CN105162433A - Fundamental component extraction method and device - Google Patents

Abstract

The invention discloses a fundamental component extraction method. The method comprises the following steps: (1) acquiring a fault signal in an electric system; (2) constructing a nonlinear state space model of the fault signal by taking a fundamental component, a fundamental angular frequency and a direct-current offset in the fault signal as state variables; (3) decomposing the fault signal in a wavelet multi-scale way to obtain N layers of smoothing signals and N layers of detailed signals; (4) updating an observed value of an unscented Kalman filter with an Nth layer smoothing signal, and acquiring a measurement noise variance of the unscented Kalman filter with an Nth layer detail signal; and (5) starting the unscented Kalman filter to estimate an amplitude and a phase angle of the fundamental component on the nonlinear state space model constructed in the step (2). Through adoption of the method, the fundamental component of the signal can be estimated rapidly and accurately, and the direct-current offset and fundamental frequency of the fault signal can be estimated in real time.

Description

A kind of extracting method of fundametal compoment and device

Technical field

The present invention relates to and extract fundametal compoment field, particularly a kind of extracting method of fundametal compoment and device.

Background technology

In electric power system Microcomputer Protection Calculation Method, how effectively the transient noise in filtering fault-signal also extracts electric parameter is rapidly and accurately Chinese scholars study hotspot problem.The fundametal compoment generally adopting all-wave and half-wave Fourier algorithm to ask for fault-signal at present carries out breakdown judge.All-wave and half-wave Fourier cannot attenuating dc component in filtered signal and non-integer harmonics components, and more responsive to frequency shift (FS), poor to measurement noises rejection ability, computing time is long, and response speed is slow.Kalman filter is incorporated into Microcomputer Protection field by the people such as Girgis, to expect the precision and the speed that improve filtering algorithm.Each harmonic is considered as noise by Kalman filter, attenuating dc component is estimated as state variable, can effectively suppress each harmonic and attenuating dc component, and algorithm only needs the sampled value of current period, amount of calculation and storage capacity little, can real-time online calculate.

But the linear state-space equation that traditional Kalman filter generally adopts does not consider Constant Direct Current component and frequency shift (FS), affect the estimated accuracy of filtering algorithm and the adaptability to frequency shift (FS).Set up the nonlinear state model containing DC offset and first-harmonic angular frequency, to adopting linear strong tracking Kalman filter estimated state after state equation linearisation, owing to have employed linearization procedure, reduce the estimated accuracy of filter, make the precision of the fundametal compoment estimated lower.

The information being disclosed in this background technology part is only intended to increase the understanding to general background of the present invention, and should not be regarded as admitting or imply in any form that this information structure has been prior art that persons skilled in the art are known.

Summary of the invention

The object of the present invention is to provide a kind of fundametal compoment extracting method, overcome existing extraction algorithm to frequency and DC offset mutation adaptability poor, make the shortcoming that the precision of fundametal compoment estimated is lower.

For achieving the above object, the invention provides a kind of fundametal compoment extracting method, comprise the following steps: 1) gather the fault-signal in electric power system; 2) Nonlinear state space model of described fault-signal is built using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable; 3) utilize multi-scale wavelet to be decomposed by described fault-signal and obtain N layer smooth signal and N layer detail signal; 4) utilize n-th layer smooth signal to upgrade the measured value of Unscented kalman filtering device, utilize n-th layer detail signal to obtain the observation noise variance of described Unscented kalman filtering device; 5) start Unscented kalman filtering device in step 2) in set up the amplitude and phase angle that Nonlinear state space model estimate fundametal compoment.

Another object of the present invention is to provide a kind of fundametal compoment extraction element, overcome existing extraction element to frequency and DC offset mutation adaptability poor, make the shortcoming that the precision of fundametal compoment estimated is lower.

For achieving the above object, the invention provides a kind of fundametal compoment extraction element, comprising: acquisition module, for gathering the fault-signal in electric power system; MBM, for building the Nonlinear state space model of described fault-signal using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable; Decomposing module, obtains N layer smooth signal and N layer detail signal for utilizing multi-scale wavelet by described fault-signal decomposition; Update module, for the measured value utilizing n-th layer smooth signal to upgrade Unscented kalman filtering device, utilizes n-th layer detail signal to obtain the observation noise variance of described Unscented kalman filtering device; Unscented kalman filtering device, for estimating amplitude and the phase angle of fundametal compoment on Nonlinear state space model.

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

1. the method in the present invention and device, using the DC offset of fault-signal, first-harmonic angular frequency and fundametal compoment as state variable, set up nonlinear state equation and the observational equation of Unscented kalman filtering device (UnscentedKalmanFilter, UKF).Then gather fault-signal to carry out multiscale analysis and obtain smooth signal and detail signal, utilize smooth signal to upgrade the measured value of Unscented kalman filtering device, reduce the interference of fault-signal transient noise, improve the convergence rate of filtering algorithm; Utilize the variance of detail signal real-time online computation and measurement noise, improve the convergence precision of filtering algorithm; And amplitude and the phase angle of fundametal compoment is estimated by Unscented kalman filtering device, because Unscented kalman filtering device does not need to carry out linearisation to non linear system, there is higher estimated accuracy.

2. the method can estimate DC offset and the fundamental frequency of fault-signal in real time, has good adaptability to frequency and DC offset sudden change.

3. the fundametal compoment estimated judges fault in conjunction with Principles of Relay Protection, can realize detection and the phase-selecting function of electric power system fault.

Other features and advantages of the present invention will be set forth in the following description, and, partly become apparent from specification, or understand by implementing the present invention.Object of the present invention and other advantages realize by structure specifically noted in write specification, claims and accompanying drawing and obtain.

Below by drawings and Examples, technical scheme of the present invention is described in further detail.

Accompanying drawing explanation

Accompanying drawing is used to provide a further understanding of the present invention, and forms a part for specification, together with embodiments of the present invention for explaining the present invention, is not construed as limiting the invention.In the accompanying drawings:

Fig. 1 is the schematic flow sheet according to fundametal compoment extracting method of the present invention.

Fig. 2 is according to power system transmission line fault model figure of the present invention.

Fig. 3 is according to fundametal compoment extracting method implementation result figure of the present invention.

Fig. 4 is the design sketch extracting fundamental frequency according to the present invention.

Fig. 5 is the design sketch extracting DC offset according to the present invention.

Fig. 6 is the structure chart according to fundametal compoment extraction element of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in detail, but is to be understood that protection scope of the present invention not by the restriction of embodiment.

As shown in Figure 1, according to the fundametal compoment extracting method of the specific embodiment of the invention, comprise the following steps:

Step S100: gather fault-signal s (t) in electric power system;

Set up electric power system as shown in Figure 2, gather fault-signal s (t) at fault f place.

Step S102: build the Nonlinear state space model of described fault-signal as state variable using the fundametal compoment in fault-signal s (t), first-harmonic angular frequency and DC offset;

In this step, suppose that the voltage of electric power system or current signal s (t) only comprise DC component and fundametal compoment, its discrete time representation is:

s _k＝A _0,k+A _1,ksin(ω _kkT _s+θ _1,k)(1)

In formula: T _sfor the sampling period, A _{0, k}for DC offset, A _{1, k}for fundamental voltage amplitude, θ _{1, k}for first-harmonic phase angle, ω _kfor first-harmonic angular frequency.Define system state variable x _{4, k}=A _{1, k}sin (ω _kkT _s+ θ _{1, k}), x _{3, k}=A _{1, k}cos (ω _kkT _s+ θ _{1, k}), x _{2, k}=ω _k, x _{1, k}=A _{0, k}.Suppose that a kth sampling period is to+1 sampling period of kth, signal is not undergone mutation, and can think A _{0, k+1}≈ A _{0, k}, A _{1, k+1}≈ A _{1, k}, ω _k+1≈ ω _k, θ _{1, k+1}≈ θ _{1, k}.Then at the state variable x in+1 sampling period of kth _{3, k+1}can be approximately:

x _3,k+1＝A _1,k+1sin(ω _k+1kT _s+ω _k+1T _s+θ _1,k+1)

≈A _1,ksin(ω _kkT _s+ω _kT _s+θ _1,k)(2)

＝x _3,kcos(x _2,kT _s)+x _4,ksin(x _2,kT _s)

In like manner, state variable x _{4, k+1}can be approximately:

x _4,k+1≈-x _3,ksin(x _2,kT _s)+x _4,kcos(x _2,kT _s)(3)

Consider process noise W _k+1, obtain system state equation formula X _k+1=f (X _k)+W _k+1represent, wherein:

$X_k={\[x_1,x_2,x_3,x_4\]}_k^T,---\left(4\right)$

$f\left(X_k\right)={\left[\begin{array}{c}{x}_1\\ x_2\\ x_{3}cos\left(x_2{T}_s\right)+x_{4}sin\left(x_2{T}_s\right)\\ -x_{3}sin\left(x_2{T}_s\right)+x_{4}cos\left(x_2{T}_s\right)\end{array}\right]}_k.---\left(5\right)$

Actual voltage or current signal also comprise harmonic component and measurement noises, and the summation of this tittle is considered as observation noise V _k.Then on the basis of formula (1), obtain systematic observation equation formula Z _k=h (X _k)+V _krepresent, wherein: Z _k=[s _k], h (X _k)=[1010] X _k.

Step S104: utilize multi-scale wavelet morphology to be decomposed by fault-signal s (t) and obtain N layer smooth signal with N layer detail signal

Wherein, in multi-scale wavelet morphological analysis, there is following relation in smooth signal and detail signal:

$s_a^i=s_a^{i+1}+s_d^{i+1}---\left(6\right)$

In formula: i=1,2 ..., N-1.

Step S106: utilize n-th layer smooth signal upgrade the measured value of Unscented kalman filtering device, utilize n-th layer detail signal online calculating observation noise variance;

Morphologic filtering has low-pass filtering effect, and the smooth signal measurement noises after Morphological Analysis greatly reduces, and Decomposition order more strong noise is fewer.Therefore, n-th layer smooth signal is selected upgrade the measured value of Unscented kalman filtering device, utilize n-th layer detail signal online calculating observation noise variance, can reduce the interference of fault-signal transient noise to filter, improves estimated accuracy.

Wherein, observation noise variance computing formula is as follows:

$R_k={\mathrm{\α}}_1{R}_{k-1}+{\mathrm{\α}}_2{s}_{d|k}^N{\left(s_{d|k}^N\right)}^T---\left(7\right)$

In formula: α ₁, α ₂for weight coefficient, meet α ₁, α ₂>=0 and α ₁+ α ₂=1.

Step S108: start Unscented kalman filtering device and setting up the amplitude and phase angle that Nonlinear state space model basis estimate fundametal compoment;

Unscented kalman filtering algorithm is utilized to estimate state variable from the measured value of fault-signal s (k) uKF algorithm is introduced Unscented transform and is similar to the non-linear of system on traditional linear Kalman filter basis, basic thought constructs a series of Sigma point based on the average of state variable and variance, then nonlinear transformation is carried out to each Sigma point, obtain average and the variance of the quantity of state after converting by being weighted summation to the Sigma point after conversion.Adopt Unscented transform can reach the estimated accuracy of more than second order to the non-linear partial of system, therefore, UKF algorithm is widely used in the state estimation of non linear system.UKF algorithm mainly contains three steps, specific as follows:

Step1:Sigma samples

According to the state estimation in a upper cycle with covariance matrix value gather 2n+1 Sigma particle { χ _i(i=0,1 ..., 2n), and dispensed is to each average of Sigma particle and the weight coefficient of covariance with (i=0,1 ..., 2n).Computing formula is as follows:

$\left\{\begin{array}{c}{\mathrm{\χ}}_{i,k-1}={\hat{X}}_{k-1},i=0\\ {\mathrm{\χ}}_{i,k-1}={\hat{X}}_{k-1}+{\mathrm{\Ψ}}_i,i=1,\mathrm{...},n\\ {\mathrm{\χ}}_{i,k-1}={\hat{X}}_{k-1}+{\mathrm{\Ψ}}_i,i=n+1,\mathrm{...},2n\\ \mathrm{\λ}={\mathrm{\α}}^2\left(n+\mathrm{\κ}\right)-n\end{array}\right.---\left(8\right)$

$\left\{\begin{array}{c}{w}_0^m=\frac{\mathrm{\λ}}{\mathrm{\λ}+n}\\ w_0^c=\frac{\mathrm{\λ}}{\mathrm{\λ}+n}+1-{\mathrm{\α}}^2+\mathrm{\β}\\ w_i^m=w_i^c=\frac{1}{2(\mathrm{\λ}+n)},i=1,\mathrm{...},2n\end{array}\right.---\left(9\right)$

λ＝α ²(n+κ)-n(10)

In formula: for the i-th row that Matrix C holesky decomposes; α (0≤α≤1) controls the distribution of sampled point, determines the dispersion degree of sampled point and average; The effect of κ ensures be a positive semidefinite matrix, usually select κ=0 or 3-n; Parameter beta is used for describing the prior distribution information of state variable, and be single argument for state variable and meet the situation of Gaussian Profile, the optimal value of β is 2.

Step2: prediction

Status predication: χ _{i, k|k-1}=f (χ _{i, k-1}) (11)

The average of computing mode prediction: ${\hat{X}}_{k|k-1}=\underset{i=0}{\overset{2n}{\Σ}}{w}_i^m{\mathrm{\χ}}_{i,k|k-1}---\left(12\right)$

Prediction covariance matrix:

${\hat{P}}_{k|k-1}=\underset{i=0}{\overset{2n}{\Σ}}{w}_i^c\left({\mathrm{\χ}}_{i,k|k-1}-{\hat{X}}_{k|k-1}\right){\left({\mathrm{\χ}}_{i,k|k-1}-{\hat{X}}_{k|k-1}\right)}^T+Q_k---\left(13\right)$

Step3: upgrade

Upgrade measured value: Z _{i, k|k-1}=h (χ _{i, k|k-1}) (14)

Calculating observation value mean value: ${\hat{Z}}_k=\underset{i=0}{\overset{2n}{\Σ}}{w}_i^m{Z}_{i,k|k-1}---\left(15\right)$

Calculate auto-covariance matrix: ${\hat{P}}_{zz}=\underset{i=0}{\overset{2n}{\Σ}}{w}_i^c(Z_{i,k|k-1}-{\hat{Z}}_k){(Z_{i,k|k-1}-{\hat{Z}}_k)}^T+R_k---\left(16\right)$

Calculate Cross-covariance:

${\hat{P}}_{xz}=\underset{i=0}{\overset{2n}{\Σ}}{w}_i^c({\mathrm{\χ}}_{i,k|k-1}-{\hat{X}}_{k|k-1}){(Z_{i,k|k-1}-{\hat{Z}}_k)}^T---\left(17\right)$

Calculate UKF gain: $K_k={\hat{P}}_{xz}{\hat{P}}_{zz}^{-1}---\left(18\right)$

State updating: ${\hat{X}}_k={\hat{X}}_{k|k-1}+K_k(Z_k-{\hat{Z}}_k)---\left(19\right)$

Upgrade covariance matrix: ${\hat{P}}_k={\hat{P}}_{k|k-1}-K_k{\hat{P}}_{zz}{K}_k^T---\left(20\right)$

Wherein, define for DC offset estimated value, for frequency estimated value, for fundamental voltage amplitude estimated value, for the estimated value of first-harmonic phase angle.UKF algorithm upgrades the estimated value of the state that obtains after each computation of Period ${\hat{X}}_k={\left[\begin{array}{cccc}{\hat{x}}_{1,k}& {\hat{x}}_{2,k}& {\hat{x}}_{3,k}& {\hat{x}}_{4,k}\end{array}\right]}^T,$ Wherein ${\hat{x}}_{4,k}={\hat{A}}_{1,k}sin({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}),$ ${\hat{x}}_{3,k}={\hat{A}}_{1,k}\cos \left({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}\right),{\hat{x}}_{2,k}={\widehat{\mathrm{\ω}}}_k,{\hat{x}}_{1,k}={\hat{A}}_{0,k}.$ Then through type (21)-(24) can calculate

${\hat{A}}_{0,k}={\hat{x}}_{1,k}---\left(21\right)$

${\hat{f}}_k={\hat{x}}_{2,k}/2\mathrm{\π}---\left(22\right)$

${\hat{A}}_{1,k}=\sqrt{{\hat{x}}_{3,k}^2+{\hat{x}}_{4,k}^2}---\left(23\right)$

${\widehat{\mathrm{\θ}}}_{1,k}={\tan }^{-1}({\hat{x}}_{4,k}/{\hat{x}}_{3,k})---\left(24\right)$

By what obtain to obtain the fundametal compoment of the fault-signal estimated, the implementation result of its fundametal compoment, fundamental frequency and DC offset is shown in Fig. 3, Fig. 4 and Fig. 5.

The multi-scale wavelet morphological analysis of step S104 in this embodiment, suppose the fault-signal of function s (x) for collecting, g (x) structural element, the domain of definition is respectively D _fand D _g.The expansion of signal s (x), burn into open and close operator are defined as follows respectively:

(s⊕g)(x)＝max{s(x-y)+g(y)}(25)

(sΘg)(x)＝min{s(x+y)-g(y)}(26)

sοg＝(sΘg)⊕g(27)

s·g＝(s⊕g)Θg(28)

The filter be made up of mathematical morphological operation is called morphological filter.Opening operation can peak noise in filtered signal waveform, and closed operation can suppress the trough noise in signal waveform.Opening and closing morphological filter OC and make and break morphological filter CO is defined as follows:

OC(s,g)＝sοg·g(29)

CO(s,g)＝s·gοg(30)

Practical application adopts mixed style filter, is defined as follows:

y(s)＝[OC(s,g)+CO(s,g)]/2(31)

The yardstick of definition Multiscale Morphological is λ, the structural element λ under yardstick λ _gbe defined as:

Structural element g is constantly expanded with the increase of λ, forms the structural element that size is different, thus reaches the object of Multiresolution Decomposition.If morphology operations is T, the morphology operations under yardstick λ is defined as morphological transformation { T _{. λ}| the set of λ >0}, wherein T _{. λ}for:

T _λ＝λT(f/λ),λ>0(33)

Then multiple dimensioned dilation and erosion computing is:

(s⊕g) _λ＝λ[(s/λ)⊕g]＝s⊕λg(34)

(sΘg) _λ＝λ[(s/λ)Θg]＝sΘλg(35)

Formula (29) basis can obtain multiple dimensioned opening and closing morphological filter:

OC _λ(s,g)＝λOC(s/λ,g)(36)

＝sΘλg⊕λg⊕λgΘλg

In like manner can obtain multiple dimensioned make and break morphological filter on formula (30) basis:

CO _λ(s,g)＝s⊕λgΘλgΘλg⊕λg(37)

The multiple dimensioned mixed style filter of actual employing, is defined as follows:

y _λ(s)＝[OC _λ(s,g)+CO _λ(s,g)]/2(38)

Utilize multiple dimensioned mixed style filter that signal is carried out the decomposition of N layer on different yardsticks, the width of structural element g is L=2 ^1-jl _j, j=1,2 ..., N is Decomposition order, L ₁for structural element is the original width of the 1st layer.Decompose the smooth signal α obtained to primary signal Continuous Approximation under different scale _jand the detail signal d to the continuous details of primary signal _j.Along with the increase of Decomposition order, the length of structural element reduces, noise more tiny in energy filtered signal.

Above-mentioned for UKF algorithm is for the fundametal compoment of suspected fault signal s (t) or the method introduction of harmonic component, and in this embodiment, adopt the N layer smooth signal of fault-signal s (t) after mathematical morphology decomposes upgrade the measured value Z of UKF filter _k, utilize n-th layer detail signal real-time online calculating observation noise variance R _k, its computing formula is as step S106 Chinese style thus obtain fundametal compoment or the harmonic component of fault-signal s (t) that fault-signal s (t) in this embodiment is estimated by UKF algorithm after mathematical morphology conversion.

Method in the present invention, using the DC offset of fault-signal, first-harmonic angular frequency and fundametal compoment as state variable, sets up nonlinear state equation and the observational equation of Unscented kalman filtering device (UnscentedKalmanFilter, UKF).Then gather fault-signal to carry out multiscale analysis and obtain smooth signal and detail signal, utilize smooth signal to upgrade the measured value of Unscented kalman filtering device, reduce the interference of fault-signal transient noise, improve the convergence rate of filtering algorithm; Utilize the variance of detail signal real-time online computation and measurement noise, improve the convergence precision of filtering algorithm; And amplitude and the phase angle of fundametal compoment is estimated by Unscented kalman filtering device, because Unscented kalman filtering device does not need to carry out linearisation to non linear system, there is higher estimated accuracy.

As shown in Figure 6, according to the another aspect of the present embodiment, provide a kind of fundametal compoment extraction element, comprising:

Acquisition module 10, for gathering the fault-signal in electric power system;

MBM 20, for building the Nonlinear state space model of described fault-signal using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable;

Decomposing module 30, obtains N layer smooth signal and N layer detail signal for utilizing multi-scale wavelet by described fault-signal decomposition;

Update module 40, for the measured value utilizing n-th layer smooth signal to upgrade Unscented kalman filtering device, utilizes n-th layer detail signal to calculate the observation noise variance of described Unscented kalman filtering device;

Unscented kalman filtering device 50, for estimating amplitude and the phase angle of fundametal compoment on Nonlinear state space model.

Above-mentioned MBM 20 builds the Nonlinear state space model of described fault-signal step using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable is:

If the discrete time representation of fault-signal is:

s _k＝A _0,k+A _1,ksin(ω _kkT _s+θ _1,k)(39)

In formula: T _sfor the sampling period, A _{0, k}for DC offset, A _{1, k}for fundamental voltage amplitude, θ _{1, k}for first-harmonic phase angle, ω _kfor first-harmonic angular frequency;

Definition Model state variable x _{4, k}=A _{1, k}sin (ω _kkT _s+ θ _{1, k}), x _{3, k}=A _{1, k}cos (ω _kkT _s+ θ _{1, k}), x _{2, k}=ω _k, x _{1, k}=A _{0, k}; Suppose that a kth sampling period is to+1 sampling period of kth, fault-signal is not undergone mutation, and thinks A _{0, k+1}≈ A _{0, k}, A _{1, k+1}≈ A _{1, k}, ω _k+1≈ ω _k, θ _{1, k+1}≈ θ _{1, k};

Then at the state variable x in+1 sampling period of kth _{3, k+1}can be approximately:

x _3,k+1＝A _1,k+1sin(ω _k+1kT _s+ω _k+1T _s+θ _1,k+1)

≈A _1,ksin(ω _kkT _s+ω _kT _s+θ _1,k)(40)

＝x _3,kcos(x _2,kT _s)+x _4,ksin(x _2,kT _s)

In like manner, state variable x _{4, k+1}can be approximately:

x _4,k+1≈-x _3,ksin(x _2,kT _s)+x _4,kcos(x _2,kT _s)(41)

Consider the process noise W of fault-signal _k+1, the state equation formula obtaining model is:

X _k+1＝f(X _k)+W _k+1(42)

$X_k={\[x_1,x_2,x_3,x_4\]}_k^T---\left(43\right)$

$X_{k+1}={\left[\begin{array}{c}{x}_1\\ x_2\\ x_{3}cos\left(x_2{T}_s\right)+x_{4}sin\left(x_2{T}_s\right)\\ -x_{3}sin\left(x_2{T}_s\right)+x_{4}cos\left(x_2{T}_s\right)\end{array}\right]}_k+W_{k+1}---\left(44\right)$

Consider that fault-signal also comprises harmonic component and measurement noises, the summation of harmonic component and measurement noises is considered as observation noise V _k; Then on the basis of formula (1), obtain the observational equation formula Z of model _k=h (X _k)+V _krepresent, wherein: Z _k=[s _k], h (X _k)=[1010] X _k.

The step of amplitude and phase angle that above-mentioned Unscented kalman filtering device estimates fundametal compoment on Nonlinear state space model is:

At Nonlinear state space model, Unscented kalman filtering device 50 estimates that the state estimation obtaining fault-signal is:

${\hat{X}}_k={\left[\begin{array}{cccc}{\hat{x}}_{1,k}& {\hat{x}}_{2,k}& {\hat{x}}_{3,k}& {\hat{x}}_{4,k}\end{array}\right]}^T---\left(45\right)$

Wherein, ${\hat{x}}_{4,k}={\hat{A}}_{1,k}\sin \left({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}\right),{\hat{x}}_{3,k}={\hat{A}}_{1,k}\cos \left({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}\right),{\hat{x}}_{2,k}={\widehat{\mathrm{\ω}}}_k,{\hat{x}}_{1,k}={\hat{A}}_{0,k};$

Thus try to achieve: ${\hat{A}}_{0,k}={\hat{x}}_{1,k}---\left(46\right)$

${\hat{f}}_k={\hat{x}}_{2,k}/2\mathrm{\π}---\left(47\right)$

${\hat{A}}_{1,k}=\sqrt{{\hat{x}}_{3,k}^2+{\hat{x}}_{4,k}^2}---\left(48\right)$

${\widehat{\mathrm{\θ}}}_{1,k}={\tan }^{-1}({\hat{x}}_{4,k}/{\hat{x}}_{3,k})---\left(49\right)$

Wherein, for DC offset estimated value, for frequency estimated value, for fundamental voltage amplitude estimated value, for the estimated value of first-harmonic phase angle.

The present invention can have multiple multi-form embodiment; above for Fig. 1-Fig. 6 by reference to the accompanying drawings to technical scheme of the present invention explanation for example; this does not also mean that the instantiation that the present invention applies can only be confined in specific flow process or example structure; those of ordinary skill in the art should understand; specific embodiments provided above is some examples in multiple its preferred usage, and the execution mode of any embodiment the claims in the present invention all should within technical solution of the present invention scope required for protection.

Last it is noted that the foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, although with reference to previous embodiment to invention has been detailed description, for a person skilled in the art, it still can be modified to the technical scheme described in foregoing embodiments, or carries out equivalent replacement to wherein portion of techniques feature.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (6)

1. a fundametal compoment extracting method, is characterized in that, comprises the following steps:

1) fault-signal in electric power system is gathered;

2) Nonlinear state space model of described fault-signal is built using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable;

3) utilize multi-scale wavelet to be decomposed by described fault-signal and obtain N layer smooth signal and N layer detail signal;

4) utilize n-th layer smooth signal to upgrade the measured value of Unscented kalman filtering device, utilize n-th layer detail signal to obtain the observation noise variance of described Unscented kalman filtering device;

5) start Unscented kalman filtering device in step 2) in set up the amplitude and phase angle that Nonlinear state space model estimate fundametal compoment.

2. fundametal compoment extracting method according to claim 1, it is characterized in that, step 2) in build the Nonlinear state space model of described fault-signal using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable step be:

If the discrete time representation of fault-signal is:

s _k＝A _0,k+A _1,ksin(ω _kkT _s+θ _1,k)(1)

In formula: T _sfor the sampling period, A _{0, k}for DC offset, A _{1, k}for fundamental voltage amplitude, θ _{1, k}for first-harmonic phase angle, ω _kfor first-harmonic angular frequency;

Definition Model state variable x _{4, k}=A _{1, k}sin (ω _kkT _s+ θ _{1, k}), x _{3, k}=A _{1, k}cos (ω _kkT _s+ θ _{1, k}), x _{2, k}=ω _k, x _{1, k}=A _{0, k}; Suppose that a kth sampling period is to+1 sampling period of kth, fault-signal is not undergone mutation, and thinks A _{0, k+1}≈ A _{0, k}, A _{1, k+1}≈ A _{1, k}, ω _k+1≈ ω _k, θ _{1, k+1}≈ θ _{1, k};

Then at the state variable x in+1 sampling period of kth _{3, k+1}can be approximately:

x _3,k+1＝A _1,k+1sin(ω _k+1kT _s+ω _k+1T _s+θ _1,k+1)

≈A _1,ksin(ω _kkT _s+ω _kT _s+θ _1,k)(2)

＝x _3,kcos(x _2,kT _s)+x _4,ksin(x _2,kT _s)

In like manner, state variable x _{4, k+1}can be approximately:

$x_{4,k+1}\≈-x_{3,k}sin\left(x_{2,k}{T}_s\right)+x_{4,k}cos\left(x_{2,k}{T}_s\right)---\left(3\right)$

Consider the process noise W of fault-signal _k+1, the state equation formula obtaining model is:

X _k+1＝f(X _k)+W _k+1(4)

$X_k={\[x_1,x_2,x_3,x_4\]}_k^T---\left(5\right)$

$X_{k+1}={\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\cos \left(x_2{T}_s\right)+x_4\sin \left(x_2{T}_s\right)\\ -x_3\sin \left(x_2{T}_s\right)+x_{4}ci\left(x_2{T}_s\right)\end{array}\right]}_k+W_{k+1}---\left(6\right)$

Consider that fault-signal also comprises harmonic component and measurement noises, the summation of harmonic component and measurement noises is considered as observation noise V _k; Then on the basis of formula (1), obtain the observational equation formula Z of model _k=h (X _k)+V _krepresent, wherein: Z _k=[s _k], h (X _k)=[1010] X _k.

3. fundametal compoment extracting method according to claim 2, is characterized in that, step 5) in start Unscented kalman filtering device in step 2) in set up amplitude and phase angle Nonlinear state space model estimating fundametal compoment step be:

At Nonlinear state space model, Unscented kalman filtering device estimates that the state estimation obtaining fault-signal is:

${\hat{X}}_k={\left[\begin{array}{cccc}{\hat{x}}_{1,k}& {\hat{x}}_{2,k}& {\hat{x}}_{3,k}& {\hat{x}}_{4,k}\end{array}\right]}^T---\left(7\right)$

Wherein, $\begin{array}{cccc}{\hat{x}}_{4,k}={\hat{A}}_{1,k}\sin ({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}),& {\hat{x}}_{3,k}={\hat{A}}_{1,k}cos({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}),& {\hat{x}}_{2,k}={\widehat{\mathrm{\ω}}}_k,& {\hat{x}}_{1,k}={\hat{A}}_{0,k}\end{array};$

Thus try to achieve: ${\hat{A}}_{0,k}={\hat{x}}_{1,k}---\left(8\right)$

${\hat{f}}_k={\hat{x}}_{2,k}/2\mathrm{\π}---\left(9\right)$

${\hat{A}}_{1,k}=\sqrt{{\hat{x}}_{3,k}^2+{\hat{x}}_{4,k}^2}---\left(10\right)$

${\widehat{\mathrm{\θ}}}_{1,k}={\tan }^{-1}({\hat{x}}_{4,k}/{\hat{x}}_{3,k})---\left(11\right)$

Wherein, for DC offset estimated value, for frequency estimated value, for fundamental voltage amplitude estimated value, for the estimated value of first-harmonic phase angle.

4. a fundametal compoment extraction element, is characterized in that, comprising:

Acquisition module, for gathering the fault-signal in electric power system;

MBM, for building the Nonlinear state space model of described fault-signal using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable;

Decomposing module, obtains N layer smooth signal and N layer detail signal for utilizing multi-scale wavelet by described fault-signal decomposition;

Update module, for the measured value utilizing n-th layer smooth signal to upgrade Unscented kalman filtering device, utilizes n-th layer detail signal to obtain the observation noise variance of described Unscented kalman filtering device;

Unscented kalman filtering device, for estimating amplitude and the phase angle of fundametal compoment on Nonlinear state space model.

5. fundametal compoment extraction element according to claim 4, it is characterized in that, described MBM builds the Nonlinear state space model of described fault-signal step using the fundametal compoment in fault-signal, first-harmonic angular frequency and DC offset as state variable is:

If the discrete time representation of fault-signal is:

s _k＝A _0,k+A _1,ksin(ω _kkT _s+θ _1,k)(12)

In formula: T _sfor the sampling period, A _{0, k}for DC offset, A _{1, k}for fundamental voltage amplitude, θ _{1, k}for first-harmonic phase angle, ω _kfor first-harmonic angular frequency;

Definition Model state variable x _{4, k}=A _{1, k}sin (ω _kkT _s+ θ _{1, k}), x _{3, k}=A _{1, k}cos (ω _kkT _s+ θ _{1, k}), x _{2, k}=ω _k, x _{1, k}=A _{0, k}; Suppose that a kth sampling period is to+1 sampling period of kth, fault-signal is not undergone mutation, and thinks A _{0, k+1}≈ A _{0, k}, A _{1, k+1}≈ A _{1, k}, ω _k+1≈ ω _k, θ _{1, k+1}≈ θ _{1, k};

Then at the state variable x in+1 sampling period of kth _{3, k+1}can be approximately:

x _3,k+1＝A _1,k+1sin(ω _k+1kT _s+ω _k+1T _s+θ _1,k+1)

≈A _1,ksin(ω _kkT _s+ω _kT _s+θ _1,k)(13)

＝x _3,kcos(x _2,kT _s)+x _4,ksin(x _2,kT _s)

In like manner, state variable x _{4, k+1}can be approximately:

x _4,k+1≈-x _3,ksin(x _2,kT _s)+x _4,kcos(x _2,kT _s)(14)

Consider the process noise W of fault-signal _k+1, the state equation formula obtaining model is:

X _k+1＝f(X _k)+W _k+1(15)

$X_k={\[x_1,x_2,x_3,x_4\]}_k^T---\left(16\right)$

$X_{k+1}={\left[\begin{array}{c}{x}_1\\ x_2\\ x_{3}cos\left(x_2{T}_s\right)+x_{4}sin\left(x_2{T}_s\right)\\ -x_{3}sin\left(x_2{T}_s\right)+x_{4}cos\left(x_2{T}_s\right)\end{array}\right]}_k+W_{k+1}---\left(17\right)$

Consider that fault-signal also comprises harmonic component and measurement noises, the summation of harmonic component and measurement noises is considered as observation noise V _k; Then on the basis of formula (1), obtain the observational equation formula Z of model _k=h (X _k)+V _krepresent, wherein: Z _k=[s _k], h (X _k)=[1010] X _k.

6. fundametal compoment extraction element according to claim 5, is characterized in that, the step of amplitude and phase angle that described Unscented kalman filtering device estimates fundametal compoment on Nonlinear state space model is:

At Nonlinear state space model, Unscented kalman filtering device estimates that the state estimation obtaining fault-signal is:

${\hat{X}}_k={\left[\begin{array}{cccc}{\hat{x}}_{1,k}& {\hat{x}}_{2,k}& {\hat{x}}_{3,k}& {\hat{x}}_{4,k}\end{array}\right]}^T---\left(18\right)$

Wherein $\begin{array}{cccc}{\hat{x}}_{4,k}={\hat{A}}_{1,k}\sin ({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}),& {\hat{x}}_{3,k}={\hat{A}}_{1,k}cos({\widehat{\mathrm{\ω}}}_k{\mathrm{kT}}_s+{\widehat{\mathrm{\θ}}}_{1,k}),& {\hat{x}}_{2,k}={\widehat{\mathrm{\ω}}}_k,& {\hat{x}}_{1,k}={\hat{A}}_{0,k}\end{array};$

Thus try to achieve: ${\hat{A}}_{0,k}={\hat{x}}_{1,k}---\left(19\right)$

${\hat{f}}_k={\hat{x}}_{2,k}/2\mathrm{\π}---\left(20\right)$

${\hat{A}}_{1,k}=\sqrt{{\hat{x}}_{3,k}^2+{\hat{x}}_{4,k}^2}---\left(21\right)$

${\widehat{\mathrm{\θ}}}_{1,k}={\tan }^{-1}({\hat{x}}_{4,k}/{\hat{x}}_{3,k})---\left(22\right)$

Wherein, for DC offset estimated value, for frequency estimated value, for fundamental voltage amplitude estimated value, for the estimated value of first-harmonic phase angle.