CN104217112B - A kind of low-frequency oscillation analysis method for power system based on polymorphic type signal - Google Patents
A kind of low-frequency oscillation analysis method for power system based on polymorphic type signal Download PDFInfo
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Abstract
The present invention discloses a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal, belongs to stability of power system analysis field.The method mainly includes：Analyze the inherent physical link between the polymorphic type curve of unit；Amplitude excursion and phase deviation evaluation index have been formulated based on the contact, the degree of accuracy that Prony algorithms extract oscillation mode has been evaluated；To avoid the excessive signal for causing a certain type of different type curve amplitude difference from being blanked, the amplitude to signal with different type carries out conversion treatment；Control oscillation modes recognition methods is given, the comprehensive evaluation index of multimachine signal is established, reflects the confidence level of Prony algorithms.Index system proposed by the present invention has engineering application value, can reflect the confidence level for extracting oscillation mode information, it is possible to select suitable Prony algorithms exponent number according to overall target.
Description
Technical field
The invention belongs to stability of power system analysis field, more particularly to a kind of power system based on polymorphic type signal
Low-frequency oscillation analysis method.
Background technology
Low-frequency oscillation of electric power system directly affects the operation of interacted system, the feature method for root physics based on inearized model
Clear concept, there is provided informative, it is but difficult to big system-computed, and be difficult to reflect nonlinear influence.System is received
Disturbing track can be comprising non-linear effects, and track obtains is influenceed smaller by system scale, as WAMS (WAMS) draws
Enter, system model, the operation of real-time monitoring system, for Low Frequency Oscillation Analysis provide important disturbed track can be independent of.
Based on trajectory analysis low-frequency oscillation, mainly include Stationary Oscillation specificity analysis and nonstationary oscillation specificity analysis, mesh
Preceding nonstationary oscillation specificity analysis is based primarily upon single track, and common method is including window Fourier ridge, Wavelet Ridge, HHT etc.；It is flat
Steady oscillating characteristic analysis is also applied for the disturbed track of multimachine suitable for single track, and common method is Prony algorithms, the algorithm meter
Calculate simple, but interference free performance is poor, and need to select suitable model order.At present, determine that Prony algorithms exponent number determines
New determinant method and singular value decomposition method etc. are common are, this kind of method is mainly used to distinguish valid data space and spatial noise,
It is difficult to evaluate the quality of different rank Prony algorithm identification results.It is true with this kind of method for there is certain nonlinear system
Determine the exponent number of algorithm, be likely to result in overfitting.There is polytype curve in the disturbed track of power system, tradition is general using single
One generator's power and angle curve, speed curves or dominant eigenvalues curve carry out analysis of the oscillation, have ignored different type curve
Relation.
The content of the invention
It is an object of the invention to propose a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal, it is based on
The internal relation of polymorphic type curve, the amplitude excursion and phase deviation for setting up the oscillation mode confidence level for evaluating Prony extractions refers to
Mark, and formulated the comprehensive evaluation index of Prony algorithm confidence levels.
A kind of low-frequency oscillation analysis method for power system based on polymorphic type signal proposed by the present invention, including following step
Suddenly：
(1) different type curve data is read, and analyzes the relation between different type curve；
(2) amplitude to different type curve carries out conversion treatment；
(3) the initial exponent number N of multi-machine Prony algorithm, each increased exponent number Δ N and top step number N are setmax, set comprehensive
Evaluation index ηAmplitudeΣAnd ηPhaseΣDesired value
(4) Prony algorithm calculating is carried out to different type curve, control oscillation modes are obtained；
(5) the amplitude excursion percentage and phase deviation percentage of each control oscillation modes are calculated, each leading vibration is evaluated
The degree of accuracy of pattern；
(6) the comprehensive evaluation index η of calculated amplitude deviationAmplitudeΣWith the comprehensive evaluation index η of phase deviationPhaseΣ, comment
Estimate the confidence level of Prony algorithms；If comprehensive assessment index is less than the desired value for setting, output result；If comprehensive assessment
Whether index then increases Prony algorithm exponent number Δ N, and judge Prony algorithms exponent number more than most high-order more than the desired value for setting
Number Nmax, if less than top step number Nmax, then return to step (4) recalculate, if greater than top step number Nmax, then export
ηAmplitudeΣ、ηPhaseΣResult when minimum.
In foregoing step (1), for generating set, its power-angle curve and speed curves are different types of curve,
Expression formula is respectively：
Wherein：δiT () represents i platforms unit with respect to inertia center generator rotor angle, νiT () represents i-th unit with respect to inertia center
Rotating speed ,-σj±iωjJ-th oscillation mode is represented, n represents oscillation mode number, δi0Represent power-angle curve DC component, AjTable
Show the amplitude of j-th oscillation mode of power-angle curve, φj0Represent the first phase of j-th oscillation mode of power-angle curve, BjRepresent that rotating speed is bent
The amplitude of j-th oscillation mode of line,Represent the first phase of j-th oscillation mode of speed curves.
There is relation between foregoing power-angle curve and speed curves：vi(t)=δ 'i(t),
Wherein, δ 'iT () represents δiThe derivative of (t)；
Obtained by the relation between above-mentioned power-angle curve and speed curves：
Amplitude and the corresponding relation of oscillation mode：
Relation between phase difference and oscillation mode：
In foregoing step (2), conversion treatment is carried out to the amplitude of different type curve and is comprised the following steps：
2-1) setting same type signal curve x has m bars, and sampled point is q, after carrying out blocking treatment to signal, sets up same
The mean oscillatory energy of type signal
Wherein, xkRepresent that kth bars curve is power-angle curve δi(t) or speed curves νiT (), i represents ith sample
Point, Δ t is sampling step length；
Blocking treatment equally 2-2) is carried out to another type signal curve y, mean oscillatory energy is obtained
2-3) with signal curve x as reference, all y signal curves are multiplied byEnter row amplitude conversion.
In foregoing step (4), obtain control oscillation modes and comprise the following steps：
4-1) jth oscillation mode accounts for the percentage η of gross energyjCalculation expression be：
Wherein：PjIt is the oscillation energy of jth oscillation mode, PΣIt is the gross energy of all oscillation modes, l is all inhomogeneities
Type curve sum, q is sampling number, and n is oscillation mode number, AijIt is i-th amplitude of curve jth oscillation mode；
Oscillation mode is ranked up according to oscillation mode energy accounting 4-2), and sets up threshold epsilon, oscillation mode energy is accounted for
It is control oscillation modes than the pattern more than ε.
In foregoing step (5),
The amplitude excursion percentage η of the control oscillation modes jjAmplitudeComputing formula it is as follows：
The phase deviation percentage η of the control oscillation modes jjPhaseComputing formula it is as follows：
The ηjAmplitudeAnd ηjPhaseData are bigger, represent that the control oscillation modes are more insincere.
In foregoing step (6),
The comprehensive evaluation index η of the amplitude excursionAmplitudeΣFor：
The comprehensive evaluation index η of the phase deviationphaseΣFor：
Wherein, m is control oscillation modes number.
It is of the invention with advantages below compared with existing Low Frequency Oscillation Analysis：
(1) low-frequency oscillation of electric power system information is present in polytype curve, and tradition generally selects a certain type curve
Information extraction is carried out, is difficult to judge for the confidence level of analysis result, it is of the invention to polymorphic type information analysis, based on different type
Physical link between curve, builds evaluation index, and the oscillation mode accuracy of information that Prony algorithms are extracted is evaluated；
(2) present invention establishes comprehensive evaluation index, can reflect the confidence level of Prony algorithms；
(3) System of Comprehensive Evaluation proposed by the present invention has engineering application value, it is possible to refer to according to overall merit
The suitable Prony algorithms exponent number of mark selection.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, below in conjunction with drawings and embodiments to this
Invention is described in further detail.
As shown in figure 1, the low-frequency oscillation analysis method for power system based on polymorphic type signal of the invention includes following step
Suddenly：
Step 1, reads different type curve data, and for generating set, power-angle curve and speed curves belong to two kinds not
The curve of same type.
In multi-computer system, unit power-angle curve and speed curves are typically aobvious using relative inertia center or angular centre
Show.Because generator rotor angle has initial phase difference, the power-angle curve of multi-computer system generally comprises DC component, and is in synchronous operation
Generating unit speed curve does not include DC component typically.Because every unit power-angle curve and speed curves include identical oscillation mode
Formula information, expression formula is：
In formula：δiT () represents i-th unit with respect to inertia center generator rotor angle；νiT () represents i-th unit with respect to inertia center
Rotating speed ,-σj±iωjJ-th oscillation mode is represented, n represents oscillation mode number, δi0Represent power-angle curve DC component, Aj
Represent the amplitude of j-th oscillation mode of power-angle curve, φj0Represent the first phase of j-th oscillation mode of power-angle curve, BjRepresent rotating speed
The amplitude of j-th oscillation mode of curve,Represent the first phase of j-th oscillation mode of speed curves.
Different with simple signal transacting, power system is physical system, there is inherence between signal with different type curve
, in real system, there is derivative relation, i.e. v between power-angle curve and speed curves in contacti(t)=δ 'i(t),
Corresponding coefficient is contrasted to understand,
There is relation in amplitude and oscillation mode：
There is relation between phase difference and oscillation mode：
Step 2, to avoid different type curve amplitude from having big difference, forms signal and floods, it is necessary to different type curve
Amplitude carry out conversion treatment.
If same type of curve is x types, another type of curve is y types, e.g., if power-angle curve is x types,
Then speed curves are y types.
After x type curves are processed through blocking, mean oscillatory energy is obtained
In formula：Q is sampling number；Δ t is step-length；M is x type curve numbers.
Similarly, after y type curves are processed through blocking, mean oscillatory energy is obtained
With signal curve x as reference, all y signal curves are multiplied byEnter row amplitude conversion, eliminate different type curve
Because dimension difference causes the huge difference of amplitude.
For example：The curve of power-angle curve y and y' is as follows, and y' is speed curves, and sampling step length is 0.05s, sampling time
It is 5s,
Y=6e-0.5tsin(10t)+2e-0.1tSin (20t),
Y'=60.08e-0.5tsin(10t+1.52)+40.00e-0.1tSin (20t+1.57),
Because signal amplitude differs larger, processing method is converted according to step 2 amplitude, with y references, at y' amplitudes
Reason, calculatesTherefore y' signals are multiplied by 13.77.
Step 3, sets the initial exponent number N of multi-machine Prony algorithm, each increased exponent number Δ N and top step number Nmax, set
Comprehensive evaluation index ηAmplitudeΣAnd ηPhaseΣDesired value
Step 4, Prony algorithm calculating is carried out to different type curve, obtains control oscillation modes.
In view of the oscillation mode information that noise and nonlinear influence, signal processing method are obtained, energy accounting is larger
Signal have confidence level higher.The oscillation mode obtained for high-order Prony algorithms is, it is necessary to the pattern information to extracting is entered
Row sequence, obtains control oscillation modes.Control oscillation modes are not only related to the initial amplitude of vibration also related to its damping.It is right
In the disturbed track of multimachine, the energy of oscillation mode is included in all oscillating curves, and jth oscillation mode accounts for the percentage of gross energy
ηjCalculating formula be：
Wherein：It is the oscillation energy of jth oscillation mode,
It is global oscillation energy,
L is all different type curves sum, and q is sampling number, and n is oscillation mode number, AijFor i-th curve jth is shaken
Swing the amplitude of pattern.
Oscillation mode is ranked up according to oscillation mode energy accounting, and sets up threshold epsilon, oscillation mode energy accounting surpasses
The pattern for crossing ε is control oscillation modes.
Step 5, calculates the amplitude excursion percentage and phase deviation percentage of each control oscillation modes, evaluates each dominating and shakes
Swing the degree of accuracy of pattern；
The amplitude excursion percentage η of control oscillation modes jjAmplitudeWith phase deviation percentage ηjPhase, such as formula (6)
(7) shown in,
The degree of accuracy of each control oscillation modes can be by corresponding ηjAmplitudeAnd ηjPhaseReflection, data are bigger, table
Show that the control oscillation modes degree of accuracy is lower, conversely, then showing that the control oscillation modes degree of accuracy is high.
Step 6, calculates the comprehensive evaluation index η of the amplitude excursion of Prony algorithm output resultsAmplitudeΣAnd phase deviation
Comprehensive evaluation index ηPhaseΣ, assess the confidence level of Prony algorithms.
For the signal with multiple control oscillation modes, it is necessary to set up comprehensive evaluation index to reflect Prony algorithms
Confidence level.In multi-computer system, there are multiple η in each unitjAmplitudeAnd ηjPhase, it is necessary to set up comprehensive evaluation index reflection
The confidence level of result.Comprehensive evaluation index needs to reflect the energy accounting and amplitude and phase deviation of each oscillation mode.Structure
Build shown in comprehensive evaluation index such as formula (8) and (9).
Wherein, ηAmplitudeΣIt is the comprehensive evaluation index of amplitude excursion, ηphaseΣIt is the comprehensive evaluation index of phase deviation, m
It is control oscillation modes number, ηjIt is the percentage of energy of control oscillation modes j.
If comprehensive assessment index is less than the desired value for setting, i.e.,Then
Show that Prony algorithms are calculated credible, then export Prony algorithm result of calculations；If comprehensive assessment index is more than the target for setting
Whether value, then increase Prony algorithm exponent number Δ N, and judge Prony algorithms exponent number more than top step number Nmax, if less than highest
Exponent number Nmax, then return to step 4 recalculate, if greater than top step number Nmax, then show that Prony algorithms do not reach precision and want
Ask, then search for η in calculating processAmplitudeΣ、ηPhaseΣProny algorithms when minimum, and export its result.
By taking foregoing y and y' signals as an example, noise takes 5dB, 10dB and 20dB respectively, Prony algorithms take respectively exponent number for 10,
20th, 40, each oscillation mode energy accounting is calculated according to formula (5), more than 2% it is leading oscillation mode with oscillation mode energy accounting
Formula output result is as shown in table 1.
The Prony algorithm output results of table 1
As shown in Table 1, the control oscillation modes information of extraction is more accurate, corresponding ηjAmplitude、ηjPhaseDeviation is smaller,
It can be seen that, the index of foundation can be used in evaluating the accuracy of identification result.Noise can produce one to the output result of Prony algorithms
Fixing to ring, the small signal amplitude of signal to noise ratio and phase deviation are larger, and high-order Prony algorithms are conducive to white-noise filtering so that main
Lead oscillation mode result more accurate.Analysis signal to noise ratio is the signal discovery of 5dB and 10dB, with carrying for Prony algorithm exponent numbers
Height, 20 rank models and 40 rank model counting accuracies are not significantly improved, it is seen that in the case where requirement is met, without using
Too high model order.
Above example is only explanation technological thought of the invention, it is impossible to limit protection scope of the present invention with this, every
According to technological thought proposed by the present invention, any change done on the basis of technical scheme each falls within the scope of the present invention
Within.
Claims (6)
1. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal, it is characterised in that comprise the following steps：
(1) different type curve data is read, and analyzes the relation between different type curve；
(2) amplitude to different type curve carries out conversion treatment；
(3) the initial exponent number N of multi-machine Prony algorithm, each increased exponent number Δ N and top step number N are setmax, overall merit is set
Index ηAmplitude∑And ηPhase∑Desired value
(4) Prony algorithm calculating is carried out to different type curve, control oscillation modes are obtained；
(5) the amplitude excursion percentage and phase deviation percentage of each control oscillation modes are calculated, each control oscillation modes are evaluated
The degree of accuracy；
(6) the comprehensive evaluation index η of calculated amplitude deviationAmplitude∑With the comprehensive evaluation index η of phase deviationPhase∑, assessment
The confidence level of Prony algorithms；
The comprehensive evaluation index η of the amplitude excursionAmplitudeΣFor：
The comprehensive evaluation index η of the phase deviationphaseΣFor：
Wherein, m is control oscillation modes number, ηjThe percentage of gross energy is accounted for for the oscillation energy of j-th control oscillation modes,
ηjAmplitudeIt is the amplitude excursion percentage of control oscillation modes j, ηjPhaseIt is the phase deviation percentage of control oscillation modes j；
If comprehensive evaluation index is less than the desired value for setting, i.e.,AndThen export
As a result；If comprehensive evaluation index is more than the desired value for setting, increase Prony algorithm exponent number Δ N, and judge Prony algorithms
Whether exponent number is more than top step number Nmax, if less than top step number Nmax, then return to step (4) recalculate, if greater than most
Exponent number N highmax, then η is exportedAmplitude∑、ηPhase∑Result when minimum.
2. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, its feature
It is that in the step (1), for generating set, its power-angle curve and speed curves are different types of curve,
Expression formula is respectively：
Wherein：δiT () represents i-th unit with respect to inertia center generator rotor angle, νiT () represents i-th unit turning with respect to inertia center
Speed ,-σj±iωjJ-th oscillation mode is represented, n represents oscillation mode number, δi0Represent power-angle curve DC component, AjRepresent
The amplitude of j-th oscillation mode of power-angle curve, φj0Represent the first phase of j-th oscillation mode of power-angle curve, BjRepresent speed curves
J-th amplitude of oscillation mode,Represent the first phase of j-th oscillation mode of speed curves.
3. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 2, its feature
It is there is relation between the power-angle curve and speed curves：vi(t)=δ 'i(t),
Wherein, δ 'iT () represents δiThe derivative of (t)；
Obtained by the relation between above-mentioned power-angle curve and speed curves：
Amplitude and the corresponding relation of oscillation mode：
Relation between phase difference and oscillation mode：
。
4. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, its feature
It is in the step (2), conversion treatment to be carried out to the amplitude of different type curve and is comprised the following steps：
2-1) setting same type signal curve x has m bars, and sampled point is q, after carrying out blocking treatment to signal, sets up same type
The mean oscillatory energy of signal
Wherein, xkRepresent that kth bars curve is power-angle curve δi(t) or speed curves νiT (), i represents ith sample point, Δ
T is sampling step length；
Blocking treatment equally 2-2) is carried out to another type signal curve y, mean oscillatory energy is obtained
2-3) with signal curve x as reference, all y signal curves are multiplied byEnter row amplitude conversion.
5. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 4, its feature
It is in the step (4), to obtain control oscillation modes and comprise the following steps：
4-1) oscillation energy of j-th oscillation mode accounts for the percentage η of gross energyjCalculation expression be：
Wherein：PjIt is j-th oscillation energy of oscillation mode, P∑It is the gross energy of all oscillation modes, l is all different types
Curve sum, q is sampling number, and n is oscillation mode number, AijIt is the amplitude of i-th curve, j-th oscillation mode；
Oscillation mode is ranked up according to oscillation mode energy accounting 4-2), and sets up threshold epsilon, oscillation mode energy accounting surpasses
The pattern for crossing ε is control oscillation modes.
6. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 2, its feature
It is, in the step (5),
The amplitude excursion percentage η of the control oscillation modes jjAmplitudeComputing formula it is as follows：
The phase deviation percentage η of the control oscillation modes jjPhaseComputing formula it is as follows：
The ηjAmplitudeAnd ηjPhaseData are bigger, represent that the control oscillation modes are more insincere.
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| CN104865497B (en) * | 2015-04-30 | 2017-08-29 | 国电南瑞科技股份有限公司 | Low-frequency oscillation site on-line identification method based on Prony algorithm |
| CN104953583B (en) * | 2015-07-01 | 2017-05-17 | 河海大学 | Method used for online monitoring of low-frequency oscillation of electric power system and based on combination of change-point detection and Prony method |
| CN105740209B (en) * | 2016-01-28 | 2018-06-29 | 大连海事大学 | A kind of Prony low-frequency oscillation analysis methods of Givens iteration |
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