CN108957130B - Electric power system harmonic detection method based on instantaneous reactive power theory - Google Patents
Electric power system harmonic detection method based on instantaneous reactive power theory Download PDFInfo
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Abstract
The invention discloses a method for detecting harmonic waves of an electric power system based on an instantaneous reactive power theory, which comprises the following steps: firstly, fast analyzing a power grid signal by using an FFT algorithm, and preliminarily acquiring frequency components of each harmonic and inter-harmonic; then two-phase rotating coordinates with the frequencies of a harmonic positive sequence and a harmonic negative sequence are respectively established, and three-phase signals of the power grid are respectively converted into the two rotating coordinate systems and then are respectively filtered; and finally, obtaining three-phase positive sequence harmonic components and three-phase negative sequence harmonic components through coordinate inverse transformation. The invention can detect the positive sequence harmonic wave, the negative sequence harmonic wave and the harmonic content of each frequency section including the inter-harmonic wave, has simple structure, is easy to realize digitalization and has strong practical value.
Description
Technical Field
The invention relates to a harmonic detection method of an electric power system, in particular to a harmonic detection method of the electric power system based on an instantaneous reactive power theory.
Background
In recent years, the installed capacity of wind power is continuously increased, and high-voltage direct-current transmission lines are more and more, so that the power electronization degree of a power system is higher and higher. As the number of power electronic devices in the power system increases, the harmonic content in the power system becomes extremely complex, and a large number of inter-harmonics also appear, which are all problems to be solved by the harmonic detection technology.
The current common harmonic detection method mainly comprises a filter method, a frequency analysis method, a wavelet analysis method and a harmonic detection method adopting an instantaneous reactive power theory.
The filter method has a simple algorithm structure, but the accuracy and the reliability are poor, and the band-pass filter and the band-stop filter are not easy to realize in engineering. The frequency analysis method generally adopts Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) to analyze the harmonics, and although the amplitude and phase of each subharmonic component can be detected, the window width is limited, so that the method is low in real-time performance, generally suitable for off-line calculation, and often low in precision and reliability when used for real-time harmonic detection. The harmonic detection method based on wavelet transformation can detect fundamental wave active current, reactive current and total harmonic current, but cannot detect the content of each harmonic, and the precision and reliability of the harmonic detection method based on wavelet transformation are poor. The harmonic detection method adopting the instantaneous reactive power theory is based on the instantaneous reactive power theory, and can accurately and reliably detect the harmonic content of the system through coordinate transformation and corresponding calculation.
However, the conventional harmonic detection algorithm based on the instantaneous reactive power theory can only detect the total harmonic content but not the content and phase angle of each harmonic, and is not suitable for some harmonic waves with specific frequency and phase sequence.
Disclosure of Invention
The invention aims to solve the technical problem of providing a power system harmonic detection method based on the instantaneous reactive power theory, which can detect positive sequence harmonics, negative sequence harmonics and harmonic content of each frequency band including inter-harmonics.
The technical scheme adopted by the invention is as follows.
A power system harmonic detection method based on an instantaneous reactive power theory is characterized by comprising the following steps:
(1) for three-phase current or voltage signals X of electric networks(s ═ a, b, c) sampling to obtain discrete sampling signals thereof;
(2) for the discrete sampling signal X in the step (1)sFast analysis is carried out by using an FFT algorithm, and frequency components of each harmonic and inter-harmonic are preliminarily obtained;
(3) mixing XsRespectively converted to frequency fpIn the positive-sequence and negative-sequence two-phase rotating coordinate system to obtain component Xd、Xq；
Wherein f ispThe harmonic frequencies of interest in the harmonics and inter-harmonics obtained in the step (2);
(4) for X in step (3)d、XqLow-pass filtering to obtain
(5) To pair
With an advancing frequency of fpInverse transformation of the positive and negative sequence coordinates to obtain fpThree phase positive and negative sequence harmonic components.
The invention further comprises the following preferred embodiments:
the step (3) specifically comprises the following steps:
3.1 converting the three-phase current or voltage by a Clark transformation matrix (1) to an abc/alpha beta coordinate system:
conversion to frequency fpIn a positive-sequence two-phase rotating coordinate system, the phase angle theta is 2 pi fpt, conversion to frequency fpIn the case of a negative-sequence two-phase rotating coordinate system, the phase angle theta is taken to be-2 pi fpt；θ
3.2 the coordinate system transformation of alpha beta/dq is carried out by a park transformation matrix (2).
The low-pass filtering in the step (4) adopts a first-order low-pass filter with a transfer function Glp(s) is expressed by the formula (3):
in the formula, ωcThe cut-off frequency of the first-order low-pass filter is [0Hz,50Hz ]]And s is the laplacian operator.
In the step (5), coordinate inverse transformation is carried out according to the transformation matrixes (1), (2) and (4) to obtain three-phase positive sequence harmonic components and three-phase negative sequence harmonic components.
Cdq/abc＝(Cαβ/dqCabc/αβ)-1 (4)
Wherein the transformation matrices (1), (2) are as described in 3.1 and 3.2.
Firstly, fast analyzing a power grid signal by using an FFT algorithm, and preliminarily acquiring frequency components of each harmonic and inter-harmonic; then two-phase rotating coordinates with the frequencies of a harmonic positive sequence and a harmonic negative sequence are respectively established, and three-phase signals of the power grid are respectively converted into the two rotating coordinate systems and then are respectively filtered; and finally, obtaining three-phase positive sequence harmonic components and three-phase negative sequence harmonic components through coordinate inverse transformation.
Compared with the prior art, the invention can obtain the following beneficial effects:
the invention provides a novel harmonic detection algorithm based on the basic principle of the instantaneous reactive power theory, which can detect both positive sequence harmonic and negative sequence harmonic, can detect the harmonic content of each frequency section including inter-harmonic, has simple structure, is easy to realize digitalization and has strong practical value.
Drawings
FIG. 1 is a schematic diagram of a method for detecting harmonic waves in an electric power system based on an instantaneous reactive power theory according to the present invention;
FIG. 2 is a schematic diagram of a harmonic detection method under an ideal test signal according to an embodiment of the present invention;
Detailed Description
The technical scheme of the invention is further detailed in the following description and the accompanying drawings.
The invention discloses a method for detecting harmonic waves of an electric power system based on an instantaneous reactive power theory, which is shown in the attached figure 1 and comprises the following steps:
(1) for three-phase current or voltage signals X of electric networks(s ═ a, b, c) sampling to obtain discrete sampling signals thereof;
(2) for the discrete sampling signal X in the step (1)sFast analysis is carried out by using an FFT algorithm, and frequency components of each harmonic and inter-harmonic are preliminarily obtained;
(3) mixing XsRespectively converted to frequency fpObtaining a component X in a two-phase rotating coordinate system of a positive sequence and a negative sequenced、Xq；
Wherein f ispThe harmonic frequencies of interest in the harmonics and inter-harmonics obtained in the step (2);
(4) for X in step (3)d、XqLow-pass filtering to obtain
(5) To pair
With an advancing frequency of fpInverse coordinate transformation of positive and negative sequences to obtain fpThree phase positive and negative sequence harmonic components.
The step (3) comprises the following steps:
3.1 the three-phase current/voltage is transformed by the Clark transformation matrix (1) in the abc/alpha beta coordinate system:
conversion to frequency fpWhen the two phases of the positive sequence rotate the coordinate system, the phase takes theta as 2 pi fpt, conversion to frequency fpWhen the two-phase of the negative sequence rotates the coordinate system, the phase takes theta as-2 pi fpt；
3.2 alpha beta/dq coordinate system transformation by park transformation matrix (2):
low-pass filtering in step (4) by using a first-order low-pass filter with a transfer function Glp(s) is expressed by the formula (3):
in the formula, ωcThe cut-off frequency of the first-order low-pass filter is [0Hz,50Hz ]]The embodiment of the application preferably has the frequency of 10 Hz; s is the laplace operator.
And (5) performing coordinate inverse transformation according to the transformation matrixes (1), (2) and (4) to finally obtain three-phase positive sequence and negative sequence harmonic components.
Cdq/abc＝(Cαβ/dqCabc/αβ)-1 (4)
Wherein the transformation matrices (1), (2) are as described in 3.1 and 3.2.
The invention is illustrated below with reference to the examples of fig. 2 and table 1.
The embodiment of the invention adopts a three-phase current test signal, wherein the test signal comprises a fundamental frequency positive sequence current with the frequency of 50Hz and the amplitude of 100A, a frequency tripling positive sequence component with the frequency of 150Hz and the amplitude of 10A, a frequency quintupling negative sequence component with the frequency of 250Hz and the amplitude of 5A and a negative sequence inter-harmonic component with the frequency of 70Hz and the amplitude of 4A; the initial phase of each harmonic is zero.
The harmonic detection method shown in fig. 2 was used to obtain the harmonic detection results shown in table 1. The results in table 1 show that the harmonic algorithm can accurately detect the positive sequence harmonic and the negative sequence harmonic in each frequency band, not only can detect integer harmonics, but also can detect inter-harmonics, and overcomes the defects of the traditional harmonic detection algorithm based on the instantaneous reactive power theory.
Table 1: harmonic detection result of the embodiment of the invention under ideal test signal
Claims (3)
1. A power system harmonic detection method based on an instantaneous reactive power theory is characterized by comprising the following steps:
(1) for three-phase current or voltage signals X of electric power systems(s ═ a, b, c) sampling to obtain discrete sampling signals thereof;
(2) for the discrete sampling signal X in the step (1)sFast analysis is carried out by using an FFT algorithm, and frequency components of each harmonic and inter-harmonic are preliminarily obtained;
(3) mixing XsRespectively converted to frequency fpObtaining a component X in a two-phase rotating coordinate system of a positive sequence and a negative sequenced、Xq；
Wherein f ispThe frequency of the concerned harmonic in the harmonic and the inter-harmonic obtained in the step (2);
(4) for X in step (3)d、XqLow-pass filtering to obtain
(5) To pair
With an advancing frequency of fpInverse coordinate transformation of positive and negative sequences to obtain fpThree-phase positive and negative sequence harmonic components of (a);
the step (3) specifically comprises the following steps:
3.1, carrying out abc/alpha beta coordinate system transformation on the three-phase current or voltage through a park transformation matrix (1), wherein the transformation matrix is as follows:
when transforming to a two-phase rotating coordinate system with fp positive sequence frequency, the phase angle theta is 2 pi fpt, when transforming to two-phase rotating coordinate system with fp negative sequence frequency, taking phase angle theta as-2 pi fpt；
3.2 transformation of the α β/dq coordinate system by means of the Clark transformation matrix (2):
2. the method for detecting harmonic waves in an electric power system based on the instantaneous reactive power theory according to claim 1, wherein: the low-pass filtering of the step (4) adopts a first-order low-pass filter, and the transfer function expression of the first-order low-pass filter is as shown in formula (3):
in the formula, ωcThe cut-off frequency of the first-order low-pass filter is [0Hz,50Hz ]]。
3. The method for detecting the harmonic waves of the power system based on the instantaneous reactive power theory as claimed in claim 2, wherein: in the step (5), coordinate inverse transformation is carried out according to the transformation matrixes (1), (2) and (4) to finally obtain three-phase positive sequence harmonic components and three-phase negative sequence harmonic components,
Cdq/abc＝(Cαβ/dqCabc/αβ)-1 (4)
the transformation matrices (1) and (2) are as described in 3.1 and 3.2.
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| CN105162137A (en) * | 2015-09-12 | 2015-12-16 | 南昌航空大学 | Reactive and harmonic current detection algorithm in complex power network |
| CN105182106A (en) * | 2015-07-27 | 2015-12-23 | 国家电网公司 | Three-phase phase-controlled rectifier harmonic characteristic analysis method based on Park transformation |
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| CN105182106A (en) * | 2015-07-27 | 2015-12-23 | 国家电网公司 | Three-phase phase-controlled rectifier harmonic characteristic analysis method based on Park transformation |
| CN105162137A (en) * | 2015-09-12 | 2015-12-16 | 南昌航空大学 | Reactive and harmonic current detection algorithm in complex power network |
| CN106771597A (en) * | 2017-03-03 | 2017-05-31 | 燕山大学 | A kind of no phase-locked loop formula SAI harmonic current detecting methods of omission Park conversion |
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