CN103869162B - 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

One kind is based on time domain quasi synchronous Dynamic Signal phasor measurement method

Technical field

The present invention relates to signal phasor measurement field, specifically one kind are based on time domain quasi synchronous Dynamic Signal phasor measurement Method.

Background technology

With widely using of the nonlinear-loads such as power electronic equipment, semiconductor device, power quality problem layer goes out not Thoroughly.How measuring and to analyze the practical situation of power system in real time, thus improving the quality of power supply, having become as power train in recent years Emphasis in system research field and focus.

At present, in power system, voltage and current is all the variations per hour doing sinusoidal variations in time, all can use phasor representation. But, IEEE Standard 1344-1995 define phasor premise be under steady state conditions, a reactor, that is, the amplitude of signal, frequency and Phase angle all keeps constant, and under rated frequency, the instantaneous measure of phase angle keeps constant with absolute reference time relatively.But In practical application, when signal frequency deviates rated frequency, phase angle changes with frequency, thus introducing error it is difficult to obtain accurately Value of calculation.

Existing phasor measurement algorithm mainly has cross zero detecting method, discrete Fourier transform (DFT) method etc..Cross zero detecting method Be compare intuitively a kind of synchronous phasor measuring method it is only necessary to by the zero crossing moment of tested power frequency component with sometime mark Standard compares and can draw phase angle difference；Cross zero detecting method principle is simple, it is easy to accomplish, but its precision is not high, and be easily subject to harmonic wave, make an uproar The impact of sound component.When electrical network medium frequency no offsets, DFT algorithm can accurately measure amplitude and the phase place of signal, and its Computational accuracy is not affected by Constant Direct Current component and integer harmonic component；But when mains frequency offsets, due to asynchronous The spectrum leakage that sampling causes, the precision of phasor measurement can decline rapidly.

For this reason, a kind of Dynamic Signal phasor measurement method studying high accuracy is ensureing power system safety and stability operation Aspect is significant.

Content of the invention

The invention provides a kind of be based on time domain quasi synchronous Dynamic Signal phasor measurement method, it is to avoid non-synchronous sampling The impact to existing phasor measurement method certainty of measurement for the spectrum leakage causing；Measured based on time domain quasi synchronous Dynamic Signal phase Quantity algorithm computational complexity is less than the existing phasor measurement algorithm based on discrete Fourier transform, and quasi synchronous based on time domain Dynamic Signal phasor measurement algorithm is easy to realize in embedded systems.

For solving above-mentioned technical problem, solution proposed by the present invention is：Estimated using time domain quasi-synchro sampling algorithm The fundamental frequency of sampled signal, does time domain plesiochronousization using fundamental frequency estimated value to sampled signal, by Newton interpolating method Reconstruct quasi-synchro sampling sequence, carries out frequency-domain analysiss using FFT to the quasi-synchro sampling sequence of interpolation reconstruction, obtains Dynamic Signal Phasor measurement result.

Technical scheme is as follows：

One kind is based on time domain quasi synchronous Dynamic Signal phasor measurement method, comprises the following steps：

Step one：Electric power signal is sampled, individually sampled signal is saved as crude sampling sample after sampling, with When to sampled signal add wave filter, to filter harmonic wave and noise jamming；

Step 2：Adopt quasi-synchro sampling algorithm to estimate fundamental frequency the sampled signal after filtered process, obtain base Wave frequency estimated value f_g；

Step 3：Using the frequency estimation f obtaining in step 2_gAnd sampling number N calculates in the signal period Obtain quasi-synchro sampling cycle λ, with λ as step-length, using Newton interpolating method to the discrete sequence in sample original in step one Row do time domain plesiochronousization and process, and interpolation reconstruction obtains quasi-synchro sampling sequence；

Step 4：To the quasi-synchro sampling sequence obtaining in step 3, a signal period is intercepted using rectangular window, carries out FFT spectrum is analyzed, and obtains the frequency domain information of signal, and calculates frequency, amplitude and the phase parameter of electric power signal, obtains dynamic Signal phasor measurement result.

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

Choose triangular self-convolution window digital band pass FIR filter, lower stopband edge frequency is 40Hz, lower passband edge frequency For 46Hz, upper passband edge frequency is 54Hz, and upper stopband edge frequency is 60Hz, passband ripple 0.01, stopband ripple 0.1.Its In, the method for designing of triangular self-convolution window digital band pass FIR filter is：First, according to the finger to stopband attenuation and intermediate zone Mark requires, and selects triangular self-convolution window, and estimates length of window；Secondly, the frequency response function of construction ideal digital wave filter, And ideal unitary impulse response is obtained according to ideal frequency response function；Finally, to impulse response function plus triangular self-convolution window Obtain design result.

Described method, in step 2, quasi-synchro sampling algorithm parameter selection rule is：

Single iteration points D is 64, and iterationses P is 5.

Mode below by way of theoretical derivation illustrates to the technique effect that the present invention reaches.

In time domain, continuous harmonic signal may generally be expressed as following form

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

In formula, k is overtone order, represents fundamental wave during k=1；A_kFor kth subharmonic amplitude；T is the time；F is fundamental signal Frequency；θ_kInitial phase angle for kth subharmonic.

Ignore the quantization error in analog-digital conversion process, and the various random error in measurement process, using sampling frequency Rate is f_sAnalysis System for Power Quality obtain N_cIndividual sample

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

In formula, n is more than or equal to 0 and to be less than or equal to N_c- 1 integer.

In order to carry out fundamental frequency estimation, filtered using the sample that triangular self-convolution window band filter obtains to sampling Ripple is processed, and filters higher hamonic wave, obtains signal as follows

U (n)=A₁sin(2πnf/f_s+θ₁) in (3) formula, A₁For fundamental voltage amplitude；θ₁For fundamental wave initial phase angle.

Quasi-synchro sampling algorithm recurrence formula is as follows

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

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

In formula：The subscript " 1 " of " X " represents the 1st quadrature computing；D be defined synchronous sampling algorithm single iteration points, D= 64；ρ_iFor the corresponding weight coefficient of numerical quadrature formula, for complexification compound trapezoidal integeration, ρ₀=ρ_D=0.5, ρ₁=ρ₂=...= ρ_D-1=1.

Estimate to obtain phase difference θ in the Δ t time, then signal fundamental frequency using quasi-synchro sampling algorithm recurrence formula Estimated value f_gFor

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

In formula, ω represents fundamental wave angular frequency, and Δ θ represents fundamental wave phase angle difference, and Δ t represents the corresponding time difference of Δ θ.

According to the quasi-synchronous algorithm parameter of patent requirements of the present invention, estimated frequency error is less than 3 × 10^-10Hz.Using (6) Frequency estimation, the original sampled signal sample in step one is carried out with time domain plesiochronousization, interpolation reconstruction obtains plesiochronous Sample sequence.Interpolation polynomial is

P (x)=u [x₀]+u[x₀,x₁](x-x₀)+L+u[x₀,x₁,L,x_m](x-x₀)L(x-x_m-1) (7)

In formula, x is sampled signal time interval, and subscript m represents m-th sampling time interval, and u [...] is difference coefficient, u [x₀]=u (x₀), k jump business is

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

With rectangular window, is intercepted to interpolation reconstruction signal one signal period, carry out frequency-domain analysiss using FFT, in signal spectrum Middle searching harmonic wave corresponding peak value spectral line, by analyzing frequency, phase place and the magnitude parameters of peak value and then acquisition electric power signal, Complete the phasor measurement of Dynamic Signal.

In sum, of the present invention a kind of it is based on time domain quasi synchronous Dynamic Signal phasor measurement method, it is to avoid non- Under synchronized sampling, spectrum leakage and fence effect that FFT causes, and the method computational complexity is less than traditional windowed interpolation Fft algorithm is it is easy to realize in embedded systems.

The invention will be further described below in conjunction with the accompanying drawings.

Brief description

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

Fig. 2 is quasi-synchro sampling algorithm iteration schematic diagram in the present invention；

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

Specific embodiment

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

As shown in figure 1, the first step, using Analysis System for Power Quality, the signal of input is sampled, obtain N_cIndividual sample This, N_cFor natural number, f_sFor sample frequency.

Second step, with triangular self-convolution window band filter to the N collecting_cIndividual sample is filtered denoising.Three The parameter of angle self-convolution window band filter is：Triangular self-convolution window band filter, lower stopband edge frequency is 40Hz, lower logical Belt 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.

3rd step, is iterated to the signal after filtering and noise reduction using quasi-synchro sampling algorithm, estimates the base of measured signal Wave frequency, obtains fundamental frequency f_g, wherein quasi-synchro sampling single iteration points D is 64, and iterationses P is 5.Frequency Estimation Comprise the following steps that：

In t₁The P*D+1 dis-crete sample values in moment are iterated, as shown in Fig. 2 the fundamental wave respectively obtaining P iteration is real Portion X^J _aWith fundamental wave imaginary part X^J _b, then t₁Fundamental phase θ in moment₁For

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

T can be obtained in the same manner₂Fundamental phase θ in moment₂, then fundamental frequency estimated value f_gFor

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

In formula, ω represents fundamental wave angular frequency, and Δ θ represents fundamental wave phase angle difference, and Δ t represents the corresponding time difference of Δ θ.

4th step, using fundamental frequency estimated value f_g, using principle shown in Fig. 3, time domain is done to crude sampling sample plesiochronous Change is processed, the signal sequence u under the conditions of interpolation reconstruction synchronized sampling_i(k).

5th step, with sequence u to interpolation reconstruction for the rectangular window_iK () is blocked, intercept the discrete sequence of a signal period Row u_i(k_i)(k_i=0,1 ..., N-1).Carry out FFT spectrum analysis to intercepting sequence, obtain.

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

In formula, k₀=f_gN/f_s；W_RK () is rectangular window frequency spectrum.

6th step, to Y (k_i) be analyzed, in Y (k_i) the middle searching corresponding peak value of each harmonic, divided by analyzing peak value Huo Qu not the frequency of each harmonic, amplitude and phase place.

So far, complete the measurement of Dynamic Signal phasor, the method for the present invention is applicable to electric power signal fundamental wave frequency deviation The situation of no frequency deviation.

Method provided by the present invention is below applied to carry out emulation experiment, to verify the reliability of method provided by the present invention Property.

Produce an emulation signal using MATLAB, signal model is as follows

Y (t)=220sin (2 π f₀t+θ₁)+2.3936sin(6πf₀t+θ₃)+1.3442sin(10πf₀t+θ₅) (12) formula In, fundamental frequency f₀Value in 49.5～50.5Hz, step-length 0.1Hz；Fundamental voltage amplitude A₁For 220V, phase theta₁=π/3rad；3 Subharmonic and 5 order harmonic components amplitudes are respectively A₃=2.3936V, A₅=1.3442V, phase place is respectively θ₃=π/4rad, θ₅= π/6rad.

Using sample frequency f_sThe Analysis System for Power Quality collection N of=3200Hz_c=512 samples are analyzed.Emulation Parameter value is as follows

Quasi-synchro sampling algorithm：Single iteration points D is 64, and iterationses P is 5

Newton interpolating method：Interpolation is counted as 11 points

FFT frequency-domain analysiss：Using rectangular window, the fft analysis of N=64 points

As shown in table 1, in table 1, aE-b represents a × 10 to simulation result^-b.

Referring to table 1, when frequency fluctuation is ± 0.5Hz, electric power signal fundamental frequency estimates that absolute error is respectively less than 8.70E-10, fundamental voltage amplitude absolute error is respectively less than 4.60E-9, and fundamental phase absolute error is respectively less than 5.90E-11；3 subharmonic Amplitude Estimation error is respectively less than 1.10E-08, and 3 subharmonic phase angle absolute errors are respectively less than 3.20E-09；5 subharmonic Amplitude Estimation Error is respectively less than 9.80E-09, and 5 subharmonic phase angular estimation absolute errors are respectively less than 2.50E-08.Therefore, demonstrate institute of the present invention The feasibility of Dynamic Signal phasor measurement method providing and correctness.

Table 1 carries out the result of emulation experiment using method provided by the present invention

Claims (2)

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

Step one：Electric power signal is sampled, individually sampled signal is saved as crude sampling sample after sampling, simultaneously right Sampled signal adds wave filter, to filter harmonic wave and noise jamming, then the sampled signal after filtered process is carried out step 2 Process；

Step 2：Adopt quasi-synchro sampling algorithm to estimate fundamental frequency the sampled signal after filtered process, obtain fundamental wave frequency Rate estimated value f_g；

Step 3：Using fundamental frequency estimated value f obtaining in step 2_gAnd sampling number N calculates in the signal period To quasi-synchro sampling cycle λ, with λ as step-length, using Newton interpolating method to the discrete serieses in sample original in step one Do time domain plesiochronousization to process, interpolation reconstruction obtains quasi-synchro sampling sequence；

Step 4：To the quasi-synchro sampling sequence obtaining in step 3, a signal period is intercepted using rectangular window, carries out FFT Spectrum analyses, obtain the frequency domain information of signal, and calculate frequency, amplitude and the phase parameter of electric power signal, are dynamically believed Number phasor measurement result；

The selection rule of step one median filter is：

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

2. method according to claim 1 it is characterised in that in step 2 quasi-synchronous algorithm parameter selection rule be：

Single iteration points D is 64, and iterationses P is 5.