CN103207931A - Sub-synchronous oscillation mode identification method based on milli molar (MM) and autoregressive moving average (ARMA) algorithm - Google Patents

Abstract

The invention discloses a sub-synchronous oscillation mode identification method based on a milli molar (MM) and autoregressive moving average (ARMA) algorithm. The method achieves sub-synchronous oscillation mode accurate identification under the interference of noise. The sub-synchronous oscillation mode identification method includes: adopting a mathematical morphological filter to perform denoising processing on sub-synchronous oscillation signals, and keeping main characteristic information of the signals; and building an ARMA model for the denoised signals, and obtaining sub-synchronous oscillation mode parameters after data pre-processing, model order determination, model parameter estimation. The sub-synchronous oscillation mode identification method can identify sub-synchronous oscillation mode parameters rapidly and accurately, has the advantages of being strong in anti-noise capacity, high in identification precision, and has good application prospect in the aspects of analysis, monitoring and early warning of sub-synchronous oscillation and designing of a damping controller on the basis of measured data.

Description

Sub-synchronous oscillation modal identification method based on MM and ARMA algorithm

Technical field

The present invention relates to the safe and stable operation of electric system, particularly a kind of sub-synchronous oscillation modal identification method based on MM and ARMA algorithm.

Background technology

Complicated along with the extension of electrical network scale and structure, the sub-synchronous oscillation problem in the electric system needs to be resolved hurrily.Identification sub-synchronous oscillation modal parameter rapidly and accurately all plays crucial effects for the formulation of monitoring, early warning and the control measure of sub-synchronous oscillation.Along with the fast development of WAMS (WAMS) correlation technique, extract the method for vibration mode because it need not detailed system model and extensive eigenwert calculates and be used widely gradually based on measured data.At present, the typical method based on the sub-synchronous oscillation modal identification of measured data has: Pu Luoni (Prony) analytic approach, wavelet analysis method, fast Fourier (FFT) method, Hilbert-yellow method of changing (HHT) etc.Traditional Prony analytic approach anti-noise ability is poor; The difficult close frequencies of distinguishing in the signal of wavelet analysis method is unfavorable for the torsional oscillation mode Parameter Extraction; The FFT method can't be extracted instantaneous frequency and the decay factor of vibration; The HHT method is had relatively high expectations to the signals sampling rate.Said method all is difficult to satisfy the requirement of the sub-synchronous oscillation modal identification under the complication system strong noise background.

Mathematical morphology (mathematical morphology, MM) be based on the development of integral geometry and random set opinion, have and calculate quick, easy, denoising and the strong characteristics of reconstruction signal ability, be widely used in fields such as image processing, shape analysis, pattern-recognition.Dong is superfine ^[1]Adopt mathematical morphology to design a kind of parallel complex morphological wave filter of many structural elements, effectively the multiple noise of filtering keeps more useful information.The employing of signal after the de-noising is estimated that based on the signal parameter of total least square method-invariable rotary technology (TLS-ESPRIT) algorithm carries out identification, thereby obtains each mode parameter of low-frequency oscillation.

Autoregressive moving-average model (ARMA) is to be based upon on the linear model basis, is a kind of practical approach of handling the dynamic random data with parameterized model, also is the classical way of System Discrimination and prediction.Arma modeling is input with the white noise, has solved unrecognizable problem when input is unknown in the system identification, has widened the application of system identification.Wu is superfine ^[2]Based on noise-like signal, adopt autoregressive moving average (ARMA) method to carry out the low frequency oscillation mode identification, thereby realize the dynamic stability early warning under the electrical network normal operating condition.

Relate to following list of references in the literary composition:

[1] Dong is superfine. based on the low frequency oscillation mode Research on Identification [J] of mathematical morphology filter technology and TLS-ESPRIT algorithm. and protecting electrical power system and control, 2012,40 (3): 114-118,123.

[2] Wu is superfine. take into account the low frequency oscillation mode noise-like signal identification [J] that model is decided rank. and Automation of Electric Systems, 2009,33 (21): 1-6.

Summary of the invention

At the problem that prior art exists, the present invention is combined mathematics shape filtering technology with autoregressive moving-average model, proposed a kind of sub-synchronous oscillation modal identification method based on mathematical morphology (MM) and autoregressive moving-average model (ARMA).

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

A kind of sub-synchronous oscillation modal identification method based on MM and ARMA algorithm comprises step:

Step 1, employing mathematics morphological filter carry out de-noising to the sub-synchronous oscillation signal;

Step 2, the sub-synchronous oscillation signal after the de-noising is made up autoregressive moving-average model, and signal is carried out pre-service;

Step 3 carries out deciding rank to the autoregressive moving-average model that makes up, and the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation;

Step 4, the autoregressive moving-average model estimates of parameters that obtains based on step 3 carries out sub-synchronous oscillation signal modal identification.

Mathematics morphological filter in the step 1 is that form open-close wave filter and form are closed-combination of Kai wave filter, is specially:

Wherein, Y (x) is the output signal of mathematics morphological filter, OC[f (x)] expression form open-close wave filter, CO[f (x)] the expression form closes-the Kai wave filter.

The structural element of the mathematics morphological filter in the step 1 is semi-circular structure element and three-legged structure element.

Can adopt the filter effect of similarity index S appraisal procedure 1, described similarity index

Wherein, f ₀(x) be the discrete sampling point of the not input signal of superimposed noise; F1 (x) is the discrete sampling point through the filtered output signal of mathematics morphological filter; X is the sampled point sequence number; Ns is total sampling number.

Adopt BIC criterion that the autoregressive moving-average model that makes up is carried out deciding rank in the step 3, and adopt weighting recursive least square method that the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation.

Adopt weighting recursive least square method that the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation, be specially:

Adopt weighting recursive least square method that the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation, calculate the weighted criterion function according to gained model parameter estimation value, judge whether the weighted criterion function satisfies the control accuracy requirement, if satisfy, then execution in step 4; Otherwise, based on current model parameter estimation value autoregressive moving-average model is proceeded model parameter estimation.

Step 4 further comprises substep:

4-1 makes up the secular equation of sub-synchronous oscillation discrete signal based on the autoregressive moving-average model estimates of parameters, and obtains the conjugate character root of secular equation;

4-2 analyzes the autoregressive moving-average model parameter based on the conjugate character root, and carries out the z territory to the conversion in s territory to analyzing gained autoregressive moving-average model parameter, thereby obtains the sub-synchronous oscillation model parameter.

Compared with prior art, the present invention has the following advantages and beneficial effect:

1, the inventive method can pick out modal parameters such as the frequency of sub-synchronous oscillation and damping ratio quickly and accurately, has strong, the identification precision advantages of higher of anti-noise ability, compare with the identification result of ARMA method with traditional Prony analytic approach, the inventive method has very high identification precision.The present invention has application promise in clinical practice at the aspects such as sub-synchronous oscillation analysis, monitoring, early warning and damping controller design based on measured data.

2, the present invention is according to the signal characteristic of electric system, by the mathematics morphological filter sub-synchronous oscillation signal is carried out de-noising, satisfied must carry out the tranquilization processing requirements to signal before setting up arma modeling in, can also effectively suppress noise to the influence of mode of oscillation identification process; The present invention introduces similarity index evaluation filter effect, and evaluation result shows that mathematics morphological filter of the present invention has good filtering effect to the sub-synchronous oscillation signal.

Description of drawings

Fig. 1 is process flow diagram of the present invention;

The various signal waveforms of Fig. 2 for relating among the embodiment 1, wherein, figure (a) is the original test signal waveform among the embodiment 1, and figure (b) is the test signal waveform that adds white Gaussian noise among the embodiment 1, and figure (c) is the signal waveform behind the mathematics shape filtering among the embodiment 1;

Fig. 3 is the IEEE first master pattern system wiring figure among the embodiment 2.

Embodiment

The present invention adopts the mathematics morphological filter that the sub-synchronous oscillation signal of electric system is carried out denoising Processing, then filtered signal is set up arma modeling, decides to obtain the sub-synchronous oscillation modal parameter after rank, the model parameter estimation through data pre-service, model.The inventive method can pick out modal parameters such as the frequency of sub-synchronous oscillation and damping ratio quickly and accurately, have strong, the identification precision advantages of higher of anti-noise ability, have application promise in clinical practice at the aspects such as sub-synchronous oscillation analysis, monitoring, early warning and damping controller design based on measured data.

The present invention will be further described below in conjunction with embodiment.

A kind of concrete enforcement of the present invention comprises step:

Step 1 based on principles of mathematical morphology design mathematics morphological filter, and adopts the mathematics morphological filter that the sub-synchronous oscillation signal is carried out denoising Processing;

The ultimate principle of mathematical morphology is as follows:

Mathematical morphology is a kind of instrument that develops, handles and analyze nonlinear properties in time domain of being handled by image, its basic thought is to utilize predefined structural element (i.e. " probe ") that signal is mated, to reach the purpose of extracting signal and suppressing noise.The fundamental operation of mathematical morphology comprises the cascade combination that expansion, burn into form are opened, form is closed and form opens and closes.

If list entries f (x) and sequential structure element g (x) are defined in F={0,1 ..., N-1} and G={0,1 ..., the discrete function on the M-1}, and N＞＞M.F (x) is defined as respectively about expansion and the erosion operation of g (x):

$(f\⊕g)\left(x\right)=\underset{(b=0~M-1)}{\max }\{f(x-b)+g\left(b\right)\}---\left(1\right)$

Wherein, " " the expression dilation operation, " ⊙ " is erosion operation.

Expansion and erosion operation are equivalent to maximal value and the minimum value filtering of discrete function in structural element respectively.Erosion operation can reduce signal peak, add the broad valley territory, and dilation operation then increases the signal valley, the expansion summit.

F (x) is respectively about opening operation and the closed operation of g (x):

Wherein,

Be opening operation, " " is closed operation.

Isolated point and the burr etc. of opening operation in can erasure signal is level and smooth and suppress peak noise; Closed operation can be filled and led up recess in the signal, hole etc. and be suppressed signal trough noise.

The building process of mathematics morphological filter is as follows:

Thereby morphological filter is to adopt the structural element that carries different shape information that signal is carried out morphology operations to realize filtering.The form opening operation can suppress the peak noise in the signal, and the form closed operation can suppress the low ebb noise in the signal, can utilize form to open the cascade form that closes with form like this noise is eliminated.Form open-close wave filter and form close-and the Kai wave filter is defined as respectively:

Wherein, OC[f (x)] expression form open-close wave filter; CO[f (x)] expression form close-the Kai wave filter.

Form open-close wave filter and form close-the Kai wave filter positive and negative impulsive noise in the filtered signal simultaneously, but be subject to the anti-extendability of opening operation and the extendability of closed operation, there is the statistics shift phenomenon in the both.The output amplitude of form open-close wave filter is less than normal, and form is closed-and the output amplitude of Kai wave filter is bigger than normal.Therefore, for making result more near original signal, adopt the form open-close in this concrete enforcement and close-wave filter of Kai average combined:

$Y\left(x\right)=\frac{\mathrm{OC}\left[f\left(x\right)\right]+\mathrm{CO}\left[f\left(x\right)\right]}{2}---\left(7\right)$

In the formula (7), Y (x) is the output signal of mathematics morphological filter.

The filter effect of mathematics morphological filter is not only closely related with variation, also is subjected to the influence of structural element.The subsynchronous oscillation of electrical power system signal is exactly the signal that is formed by a plurality of sine-wave oscillation signal combination with attenuated form, consider subsynchronous oscillation of electrical power system signal characteristic and engineering calculation requirement, in this concrete enforcement, choose semi-circular structure element and three-legged structure element and make up morphological filter.

For the filter effect of qualitative assessment mathematics morphological filter, introduce similarity index S assessment filter effect in this concrete enforcement:

$S=1-\frac{1}{N_s}\sqrt{\underset{x=1}{\overset{N_s}{\mathrm{\Σ}}}{(f_0\left(x\right)-f_1\left(x\right))}^2}---\left(8\right)$

In the formula (8),

f ₀(x) be the discrete sampling point of the not input signal of superimposed noise, that is, and the discrete sampling of original input signal point;

f ₁(x) be discrete sampling point through the filtered output signal of mathematics morphological filter;

N _sBe total sampling number;

X is the sampled point sequence number.

As can be seen, the similarity index of original input signal is 1 from formula (8), and therefore, the similarity index illustrates filtered signal more near original signal more near 1, and namely filter effect is more good.

Step 2, the sub-synchronous oscillation signal after the de-noising is made up autoregressive moving-average model, the line data pre-service of going forward side by side;

The essence of autoregressive moving average (ARMA) model is a kind of difference form of hypothesis input signal system's differential equation of higher order group when being white noise.Random perturbation is considered as white noise if load by a small margin when power system stability is moved, and then can adopt arma modeling that the electric system response is described.

With the discrete sampling point of sub-synchronous oscillation signal be expressed as steadily, the time series { y of zero-mean _t, to time series { y _tMake up arma modeling, structure as the formula (9):

In the formula (9),

N, m are respectively the order of autoregression (AR) part and running mean (MA) part of arma modeling;

y _tAnd y _T-iRefer to time series { y respectively _tIn sequence number be the data sampling point of t and t-i;

And θ _jBe respectively autoregressive coefficient and running mean coefficient, i=1,2 ..., n, j=1,2 ..., m;

{ a _tBe white Gaussian noise, a _tAnd a _T-jRepresent that respectively sequence number is the corresponding white Gaussian noise of data sampling point of t and t-j, a _tObey average and be 0, standard deviation is σ _aNormal distribution, that is, satisfy

Can put sequence number t according to data sampling and obtain a _tMoment corresponding: definition a ₀Corresponding benchmark is t constantly ₀, establish the data sampling frequency f _s, a then _tThe corresponding moment is

The data pre-service is used for burst is become steady, the zero-mean sequence that meets the arma modeling requirement, comprise signal is carried out down-sampled processing, abnormal data detection, fills up obliterated data, goes and pulverised processing, standardization etc., Signal Pretreatment belongs to the known technology in this area, does not do at this and gives unnecessary details.

Step 3, arma modeling is carried out deciding rank based on the model of BIC criterion, adopt weighting recursive least square method that the arma modeling of deciding behind the rank is carried out parameter estimation;

3.1 the arma modeling based on Bayes's information (BIC) criterion is decided rank

The accuracy of model order will be directly connected to sub-synchronous oscillation pattern analysis result's accuracy: if model order is too high, then model will comprise too much uncorrelated oscillationg component; If model order is low excessively, model then can not be contained enough mode of oscillation information.Therefore, have only the proper model of selection exponent number, corresponding model could reflect the dynamic perfromance of system comprehensively, exactly.

The typical case of arma modeling decides the rank method and mainly comprises concentrated residual sum of squares (RSS) test criterion and Akaike's Information Criterion.Wherein, concentrate the residual sum of squares (RSS) test criterion mainly to comprise residual sum of squares (RSS) criterion and homogeneity test of variance method; Akaike's Information Criterion is to be proposed by Chi Chi, mainly comprises red pond quantity of information (AIC) criterion and BIC criterion.But the residual sum of squares (RSS) criterion does not provide differentiates the module that significantly descends, and is not easy to Computer Processing; The homogeneity test of variance method satisfies the big limitation of existence because the precondition of its use is difficult; The applicable models order that AIC criterion is determined is often higher.Therefore, adopt BIC criterion to carry out arma modeling in this concrete enforcement and decide rank, this criterion function δ _BIC(p) be defined as follows:

${\mathrm{\δ}}_{\mathrm{BIC}}\left(p\right)=N_{s}1n{\mathrm{\σ}}_a^2+p1n{N}_s---\left(10\right)$

In the formula (10),

N _sBe total sampling number;

Be a _tVariance;

P is the arma modeling exponent number, and p=n+m, n, m are respectively the order of autoregression (AR) part and running mean (MA) part of arma modeling.

The BIC function constitutes by 2: the 1st N _sLn

The fine or not degree that has reflected the model fitting degree diminishes with the rising of model order; The 2nd plnN _sThe weighing factor that has reflected the model order height.Compare AIC criterion, among the BIC effect of model order bigger, the applicable models order of judging is lower.

3.2 the model parameter estimation based on the weighting Recursive Least Squares

The key that adopts arma modeling to carry out the sub-synchronous oscillation modal identification is parameter estimation, adopts weighting recursive least square method to carry out parameter estimation in this concrete enforcement, and is as follows to the arma modeling variation of formula (9):

（11）

In the formula (11),

y _T-1, y _T-2... y _T-nRepresent time series { y respectively _tIn sequence number be t-1, t-2 ... the data sampling point of t-n;

a _T-1, a _T-2... a _T-m, a _tRepresent white Gaussian noise { a respectively _tIn sequence number be t-1, t-2 ... the white Gaussian noise that the data sampling point of t-m, t is corresponding.

White noise a _t, a _T-m... a _T-2, a _T-1Use its estimated value respectively

The approximate replacement, can get the least square form of arma modeling:

${\mathrm{\γ}}_t={\mathrm{\γ}}_t^T\mathrm{\β}+a_t---\left(12\right)$

In the formula (12),

${\mathrm{\γ}}_t^T=[y_{t-1},y_{t-2},\·\·\·,y_{t-n},-a_{t-1}^{^},a_{t-2}^{^},\·\·\·,a_{t-m}^{^}].$

For embodying the time variation of system, introduce forgetting factor α (0＜α＜1), to emphasize the effect of most recent data, think that the data of present moment are more reliable than past data constantly.

Definition weighted criterion function J (β):

$J\left(\mathrm{\β}\right)=\underset{k=n+1}{\overset{t}{\mathrm{\Σ}}}{\mathrm{\α}}^{t-k}{(y_k-{\mathrm{\γ}}_k^T\mathrm{\β})}^2---\left(13\right)$

In the formula (13),

T is data sampling point sequence number;

N is the AR part exponent number of arma modeling;

Model is to the speed of forgeing of historical data, 0.95≤α≤0.99 in the forgetting factor α reflection recursive process.

Can prove, make weighted criterion function J (β) arma modeling parameter estimation hour as follows:

$\left\{\begin{array}{c}{\widehat{\mathrm{\β}}}_{t+1}={\widehat{\mathrm{\β}}}_t+K_{t+1}(y_{t+1}-{\mathrm{\γ}}_{t+1}^T{\widehat{\mathrm{\β}}}_t)\\ K_{t+1}=\frac{1}{\mathrm{\α}+{\mathrm{\γ}}_{t+1}^T{P}_t{\mathrm{\γ}}_{t+1}}\\ P_{t+1}=\frac{1}{\mathrm{\α}}[I-P_t\frac{{\mathrm{\γ}}_{t+1}{\mathrm{\γ}}_{t+1}^T}{\mathrm{\α}+{\mathrm{\γ}}_{t+1}^T{P}_t{\mathrm{\γ}}_{t+1}}]P_t\end{array}\right.---\left(14\right)$

In the formula (14):

Initial value is 0, namely

P _tInitial value is μ I, i.e. P ₀=μ I; I is (n+m) rank unit matrixs, and μ is empirical value, in this concrete enforcement, and μ=10 ⁵

Whenever carry out model parameter estimation one time, judge whether weighted criterion function J (β) satisfies the control accuracy requirement, if satisfy, then execution in step 4; Otherwise, based on current model parameter estimation value

Arma modeling is proceeded parameter estimation.In this concrete enforcement control accuracy is made as 10 ^-4

Step 4 is based on the estimates of parameters of arma modeling

Carry out sub-synchronous oscillation signal modal identification, and preserve the sub-synchronous oscillation modal parameter that obtains, detailed process is as follows:

Estimated parameter based on arma modeling obtains discrete signal y _tSecular equation:

In the formula (15), z is the power system state variable;

Be autoregressive coefficient, i=1,2 ..., n.

Find the solution formula (15) and can obtain conjugate character root λ based on discrete system _iWith

, the model parameter of being analyzed gained by eigenwert is carried out the z territory to the conversion in s territory, thereby derives the sub-synchronous oscillation modal parameter computing formula based on arma modeling:

$\left\{\begin{array}{c}{f}_i=\frac{\sqrt{1n{\mathrm{\λ}}_{i}1n{\mathrm{\λ}}_i^{*}}\×\sqrt{1-{\mathrm{\ξ}}_i^2}}{2\mathrm{\π\Δ}}\\ {\mathrm{\ξ}}_i=-\frac{1n\left|{\mathrm{\λ}}_i\right|}{\sqrt{1n{\mathrm{\λ}}_{i}1n{\mathrm{\λ}}_i^{*}}}\end{array}\right.---\left(16\right)$

In the formula (16):

Δ is sampling time interval;

f _iBe oscillation frequency, unit is Hz;

ξ _iDamping ratio for associative mode.

The invention will be further described below in conjunction with drawings and Examples.

Embodiment 1

Present embodiment will carry out modal identification to a hypothesis testing signal that contains noise, and this test signal x (T) is: x (T)=1.5e ^-0.15tSin (2 π * 15T+ π/4)+2.6e ^-0.2tSin (2 π * 25T+ π/5)+3e ^-0.5tSin (2 π * 32T+ π/3)

Wherein, T represents constantly.

Test signal x (T) comprises 3 mode of oscillation, and the frequency of these 3 mode of oscillation is respectively 15Hz, 25Hz and 32Hz, and corresponding damping ratio is respectively 0.1592%, 0.1273%, 0.2487%.To this test signal x (T) add that average is 0, variance is 0.4 white Gaussian noise, adds the shock vibration of opposite in sign simultaneously constantly at 0.3s and 0.7s.

To adopt the inventive method that above-mentioned test signal x (T) is carried out modal identification below, concrete steps are as follows:

Step 1, adopt form open-close wave filter and form close-the mathematics morphological filter of Kai wave filter combination carries out de-noising to the sub-synchronous oscillation signal.

See Fig. 2, the original test signal waveform is seen Fig. 2 (a) in the present embodiment, the test signal waveform that adds white Gaussian noise is seen Fig. 2 (b), adopts the mathematics morphological filter that the test signal that adds white Gaussian noise is carried out de-noising, and the signal waveform after the de-noising is seen Fig. 2 (c).

As calculated, the similarity index S of signal and original test signal is 0.9934 after the filtering of mathematics morphological filter, shows that the mathematics morphological filter has extraordinary filter effect to the test signal that contains noise.

Step 2, the signal after the de-noising is set up arma modeling, the line data pre-service of going forward side by side.

Step 3, based on BIC criterion arma modeling is carried out deciding rank, and adopt weighting recursive least square method that the arma modeling of deciding behind the rank is carried out model parameter estimation.

Step 4, at each model parameter estimation, calculate weighted criterion function J (β) according to gained model parameter estimation value, and judge whether J (β) satisfies the control accuracy requirement, if satisfy, then by formula (15) calculate oscillation frequency and the damping ratio of sub-synchronous oscillation signal, and preserve gained sub-synchronous oscillation modal parameter; Otherwise, based on current model parameter estimation value

Arma modeling is proceeded parameter estimation.

Adopt Pu Luoni (Prony) analytic approach and ARMA method that the present embodiment test signal is carried out modal identification, identification result sees Table 1.As shown in Table 1, above-mentioned three kinds of methods all can pick out three kinds of mode of hypothesis testing signal, the identification result of ARMA method and the inventive method is more near original signal, wherein, the inventive method error is littler, fitting precision is higher, and it in 0.05%, is no more than 3% to the identification error of damping ratio to the error of frequency estimation.

Table 1 pair contains the identification result contrast of noise testing signal

Embodiment 2

See IEEE shown in Figure 3 first master pattern, choose generator speed deviation delta ω as analytic signal.At 1.5s constantly, through transition impedance generation three-phase shortcircuit, trouble duration is 0.075s in Node B in system.For testing the noiseproof feature of the inventive method, at the white noise of original signal stack 20dB.There are 5 torsional oscillation modes in the generator shaft system of IEEE first master pattern, and frequency is followed successively by 15.71Hz, 20.21Hz, 25.55Hz, 32.28Hz and 47.45Hz.

Adopt the inventive method (specifically referring to the step 1 among the embodiment 1～4), Prony analytic approach and ARMA method that the generator speed deviation signal that contains noise is carried out modal identification respectively, identification result is as shown in table 2.When adopting the inventive method to carry out modal identification, the similarity index S of signal and original signal is 0.99969 after the filtering of mathematics morphological filter, with 1 very approaching, illustrate that the mathematics morphological filter is good to the filter effect of the generator speed deviation signal that contains noise.

Three kinds of methods of table 2 are to containing the contrast of noise generator speed deviation signal identification result

As shown in Table 2, when noise is 20dB, above-mentioned three kinds of methods all can pick out 5 kinds of mode of the generator shaft system of IEEE first master pattern, but the identification result precision of ARMA method and the inventive method all is higher than conventional P rony analytic approach, but the identification result of the inventive method has good noiseproof feature more near theoretical value.

The inventive method has proposed a kind of sub-synchronous oscillation modal parameter discrimination method of novel practical in conjunction with mathematics shape filtering technology and autoregressive moving average (ARMA) model.This method adopts the mathematics shape filtering that signal is carried out denoising Processing, and introduces the similarity index and estimate its filter effect; Filtered signal is set up arma modeling, decide to calculate the sub-synchronous oscillation modal parameter after rank, the model parameter estimation through data pre-service, model.Hypothesis testing signal among the embodiment and IEEE first master pattern show, this method can pick out modal parameters such as the frequency of sub-synchronous oscillation and damping ratio quickly and accurately.Compare with the ARMA algorithm with traditional Prony analytic approach, the inventive method has antinoise and the high characteristics of identification precision.Therefore, the present invention has application promise in clinical practice at the aspects such as sub-synchronous oscillation analysis, monitoring, early warning and damping controller design based on measured data.

Claims (9)

1. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm is characterized in that, comprises step:

Step 1, employing mathematics morphological filter carry out de-noising to the sub-synchronous oscillation signal;

Step 2, the sub-synchronous oscillation signal after the de-noising is made up autoregressive moving-average model, and signal is carried out pre-service;

Step 3 carries out deciding rank to the autoregressive moving-average model that makes up, and the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation;

Step 4, the arma modeling estimates of parameters that obtains based on step 3 carries out sub-synchronous oscillation signal modal identification.

2. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 1 is characterized in that:

Mathematics morphological filter described in the step 1 is that form open-close wave filter and form are closed-combination of Kai wave filter.

3. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 2 is characterized in that:

Described mathematics morphological filter is: Wherein, Y (x) is the output signal of mathematics morphological filter, OC[f (x)] expression form open-close wave filter, CO[f (x)] the expression form closes-the Kai wave filter.

4. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 1 is characterized in that:

The structural element of the mathematics morphological filter described in the step 1 is semi-circular structure element and three-legged structure element.

5. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 1 is characterized in that:

Adopt the filter effect of similarity index S appraisal procedure 1, described similarity index

Wherein, f ₀(x) be the discrete sampling point of the not input signal of superimposed noise; f ₁(x) be discrete sampling point through the filtered output signal of mathematics morphological filter; X is the sampled point sequence number; N _sBe total sampling number.

6. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 1 is characterized in that:

Adopt BIC criterion that the autoregressive moving-average model that makes up is carried out deciding rank in the step 3.

7. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 1 is characterized in that:

Adopt weighting recursive least square method that the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation in the step 3.

8. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 7 is characterized in that:

Described employing weighting recursive least square method is carried out model parameter estimation to the autoregressive moving-average model of deciding behind the rank, is specially:

Adopt weighting recursive least square method that the autoregressive moving-average model of deciding behind the rank is carried out model parameter estimation, calculate the weighted criterion function according to gained model parameter estimation value, judge whether the weighted criterion function satisfies the control accuracy requirement, if satisfy, then execution in step 4; Otherwise, based on current model parameter estimation value autoregressive moving-average model is proceeded model parameter estimation.

9. the sub-synchronous oscillation modal identification method based on MM and ARMA algorithm as claimed in claim 1 is characterized in that:

Step 4 further comprises substep:

4-1 makes up the secular equation of sub-synchronous oscillation discrete signal based on the autoregressive moving-average model estimates of parameters, and obtains the conjugate character root of secular equation;

4-2 analyzes the autoregressive moving-average model parameter based on the conjugate character root, and carries out the z territory to the conversion in s territory to analyzing gained autoregressive moving-average model parameter, thereby obtains the sub-synchronous oscillation model parameter.

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