CN104635094A - Method for improving PMU (power management unit) synchronous phasor measurement precision - Google Patents

Abstract

The invention discloses a method for improving the PMU (power management unit) synchronous phasor measurement precision under the dynamic conditions such as out-of-band interference, system low-frequency oscillation, power oscillation, system out of step, short circuit or broken circuit fault, and belongs to the technical field of electric automation. The method comprises the following steps that the high-precision synchronous sampling is carried out; DFT (discrete Fourier transform) phasor calculation and pre-filtering are carried out; the high-precision frequency measurement is carried out, and the DFT calculation phasor under the frequency deviation condition is corrected; on the basis of the phasor, the frequency and the frequency change rate worked out in the step SS3, the filtering is carried out through a rear-mounted up-supply filter, and the data is sent to a back end data concentrator; test and verification are carried out. The method has the advantages that the inhabitation on the spectrum leakage and picket fence effect during the frequency offset by a DFT algorithm is realized, the spectrum aliasing phenomenon during the calculation of components with the oscillation frequency being higher than the Nyquist frequency is avoided, and the dynamic measuring performance of the PMU under the conditions of modulation, phase step and the like is improved.

Description

A kind of method promoting PMU synchronous phasor measurement precision

Technical field

The present invention relates to a kind of under the dynamic conditions such as the outer interference of band, low frequency oscillations and oscillation of power, system step-out, short circuit or disconnection fault, promote the method for PMU synchronous phasor measurement precision, belong to technical field of electric power automation.

Background technology

Synchronous phasor measurement unit (phasor measurement unit, PMU) as WAMS (wide area measurement system, WAMS) raw data source, its measuring accuracy for Power Network Status Estimation, the important in inhibitings such as electricity net safety stable monitoring.

The definition of synchronized phasor as shown in Figure 1, simulating signal corresponding phasor form is when the maximal value of v (t) appears at pulse per second (PPS), the angle of phasor is 0 degree, and when v (t) positive going zeror crossing point is synchronous with pulse per second (PPS), the angle of phasor is-90 to spend.

When phasor amplitude is constant, the phase place of phasor and the frequency of simulating signal should meet following relation:

Namely, when the frequency of phasor equals 50Hz, the angle of phasor is constant; When the frequency of phasor is greater than 50Hz, the angle of phasor increases gradually, and when the frequency of phasor is less than 50Hz, the angle of phasor reduces gradually.

It is typical modulated process that electric system occurs when vibrating, and modulation frequency range is at 0.1Hz-2.5Hz.In order to realize the accurate identification of vibrating, requiring that PMU can follow the tracks of amplitude and the phase angle of phasor fast and accurately, good amplitude versus frequency characte can be had at passband simultaneously.During the fault that is short-circuited, likely there is transition in amplitude, the phase angle of voltage signal, is step process.In order to reflect the state before and after electric network fault strictly according to the facts, requiring that PMU can tracking signal transition, making error fall into accuracy rating as early as possible, and controlling the overshoot of response.

The Measurement Algorithm existence two large class problems that current PMU is general:

(1) algorithm that PMU adopts usually is at present based on DFT (discrete Fourier transform, DFT) algorithm, DFT algorithm has spectral leakage and fence effect when frequency deviation, equalization effect can affect dynamic accuracy, therefore in modulated process, the measured value of PMU can exceed accuracy rating, and its concrete reason is analyzed as follows:

The DFT formula calculating fundamental phasors is as follows:

In formula, for fundamental phasors, x (k) is dis-crete sample values, and N is every cycle sampling number.

Sampled signal in time window is multiplied with synchronous orthogonal coefficient by being in the nature that DFT calculates, and then averaging obtains phasor; Under steady state conditions, DFT can filtering harmonic wave effectively, obtains fundamental phasors accurately.

Suppose that signal generation amplitude is vibrated, its expression formula is:

In formula, X _mfor fundamental phasors amplitude, f is fundamental frequency, for modulating part initial phase angle.

Original sample value is multiplied by orthogonal coefficient:

Real imaginary part when all-round DFT calculates is f by constant, frequency _acomponent and high fdrequency component composition.When adopting all-round DFT to carry out phasor calculation, frequency is that the high fdrequency component of 2f can by filtering, and frequency is 2f-f _aand 2f+f _ahigh fdrequency component then can exist residual, thus result in the generation of spectral leakage.Spectral leakage makes the phasor measurement result of PMU there is deviation, affect the various analytical applications based on PMU data, making systems axiol-ogy to there is not the higher-order of oscillation, wide-area control system mistake time serious, may be made to send out steering order, totally unfavorable to the safe and stable operation of wide area system.

(2) at synchronized phasor by substation in the process of master station transmission, transfer rate Fs limits signal bandwidth, according to sampling thheorem, exceedes the interference of nyquist frequency Fs/2, then can cause spectral aliasing if existed in signal.Specifically, if electric system fundamental frequency is expressed as f ₀, phasor uploading rate is expressed as F _s, then nyquist frequency is F _s/ 2, main website can accurate measurement electric system letter frequency band be [f ₀-(F _s/ 2), f ₀+ (F _s/ 2) frequency], beyond this frequency band range is called as the outer frequency of band.Therefore, when carrying out the transmission of different rates phasor, suppress to disturb outward with filter out-band, it is as follows that the outer interference of band calculates to synchronized phasor the analysis of causes producing error:

Suppose to there is the out-of-band signaling relevant to real-time transfer rate in input signal, expression formula is as follows:

In formula, X _mfor fundamental phasors amplitude, f is fundamental frequency, for phasor initial phase angle, X _dfor the which amplitude modulation degree of depth, f _dthe outer frequency of band, it is modulating part initial phase angle.

Original sample value is multiplied by orthogonal coefficient:

When input signal exists out-of-band signaling, the real imaginary part that DFT calculates is except constant, and also there is frequency is | f _d-f| and f _dtwo components of+f.When adopting all-round DFT to carry out phasor calculation, frequency is | f _d-f| and f _dtwo components of+f cannot filtering completely, easily causes alarm by mistake, and high-frequency signal residual in spectral leakage, then increase the weight of the impact of spectral aliasing further.

Summary of the invention

Order of the present invention is to provide a kind of method promoting PMU synchronous phasor measurement precision, the spectral leakage of DFT algorithm when frequency deviation and fence effect are suppressed, to avoid calculating in phasor containing the aliasing occurred during the component of oscillation frequency higher than nyquist frequency, improve the kinetic measurement performance of PMU under the conditions such as modulation, step.

The present invention adopts following technical scheme: a kind of method promoting PMU synchronous phasor measurement precision, is characterized in that, comprise the steps:

SS1 high-precise synchronization sample: PMU first by input PT/CT analog signals through anti-aliasing analog filtering (analogue low pass filtering, passband is 3.1KHz) after carry out A/D conversion, when analog to digital conversion, sampled value is stamped accurate absolute time mark, and stored in data buffer;

SS2DFT phasor calculation and pre-filtering: the sampled value of the data buffer produced by step SS1 carries out DFT conversion, then low-pass filtering is carried out to the real imaginary part of DFT calculating phasor, prefilter adopts FIR lowpass digital filter; The ripple method designs such as described FIR lowpass digital filter employing, group delay is 50 milliseconds, and passband edges frequency is 5Hz, and passband gain is 0.0002dB, and stop band gain is-80dB;

SS3 high accuracy frequency measurement DFT under frequency of amendment drift condition calculates phasor: the result of calculation based on step SS2 adopts the phasor measurement multiprecision arithmetic based on equal interval sampling, calculated the iteration of phasor by continuous 3 DFT, in 5ms, frequency, frequency change rate DFT under frequency of amendment drift condition calculates phasor can be calculated accurately;

The phasor that SS4 calculates based on step SS3, frequency and frequency change rate are again after sending filter filtering on one rearmounted, on deliver to the data concentrator of rear end, described rearmounted on send wave filter to be FIR lowpass digital filter, the ripple method designs such as described FIR lowpass digital filter employing, and select different parameters according to different phasor uploading rate;

SS5 test and validation: clock source provides common benchmark to PMU and test source, theoretical value for generating waveform playback, and compares with the simulation main website off-line files of calling and carries out error analysis; When carrying out error analysis, clip the data of each a second before and after test and carry out point-by-point comparison and get maximum error, avoid analog quantity to apply and exit steps jumping over the impact of journey; Test event comprises ± 5Hz rated frequency deviation test, and 10%2-13 subharmonic, outside band, step, 5Hz amplitude phase angle is modulated simultaneously, 1Hz/s frequency slope.

Preferably, described step SS1 specifically comprises: signal when PMU device can be accessed by the B code pair of GPS/ big dipper clock, is decoded by fpga chip, produces 1PPS signal, and producing the 4K sampled signal synchronous with 1PPS signal, this signal enabling AD sampling A/D chip carries out analog to digital conversion; PT/CT analog signals accesses A/D conversion chip after anti-aliasing analog filtering (analogue low pass filtering passband is 3.1KHz), and analog-to-digital result is put into data buffer and carried out DFT phasor calculation.

Preferably, the low-pass filtering described in described step SS2 specifically comprises: the higher-order of oscillation component that filtering spectral leakage and the outer frequency of band produce, and eliminate interference, improve phasor calculation precision, the phasor calculation formula adding prefilter is as follows:

$X\left(i\right)=\frac{\sqrt{2}}{\mathrm{Gain}}\·\underset{k=-\frac{L}{2}}{\overset{\frac{L}{2}}{\mathrm{\Σ}}}x(i+k)\·W_k\·e^{-j\·2\mathrm{\π}{f}_0\frac{i+k}{N}}---\left(8\right)$

$\mathrm{Gain}=\underset{k=-\frac{L}{2}}{\overset{\frac{L}{2}}{\mathrm{\Σ}}}{W}_k---\left(9\right)$

In formula (8), (9), f ₀for mains frequency; L is for there being limit for length's unit impact response digital filter exponent number; W _kfor low-pass filter coefficients, N is sampling number, and x (i+k) is i+k moment phasor value.

Preferably, described step SS3 specifically comprises: the time domain sinusoidal signal that is sampled of case of external input is

A kth sampled point in r window can be expressed as:

Phasor computing algorithm adopts recurrence DFT formula to be expressed as:

${\hat{X}}_r={\hat{X}}_{r-1}+2\×\frac{\sqrt{2}}{N}[x_r(N-1)-x_{r-N/2}(N-1)]e^{-j\frac{2\mathrm{\π}}{N}(r-1)}---\left(12\right)$

Again because

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}{e}^{\mathrm{j\θk}}=\frac{\sin (\mathrm{\θN}/2)}{\sin (\mathrm{\θ}/2)}{e}^{\mathrm{j\θ}(N-1)/2}---\left(13\right)$

Order

$\mathrm{\θ}=\frac{2\mathrm{\π\Δf}}{f_{0}N}---\left(14\right)$

Namely obtaining by formula (11), (12), (13), (14) the original phasor that DFT calculates is:

${\hat{X}}_r=2\×{\stackrel{\‾}{X}}_r\frac{\sin (\mathrm{\θN}/4)}{N\sin (\mathrm{\θ}/2)}{e}^{\mathrm{j\θ}(N-2)/4}+C_r---\left(15\right)$

In formula:

$C_r=2\×{\stackrel{\‾}{X}}_r^{*}\frac{\sin (\mathrm{\θN}/4)}{N\sin [(\mathrm{\θ}+\frac{4\mathrm{\π}}{N})/2]}{e}^{-j[(\mathrm{\θ}+\frac{4\mathrm{\π}}{N})(N-2)/4+\frac{4\mathrm{\πr}}{N}]}---\left(16\right)$

Formula (15) gives recurrence Fu Shi algorithm r and walks the original phasor that there is spectrum leakage error calculating and obtain phasor true in theory between relational expression, for the phasor that there is spectrum leakage error that Fu Shi algorithm calculates, C _rthe frequency leakage item that initial phase angle corresponding to data window is relevant, for the true phasor of theory; Can solving equation (15) be passed through thus, (16) obtain revised free from error true phasor if every m subsynchronous phasor of sampling calculating 1 adopt 3 equally spaced phasors set up Simultaneous Equations:

Solve 3 simultaneous equations, obtain:

$e^{-\mathrm{jm\θ}}=f(r-2m)+\sqrt{f^2(r-2m)-e^{j\frac{4\mathrm{\π}}{N}m}}---\left(20\right)$

$C_r=\frac{{\hat{X}}_r{e}^{-\mathrm{jm\θ}}-{\hat{X}}_{r-m}}{e^{-\mathrm{jm\θ}}-e^{\mathrm{jm\θ}}{e}^{j\frac{4\mathrm{\π}}{N}m}}---\left(21\right)$

In formula: $f(r-2m)=\frac{{\hat{X}}_{r-2m}+e^{j\frac{4\mathrm{\π}}{N}m}{\hat{X}}_r}{2{\hat{X}}_{r-m}}---\left(22\right)$

Make Φ _m=e ^{-jm θ}, then $C_r=\frac{{\hat{X}}_r{{\mathrm{\Φ}}_m-\hat{X}}_{r-m}}{{\mathrm{\Φ}}_m-{\mathrm{\Φ}}_m^{*}{e}^{j\frac{4\mathrm{\π}}{N}m}}---\left(23\right)$

${\stackrel{\‾}{X}}_r=(\hat{X}-C_r)\frac{N\sin (\mathrm{\θ}/2)}{2\×\sin (\mathrm{\θN}/4)}{e}^{-\mathrm{j\θ}(N-2)/4}---\left(24\right)$

In the hope of θ, then θ can be substituted into formula (14) by formula (20), the side-play amount of ongoing frequency relative system rated frequency can be tried to achieve, and then can in the hope of system frequency and frequency change rate; be the phasor of step SS2 result of calculation, through type (21) can calculate C _r, then the substantial synchronization phasor in frequency shift (FS) situation can be calculated by formula (24)

Preferably, described step SS4 Selecting parameter is: when transfer rate is 25Hz, group delay 250 milliseconds, passband edges 5Hz, passband gain 0.0002dB, stop band gain-40dB; When transfer rate is 50Hz, group delay 125 milliseconds, passband edges 5Hz, passband gain 0.0002dB, stop band gain-60dB; When transfer rate is 100Hz, without the need to postfilter.

The beneficial effect that the present invention reaches: the spectral leakage of DFT algorithm when frequency deviation and fence effect are suppressed, to avoid calculating in phasor containing the aliasing occurred during the component of oscillation frequency higher than nyquist frequency, improve the kinetic measurement performance of PMU under the conditions such as modulation, step

Accompanying drawing explanation

Fig. 1 is the transformational relation figure between waveform signal and synchronized phasor.

Fig. 2 is a kind of process flow diagram promoting the method for PMU synchronous phasor measurement precision of the present invention.

Fig. 3 is the amplitude-versus-frequency curve figure of equiripple filter of the present invention.

Fig. 4 is PMU test macro configuration diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.Following examples only for technical scheme of the present invention is clearly described, and can not limit the scope of the invention with this.

As shown in Figure 1 be transformational relation figure between waveform signal and synchronized phasor, Fig. 2 is a kind of process flow diagram promoting the method for PMU synchronous phasor measurement precision of the present invention, the present invention proposes a kind of method promoting PMU synchronous phasor measurement precision, it is characterized in that, comprises the steps:

SS1 high-precise synchronization sample: PMU first by input PT/CT analog signals through anti-aliasing analog filtering (analogue low pass filtering, passband is 3.1KHz) after carry out A/D conversion, when analog to digital conversion, sampled value is stamped accurate absolute time mark, and stored in data buffer; Described step SS1 specifically comprises: signal when PMU device can be accessed by the B code pair of GPS/ big dipper clock, decoded by fpga chip, produce 1PPS signal, and produce the 4K sampled signal synchronous with 1PPS signal, this signal enabling AD sampling A/D chip carries out analog to digital conversion; PT/CT analog signals accesses A/D conversion chip after anti-aliasing analog filtering (analogue low pass filtering passband is 3.1KHz), and analog-to-digital result is put into data buffer and carried out DFT phasor calculation.

SS2DFT phasor calculation and pre-filtering: the sampled value of the data buffer produced by step SS1 carries out DFT conversion, then low-pass filtering is carried out to the real imaginary part of DFT calculating phasor, prefilter adopts FIR lowpass digital filter; The ripple method designs such as described FIR lowpass digital filter employing, group delay is 50 milliseconds, and passband edges frequency is 5Hz, and passband gain is 0.0002dB, and stop band gain is-80dB; Low-pass filtering described in described step SS2 specifically comprises: the higher-order of oscillation component that filtering spectral leakage and the outer frequency of band produce, and eliminate interference, improve phasor calculation precision, the phasor calculation formula adding prefilter is as follows:

$X\left(i\right)=\frac{\sqrt{2}}{\mathrm{Gain}}\·\underset{k=-\frac{L}{2}}{\overset{\frac{L}{2}}{\mathrm{\Σ}}}x(i+k)\·W_k\·e^{-j\·2\mathrm{\π}{f}_0\frac{i+k}{N}}---\left(8\right)$

$\mathrm{Gain}=\underset{k=-\frac{L}{2}}{\overset{\frac{L}{2}}{\mathrm{\Σ}}}{W}_k---\left(9\right)$

In formula (8), (9), f ₀for mains frequency; L is for there being limit for length's unit impact response digital filter exponent number; W _kfor low-pass filter coefficients, N is sampling number, and x (i+k) is i+k moment phasor value.

Usually, the exponent number of wave filter is higher, and stopband attenuation is larger, and passband error is less, and transitional zone is narrower, but step response can be slower, and time delay also can be longer.Relative to the 20ms time delay of complete cycle ripple DFT phasor calculation, the group delay of wave filter wants large many, and at this moment performance of filter still may can not meet requirement.Therefore, need the wave filter of devise optimum, with the filtering performance that low order realization is as far as possible best.

FIR filter design mainly contains window function metht, frequency sampling method and method such as ripple such as grade.The shortcoming of window function metht is: be not easy the wave filter designing cutoff frequency given in advance; The filter order gone out designed by when meeting same design objective is usually bigger than normal.The shortcoming of frequency sampling method is that the value of cutoff frequency is limited.And the approximate error of window function metht and frequency sampling method is not equally distributed on frequency band interval, larger near band edge error, less away from band edge error.Be a kind of optimal-design method Deng the best approximatioss of ripple, the filter freguency response designed in this way is minimum relative to ideal filter maximum error, and the amplitude versus frequency characte of equiripple filter as shown in Figure 3.

SS3 high accuracy frequency measurement DFT under frequency of amendment drift condition calculates phasor: the result of calculation based on step SS2 adopts the phasor measurement multiprecision arithmetic based on equal interval sampling, calculated the iteration of phasor by continuous 3 DFT, in 5ms, frequency, frequency change rate DFT under frequency of amendment drift condition calculates phasor can be calculated accurately; Described step SS3 specifically comprises: the time domain sinusoidal signal that is sampled of case of external input is

A kth sampled point in r window can be expressed as:

Phasor computing algorithm adopts recurrence DFT formula to be expressed as:

${\hat{X}}_r={\hat{X}}_{r-1}+2\×\frac{\sqrt{2}}{N}[x_r(N-1)-x_{r-N/2}(N-1)]e^{-j\frac{2\mathrm{\π}}{N}(r-1)}---\left(12\right)$

Again because

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}{e}^{\mathrm{j\θk}}=\frac{\sin (\mathrm{\θN}/2)}{\sin (\mathrm{\θ}/2)}{e}^{\mathrm{j\θ}(N-1)/2}---\left(13\right)$

Order

$\mathrm{\θ}=\frac{2\mathrm{\π\Δf}}{f_{0}N}---\left(14\right)$

Namely obtaining by formula (11), (12), (13), (14) the original phasor that DFT calculates is:

${\hat{X}}_r=2\×{\stackrel{\‾}{X}}_r\frac{\sin (\mathrm{\θN}/4)}{N\sin (\mathrm{\θ}/2)}{e}^{\mathrm{j\θ}(N-2)/4}+C_r---\left(15\right)$

In formula:

$C_r=2\×{\stackrel{\‾}{X}}_r^{*}\frac{\sin (\mathrm{\θN}/4)}{N\sin [(\mathrm{\θ}+\frac{4\mathrm{\π}}{N})/2]}{e}^{-j[(\mathrm{\θ}+\frac{4\mathrm{\π}}{N})(N-2)/4+\frac{4\mathrm{\πr}}{N}]}---\left(16\right)$

Formula (15) gives recurrence Fu Shi algorithm r and walks the original phasor that there is spectrum leakage error calculating and obtain phasor true in theory between relational expression, for the phasor that there is spectrum leakage error that Fu Shi algorithm calculates, C _rthe frequency leakage item that initial phase angle corresponding to data window is relevant, for the true phasor of theory; Can solving equation (15) be passed through thus, (16) obtain revised free from error true phasor if every m subsynchronous phasor of sampling calculating 1 adopt 3 equally spaced phasors set up Simultaneous Equations:

Solve 3 simultaneous equations, obtain:

$e^{-\mathrm{jm\θ}}=f(r-2m)+\sqrt{f^2(r-2m)-e^{j\frac{4\mathrm{\π}}{N}m}}---\left(20\right)$

$C_r=\frac{{\hat{X}}_r{e}^{-\mathrm{jm\θ}}-{\hat{X}}_{r-m}}{e^{-\mathrm{jm\θ}}-e^{\mathrm{jm\θ}}{e}^{j\frac{4\mathrm{\π}}{N}m}}---\left(21\right)$

In formula: $f(r-2m)=\frac{{\hat{X}}_{r-2m}+e^{j\frac{4\mathrm{\π}}{N}m}{\hat{X}}_r}{2{\hat{X}}_{r-m}}---\left(22\right)$

Make Φ _m=e ^{-jm θ}, then

$C_r=\frac{{\hat{X}}_r{{\mathrm{\Φ}}_m-\hat{X}}_{r-m}}{{\mathrm{\Φ}}_m-{\mathrm{\Φ}}_m^{*}{e}^{j\frac{4\mathrm{\π}}{N}m}}---\left(23\right)$

${\stackrel{\‾}{X}}_r=(\hat{X}-C_r)\frac{N\sin (\mathrm{\θ}/2)}{2\×\sin (\mathrm{\θN}/4)}{e}^{-\mathrm{j\θ}(N-2)/4}---\left(24\right)$

In the hope of θ, then θ can be substituted into formula (14) by formula (20), the side-play amount of ongoing frequency relative system rated frequency can be tried to achieve, and then can in the hope of system frequency and frequency change rate; be the phasor of step SS2 result of calculation, through type (21) can calculate C _r, then the substantial synchronization phasor in frequency shift (FS) situation can be calculated by formula (24)

The phasor that SS4 calculates based on step SS3, frequency and frequency change rate are again after sending filter filtering on one rearmounted, on deliver to the data concentrator of rear end, described rearmounted on send wave filter to be FIR lowpass digital filter, the ripple method designs such as described FIR lowpass digital filter employing, and select different parameters according to different phasor uploading rate; Low-frequency oscillation of electric power system frequency is 0.1Hz ~ 2.5Hz, according to previous analysis result, the high fdrequency component scope that spectral leakage causes is 97.5Hz ~ 102.5Hz, digital filter should the component of effective these frequency ranges of filtering, synchronous phasor measuring device detects test specification and defines the outer frequency range of band corresponding to different uploading rate, and ginseng is shown in Table 1.

Table 1 transfer rate and the outer frequency table of comparisons of band

Uploading rate	Be with outer frequency range
		25Hz	10Hz～37.5Hz 62.5Hz～100Hz
50Hz	10Hz～25Hz 75～100Hz
		100Hz	100Hz～150Hz

According to emulation testing, the calculating phasor of prefilter to DFT is carried out filtering and is inhibit DFT spectrum leakage and the outer interference of part band, but can not inhibition zone disturb outward completely.Therefore also need after the phasor of step SS3, frequency and frequency change rate calculate again after sending wave filter on one rearmounted again on deliver to the data concentrator of rear end, postfilter selects different parameters according to different phasor uploading rate.During transfer rate 25Hz, group delay 250 milliseconds, passband edges 5Hz, passband gain 0.0002dB, stop band gain-40dB; During transfer rate 50Hz, group delay 125 milliseconds, passband edges 5Hz, passband gain 0.0002dB, stop band gain-60dB, during transfer rate 100Hz, without the need to arranging postfilter.

SS5 test and validation: in order to the actual effect of verification algorithm, has built PMU test macro configuration diagram of the present invention as shown in Figure 4 and has surveyed, and compared with not adopting the PMU of hereinbefore method.Clock source provides common benchmark to PMU and test source, and theoretical value for generating waveform playback, and compares with the simulation main website off-line files of calling and carries out error analysis.When carrying out error analysis, clip the data of each a second before and after test and carry out point-by-point comparison and get maximum error, avoid analog quantity to apply and exit steps jumping over the impact of journey.Test event comprises ± 5Hz rated frequency deviation test, and 10%2-13 subharmonic, outside band, step, 5Hz amplitude phase angle is modulated simultaneously, and 1Hz/s frequency slope is as shown in table 2.

Table 2 dynamic property accuracy test contrasts

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and distortion, these improve and distortion also should be considered as protection scope of the present invention.

Claims (5)

1. promote a method for PMU synchronous phasor measurement precision, it is characterized in that, comprise the steps:

SS1 high-precise synchronization sample: PMU first by input PT/CT analog signals through anti-aliasing analog filtering (analogue low pass filtering, passband is 3.1KHz) after carry out A/D conversion, when analog to digital conversion, sampled value is stamped accurate absolute time mark, and stored in data buffer;

SS2 DFT phasor calculation and pre-filtering: the sampled value of the data buffer produced by step SS1 carries out DFT conversion, then low-pass filtering is carried out to the real imaginary part of DFT calculating phasor, prefilter adopts FIR lowpass digital filter; The ripple method designs such as described FIR lowpass digital filter employing, group delay is 50 milliseconds, and passband edges frequency is 5Hz, and passband gain is 0.0002dB, and stop band gain is-80dB;

SS3 high accuracy frequency measurement DFT under frequency of amendment drift condition calculates phasor: the result of calculation based on step SS2 adopts the phasor measurement multiprecision arithmetic based on equal interval sampling, calculated the iteration of phasor by continuous 3 DFT, in 5ms, frequency, frequency change rate DFT under frequency of amendment drift condition calculates phasor can be calculated accurately;

The phasor that SS4 calculates based on step SS3, frequency and frequency change rate are again after sending filter filtering on one rearmounted, on deliver to the data concentrator of rear end, described rearmounted on send wave filter to be FIR lowpass digital filter, the ripple method designs such as described FIR lowpass digital filter employing, and select different parameters according to different phasor uploading rate;

SS5 test and validation: clock source provides common benchmark to PMU and test source, theoretical value for generating waveform playback, and compares with the simulation main website off-line files of calling and carries out error analysis; When carrying out error analysis, clip the data of each a second before and after test and carry out point-by-point comparison and get maximum error, avoid analog quantity to apply and exit steps jumping over the impact of journey; Test event comprises ± 5Hz rated frequency deviation test, and 10%2-13 subharmonic, outside band, step, 5Hz amplitude phase angle is modulated simultaneously, 1Hz/s frequency slope.

2. a kind of method promoting PMU synchronous phasor measurement precision according to claim 1, it is characterized in that, described step SS1 specifically comprises: signal when PMU device can be accessed by the B code pair of GPS/ big dipper clock, decoded by fpga chip, produce 1PPS signal, and producing the 4K sampled signal synchronous with 1PPS signal, this signal enabling AD sampling A/D chip carries out analog to digital conversion; PT/CT analog signals accesses A/D conversion chip after anti-aliasing analog filtering (analogue low pass filtering passband is 3.1KHz), and analog-to-digital result is put into data buffer and carried out DFT phasor calculation.

3. a kind of method promoting PMU synchronous phasor measurement precision according to claim 1, it is characterized in that, low-pass filtering described in described step SS2 specifically comprises: the higher-order of oscillation component that filtering spectral leakage and the outer frequency of band produce, eliminate interference, improve phasor calculation precision, the phasor calculation formula adding prefilter is as follows:

$X\left(i\right)=\frac{\sqrt{2}}{\mathrm{Gain}}\·\underset{k=-\frac{L}{2}}{\overset{\frac{L}{2}}{\mathrm{\Σ}}}x(i+k)\·W_k\·e^{-j\·2\mathrm{\π}{f}_0\frac{i+k}{N}}---\left(8\right)$

$\mathrm{Gain}=\underset{k=-\frac{L}{2}}{\overset{\frac{L}{2}}{\mathrm{\Σ}}}{W}_k---\left(9\right)$ In formula (8), (9), f ₀for mains frequency; L is for there being limit for length's unit impact response digital filter exponent number; W _kfor low-pass filter coefficients, N is sampling number, and x (i+k) is i+k moment phasor value.

4. a kind of method promoting PMU synchronous phasor measurement precision according to claim 1, it is characterized in that, described step SS3 specifically comprises: the time domain sinusoidal signal that is sampled of case of external input is

A kth sampled point in r window can be expressed as:

Phasor computing algorithm adopts recurrence DFT formula to be expressed as:

${\hat{X}}_r={\hat{X}}_{r-1}+2\×\frac{\sqrt{2}}{N}[x_r(N-1)-x_{r-N/2}(N-1)]e^{-j\frac{2\mathrm{\π}}{N}(r-1)}---\left(12\right)$

Again because

$\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}{e}^{\mathrm{j\θk}}=\frac{\sin (\mathrm{\θN}/2)}{\sin (\mathrm{\θ}/2)}{e}^{\mathrm{j\θ}(N-1)/2}---\left(13\right)$

Order

$\mathrm{\θ}=\frac{2\mathrm{\π\Δf}}{f_{0}N}---\left(14\right)$

Namely obtaining by formula (11), (12), (13), (14) the original phasor that DFT calculates is:

${\hat{X}}_r=2\×{\stackrel{\‾}{X}}_r\frac{\sin (\mathrm{\θN}/4)}{N\sin (\mathrm{\θ}/2)}{e}^{\mathrm{j\θ}(N-2)/4}+C_r---\left(15\right)$

In formula:

$C_r=2\×{\stackrel{\‾}{X}}_r^{*}\frac{\sin (\mathrm{\θN}/4)}{N\sin [(\mathrm{\θ}+\frac{4\mathrm{\π}}{N})/2]}{e}^{-j[(\mathrm{\θ}+\frac{4\mathrm{\π}}{N})(N-2)/4+\frac{4\mathrm{\πr}}{N}]}---\left(16\right)$ Formula (15) gives recurrence Fu Shi algorithm r and walks the original phasor that there is spectrum leakage error calculating and obtain phasor true in theory between relational expression, for the phasor that there is spectrum leakage error that Fu Shi algorithm calculates, C _rthe frequency leakage item that initial phase angle corresponding to data window is relevant, for the true phasor of theory; Can solving equation (15) be passed through thus, (16) obtain revised free from error true phasor if every m subsynchronous phasor of sampling calculating 1 adopt 3 equally spaced phasors set up Simultaneous Equations:

Solve 3 simultaneous equations, obtain:

$e^{-\mathrm{jm\θ}}=f(r-2m)+\sqrt{f^2(r-2m)-e^{j\frac{4\mathrm{\π}}{N}m}}---\left(20\right)$

$C_r=\frac{{\hat{X}}_r{e}^{-\mathrm{jm\θ}}-{\hat{X}}_{r-m}}{e^{-\mathrm{jm\θ}}-e^{\mathrm{jm\θ}}{e}^{j\frac{4\mathrm{\π}}{N}m}}---\left(21\right)$

In formula: $f(r-2m)=\frac{{\hat{X}}_{r-2m}+e^{j\frac{4\mathrm{\π}}{N}m}{\hat{X}}_r}{{2\hat{X}}_{r-m}}---\left(22\right)$

Make Φ _m=e ^{-jm θ}, then

$C_r=\frac{{\hat{X}}_r{\mathrm{\Φ}}_m-{\hat{X}}_{r-m}}{{\mathrm{\Φ}}_m-{\mathrm{\Φ}}_m^{*}{e}^{j\frac{4\mathrm{\π}}{N}m}}---\left(23\right)$

${\stackrel{\‾}{X}}_r=(\hat{X}-C_r)\frac{N\sin (\mathrm{\θ}/2)}{2\×\sin (\mathrm{\θN}/4)}{e}^{-\mathrm{j\θ}(N-2)/4}---\left(24\right)$

In the hope of θ, then θ can be substituted into formula (14) by formula (20), the side-play amount of ongoing frequency relative system rated frequency can be tried to achieve, and then can in the hope of system frequency and frequency change rate; be the phasor of step SS2 result of calculation, through type (21) can calculate C _r, then the substantial synchronization phasor in frequency shift (FS) situation can be calculated by formula (24)

5. a kind of method promoting PMU synchronous phasor measurement precision according to claim 1, is characterized in that, described step SS4 Selecting parameter is: when transfer rate is 25Hz, group delay 250 milliseconds, passband edges 5Hz, passband gain 0.0002dB, stop band gain-40dB; When transfer rate is 50Hz, group delay 125 milliseconds, passband edges 5Hz, passband gain 0.0002dB, stop band gain-60dB; When transfer rate is 100Hz, without the need to postfilter.