CN106970264B - Improved phase difference correction method considering power grid frequency change rate - Google Patents
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Abstract
The invention discloses an improved phase difference correction method considering the frequency change rate of a power grid, which corrects a normalized frequency correction value based on the frequency change rate, is more suitable for the condition of dynamic frequency change than the traditional method, can realize accurate and quick harmonic parameter measurement when the frequency fluctuation range is larger, the frequency change is uncertain and even the frequency is collapsed, can accurately judge the change of the frequency change rate, is beneficial to timely taking emergency control measures when the system frequency is abnormal, and can prevent major power system accidents such as large-scale power failure and the like.
Description
Technical Field
The invention belongs to the technical field of power harmonic analysis, and particularly relates to an improved phase difference correction method considering the frequency change rate of a power grid.
Background
The power harmonic problem has attracted people's attention as early as 20 th century, and with the rapid development of power electronic technology and the wide application of various nonlinear loads, the harmonic pollution is becoming more and more serious. The online measurement of the power harmonic is an important technical means for controlling harmonic pollution, and in recent years, the proposal and development of technologies such as microgrid and new energy grid connection and the like provide a new application background for the accurate and rapid monitoring of power harmonic parameters. Fast Fourier Transform (FFT) is one of the commonly used algorithms for power harmonic parameter measurement, and can accurately obtain the parameters of each harmonic under synchronous sampling, while under asynchronous sampling, the measurement of harmonic parameters will have larger errors due to spectrum leakage caused by time domain truncation and fence effect caused by frequency domain discretization.
In actual operation of the power grid, due to imbalance between the generator and the load, the fundamental frequency of the power grid is in dynamic change, frequency offset is generated, and ideal synchronous sampling is impossible. Therefore, scholars at home and abroad propose various harmonic analysis methods based on FFT under asynchronous sampling. In the time domain, an algorithm based on time domain quasi-synchronization is generally adopted. In the frequency domain, discrete spectrum correction algorithms such as a windowing interpolation method, an energy center-of-gravity method, a spectrum centroid method, a phase difference correction method and the like are mostly adopted.
Principle of the conventional phase difference correction method:
assuming that mutual interference among harmonic components of the power grid signal is negligible, the k-th harmonic component in the power signal is:
wherein A iskIs the amplitude of the harmonics,
is an initial phase angle, fkIs the frequency.
Setting the time domain analytic expression of a sampling window as w (T), the frequency domain analytic expression as W (f), and the sampling window length as T, then performing window truncation on the harmonic component time domain and performing Fourier transform, only considering the positive half part of the frequency spectrum, including:
the phase after the window truncation of the harmonic signal is known from the formula (2):
the peak frequency f corresponding to the subharmonic in the discrete spectrum needs to be corrected to obtain the actual frequency fkLet the frequency be corrected by
Namely:
the phase in equation (3) can be expressed as:
shifting the harmonic signal to the left in time domain for a time length t0Then, thenIts initial phase is changed as follows
The phase of the signal after translation is therefore:
subtracting the equation (5) from the equation (6), the phase difference between the two signals is:
from equation (7), the frequency correction amount can be derived as:
in the actual measurement process, the k-th harmonic component x is dealt with firstlyk(T) windowing a sampling window of length T and applying fsThe sampling frequency of the sampling device is subjected to discrete sampling, two sections of sampling sequences with the length of N points are taken, the second section of signals is delayed by L points compared with the first section, wherein the relation between the number of sampling sequence points and the length of a sampling window is N-T.fs. After windowing and sampling, N-point FFT analysis is respectively carried out on the two sequences to obtain discrete spectrum sequences. Assuming that the peak spectral line number corresponding to k-th harmonic in the spectral sequence is mkNormalized frequency correction amount is Δ mkThe frequency resolution is delta f ═ fsN, the following relationship can be deduced:
the time length of the second signal translation stage is as follows:
t0＝L/fs(9)
the frequency correction amount is:
the peak frequency corresponding to this subharmonic is:
f＝mkΔf (11)
the normalized frequency correction amount obtained by substituting equations (9), (10), and (11) for equation (8) is:
set the peak spectral line number mkCorresponding to a spectral line amplitude of AmkNormalized sampling window spectrum has a modulo function of W1(m) the real and imaginary parts of the signal FFT are R, respectivelykAnd IkThe frequency, amplitude and phase corrections can be made according to equation (12), which is:
fk＝(mk+Δmk)fs/N (13)
Δ m in the formulae (13), (14) and (15)kIs the normalized frequency correction amount in equation (12).
According to the definition of IEEE, the frequency of an electric power system is a function of time, and the derivative of the frequency with time is called the frequency rate of change (ROCOF). When the power system operates normally, the power generation is adjusted in time along with the change of the load, the power frequency is 50Hz and is kept stable, the frequency deviation is generally limited to +/-0.2 Hz, when the system capacity is small, the limit value is widened to +/-0.5 Hz, at the moment, the value of ROOF is approximately equal to 0, and the precision of the phase difference correction method for measuring the power harmonic parameters is high. When a power system suffers from severe disturbance, the system frequency may generate large oscillation change, at this time, the value of ROCOF is not zero, and the accuracy of the phase difference correction method for measuring power harmonic parameters is sharply reduced, because the method considers that the actual frequency is a fixed value in the derivation process of the normalized frequency correction value.
The system frequency generates larger deviation, which causes larger damage to the power system and users, so that the measurement of harmonic parameters also has higher precision and real-time performance when the frequency change rate is larger, thereby accurately and timely judging the system state and preventing major accidents from happening.
Disclosure of Invention
The invention provides an improved phase difference correction method considering the frequency change rate aiming at the condition that the measurement precision of the traditional phase difference correction method in a power grid with dynamically changed fundamental frequency is low, the normalized frequency correction value is corrected based on the frequency change rate, and the method has higher precision and better real-time property in the power grid with dynamically changed fundamental frequency.
Analysis of the principle in the background art can find that the correction formulas of the harmonic parameters in the phase difference correction method are equal to the normalized frequency correction quantity DeltamkTherefore, the measurement accuracy of each harmonic parameter is related to Δ mkIs directly related to the calculation accuracy of (c). However, in the conventional phase difference correction method, in the process of deriving the frequency correction amount formula, the analyzed signal frequency is considered to be constant, and the influence of the dynamic change of the frequency on the normalized frequency correction amount is not considered.
When the fundamental frequency changes dynamically to deviate from the rated frequency of 50Hz, the sampling window length is no longer equal to integral multiple of the fundamental period, i.e. asynchronous sampling occurs. At this time, the real frequency component continuously moves between the frequencies corresponding to the spectral lines of the FFT, causing a spectrum leakage phenomenon Δ mkThe calculation of (a) will have a large error. Because the frequency change rate is not zero and the fundamental frequencies of two sampling sequences in the phase difference correction method are different, the formula of the normalized frequency correction value has errors.
The invention improves the traditional phase difference correction method under the condition of considering the frequency change rate as follows:
assume the fundamental frequency f of the power signal x (t)1By df1Rate of change of/dt, ROOF1＝df1Dt, then the frequency rate of change of the k-th harmonic is ROOFk＝dfk/dt＝k·df1And/dt. The frequencies of the first section signal and the second section signal are respectively fkAnd f'kThen the frequency offset of the two signals is dfkNamely:
f′k＝fk+dfk(16)
the frequency offset is considered herein to be equal to the product of the frequency rate of change of the signal and time, so that:
dfk＝ROCOFk·t0＝kt0·df1/dt (17)
substituting formula (9) for formula (17) to obtain:
dfk＝(kL/fs)·df1/dt (18)
since the frequency of the second signal is changed, the initial phase should be corrected to
Therefore, the phase of the second segment signal in equation (6) should be corrected to:
equation (5) is subtracted from equation (19), and the phase difference between the two signals is obtained by combining equation (4):
the corrected frequency correction amount is:
when discrete spectrum correction is performed, the normalized frequency correction amount corrected by substituting equations (9), (10) and (11) for equation (21):
in the actual calculation, orderBecause the range of the phase is (-pi, pi), the period is 2 pi, and the delta may exceed this interval, the following processing is required: let delta' mod (delta, 2 pi), and let
So that δ "is in the range of (- π, π). After processing, the corrected normalized frequency correction amount is:
the formula (23) is substituted into the formulas (13), (14) and (15) to obtain the corrected frequency, amplitude and phase correction formulas.
The calculation result of the phase correction formula is the same as the processing of delta
May not be within the (-pi, pi) interval, therefore, it is also necessary to make
Reissue to order
The results obtained are in the range (-pi, pi)As a final correction result.
The invention provides an improved method considering frequency change rate, aiming at the condition that the accuracy of measuring power harmonic parameters by a traditional phase difference correction method is low when fundamental frequency dynamically changes. When the normalized frequency correction value is calculated, the influence of the frequency change rate is considered on the basis of the traditional method, and a corrected normalized frequency correction value formula is deduced. The result of the difference quotient operation of the fundamental wave frequencies measured at the previous time and the current time is used as a calculation value of the frequency change rate, and two different methods are provided for realizing online measurement and are respectively suitable for single measurement in an unscheduled mode and continuous online real-time measurement. The simulation comparison and analysis are respectively carried out on the traditional method and the improved method of the invention under the conditions of stable frequency, large-range fluctuation of fundamental frequency, uncertain fundamental frequency change but bounded frequency and frequency collapse, and finally, the real-time performance of the improved method is analyzed. Simulation analysis results show that the improved phase difference correction method considering the frequency change rate is more suitable for the condition of dynamic frequency change than the traditional method, can realize accurate and quick harmonic parameter measurement when the frequency fluctuation range is large, the frequency change is uncertain, and even the frequency collapse occurs, can accurately judge the change of the frequency change rate, is beneficial to timely taking emergency control measures when the system frequency is abnormal, and prevents major power system accidents such as large-scale power failure and the like.
Drawings
Fig. 1 is a schematic view of a measurement flow of method 1.
Fig. 2 is a schematic view of a measurement flow of method 2.
FIG. 3 is a diagram illustrating the comparison of the root mean square error of the harmonic amplitudes under the condition of stable frequency.
FIG. 4 is a diagram showing the comparison of root mean square error of harmonic amplitudes under the condition of wide fluctuation of fundamental frequency.
Fig. 5 is a diagram illustrating a frequency variation curve in a certain time period under the condition that the fundamental frequency variation is uncertain and bounded.
FIG. 6 is a diagram showing a comparison of root mean square error of harmonic amplitudes under uncertain and bounded fundamental frequency variations.
FIG. 7 is a diagram illustrating a comparison of root mean square error of harmonic amplitudes under frequency collapse.
Detailed Description
In order to more specifically describe the present invention, the following detailed description of the embodiments of the present invention is provided with reference to the accompanying drawings.
The improved phase difference correction method can be applied to the on-line measurement of electric power harmonic waves, wherein the frequency change rate ROOF of the fundamental wave1(i.e., df)1Dt) is an important parameter, and the fundamental frequency difference between the previous measurement and the next measurement is divided by the time interval between the two measurements, namely, the fundamental frequency difference quotient between the previous measurement and the current measurement is calculated.
Two specific implementation methods for online measurement by using the improved phase difference correction method of the invention are described as follows:
the measurement process of method 1 is described with reference to fig. 1: two continuous measurements are made on the fundamental wave by using a traditional phase difference correction method, the frequency change rate is obtained by dividing the difference between the frequency of the fundamental wave measured for the second time and the frequency of the fundamental wave measured for the first time by the time interval of the two measurements, the frequency change rate is substituted into the equations (18), (22) and (23) to correct the normalized frequency correction amount of the second measurement, and then the corrected frequency, amplitude and phase are obtained by the equations (13), (14) and (15) as the final result of the measurement. The method 1 can be applied to one-time measurement in an unscheduled period, does not need to carry out continuous measurement for multiple times, and can be carried out under the conditions of random change and continuous change of the frequency change rate
The measurement process of method 2 is described with reference to fig. 2: the continuous measurement is carried out in the on-line measurement process, the frequency change rate is obtained by subtracting the fundamental wave frequency measured in the previous time from the fundamental wave frequency measured in each time and dividing the frequency by the time interval of the two measurements, and the frequency change rate is substituted into the equations (18), (22), (23) and the equations (13), (14) and (15) to correct the current measurement. In the process of on-line measurement, except that the first measurement cannot be corrected by the method, the subsequent measurement can be corrected by adopting a correction method. The method 2 is mainly applied to a plurality of continuous measurement occasions, is not different from the method 1 in nature, and only aims to improve the real-time performance of the algorithm, the frequency measured in the previous time is used for calculating the frequency change rate of the time, so that the sampling time in continuous online measurement is shortened by half.
Taking a phase difference correction method based on Hanning window as an example, the improved method considering frequency change rate and the traditional method not considering frequency change rate are respectively applied to carry out numerical simulation comparison, so as to verify that the improved phase difference correction method has higher precision and stronger real-time performance than the traditional phase difference correction method,
the frequency correction formula of the conventional method is the same as the formula (13) of the present invention.
The amplitude correction formula is:
the phase correction formula is:
wherein, Δ mkFor the normalized frequency correction amount in equation (12), N is the number of sampling points per sequence in the phase difference correction method, and mkThe peak spectral line number corresponding to the k harmonic.
Since the measured harmonic orders are generally 2 nd to 19 th, the simulation signal model is constructed as follows:
the parameters of each harmonic in the simulated signal are shown in table 1.
TABLE 1 simulation Signal parameters of the harmonics
According to the current technical standard, selecting a proper sampling window length, and considering the accuracy of the algorithm to be ensured, sampling needs at least 4 fundamental wave periods, so the sampling frequency f in the simulationsThe frequency is set to 6400Hz, the length of each section of sampling sequence is N-640 points, and the number of the second section of signal translation points is L-128 points.
Under the setting, frequency change models in four states of stable frequency, large-range fluctuation of fundamental frequency, uncertain but bounded fundamental frequency change and frequency collapse are respectively established so as to verify the measurement accuracy and the real-time performance of the improved phase difference correction method in different running states of the power grid.
1. Simulation analysis under stable frequency
Under the condition of stable operation of the power system, the frequency deviation is generally limited to +/-0.2 Hz. To simulate the stable frequency situation, the frequency variation is modeled in the simulation as follows:
f1＝49.9+0.1×sin(2π×0.1t) (27)
namely, the initial value of the fundamental frequency is 49.9Hz, the signal takes 10s as the period in the measuring process, and sinusoidal change occurs between 49.8Hz and 50 Hz. 10000 consecutive measurements were made using the conventional method and the modified method of the present invention (including method 1 and method 2), respectively, and the total time of the measurements was recorded. Since the Root Mean Square Error (RMSE) reacts very sensitively to the extra large or very small errors in a set of measurements, does not overwhelm the large random errors in the measurements, and can better reflect the accuracy of the measurements, a root mean square error curve of the amplitudes of the harmonics of the conventional methods, method 1 and method 2, is plotted as shown in fig. 3.
As can be seen from fig. 3, compared with the phase difference correction method without taking ROCOF into account, the method 1 and the method 2 have a certain improvement in the measurement accuracy of the amplitude of each harmonic of the signal under the condition of stable frequency, and the measurement accuracy reaches 10 except for the harmonics of 2 and 14-4The accuracy of sub, 5, 15, 17 and 19 harmonics reaches 10-5Next, the process is carried out. The improvement is more pronounced for odd harmonics than for even harmonics. Observing fig. 3, it is found that the difference in measurement accuracy between method 1 and method 2 is not significant. The total time of 10000 times of measurement of the traditional method, the method 1 and the method 2 is 11.356s, 21.028s and 11.557s respectively, so the method 2 has more advantages in real time than the method 1 and is more suitable for online real-time measurement of power harmonics.
2. Simulation analysis under condition of fundamental frequency large-range fluctuation
When the power grid is in a local fault, the fundamental frequency may fluctuate in a large range, and in order to simulate the situation that the fundamental frequency fluctuates in a large range, a frequency change model is set as follows:
f1＝50+7.5×sin(2π×0.2t) (28)
i.e. the fundamental frequency starts at 50Hz, a sinusoidal fluctuation occurs with a period of 5s, with a fluctuation amplitude of ± 7.5 Hz. 10000 times of continuous measurements were performed by the conventional method and the improved method of the present invention (including method 1 and method 2), respectively, and the root mean square error curves of the amplitudes of the harmonics of the conventional method, method 1 and method 2 were plotted as shown in fig. 4.
As can be seen from FIG. 4, the measurement accuracy of the method 1 and the method 2 for the amplitude of each harmonic of the signal is greatly improved in the case of wide-range fluctuation of the fundamental frequency compared with the phase difference correction method without taking ROOF into account, and the measurement accuracy of the harmonic of more than 3 times reaches 10-2Sub, 18 and 19 timesThe accuracy of harmonic wave reaches 10-3Next, the process is carried out. The improvement on odd harmonics is more obvious than the improvement on even harmonics, the measurement accuracy of the odd harmonics is 3-15 times that of the traditional method, and the measurement accuracy of the even harmonics is 1.1-5 times that of the traditional method. The amplitude measurement accuracy of the fundamental wave is 25 times that of the traditional method, the amplitude measurement accuracy is improved by one order of magnitude, the amplitude measurement accuracy of the second harmonic is improved by 25 percent compared with the traditional method, and the accuracy requirement of IEC (International electrotechnical Commission) standard is met. The difference in measurement accuracy between method 1 and method 2 is not significant.
3. Simulation analysis under uncertain fundamental frequency change and bounded condition
When the power system is actually operated, because the change of the load has randomness, the frequency change is often uncertain, and in order to simulate the situation that the fundamental frequency change is uncertain, a model of the fundamental frequency change is set as:
f1(i)＝f1(i-1)+0.001×[2·rand(1)-1](29)
wherein i represents a sampling point number, i is 0,1,2,3, …; f. of1(i) Indicating the fundamental frequency at the sampling instant of the ith sample point.
Setting f1(0) When f is 50, and1(i) if it is greater than 57.5, let f1(i) When f is 57.51(i) When less than 42.5, let f1(i) 42.5. That is, the fundamental frequency starts from 50Hz, random offset within the range of +/-0.001 Hz occurs in each sampling time interval, and the variation range of the fundamental frequency in simulation is 42.5 Hz-57.5 Hz. Since the maximum frequency shift that can occur in each sampling interval is 0.001Hz, the frequency rate of change in the model is + -6.4 Hz/s when the sampling frequency is 6400 Hz. Considering that the system frequency is unlikely to generate frequent abrupt changes in practical situations, it is also necessary to smooth the frequency variation curve. The frequency curve over a certain period of time in the simulation is shown in fig. 5.
Because the method 2 has strong real-time performance, 10000 times of continuous measurement are respectively carried out by comparing the traditional method with the method 2, and a root mean square error curve of each harmonic amplitude of the traditional method and the method 2 is drawn as shown in fig. 6.
As can be seen from FIG. 6The improved phase difference correction method has certain improvement on the measurement accuracy of each harmonic amplitude of the signal under the condition that the fundamental frequency change is uncertain and bounded compared with the phase difference correction method without considering ROOF, and the measurement accuracy reaches 10 except 1,2,3, 4 and 6 harmonics-3Next, the process is carried out. The amplitude measurement accuracy of the fundamental wave is 4.5 times that of the traditional method, the amplitude measurement accuracy of the second harmonic is 4.6 times that of the traditional method, and the amplitude measurement accuracy of other subharmonics is 1.4-2.4 times that of the traditional method. Therefore, when the frequency change is uncertain, the improved phase difference correction method has higher measurement accuracy compared with the traditional method, and is more suitable for the actual measurement of the dynamic power grid.
4. Simulation analysis under frequency collapse
The frequency of the power grid generates large deviation, which causes great damage to the power system and users, and if the power grid suffers from serious active shortage, the frequency may be rapidly reduced, even the frequency is broken down. To simulate the frequency collapse, the frequency change model used was as follows:
f1＝50-3t (30)
i.e. the fundamental frequency starts at 50Hz in normal operation and suddenly collapses in frequency, falling at a rate of-3 Hz/s. Due to the fact that the method 2 is high in real-time performance, the traditional method and the method 2 are used for comparing, signals are respectively measured continuously, when the frequency drop amplitude exceeds 7.5Hz, the measurement is stopped, the average value of the frequency change rate is recorded, and a root mean square error curve of each harmonic amplitude of the traditional method and the method 2 is drawn and is shown in figure 7.
As can be seen from FIG. 7, the improved phase difference correction method of the present invention has a much higher measurement accuracy for each harmonic amplitude of a signal under the condition of frequency collapse than the phase difference correction method without taking ROOF into account, and the measurement accuracy reaches 10 except for the second harmonic-2The accuracy of suborder, 18 and 19 harmonics reaches 10-3Next, the process is carried out. The improvement is more pronounced for odd harmonics than for even harmonics. The accuracy of measuring odd harmonics is 2.5-10 times of that of the original method, the amplitude measurement accuracy of fundamental waves is 46 times of that of the original method, and the amplitude measurement accuracy is improved by one order of magnitude. To pairIn even harmonics, the measurement accuracy of only 14 harmonics is not improved, the measurement accuracy of other even harmonics is 1.2-2.8 times of that of the original method, and the measurement accuracy of the second harmonic is 2.6 times of that of the original method, so that the accuracy requirement of the IEC standard is met. The result of the frequency change rate measurement is-3.00002451273211 Hz/s, which proves that the improved method can accurately calculate the frequency change rate and can also accurately measure the power harmonic parameters in the event of frequency collapse.
5. Real-time analysis of simulations
The IEC standard limits the analysis window length of a 50Hz power system to 10 cycles, i.e. 200 ms. The invention is at the sampling frequency fs6400Hz, under the condition that the length of each sampling sequence is N-640, the measurement accuracy requirement of the IEC standard can be met only by the sampling window length of 100ms, so that the system state can be judged in real time, and major accidents are prevented.
Claims (1)
1. An improved phase difference correction method considering the frequency change rate of a power grid is characterized in that the method is improved on the basis of a traditional phase difference correction method as follows:
assume the fundamental frequency f of the power signal x (t)1By df1Rate of change of/dt, ROOF1＝df1Dt, then the frequency rate of change of the k-th harmonic is ROOFk＝dfk/dt＝k·df1Dt, the frequencies of the first stage signal and the second stage signal are respectively fkAnd f'kThen the frequency offset of the two signals is dfkNamely:
f′k＝fk+dfk(1)
the frequency offset is considered herein to be equal to the product of the frequency rate of change of the signal and time, so that:
dfk＝ROCOFk·t0＝kt0·df1/dt (2)
time length for shifting the second segment signal: t is t0＝L/fsWherein f issFor the sampling frequency, L is the number of points of the second section signal after the first section signal, and is obtained by substituting equation (2):
dfk＝(kL/fs)·df1/dt (3)
since the frequency of the second signal is changed, the initial phase should be corrected toThe phase of the signal after translation is therefore:
the phase of the second segment signal should be corrected to:
the phase difference of the two signals is obtained as follows:
wherein the content of the first and second substances,
is the initial phase angle of k harmonics, T is the sampling window length, phi is the phase after the harmonic signal is cut off by adding a window;
the corrected frequency correction amount is:
when the discrete spectrum correction is carried out, the time length of the second section of signal translation is as follows: t is t0＝L/fsFrequency correction amount:
peak frequency corresponding to this subharmonic: f is mkΔ f may be substituted for the corrected normalized frequency correction amount of equation (6):
where Δ f is the frequency resolution, mkThe peak value spectral line number corresponding to the k-th harmonic wave is obtained, and N is the length of the sampling sequence; in the actual calculation, order
Because the range of the phase is (-pi, pi), the period is 2 pi, and the delta may exceed this interval, the following processing is required: let delta' mod (delta, 2 pi), and let
The corrected normalized frequency correction value after processing is that delta' is in the range of (-pi, pi):
substituting the formula (8) into the correction formula f of frequency, amplitude and phasek＝(mk+Δmk)fs/N、 
Obtaining a corrected frequency, amplitude and phase correction formula, wherein AmkIs the spectral line amplitude, W1(m) is the modulus function of the normalized sampling window spectrum, RkAnd IkIs the real and imaginary parts of the signal;
the calculation result of the phase correction formula is the same as the processing of delta
May not be within the (-pi, pi) interval, therefore, it is also necessary to make
Reissue to order
The results obtained are in the range (-pi, pi)
As a final correction result.
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