CN105891599A - Power frequency tracking method based on improved DODF-WSPD - Google Patents

Abstract

The invention relates to a power frequency tracking method based on improved DODF-WSPD. The method is based on dual orthogonal digital filters, inputs a signal into sine and cosine orthogonal finite impact response digital filters with a phase difference of [pi]/2, subjects the input signal and the coefficients of the two filters to convolution separately to obtain two complex signals, extracts from the two complex signals the phase information of a final output signal, and computes an actual frequency value by using a weighted smoothing phase difference method. The power frequency tracking method has high frequency tracking measurement precision and noise immunity on static and dynamic conditions of a power system, is simple in computation and low in start time lag, and may accurately measures and tracks signal frequency stabilization, abrupt change and periodical change.

Description

A kind of mains frequency tracking based on the DODF-WSPD improved

Technical field

The present invention relates to power system frequency tracking technique field, a kind of electricity based on the DODF-WSPD improved Net frequency tracking method.

Background technology

Along with the upgrading of China " 13 " industrial structure and the implementing in full of layout optimization, modern power network is towards intelligence The continuous Promotion Transformation of energyization and cleaning sustainability direction.The thermoelectricity that a large amount of production capacities fall behind is phased out, and takes and generation Be the grid integration of a large amount of clean energy resource (such as: photovoltaic, wind-powered electricity generation, water power, nuclear power etc.).And the access of these distributed energies Also making modern power network become increasingly complex changeable, failure risk highlights day by day.Frequency as the important parameter of electric power signal, it Size direct reaction electrical network whether be in steady statue.Therefore, the detecting and tracking of signal frequency is to safeguarding electricity net safety stable Run most important.How going to realize the accurate real-time tracking to mains frequency is the most all study hotspot both domestic and external.

At present, the Measurement Algorithm of power system frequency can be largely classified into Hardware Method and the big class of Software Method two.Hardware Method master To realize with phaselocked loop, although the burden of processor can be reduced to a certain extent, but increase peripheral circuit and can make hardware Volume becomes big, and cost is greatly increased, and filter effect is limited, and measurement can be caused bigger error by interference signal.By contrast, soft Part rule better conforms to the tendency of the day, and not only substantially without outer circuits, and many algorithms itself carry filter function, and this allows for The robustness of Software Method, real-time and accuracy have obtained sufficient guarantee.In Software Method, commonly used algorithm includes 3 points Method, least fibre method, method of least square, expansion Kalman filtering method, adaptive notch method, Fourier and improved method thereof, little Wave analysis and intelligent algorithm etc..These algorithms have different effects in different occasions, to the tracking measurement of mains frequency or Person estimates to be not quite similar.Such as, line-of-sight course calculates and is simply easily achieved, but anti-interference is poor；Least fibre method, a young waiter in a wineshop or an inn Multiplication and adaptive notch method cannot ensure output accuracy and response characteristic under strong jamming, but accuracy and robustness have had very Big raising；And expand Kalman filtering method and wavelet analysis rule and be respectively present that tracking overshoot is big and actual application difficult etc. is asked Topic；Furthermore currently using the wider Fourier of scope and improved method thereof exactly, such algorithm mainly deficiency is computationally intensive And the problem such as the cost price that caused the requirement of hardware is high.

Summary of the invention

In view of this, it is an object of the invention to provide a kind of DODF-WSPD (Dual Orthogonal based on improvement Digital Filters and Weighted Smoothing Phased Difference) mains frequency tracking. This algorithm can not only be owned by higher tracking accuracy and noise immunity under power system static dynamic condition, and algorithm meter Calculate simple, and it is little to start time lag, the situation such as, sudden change stable to signal frequency and cyclically-varying can accurately measure tracking.

The present invention uses below scheme to realize: a kind of mains frequency tracking based on the DODF-WSPD improved, the most right Electric power signal carries out discretization, then signal is passed through the sine and the filter of cosine orthogonal finite impulse response numeral that phase contrast is pi/2 In ripple device, by input signal, coefficient with two filter carries out convolutional calculation respectively, obtains two groups of complex signals.From two groups of complex signals In extract the phase information of final output signal, utilize weighted smoothing phase-difference method to calculate actual frequency values, therein add Weight coefficient quotes the weight coefficient in M&M algorithm.For improving the precision of algorithm, once change during algorithm can be calculated Generation.Finally, choose 4 rank, the Butterworth wave filter of cut-off frequency 15Hz carries out smothing filtering to aircraft pursuit course, to enter one Step improves algorithm capacity of resisting disturbance.It specifically comprises the following steps that

Step S1: electric power signal x (n) of given discretization:

$x\left(n\right)=\sin (\frac{2{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{3})+0.01\sin (\frac{6{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{6})+0.03\sin \left(\frac{10{\mathrm{\πnf}}_0}{f_s}\right)+0.02\sin (\frac{14{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{3})+\mathrm{\μ}$

In formula, f_sFor signal sampling frequency, f₀For electrical network rated frequency, n is sampling number, and μ is white Gaussian noise interference letter Number；

Step S2: signal x (n) is each led into sine and cosine orthogonal finite impulse response numeral that phase contrast is pi/2 In wave filter, obtain two groups of complex signals；Wherein, the coefficient of two FIR filter is respectively as follows:

$H_s\left(k\right)=sin(\frac{2\mathrm{\π}k}{N}+\frac{\mathrm{\π}}{N})$

$H_c\left(k\right)=cos(\frac{2\mathrm{\π}k}{N}+\frac{\mathrm{\π}}{N})$

In formula: k=1,2 ... 50*N；N=f_s/f₀I.e. one periodic sampling is counted；

With above-mentioned two coefficient, input signal is carried out convolutional calculation respectively, and the complex signal that can obtain two orthogonal filters is defeated Go out to be respectively as follows:

$x_1\left(n\right)=\underset{k=0}{\overset{N-1}{\Σ}}x(n-k)H_s\left(k\right)=X_{1}sin\left(\mathrm{\ω}\right(n)+\mathrm{\θ})$

$x_2\left(n\right)=\underset{k=0}{\overset{N-1}{\Σ}}x(n-k)H_c\left(k\right)=X_{2}cos\left(\mathrm{\ω}\right(n)+\mathrm{\θ})$

In formula: X₁And X₂Being the amplitude of two filter output signals, ω is the frequency information corresponding to difference, and θ is one Individual definite value；

Step S3: assuming that X₁≈X₂, two groups of complex signals in step S2 are divided by, it is possible to obtain the phase of final output signal Position information:

$\mathrm{\ψ}\left(n\right)=\mathrm{\ω}\left(n\right)+\mathrm{\θ}=arctan\frac{x_1\left(n\right)}{x_2\left(n\right)};$

Step S4: utilize weighted smoothing phase-difference method, is calculated by L data before intercepting a certain moment, by Draw close the actual frequency values in this moment in weight coefficient ω, its expression formula is as follows:

$f\left(x\right)=f_0+\frac{1}{2\mathrm{\π}}\frac{{\mathrm{Nf}}_0}{L}\underset{m=1}{\overset{L}{\Σ}}\mathrm{\ω}\left(m\right)\[\mathrm{\ψ}(x-m)-\mathrm{\ψ}(x-m-1)\]$

Wherein,

In above-mentioned two formulas: x=L+2 ..., 50 × N；L=40 is the data length of intercepting；M=1,2 ..., L；

Step S5: owing to the output amplitude of two filter being assumed to equal in step S3, but physical presence deviation, therefore need Value of calculation to be utilized iteration again is once come to be corrected it, it is ensured that two amplitudes are equal；Utilize and step S4 calculates Actual frequency values f in a certain moment, is substituted into following two formulas, calculates the output amplitude of two wave filter, then carries out it Suitable correction；The amplitude-frequency response of two orthogonal filter outputs is:

$\left|H_s\left(f\right)\right|=\frac{2sin({\mathrm{\πf}}_0/f_s)sin(\mathrm{\π}Nf/f_s)cos(\mathrm{\π}f/f_s)}{cos(2\mathrm{\π}f/f_s)-\cos (2{\mathrm{\πf}}_0/f_s)}$

$\left|H_c\left(f\right)\right|=\frac{2\cos ({\mathrm{\πf}}_0/f_s)\sin (\mathrm{\π}Nf/f_s)\sin (\mathrm{\π}f/f_s)}{\cos (2\mathrm{\π}f/f_s)-\cos (2{\mathrm{\πf}}_0/f_s)};$

Step S6: utilize 4 rank, the frequency curve of final output is entered by the Butterworth wave filter of cut-off frequency 15Hz Row smothing filtering, in order to improve algorithm capacity of resisting disturbance further.

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

1, under power system static condition and dynamic condition, it is owned by higher frequency-tracing measurement precision and has relatively Good noise immunity.

2, algorithm calculates simple, and it is little to start time lag, can the situation such as, sudden change stable to signal frequency and cyclically-varying enter Row accurately measures tracking.

Accompanying drawing explanation

Fig. 1 is the algorithm flow chart of the embodiment of the present invention.

Fig. 2 is that signal does not contains under disturbed condition, and this algorithm follows the tracks of contrast with the signal frequency using the Kay algorithm weights factor Figure.

Fig. 3 is in the case of signal contains 3,5,7 subharmonic and white Gaussian noise (20dB), and this algorithm adds with using Kay algorithm The signal frequency tracking error comparison diagram of weight factor.

Fig. 4 is signal containing under harmonic wave and disturbed condition, this algorithm tracking situation to frequency discontinuity.Fig. 5 is that signal exists Containing under harmonic wave and disturbed condition, this algorithm tracking periodically variable to frequency situation.

Fig. 6 is that signal does not contains under disturbed condition, when this algorithm takes different L-value, and the comparison diagram of algorithm keeps track error.

Detailed description of the invention

Below in conjunction with the accompanying drawings and embodiment the present invention will be further described.

The present embodiment provides a kind of mains frequency tracking based on the DODF-WSPD improved, and first enters electric power signal Row discretization, then signal is passed through in the sine and the orthogonal limited impulse response digital filter of cosine that phase contrast is pi/2, by defeated Enter the signal coefficient respectively with two filter and carry out convolutional calculation, obtain two groups of complex signals.Extract from two groups of complex signals The phase information of whole output signal, utilizes weighted smoothing phase-difference method to calculate actual frequency values, and weight coefficient therein is quoted Weight coefficient in M&M algorithm.For improving the precision of algorithm, carry out an iteration during algorithm can be calculated.Finally, choose 4 rank, the Butterworth wave filter of cut-off frequency 15Hz carry out smothing filtering to aircraft pursuit course, anti-to improve algorithm further Interference performance.As it is shown in figure 1, it specifically comprises the following steps that

Step S1: electric power signal x (n) of given discretization:

$x\left(n\right)=\sin (\frac{2{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{3})+0.01\sin (\frac{6{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{6})+0.03\sin \left(\frac{10{\mathrm{\πnf}}_0}{f_s}\right)+0.02\sin (\frac{14{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{3})+\mathrm{\μ}$

In formula, f_sFor signal sampling frequency, f₀For electrical network rated frequency, n is sampling number, and μ is white Gaussian noise interference letter Number；

Step S2: signal x (n) is each led into sine and cosine orthogonal finite impulse response numeral that phase contrast is pi/2 In wave filter, obtain two groups of complex signals；Wherein, the coefficient of two FIR filter is respectively as follows:

$H_s\left(k\right)=sin(\frac{2\mathrm{\π}k}{N}+\frac{\mathrm{\π}}{N})$

$H_c\left(k\right)=cos(\frac{2\mathrm{\π}k}{N}+\frac{\mathrm{\π}}{N})$

In formula: k=1,2 ... 50*N；N=f_s/f₀I.e. one periodic sampling is counted；

With above-mentioned two coefficient, input signal is carried out convolutional calculation respectively, and the complex signal that can obtain two orthogonal filters is defeated Go out to be respectively as follows:

$x_1\left(n\right)=\underset{k=0}{\overset{N-1}{\Σ}}x(n-k)H_s\left(k\right)=X_{1}sin\left(\mathrm{\ω}\right(n)+\mathrm{\θ})$

$x_2\left(n\right)=\underset{k=0}{\overset{N-1}{\Σ}}x(n-k)H_c\left(k\right)=X_{2}cos\left(\mathrm{\ω}\right(n)+\mathrm{\θ})$

In formula: X₁And X₂Being the amplitude of two filter output signals, ω is the frequency information corresponding to difference, and θ is one Individual definite value；

Step S3: assuming that X₁≈X₂, two groups of complex signals in step S2 are divided by, it is possible to obtain the phase of final output signal Position information:

$\mathrm{\ψ}\left(n\right)=\mathrm{\ω}\left(n\right)+\mathrm{\θ}=arctan\frac{x_1\left(n\right)}{x_2\left(n\right)};$

Step S4: utilize weighted smoothing phase-difference method, is calculated by L data before intercepting a certain moment, by Draw close the actual frequency values in this moment in weight coefficient ω, its expression formula is as follows:

$f\left(x\right)=f_0+\frac{1}{2\mathrm{\π}}\frac{{\mathrm{Nf}}_0}{L}\underset{m=1}{\overset{L}{\Σ}}\mathrm{\ω}\left(m\right)\[\mathrm{\ψ}(x-m)-\mathrm{\ψ}(x-m-1)\]$

Wherein,

In above-mentioned two formulas: x=L+2 ..., 50 × N；L=40 is the data length of intercepting；M=1,2 ..., L；

Step S5: owing to the output amplitude of two filter being assumed to equal in step S3, but physical presence deviation, therefore need Value of calculation to be utilized iteration again is once come to be corrected it, it is ensured that two amplitudes are equal；Utilize and step S4 calculates Actual frequency values f in a certain moment, is substituted into following two formulas, calculates the output amplitude of two wave filter, then carries out it Suitable correction；The amplitude-frequency response of two orthogonal filter outputs is:

$\left|H_s\left(f\right)\right|=\frac{2sin({\mathrm{\πf}}_0/f_s)sin(\mathrm{\π}Nf/f_s)cos(\mathrm{\π}f/f_s)}{cos(2\mathrm{\π}f/f_s)-\cos (2{\mathrm{\πf}}_0/f_s)}$

$\left|H_c\left(f\right)\right|=\frac{2\cos ({\mathrm{\πf}}_0/f_s)\sin (\mathrm{\π}Nf/f_s)\sin (\mathrm{\π}f/f_s)}{\cos (2\mathrm{\π}f/f_s)-\cos (2{\mathrm{\πf}}_0/f_s)};$

Step S6: utilize 4 rank, the frequency curve of final output is entered by the Butterworth wave filter of cut-off frequency 15Hz Row smothing filtering, to improve algorithm capacity of resisting disturbance further.

In the present embodiment, can obtain under signal is without disturbed condition, this algorithm and the employing Kay algorithm weights factor Signal frequency follow the tracks of comparison diagram, as shown in Figure 2；In the case of signal is containing 3,5,7 subharmonic and white Gaussian noise (20dB), this Algorithm and the signal frequency tracking error comparison diagram using the Kay algorithm weights factor, as shown in Figure 3.When signal containing harmonic wave and Under disturbed condition, this algorithm is to the tracking situation of frequency discontinuity as shown in Figure 4.When signal is containing under harmonic wave and disturbed condition, this Algorithm tracking periodically variable to frequency situation is as shown in Figure 5.Under signal is without disturbed condition, this algorithm takes different L During value, the comparison diagram of algorithm keeps track error is as shown in Figure 6.

The foregoing is only presently preferred embodiments of the present invention, all impartial changes done according to scope of the present invention patent with Modify, all should belong to the covering scope of the present invention.

Claims (1)

1. one kind based on the mains frequency tracking of DODF-WSPD improved, it is characterised in that: specifically include following steps:

Step S1: electric power signal x (n) of given discretization:

$x\left(n\right)=sin(\frac{2{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{3})+0.01sin(\frac{6{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{6})+0.03sin\left(\frac{10{\mathrm{\πnf}}_0}{f_s}\right)+0.02sin(\frac{14{\mathrm{\πnf}}_0}{f_s}+\frac{\mathrm{\π}}{3})+\mathrm{\μ}$

In formula, f_sFor signal sampling frequency, f₀For electrical network rated frequency, n is sampling number, and μ is that white Gaussian noise disturbs signal；

Step S2: signal x (n) is each led into sine and cosine orthogonal finite impulse response digital filtering that phase contrast is pi/2 In device, obtain two groups of complex signals；Wherein, the coefficient of two FIR filter is respectively as follows:

$H_s\left(k\right)=sin(\frac{2\mathrm{\π}k}{N}+\frac{\mathrm{\π}}{N})$

$H_c\left(k\right)=cos(\frac{2\mathrm{\π}k}{N}+\frac{\mathrm{\π}}{N})$

In formula: k=1,2 ... 50*N；N=f_s/f₀I.e. one periodic sampling is counted；

Input signal is carried out convolutional calculation with above-mentioned two coefficient respectively, the complex signal output point of two orthogonal filters can be obtained It is not:

$x_1\left(n\right)=\underset{k=0}{\overset{N-1}{\Σ}}x(n-k)H_s\left(k\right)=X_{1}sin\left(\mathrm{\ω}\right(n)+\mathrm{\θ})$

$x_2\left(n\right)=\underset{k=0}{\overset{N-1}{\Σ}}x(n-k)H_c\left(k\right)=X_{2}cos\left(\mathrm{\ω}\right(n)+\mathrm{\θ})$

In formula: X₁And X₂Being the amplitude of two filter output signals, ω is the frequency information corresponding to difference, and θ is one to be determined Value；

Step S3: assuming that X₁≈X₂, two groups of complex signals in step S2 are divided by, it is possible to obtain the phase place letter of final output signal Breath:

$\mathrm{\ψ}\left(n\right)=\mathrm{\ω}\left(n\right)+\mathrm{\θ}=arctan\frac{x_1\left(n\right)}{x_2\left(n\right)};$

Step S4: utilize weighted smoothing phase-difference method, is calculated, by means of adding by L data before intercepting a certain moment Weight coefficient ω draws close the actual frequency values in this moment, and its expression formula is as follows:

$f\left(x\right)=f_0+\frac{1}{2\mathrm{\π}}\frac{{\mathrm{Nf}}_0}{L}\underset{m=1}{\overset{L}{\Σ}}\mathrm{\ω}\left(m\right)\[\mathrm{\ψ}(x-m)-\mathrm{\ψ}(x-m-1)\]$

Wherein,

In above-mentioned two formulas: x=L+2 ..., 50 × N；L=40 is the data length of intercepting；M=1,2 ..., L；

Step S5: owing to the output amplitude of two filter being assumed to equal in step S3, but physical presence deviation, therefore need profit Once come it is corrected with value of calculation again iteration, it is ensured that two amplitudes are equal；Utilize calculate in step S4 a certain Actual frequency values f in moment, is substituted into following two formulas, calculates the output amplitude of two wave filter, then carries out it suitably Correction；The amplitude-frequency response of two orthogonal filter outputs is:

$\left|H_s\left(f\right)\right|=\frac{2sin({\mathrm{\πf}}_0/f_s)sin(\mathrm{\π}Nf/f_s)cos(\mathrm{\π}f/f_s)}{cos(2\mathrm{\π}f/f_s)-\cos (2{\mathrm{\πf}}_0/f_s)}$

$\left|H_c\left(f\right)\right|=\frac{2\cos ({\mathrm{\πf}}_0/f_s)sin(\mathrm{\π}Nf/f_s)\sin (\mathrm{\π}f/f_s)}{cos(2\mathrm{\π}f/f_s)-\cos (2{\mathrm{\πf}}_0/f_s)};$

Step S6: utilize 4 rank, the frequency curve of final output is put down by the Butterworth wave filter of cut-off frequency 15Hz Sliding filtering, in order to improve algorithm capacity of resisting disturbance further.