CN108982966B - Harmonic phase angle analysis method based on linear correction algorithm - Google Patents
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Abstract
The invention relates to a harmonic phase angle analysis method based on a linear correction algorithm, which comprises the following steps: (1) samplingW+2Sampling point data (WDetermined by the integration method); (2) from the sampling pointi=0Using quasi-synchronous DFT equations
Analysis ofW+1Obtaining fundamental wave information from data
And
(ii) a (3) From the sampling pointi=1Using quasi-synchronous DFT formula analysisW+1Obtaining fundamental wave information from data
And
(ii) a (4) Using formulas
Calculating the frequency drift of a signal
(ii) a (5) From the sampling pointi=0Using quasi-synchronous DFT formula analysisW+1Obtaining the information of each harmonic wave by the data
And
(ii) a (6) Using formulas
Calculating amplitude angles of the harmonics; (7) using formulas
And linearly correcting harmonic phase angles of the harmonics. The method is beneficial to more accurately obtaining the information of amplitude and phase angles, frequencies and the like of each harmonic wave in the fields of harmonic wave analysis such as power quality monitoring, electronic product production inspection, electrical equipment monitoring and the like.
Description
The application has the following application numbers: 201510258020.3 entitled "a harmonic phase angle analysis method", filed as follows: divisional application of the invention patent application on 19/05/2015.
Technical Field
The invention relates to a high-precision harmonic phase angle analysis method.
Background
The harmonic analysis technology is widely applied to the fields of power quality monitoring, electronic product production inspection, electrical equipment monitoring and the like, and is an important technical means for power grid monitoring, quality inspection and equipment monitoring. The most widely used techniques for harmonic analysis are Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) at present. The harmonic analysis technology combining the quasi-synchronous sampling technology and the DFT technology can improve the accuracy of harmonic analysis, and the formula is as follows:
in the formula:kfor the order of harmonics to be obtained (e.g. fundamental waves)k=1Harmonic of order 3k=3) (ii) a sin and cos are sine and cosine functions, respectively; whilea k Andb k are respectively askReal and imaginary parts of the subharmonics;nis the iteration number;Wdetermined by the integration method, when the complex trapezoidal integration method is adopted,W=nN；
is a primary weighting coefficient;
is the sum of all weighting coefficients;f(i)is the ith sampling value of the analysis waveform;Nis the number of samples in a cycle.
In engineering applications, harmonic analysis always performs finite point sampling and synchronization sampling which is difficult to achieve strictly. Thus, when the quasi-synchronous DFT is applied to harmonic analysis, long-range leakage caused by truncation effect and short-range leakage caused by barrier effect exist, so that the accuracy of the analysis result is not high, even the analysis result is not credible.
FIG. 1 presents an error plot of harmonic analysis for any given example using quasi-synchronous DFT. As can be seen from the figure, the harmonic angle of the quasi-synchronous DFT algorithm has extremely large errors except for 50Hz, and is basically not credible.
Disclosure of Invention
The invention aims to solve the technical problem of providing a high-precision harmonic phase angle analysis method based on a linear correction algorithm so as to effectively improve the analysis error of a quasi-synchronous DFT harmonic analysis technology and obtain a high-precision harmonic analysis result, thereby improving the effectiveness of quality and state judgment of instruments and equipment in the fields of power quality monitoring, electronic product production inspection, electrical equipment monitoring and the like based on a harmonic analysis theory.
The technical scheme for realizing the aim of the invention is to provide a harmonic phase angle analysis method based on a linear correction algorithm, which comprises the following steps:
(1) w +2 sampling point data { f (i) =0,1, …, W +1} are sampled at equal intervals (W is determined by a selected integration method, the invention does not specify a certain integration method, common integration methods include a complex trapezoidal integration method W = nN, a complex rectangular integration method W = N (N-1), a complex simpson integration method W = N (N-1)/2 and the like, and a suitable integration method can be selected according to the practical situation of the application of the invention.
(2) From the sampling pointi=0Start of applying quasi-synchronous DFT formula
(3) from the sampling pointi=1Using quasi-synchronous DFT formula analysisW+1Obtaining fundamental wave information from data
And
；
(4) applying the formula:
calculating the frequency drift of the signal
；
(5) From the sampling pointi=0Begin applying quasi-synchronous DFT formula analysisW+1Obtaining the information of each harmonic wave by the data
And
；
(6) using formulas
Calculating amplitude angles of the harmonics;
(7) using formulas
And linearly correcting harmonic phase angles of the harmonics.
The equally spaced sampling is based on the period of the ideal signal for harmonic analysisTSum frequencyfSampling in one cycleNAt a point, i.e. at a sampling frequency off s =NfAnd is andN≥64。
the samplingW+2The sampling point data is selected according to the selected integration method, if the trapezoidal integration method is adopted, the sampling point data is selected correspondinglyW=nN(ii) a If the complex rectangular integral method is adopted, thenW=n(N-1)(ii) a If the Simpson integration method is adopted, thenW=n(N-1)/2. Then according to the sampling frequencyf s =NfObtaining a sequence of sample point data{f(i),i=0,1,…,W+ 1}，nFor the number of iterations, in generaln≥3(ii) a And finally, carrying out harmonic analysis on the data sequence.
Coefficient of first iteration
By integration methods, ideal period sampling pointsNAnd number of iterationsnDecision, specific derivation procedures see literature [ wearable in the middle of the world ] several problems in quasi-synchronous sampling applications [ J]Electrical measuring and instrumentation, 1988, (2): 2-7.
Drift of signal frequency
Based on the phase angle difference of the fundamental wave of adjacent sampling points and the number of sampling points in an ideal periodNObtained by a fixed relationship of the frequency of the signal
Can also be used for correcting the frequency of fundamental wave and higher harmonic wavef 1 And frequencies of higher harmonicsf k （
）。
The invention has the positive effects that: (1) and (5) analyzing the result of the harmonic phase angle with high precision. As for the analysis example given in FIG. 1, the accuracy of the analysis obtained by the present invention is improved to 10-8Stage (fig. 2).
(2) The method provided by the invention fundamentally solves the problem of low analysis precision of quasi-synchronous DFT harmonic phase angles, does not need to perform complicated inversion and correction, and is simple in algorithm.
(3) Compared with quasi-synchronous DFT, the harmonic analysis technology of the invention only needs to add one sampling point to solve the problem of large error of quasi-synchronous DFT analysis, and is easy to realize.
(4) The invention is technically feasible for improving the existing instrument and equipment, and the analysis result can be improved to 10 without increasing any hardware expense-8And (4) stages.
(5) The method is also suitable for the harmonic analysis process of carrying out multiple iterations instead of one iteration, and only one iteration needs to be decomposed into multiple iterations to realize the harmonic analysis process. One iteration is essentially the same as multiple iterations, except that in the calculation, the multiple iterations are subjected to step-by-step calculation, and the process of the multiple iterations is combined into iteration coefficients in one iteration
The calculation is completed in one time, so the method is also suitable for a plurality of iterative processes.
Drawings
FIG. 1 is a harmonic phase analysis error plot of a quasi-synchronous DFT.
FIG. 2 is a harmonic phase angle analysis error map of the present invention.
Detailed Description
(example 1)
The harmonic phase angle analysis method based on the linear correction algorithm in the embodiment comprises the following steps:
first, sampling at equal intervalsW+2Sampling points to obtain a discrete sequence of the signal to be analyzed{f(i),i=0,1,…, Wq+1}。WBy an integration method, number of iterationsnAnd number of samples taken in an ideal periodNAnd (4) jointly determining.
The equal interval sampling means that: based on the frequency of the desired signal for harmonic analysis (e.g. frequency of power frequency signal)fFor 50Hz with a period of 20 mS) determining the sampling frequencyf S =NfAt the sampling frequencyf S Is uniformly sampled in one periodNAnd (4) point. Generally, periodic sampling pointsN=64Or more, better harmonic analysis result can be obtained, and the iteration timesn=3~5A more ideal harmonic analysis result can be obtained.
The integration method includes various methods such as a trapezoidal integration method, a rectangular integration method, and a simpson method, and can be selected according to actual conditions. If the method of complex trapezoidal integration is adopted, thenW=nN(ii) a If the complex rectangular integral method is adopted, thenW=n (N-1)(ii) a If the Simpson integration method is adopted, thenW=n(N-1)/2。
Second, from the sampling pointi=0Start of applying quasi-synchronous DFT formula
again, from the sampling pointi=1Using quasi-synchronous DFT formula analysisW+1Obtaining fundamental wave information from data
And
；
again, the formula is applied:
calculating the frequency drift of the signal
；
Again, from the sampling pointi=0Begin applying quasi-synchronous DFT formula analysisW+1Obtaining the information of each harmonic from the data
；
Then, apply the formula
Calculating amplitude angles of the harmonics;
finally, the formula is applied
And linearly correcting harmonic phase angles of the harmonics.
It will be appreciated by persons skilled in the art that the above embodiments are only intended to illustrate the present invention, and not to limit the present invention, and that the present invention may be further modified, and that within the spirit and scope of the present invention, changes and modifications to the above described embodiments will fall within the scope of the appended claims.
Claims (2)
1. A harmonic phase angle analysis method based on a linear correction algorithm is characterized by comprising the following steps: the method comprises the following steps:
(1) equidistant samplingW+2Data of each sampling point{f(i),i=0,1,…,W+1}(ii) a The samplingW+2The data of each sampling point adopts a complex Simpson integration method, thenW=n(N-1)/2；
(2) From the sampling pointi=0Start of applying quasi-synchronous DFT formula
Analysis ofW+1Obtaining fundamental wave information from data
And
；
(3) from the sampling pointi=1Using quasi-synchronous DFT formula analysisW+1Obtaining fundamental wave information from data
And
；
(4) applying the formula:
calculating the frequency drift of the signal
；
(5) From the sampling pointi=0Begin applying quasi-synchronous DFT formula analysisW+1Obtaining the information of each harmonic wave by the data
And
；
(6) using formulas
Calculating amplitude angles of the harmonics;
(7) using formulas
Linearly correcting harmonic angles of each harmonic;
in the formula:kthe number of harmonics to be obtained; sin and cos are sine and cosine functions, respectively; whilea k Andb k are respectively askReal and imaginary parts of the subharmonics;nis the iteration number;Wdetermined by an integration method;
is a primary weighting coefficient;
is the sum of all weighting coefficients;f(i)is the ith sampling value of the analysis waveform;Nthe number of sampling times in a period;
in the step (1), the equidistant sampling is based on the period of the ideal signal for harmonic analysisTSum frequencyfSampling in one cycleNAt a point, i.e. at a sampling frequency off s =NfAnd is andN≥64。
2. the harmonic phase angle analysis method based on the linear correction algorithm according to claim 1, characterized in that: in the step (1), the samplingW+2The data of each sampling point is selected according to the selected integration method and then according to the sampling frequencyf s =NfObtaining a sequence of sample point data{f(i),i=0,1,…,W+1}；nIn order to be able to perform the number of iterations,n≥3(ii) a And finally, carrying out harmonic analysis on the data sequence.
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