is a graph of the wavelet 5-layer decomposition result of the time-varying distortion current signal Daubechies 40.
Fig. 20 is a graph comparing a time-varying distortion voltage signal reconstructed voltage fundamental wave signal, a reconstructed voltage distortion signal and an original signal.
Fig. 21 is a graph comparing a time-varying distortion current signal reconstructed current fundamental wave signal, a reconstructed current distortion signal and an original signal.
Fig. 22 is an empirical wavelet transform adaptive spectral partitioning diagram of a time-varying distortion voltage signal.
Fig. 23 is an empirical wavelet transform adaptive spectral partitioning diagram of a time-varying distortion current signal.
Fig. 24 is an exploded view of distortion voltage by empirical wavelet transform for each mode.
Fig. 25 is an exploded view of distortion current by empirical wavelet transform for each mode.
Fig. 26 is a graph comparing a time varying distortion voltage signal reconstructed voltage fundamental signal with an original voltage fundamental signal.
FIG. 27 is a graph of a time varying distorted voltage signal reconstructed voltage distorted signal compared to an original voltage distorted signal.
Fig. 28 is a graph comparing a time-varying distortion current signal reconstructed current fundamental signal with an original current fundamental signal.
Fig. 29 is a graph of a time varying distortion current signal reconstructed current distortion signal compared to an original current distortion signal.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
1. Electricity metering of distorted signals
1.1 Generation of distorted signals in Power systems
Ideally the grid should supply power to the load at a fixed 50Hz frequency and a standard sinusoidal waveform, but the grid voltage current is distorted by the presence of increasingly nonlinear loads. The nonlinear load refers to an electrical device having a nonlinear impedance characteristic, which is a function of voltage or current applied to the electrical device impedance. When the nonlinear load is applied with voltage or current with standard sine waveform, distorted current or voltage is formed at the connection point of the nonlinear load and the power grid, so that the voltage or current of the power grid is distorted, and adverse effects such as equipment overheating, relay protection misoperation, equipment insulation damage and the like are caused. According to different load properties, nonlinear loads can be roughly divided into three types, namely ferromagnetic saturation type loads, electronic switch type loads and arc type loads. In addition, some random non-linear signals are generated in the power grid, such as: when a far end of the system breaks down and a large-capacity motor is started, voltage sag or voltage rise can be generated, equipment is easily stopped, and a sensitive load cannot normally run; transient oscillation is generated when line load and capacitor bank switching are carried out; the lightning electric shock circuit and the inductive circuit are opened and closed to cause transient pulse to cause insulation damage of equipment.
1.2 theoretical power of distorted Signal
Assuming that the voltage signal and the current signal in the power grid are u (t) and i (t), respectively, then
u(t)＝u0(t)+u1(t)+∑uh(t)+∑up(t)+uc(t) (1)
Wherein u in the formula0(t) is a direct current voltage signal; u. of1(t) is a fundamental voltage signal; u. ofh(t) is a harmonic voltage signal; u. ofp(t) is an inter-harmonic voltage signal; u. ofcAnd (t) is other forms of voltage signals.
i(t)＝i0(t)+i1(t)+∑ih(t)+∑ip(t)+ic(t) (2)
Wherein, in the formula i0(t) is a direct current signal; i.e. i1(t) is a fundamental current signal; i.e. ih(t) is the harmonic current signal; i.e. ip(t) is the inter-harmonic current signal; i.e. ic(t) is other forms of current signals.
Removing fundamental wave component u of voltage and current1(t) and i1(t), the voltage distortion component us(t), current distortion component is(t) are respectively:
us(t)＝u0(t)+∑uh(t)+∑up(t)+uc(t) (3)
is(t)＝i0(t)+∑ih(t)+∑ip(t)+ic(t) (4)
the power p (t) in the grid is then:
wherein in the formula, p1(t) power generated by the action of the fundamental voltage current signal; p is a radical of1s(t) is the power generated by the action of the fundamental voltage signal and the distortion current signal; p is a radical ofs1(t) is the power generated by the action of the distorted voltage signal and the fundamental current signal; p is a radical ofssAnd (t) is the power generated by the distorted voltage signal and current signal.
2. Distortion signal electric quantity metering based on empirical wavelet transform
Fig. 1 shows an electric energy calculation process based on empirical wavelet transform, and the principle of electric quantity measurement is as follows: firstly, converting a signal to be observed from a time domain into a frequency domain for normalization processing and adaptively dividing a frequency spectrum, performing empirical wavelet transformation in each frequency domain, and decomposing the signal to be observed into the sum of amplitude modulation and frequency modulation (AM-FM) components. Assuming that it can be decomposed into N AM-FM components, the empirical wavelet transform has the following specific transformation steps:
step S1: spectrum partitioning
Firstly, the number of signals N to be observed is determined. Maximum amplitude sequence of signal frequency spectrum according to amplitude
Performing descending arrangement processing, wherein M is the total number of the maximum amplitude values of the signal frequency spectrum, and i is the serial number of the maximum amplitude values of the signal frequency spectrum after descending arrangement processing; and set a threshold value of M theretoM+α(M1-MM) The range is adjustable, wherein the alpha epsilon (0, 1) represents the relative amplitude ratio; in the arranged sequence, marking the maximum values larger than the threshold value as main maximum values, wherein the number of the main maximum values is the number N of the signals to be observed; then, the boundary omega of the divided spectrum is determinedn. The frequency omega corresponding to two adjacent main maxima in the frequency spectrumnAnd Ωn+1The midpoint of (a) is the boundary omega of the divided spectrumnWhere N-1, 2, …, N-1, denotes the nth spectral boundary; omega0＝0，ωN＝π。
Wherein around each ωnDefine a transition section TnWidth of 2 munIn which μn＝γωnAnd gamma is a coefficient;
step S2: mathematical model of empirical wavelet and empirical scale
Spectral boundary omeganAfter the determination, an empirical wavelet psi is constructed with reference to the Meyer wavelet construction methodn(omega) is as in formula (6) and empirical scale
As shown in formula (7), respectively:
wherein, in the formulas (6) and (7)
Let the intermediate variable
Then
Step S3: empirical wavelet transform and inverse transform
The original signal f (t) is compared with the empirical scale
And empirical wavelet psin(t) obtaining an approximation coefficient by inner product processing
As shown in equation (10) and detail coefficients
As shown in formula (11):
wherein the content of the first and second substances,
representing empirical dimensions
Complex conjugation of (a);
representing empirical wavelet psin(t) complex conjugation;
a Fourier transform representing the original signal f (t);
representing empirical dimensions
Fourier transform of (1);
empirical wavelet psin(t) Fourier transform; f-1[.]For the inverse fourier transform, f (τ) is the original signal at time τ.
Reconstructing the original signal is shown in equation (12)
Wherein "+" is convolution processing;
indicating an empirical scale, #n(t) represents an empirical wavelet;
representing empirical dimensions
Fourier transform of (1);
representing empirical wavelet psin(t) Fourier transform;
representing approximation coefficients
The fourier transform of (a) the signal,
showing detail coefficients
Fourier transform of (1); f-1[.]Is an inverse fourier transform.
Empirical mode f obtained by decomposition of raw signal f (t)k(t) is defined as
Then
Wherein the content of the first and second substances,
in order to approximate the coefficients of the coefficients,
is the kth single component detail coefficient; n represents the total number of single componentsCounting; psik(t) is the kth single-component empirical wavelet;
is an empirical scale.
The fundamental voltage, the distortion voltage, the fundamental current and the distortion current of each original voltage signal and each original current signal can be respectively obtained by calculating the wavelet coefficients of each frequency band component of the distortion voltage and each frequency band component of the distortion current and substituting the wavelet coefficients into a reconstruction formula (12); then the active power p is:
can respectively calculate power P1，P1s，Ps1And PssAnd further obtaining the total power of the distorted signal based on the empirical wavelet transform.
3. Distortion signal simulation analysis based on empirical wavelet transformation
3.1 Stable distortion Signal simulation analysis
Firstly, establishing a power grid voltage and current signal which only contains steady fundamental wave, 3-order harmonic wave, 7-order harmonic wave and 9.5-order inter-harmonic wave simulation analysis, wherein the specific voltage and current signal expression is as follows:
wherein u (t) is the constructed steady-state distortion voltage signal, f0Is the fundamental wave 50 Hz;
wherein i (t) is the constructed steady state distortion voltage signal, f0Is the fundamental wave 50 Hz;
and carrying out sampling analysis on the simulation signal at a sampling frequency of 6400Hz, and sampling 0.6 second of discrete data.
(1) Empirical mode decomposition of distorted voltage and current signals
After empirical mode decomposition is performed on the distortion voltage signal and the current signal data, the distortion voltage decomposition result is shown in fig. 2, wherein RES component in the diagram is a fundamental voltage signal, IMF2 is a 3-order harmonic component signal, and IMF1 is a 7-order harmonic and 9.5-order inter-harmonic aliasing component; distortion current decomposition results are shown in fig. 3, where RES component is a fundamental current signal, IMF2 is a 3-th harmonic component signal, and IMF1 is a 7-th harmonic and 9.5-th inter-harmonic aliasing component; from fig. 2 and 3, it can be seen that although the empirical mode decomposition has good adaptivity and does not require parameter selection, and the fundamental voltage signal and the fundamental current signal can be extracted from the original signal, the IMF1 does not effectively separate the 7 th harmonic from the 9.5 th harmonic.
(2) 5-layer decomposition of distorted voltage and current signals using Daubechies40 wavelet basis
After 5-level decomposition of the distorted voltage current signal data using Daubechies40 wavelet basis, the distorted voltage decomposition results are shown in fig. 4, where d1-d5 represent 1-5 level detail distortion voltage components of wavelet transform and a5 represents 5 level distortion voltage approximation components. S represents the original voltage simulation signal (i.e., the signal to be decomposed). The distortion current decomposition result is shown in fig. 5, wherein d1-d5 in the figure represent detail distortion current components of 1-5 layers of wavelet transformation, and a5 represents approximate components of 5 th layer distortion current. S represents the original current emulation signal (i.e., the signal to be decomposed). From fig. 4 and 5, it can be known that Daubechies40 wavelet basis decomposition can more accurately separate the fundamental 50Hz signal. Then, the inverse transformation of the wavelet transform is used to reconstruct the fundamental voltage current signal and the distorted voltage current signal, respectively, and the comparison graph of the reconstructed fundamental voltage signal, the reconstructed distorted voltage signal and the original signal is shown in fig. 6, and the comparison graph of the reconstructed fundamental current signal, the reconstructed distorted current signal and the original signal is shown in fig. 7, and it can be seen from fig. 6 and 7 that the wavelet transform has a high degree of reduction of the steady-state signal.
(3) Empirical wavelet transform decomposition of distorted voltage and current signals
Firstly, self-adaptive frequency spectrum division is carried out, the original distortion voltage signal and the current signal are divided into 4 modes according to a frequency spectrum diagram in a self-adaptive mode, the self-adaptive frequency spectrum division of the distortion voltage signal is shown in fig. 8, and the self-adaptive frequency spectrum division of the distortion current signal is shown in fig. 9. Then, each mode is subjected to empirical wavelet transform, and an exploded view of distortion voltage of the empirical wavelet transform is shown in fig. 10, wherein ewt (1), ewt (2), ewt (3) and ewt in the diagram
(4) The distortion voltage is decomposed by empirical wavelet transform in a first mode, a second mode, a third mode and a fourth mode respectively; fig. 11 shows an exploded view of distortion current of empirical wavelet transform, wherein ewt (1), ewt (2), ewt (3), and ewt (4) in the diagram are respectively a first mode, a second mode, a third mode, and a fourth mode of distortion current decomposed by empirical wavelet transform.
From fig. 8 to fig. 11, it can be known that the empirical wavelet transform realizes the adaptivity of decomposition, and the number of decomposition layers is selected without experiments; and can accurately resolve the fundamental wave signal and each layer of harmonic wave signal without mode aliasing between the signals.
Then reconstructing the distorted voltage current signal, wherein a comparison graph of the reconstructed voltage fundamental wave signal and the original voltage fundamental wave signal is shown in fig. 12, and a comparison graph of the reconstructed voltage distorted signal and the original voltage distorted signal is shown in fig. 13; a comparison graph of the reconstructed current fundamental wave signal and the original current fundamental wave signal is shown in fig. 14, and a comparison graph of the reconstructed current distortion signal and the original current distortion signal is shown in fig. 15; comparing the reconstructed signals of fig. 12 to 15 with the original signal, it can be found that the degree of reduction is high.
And finally, calculating the power generated by the fundamental voltage current, the power generated by the fundamental voltage and the distortion current, the power generated by the distortion voltage and the fundamental current, and the power generated by the distortion voltage and the distortion current by using the reconstructed signals according to a power formula.
The measurement result of the wavelet transform power of the steady-state distortion signal is shown in table 1, the measurement result of the empirical mode decomposition power of the steady-state distortion signal is shown in table 2, and the measurement result of the empirical wavelet transform power of the steady-state distortion signal is shown in table 3;
TABLE 1 Steady-State distortion signal wavelet transform power measurement results
| Theoretical value | Wavelet transform | Relative error% | |
| P1 | 11000 | 10990.18674 | -8.9211 |
| P | |||
| 1s | 0 | 1.95639 | - |
| Ps1 | 0 | -1.48292 | - |
| Pss | -176.78 | -172.07711 | -2.6 |
TABLE 2 empirical mode decomposition power measurement results for steady state distortion signals
| Theoretical value | Empirical mode decomposition | Relative error% | |
| P1 | 11000 | 10997.13616 | -2.6035 |
| P | |||
| 1s | 0 | 1.09e-12 | - |
| Ps1 | 0 | -2.25e-13 | - |
| Pss | -176.78 | -176.73067 | -2.7905e-2 |
TABLE 3 empirical wavelet transform power measurement of steady state distortion signals
| Theoretical value | Empirical wavelet transform | Relative error% | |
| P1 | 11000 | 10997.6024 | -2.176 |
| P | |||
| 1s | 0 | 1.934e-13 | - |
| Ps1 | 0 | -1.994e-11 | - |
| Pss | -176.78 | -176.69609 | -4.7466e-2 |
From tables 1, 2, and 3, it can be seen that in the steady state signal, the power generated by the action of the fundamental voltage signal and the distortion current signal and the power generated by the action of the distortion voltage signal and the fundamental current signal are approximately zero, that is, no exchange power is generated in the fundamental part and the distortion part, and the theoretical calculation value is consistent with that. Empirical wavelet decomposition has a lower relative error in power on each power component than wavelet decomposition. In contrast to empirical mode decomposition, empirical wavelet transform operates on a power component P1，P1sThe relative error is lower. Meanwhile, as shown in fig. 4 to fig. 15, the reason that the error generated by the conventional wavelet transform is higher than that generated by the empirical wavelet transform is that there is spectrum aliasing, different harmonic signals cannot be separated well, and the error of the reconstructed signal at the initial position is large, so that there is a large error between the reconstructed fundamental wave and distorted signal and the real signal.
3.2 time-varying distortion signal simulation analysis
Time-varying harmonic signals and transient oscillation signals are two common transient signals in a power grid, and according to the prior art, Wu Jian chapter, Meifei, Panyi, Zhou Cheng, Shitian and Zheng Jiang and Yong, a novel power quality disturbance detection method [ J ] based on improved empirical wavelet transformation, a novel power automation device 2020,40(06): 142) 151. a composite distortion signal mathematical model of fundamental wave, time-varying harmonic and transient oscillation is constructed as follows:
wherein u (t) is a constructed time-varying distortion voltage signal; i (t) is the constructed time-varying distortion current signal; f. of0Is the fundamental 50 Hz. The 3 rd order and 7 th order harmonics of the constructed transient signal are generated in 0.2s, and the amplitude is reduced after 0.4 s. The 11 th harmonic current signal is generated at 0.4 seconds, and the total sampling time is 0.6s, so that the 11 th harmonic current signal is used for simulating the composite disturbance in the power grid.
(1) Using empirical mode decomposition for composite distorted signals
The empirical mode distortion voltage decomposition diagram is shown in fig. 16, wherein IMF1, IMF2, IMF3, IMF4, IMF5, IMF6 and IMF7 in the diagram are respectively a first mode, a second mode, a third mode, a fourth mode, a fifth mode, a sixth mode and a seventh mode obtained by empirical mode decomposition, and RES is a residual component; the empirical mode distortion current decomposition diagram is shown in fig. 17, wherein in the diagram, IMF1, IMF2, IMF3, IMF4, IMF5, IMF6 and IMF7 represent a first mode, a second mode, a third mode, a fourth mode, a fifth mode, a sixth mode and a seventh mode obtained by empirical mode decomposition, and RES is a residual component; as can be seen from fig. 16 and 17, empirical mode decomposition does not resolve the fundamental wave signal, and modal aliasing also occurs in the decomposition of the distorted signal. Therefore, the voltage and current signals cannot be measured.
(2) 5-layer decomposition of complex distorted signals using Daubechies40 wavelet basis
5-layer decomposition is carried out on the time-varying distortion signal by using Daubechies40 wavelet basis, and the distortion voltage decomposition result is shown in fig. 18, wherein d1-d5 in the figure are 1-5 layers of distortion voltage detail components of wavelet transformation, a5 is a5 th layer of distortion voltage approximate component, and S is an original distortion voltage simulation signal (namely, a signal to be decomposed); the distortion current decomposition result is shown in fig. 19, wherein d1-d5 in the figure are detail components of distortion current of 1-5 layers of wavelet transform, a5 is approximate component of distortion current of 5 th layer, and S is original simulation signal of distortion current (i.e. signal to be decomposed); then, the inverse transformation of the wavelet transformation is used to reconstruct the fundamental wave voltage signal, the current signal, the distorted voltage signal and the current signal respectively, a comparison graph of the reconstructed voltage fundamental wave signal, the reconstructed voltage distorted signal and the original signal is shown in fig. 20, and a comparison graph of the reconstructed current fundamental wave signal, the reconstructed current distorted signal and the original signal is shown in fig. 21, so that as can be seen from fig. 20 and 21, the reconstructed distorted signal has an obvious 'end point' effect at the initial position and has a larger error compared with the original distorted signal.
(3) Empirical wavelet transform decomposition of complex distorted signals
Firstly, performing adaptive spectrum division on a composite signal by empirical wavelet transform, adaptively dividing a composite distortion voltage signal into 3 modes according to a spectrogram, and as a result, as shown in fig. 22, adaptively dividing a composite distortion current signal into 4 modes according to the spectrogram, as a result, as shown in fig. 23, and then performing empirical wavelet transform on each mode, wherein a distortion voltage exploded view is shown in fig. 24, wherein ewt (1), ewt (2), ewt (3) and ewt (4) in the graph are respectively a first mode, a second mode, a third mode and a fourth mode decomposed by the empirical wavelet transform of distortion voltage; the distortion current decomposition diagram is shown in fig. 25, wherein ewt (1), ewt (2), ewt (3) and ewt (4) in the diagram are respectively a first mode, a second mode, a third mode and a fourth mode of the distortion current decomposed by empirical wavelet transform.
It can be known from fig. 24 and 25 that different harmonics can be accurately resolved by empirical wavelet transform, and compared with the conventional wavelet transform mode, the mode aliasing phenomenon is reduced, and the positioning capability is good in the time domain, so that the starting time and the change time of different harmonics can be accurately reflected, but a certain "endpoint" effect exists in a small part of the starting time of each mode.
Then, the composite signal is reconstructed, a comparison graph of the reconstructed voltage fundamental wave signal and the original voltage fundamental wave signal is shown in fig. 26, and a comparison graph of the reconstructed voltage distortion signal and the original voltage distortion signal is shown in fig. 27; a comparison graph of the reconstructed current fundamental wave signal and the original current fundamental wave signal is shown in fig. 28, and a comparison graph of the reconstructed current distortion signal and the original current distortion signal is shown in fig. 29.
And finally, calculating the fundamental wave power, the power generated by the fundamental wave voltage and the distortion current, the power generated by the distortion voltage and the fundamental wave current, and the power generated by the distortion voltage and the distortion current by using the reconstructed signal according to a power formula.
The wavelet transformation power measurement result of the time-varying distortion signal is shown in table 4, and the empirical wavelet transformation power measurement result of the time-varying distortion signal is shown in table 5;
TABLE 4 wavelet transform power measurement results for time varying distortion signals
| Theoretical value | Wavelet transform | Relative error% | |
| P1 | 11000 | 10995.80105 | -3.8172e-2 |
| P1s | 0.22140 | -1.84068 | -931.38 |
| Ps1 | 0 | -1.0474 | - |
| Pss | -84.9528 | -82.3201 | -3.1 |
TABLE 5 empirical wavelet transform power measurement of time varying distortion signals
| Theoretical value | Empirical wavelet transform | Relative error% | |
| P1 | 11000 | 10997.5194 | -2.255e-2 |
| P1s | 0.22140 | 0.21257 | -3.99 |
| |
0 | 0.009318 | - |
| Pss | -84.9528 | -84.7347 | -0.26 |
As can be seen from tables 3 and 4, the empirical wavelet transform under the constructed complex distortion model has a relatively low relative error compared with the conventional wavelet transform, and it can be seen from the reconstructed signal that the "endpoint" effect is reduced to a certain extent by the empirical wavelet transform, and the empirical wavelet transform has a higher degree of restorability, and can more adaptively analyze the complex signal of the power grid, and at the same time, can accurately measure the power of the distortion signal.
All the embodiments in the present specification are described in a related manner, and the same and similar parts among the embodiments may be referred to each other, and each embodiment focuses on the differences from the other embodiments.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (8)
1. The distortion signal electricity metering method based on the empirical wavelet is characterized by comprising the following specific steps of:
step S1: collecting original voltage signals and current signals in a power grid as signals to be observed;
step S2: performing empirical wavelet transform on a signal to be observed, specifically:
firstly, carrying out self-adaptive frequency spectrum division on a signal to be observed, and dividing the signal to be observed into different modes; then, performing empirical wavelet transform on each mode to decompose a signal to be observed;
step S3: and extracting a fundamental wave signal and a distortion signal of a signal to be observed from the empirical wavelet transform decomposition result, and further obtaining the active power P.
2. The empirical wavelet based distortion signal electricity metering method according to claim 1, wherein the step S2 of adaptively dividing the spectrum specifically comprises: firstly, determining the number of signals N to be observed; then, the boundary omega of the divided spectrum is determinednWhere n is the nth spectral boundary around each ωnDefine a transition section TnWidth of 2 munIn which μn＝γωnAnd gamma is a coefficient.
3. The empirical wavelet based distortion signal electricity metering method according to claim 1, wherein the empirical wavelet transform performed in each modality in step S2 includes the following specific steps:
step S2.1: from the determined spectral boundary ωnConstruction of empirical wavelet psin(omega) mathematical models and empirical scales
A mathematical model;
step S2.2: and performing empirical wavelet transform and inverse transform.
4. The empirical wavelet based distortion signal electricity metering method of claim 3, wherein the empirical wavelet ψ isnThe (ω) mathematical model is:
said empirical measure
The mathematical model is as follows:
wherein the content of the first and second substances,
let the intermediate variable
Then
5. The distortion signal electricity metering method based on the empirical wavelet as claimed in claim 3, wherein the specific steps of performing the empirical wavelet transform and the inverse transform are as follows:
step S2.2.1: the original signal f (t) is compared with the empirical scale
Performing inner product processing to obtain approximate coefficient
Comprises the following steps:
the original signal f (t) is compared with the empirical wavelet psin(t) performing inner product processing to obtain detail coefficient
Comprises the following steps:
wherein the content of the first and second substances,
is a scale of experience
Complex conjugation of (a);
for empirical wavelets psin(t) complex conjugation;
fourier transform of the original signal f (t);
is a scale of experience
Fourier transform of (1);
for empirical wavelets psin(t) Fourier transform; f-1[.]F (tau) is an original signal at the time of tau for inverse Fourier transform;
step S2.2.2: reconstructing an original signal, and decomposing the original signal into a mathematical model of the sum of amplitude modulation and frequency modulation components:
wherein "+" is convolution processing;
indicating an empirical scale, #n(t) represents an empirical wavelet;
representing empirical dimensions
Fourier transform of (1);
representing empirical wavelet psin(t) Fourier ofTransforming;
representing approximation coefficients
The fourier transform of (a) the signal,
showing detail coefficients
Fourier transform of (1); f-1[.]Is an inverse fourier transform.
6. The empirical wavelet based distorted semaphore electric quantity measuring method as claimed in claim 5, wherein said empirical mode f obtained by decomposing into AM and FM componentsk(t) is:
then
Wherein the content of the first and second substances,
in order to approximate the coefficients of the coefficients,
is the kth single component detail coefficient; n represents the total number of single components; psik(t) is the kth single-component empirical wavelet;
is an empirical scale.
7. A distortion signal electricity metering method based on empirical wavelet as claimed in claim 1, wherein the active power P in step S3 is the power P generated by the fundamental wave voltage current signal action1(t) power p generated by the action of fundamental voltage signal and distorted current signal1s(t) power p generated by the action of the distorted voltage signal and the fundamental current signals1(t), power p generated by distorted voltage signal and current signalss(t) composition.
8. The empirical wavelet based distortion signal electricity measuring method according to claim 2, wherein the number of signals N to be observed and the partition spectrum boundary ω are determinednThe method specifically comprises the following steps: maximum amplitude sequence of signal frequency spectrum according to amplitude
Performing descending arrangement processing, wherein M is the total number of the maximum amplitude values of the signal frequency spectrum, and i is the serial number of the maximum amplitude values of the signal frequency spectrum after descending arrangement processing; and set a threshold value of M theretoM+α(M1-MM) The range is adjustable, wherein the alpha epsilon (0, 1) represents the relative amplitude ratio; in the arranged sequence, marking the maximum values larger than the threshold value as main maximum values, wherein the number of the main maximum values is the number N of the signals to be observed; then, the boundary omega of the divided spectrum is determinednThe frequency omega corresponding to two adjacent main maximums in the frequency spectrumnAnd Ωn+1The midpoint of (a) is the boundary omega of the divided spectrumnWhere N-1, 2, …, N-1, denotes the nth spectral boundary; omega0＝0，ωN＝π。
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