CN104198809A - 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 large electrical network of China's extra-high voltage, the continuous expansion of interconnected network, power system oscillation accident happens occasionally.When the transmission line of electricity transmission power value of overstepping the extreme limit, the electrical network asynchronous combined floodgate that is short-circuited between fault, ring system (or side by side double loop) open loop suddenly, large capacity unit tripping or loss of excitation, power supply, fail to pull into synchronous etc., all may make electric system that vibration in various degree occurs.

When there is vibration in complicated electric power system, in system, may there are a plurality of oscillation frequency, this multi-frequency state has brought very big impact to the correct operation of relay protection.Accurately each frequency of identification be eliminate negative phase-sequence out-of-balance current, prevent directional element error starting, the accurate important foundation of measuring distance resistance value.

Frequency measurement method generally has algorithm, wavelet analysis method, zero-crossing method, signal based on Fourier transform to remove modulation method, function analytical method, approximation of function method (as least square method, Kalman filtering algorithm) and artificial neural network method etc. at present; These methods are to be all 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 frequency measurement method that the invention provides a kind of electric system oscillation of multi frequency, comprises the steps:

(1) with time interval T _svoltage signal in electrical network is carried out to the sampling of n group, and the individual sampled voltage of every group of collection (2n+1), obtains n group sampled value;

I group sampled value is i represents the sequence number of n group sampled value, i=1,2,3 ... n; u _{(i) j}be j sampled voltage in i group 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) 2n+1 element in i group sampled value combined and 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 ... after n, obtain n (n+1) * 1 matrix X _(k);

X _{(k) w}be w element of k matrix, w=1,2...n+1, 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 formed 1 * n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}it is first element of k matrix;

(4) by (n+1) * 1 matrix X _(k)in first element remove and formed n * 1 matrix by the n a being left element, n n * 1 matrix forms 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 ₁after taking advantage of with the anti-phase of described n * n matrix X ', obtain 1 * n matrix X=[x ₁x ₂x _n]; According to described 1 * n matrix X=[x ₁x ₂x _n] and frequency measurement factor S _vstructure monobasic 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 monobasic 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 and separate s ' _v, 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: $\left\{\begin{array}{c}{x}_{\left(k\right)1}=u_{\left(i\right)n+1}\\ x_{\left(k\right)2}=(u_{\left(i\right)n}+u_{\left(i\right)n+2})/2\\ x_{\left(k\right)3}=(u_{\left(i\right)n-1}+{2u}_{\left(i\right)n+1}+u_{\left(i\right)n+3})/4\\ \·\·\·\\ x_{\left(k\right)n+1}=(u_{\left(i\right)1}+{\mathrm{nu}}_{\left(i\right)3}+...+{\mathrm{nu}}_{\left(i\right)2n-1}+u_{\left(i\right)2n+1})/2^n\end{array}\right.,$ _{u (i) n}be n sampled voltage in i group sampled value, the coefficient of sampled voltage meets pascal's triangle rule.

The present invention is by gathering voltage signal, and the voltage signal of collection is combined, and that by pull-in frequency, measures the factor to make complicated multi-frequency measurement problem reduction be equation with one unknown quantity solves, thereby accurately obtains all frequencies of system.

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 clearer, 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, is not intended to limit the present invention.

The present invention samples to the voltage signal in electrical network with Fixed Time Interval, and every group of sampling, to 2n+1 point of signal continuous sampling, 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; Transition matrix and the triangle identical transformation of utilizing frequency measurement factor structure to form, realize peeling off of each frequency component; By matrix conversion computing, peel off single frequency component; Solve frequency.By pull-in frequency, measure the factor, and carry out a series of matrix operation and conversion, what to make complicated multi-frequency measurement problem reduction be equation with one unknown quantity solves, thereby accurately obtains all frequencies of system.

In embodiments of the present invention, when complicated electric power system is vibrated, have n unit in asynchronous operation state in p unit, according to superposition principle, the oscillating voltage of circuit is comprised of n frequency component, can be expressed as: (1); U wherein _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 is more than or equal to 3 integer, and n is more than or equal to 2 integer.

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

(1) with time interval T _svoltage signal in electrical network is carried out to the sampling of n group, and every group gathers 2n+1 sampled voltage, obtains n group sampled value; I group sampled value is i represents the sequence number of n group sampled value, i=1,2,3 ... n; u _{(i) j}be j sampled voltage in i group sampled value; J represents the sequence number of 2n+1 sampled voltage, j=1,2,3 ... 2n+1;

(2) 2n+1 element in i group sampled value combined and 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}be w element of k matrix, w=1,2...n+1.I traversal 1,2 ... after n, obtain n (n+1) * 1 matrix X _(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 formed 1 * n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}it is first element of k matrix;

(4) by (n+1) * 1 matrix X _(k)in first element remove and formed n * 1 matrix by the n a being left element, n n * 1 matrix forms 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 ₁after taking advantage of with the anti-phase of described n * n matrix X ', obtain 1 * n matrix X=[x ₁x ₂x _n]; According to described 1 * n matrix X=[x ₁x ₂x _n] and frequency measurement factor S _vstructure monobasic 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 monobasic 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 and separate s ' _v, 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 monobasic 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.As for how to go, solve a monobasic n equation of n th order n, 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) the measured frequency of the method contribute to eliminate negative phase-sequence out-of-balance current, prevent directional element error starting, accurate measuring distance resistance value, further improve the performance of relay protection, contribute to promote the safety and reliability of electric system;

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

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

(4) solved existing frequency measurement method system exist two cannot accurate frequency measurement during with upper frequency problem;

(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 to obtain f in formula (1) _vvalue, and the difficult point of multi-frequency measurement is: one, each component of voltage contains U _v, f _v, α _vthree unknown quantitys, these three unknown quantitys are coupled with nonlinear relationship, cannot be by simple matrix operation by f _vfrom U _vand α _vin peel off out; Its two, suppose by certain conversion by f _vfrom u _vand α _vin peel off out, but each sampled value of voltage signal all comprises the information of all frequency components, 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 fv from other n-1 unknown frequency, peel off out in n unit nonlinear equation, be also a very complicated problem.Visible, from voltage signal, peel off each frequency component, and then peel off single frequency component, be the key of multi-frequency measurement algorithm.

First be to peel off each frequency component.

V the component of voltage u for voltage signal in formula (1) _v=U _vsin (2 π f _vt+ α _v), while supposing sampling m point, the phase angle of this component of voltage is β, the m point sampling value of this component of voltage is u _v[m]=U _vsin β.Introduce corresponding with v component of voltage factor s that solves _v=cos (2 π f _vt _s)=cos (ω _vt _s), each sampled value of this component of voltage is 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 before the interior sampled value of bracket meets the rule of pascal's triangle.

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

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

Solve factor s _vonly contain corresponding f _vinformation, if can be 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 peeling off out.

Want a cancellation n unknown quantity, at least need n+1 the equation n ary operation that disappears, so the l value in formula (7) is n.Cancellation u _v[m], (v=1,2...n), thus make each frequency component peel off out from voltage signal.

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

The concrete grammar that each frequency component is peeled off in realization 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=[u that when U is sampling m point, the sampled value of each component of voltage forms ₁[m] u ₂[m] u ₃[m] ... u _n[m]] ^t.

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

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

Make first behavior 1 * n matrix S in transition matrix S ₁, 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), one only about unknown quantity s _v, the n unit equation of (v=1,2...n), and s _vonly contain corresponding f _vinformation, each frequency component is peeled off out from the amplitude of voltage signal and phase angle, next will carry out peeling off of single frequency component.

Peeling off single frequency component actual is to solve specific s _vprocess.Formula (11) is a n unit equation, solves specific s _vat least need n equation.Because every group of sampled value all can obtain form as the equation of cotype (11), only x _{(k) 1}and X ' _(k)because the group of sampled value is different, 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 formed 1 * n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}it is first element of k matrix;

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

Above analysis interpretation in step (3) and step (4), need to obtain 1 * n matrix X why ₁and n * n matrix X '.

Solve in formula (12) and need to ask S ₂contrary, 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.Enable to ask for expression formula, acquisition be one group of n unit nonlinear equation, solving of this system of equations is also very complicated.

Observing transition matrix S can find, the every 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 peeled off out, can realize peeling off of single frequency.Therefore take following conversion 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, establish X=[x ₁x ₂x _n], X and S ₂in any row all meet following formula, (14); So far, single frequency component is peeled off 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 explained why step (5) is constructed monobasic n equation of n th order n and why can solve frequency according to the solution of equation in step (6).

The electric system of take is respectively example when three hunting of frequencys, and institute of the present invention extracting method is carried out to emulation testing.

The amplitude of each component of voltage of oscillating voltage is chosen at random, and initial phase angle is also chosen at random.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 frequencys

As seen from Table 1, system is when three hunting of frequencys, and institute of the present invention extracting method can accurately be measured 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 modifications of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.

Claims (2)

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

(1) with time interval T _svoltage signal in electrical network is carried out to the sampling of n group, and the individual sampled voltage of every group of collection (2n+1), obtains n group sampled value;

I group sampled value is i represents the sequence number of n group sampled value, i=1,2,3 ... n; u _{(i) j}be j sampled voltage in i group 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) 2n+1 element in i group sampled value combined and 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 ... after n, obtain n (n+1) * 1 matrix X _(k);

X _{(k) w}be w element of k matrix, w=1,2...n+1, 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 formed 1 * n matrix X ₁=[x _{(1) 1}x _{(2) 1}x _{(k) 1}x _{(n) 1}]; x _{(k) 1}it is first element of k matrix;

(4) by (n+1) * 1 matrix X _(k)in first element remove and formed n * 1 matrix by the n a being left element, n n * 1 matrix forms 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 ₁after taking advantage of with the anti-phase of described n * n matrix X ', obtain 1 * n matrix X=[x ₁x ₂x _n]; According to described 1 * n matrix X=[x ₁x ₂x _n] and frequency measurement factor S _vstructure monobasic 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 monobasic 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 and separate s ' _v, and according to f _v=arccos (s ' _v)/2 π T _sobtain n survey frequency; V=1,2...n.

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