CN111551785A - Frequency and harmonic detection method based on unscented Kalman filter - Google Patents

Frequency and harmonic detection method based on unscented Kalman filter Download PDF

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CN111551785A
CN111551785A CN202010359460.9A CN202010359460A CN111551785A CN 111551785 A CN111551785 A CN 111551785A CN 202010359460 A CN202010359460 A CN 202010359460A CN 111551785 A CN111551785 A CN 111551785A
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harmonic
frequency
phase
amplitude
unscented kalman
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CN111551785B (en
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吕广强
安路
蒋海峰
王宝华
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G01R23/165—Spectrum analysis; Fourier analysis using filters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

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Abstract

The invention discloses a frequency and harmonic detection method based on unscented Kalman filtering, which defines a fundamental frequency component in an observation state variable, can directly measure the fundamental frequency without a separate frequency measurement algorithm, and solves the problems of inaccurate zero crossing point detection when the harmonic is serious and asynchronous interpolation period method sampling in the existing frequency measurement method, such as a zero crossing point method, which cause linearization error. The amplitude and the phase of each harmonic are directly selected as the components of the state variables, so that the amplitude and the phase information of each harmonic can be directly measured without further calculation; by using unscented Kalman filtering, the problems of frequency spectrum leakage and barrier effect caused by sampling asynchrony of a Fourier transform method during frequency measurement or harmonic measurement are avoided.

Description

Frequency and harmonic detection method based on unscented Kalman filter
Technical Field
The invention relates to the field of power quality detection of power systems, in particular to a frequency and harmonic detection method based on unscented Kalman filtering.
Background
The measurement of frequency in the power system is the basis for the measurement of other parameters of the quality of electric energy. Taking harmonic measurement as an example, the frequency of each harmonic is a multiple of the frequency of the fundamental wave, and if the amplitude and phase of each harmonic are to be measured accurately, the fundamental frequency must be known, i.e., it needs to be measured in advance.
The frequency measurement method comprises a zero crossing point method, wherein the frequency is calculated by detecting the time interval between two zero crossing points of a waveform, but the frequency measurement is inaccurate due to inaccurate zero crossing point detection when harmonic waves are serious, and meanwhile, the problem of zero drift of a device can bring errors to the measurement. The interpolation period method carries out interpolation processing near the zero crossing point, reduces the difficulty of zero crossing point detection, but the sampling is asynchronous, which can cause linearization error. The fourier transform method can be used for measuring frequency and harmonic wave, but the method needs to obtain data of one period before calculation, has poor real-time performance, and has the problems of frequency spectrum leakage and barrier effect caused by the fact that the sampling period and the waveform period are not strictly synchronous. In the traditional algorithm for measuring harmonic waves by Kalman filtering, most state variables are selected as
Figure BDA0002474557930000011
The amplitude and phase cannot be derived directly from the state variables and further calculations are required.
Disclosure of Invention
The invention aims to provide a frequency and harmonic detection method based on unscented Kalman filtering.
The technical scheme for realizing the purpose of the invention is as follows: a frequency and harmonic detection method based on unscented Kalman filtering comprises the following steps:
step 1, establishing a signal model containing harmonic waves:
Figure BDA0002474557930000012
where y is the observed signal, r is the harmonic order, M is the total harmonic order, f is the fundamental frequency, ArIs the amplitude of the order r of the harmonic,
Figure BDA0002474557930000013
is the R harmonic phase, e is zero mean gaussian white noise with covariance R;
step 2, selecting observation state variables:
Figure BDA0002474557930000014
wherein A isr,kIs the magnitude of the order r harmonic at time k,
Figure BDA0002474557930000021
is the phase of the subharmonic of time k, fkIs the fundamental frequency at time k;
step 3, establishing a system dynamic equation and a measurement equation:
Figure BDA0002474557930000022
wherein the content of the first and second substances,
Figure BDA0002474557930000023
Figure BDA0002474557930000024
ηkand ekIs process noise and observation noise, the variance is QkAnd Rk，TsIs the sampling interval;
step 4, performing unscented Kalman filtering to obtain an estimated value of the state variable:
Figure BDA0002474557930000025
wherein the content of the first and second substances,
Figure BDA0002474557930000026
is the amplitude of the r-th harmonic at time k obtained by the algorithm,
Figure BDA0002474557930000027
the phase of the r-th harmonic at time k, obtained by the algorithm, is 1,2, …, M,
Figure BDA0002474557930000028
is obtained by an algorithmThe fundamental frequency at time k.
Compared with the prior art, the invention has the following remarkable advantages: the detection method of the invention gives consideration to the frequency detection problem when establishing the harmonic detection model, does not need a separate frequency measurement algorithm any more, and avoids some problems existing in the existing frequency measurement method; the detection method can directly measure the amplitude and phase information of each harmonic without further calculation; the detection method of the invention avoids the problems of frequency spectrum leakage and barrier effect caused by asynchronous sampling of the Fourier transform method.
Drawings
FIG. 1 is a flow chart of an algorithm used by the present invention.
Fig. 2 is a diagram showing the detection result of the fundamental frequency in the embodiment of the present invention.
FIG. 3 is a diagram illustrating the detection result of each harmonic amplitude in the embodiment of the present invention.
Fig. 4 is a diagram illustrating the detection result of each harmonic phase in the embodiment of the present invention.
Detailed Description
As shown in fig. 1, a frequency and harmonic detection method based on unscented kalman filter includes the following steps:
step 1, establishing a signal model containing harmonic waves:
Figure BDA0002474557930000031
where y is the observed signal, r is the harmonic order, M is the total harmonic order, f is the fundamental frequency, ArIs the amplitude of the order r of the harmonic,
Figure BDA0002474557930000032
is the R harmonic phase, e is zero mean gaussian white noise with covariance R;
step 2, selecting observation state variables:
Figure BDA0002474557930000033
each specific subharmonic has its amplitude and phase in pairTwo components, the fundamental frequency corresponds to one component, where Ar,kIs the magnitude of the order r harmonic at time k,
Figure BDA0002474557930000034
is the phase of the subharmonic of time k, fkIs the fundamental frequency at time k;
step 3, establishing a system dynamic equation and a measurement equation:
Figure BDA0002474557930000035
wherein the content of the first and second substances,
Figure BDA0002474557930000036
Figure BDA0002474557930000037
ηkand ekIs process noise and observation noise, the variance is QkAnd Rk，TsIs the sampling interval;
step 4, performing unscented Kalman filtering to obtain an estimated value of the state variable:
Figure BDA0002474557930000038
wherein the content of the first and second substances,
Figure BDA0002474557930000039
is the amplitude of the r-th harmonic at time k obtained by the algorithm,
Figure BDA00024745579300000310
the phase of the r-th harmonic at time k, obtained by the algorithm, is 1,2, …, M,
Figure BDA00024745579300000312
is the fundamental frequency at time k obtained by the algorithm. These amplitude, phase and frequency information are the final result of the detection method.
The invention selects the state variable
Figure BDA00024745579300000311
The frequency and the amplitude and the phase of each harmonic can be directly measured at one time, a separate frequency measurement algorithm is not needed, the amplitude and the phase are not needed to be further calculated, and the problems of the frequency and harmonic detection method are solved. The unscented Kalman filtering does not need to strictly control the number of sampling points in each waveform period, namely, the problems of frequency spectrum leakage and barrier effect caused by asynchronous sampling of the Fourier transform method do not exist.
The present invention will be described in detail with reference to examples.
Examples
This section will describe the embodiments of the present invention in detail by taking the detection of 3, 5 th harmonic components in the output waveform of the system as an example.
Step 1, generating an expression containing 3 and 5 harmonic components in advance in simulation according to a model set by an algorithm:
Figure BDA0002474557930000041
wherein A is1＝1，
Figure BDA0002474557930000042
A3＝0.23，
Figure BDA0002474557930000043
A5＝0.13，
Figure BDA0002474557930000044
ω＝2πf＝2π×50.1；
Then adding a certain white Gaussian noise signal into the amplitude, the phase and the frequency, and discretizing to simulate the system state:
Figure BDA0002474557930000045
wherein, ηk～N(0,Qk)，Qk＝0.001*[0.04,0.001,0.01,0.0004,0.002,0.0001,0.01]T；
And finally, adding Gaussian white noise with the signal-to-noise ratio of 35dB into the i signal, discretizing, and simulating signals collected by a mutual inductor:
Figure BDA0002474557930000046
wherein, Ts＝0.0002，ekUsed for corresponding to the added Gaussian white noise signal;
step 2, selecting observation state variables:
Figure BDA0002474557930000047
the state variables comprise amplitude phase information of fundamental waves, 3 and 5 harmonics and fundamental wave frequency information;
step 3, establishing a system dynamic equation and a measurement equation:
Figure BDA0002474557930000048
wherein the content of the first and second substances,
Figure BDA0002474557930000049
Figure BDA00024745579300000410
step 4, performing unscented kalman filtering, which mainly comprises two steps of prediction and updating, specifically as follows:
r in the following calculationk＝0.02；
Equation of state prediction
Calculation of Sigma points:
Figure BDA0002474557930000051
Figure BDA0002474557930000052
represents (n + λ) Pk-1Column i of square root, where n is 7 and λ is α2(n + K) -n, α ═ 1 for the scale correction factor, and κ ═ 2 for the prior knowledge of the higher order state distribution;
and (3) prediction:
Figure BDA0002474557930000053
Figure BDA0002474557930000054
Figure BDA0002474557930000055
Figure BDA0002474557930000056
observation equation prediction
Calculation of Sigma points:
Figure BDA0002474557930000057
Figure BDA0002474557930000058
represents (n + λ) Pk|k-1Column i of the square root;
and (3) prediction:
Figure BDA0002474557930000059
Figure BDA00024745579300000510
Figure BDA00024745579300000511
status update
Figure BDA0002474557930000061
Figure BDA0002474557930000062
Figure BDA0002474557930000063
The calculation results of the algorithm are shown in fig. 2, fig. 3, and fig. 4, which are the fundamental frequency detection result, the amplitude detection result of each harmonic, and the phase detection result of each harmonic, respectively.
The detection method of the invention gives consideration to the frequency detection problem when establishing the harmonic detection model, does not need a separate frequency measurement algorithm any more, and avoids some problems existing in the existing frequency measurement method; the detection method can directly measure the amplitude and phase information of each harmonic without further calculation; the detection method of the invention avoids the problems of frequency spectrum leakage and barrier effect caused by asynchronous sampling of the Fourier transform method.
The embodiments and drawings are to describe the function of the invention and not to limit the invention, and any equivalent changes made on the basis of the invention are included in the protection scope of the invention.

Claims (2)

1. A frequency and harmonic detection method based on unscented Kalman filtering is characterized by comprising the following steps:
step 1, establishing a signal model containing harmonic waves:
Figure FDA0002474557920000011
where y is the observed signal, r is the harmonic order, M is the total harmonic order, f is the fundamental frequency, ArIs the amplitude of the order r of the harmonic,
Figure FDA0002474557920000012
is the R harmonic phase, e is zero mean gaussian white noise with covariance R;
step 2, selecting observation state variables:
Figure FDA0002474557920000013
wherein A isr,kIs the magnitude of the order r harmonic at time k,
Figure FDA0002474557920000014
is the phase of the subharmonic of time k, fkIs the fundamental frequency at time k;
step 3, establishing a system dynamic equation and a measurement equation:
Figure FDA0002474557920000015
wherein the content of the first and second substances,
Figure FDA0002474557920000016
Figure FDA0002474557920000017
ηkand ekIs process noise and observation noise, the variance is QkAnd Rk，TsIs the sampling interval;
step 4, performing unscented Kalman filtering to obtain an estimated value of the state variable:
Figure FDA0002474557920000018
wherein the content of the first and second substances,
Figure FDA0002474557920000019
is k times obtained by algorithmThe amplitude of the order r harmonic is carved,
Figure FDA00024745579200000110
the phase of the r-th harmonic at time k, obtained by the algorithm, is 1,2, …, M,
Figure FDA00024745579200000111
is the fundamental frequency at time k obtained by the algorithm.
2. The unscented kalman filter-based frequency and harmonic detection method according to claim 1, wherein in the observation state variables selected in step 2, the amplitude and phase of each specific subharmonic correspond to two components, and the fundamental frequency corresponds to one component.
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