CN107589299B - Electric power signal synchronous phasor measuring method based on multi-frequency the measures model - Google Patents
Electric power signal synchronous phasor measuring method based on multi-frequency the measures model Download PDFInfo
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Abstract
The invention discloses a kind of electric power signal synchronous phasor measuring methods based on multi-frequency the measures model, its step is, 2L+1 sections of electric power signal discrete series x (n) are intercepted to electric power signal discrete series adding window in power grid and carry out discrete Fourier transform, electric power signal is obtained in the phasor measurement discreet value X (l) of 2L+1 data window, and utilizes the rough estimate frequency of phasor measurement discreet value X (l) the calculating benchmark moment electric power signal obtained.It recycles surrounding frequency point information to establish multi-frequency the measures model, is modified using phasor measurement discreet value X (0) of the multi-frequency the measures model to reference instant, obtains correction value;Finally, obtaining report moment t by phase shift operationrepThe phasor measurements of electric power signal in power grid
Description
Technical field
The present invention relates to electric power signal synchronous phasor measuring methods in electric system.
Background technique
Basis and core as power grid Wide Area Measurement System, synchronous phasor measurement unit are installed extensively to obtain power grid
Global dynamic variation characteristic, the accuracy of algorithm will directly influence the advanced application performance of Wide Area Measurement System.
Discrete fourier transform algorithm simple operation, principle are simple, response speed is very fast, and have good inhibition to harmonic wave
Characteristic.Discrete fourier transform algorithm needs to carry out adding window truncation to electric power signal when handling signal, if being just truncated one
Or integer signal period sequence, this finite length sequence can represent former Infinite Sequences, therefore obtained result compared with
It is accurate;But when electric power signal fundamental frequency shifts, then integer period, i.e. non-synchronous sampling cannot be truncated, so that
After signal spectral analysis, it other than the main lobe having originally, there is also the secondary lobe that originally should not have, generate spectral leakage.Together
When, in non-synchronous sampling, each secondary signal component is failed on the frequency discrimination just fallen in frequency spectrum point, but falls in two
Between frequency discrimination point.It is not directly available the exact value of phasor in this way, and can only be come with the value of the frequency discrimination point closed on close
Like replacement, i.e. fence effect.It can thus be seen that using discrete fourier transform algorithm electric power signal fundamental frequency deviate compared with
Occurs serious non-synchronous sampling in the case where big, caused spectral leakage and barrage may be such that discrete fourier becomes
Scaling method generates large error, or even obtains a not available result.Although in conclusion discrete fourier transform algorithm energy
It is enough to synchronize phasor measurement under certain condition, but still have some limitations.
In addition, by external disturbance or break down in dynamic process when power grid, the parameter of electric power signal with
Time change, algorithm the error of algorithm can be also increased to the unreasonable embodiment of electric power signal dynamic characteristic.The standard of phasor measurement
Exactness directly influences the application effect of Wide Area Measurement System, and synchronous phasor measurement inaccuracy finally will lead to the dynamic peace of power grid
Full monitoring capacity reduces, and influences the safe and stable operation of power grid.
Summary of the invention
The object of the present invention is to provide a kind of electric power signal synchronous phasor measuring methods based on multi-frequency the measures model, should
The phasor effects that method measures are more accurate, reliable.
The present invention is to solve its technical problem, and used technical solution is a kind of electricity based on multi-frequency the measures model
Force signal synchronous phasor measuring method, the steps include:
A, electric power phasor and the processing of fundamental signal frequency estimation
Sampling is measured to voltage in power grid or current signal by power measuring instrument, obtains the discrete letter of electric power in power grid
Number sequence, digital signal processor intercept to obtain 2L+1 electric power discrete signal window by window function, each discrete signal window
Length is the primitive period;Discrete Fourier transform is carried out to electric power discrete signal window, obtains the mutually measurement of electric power discrete signal window
Measure discreet value X (l), wherein l indicate electric power discrete signal window serial number, l=0, ± 1, ± 2 ..., ± L, L be front half section or after
Half section of electric power discrete signal window sum, value 3-5;Recycle the phasor measurement discreet value X of electric power discrete signal window
(l), the rough estimate frequency of the electric power signal at the 0th electric power discrete signal window center moment, i.e. the electric power letter of reference instant are calculated
Number rough estimate frequency
B, multi-frequency the measures model corrects phasor measurement discreet value
The rough estimate frequency of the electric power signal of digital signal processor reference instant2M+1 Frequency point of surrounding, if
The vertical multi-frequency the measures model being made of the sub- phasor of 2M+1 speed;It is discrete to the 0th electric power by multi-frequency the measures model
Signal window, that is, reference instant phasor measurement discreet value X (0) is modified, and obtains the phasor measurement correction value of reference instantFinally, obtaining report moment t by phase shift operationrepThe phasor measurements of electric power signal in power grid
Compared with prior art, the beneficial effects of the present invention are:
The sub- phasor of multiple and different speeds is set, while guaranteeing that the speed of sub- phasor is distributed in actual frequency week
It encloses, to make full use of peripheral information, phasor measurement estimated value is modified, spectrum leakage and fence effect are reduced with this
Influence to phasor measurement realizes more accurate synchronous phasor measurement.
Further, the phasor measurement discreet value X (l) that electric power discrete signal window is utilized in step A of the invention, calculates base
The rough estimate frequency for the electric power signal carved on timeConcrete operations be:
Digital signal processor calculates phasor measurement and estimates according to the phasor measurement discreet value X (l) of electric power discrete signal window
The phase difference of value Wherein angle () expression takes angle function, and * expression takes altogether
Yoke, ∑ () indicate summing function;
Digital signal processor calculates the rough estimate frequency of the electric power signal of reference instant Wherein round () indicates bracket function, f0For fundamental frequency, 50Hz is taken.
Further, the multi-frequency the measures model in step B of the invention is established using the following method:
The mathematical model X'(t of B1, electric power signal phasor value) and electric power signal mathematical model x'(t) expression formula difference
Are as follows:
Wherein, m is the serial number of the sub- phasor of speed, value m=0, ± 1, ± 2 ..., ± M, M are speed
The maximum speed value of sub- phasor, and the value of M meets M≤L;AmIndicate the low-frequency band limit of the sub- phasor of m-th of speed
Phasor, Δ f indicate that the frequency interval between sub- phasor, e are the bottom of natural logrithm, and j is imaginary unit, and Re expression takes phasor real
Portion, t are report moment trepWith the difference of reference instant;
To the mathematical model x'(t of electric power signal) discrete processes are carried out, obtain the multi-frequency phase of electric power signal discrete series
Measure mathematical model x (n) ':
Wherein, n is sampling instant,For rough estimate angular frequency, expression formula isfsFor sample frequency;
Δ ω is angular frequency interval, and expression formula is the π Δ of Δ ω=2 f/fs;
The mathematical model x'(n of electric power signal discrete series) is carried out adding window Fourier transformation by B2, digital signal processor,
Obtain the model X'(l of phasor measurement discreet value):
Wherein, frequency filtering ω0=2 π f0/fs, h () is window function, and N is the electric power in an electric power signal discrete window
The number of signal discrete value;
Further, in step B of the invention by multi-frequency the measures model to the phasor measurement discreet value X of reference instant
(0) it is modified, obtains the phasor measurement correction value of reference instantMethod particularly includes:
B3, digital signal processor are by phasor measurement estimated value X (l) generation of electric power discrete signal window obtained in step A
Enter phasor measurement discreet value model X'(l) in, even X (l)=X'(l);Obtain the 2L+1 sub- phasors Han m-th of speed
Low-frequency band limits phasor AmEquation, by these equations simultaneousnesses form equation group, using least square solution obtain m-th of rotary frequency
The low-frequency band of the sub- phasor of rate limits phasor AmValue, and then obtain the phasor measurement correction value of reference instant
Further, the specific method of phase shift operation is in step B of the invention:
B4, report moment trepIt is obtained from GPS device by digital signal processor, will report moment trepWith reference instant
Poor t and the sub- phasor of m-th of speed that walks of B3 low-frequency band limit phasor Am, substitute into the mathematics of electric power phasor in B1 step
Model X'(t) in get to report moment trepThe phasor value of the electric power signal of power grid
Specific embodiment
The present invention is described in further detail With reference to embodiment.
Embodiment
A kind of specific embodiment of the invention is a kind of electric power signal synchronous phasor measurement based on Domain Dynamic model
Method the steps include:
A kind of electric power signal synchronous phasor measuring method based on multi-frequency the measures model, the steps include:
A, electric power phasor and the processing of fundamental signal frequency estimation
Sampling is measured to voltage in power grid or current signal by power measuring instrument, obtains the discrete letter of electric power in power grid
Number sequence, digital signal processor intercept to obtain 2L+1 electric power discrete signal window by window function, each discrete signal window
Length is the primitive period;Discrete Fourier transform is carried out to electric power discrete signal window, obtains the mutually measurement of electric power discrete signal window
Measure discreet value X (l), wherein l indicate electric power discrete signal window serial number, l=0, ± 1, ± 2 ..., ± L, L be front half section or after
Half section of electric power discrete signal window sum, value 3-5;Recycle the phasor measurement discreet value X of electric power discrete signal window
(l), the rough estimate frequency of the electric power signal at the 0th electric power discrete signal window center moment, i.e. the electric power letter of reference instant are calculated
Number rough estimate frequency
Wherein, using the phasor measurement discreet value X (l) of electric power discrete signal window, the electric power signal of reference instant is calculated
Rough estimate frequencyConcrete operations be:
Digital signal processor calculates phasor measurement and estimates according to the phasor measurement discreet value X (l) of electric power discrete signal window
The phase difference of value Wherein angle () expression takes angle function, and * expression takes altogether
Yoke, ∑ () indicate summing function;
Digital signal processor calculates the rough estimate frequency of the electric power signal of reference instant Wherein round () indicates bracket function, f0For fundamental frequency, 50Hz is taken.
B, multi-frequency the measures model corrects phasor measurement discreet value
The rough estimate frequency of the electric power signal of digital signal processor reference instant2M+1 Frequency point of surrounding,
Set up the multi-frequency the measures model being made of the sub- phasor of 2M+1 speed;By multi-frequency the measures model to the 0th electric power from
Scattered signal window, that is, reference instant phasor measurement discreet value X (0) is modified, and obtains the phasor measurement correction value of reference instantFinally, obtaining report moment t by phase shift operationrepThe phasor measurements of electric power signal in power grid
Above-mentioned multi-frequency the measures model is established using the following method:
The mathematical model X'(t of B1, electric power signal phasor value) and electric power signal mathematical model x'(t) expression formula difference
Are as follows:
Wherein, m is the serial number of the sub- phasor of speed, value m=0, ± 1, ± 2 ..., ± M, M are speed
The maximum speed value of sub- phasor, and the value of M meets M≤L;AmIndicate the low-frequency band limit of the sub- phasor of m-th of speed
Phasor, Δ f indicate that the frequency interval between sub- phasor, e are the bottom of natural logrithm, and j is imaginary unit, and Re expression takes phasor real
Portion, t are report moment trepWith the difference of reference instant;
To the mathematical model x'(t of electric power signal) discrete processes are carried out, obtain the multi-frequency phase of electric power signal discrete series
Measure mathematical model x (n) ':
Wherein, n is sampling instant,For rough estimate angular frequency, expression formula isfsFor sample frequency;
Δ ω is angular frequency interval, and expression formula is the π Δ of Δ ω=2 f/fs;
The mathematical model x'(n of electric power signal discrete series) is carried out adding window Fourier transformation by B2, digital signal processor,
Obtain the model X'(l of phasor measurement discreet value):
In formula, frequency filtering ω0=2 π f0/fs, h () is window function, and N is the electric power in an electric power signal discrete window
The number of signal discrete value;
Above-mentioned is modified by phasor measurement discreet value X (0) of the multi-frequency the measures model to reference instant, obtains benchmark
The phasor measurement correction value at momentMethod particularly includes:
B3, digital signal processor are by phasor measurement estimated value X (l) generation of electric power discrete signal window obtained in step A
Enter phasor measurement discreet value model X'(l) in, even X (l)=X'(l);Obtain the 2L+1 sub- phasors Han m-th of speed
Low-frequency band limits phasor AmEquation, by these equations simultaneousnesses form equation group, using least square solution obtain m-th of rotary frequency
The low-frequency band of the sub- phasor of rate limits phasor AmValue, and then obtain the phasor measurement correction value of reference instant
The specific method of above-mentioned phase shift operation is:
B4, report moment trepIt is obtained from GPS device by digital signal processor, will report moment trepWith reference instant
Poor t and the sub- phasor of m-th of speed that walks of B3 low-frequency band limit phasor Am, substitute into the mathematics of electric power phasor in B1 step
Model X'(t) in get to report moment trepThe phasor value of the electric power signal of power grid
Emulation experiment
For the measurement accuracy of the verifying present invention in a dynamic condition, the ideal under frequency shift (FS) and amplitude oscillatory condition is established
Dynamic Signal model, respectively with the method for the present invention and discrete Fourier transform method to frequency shift (FS) and oscillator signal in the case of
Two kinds of signals measure, to compare its dynamic property.In emulation, the frequency f of rotation modulation phasor0It is taken as 50Hz, to adopt
Sample frequency fs=2.4kHz samples signal, is taken as N=48 using rectangular data window and its data amount check.Sub- phasor is set
Sum is 3, i.e. M=1, and data window number is 7, solves phasor measurements using least square method.In emulation amplitude error and
Index of the phase angle error as measure algorithm performance.
A, the emulation under frequency shift (FS)
In electric system when failure, the fundamental frequency of electric power signal will appear certain offset.Electric power signal is arranged to carry out
Test:
X (t)=cos [2 π (f0+Δf0')t]
Wherein f0Fundamental frequency 50Hz when being operated normally for system, if fundamental frequency shifted by delta f0' value from -5Hz to
5Hz, interval are fixed as 1Hz, i.e. fundamental frequency is respectively 45Hz, 46Hz ... 55Hz.With discrete Fourier transform method and
The method of the present invention carries out phasor measurement to the frequency offset signals.The amplitude error obtained using discrete Fourier transform method is most
Big value is 0.0679, and the use of the amplitude error maximum value that the method for the present invention obtains is 1.6716 × 10-5, can be neglected;It is right
The use of the maximum value that discrete Fourier transform method obtains is 1.401 in phase angle error, and is obtained most using the method for the present invention
Big value only 0.0042.It follows that when signal frequency shifts, compared to discrete Fourier transform method, the present invention
Method possesses better performance, and measurement accuracy is higher.
B, the emulation under signal oscillating
Power system oscillation would generally cause the step-out between interconnection overcurrent tripping, system and system and unit and system
And off-the-line, seriously threaten the stabilization of electric system.It is even electric on the basis of consideration low-frequency oscillation according to synchronous phasor measurement standard
More violent disturbance in Force system, setting signal model are as follows:
X (t)=[1+kxcos(ωt)]×cos[ω0t+kacos(ωt)]
Work as kx=1, ka=0 vibrates for amplitude;Wherein, ω0=2 π f0, f0The π of=45Hz, ω=2 R is oscillation angular frequency, and R is
Frequency of oscillation, R value are 5Hz.Phasor is carried out to the oscillator signal with discrete Fourier transform method and the method for the present invention
Measurement.The amplitude error and phase angle error maximum value obtained using discrete Fourier transform method is respectively 0.16 and 2.94;
And the use of two kinds of index maximum values that the method for the present invention obtains is respectively 0.00645 and 0.008, it is negligible.It follows that working as
When amplitude oscillation occurs for electric system, compared to Fourier methods, it is higher that the method for the present invention realizes precision to Dynamic Signal
Measurement.
The method of the present invention and discrete Fourier transform method measuring result error are as shown in the table.It can be seen that this method is to dynamic
In the case of signal fundamental phasors realize the higher measurement of precision.
Discrete Fourier transform method and calculation method estimated result comparison sheet of the present invention
Claims (5)
1. a kind of electric power signal synchronous phasor measuring method based on multi-frequency the measures model, the steps include:
A, electric power phasor and the processing of fundamental signal frequency estimation
Sampling is measured to voltage in power grid or current signal by power measuring instrument, obtains electric power discrete signal sequence in power grid
Column, digital signal processor intercept to obtain 2L+1 electric power discrete signal window by window function, each electric power discrete signal window
Length is the primitive period;Discrete Fourier transform is carried out to electric power discrete signal window, obtains the mutually measurement of electric power discrete signal window
Measure discreet value X (l), wherein l indicate electric power discrete signal window serial number, l=0, ± 1, ± 2 ..., ± L, L be front half section or after
Half section of electric power discrete signal window sum, value 3-5;Recycle the phasor measurement discreet value X of electric power discrete signal window
(l), the rough estimate frequency of the electric power signal at the 0th electric power discrete signal window center moment, i.e. the electric power letter of reference instant are calculated
Number rough estimate frequency
B, multi-frequency the measures model corrects phasor measurement discreet value
The rough estimate frequency of the electric power signal of digital signal processor reference instantAround 2M+1 Frequency point, set up by
The multi-frequency the measures model that the sub- phasor of 2M+1 speed is constituted;By multi-frequency the measures model to the 0th electric power discrete signal
Window, that is, reference instant phasor measurement discreet value X (0) is modified, and obtains the phasor measurement correction value of reference instantMost
Afterwards, by phase shift operation, report moment t is obtainedrepThe phasor measurements of electric power signal in power gridM is speed
The maximum speed value of sub- phasor, and the value of M meets M≤L.
2. as described in claim 1 based on the electric power signal synchronous phasor measuring method of multi-frequency the measures model, feature exists
In: the phasor measurement discreet value X (l) of electric power discrete signal window is utilized in the step A, calculates the electric power signal of reference instant
Rough estimate frequencyConcrete operations be:
Digital signal processor calculates phasor measurement discreet value according to the phasor measurement discreet value X (l) of electric power discrete signal window
Phase differenceWherein angle () expression takes angle function, and * expression takes altogether
Yoke, ∑ () indicate summing function;
Digital signal processor calculates the rough estimate frequency of the electric power signal of reference instant Its
Middle round () indicates bracket function, f0For fundamental frequency, 50Hz is taken.
3. as described in claim 1 based on the electric power signal synchronous phasor measuring method of multi-frequency the measures model, feature exists
In: the multi-frequency the measures model in the step B is established using the following method:
The mathematical model X'(t of B1, electric power signal phasor value) and electric power signal mathematical model x'(t) expression formula is respectively as follows:
Wherein, m is the serial number of the sub- phasor of speed, value m=0, ± 1, ± 2 ..., ± M;AmIndicate m-th of rotary frequency
The low-frequency band of the sub- phasor of rate limits phasor, and Δ f indicates that the frequency interval between sub- phasor, e are the bottom of natural logrithm, and j is imaginary number list
Position, Re expression take phasor real part, and t is report moment trepWith the difference of reference instant;
To the mathematical model x'(t of electric power signal) discrete processes are carried out, obtain the multi-frequency phasor number of electric power signal discrete series
Learn model x'(n):
Wherein, n is sampling instant,For rough estimate angular frequency, expression formula isfsFor sample frequency;Δ ω is
Angular frequency interval, expression formula are the π Δ of Δ ω=2 f/fs;
B2, digital signal processor carry out the multi-frequency phasor mathematical model x'(n of electric power signal discrete series) in adding window Fu
Leaf transformation obtains the model X'(l of phasor measurement discreet value):
Wherein, frequency filtering ω0=2 π f0/fs, h () is window function, and N is the electric power signal in an electric power signal discrete window
The number of discrete value.
4. electric power signal synchronous phasor measuring method its feature based on multi-frequency the measures model exists as claimed in claim 3
In: it is modified in the step B by phasor measurement discreet value X (0) of the multi-frequency the measures model to reference instant, obtains benchmark
The phasor measurement correction value at momentMethod particularly includes:
The phasor measurement estimated value X (l) of electric power discrete signal window obtained in step A is substituted into phase by B3, digital signal processor
Measurement discreet value model X'(l) in, even X (l)=X'(l);Obtain the low frequency of the 2L+1 sub- phasors Han m-th of speed
Band limit phasor AmEquation, these equations simultaneousnesses are formed into equation group, obtain m-th speed using least square solution
The low-frequency band of phasor limits phasor AmValue, and then obtain the phasor measurement correction value of reference instant。
5. as claimed in claim 4 based on the electric power signal synchronous phasor measuring method of multi-frequency the measures model, feature exists
In: the specific method of phase shift operation is in the step B:
B4, report moment trepIt is obtained from GPS device by digital signal processor, will report moment trepWith the difference of reference instant
The low-frequency band for the sub- phasor of m-th of speed that t and B3 step obtains limits phasor Am, substitute into electric power signal phasor value in B1 step
Mathematical model X'(t) in get to report moment trepThe phasor measurements of the electric power signal of power grid
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CN109633266B (en) * | 2019-02-26 | 2020-12-01 | 重庆新世杰电气股份有限公司 | Frequency measurement method, system, device and computer readable storage medium |
CN110376435A (en) * | 2019-08-05 | 2019-10-25 | 西南交通大学 | It is a kind of based on band it is outer-synchronous phasor measuring method of multi-frequency model |
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