CN110837003B - Double-window full-phase DFT (discrete Fourier transform) synchronous phasor measurement method and system based on triangular window - Google Patents

Double-window full-phase DFT (discrete Fourier transform) synchronous phasor measurement method and system based on triangular window Download PDF

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CN110837003B
CN110837003B CN201911196367.4A CN201911196367A CN110837003B CN 110837003 B CN110837003 B CN 110837003B CN 201911196367 A CN201911196367 A CN 201911196367A CN 110837003 B CN110837003 B CN 110837003B
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金涛
张伟锋
黄宇升
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Fuzhou University
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Abstract

The invention relates to a method and a system for measuring a double-window full-phase DFT synchronous phasor based on triangular windows. The invention is beneficial to ensuring higher measurement precision and shorter response time.

Description

Double-window full-phase DFT (discrete Fourier transform) synchronous phasor measurement method and system based on triangular window
Technical Field
The invention relates to the technical field of synchronous phasor measurement of a power system, in particular to a double-window full-phase DFT synchronous phasor measurement method and system based on a triangular window.
Background
The importance of phasor measurement to each link of a power grid is self-evident, but the importance is limited by cost, in the past, synchronous Phasor Measurement Units (PMUs) are mostly configured in power generation and power transmission links, and with the development of the power grid, phasor measurement units on power distribution and power utilization sides will follow up, so that corresponding research will be more and more. The access of various distributed energy of distribution network side for the structure changes greatly, and the environment is more complicated, and the electric energy quality descends, and stability receives very big challenge, still remains to solve the dynamic real-time supervision of distribution network side, finds that a precision is high, the fast synchronous phasor measurement algorithm of response satisfies the phasor measurement of distribution network and has important meaning.
At present, researches related to phasor measurement are available, new algorithms are continuously proposed, and effects are different. The early zero-crossing point detection method and the digital differential method are rarely applied nowadays, the Kalman filtering method is excellent in state estimation, but the selection of an initial value depends on experience, the specific application of the algorithm is limited by the problems of high precision difference and humanity in the actual power grid environment with harmonic waves and interference, the Discrete Fourier Transform (DFT) method is the most commonly used algorithm for synchronous phasor measurement due to the unique advantage of the DFT method in signal processing, however, the asynchronous sampling caused by power grid frequency fluctuation can cause frequency spectrum leakage and barrier effect, the result error of DFT is increased, and the calculation result is not satisfactory. Therefore, researchers are constantly improving the algorithms to address this problem. These improved algorithms generally fall into the following categories:
the windowing spectral line interpolation method inhibits the frequency spectrum leakage by continuously searching good window functions which generally have the advantages of small sidelobe peak value level and large sidelobe gradual attenuation rate, such as a Nuttall window, a Kaiser window, a self-convolution window of each window and the like; in addition to improving the window function, adding spectral lines for calculation theoretically also improves the accuracy of the algorithm, because spectral line interpolation can suppress the fence effect, and the current algorithms usually mainly use double spectral lines, three spectral lines and four spectral lines. Although the windowing spectral line interpolation method can achieve high calculation accuracy, the premise is that the number of sampling points required by each DFT is too large, the response speed is low, the calculation amount of the algorithm is large, and the real-time performance is greatly reduced.
Another algorithm derives from the DFT itself and corrects the error caused by non-synchronous sampling, so that the calculation result is more accurate, but the measurement accuracy is reduced when the frequency offset is large, and the requirement cannot be met well.
Disclosure of Invention
In view of this, the present invention provides a method and a system for dual-window full-phase DFT synchronous phasor measurement based on a triangular window, which is beneficial to ensuring higher measurement accuracy and shorter response time.
The invention is realized by adopting the following scheme: a double-window full-phase DFT synchronous phasor measurement method based on triangular windows utilizes two triangular windows to preprocess collected signals, carries out Fourier transform on the processed data to obtain high-precision phase angle estimation, carries out frequency spectrum correction based on a time shift phase difference correction method to obtain the estimation result of frequency and amplitude, and realizes the measurement of synchronous phasor.
Further, the method specifically comprises the following steps:
step S1: intercepting the signal sequence, intercepting 3N-1 sampling points, and taking the first 2N-1 points as a first subsequence x1(N) taking the last 2N-1 points as a second subsequence x2(n)；
Step S2: performing full-phase data preprocessing on the two subsequences;
step S3: DFT calculation is carried out on the preprocessing result to obtain a phase value of a main spectral line
Figure BDA0002294754900000021
And
Figure BDA0002294754900000022
step S4: the phase estimation is carried out, the full-phase DFT algorithm has phase invariance, the obtained phase value has high precision and does not need to be corrected further, and therefore the phase estimation values of the two sequences are the phase values of the main spectral line
Figure BDA0002294754900000031
And
Figure BDA0002294754900000032
step S5: performing frequency estimation, and calculating the frequency according to the relation between the phase difference and the frequency of the two subsequences;
step S6: carrying out amplitude estimation, and correcting the amplitude by applying a full-phase time-shifting phase difference correction method to obtain high-precision amplitude estimation;
step S7: and judging whether the calculation reaches a preset condition, if so, ending, and otherwise, returning to the step S1.
Further, step S2 is specifically: the convolution window is formed by convolution of two triangular windows with the length of N, wherein the time domain expression of the triangular window is as follows:
Figure BDA0002294754900000033
wherein N is 0,1,2, …, N-1;
multiplying the two subsequences obtained in step S1 by convolution window to obtain two groups of products of 2N-1 points, and adding the data of N points at the interval of the products to obtain two groups of preprocessing results y with length of N1(n)、y2(n)。
Further, step S5 specifically includes the following steps:
step S51: the relationship between the phase difference and the frequency of the two subsequences is:
Figure BDA0002294754900000034
in the formula, n0Delaying the second sequence by the number of samples of the first sequence, omega*＝2πβ/N＝2πfTsIs the true angular frequency of the signal, f is the frequency of the signal, TsThe sampling interval time is, beta is the actual spectral line position of the signal in the frequency spectrum;
step S52: in fact, for algorithmic reasons, the phase difference
Figure BDA0002294754900000041
Is limited to [ -2 π,2 π]This is called "phase ambiguity", and therefore the present invention corrects the phase difference using the following equation:
Figure BDA0002294754900000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002294754900000043
is the phase difference to be corrected; setting default frequency resolution as ideal fundamental frequency f of power grid0And obtaining the frequency offset rate as follows:
Figure BDA0002294754900000044
step S53: delay value n0Selecting as N, and calculating the frequency offset ratio
Figure BDA0002294754900000045
The formula of (c) is simplified as:
Figure BDA0002294754900000046
step S54: the frequency estimate was obtained as:
Figure BDA0002294754900000047
further, step S6 specifically includes the following steps:
step S61: the magnitude spectrum function of the triangular window is:
Figure BDA0002294754900000048
the calculation formula of the double-window apDFT is as follows:
Figure BDA00022947549000000410
where w is 2 π k/N, the kth line angular frequency, ω*＝2πβ/N＝2πfTsF (—) is the frequency spectrum of the window function, a is the actual amplitude of the signal,
Figure BDA0002294754900000049
is the actual phase of the signal;
step S62: there are two equations in step S61 to obtain an amplitude estimate as:
Figure BDA0002294754900000051
the invention also provides a triangular window-based double-window full-phase DFT synchronous phasor measurement system, which comprises a memory, a processor and a computer program stored on the memory and capable of being executed by the processor, wherein the processor can realize the method steps when the computer program is executed.
The present embodiment also provides a computer-readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the method steps as described above.
Compared with the prior art, the invention has the following beneficial effects:
1. the method has simple form and small calculation amount.
2. The method has high phasor measurement precision and better real-time performance.
3. The method of the invention can still keep higher precision when the frequency deviation is serious, and has good performance under the dynamic condition of the power grid.
4. The method has strong anti-interference capability and still meets the requirement of synchronous phasor measurement in harmonic and noise environments.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
FIG. 2 is a schematic block diagram of full phase data preprocessing according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of a specific process of full-phase time-shift phase difference spectrum calibration according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1 to fig. 3, this embodiment provides a method for measuring a synchronous phasor by using a dual-window full-phase DFT based on triangular windows, which preprocesses an acquired signal by using two triangular windows, performs fourier transform on the processed data to obtain a high-precision phase angle estimation, and performs spectrum correction based on a time-shift phase difference correction method to obtain an estimation result of frequency and amplitude, thereby achieving measurement of the synchronous phasor.
In this embodiment, the method specifically includes the following steps:
step S1: intercepting the signal sequence, intercepting 3N-1 sampling points, and taking the first 2N-1 points as a first subsequence x1(N) taking the last 2N-1 points as a second subsequence x2(n)；
Step S2: performing full-phase data preprocessing on the two subsequences;
step S3: DFT calculation is carried out on the preprocessing result to obtain a phase value of a main spectral line
Figure BDA0002294754900000061
And
Figure BDA0002294754900000062
step S4: the phase estimation is carried out, the full-phase DFT algorithm has phase invariance, the obtained phase value has high precision and does not need to be corrected further, and therefore the phase estimation values of the two sequences are the phase values of the main spectral line
Figure BDA0002294754900000063
And
Figure BDA0002294754900000064
step S5: performing frequency estimation, and calculating the frequency according to the relation between the phase difference and the frequency of the two subsequences;
step S6: carrying out amplitude estimation, and correcting the amplitude by applying a full-phase time-shifting phase difference correction method to obtain high-precision amplitude estimation;
step S7: and judging whether the calculation reaches a preset condition, if so, ending, and otherwise, returning to the step S1.
As shown in fig. 2, in this embodiment, step S2 specifically includes: the convolution window is formed by convolution of two triangular windows with the length of N, wherein the time domain expression of the triangular window is as follows:
Figure BDA0002294754900000071
wherein N is 0,1,2, …, N-1;
multiplying the two subsequences obtained in step S1 by convolution window to obtain two groups of products of 2N-1 points, and adding the data of N points at the interval of the products to obtain two groups of preprocessing results y with length of N1(n)、y2(n) of (a). FIG. 2 is a flow chart illustrating a process of one set of sub-sequences.
In this embodiment, step S5 specifically includes the following steps:
step S51: the relationship between the phase difference and the frequency of the two subsequences is:
Figure BDA0002294754900000072
in the formula, n0Delaying the second sequence by the number of samples of the first sequence, omega*＝2πβ/N＝2πfTsIs the true angular frequency of the signal, f is the frequency of the signal, TsThe sampling interval time is, beta is the actual spectral line position of the signal in the frequency spectrum;
step S52: in fact, for algorithmic reasons, the phase difference
Figure BDA0002294754900000073
Is limited to [ -2 π,2 π]This is called "phase ambiguity", and therefore the present invention corrects the phase difference using the following equation:
Figure BDA0002294754900000081
in the formula (I), the compound is shown in the specification,
Figure BDA0002294754900000082
is the phase difference to be corrected; setting default frequency resolution as ideal fundamental frequency f of power grid0And obtaining the frequency offset rate as follows:
Figure BDA0002294754900000083
step S53: delay value n0Selecting as N, and calculating the frequency offset ratio
Figure BDA0002294754900000084
The formula of (c) is simplified as:
Figure BDA0002294754900000085
step S54: the frequency estimate was obtained as:
Figure BDA0002294754900000086
in this embodiment, step S6 specifically includes the following steps:
step S61: the magnitude spectrum function of the triangular window is:
Figure BDA0002294754900000087
the calculation formula of the double-window apDFT is as follows:
Figure BDA0002294754900000089
where w is 2 π k/N, the kth line angular frequency, ω*＝2πβ/N＝2πfTsF (—) is the frequency spectrum of the window function, a is the actual amplitude of the signal,
Figure BDA0002294754900000088
is the actual phase of the signal;
step S62: there are two equations in step S61 to obtain an amplitude estimate as:
Figure BDA0002294754900000091
the present embodiment also provides a triangular window-based dual-window full-phase DFT synchronized phasor measurement system, including a memory, a processor and a computer program stored on the memory and capable of being executed by the processor, where the processor is capable of implementing the method steps as described above when executing the computer program.
The present embodiment also provides a computer-readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the method steps as described above.
With the development of the current power distribution network, the synchronized phasor measurement is increasingly applied to the power distribution network side, and the complex environment of the power distribution network side also puts higher requirements on the synchronized phasor measurement technology. The traditional algorithm or the calculation amount is large, and the real-time performance is poor; or the precision is not high and the anti-interference capability is weak. In order to make up for the deficiencies of the conventional algorithm and improve the phasor measurement precision, the synchronization phasor measurement algorithm of the double-window full-phase DFT based on the triangular window provided by the embodiment utilizes two triangular windows to preprocess the acquired signals, performs fourier transform on the processed data, and performs frequency spectrum correction based on a time-shift phase difference correction method to obtain the estimation results of frequency, amplitude and phase angle. The method has the advantages of high measurement precision, high response speed and the like, and has good anti-interference capability.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.

Claims (6)

1. A double-window full-phase DFT synchronous phasor measurement method based on triangular windows is characterized in that collected signals are preprocessed by two triangular windows, processed data are subjected to Fourier transform to obtain high-precision phase angle estimation, frequency spectrum correction is carried out based on a time shift phase difference correction method to obtain estimation results of frequency and amplitude, and measurement of synchronous phasors is achieved;
the method for preprocessing the acquired signals by utilizing the two triangular windows specifically comprises the following steps:
step S1: intercepting the signal sequence, intercepting 3N-1 sampling points, and taking the first 2N-1 points as a first subsequence x1(N) taking the last 2N-1 points as a second subsequence x2(n)；
Step S2: performing full-phase data preprocessing on the two subsequences;
wherein, step S2 specifically includes:
the convolution window is formed by convolution of two triangular windows with the length of N, wherein the time domain expression of the triangular window is as follows:
Figure FDA0002710623370000011
wherein N is 0,1,2, …, N-1;
multiplying the two subsequences obtained in step S1 by convolution window to obtain two groups of products of 2N-1 points, and adding the data of N points at the interval of the products to obtain two groups of preprocessing results y with length of N1(n)、y2(n) 。
2. The method for measuring the synchronous phasor by the dual-window full-phase DFT synchronous phasor based on the triangular window as claimed in claim 1, wherein the step of performing Fourier transform on the processed data to obtain high-precision phase angle estimation, and performing spectrum correction based on a time shift phase difference correction method to obtain the estimation result of frequency and amplitude, so as to realize the measurement of the synchronous phasor specifically comprises the following steps:
step S3: DFT calculation is carried out on the preprocessing result to obtain a phase value of a main spectral line
Figure FDA0002710623370000021
And
Figure FDA0002710623370000022
step S4: performing phase estimation, wherein the phase estimation values of the two sequences are phase values of the main spectral line
Figure FDA0002710623370000023
And
Figure FDA0002710623370000024
step S5: performing frequency estimation, and calculating the frequency according to the relation between the phase difference and the frequency of the two subsequences;
step S6: carrying out amplitude estimation, and correcting the amplitude by applying a full-phase time-shifting phase difference correction method to obtain high-precision amplitude estimation;
step S7: and judging whether the calculation reaches a preset condition, if so, ending, and otherwise, returning to the step S1.
3. The method of claim 2, wherein the step S5 specifically includes the following steps:
step S51: the relationship between the phase difference and the frequency of the two subsequences is:
Figure FDA0002710623370000025
in the formula, n0Delaying the second sequence by the number of samples of the first sequence, omega*＝2πβ/N＝2πfTs，ω*Is the true angular frequency of the signal, f is the frequency of the signal, TsFor the sampling interval time, beta is the actual spectral line position of the signal in the spectrum；
Step S52: the phase difference is corrected using the following equation:
Figure FDA0002710623370000026
in the formula (I), the compound is shown in the specification,
Figure FDA0002710623370000027
is the phase difference to be corrected; setting default frequency resolution as ideal fundamental frequency f of power grid0And obtaining the frequency offset rate as follows:
Figure FDA0002710623370000028
step S53: the second sequence being delayed by the number n of samples of the first sequence0Selecting as N, and calculating the frequency offset ratio
Figure FDA0002710623370000031
The formula of (c) is simplified as:
Figure FDA0002710623370000032
step S54: the frequency estimate was obtained as:
Figure FDA0002710623370000033
4. the method of claim 2, wherein the step S6 specifically includes the following steps:
step S61: the magnitude spectrum function of the triangular window is:
Figure FDA0002710623370000034
the calculation formula of the double-window apDFT is as follows:
Figure FDA0002710623370000035
where ω is 2 π k/N, ω is the kth line angular frequency, ω is*＝2πβ/N＝2πfTs，ω*F (×) is the frequency spectrum of the window function, a is the actual amplitude of the signal,
Figure FDA0002710623370000036
is the actual phase of the signal; y isap(k) Is a double window apDFT;
step S62: the amplitude estimate is obtained from the two equations in step S61 as:
Figure FDA0002710623370000037
in the formula (I), the compound is shown in the specification,
Figure FDA0002710623370000038
is the frequency offset rate.
5. A triangular window based dual-window full-phase DFT synchronous phasor measurement system, comprising a memory, a processor and a computer program stored on the memory and executable by the processor, characterized in that the processor is capable of implementing the method steps of any of claims 1-4 when executing the computer program.
6. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method steps of any one of claims 1 to 4.
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