CN103869162A - Dynamic signal phasor measurement method based on time domain quasi-synchronization - Google Patents

Abstract

The invention discloses a dynamic signal phasor measurement method based on time domain quasi-synchronization. The dynamic signal phasor measurement method based on the time domain quasi-synchronization comprises the following steps: estimating the fundamental wave frequency of a sampled signal by a time domain quasi-synchronization sampling algorithm; carrying out time domain quasi-synchronization on the sampled signal by the estimated value of the fundamental wave frequency; reconstructing a quasi-synchronization sampling sequence by Newton interpolation; carrying out frequency domain analysis on the reconstructed quasi-synchronization sampling sequence by FFT (fast Fourier transform) to obtain a dynamic signal phasor measurement result. According to the method, the influence on the measurement precision of the traditional phasor measurement method by frequency spectrum leakage caused by nonsynchronous sampling is avoided. The computation complexity of the dynamic signal phasor measurement method based on the time domain quasi-synchronization is smaller than the computation complexity of the traditional phasor measurement method based on the discrete Fourier transform, and the dynamic signal phasor measurement method based on the time domain quasi-synchronization is easy to realize in an embedded system.

Description

A kind of based on the quasi synchronous Dynamic Signal phasor measurement of time domain method

Technical field

The present invention relates to signal phasor measurement field, specifically a kind of based on the quasi synchronous Dynamic Signal phasor measurement of time domain method.

Background technology

Along with being widely used of the nonlinear-load such as power electronic equipment, semiconductor devices, power quality problem emerges in an endless stream.How to measure and to analyze in real time the actual conditions of electric system, thereby improve the quality of power supply, become emphasis and focus in electric system research field in recent years.

At present, in electric system, voltage and current is all the variations per hour that does in time sinusoidal variations, all can use phasor representation.But the prerequisite of IEEE Standard1344-1995 definition phasor is under steady state conditions, the amplitude of signal, frequency and phase angle all remain unchanged, and under rated frequency, the transient measurement value of phase angle remains unchanged with absolute reference time relatively.But in actual applications, when signal frequency departs from rated frequency, phase angle is with frequency change, thereby introducing error is difficult to obtain calculated value accurately.

Existing phasor measurement algorithm mainly contains zero passage detection method, discrete Fourier transformation (DFT) method etc.Zero passage detection method is more a kind of synchronous phasor measuring method, only the zero crossing moment of tested power frequency component need to be compared and can draw phase angle difference with standard sometime; Zero passage detection method principle is simple, be easy to realize, but its precision is not high, and is subject to the impact of harmonic wave, noise component.When electrical network medium frequency is without when skew, DFT algorithm is amplitude and the phase place of measuring-signal exactly, and its computational accuracy is not subject to the impact of Constant Direct Current component and integer harmonic component; But in the time that mains frequency has skew, due to the spectrum leakage that non-synchronous sampling causes, the precision of phasor measurement can decline rapidly.

For this reason, a kind of study pin-point accuracy Dynamic Signal phasor measurement method guarantee aspect power system safety and stability operation significant.

Summary of the invention

The invention provides a kind ofly based on the quasi synchronous Dynamic Signal phasor measurement of time domain method, avoided the impact on existing phasor measurement method measuring accuracy of spectrum leakage that non-synchronous sampling causes; Be less than the existing phasor measurement algorithm based on discrete Fourier transformation based on the quasi synchronous Dynamic Signal phasor measurement of time domain algorithm computational complexity, and be easy to realize in embedded system based on the quasi synchronous Dynamic Signal phasor measurement of time domain algorithm.

For solving the problems of the technologies described above, the solution that the present invention proposes is: utilize the accurate synchronized sampling algorithm of time domain to estimate the fundamental frequency of sampled signal, utilize fundamental frequency estimated value to do the accurate synchronization of time domain to sampled signal, by the accurate synchronized sampling sequence of Newton interpolating method reconstruct, utilize FFT to carry out frequency-domain analysis to the accurate synchronized sampling sequence of interpolation reconstruction, obtain Dynamic Signal phasor measurement result.

Technical scheme of the present invention is as follows:

A kind of based on the quasi synchronous Dynamic Signal phasor measurement of time domain method, comprise the following steps:

Step 1: electric power signal is sampled, separately sampled signal is saved as afterwards to crude sampling sample in sampling, sampled signal is added to wave filter, with filtering harmonic wave and noise simultaneously;

Step 2: to adopt accurate synchronized sampling algorithm to estimate fundamental frequency through filtering sampled signal after treatment, obtain fundamental frequency estimated value f _g;

Step 3: utilize the frequency estimation f obtaining in step 2 _gand sampling number N calculates accurate synchronized sampling cycle λ in the signal period, take λ as step-length, adopt Newton interpolating method to do the accurate synchronization process of time domain to the discrete series in original sample in step 1, interpolation reconstruction obtains accurate synchronized sampling sequence;

Step 4: to the accurate synchronized sampling sequence obtaining in step 3, adopt rectangular window to intercept a signal period, carry out FFT spectrum analysis, obtain the frequency domain information of signal, and calculate frequency, amplitude and the phase parameter of electric power signal, obtain Dynamic Signal phasor measurement result.

Described method, the selection rule of step 1 median filter is:

Choose triangular self-convolution window digital band pass FIR wave filter, lower stopband edge frequency is 40Hz, and lower passband edge frequency is 46Hz, and upper passband edge frequency is 54Hz, and upper stopband edge frequency is 60Hz, passband ripple 0.01, stopband ripple 0.1.Wherein, the method for designing of triangular self-convolution window digital band pass FIR wave filter is: first, according to the index request to stopband attenuation and transitional zone, select triangular self-convolution window, and estimate length of window; Secondly, the frequency response function of structure ideal digital wave filter, and obtain desirable unit impulse response according to ideal frequency response function; Finally, paired pulses response function adds triangular self-convolution window and obtains design result.

Described method, in step 2, accurate synchronized sampling algorithm parameter selection rule is:

The single iteration D that counts is 64, and iterations P is 5.

The technique effect that the mode of deriving by theory is below reached the present invention describes.

In time domain, continuous harmonic signal can be expressed as form conventionally

$u\left(t\right)=\underset{k}{\mathrm{\Σ}}{A}_k\sin (2\mathrm{\πfkt}+{\mathrm{\θ}}_k)---\left(1\right)$

In formula, k is overtone order, represents first-harmonic when k=1; A _kit is k subharmonic amplitude; T is the time; F is the frequency of fundamental signal; θ _kit is the initial phase angle of k subharmonic.

Ignore the quantization error in analog-digital conversion process, and various stochastic errors in measuring process, utilize sample frequency for f _sanalysis System for Power Quality obtain N _cindividual sample

$u\left(n\right)=\underset{k}{\mathrm{\Σ}}{A}_k\sin (2\mathrm{\πknf}/f_s+{\mathrm{\θ}}_k)---\left(2\right)$

In formula, n is for being more than or equal to 0 and be less than or equal to N _c-1 integer.

In order to carry out fundamental frequency estimation, the sample that utilizes triangular self-convolution window bandpass filter to obtain sampling carries out filtering processing, and filtering higher hamonic wave, obtains signal as follows

u(n)=A ₁sin(2πnf/f _s+θ ₁) (3)

In formula, A ₁for fundamental voltage amplitude; θ ₁for first-harmonic initial phase angle.

Accurate synchronized sampling algorithm recursion formula is as follows

$X_a^1=\frac{2}{\underset{i=i_0}{\overset{D+i_0}{\mathrm{\Σ}}}}\underset{i=i_0}{\overset{D+i_0}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{i}u\left(t_i\right)\cos \left(2\mathrm{\π}\frac{i}{D}\right)---\left(4\right)$

$X_b^1=\frac{2}{\underset{i=i_0}{\overset{D+i_0}{\mathrm{\Σ}}}{\mathrm{\ρ}}_i}\underset{i=i_0}{\overset{D+i_0}{\mathrm{\Σ}}}{\mathrm{\ρ}}_{i}u\left(t_i\right)\sin \left(2\mathrm{\π}\frac{i}{D}\right)---\left(5\right)$

In formula: the subscript " 1 " of " X " represents the 1st quadrature computing; The D synchronized sampling algorithm single iteration that is as the criterion is counted, D=64; ρ _ifor weighting coefficient corresponding to numerical quadrature formula, for the trapezoidal quadrature formula of complexification,

ρ ₀=ρ _D=0.5，ρ ₁=ρ ₂=…=ρ _D-1=1。

Utilize accurate synchronized sampling algorithm recursion formula to estimate to obtain the phase difference θ in the Δ t time, signal fundamental frequency estimated value f _gfor

$f_g=\frac{2\mathrm{\π}}{\mathrm{\ω}}=\frac{2\mathrm{\π\Δt}}{\mathrm{\Δ\θ}}---\left(6\right)$

In formula, ω represents first-harmonic angular frequency, and Δ θ represents first-harmonic phase angle difference, and Δ t represents the mistiming that Δ θ is corresponding.

The quasi-synchronous algorithm parameter requiring according to patent of the present invention, estimated frequency error is less than 3 × 10 ^-10hz.The frequency estimation that utilizes (6), carries out the accurate synchronization of time domain to the original sampled signal sample in step 1, and interpolation reconstruction obtains accurate synchronized sampling sequence.Interpolation polynomial is

P(x)=u[x ₀]+u[x ₀,x ₁](x-x ₀)+…+u[x ₀,x ₁,…,x _m](x-x ₀)…(x-x _m-1) (7)

In formula, x is the sampled signal time interval, and subscript m represents m sampling time interval, u[... ] be difference coefficient, u[x ₀]=u (x ₀), k jump business is

$u[x_i,x_{i+1},\·\·\·,x_{i+k}]=\frac{u[x_{i+1},\·\·\·,x_{i+k}]}{x_{i+k}-x_i}-\frac{u[x_i,\·\·\·,x_{i+k-1}}{x_{i+k}-x_i}---\left(8\right)$

With rectangular window to interpolation reconstruction signal intercept a signal period, utilize FFT to carry out frequency-domain analysis, in signal spectrum, find the peak value spectral line that harmonic wave is corresponding, by analyzing peak value and then obtaining frequency, phase place and the amplitude parameter of electric power signal, completed the phasor measurement of Dynamic Signal.

In sum, one of the present invention, based on the quasi synchronous Dynamic Signal phasor measurement of time domain method, has been avoided under non-synchronous sampling the spectrum leakage that FFT causes and fence effect, and the method computational complexity is less than traditional Interpolating Window FFT Algorithm, be easy to realize in embedded system.

Below in conjunction with accompanying drawing, the invention will be further described.

Accompanying drawing explanation

Fig. 1 realizes the program flow diagram based on the quasi synchronous Dynamic Signal phasor measurement of time domain in the present invention;

Fig. 2 is accurate synchronized sampling algorithm iteration schematic diagram in the present invention;

Fig. 3 is Newton interpolating method reconfiguration principle figure in the present invention.

Embodiment

The present invention realizes program circuit based on the quasi synchronous harmonic analysis and measurement method of time domain as shown in Figure 1.

As shown in Figure 1, the first step, utilizes Analysis System for Power Quality to sample to the signal of input, obtains N _cindividual sample, N _cfor natural number, f _sfor sample frequency.

Second step, by triangular self-convolution window bandpass filter to the N collecting _cindividual sample carries out filtering and noise reduction processing.The parameter of triangular self-convolution window bandpass filter is: triangular self-convolution window bandpass filter, and lower stopband edge frequency is 40Hz, lower passband edge frequency is 46Hz, upper passband edge frequency is 54Hz, upper stopband edge frequency is 60Hz, passband ripple 0.01, stopband ripple 0.1.

The 3rd step, the signal after utilizing accurate synchronized sampling algorithm to filtering and noise reduction carries out iteration, estimates the fundamental frequency of measured signal, obtains fundamental frequency f _g, wherein the accurate synchronized sampling single iteration D that counts is 64, iterations P is 5.The concrete steps of Frequency Estimation are as follows:

At t ₁the P*D+1 in moment discrete sampling value carried out iteration, as shown in Figure 2, obtains respectively the first-harmonic real part X of P iteration ^j _awith first-harmonic imaginary part X ^j _b, t ₁the fundamental phase θ in moment ₁for

${\mathrm{\θ}}_1=\arctan \frac{X_a^J}{X_b^J}---\left(9\right)$

In like manner can obtain t ₂the fundamental phase θ in moment ₂, fundamental frequency estimated value f _gfor

$f_g=\frac{2\mathrm{\π}}{\mathrm{\ω}}=\frac{2\mathrm{\π\Δt}}{\mathrm{\Δ\θ}}=\frac{2\mathrm{\π}(t_2-t_1)}{{\mathrm{\θ}}_2-{\mathrm{\θ}}_1}---\left(10\right)$

In formula, ω represents first-harmonic angular frequency, and Δ θ represents first-harmonic phase angle difference, and Δ t represents the mistiming that Δ θ is corresponding.

The 4th step, utilizes fundamental frequency estimated value f _g, utilize principle shown in Fig. 3 to do the accurate synchronization process of time domain to crude sampling sample, the burst u under interpolation reconstruction synchronized sampling condition _i(k).

The 5th step, the sequence u with rectangular window to interpolation reconstruction _i(k) block, intercept the discrete series u of a signal period _i(k _i) (k _i=0,1 ..., N-1).Carry out FFT spectrum analysis to intercepting sequence, obtain.

$\left(k_i\right)=\frac{A_0}{2j}{e}^{j{\mathrm{\θ}}_0}{W}_R(2\mathrm{\π}(k_i-k_0)/N)---\left(11\right)$

In formula, k ₀=f _gn/f _s; W _r(k) be rectangular window frequency spectrum.

The 6th step, to Y (k _i) analyze, at Y (k _i) in find peak value corresponding to each harmonic, obtain respectively frequency, amplitude and the phase place of each harmonic by analyzing peak value.

So far, completed the measurement of Dynamic Signal phasor, method of the present invention has frequency deviation and the situation without frequency deviation applicable to electric power signal first-harmonic.

Below apply method provided by the present invention and carry out emulation experiment, to verify the reliability of method provided by the present invention.

Utilize MATLAB to produce a simulate signal, signal model is as follows

y(t)=220sin(2πf ₀t+θ ₁)+2.3936sin(6πf ₀t+θ ₃)+1.3442sin(10πf ₀t+θ ₅) (12)

In formula, fundamental frequency f ₀value in 49.5～50.5Hz, step-length 0.1Hz; Fundamental voltage amplitude A ₁for 220V, phase theta ₁=π/3rad; 3 subharmonic and 5 order harmonic components amplitudes are respectively A ₃=2.3936V, A ₅=1.3442V, phase place is respectively θ ₃=π/4rad, θ ₅=π/6rad.

Utilize sample frequency f _sthe Analysis System for Power Quality of=3200Hz gathers N _c=512 samples are analyzed.Simulation parameter value is as follows

Accurate synchronized sampling algorithm: the single iteration D that counts is 64, and iterations P is 5

Newton interpolating method: it is 11 points that interpolation is counted

FFT frequency-domain analysis: use rectangular window, N=64 fft analysis of counting

Simulation result is as shown in table 1, and in table 1, aE-b represents a × 10 ^-b.

Referring to table 1, when frequency jitter be ± when 0.5Hz, electric power signal fundamental frequency estimates that absolute error is all less than 8.70E-10, fundamental voltage amplitude absolute error is all less than 4.60E-9, fundamental phase absolute error is all less than 5.90E-11; 3 subharmonic Amplitude Estimation errors are all less than 1.10E-08, and 3 subharmonic phase angle absolute errors are all less than 3.20E-09; 5 subharmonic Amplitude Estimation errors are all less than 9.80E-09, and 5 subharmonic phase angles estimate that absolute error is all less than 2.50E-08.Therefore feasibility and the correctness of Dynamic Signal phasor measurement method provided by the present invention, have been verified.

Table 1 utilizes method provided by the present invention to carry out the result of emulation experiment

Claims (3)

1. based on the quasi synchronous Dynamic Signal phasor measurement of a time domain method, it is characterized in that, comprise the following steps:

Step 1: electric power signal is sampled, separately sampled signal is saved as afterwards to crude sampling sample in sampling, sampled signal is added to wave filter simultaneously, with filtering harmonic wave and noise, then will carry out the processing of step 2 through filtering sampled signal after treatment;

Step 2: to adopt accurate synchronized sampling algorithm to estimate fundamental frequency through filtering sampled signal after treatment, obtain fundamental frequency estimated value f _g;

Step 3: utilize the frequency estimation f obtaining in step 2 _gand sampling number N calculates accurate synchronized sampling cycle λ in the signal period, take λ as step-length, adopt Newton interpolating method to do the accurate synchronization process of time domain to the discrete series in original sample in step 1, interpolation reconstruction obtains accurate synchronized sampling sequence;

Step 4: to the accurate synchronized sampling sequence obtaining in step 3, adopt rectangular window to intercept a signal period, carry out FFT spectrum analysis, obtain the frequency domain information of signal, and calculate frequency, amplitude and the phase parameter of electric power signal, obtain Dynamic Signal phasor measurement result.

2. method according to claim 1, is characterized in that, the selection rule of step 1 median filter is:

Choose triangular self-convolution window bandpass filter, lower stopband edge frequency is 40Hz, and lower passband edge frequency is 46Hz, and upper passband edge frequency is 54Hz, and upper stopband edge frequency is 60Hz, passband ripple 0.01, stopband ripple 0.1.

3. method according to claim 1, is characterized in that, in step 2, quasi-synchronous algorithm parameter selection rule is:

The single iteration D that counts is 64, and iterations P is 5.