CN107086566B - LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information - Google Patents
LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information Download PDFInfo
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- CN107086566B CN107086566B CN201710256704.9A CN201710256704A CN107086566B CN 107086566 B CN107086566 B CN 107086566B CN 201710256704 A CN201710256704 A CN 201710256704A CN 107086566 B CN107086566 B CN 107086566B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
Abstract
The invention discloses a kind of LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information, it include: according to low-frequency oscillation state measured data under interconnected electric power system failure, Various types of data signal in predeterminable area is integrated according to time point sequence, constitute oscillator signal matrix, the time window length for acquiring signal is matrix line number, it is taken as oneself and knows two periods of low-limit frequency mode in the predeterminable area, matrix columns is the quantity for measuring oscillator signal type；LMD is carried out to each column signal of the signal matrix to decompose to obtain Oscillatory mode shape component and remaining trend component；The relevant parameter of each Oscillatory mode shape component is calculated according to the Oscillatory mode shape component, the relevant parameter includes instantaneous frequency, instantaneous amplitude and damping.The present invention has the advantage that local envelope optimization may be implemented, it is effectively improved the end effect of LMD decomposition, realizes the oscillation characteristics identification based on this decomposition result.
Description
Technical field
The present invention relates to low-frequency oscillation analysis technical fields, and in particular to a kind of LMD based on Wide-area Measurement Information
Interconnected electric power system low-frequency oscillation analysis method.
Background technique
The interconnection phenomenon of large-scale power system is more and more common, the purpose is to improve the reliability of hair, transmission of electricity and economy,
But the expansion of system scale, so that electric network composition and the complicated diversification of the method for operation, cause system instability more prominent.
The transmittability of the weak interconnection limitation interconnection of big regional power grid, and the damping that can be greatly reduced between system, certain weak connections are very
To causing system to go out negative damping, so that the system frequency of occurrences is the low-frequency oscillation of 0.1~2.5Hz, the machine of the oscillation is participated in
Group rotor is opposite to be swung, and power transmission anomalous effects system operates normally on transmission line of electricity, system step-out when serious, and may draw
Send out the serious consequences such as cascading failure, large-area power-cuts.
The dynamic characteristic of low-frequency oscillation, needs to extract the instantaneous parameters of oscillating signal, and picks out the resistance of oscillation
Buddhist nun obtains oscillation characteristics progress associated regulatory than size, to run controllers comprehensively, accurately holds the small interference of raising system
The installation of the stabilization control device such as power system stabilizer, PSS is instructed in the direction of stability.And low-frequency oscillation of electric power system is believed
Number it is nonlinear time-varying composite signal, therefore needs to carry out Oscillatory mode shape decomposition to it before parameter extraction.
At present oscillator signal decompose method mainly have Fourier transformation, wavelet transformation, pencil of matrix identification, Prony algorithm,
HHT (Hilbert-Huang transform) algorithm etc..Fourier transformation cannot extract the local feature of signal, not be suitable for non-linear letter
Number；Wavelet transformation has certain limitation for the selection of small echo, does not have good adaptability；Pencil of matrix identification method can be estimated
Meter systems Oscillatory mode shape has preferably noise resisting ability, but the time-varying characteristics of signal cannot be analyzed accurately；Prony
Algorithm is as a kind of common oscillating signal analysis method, and there are still some problems, as problem of determining the order processing is inaccurate, anti-
Noise jamming scarce capacity etc..HHT is a kind of novel Time Domain Analysis, including empirical mode decomposition (EMD) and Martin Hilb
Spy's two processes of variation, this method fully consider signal local scale feature, can identify that nonlinear properties Oscillatory mode shape combines,
And the multiple information for obtaining Oscillatory mode shape include instantaneous frequency, instantaneous amplitude, damping.But due to its decomposition method itself
Limitation will appear envelope in the process, owe the problems such as envelope, modal overlap, and the obtained corresponding physical significance of each component is not
It is clear, meanwhile, the edge effect and negative frequency being likely to occur when calculating instantaneous frequency and instantaneous amplitude using Hilbert method are asked
Topic limits the actual application ability of this method.The local mean value that occurs on EMD decomposition base decompose (LMD) method compared with point
There is significant superiority in terms of solution method and variable physical expression of significance, be conducive to improve the accurate of oscillating signal decomposition
Property and signal completeness, the physical characteristic of the calculating definitely expression signal of instantaneous parameters.But there are still three factors
It is main to influence LMD Decomposition Accuracy, it is respectively as follows: sample frequency, sliding average span, end effect processing.
Summary of the invention
The present invention is directed at least solve one of above-mentioned technical problem.
For this purpose, it is an object of the invention to propose a kind of LMD interconnected electric power system low-frequency oscillation based on Wide-area Measurement Information point
Analysis method may be implemented local envelope optimization, be effectively improved the end effect of LMD decomposition, realizes the vibration based on this decomposition result
Swing feature identification.
To achieve the goals above, embodiment of the invention discloses a kind of LMD interconnecting electric power system based on Wide-area Measurement Information
System low-frequency oscillation analysis method, comprising the following steps: right according to low-frequency oscillation state measured data under interconnected electric power system failure
Various types of data signal is integrated according to time point sequence in predeterminable area, is constituted oscillator signal matrix, is acquired the time of signal
Window length is matrix line number, takes two periods of low-limit frequency mode in the predeterminable area, and matrix columns is measurement oscillation letter
The quantity of number type；LMD is carried out to each column signal of the signal matrix to decompose to obtain Oscillatory mode shape component and remaining trend point
Amount；The relevant parameter of each Oscillatory mode shape component is calculated according to the Oscillatory mode shape component, the relevant parameter includes instantaneous frequency
Rate, instantaneous amplitude and damping.
Further, the step of LMD decomposition being carried out to signal include: by multiple iteration with separate the multiple parts of generation
Envelope function and local mean function；Multipair envelope signal is obtained according to the multiple local envelope function and local mean function
With the combination of pure FM signal, wherein the corresponding pure FM signal of each pair of envelope signal constitutes a production function PF points
Measure signal.
Further, further includes: local envelope curve between rational spline interpolating function building extreme point is used, by adjusting
Parameter realizes the in due course change of curve shape, using extreme value symmetric points as the carry out envelop optimization of foundation；For end effect phenomenon
Inhibited using adaptive waveform continuation method.
Further, before local mean value further include: define orthogonality criterion OC (Orthogonality
Criterion the adjacent OC difference iterated to calculate twice is judged item by) calculation method
Part.
Further, parameter extraction is carried out using the method for calculation and obtains the instantaneous frequency, the instantaneous amplitude and institute
State damping.
Further, further includes: according to Oscillatory mode shape instantaneous frequency size determine oscillation mode belong to inter-area oscillations or
Local oscillations, and divide the participation unit of each oscillation mode；One is carried out to the power system dynamic stability characteristic according to damping size
Fixed evaluation obtains the Characteristics of Low Frequency Oscillations information of interconnected network in the predeterminable area.
Further, further includes: in inter-area oscillation mode, the oscillator signal matrix is frequency signal, by the frequency
Rate signal is filtered signal using bandpass filter；Filtered signal is subjected to LMD and decomposes the Oscillatory mode shape point obtained
Amount.
LMD interconnected electric power system low-frequency oscillation analysis method according to an embodiment of the present invention based on Wide-area Measurement Information, relatively
For the prior art, have the advantages that
(1) analysis that low-frequency oscillation of electric power system is carried out using signal analysis method more makes effective use of wide area letter
The timeliness and accuracy of breath, and it is more intuitive, convenient compared with traditional theoretical analysis method, and model believes low-frequency oscillation
Number identification have adaptivity.
(2) it in the improvement of part mean decomposition method, proposes that signal is effectively treated using adaptive waveform continuation method
End effect of the left and right ends in decomposable process introduces the envelope function acquisition methods based on rational spline interpolating function and improves
The use of the accuracy of local envelope, OC criterion has faster convergence rate compared with classical termination condition.
(3) according to oscillator signal decompose as a result, using the method for calculation can directly obtain Oscillatory mode shape instantaneous frequency,
The information such as instantaneous amplitude, damping instruct the progress of relevant stable control measure, and can be straight according to needing to add bandpass filter
It obtains and takes inter-area oscillations signal.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, in which:
Fig. 1 is the stream of the LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information of the embodiment of the present invention
Cheng Tu.
Specific embodiment
The embodiment of the present invention is described below in detail, examples of the embodiments are shown in the accompanying drawings, wherein from beginning to end
Same or similar label indicates same or similar element or element with the same or similar functions.Below with reference to attached
The embodiment of figure description is exemplary, and for explaining only the invention, and is not considered as limiting the invention.
Referring to following description and drawings, it will be clear that these and other aspects of the embodiment of the present invention.In these descriptions
In attached drawing, some particular implementations in the embodiment of the present invention are specifically disclosed, to indicate to implement implementation of the invention
Some modes of the principle of example, but it is to be understood that the scope of embodiments of the invention is not limited.On the contrary, of the invention
Embodiment includes all changes, modification and the equivalent fallen within the scope of the spirit and intension of attached claims.
The present invention is described below in conjunction with attached drawing.
Fig. 1 is the stream of the LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information of the embodiment of the present invention
Cheng Tu.As shown in Figure 1, the LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information of the embodiment of the present invention, packet
Include following steps:
S1: according to low-frequency oscillation state measured data under interconnected electric power system failure, Various types of data in predeterminable area is believed
Number according to time point sequence integrated, constitute oscillator signal matrix, acquire signal time window length be matrix line number, take pre-
If two periods of low-limit frequency mode in region, matrix columns is the quantity for measuring oscillator signal type；
S2: LMD is carried out to each column signal of signal matrix and decomposes to obtain Oscillatory mode shape component and remaining trend component；
S3: calculating the relevant parameter of each Oscillatory mode shape component according to Oscillatory mode shape component, and relevant parameter includes instantaneous frequency
Rate, instantaneous amplitude and damping.
In one embodiment of the invention, the step of carrying out LMD decomposition to signal includes: by multiple iteration and to divide
From the multiple local envelope functions of generation and local mean function；It is obtained according to multiple local envelope functions and local mean function more
Combination to envelope signal and pure FM signal, wherein the corresponding pure FM signal of each pair of envelope signal constitutes a life
Produce function PF component signal.
In one embodiment of the invention, further includes: locally wrapped between constructing extreme point using rational spline interpolating function
Network curve realizes the in due course change of curve shape by adjusting parameter, using extreme value symmetric points as the carry out envelop optimization of foundation；It is right
Inhibited in end effect phenomenon using adaptive waveform continuation method.
In one embodiment of the invention, before local mean value further include: define orthogonality criterion OC
(Orthogonality criterion) calculation method, using the adjacent OC difference iterated to calculate twice as interative computation
Process terminates Rule of judgment.
In one embodiment of the invention, parameter extraction is carried out using the method for calculation and obtains instantaneous frequency, instantaneous width
Value and damping.
In one embodiment of the invention, further includes: oscillation mode category is determined according to Oscillatory mode shape instantaneous frequency size
In inter-area oscillations or local oscillations, and divide the participation unit of each oscillation mode；According to damping size to system dynamic
Stability characteristic (quality) carries out certain evaluation, obtains the Characteristics of Low Frequency Oscillations information of interconnected network in predeterminable area.
In one embodiment of the invention, further includes: in inter-area oscillation mode, oscillator signal matrix is frequency letter
Number, frequency signal is filtered signal using bandpass filter；Filtered signal is subjected to LMD and decomposes the oscillation obtained
Modal components.
To make it is further understood that the application, will be described in detail by following embodiment.
The power-angle oscillation signal matrix of all units, the matrix line number are time window length, acquire the time window of signal
Degree is taken as oneself and knows two periods of low-limit frequency mode in information, and matrix columns is the quantity of measuring signal, i.e. unit number；For
The each column of signal matrix are that each oscillator signal carries out the following processing in the low-frequency oscillation.
First against the end effect problem being likely to occur in LMD decomposition, firstly for original signal before decomposition starts
x0(t) left and right ends carry out adaptive waveform continuation, and by taking the continuation of left end as an example, process is as follows:
If original signal x0(t) in, m0 i、n0 iRespectively its maximum and minimum, respectively corresponding the time isWith
If x0(t) left end point data is x0(1), with x0(1)-m0 1-n0 13 points of compositions, one triangular waveform, is referred to as signature waveform,
Then along signal x0(t) search to the right and the highest triangular waveform of signature waveform matching degree, it is assumed that the matching waveform is x0(i)-
m0 i-n0 i, the waveform of (front) is as x on the left of the matching waveform0(t) continuation waveform is (if right side continuation is by the matching waveform
The waveform on right side is used as right side continuation waveform), the trend feature that the method can retain waveform variation is constant.
(1) it calculates and removes x0(1) the endpoint value x of other all triangular waveforms of first triangular waveform where0(i), the end
Point corresponding time point may be expressed as:
If finding outIt is not sampled point, usable interpolation method finds out its explicit value, and the selection of interpolation method can basis
Depending on needing.
(2) all triangular waveforms are calculated and signature waveform are matched " distance ":
D0(i)=| m0 i-m0 1|+|n0 i-n0 1|+|x0(i)-x0(1)| (2)
(3) the smallest distance value minD is hunted out0(i), given threshold ε, when meeting minD0(i) < ε when, take this apart from right
The triangular wave answered is best match waveform, by the part continuation before this triangular wave to original signal x0(1) front, can be completed wave
Continuation on the left of shape.The size of threshold epsilon value can be adjusted according to the actual situation, and value is smaller to illustrate that original signal waveform has more
Strong regularity, it is on the contrary then mean that remote signal inherent law is poor, or may be that there are larger exceptions for data boundary.
Continuation is carried out for waveform on the right side of signal after the same method, that is, completes entire original waveform x0(t) adaptive
Answer waveform continuation.
Based on the signal x (t) for completing above-mentioned adaptive waveform continuation, LMD decomposes that specific step is as follows in the present invention:
(1) local minizing point and the Local modulus maxima for fitting signal x (t) respectively obtain envelope up and down, respectively
It is denoted as bu(t) and bl(t)。
Wherein, all extreme point n of signal x (t)i, find out each adjacent Local Extremum niAnd ni+1Average value:
Find out each adjacent Local Extremum niAnd ni+1The half of difference is as partial amplitudes:
(2) average value of envelope up and down is calculated as local mean value letter based on step (1), rational spline interpolating function
Number, may be expressed as:
The half of envelope absolute value of the difference up and down is calculated as the envelope estimation function in original method, may be expressed as:
(3) by the local mean value function m of signal x (t)11(t) separation from x (t), can be obtained h11(t):
h11(t)=x (t)-m11(t) (7)
(4) h is recycled11(t) divided by envelope estimation function a11(t), thus to h11(t) it is demodulated, s can be obtained11(t):
(5) for s11(t) it repeats the above steps (1) and step (2), s can be obtained11(t) envelope estimation function a12(t)。
Termination Rule of judgment with OC orthogonality criterion as interative computation, to reach the s of acquisition1pIt (t) is pure FM signal, no
When meeting the condition, then needing to repeat the above steps carries out iteration calculating p times.OC rule definition are as follows:
In this iterative process, mij(t) what is indicated is the calculated during part refers both to decompose when solving i-th of PF component
J local mean value function.With being continuously increased for the number of iterations, mij(t) value levels off to 0, and the value of OC constantly levels off to therewith
1, when OC reaches minimum value, the number of iterations increases bring and changes the increase for being OC value or vibration.Therefore, OC is reached most
Decomposition number when small value is denoted as best the number of iterations, while defining the difference oc for the OC that adjacent iteration twice obtainseIt is whether small
Rule of judgment is terminated as interative computation process in 0.
oce=ocj-ocj1 (10)
(6) corresponding pure FM signal s is can be obtained into the multiplication of all local envelopes function obtained in iterative process1p(t)
Envelope signal:
a1(t)=a11(t)a12(t)…a1p(t) (11)
Envelope signal a1(t) that represent is exactly its instantaneous amplitude, instantaneous frequency f1(t) pure FM signal s can be passed through1p
(t) it obtains, it may be assumed that
(7) in the decomposable process of signal x (t), by envelope signal a1(t) corresponding pure FM signal s1p(t) it constitutes
First production function PF component signal:
PF1(t)=a1(t)s1p(t) (13)
First PF component is separated from signal x (t), a new signal μ can be obtained1(t), using this new signal as to
Decomposed signal repeats above-mentioned decomposition method, obtains multiple PF components and residual signal μk(t), until termination condition μkIt (t) is constant
Or until monotonic function, if μk(t) energy very little can also terminate decomposition, so far complete entire decomposable process.
Finally, signal x (t) decomposition result is represented by following formula:
Wherein, r is the number for implementing to decompose, it is determined by signal x (t) feature.
Next, calculating the extraction for carrying out instantaneous parameters for each PF component using the method for calculation, it is assumed that its is single
Discrete oscillating signal x (k) may be expressed as:
X (k)=Xe-αkΔt cos(2πfkΔt+φ) (15)
In above formula (15), X is signal initial magnitude, and α is signal decay factor (damping), and k is discrete signal samples points,
F is signal frequency, and Δ t is the sampling interval, and φ is initial phase；Signal x (k) is unfolded below according to Euler's formula, as follows:
Enable a=ej2πfkΔt, b=e-αΔt,Z=Re [a], then:
X (k)=Abkak+A*bka-k (17)
Wherein, A*It is the conjugate function of A.When signal length is greater than 4 and meets single discrete oscillating signal x (k)
Expression formula when, by formula (17), (18), (19) can calculate separately out instantaneous frequency f, instantaneous amplitude h and damping α:
H=Xe-αkΔt=2 | A | e-αkΔt
According to oscillation or area oscillation between frequency of oscillation size unit, may determine that simultaneously according to the size of frequency values
A group of planes in the same area oscillation mode.The vibration of certain frequency range can be filtered out by the effect of bandpass filter simultaneously
Signal is swung, oscillation mode between inter-area oscillation mode or unit is extracted.
It approximate can judge that the leading Oscillatory mode shape of system, damping α are big in conjunction with the size and frequecy characteristic of oscillation amplitude
The small important indication as low-frequency oscillation control.
In addition, its of the LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information of the embodiment of the present invention
It constitute and effect be all for a person skilled in the art it is known, in order to reduce redundancy, do not repeat them here.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means specific features, structure, material or spy described in conjunction with this embodiment or example
Point is included at least one embodiment or example of the invention.In the present specification, schematic expression of the above terms are not
Centainly refer to identical embodiment or example.Moreover, particular features, structures, materials, or characteristics described can be any
One or more embodiment or examples in can be combined in any suitable manner.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that: not
A variety of change, modification, replacement and modification can be carried out to these embodiments in the case where being detached from the principle of the present invention and objective, this
The range of invention is by claim and its equivalent limits.
Claims (4)
1. a kind of LMD interconnected electric power system low-frequency oscillation analysis method based on Wide-area Measurement Information, which is characterized in that including following step
It is rapid:
According to low-frequency oscillation state measured data under interconnected electric power system failure, to Various types of data signal in predeterminable area according to when
Between point sequence integrated, constitute oscillator signal matrix, acquire signal time window length be matrix line number, take the preset areas
Two periods of low-limit frequency mode in domain, matrix columns are the quantity for measuring oscillator signal type；
LMD is carried out to each column signal of the signal matrix to decompose to obtain Oscillatory mode shape component and remaining trend component；
The relevant parameter of each Oscillatory mode shape component is calculated according to the Oscillatory mode shape component, the relevant parameter includes instantaneous frequency
Rate, instantaneous amplitude and damping；
Wherein, include: to the step of signal progress LMD decomposition
Using local envelope curve between rational spline interpolating function building extreme point, the suitable of curve shape is realized by adjusting parameter
When change, using extreme value symmetric points as the carry out envelop optimization of foundation；Adaptive waveform continuation side is used for end effect phenomenon
Method is inhibited；
Orthogonality criterion OC (Orthogonality criterion) calculation method is defined, adjacent iterative calculation twice is obtained
OC difference as interative computation process terminate Rule of judgment；
Multiple local envelope functions and part mean function are generated with separating by multiple iteration；
The combination of multipair envelope signal Yu pure FM signal is obtained according to the multiple local envelope function and local mean function,
Wherein, the corresponding pure FM signal of each pair of envelope signal constitutes a production function PF component signal.
2. the LMD interconnected electric power system low-frequency oscillation analysis method according to claim 1 based on Wide-area Measurement Information, feature
It is, parameter extraction is carried out using the method for calculation and obtains the instantaneous frequency, the instantaneous amplitude and the damping.
3. the LMD interconnected electric power system low-frequency oscillation analysis method according to claim 2 based on Wide-area Measurement Information, feature
It is, further includes:
Determine that oscillation mode belongs to inter-area oscillations or local oscillations according to Oscillatory mode shape instantaneous frequency size, and divides each vibration
Swing the participation unit of mode；
Certain evaluation is carried out to the power system dynamic stability characteristic according to damping size, obtains interconnected network in the predeterminable area
The Characteristics of Low Frequency Oscillations information.
4. the LMD interconnected electric power system low-frequency oscillation analysis method according to claim 1 based on Wide-area Measurement Information, feature
It is, further includes:
In inter-area oscillation mode, the oscillator signal matrix is frequency signal, and the frequency signal is utilized bandpass filter
Signal is filtered；
Filtered signal is subjected to LMD and decomposes the Oscillatory mode shape component obtained.
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| CN109617051B (en) * | 2018-12-05 | 2022-06-14 | 国网黑龙江省电力有限公司电力科学研究院 | New energy power system low-frequency oscillation parameter identification method |
| CN109659957B (en) * | 2019-01-10 | 2022-05-17 | 东北电力大学 | APIT-MEMD-based power system low-frequency oscillation mode identification method |
| CN113361389B (en) * | 2021-06-03 | 2023-01-20 | 山东阅芯电子科技有限公司 | Method for processing high-frequency oscillation characteristics of signal |
| CN113608018A (en) * | 2021-06-30 | 2021-11-05 | 中冶南方都市环保工程技术股份有限公司 | Adaptive VMD detection method and device for improving harmonic detection precision and storage medium |
| CN114665992B (en) * | 2022-03-22 | 2023-10-27 | 吉林省广播电视研究所(吉林省广播电视局科技信息中心) | Method for measuring signal index based on average extremum |
| CN115015682B (en) * | 2022-08-09 | 2022-11-08 | 南京佑友软件技术有限公司 | Real-time online monitoring method for power quality |
| CN115204243B (en) * | 2022-09-15 | 2023-02-07 | 西南交通大学 | LMD endpoint effect improvement method based on similar triangular waveform matching continuation |
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