CN109687474A - Referential current detection algorithm and system based on Kalman filtering - Google Patents
Referential current detection algorithm and system based on Kalman filtering Download PDFInfo
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- H—ELECTRICITY
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- 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
- Y02E40/50—Arrangements for eliminating or reducing asymmetry in polyphase networks
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Abstract
The invention discloses a kind of referential current detection algorithm and system based on Kalman filtering, comprising: the load current instantaneous value in measurement threephase load；It is converted using clark, by the load current instantaneous value conversion in threephase load into alpha-beta two-phase orthogonal coordinate system: obtaining instantaneous active electric current i by coordinate transformpWith reactive current iq；Based on ip_iqEstablish discrete system state equation and measurement equation；Using Kalman filter to ipAnd iqIt is filtered, obtains DC component；Fundamental positive sequence electric current is obtained by coordinate inverse transformation, fundamental positive sequence electric current and load current are subtracted each other to obtain total compensation electric current.The method of the present invention can quickly track the variation of load current, compensation current-order reference signal be detected, compared with the algorithm for using Butterworth LPF, its detection speed is fast, real-time is good, and three-phase amplitude fluctuations are small, so that compensation speed is faster, effect is more reliable.
Description
Technical Field
The invention relates to an instruction current detection algorithm and system of Kalman filtering.
Background
With the development and application of power electronic technology, power electronic equipment is widely applied to a three-phase four-wire system power system, so that harmonic pollution is increasingly serious, the power grid loss is increased, the service life of the electrical equipment is shortened, and the like. The three-phase load access is easy to be asymmetrical, so that three phases are unbalanced, zero line current is generated, and if the zero line current is too large, power equipment can be burnt. Most of the power quality regulators have the functions of compensating harmonic waves, three-phase imbalance and the like and improving the power quality. The real-time performance of the detection of the compensation current command signal is one of the main factors influencing the compensation effect of the power quality regulator.
The traditional command current detection algorithm has fast Fourier in frequency domainA transform (FFT) algorithm, a Discrete Fourier Transform (DFT) algorithm and the like, but the algorithm is complex, the calculated amount is large, and the generated delay is large; in the time domain, i is mainly based on the theory of instantaneous reactive powerp-iqMethod and id-iqIn the method, a Butterworth Filter (BF) is commonly used in the algorithm for ip(or i)d) And iqFiltering is carried out to obtain a direct current component, and then inverse transformation is carried out, but the inherent delay characteristic of BF makes the detection real-time ratio worse.
The prior art proposes that good detection precision and good dynamic response can be obtained by comprehensively utilizing an average filter and BF, but the complexity of an algorithm is increased by utilizing the two filters simultaneously; in the prior art, i is realized by using a variable step LMS algorithmp_iqIn theory, the function of the low-pass filter is to apply the autocorrelation function of the current error and the last error to control the step updating, so that the noise interference is eliminated to a certain extent, but the tracking waveform can generate a certain steady-state offset error, and when the load suddenly changes, the tracking precision can be reduced.
Disclosure of Invention
In order to solve the problems, the invention provides an instruction current detection algorithm and system based on Kalman filtering, which can quickly track the change of load current, detect a compensation current instruction reference signal, and have higher compensation speed and more reliable effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
in one or more embodiments, a kalman filter-based instruction current detection algorithm is disclosed, including:
measuring load current transients i in a three-phase loada，ib，ic；
And transforming the instantaneous value of the load current in the three-phase load into α - β two-phase orthogonal coordinate system by utilizing a clark transformation:
obtaining instantaneous active current i through coordinate transformationpAnd a reactive current iq；
Based on ip_iqEstablishing a state equation and a measurement equation of a discrete system;
using Kalman filter to the active current ipAnd a reactive current iqFiltering to obtain a direct current component;
and obtaining fundamental wave positive sequence current through coordinate inverse transformation, and subtracting the fundamental wave positive sequence current from the load current to obtain total compensation current.
Further, by means of clark transformation, the load current instantaneous value in the three-phase load is transformed into α - β two-phase orthogonal coordinate system, specifically:
wherein,
further, the instantaneous active current i is obtained through clark transformation and coordinate transformationpAnd a reactive current iqThe method specifically comprises the following steps:
wherein,ω is the fundamental angular frequency.
Further, based on ip_iqMethod for establishing discrete system stateThe equation for measuring and measuring is specifically as follows:
for active current ip：
Wherein,being a state transition matrix, Hp1×16For measuring the matrix, Xp16×1(k +1) is the k +1 value of the active current state variable, Xp16×1(k) K value for active current state variable, w (k) process noise, v (k) measurement noise, zp (k) active current measurement;
for reactive current iq：
Being a state transition matrix, Hq1×16For measuring the matrix, Xq16×1(k +1) is the k +1 th value of the reactive current state variable, Xq16×1(k) K value for reactive current state variable, w (k) process noise, v (k) measurement noise, zq (k) reactive current measurement.
Further, the Kalman filter is utilized to process the active current ipAnd a reactive current iqFiltering to obtain a direct current component, specifically:
setting initial values of state variables according to the established state equation and measurement equation of the discrete system, substituting the initial values into a Kalman filtering algorithm formula, and performing cyclic recursion in sequence to obtain the state variables of each moment, wherein Xq111And Xp111The active direct current component and the reactive direct current component of the fundamental wave are respectively;xq is added111And Xp111And obtaining the three-phase fundamental current after inverse transformation.
In one or more embodiments, a kalman filter-based instruction current detection system includes a server, where the server includes a memory, a processor, and a computer program stored in the memory and running on the processor, and the processor implements the kalman filter-based instruction current detection method when executing the computer program.
In one or more embodiments, a computer-readable storage medium is disclosed, on which a computer program is stored, which, when executed by a processor, performs the above-described kalman-filter-based instruction current detection method.
Compared with the prior art, the invention has the beneficial effects that:
the method can quickly track the change of the load current and detect the compensation current instruction reference signal, and compared with the algorithm using the Butterworth LPF, the method has the advantages of high detection speed, good real-time performance and small three-phase amplitude fluctuation, so that the compensation speed is higher and the effect is more reliable.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a Kalman filtering based command current detection method;
FIG. 2 is a three-phase load current waveform diagram;
FIG. 3 is a waveform diagram of a KF-based compensation current command signal;
FIG. 4 is a KF-based three-phase fundamental current signal waveform diagram;
FIG. 5 is a KF-based three-phase fundamental current stabilization error waveform;
FIG. 6 is a KF-based three-phase fundamental current stabilization error waveform after sudden loading;
FIG. 7 is a waveform diagram of a compensation current command signal based on a Butterworth LPF;
FIG. 8 is a three-phase fundamental current waveform diagram based on a Butterworth LPF;
FIG. 9 is a three-phase fundamental current stabilization error waveform diagram based on a Butterworth LPF;
FIG. 10 is a three-phase fundamental current stabilization error waveform diagram based on a Butterworth LPF after a load is suddenly applied.
Detailed Description
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.
Example one
In one or more embodiments, a kalman filter based command current detection algorithm is disclosed, as shown in fig. 1, and includes: first to ia，ib，icPerform a clark transform and C2s/2rTransforming to obtain ip，iq. Based on i againp_iqAfter a state equation and a measurement equation of a discrete system are established, a Kalman filter is used for ip，iqAnd filtering to obtain a direct current component, performing inverse transformation to obtain a fundamental wave positive sequence current, and subtracting the fundamental wave positive sequence current from the load current to obtain a total compensation current.
Load current transient i in a three-phase loada，ib，icMeasured by a current transformer. The load current in the three-phase asymmetric load system is expressed as follows:
wherein subscripts 1, 2, 0 represent positive, negative, zero sequence components, respectively; i is0＝I0nsin(hwt+θ0n) For the zero-sequence current component, n is the highest harmonic to be considered, θhIs the phase angle of the h harmonic current; i is1hIs the amplitude of the h-th harmonic positive sequence current, I2hBit h subharmonic negative sequence component amplitude; ω 2 pi f is the fundamental angular frequency.
And transforming the three-phase load current into a α - β two-phase orthogonal coordinate system by utilizing a clark transformation:
wherein:then substituting to obtain:
from the above equation, i after coordinate transformationα，iβHas no zero sequence component.
And then instantaneous active and reactive currents are obtained through conversion:
wherein:
substituting the formula to obtain:
at this time, ip，iqContaining a dc component and an ac component.
Based on ip_iqEstablishing a state equation and a measurement equation; formula (4):
with ipFor example, for ipThe nth harmonic of (1) is:
decomposing to obtain:
any subharmonic contains four components.
Thereby selecting the state variables:
then the discrete state equation for the nth harmonic is:
and the state transition matrix phi is equal to I4Is an identity matrix of 4 orders; in the formula, the first digits 1 and 2 in the subscript represent positive sequence and negative sequence, the middle n represents harmonic degree, and the third digits 1 and 2 represent the several components in the positive sequence and the negative sequence.
The measurement equation according to equation (6) is:
wherein Hp (k) is [ cos (n-1) delta-sin (n-1) delta-cos (n +1) delta sin (n +1) delta ]
Wherein: δ ω kT, T is the sampling period and k is the sampling point.
If the fundamental wave and multiple harmonics are considered simultaneously, only a state column vector is formed by correspondingly combining state variables of the fundamental wave and the harmonics in sequence, and a state equation and a measurement equation are written in a column.
Same reason for iqEstablishing a discrete state equation and a measurement equation of the n-th harmonic:
wherein:
Hq(k)＝[cos(n-1)δ sin(n-1)δ cos(n+1)δ sin(n+1)δ]。
considering that the nonlinear load current contains not only fundamental wave but also harmonic wave, mainly considering 3, 5 and 7 harmonics, there are 16 state variables. Respectively establish the base on ip_iqDiscrete system equations.
For ipComprises the following steps:
wherein,being a state transition matrix, Hp1×16For measuring the matrix, Xp16×1(k +1) is the k +1 value of the active current state variable, Xp16×1(k) K value for active current state variable, w (k) process noise, v (k) measurement noise, zp (k) active current measurement;
wherein the state transition matrix:is a 16-order identity matrix;
measuring a matrix:
Hp1×16＝[1 0 -cos2δ sin2δ cos2δ -sin2δ -cos4δ sin4δ
cos4δ -sin4δ -cos6δ sin6δ cos6δ -sin 6δ -cos8δ sin8δ]
for i in the same wayqComprises the following steps:
wherein,being a state transition matrix, Hq1×16For measuring the matrix, Xq16×1(k +1) is the k +1 th value of the reactive current state variable, Xq16×1(k) K value for reactive current state variable, w (k) process noise, v (k) measurement noise, zq (k) reactive current measurement.
Wherein the state transition matrix:namely a 16-order identity matrix;
measuring a matrix:
Hq1×16＝[1 0 cos2δ sin2δ cos2δ sin2δ cos4δ sin4δ
cos4δ sin4δ cos6δ sin6δ cos6δ sin6δ cos8δ sin8δ]
after a system discrete equation is established, setting an initial value i of a state variablepAnd iqTaking the same initial value: x (0|0) [ 0000000000000000 ]]TInitial covariance value P (0|0) ═ 10I16×16The selection of the noise in the system process and the noise in the measurement can influence the speed and the precision of the filtering, and the comprehensive consideration is that R is 0.01 and Q is 0.012I16×16. Then substituting the state variable into a Kalman filtering algorithm formula, and circularly recurrently obtaining the state variable of each moment, wherein Xq111And Xp111Is the fundamental dc component. Therefore, only Xq is required111And Xp111And obtaining three-phase fundamental current after inverse transformation, and subtracting the three-phase fundamental current from the three-phase load current to finally obtain the total command current needing to be compensated.
And simulating the three-phase load unbalanced harmonic current by using MATLAB (matrix laboratory) according to the listed initial values and the established state transition matrix and observation matrix to verify the validity of the detection algorithm of the Kalman filter. And compared and analyzed with a command signal and fundamental current obtained by a detection algorithm using a Butterworth low-pass filter. The simulation power supply system is a three-phase four-wire system, the input voltage is 380v, the three-phase load is a three-phase diode inverter bridge with an inductive load, the B-phase diode inverter bridge is connected in parallel with the single-phase diode inverter bridge with the inductive load, the fundamental frequency f is 50hz, the sampling frequency is 100khz, and the simulation time is 0.4 s. At 0.2s, a resistive-inductive load was connected in parallel at B.
Defining a method for calculating the reaching of the three-phase current instantaneous value to a stable point: taking a transition period and a stable period which correspond to each phase period and have equal length, taking the difference of the current instantaneous values of corresponding points, and recording the difference as a stable error, wherein when the stable error | e | of the three-phase current instantaneous values is less than 0.01A, the moment is considered as the moment reaching the stability.
As shown in fig. 2, it can be seen from fig. 2 that the amplitude fluctuation of the load current at the beginning of the simulation is small, but the ripple content is large. It is calculated by definition that the reduction of the load current ripple reaches a steady state after 3600 points (1.8 cycles) from the start of the simulation. After the load was suddenly applied at 20k point (0.2s), it was calculated by definition that the stabilization was achieved at 850 points. I.e. the load current reaches a steady state after a sudden load application over 0.43 cycles.
The three-phase compensation command signal obtained based on the kalman filter is shown in fig. 3, and the three-phase fundamental current is shown in fig. 4.
As can be seen from fig. 3 and 4, the detection algorithm based on KF can detect and obtain three-phase compensation command signals and stable and balanced three-phase fundamental currents. From the simulation, according to the method of calculating the stabilization point by definition, it is found that the three-phase fundamental current is stabilized with the stabilization error | e | <0.01A of the three-phase fundamental current after 1100 points (0.55 cycles) as shown in fig. 5. After the three-phase fundamental current is stabilized, the absolute value of the error of every two of the peak values of the three-phase fundamental current is calculated to be less than 0.01A, so that the three-phase balance is achieved when the three-phase fundamental current is stabilized.
After the load is suddenly added at the position of 0.2s, the detection algorithm based on the Kalman filter can also obtain a three-phase compensation command signal and stable and balanced three-phase fundamental current. According to the method of calculating the stable point by definition, it is found that as shown in fig. 6, when the stable error | e | <0.01A occurs after 1200 points (0.6 cycles) have passed since the load was suddenly applied, the three-phase fundamental current becomes stable. After the three-phase fundamental current is stable, the absolute value of the difference between every two peak values of the three-phase fundamental current is calculated to be less than 0.01A, so that three-phase balance is achieved when the three-phase fundamental current is stable.
To compare the real-time performance of the proposed algorithm, a comparison is made with the detection algorithm of a Butterworth low-pass filter. Fig. 7 and 8 show three-phase compensation current command signals and three-phase fundamental currents obtained by the algorithm, respectively.
From the simulation, according to the method of calculating the stabilization point by definition, as shown in fig. 9, the three-phase fundamental current stabilization error | e | <1A after 2 cycles (4000 points) until the stabilization error | e | <0.01A after the 4.5 th cycle (9000 points). And calculating the difference between every two of the three-phase fundamental wave peak currents after 4.5 periods to obtain the maximum error absolute value of 0.11A.
After the load is suddenly applied at 0.2s, according to the method of calculating the stable point by definition, as shown in fig. 10, the stable error | e | <0.5A after 2 cycles (4000 points) from the sudden load until the stable error | e | <0.01A after the 4.5 th cycle (9000 points). And calculating the difference between every two of the three-phase fundamental wave peak currents after 4.5 periods to obtain the maximum error absolute value of 0.36A.
According to the analysis, the detection algorithms of the two filters can be used for detecting the three-phase balanced fundamental current and the three-phase unbalanced harmonic current to be compensated. When command signals obtained based on a KF detection algorithm are compensated, three-phase fundamental wave current reaches a stable and balanced state through 0.55 cycles; the detection algorithm based on the Butterworth LPF needs 4.5 cycles before reaching the stable state, and the three-phase amplitude fluctuates.
When the system is loaded suddenly, the detection algorithms of the two filters can be used for detecting the three-phase unbalanced harmonic current and the three-phase balanced fundamental current which need to be compensated. When compensation is carried out by using a compensation command signal obtained by a KF detection algorithm, the three-phase fundamental current reaches a stable and balanced state through 0.6 period. And based on the Butterworth LPF, the three-phase fundamental current needs 4.5 cycles to reach a stable state, and the three-phase amplitude fluctuates.
Therefore, the provided compensation current detection algorithm based on KF can quickly track the change of load current and detect a compensation current instruction reference signal, and compared with the algorithm using a Butterworth LPF, the algorithm has the advantages of high detection speed, good real-time performance and small three-phase amplitude fluctuation, so that the compensation speed is higher, and the effect is more reliable.
Example two
In one or more embodiments, a kalman filter based instruction current detection system includes a server, where the server includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the kalman filter based instruction current detection method according to an embodiment when executing the computer program.
EXAMPLE III
In one or more embodiments, a computer-readable storage medium is disclosed, on which a computer program is stored, which, when executed by a processor, performs a kalman filter-based instruction current detection method according to an embodiment.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (7)
1. An instruction current detection algorithm based on Kalman filtering is characterized by comprising the following steps:
measuring load current transients i in a three-phase loada，ib，ic；
And transforming the instantaneous value of the load current in the three-phase load into α - β two-phase orthogonal coordinate system by utilizing a clark transformation:
obtaining instantaneous active current i through coordinate transformationpAnd a reactive current iq；
Based on ip_iqEstablishment of separationA scattered system state equation and a measurement equation;
using Kalman filter to the active current ipAnd a reactive current iqFiltering to obtain a direct current component;
and obtaining fundamental wave positive sequence current through coordinate inverse transformation, and subtracting the fundamental wave positive sequence current from the load current to obtain total compensation current.
2. The Kalman filtering based command current detection algorithm as claimed in claim 1, wherein a load current instantaneous value in a three-phase load is transformed into α - β two-phase orthogonal coordinate system by means of clark transformation, specifically:
wherein,
3. the Kalman filtering based command current detection algorithm as claimed in claim 1, characterized in that instantaneous active current i is obtained through coordinate transformation by means of clark transformationpAnd a reactive current iqThe method specifically comprises the following steps:
wherein,ω is the fundamental angular frequency.
4. The Kalman filtering based command current detection algorithm of claim 1, characterized in that based on ip_iqEstablishing a state equation and a measurement equation of a discrete system, specifically:
for active current ip：
Wherein,being a state transition matrix, Hp1×16For measuring the matrix, Xp16×1(k +1) is the k +1 value of the active current state variable, Xp16×1(k) K value for active current state variable, w (k) process noise, v (k) measurement noise, zp (k) active current measurement;
for reactive current iq：
Being a state transition matrix, Hq1×16For measuring the matrix, Xq16×1(k +1) is the k +1 th value of the reactive current state variable, Xq16×1(k) K value for reactive current state variable, w (k) process noise, v (k) measurement noise, zq (k) reactive current measurement.
5. The Kalman filtering based instruction current detection algorithm of claim 1, characterized in that the active current i is measured by Kalman filterpAnd a reactive current iqFiltering to obtain a direct current component, specifically:
setting initial values of state variables according to the established state equation and measurement equation of the discrete system, substituting the initial values into a Kalman filtering algorithm formula, and performing cyclic recursion in sequence to obtain the state variables of each moment, wherein Xq111And Xp111The active direct current component and the reactive direct current component of the fundamental wave are respectively; xq is added111And Xp111To carry out the inverseAfter conversion, three-phase fundamental current is obtained.
6. A kalman filter based instruction current detection system, comprising a server, wherein the server comprises a memory, a processor and a computer program stored in the memory and operable on the processor, and the processor implements the kalman filter based instruction current detection method according to any one of claims 1 to 5 when executing the program.
7. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, performs the kalman filter-based instruction current detection method according to any one of claims 1 to 5.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN113741344A (en) * | 2021-08-03 | 2021-12-03 | 南京工大数控科技有限公司 | Intelligent fault diagnosis system and method for numerical control machine tool |
| CN113889843A (en) * | 2021-09-28 | 2022-01-04 | 桂林市啄木鸟医疗器械有限公司 | Semiconductor laser power control method, device, system and readable storage medium |
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