CN104198809B - Frequency measuring method for multi-frequency oscillation of electrical power system - Google Patents

Abstract

The invention discloses a frequency measuring method for multi-frequency oscillation of an electrical power system. The frequency measuring method for the multi-frequency oscillation of the electrical power system includes steps that (1) sampling n groups of voltage signals in a power grid according to a time interval Ts to obtain n groups of sampled values, wherein each group comprises (2n+1) voltage signals; (2) combining 2n+1 elements in the i group of sampled values to obtain n+1 elements and forming an (n+1)*1 matrix; after traversing 1, 2, ..., n, obtaining n (n+1)*1 matrices X(k); (3) extracting the first element of each matrix in the n (n+1)*1 matrices X(k) to form a 1*n matrix; (4) removing the first element from the (n+1)*1 matrix X(k), using the surplus n elements to form an n*1 matrix, and forming an n*n matrix through n n*1 matrices; (5) multiplying the 1*n matrix X1 by the inverse of the n*n matrix X' to obtain a 1*n matrix; forming an n equation with one unknown FORMULA (shown in the description) according to the 1*n matrix and a frequency measuring factor sv; (6) obtaining n solutions s'v according to the n equation with one unknown FORMULA (shown in the description), and obtaining n measuring frequencies according to FORMULA (shown in the description). The frequency measuring method for the multi-frequency oscillation of the electrical power system is capable of obtaining all the frequencies in the electrical power system.

Description

A kind of frequency measurement method of electric system oscillation of multi frequency

Technical field

The invention belongs to the parameter identification technique field of AC transmission system, more specifically, relate to a kind of frequency measurement method of electric system oscillation of multi frequency.

Background technology

Along with the progressively development of the trans-regional bulk power grid of China's extra-high voltage, the continuous expansion of interconnected network, power system oscillation accident happens occasionally.When transmission line of electricity transmission power over-limit condition, the electrical network asynchronous combined floodgate between fault, ring system (or side by side double loop) open loop suddenly, large sized unit tripping operation or loss of excitation, power supply that is short-circuited is failed to pull into synchronous etc., the vibration that electric system occurs in various degree all may be made.

When vibration occurs complicated electric power system, may occur multiple oscillation frequency in system, this multi-frequency state brings extreme influence to the correct operation of relay protection.Each frequency of accurate recognition is elimination negative phase-sequence out-of-balance current, prevents the important foundation of directional element error starting, accurately measuring distance resistance value.

Current frequency measurement method generally has and removes modulation method, function analytical method, functional approaching (as least square method, Kalman filtering algorithm) and artificial neural network method etc. based on the algorithm of Fourier transform, wavelet analysis method, zero-crossing method, signal; These methods are all be based upon on the basis of single frequency signal, and when system generation oscillation of multi frequency, said method all exists the even complete inapplicable problem of precision deficiency.

Summary of the invention

For the defect of prior art, the object of the present invention is to provide a kind of frequency measurement method of electric system oscillation of multi frequency, be intended to solve prior art and can only measure unifrequent problem.

The invention provides a kind of frequency measurement method of electric system oscillation of multi frequency, comprise the steps:

(1) with time interval T _sthe sampling of n group is carried out to the voltage signal in electrical network, often organizes collection (2n+1) individual sampled voltage, obtain n group sampled value;

I-th group of sampled value is ${\stackrel{\→}{U}}_i=\left[\begin{array}{cccccc}{u}_{\left(i\right)1}& u_{\left(i\right)2}& \·\·\·& u_{\left(i\right)j}& \·\·\·& u_{\left(i\right)2n+1}\end{array}\right];$ I represents the sequence number of n group sampled value, i=1,2,3 ... n; u _{(i) j}it is a jth sampled voltage in i-th group of sampled value; J represents the sequence number of 2n+1 sampled voltage, j=1,2,3 ... 2n+1; Sample frequency f _s=1/T _s;

(2) carry out combination to 2n+1 element in i-th group of sampled value obtain n+1 element and form (n+1) × 1 matrix X _(k)=[x _{(k) 1}x _{(k) 2}x _{(k) w}x _{(k) n+1}] ^t, i traversal 1,2 ... n (n+1) × 1 matrix X is obtained after n _(k);

X _{(k) w}for w element of a kth matrix, w=1,2...n+1, k represent the sequence number of n matrix, k=1,2...n; The value of k is constantly equal to the value of i;

(3) by n (n+1) × 1 matrix X _(k)in first element extraction of each matrix out define 1 × n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}for first element of a kth matrix;

(4) by (n+1) × 1 matrix X _(k)in first element remove and define n × 1 matrix by n the element be left, n n × 1 matrix forms a n × n matrix $X^{\′}=\left[\begin{array}{cccc}{x}_{\left(1\right)2}& x_{\left(2\right)2}& \·\·\·& x_{\left(n\right)2}\\ x_{\left(1\right)3}& x_{\left(2\right)3}& \·\·\·& x_{\left(n\right)3}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_{\left(1\right)n+1}& x_{\left(2\right)n+1}& \·\·\·& x_{\left(n\right)n+1}\end{array}\right];$

(5) by described 1 × n matrix X ₁1 × n matrix X=[x is obtained after taking advantage of with the anti-phase of described n × n matrix X ' ₁x ₂x _n]; According to described 1 × n matrix X=[x ₁x ₂x _n] and frequency measurement factor s _vstructure unitary n equation of n th order n $x_1{s}_v+x_2{s}_v^2+\·\·\·+x_{n-1}{s}_v^{n-1}+x_n{s}_v^n=1;$

(6) according to described unitary n equation of n th order n $x_1{s}_v+x_2{s}_v^2+\·\·\·+x_{n-1}{s}_v^{n-1}+x_n{s}_v^n=1$ Obtain n solution and according to f _v=arccos (s ' _v)/2 π T _sobtain n survey frequency; V=1,2...n.

Wherein, (n+1) × 1 matrix X in step (2) _(k)in each element be specially: $\left\{\begin{array}{c}{x}_{\left(k\right)1}=u_{\left(i\right)n+1}\\ x_{\left(k\right)2}=(u_{\left(i\right)n}+u_{\left(i\right)n+1})/2\\ x_{\left(k\right)3}=(u_{\left(i\right)n-1}+{2u}_{\left(i\right)n+1}+u_{\left(i\right)n+3})/4\\ \·\·\·\\ x_{\left(k\right)n+1}=(u_{\left(i\right)1}+{\mathrm{nu}}_{\left(i\right)3}+\·\·\·+{\mathrm{nu}}_{\left(i\right)2n-1}+u_{\left(i\right)2n+1})/2^n\end{array}\right.,$ U _{(i) n}be the n-th sampled voltage in i-th group of sampled value, the coefficient of sampled voltage meets pascal's triangle rule.

The voltage signal of collection by gathering voltage signal, and combines by the present invention, measures the factor and makes complicated multi-frequency measurement problem reduction be solving of equation with one unknown quantity, thus accurately obtain all frequencies of system by pull-in frequency.

Accompanying drawing explanation

The realization flow figure of the frequency measurement method of the electric system oscillation of multi frequency that Fig. 1 provides for the embodiment of the present invention.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

The present invention samples to the voltage signal in electrical network with Fixed Time Interval, and often group sampling is to signal continuous sampling 2n+1 point, forms a group, carries out the sampling of n group, obtains n group sampled value; Each group sampled value is combined by specific rule; Introduce the frequency measurement factor corresponding with each frequency component; Utilize transition matrix and the triangle identical transformation of frequency measurement factor structure, realize the stripping of each frequency component; Single frequency component is peeled off by matrix conversion computing; Solve frequency.Measure the factor by pull-in frequency, and carry out a series of matrix operation and conversion, make complicated multi-frequency measurement problem reduction be solving of equation with one unknown quantity, thus accurately obtain all frequencies of system.

In embodiments of the present invention, when complicated electric power system is vibrated, have n unit to be in asynchronous operation state in p unit, according to superposition principle, the oscillating voltage of circuit is made up of n frequency component, can be expressed as: wherein U _vfor the amplitude of each component of voltage, f _vfor the frequency of each component of voltage, α _vfor the initial phase angle of each component of voltage, the sample frequency of voltage signal is T _s; P be more than or equal to 3 integer, n be more than or equal to 2 integer.

As shown in Figure 1, the frequency measurement method of electric system oscillation of multi frequency that the embodiment of the present invention provides comprises the following steps:

(1) with time interval T _scarry out the sampling of n group to the voltage signal in electrical network, often group gathers 2n+1 sampled voltage, obtains n group sampled value; I-th group of sampled value is i represents the sequence number of n group sampled value, i=1,2,3 ... n; u _{(i) j}it is a jth sampled voltage in i-th group of sampled value; J represents the sequence number of 2n+1 sampled voltage, j=1,2,3 ... 2n+1;

(2) carry out combination to 2n+1 element in i-th group of sampled value obtain n+1 element and form (n+1) × 1 matrix X _(k)=[x _{(k) 1}x _{(k) 2}x _{(k) w}x _{(k) n+1}] ^t, x _{(k) w}for w element of a kth matrix, w=1,2...n+1.I traversal 1,2 ... n (n+1) × 1 matrix X is obtained after n _(k); K represents the sequence number of n matrix, k=1,2...n; The value of k is constantly equal to the value of i;

(3) by n (n+1) × 1 matrix X _(k)in first element extraction of each matrix out define 1 × n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}for first element of a kth matrix;

(4) by (n+1) × 1 matrix X _(k)in first element remove and define n × 1 matrix by n the element be left, n n × 1 matrix forms a n × n matrix $X^{\′}=\left[\begin{array}{cccc}{x}_{\left(1\right)2}& x_{\left(2\right)2}& \·\·\·& x_{\left(n\right)2}\\ x_{\left(1\right)3}& x_{\left(2\right)3}& \·\·\·& x_{\left(n\right)3}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_{\left(1\right)n+1}& x_{\left(2\right)n+1}& \·\·\·& x_{\left(n\right)n+1}\end{array}\right];$

(5) by described 1 × n matrix X ₁1 × n matrix X=[x is obtained after taking advantage of with the anti-phase of described n × n matrix X ' ₁x ₂x _n]; According to described 1 × n matrix X=[x ₁x ₂x _n] and frequency measurement factor s _vstructure unitary n equation of n th order n $x_1{s}_v+x_2{s}_v^2+\·\·\·+x_{n-1}{s}_v^{n-1}+x_n{s}_v^n=1;$

(6) according to described unitary n equation of n th order n $x_1{s}_v+x_2{s}_v^2+\·\·\·+x_{n-1}{s}_v^{n-1}+x_n{s}_v^n=1$ Obtain n solution and according to f _v=arccos (s ' _v)/2 π T _sobtain n survey frequency; V=1,2...n.Wherein, when n is less than or equal to 4, above-mentioned unitary n equation of n th order n has analytic solution; When n is greater than 4, can solve by methods such as Newton iteration methods.Solve a unitary n equation of n th order n as how to go, this is technological means well known in the art, is not described in detail in this its concrete solution procedure.

The frequency measurement method of electric system oscillation of multi frequency of the present invention has the following advantages:

(1) frequency measured by the method contributes to elimination negative phase-sequence out-of-balance current, prevents directional element error starting, accurately measuring distance resistance value, improves the performance of relay protection further, contributes to the safety and reliability promoting electric system;

(2) frequency measured by the method contributes to state and the characteristic of electric system when analyzing vibration;

(3) the method does not adopt any approximate data in mathematical derivation process, has higher degree of accuracy;

(4) solving existing frequency measurement method cannot the problem of accurate frequency measurement when system exists two or more frequency;

(5) this method frequency measurement scope is large, and has the higher advantage of the strong precision of system oscillation Shaoxing opera.

In the embodiment of the present invention, the object of frequency measurement is f in acquisition formula (1) _vvalue, and the difficult point of multi-frequency measurement is: one, and each component of voltage contains U _v, f _v, α _vthree unknown quantitys, these three unknown quantitys are coupled with nonlinear relationship, cannot by simple matrix operation by f _vfrom U _vand α _vin be stripped out; Its two, suppose by certain conversion by f _vfrom U _vand α _vin be stripped out, but each sampled value of voltage signal all comprises the information of all frequency components, namely each sampled value all forms one by each unknown frequency f _v, how the n unit nonlinear equation that (v=1,2...n) forms, obtain specific f _v, make specific f _vbeing stripped out from other n-1 unknown frequency in n unit nonlinear equation, is also a very complicated problem.Visible, from voltage signal, peeling off each frequency component, and then peel off single frequency component, is the key of multi-frequency measurement algorithm.

First be peel off each frequency component.

For v component of voltage u of voltage signal in formula (1) _v=U _vsin (2 π f _vt+ α _v), suppose that the phase angle of this component of voltage during sampling m point is β, then the m point sampling value of this component of voltage is u _v[m]=U _vsin β.Introduce and corresponding with v component of voltage solve factor s _v=cos (2 π f _vt _s)=cos (ω _vt _s), what each sampled value of this component of voltage was corresponding with it solves factor s _vmeet following relation.

$\left\{\begin{array}{c}{u}_v\left[m\right]s_v=U\sin \mathrm{\β}\·\cos \left({\mathrm{\ω}}_v{T}_s\right)\\ =U(\sin (\mathrm{\β}-{\mathrm{\ω}}_v{T}_s)+\sin (\mathrm{\β}+{\mathrm{\ω}}_v{T}_s))/2\\ =\left(u_v\right[m-1]+u_v[m+1\left]\right)/2\\ u_v\left[m\right]s_v^2=\left(u_v\right[m-1]+u_v[m+1\left]\right)s_v/2\\ =\left(u_v\right[m-2]+{2u}_v[m]+u_v[m+2\left]\right)/4\\ \·\·\·\\ u_v{\left[m\right]s}_v^l=\left(u_v\right[m-l]+{\mathrm{lu}}_v[m-l+2]+\·\·\·\\ +{\mathrm{lu}}_v[m+l-2]+u_v[m+l])/2^l\end{array}\right.---\left(6\right);$ Wherein, the coefficient in bracket before sampled value meets the rule of pascal's triangle.

Each component of voltage all meets above-mentioned formula (6) relation, can be obtained by superposition principle

$\left\{\begin{array}{c}\underset{v=1}{\overset{n}{\mathrm{\Σ}}}{u}_v\left[m\right]=u\left[m\right]\\ \underset{v=1}{\overset{n}{\mathrm{\Σ}}}{u}_v{\left[m\right]s}_v=\left(u\right[m-1]+u[m+1\left]\right)/2\\ \underset{v=1}{\overset{n}{\mathrm{\Σ}}}{u}_v\left[m\right]s_v^2=\left(u\right[m-2]+2u[m]+u[m+2\left]\right)/4\\ \·\·\·\\ \underset{v=1}{\overset{n}{\mathrm{\Σ}}}{u}_v{\left[m\right]s}_v^l=\left(u\right[m-l]+\mathrm{lu}[m-l+2]+\·\·\·+\\ +\mathrm{lu}[m+l-2]+u[m+l])/2^l\end{array}\right.---\left(7\right);$ Being the sampled value of voltage signal on the right of equation, is known quantity, m the sampled value that u [m] is voltage signal.Therefore only unknown quantity u is contained in formula (7) _v[m], (v=1,2...n) and unknown quantity s _v, (v=1,2...n).

Solve factor s _vonly containing corresponding f _vinformation, if can by n unknown quantity u of formula (7) _v[m], (v=1,2...n) filtering, obtains one only about unknown quantity s _v, the equation of (v=1,2...n), just can realize f _vfrom U _vand α _vin the object that is stripped out.

Want a cancellation n unknown quantity, at least need n+1 equation to carry out disappearing n ary operation, the l value therefore in formula (7) is n.Cancellation u _v[m], (v=1,2...n), thus each frequency component is stripped out from voltage signal.

It should be noted that when l value is n, in observation type (7), the right of equal sign can find, solving equation group needs one group of sample sequence be made up of 2n+1 continuous print sampled value, if i-th group of sample sequence is expressed as vector ${\stackrel{\→}{U}}_i=\left[\begin{array}{cccc}u[m-n]& u[m-n+1]& \·\·\·& u[m+n]\end{array}\right]---\left(8\right);$ Visible, the intermediate point that u [m] is this group sample sequence.

The concrete grammar realizing peeling off each frequency component can represent with following matrix operation, SU=X _(i)(9); Wherein S forms (n+1) × n transition matrix by solving the factor $S=\left[\begin{array}{cccc}1& 1& \·\·\·& 1\\ s_1& s_2& \·\·\·& s_n\\ s_1^2& s_2^2& \·\·\·& s_n^2\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ s_1^n& s_2^n& \·\·\·& s_n^n\end{array}\right];$ N × 1 matrix U=[the u of the sampled value composition of each component of voltage when U is sampling m point ₁[m] u ₂[m] u ₃[m] ... u _n[m]] ^t.

X _(k)be (the n+1) × 1 matrix X after i-th group of sample sequence combination _(k)=[x _{(k) 1}x _{(k) 2}x _{(k) w}x _{(k) n+1}] ^t, x _{(k) w}for w element of a kth matrix, w=1,2...n+1.X _(k)in element combined by sampled value, corresponding with the expression formula in formula (7) on the right of equation $\left\{\begin{array}{c}{x}_{\left(k\right)1}=u\left[m\right]\\ x_{\left(k\right)2}=\left(u\right[m-1]+u[m+1\left]\right)/2\\ x_{\left(k\right)3}=\left(u\right[m-2]+2u[m]+u[m+2\left]\right)/4\\ \·\·\·\\ x_{\left(k\right)n+1}=\left(u\right[m-n]+\mathrm{nu}[m-n+2]+\·\·\·\\ +\mathrm{nu}[m+n-2]+u[m+n])/2^n\end{array}\right.;$

(n+1) × 1 matrix X in above formula and step (2) _(k)in the expression formula of each element be the same in essence, for no other reason than that the different and slightly difference of the expression way of sampled value.Why above analysis interpretation step (2) needs specifically to combine sampled value.

Make first behavior 1 × n matrix S in transition matrix S ₁, then formula (9) can be converted into $\left\{\begin{array}{c}{S}_{1}U=x_{\left(k\right)1}\\ S_{2}U=X_{\left(k\right)}^{\′}\end{array}\right.$ (10); Wherein $S_2=\left[\begin{array}{cccc}{s}_1& s_2& \·\·\·& s_n\\ s_1^2& s_2^2& \·\·\·& s_n^2\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ s_1^n& s_2^n& \·\·\·& s_n^n\end{array}\right];$ X ' _(k)=[x _{(k) 2}x _{(k) 3}x _{(k) n+1}] ^t; Solution formula (10) can obtain $x_{\left(k\right)1}=S_1{s}_2^{-1}{X}_{\left(k\right)}^{\′}---\left(11\right).$

By above-mentioned computing and be converted to formula (11), namely one only about unknown quantity s _v, the n unit equation of (v=1,2...n), and s _vonly containing corresponding f _vinformation, namely each frequency component is stripped out from the amplitude of voltage signal and phase angle, next will carry out the stripping of single frequency component.

Peeling off single frequency component actual is solve specific s _vprocess.Formula (11) is a n unit equation, solves specific s _vat least need n equation.The equation of form as cotype (11) all can be obtained, only x owing to often organizing sampled value _{(k) 1}and X ' _(k)different because of the group difference of sampled value, sampling n group sequence can obtain n n unit equation.Available matrix operation is expressed as follows,

Wherein, X ₁for n (n+1) × 1 matrix X _(k)in first element extraction of each matrix out define 1 × n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}for first element of a kth matrix;

(n+1) × 1 matrix X _(k)in first element remove and define n × 1 matrix by n the element be left, n n × 1 matrix forms a n × n matrix $X^{\′}=\left[\begin{array}{cccc}{x}_{\left(1\right)2}& x_{\left(2\right)2}& \·\·\·& x_{\left(n\right)2}\\ x_{\left(1\right)3}& x_{\left(2\right)3}& \·\·\·& x_{\left(n\right)3}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ x_{\left(1\right)n+1}& x_{\left(2\right)n+1}& \·\·\·& x_{\left(n\right)n+1}\end{array}\right];$

Acquisition 1 × n matrix X why is needed in above analysis interpretation step (3) and step (4) ₁and n × n matrix X '.

Solve in formula (12) and need to ask S ₂inverse, due to S ₂in all elements by unknown quantity s _k, (k=1,2...n) forms, and the calculated amount of inverting is very huge.Namely enablely to ask for expression formula, acquisition be one group of n unit nonlinear equation, solving of this system of equations is also very complicated.

Observe transition matrix S can find, the often row in S all only have a unknown quantity, and the expression formula of every column element is all identical.If arbitrary row of S can be stripped out, the stripping of single frequency can be realized.Therefore following conversion is taked herein.

X ' is taken advantage of on formula (12) right side, both sides ^-1, and then S is taken advantage of on the right side ₂, obtain X ₁x ' ^-1s ₂=S ₁(13); Solve X ₁x ' ^-1obtain 1 × n matrix X, if X=is [x ₁x ₂x _n], X and S ₂in any row all meet following formula, $x_1{s}_v+x_2{s}_v^2+\·\·\·+x_{n-1}{s}_v^{n-1}+x_n{s}_v^n=1---\left(14\right);$ So far, single frequency component is stripped out.In fact, according to s in formula (14) _vinterchangeability, n solution of formula (14) is s _v, the value of (v=1,2...n).

More than explain why step (5) constructs unitary n equation of n th order n and why can solve frequency according to non trivial solution in step (6).

When being in three hunting of frequencys respectively for electric system, emulation testing is carried out to institute of the present invention extracting method.

The amplitude random selecting of each component of voltage of oscillating voltage, initial phase angle is random selecting also.Adopt asynchronous-sampling, sampling period T _s=1/400s.When electric system is in three hunting of frequencys, frequency fluctuates between 40Hz ~ 60Hz; Simulation result is as shown in table 1.

The simulation result of table 1 three hunting of frequency

As seen from Table 1, when system is in three hunting of frequencys, institute of the present invention extracting method can accurately measure all frequencies, and measuring error is less than 1 × 10 ^-5hz.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. a frequency measurement method for electric system oscillation of multi frequency, is characterized in that, comprises the steps:

(1) with time interval T _sthe sampling of n group is carried out to the voltage signal in electrical network, often organizes collection (2n+1) individual sampled voltage, obtain n group sampled value;

I-th group of sampled value is i represents the sequence number of n group sampled value, i=1,2,3 ... n; u _{(i) j}it is a jth sampled voltage in i-th group of sampled value; J represents the sequence number of 2n+1 sampled voltage, j=1,2,3 ... 2n+1; Sample frequency f _s=1/T _s;

(2) carry out combination to 2n+1 element in i-th group of sampled value obtain n+1 element and form (n+1) × 1 matrix X _(k)=[x _{(k) 1}x _{(k) 2}x _{(k) w}x _{(k) n+1}] ^t, i traversal 1,2 ... n (n+1) × 1 matrix X is obtained after n _(k);

X _{(k) w}for w element of a kth matrix, w=1,2...n+1, k represent the sequence number of n matrix, k=1,2...n; The value of k is constantly equal to the value of i;

(3) by n (n+1) × 1 matrix X _(k)in first element extraction of each matrix out define 1 × n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}for first element of a kth matrix;

(4) by (n+1) × 1 matrix X _(k)in first element remove and define n × 1 matrix by n the element be left, n n × 1 matrix forms a n × n matrix

(5) by described 1 × n matrix X ₁1 × n matrix X=[x is obtained after taking advantage of with the anti-phase of described n × n matrix X ' ₁x ₂x _n]; According to described 1 × n matrix X=[x ₁x ₂x _n] and frequency measurement factor s _vstructure unitary n equation of n th order n

(6) according to described unitary n equation of n th order n obtain n and separate s _v', and according to f _v=arccos (s _v')/2 π T _sobtain n survey frequency; V=1,2 ... n;

(n+1) × 1 matrix X in step (2) _(k)in each element be specially: u _{(i) n}be the n-th sampled voltage in i-th group of sampled value, the coefficient of sampled voltage meets pascal's triangle rule.