CN106970264A - A kind of improvement phase difference correction method for considering mains frequency rate of change - Google Patents
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Abstract
The invention discloses a kind of improvement phase difference correction method for considering mains frequency rate of change, this method is corrected based on frequency change rate to normalized frequency correcting value, the improvement phase difference correction method of the consideration frequency change rate of the present invention is more suitable for the situation of frequency dynamic change compared with conventional method, it is larger in frequency fluctuation scope, frequency change does not know realize that accurate quickly harmonic parameters are measured during even occurrence frequency collapse yet, it is capable of the change of accurate determination frequency rate of change, be conducive to taking emergent control measure in time when system frequency occurs abnormal, prevent the generation of the great power system accident such as massive blackout.
Description
Technical field
The invention belongs to Electric Power Harmonic Analysis technical field, more particularly to a kind of improvement phase for considering mains frequency rate of change
Potential difference correction method.
Background technology
Electric harmonic problem is just attract attention from 1920s, with flying for Power Electronic Technique
Speed development and the extensive use of various nonlinear-loads, harmonic pollution are on the rise.The on-line measurement of electric harmonic is to administer humorous
The important technical of ripple pollution, and the proposition and development of the technology such as microgrid and new-energy grid-connected are then joined for electric harmonic in recent years
Several accurate, fast slowdown monitorings propose new application background.Fast Fourier Transform (FFT) (FFT) is the normal of electric harmonic parameter measurement
With one of algorithm, the parameter of each harmonic can be accurately obtained under synchronized sampling, and because time domain is cut under non-synchronous sampling
The fence effect that the disconnected spectrum leakage caused and frequency domain discretization are caused, the measurement of harmonic parameters there will be larger error.
In the actual motion of power network, due to the imbalance between generator and load, power network fundamental frequency is in dynamic
In change, frequency shift (FS) is generated, it is impossible to realize preferable synchronized sampling.Therefore, domestic and foreign scholars propose it is a variety of
Harmonic analysis method based on FFT under non-synchronous sampling.It is general using based on the quasi synchronous algorithm of time domain in time domain.In frequency domain,
It is then many using discrete spectrum correcting algorithms such as windowed interpolation method, power enhanced, spectrum centroid method, phase difference correction methods.
The principle of conventional phase difference correction method：
Assuming that interfering between each harmonic component of power network signal is ignored, the k order harmonic components in electric power signal
For：
Wherein, AkFor the amplitude of harmonic wave,For initial phase angle, fkFor frequency.
If the time domain analytic expression of sample window is w (t), frequency domain analytic expression is W (f), a length of T of sample window, the then harmonic component
Time-domain windowed is blocked and does Fourier transformation, only considers the positive half of frequency spectrum, has：
By formula (2) understand the harmonic signal adding window block after phase be：
The corresponding crest frequency f of the subharmonic of this in discrete spectrum need to can just obtain actual frequency f by correctionkIf, frequency
Rate correcting value isI.e.：
Then the phase in formula (3) is represented by：
By the harmonic signal in time domain to left time span t0, then also change is turned to its initial phase therewithTherefore the signal phase after translation is：
Formula (6) subtracts formula (5), and the phase difference that can obtain two segment signals is：
It can derive that frequency correction amount is by formula (7)：
In actual measurement process, k order harmonic components x is tackled firstk(t) a length of T of adding window sample window and with fsSampling
Frequency carries out discrete sampling, takes the sample sequence that two segment length are N points, and second segment sequence delays L points than first paragraph, wherein, adopt
Sample sequence is counted and the relation of sample window length is N=Tfs.After Window sampling, two sections of sequences are done with N point fft analysis respectively and is obtained
To discrete spectrum sequence.Assuming that in spectrum sequence, the corresponding peak value spectral line number of k subharmonic is mk, normalized frequency correcting value is
Δmk, frequency resolution is Δ f=fs/ N, then can be derived from relationship below：
Second segment sequence translation time span be：
t0=L/fs (9)
Frequency correction amount is：
The corresponding crest frequency of the subharmonic is：
F=mkΔf (11)
Formula (9), (10), (11) substitution formula (8) can be obtained normalized frequency correcting value and be：
If peak value spectral line mkCorresponding spectral line amplitude is Amk, the modular function of normalized sample window frequency spectrum is W1(m), believe
Number FFT real and imaginary parts are respectively RkAnd Ik, the correction of line frequency, amplitude and phase, updating formula can be entered according to formula (12)
Respectively：
fk=(mk+Δmk)fs/N (13)
Δ m in formula (13), (14), (15)kFor the normalized frequency correcting value in formula (12).
According to IEEE definition, the frequency of power system is the function of time, and the derivative of frequency versus time is referred to as frequency change
Rate (ROCOF).When Operation of Electric Systems is normal, generating is adjusted in time with load variations, and power frequency is 50Hz and keeps stable,
Frequency departure is defined generally to ± 0.2Hz, when power system capacity is smaller, and limit value relaxes as ± 0.5Hz, and now, ROCOF value is about
Equal to 0, phase difference correction method measurement electric harmonic parameters precision is higher.When power system is by serious disturbance, system frequency can
Larger change in oscillation can be produced, now, ROCOF value is not zero, phase difference correction method measurement electric harmonic parameters precision is anxious
Sharp fall is low, and reason is that this method thinks that actual frequency is a definite value in the derivation of normalized frequency correcting value.
System frequency produces larger skew, can all cause larger infringement with user in itself to power system, therefore will
Asking the measurement of harmonic parameters also has higher precision and real-time when frequency change rate is larger, so as to accurately and in time
Judge system mode, prevent major accident.
The content of the invention
The present invention is carried for the poor correction method relatively low situation of measurement accuracy in the power network of fundamental frequency dynamic change of conventional phase
A kind of improvement phase difference correction method for considering frequency change rate is gone out, normalized frequency correcting value has been carried out based on frequency change rate
Amendment, this method has higher precision and preferable real-time in the power network of fundamental frequency dynamic change.
Analysis in background technology to principle is it can be found that the updating formula of each harmonic parameters is equal in phase difference correction method
With normalized frequency correction amount delta mkIt is relevant, thus each harmonic parameters measurement accuracy with Δ mkComputational accuracy it is directly related.
But traditional phase difference correction method is during frequency correction amount formula is derived, it is believed that the signal frequency analyzed is constant not
Become, do not change the influence caused to normalized frequency correcting value in view of frequency dynamic.
When fundamental frequency dynamic change causes to deviate 50Hz rated frequency, sample window length is no longer equal to integral multiple fundamental wave week
Phase, that is, it there occurs non-synchronous sampling.Now, actual frequency composition is constantly moved between the corresponding frequency of each spectral lines of FFT, is produced
Spectrum leakage phenomenon, Δ mkResult of calculation there will be larger error.Because frequency change rate is not zero, phase difference correction method
In two sections of sample sequences fundamental frequency it is different, therefore there is error in the formula of normalized frequency correcting value.
The present invention is improved the poor correction method of conventional phase as follows in the case where considering frequency change rate：
Assuming that electric power signal x (t) fundamental frequency f1With df1/ dt speed change, i.e. ROCOF1=df1/ dt, then k subharmonic
Frequency change rate be ROCOFk=dfk/ dt=kdf1/dt.The frequency of first segment signal and the second segment signal is respectively fkWith
f′k, then the frequency offset of two segment signals is dfk, i.e.,：
f′k=fk+dfk (16)
Think that frequency offset is equal to the frequency change rate and the product of time of signal herein, therefore：
dfk=ROCOFk·t0=kt0·df1/dt (17)
Formula (9) is substituted into formula (17) to obtain：
dfk=(kL/fs)·df1/dt (18)
Because second segment signal frequency is changed, initial phase should be modified toCause
The phase of the second segment signal should be modified in this formula (6)：
Formula (19) subtracts formula (5), in conjunction with formula (4) push away two segment signals phase difference：
The frequency correction amount then corrected is：
Discrete spectrum timing is carried out, formula (9), (10), (11) are substituted into the normalized frequency school that formula (21) must can be corrected
Positive quantity：
In actual calculating, orderBecause the span of phase is (- π, π), the cycle is 2 π, δ
It can exceed that this is interval, it is therefore desirable to carry out following handle：δ '=mod (δ, 2 π) is made, then is made
δ " is set to be in the range of (- π, π).After treatment, the normalized frequency correcting value of amendment is：
Formula (23) is substituted into the frequency that can be corrected in formula (13), (14), (15), amplitude, phasing formula.
With the processing to δ similarly, the result of calculation of phasing formulaIt is possible to not in (- π, π) is interval, therefore
Need orderMake againBy the resulting result in the range of (- π, π)It is used as final correction result.
The poor correction method measurement electric harmonic parameters precision of conventional phase relatively low feelings when the present invention is directed to fundamental frequency dynamic change
A kind of condition, it is proposed that improved method of consideration frequency change rate.When calculating normalized frequency correcting value, in the base of conventional method
The influence of frequency change rate is considered on plinth, the normalized frequency correcting value formula of amendment has been derived.By previous with being measured when secondary
Fundamental frequency carry out difference coefficient computing obtained by result as frequency change rate calculated value, and propose two kinds of different methods
On-line measurement is realized, irregular single measurement and continuous On-line sampling system is respectively suitable for.By conventional method and this
The improved method of invention is respectively in frequency stabilization, fundamental frequency wide fluctuations, pitch variation unknown-but-bounded and collapse of frequency feelings
Simulation comparison and analysis are carried out under condition, finally the real-time to improved method is analyzed.Simulation analysis result shows, this hair
The improvement phase difference correction method of bright consideration frequency change rate is more suitable for the situation of frequency dynamic change compared with conventional method, in frequency
Also it can realize that accurate quickly harmonic parameters are surveyed when rate fluctuation range is larger, frequency change is uncertain or even occurrence frequency collapses
Amount, is capable of the change of accurate determination frequency rate of change, is conducive to taking emergent control in time when exception occurs for system frequency
Measure, prevents the generation of the great power system accident such as massive blackout.
Brief description of the drawings
Fig. 1 is the measurement procedure schematic diagram of method 1.
Fig. 2 is the measurement procedure schematic diagram of method 2.
Fig. 3 is harmonic amplitude root-mean-square error comparison schematic diagram in the case of frequency stabilization.
Fig. 4 is harmonic amplitude root-mean-square error comparison schematic diagram in the case of fundamental frequency wide fluctuations.
Fig. 5 is the frequency variation curve schematic diagram in certain time period in the case of pitch variation unknown-but-bounded.
Fig. 6 is harmonic amplitude root-mean-square error comparison schematic diagram in the case of pitch variation unknown-but-bounded.
Fig. 7 is harmonic amplitude root-mean-square error comparison schematic diagram in the case of collapse of frequency.
Embodiment
In order to more specifically describe the present invention, preferred embodiment comes to technical scheme below in conjunction with the accompanying drawings and specifically
It is described in detail.
The improvement phase difference correction method of the present invention can apply to the frequency change of electric harmonic on-line measurement, wherein fundamental wave
Rate ROCOF1(i.e. df1/ dt) it is an important parameter, measure with the difference of the front and rear fundamental frequency measured twice divided by twice
Time interval is tried to achieve, i.e., previous to carry out difference coefficient computing with working as the secondary fundamental frequency measured.
Two kinds of specific implementation methods that phase difference correction method carries out on-line measurement of improving with the present invention are described below：
With reference to the measurement process of the illustration method 1 of accompanying drawing 1：Fundamental wave is carried out with traditional phase difference correction method continuous twice
Measurement, frequency change rate by second and for the first time, try to achieve by the difference of the fundamental frequency of measurement divided by the time interval measured twice,
Substituted into formula (18), (22), in (23) second of measurement of amendment normalized frequency correcting value, then by formula (13),
(14) frequency that, (15) are corrected, amplitude, phase as measurement final result.Method 1 can apply to irregular one
Secondary property measurement, it is not necessary to repeatedly continuous measurement, can be carried out in the case where frequency change rate changes with consecutive variations at random
With reference to the measurement process of the illustration method 2 of accompanying drawing 2：Continuously measured during on-line measurement, frequency change
Rate subtracts the time interval that the previous fundamental frequency measured measures again divided by twice by the fundamental frequency measured every time and tried to achieve, by it
Substitution formula (18), (22), (23) in formula (13), (14), (15) to this measurement with being modified.During on-line measurement except
Outside measurement for the first time can not be modified with the method for the present invention, measurement afterwards can use modification method.Method 2 mainly should
For repeatedly continuous measurement occasion, with the substantially indistinction of method 1, it is intended merely to improve the real-time of algorithm, is measured previous
Frequency be used for the calculating of this frequency change rate so that the sampling time in continuous on-line measurement shortens half.
Below by taking a kind of phase difference correction method based on Hanning window as an example, respectively with the consideration frequency change rate of the present invention
Improved method and do not consider frequency change rate conventional method carry out numerical simulation contrast, verify the present invention improved phase
The more traditional phase difference correction method of poor correction method has higher precision and stronger real-time,
The frequency correction formula of conventional method is identical with formula (13).
Amplitude rectification formula is：
Phasing formula is：
Wherein, Δ mkFor the normalized frequency correcting value in formula (12), N is the sampling of every section of sequence in phase difference correction method
Points, mkFor the corresponding peak value spectral line number of k subharmonic.
Because the overtone order of measurement is generally the 2nd to the 19th time, therefore the emulation signal model of construction is as follows：
The parameter for emulating each harmonic in signal is as shown in table 1.
Table 1 emulates the parameter of signal each harmonic
According to current art standards, the appropriate sample window of selection is long, while in view of the precision of algorithm to be ensured, sampling is extremely
4 primitive periods are needed less, therefore sample frequency f in emulationsIt is set as 6400Hz, every section of sample sequence length is N=640
Point, second segment sequence translation points are L=128 points.
Under setting herein, frequency stabilization, fundamental frequency wide fluctuations, pitch variation unknown-but-bounded and frequency are set up respectively
The frequency variation model under four kinds of states is collapsed, to verify the improvement phase difference correction method of the present invention in the different running statuses of power network
Under measurement accuracy and real-time.
1. the simulation analysis in the case of frequency stabilization
Under power system stability running situation, frequency departure is defined generally to ± 0.2Hz.For the feelings that analog frequency is stable
The model that frequency change is set up in condition, emulation is as follows：
f1=49.9+0.1 × sin (2 π × 0.1t) (27)
I.e. fundamental frequency initial value is 49.9Hz, and signal occurs just using 10s as the cycle between 49.8Hz~50Hz in measurement process
String changes.10000 times are carried out respectively continuously using the improved method (including method 1 and method 2) of conventional method and the present invention
Measurement, record measurement total time.Because root-mean-square error (RMSE) is reacted very the especially big or special small error in one group of measurement
Sensitivity, will not flood larger random error in measurement, can preferably reflected measurement precision, therefore draw conventional method, side
The root-mean-square error curve of method 1 and each harmonic amplitude of method 2 is as shown in Figure 3.
From the figure 3, it may be seen that method 1 and method 2 less consider ROCOF phase difference correction method in the case of frequency stabilization to letter
The measurement accuracy of number each harmonic amplitude improves, and in addition to 2,14 subharmonic, measurement accuracy has reached 10-4It is secondary,
5th, the precision of 15,17 and 19 subharmonic is even more to have reached 10-5It is secondary.For improving than the improvement for even-order harmonic for odd harmonic
Become apparent.Observe Fig. 3 and find that method 1 and the difference in measurement accuracy of method 2 is not obvious.Conventional method, method 1, method
10000 times of 2 measurement total times are respectively 11.356s, 21.028s and 11.557s, therefore ratio method 1 in real-time of method 2
Advantageously, it is more suitable for electric harmonic On-line sampling system.
2. the simulation analysis in the case of fundamental frequency wide fluctuations
When power network locally breaks down, fundamental frequency is likely to occur large range of fluctuation, for the simulation a wide range of ripple of fundamental frequency
Dynamic situation, be by the model specification that frequency changes：
f1=50+7.5 × sin (2 π × 0.2t) (28)
That is fundamental frequency is since 50Hz, and generating period is 5s sinusoidal fluctuation, and fluctuating range is ± 7.5Hz.Using tradition side
The improved method (including method 1 with method 2) of method and the present invention carry out 10000 continuous measurements respectively, draw conventional method,
The root-mean-square error curve of method 1 and each harmonic amplitude of method 2 is as shown in Figure 4.
As shown in Figure 4, to the measurement accuracy of signal each harmonic amplitude in fundamental frequency a wide range of ripple occurs for method 1 and method 2
Less consider that ROCOF phase difference correction method is greatly improved in the case of dynamic, more than 3 times harmonic measure precision reaches
10-2Secondary, the precision of 18 and 19 subharmonic is even more to have reached 10-3It is secondary.Improve ratio changing for even-order harmonic for odd harmonic
Kind to become apparent, test odd precision is 3~15 times of conventional method, and test even precision is conventional method
1.1~5 times.The amplitude measurement precision of fundamental wave is 25 times of conventional method, improves an order of magnitude, the measurement essence of second harmonic
Degree improves 25% compared with conventional method, has reached the required precision of IEC (International Electrotechnical Commission) standard.Method 1 and method 2 exist
Difference is not obvious in measurement accuracy.
3. the simulation analysis in the case of pitch variation unknown-but-bounded
During power system actual motion, because the change of load has randomness, frequency change is often uncertain, is
The uncertain situation of pitch variation is simulated, is by the model specification of pitch variation：
f1(i)=f1(i-1)+0.001×[2·rand(1)-1] (29)
Wherein, i represents sampled point sequence number, i=0,1,2,3 ...；f1(i) fundamental wave at ith sample point sampling moment is represented
Frequency.
Set f1(0)=50, and f is worked as1(i) when being more than 57.5, f is made1(i)=57.5, f is worked as1(i) when being less than 42.5, f is made1
(i)=42.5.That is fundamental frequency is since 50Hz, the random offset in each sampling time interval in the range of generation ± 0.001Hz,
Pitch variation scope is 42.5Hz~57.5Hz in emulation.Because the peak frequency that may occur in each sampling time interval is inclined
Move as 0.001Hz, therefore when sample frequency is 6400Hz, the excursion of frequency change rate is ± 6.4Hz/s in the model.
In view of under actual conditions, system frequency can not possibly be produced and is frequently mutated, therefore also need to put down frequency variation curve
Sliding processing.Frequency variation curve in emulation in certain time period is as shown in Figure 5.
It is compared, is carried out 10000 times respectively with method 2 because the real-time of method 2 is stronger, therefore using conventional method
Continuous measurement, the root-mean-square error curve for drawing conventional method and each harmonic amplitude of method 2 is as shown in Figure 6.
It will be appreciated from fig. 6 that the present invention improvement phase difference correction method to the measurement accuracy of signal each harmonic amplitude in fundamental frequency
Less consider that ROCOF phase difference correction method improves in the case of change unknown-but-bounded, except 1,2,3,4,6 times
Outside harmonic wave, measurement accuracy has reached 10-3It is secondary.The amplitude measurement precision of fundamental wave is 4.5 times of conventional method, the width of second harmonic
It is 4.6 times of conventional method to be worth measurement accuracy, and the amplitude measurement precision of other subharmonic is 1.4~2.4 times of conventional method.By
This understands, when frequency change is uncertain, and phase difference correction method of improving of the invention has higher measurement essence compared with conventional method
Degree, is more suitable for the actual measurement of dynamic power network.
4. the simulation analysis in the case of collapse of frequency
Mains frequency produces larger skew, larger infringement can be all caused with user in itself to power system, if power network
By serious active vacancy, it is possible to frequency is occurred quick decline, even result in collapse of frequency.Collapsed for analog frequency
Situation, the frequency variation model of use is as follows：
f1=50-3t (30)
That is 50Hz of fundamental frequency when normal operation, unexpected occurrence frequency collapse, frequency is dropped with -3Hz/s speed.
It is compared, respectively signal is continuously measured with method 2 because the real-time of method 2 is stronger, therefore using conventional method,
Stop measurement when frequency drop-off range is more than 7.5Hz, the average value of recording frequency rate of change draws conventional method and method 2
The root-mean-square error curve of each harmonic amplitude is as shown in Figure 7.
As shown in Figure 7, improvement phase difference correction method of the invention to the measurement accuracy of signal each harmonic amplitude in frequency
Less consider that ROCOF phase difference correction method is greatly improved in the case of collapse, in addition to second harmonic, measurement accuracy is equal
Reach 10-2Secondary, the precision of 18 and 19 subharmonic is even more to have reached 10-3It is secondary.Improvement for odd harmonic is more humorous than for even
The improvement of ripple becomes apparent.The precision for measuring odd harmonic is 2.5~10 times of former method, and the amplitude measurement precision of fundamental wave is original
46 times of method, improve an order of magnitude.For even-order harmonic, the measurement accuracy of only 14 subharmonic is not improved,
The measurement accuracy of other even-order harmonics is 1.2~2.8 times of former method, and the measurement accuracy of second harmonic is 2.6 times of former method,
The required precision of IEC standard is reached.The measurement result of frequency change rate is -3.00002451273211Hz/s, it was demonstrated that this hair
Bright improved method can be precisely calculated frequency change rate, and it is humorous in collapse of frequency accident also accurately to measure electric power
Wave parameter.
5. the real time analysis of emulation
IEC standard limits a length of 10 cycles of analysis window of 50Hz power systems, i.e. 200ms.The present invention is in sampling frequency
Rate fsFor 6400Hz, every section of sample sequence length is under conditions of N=640, it is only necessary to which 100ms sample window length is that can reach IEC
The measurement accuracy requirement of standard, thus system mode can be judged more in real time, prevent major accident.
Claims (1)
1. a kind of improvement phase difference correction method for considering mains frequency rate of change, it is characterised in that this method is in conventional phase
Following improve is carried out on the basis of poor correction method：
Assuming that electric power signal x (t) fundamental frequency f1With df1/ dt speed change, i.e. ROCOF1=df1/ dt, then k subharmonic frequency
Rate of change is ROCOFk=dfk/ dt=kdf1/dt.The frequency of first segment signal and the second segment signal is respectively fkWith f 'k, then
The frequency offset of two segment signals is dfk, i.e.,：
f′k=fk+dfk (1)
Think that frequency offset is equal to the frequency change rate and the product of time of signal herein, therefore：
dfk=ROCOFk·t0=kt0·df1/dt (2)
The time span that second segment sequence is translated：t0=L/fsSubstitution formula (2)：
dfk=(kL/fs)·df1/dt (3)
Because second segment signal frequency is changed, initial phase should be modified to
Therefore the signal phase after translating：In the phase of the second segment signal should be modified to：
Push away the phase differences of two segment signals is：
The frequency correction amount then corrected is：
Carry out discrete spectrum timing, the time span that second segment sequence is translated：t0=L/fs, frequency correction amount：The corresponding crest frequency of the subharmonic：F=mkΔ f substitutes into the normalized frequency correcting value that formula (6) must can be corrected：
In actual calculating, orderBecause the span of phase is (- π, π), the cycle is 2 π, δ
It can exceed that this is interval, it is therefore desirable to carry out following handle：δ '=mod (δ, 2 π) is made, then is made
δ " is set to be in the range of (- π, π), after treatment, the normalized frequency correcting value of amendment is：
Formula (8) is substituted into the updating formula f of frequency, amplitude, phasek=(mk+Δmk)fs/N、 In, you can the frequency corrected, amplitude, phasing formula；
With the processing to δ similarly, the result of calculation of phasing formulaIt is possible to not in (- π, π) is interval, therefore is also required to
OrderMake againBy the resulting result in the range of (- π, π)Make
For final correction result.
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| 杨志坚 等: "高斯白噪声背景下时移相位差校正法的频率估计精度分析", 《振动工程学报》 * |
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| CN107579509B (en) * | 2017-09-14 | 2019-01-18 | 南京国电南自电网自动化有限公司 | A method of solving sampling frequency deviation influences current protection directional element |
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| CN109980778A (en) * | 2019-03-07 | 2019-07-05 | 国网安徽省电力有限公司电力科学研究院 | A kind of dry reactor monitoring method and its device based on waveform reduction technique |
| CN112881799A (en) * | 2021-01-18 | 2021-06-01 | 国网湖北省电力有限公司营销服务中心(计量中心) | FFT (fast Fourier transform) -based harmonic detection method for ground power system |
| CN113063987A (en) * | 2021-03-26 | 2021-07-02 | 湖南大学 | Broadband frequency coupling admittance on-line measurement method and system of power electronic equipment |
| CN116358864A (en) * | 2023-06-01 | 2023-06-30 | 西安因联信息科技有限公司 | Method and system for diagnosing fault type of rotary mechanical equipment |
| CN116358864B (en) * | 2023-06-01 | 2023-08-29 | 西安因联信息科技有限公司 | Method and system for diagnosing fault type of rotary mechanical equipment |
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