CN106771507B - Reactive current rapid detection method based on voltage reference split-phase synchronization - Google Patents

Reactive current rapid detection method based on voltage reference split-phase synchronization Download PDF

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CN106771507B
CN106771507B CN201710049517.3A CN201710049517A CN106771507B CN 106771507 B CN106771507 B CN 106771507B CN 201710049517 A CN201710049517 A CN 201710049517A CN 106771507 B CN106771507 B CN 106771507B
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phase
current
reactive current
fundamental wave
lpf
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CN106771507A (en
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许胜�
徐子超
曹健
夏华凤
周澄
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Jiangsu Naquan Hongyuan New Energy Technology Co ltd
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Taizhou University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G01R19/06—Measuring real component; Measuring reactive component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/26—Arrangements for eliminating or reducing asymmetry in polyphase networks
    • 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
    • Y02E40/30—Reactive power compensation
    • 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
    • Y02E40/50—Arrangements for eliminating or reducing asymmetry in polyphase networks

Abstract

The invention relates to a method for quickly detecting reactive current, which belongs to the technical field of electricians, in particular to a method for quickly detecting reactive current based on voltage reference split-phase synchronization, and on one hand, based on an instantaneous reactive power theory, compared with a method for detecting the reactive current in a Fast Fourier Transform (FFT) equal frequency domain, the method for quickly detecting the reactive current based on the voltage reference split-phase synchronization has the advantages of high detection speed and strong real-time property; on the other hand, the method overcomes the defect that the existing reactive current detection method based on the instantaneous reactive power theory cannot realize split-phase reactive current detection, and particularly under the condition of unbalanced load, the method can accurately detect the reactive current of each phase load, while the existing reactive current detection method based on the instantaneous reactive power theory cannot realize the accurate detection of the reactive current of the unbalanced load.

Description

Reactive current rapid detection method based on voltage reference split-phase synchronization
Technical Field
The invention relates to a method for quickly detecting reactive current, belongs to the technical field of electricians, and particularly relates to a method for quickly detecting reactive current based on voltage reference phase splitting synchronization, which can realize phase splitting, real-time and accurate detection of reactive current of any load.
Background
The fast and accurate detection of reactive current is a prerequisite for realizing reactive Power effective compensation of Power quality management devices such as Active Power Filters (APFs) and Static Var Generators (SVGs), and is also one of key technologies for determining device performance. Therefore, the reactive current detection technology is always the key point and the hot point of research in the field of electric energy quality control, and through development of a plurality of years, a plurality of current detection methods are proposed in sequence, wherein the two methods which are more mature and wide in application in engineering are mainly as follows:
first, various frequency domain detection methods based on Fourier series technique are mainly Fast Fourier Transform (FFT) detection methods. The method carries out Fourier analysis according to the collected current value of a power frequency period, and finally obtains the required reactive power and harmonic current. However, the algorithm is complex, has poor timeliness, and is not suitable for being applied to the compensation field with high real-time requirement.
Secondly, various time domain current detection methods based on the three-phase circuit instantaneous reactive power theory have high real-time performance. However, at present, the existing detection method based on the instantaneous reactive power theory cannot realize current split-phase detection, and particularly, when three-phase loads are unbalanced, the reactive current of each phase load cannot be accurately detected. For example, the existing reactive current detection method based on the instantaneous reactive power theory can accurately detect the fundamental wave positive sequence reactive current in the three-phase load current, and when the three-phase load is balanced, the three-phase fundamental wave positive sequence reactive current is the three-phase load fundamental wave reactive current; when the three-phase load is unbalanced, particularly for a three-phase four-wire system, the three-phase fundamental positive-sequence reactive current is not equal to the three-phase load fundamental reactive current due to the presence of the negative-sequence and zero-sequence currents.
Therefore, the invention provides a split-phase rapid detection method of reactive current based on the instantaneous reactive power theory, on one hand, the real-time performance of the instantaneous reactive power theory detection method is fully exerted; on the other hand, the method overcomes the defect that the existing detection method based on the instantaneous reactive power theory can not realize the detection of the split-phase reactive current, and particularly under the condition of unbalanced load, the method can accurately detect the reactive current of each phase load.
Disclosure of Invention
The invention aims to realize phase-splitting, real-time and accurate detection of reactive current of any load.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
a reactive current rapid detection method based on voltage reference split-phase synchronization comprises A-phase reactive current detection, B-phase reactive current detection and C-phase reactive current detection,
the A-phase reactive current detection method comprises the following steps:
(1) defining a three-phase arbitrary load current matrix as i:
wherein:
Figure GDA0002142910930000021
Figure GDA0002142910930000023
Figure GDA0002142910930000024
defining the zero sequence current of any three-phase load as i0:
Figure GDA0002142910930000025
(2) Defining positive sequence transformation matrix by using A-phase power grid voltage as synchronous reference signal
Figure GDA0002142910930000026
Negative sequence transformation matrix
Figure GDA0002142910930000027
And zero sequence transformation matrix C0Comprises the following steps:
Figure GDA0002142910930000028
Figure GDA00021429109300000210
(3) application ofConverting three-phase current i in the abc coordinate system into a fundamental wave positive sequence Synchronous Rotating coordinate System (SRF), wherein the current on the converted fundamental wave positive sequence SRF is defined as
Figure GDA0002142910930000033
Wherein:
Figure GDA0002142910930000034
Figure GDA0002142910930000035
using a Low Pass Filter (LPF) to Filter out
Figure GDA0002142910930000036
Traffic in (1) to obtain
Figure GDA0002142910930000037
Is defined as the DC value
Figure GDA0002142910930000038
Figure GDA0002142910930000039
(4) Application of
Figure GDA00021429109300000310
Three-phase current i in the abc coordinate system is converted into a fundamental wave negative sequence SRF, and the three-phase current i is convertedThe current on the fundamental negative sequence SRF is defined as
Figure GDA00021429109300000311
Figure GDA00021429109300000312
Wherein:
Figure GDA00021429109300000313
Figure GDA00021429109300000314
filtering by LPFTraffic in (1) to obtain
Figure GDA00021429109300000316
Is defined as the DC value
Figure GDA00021429109300000317
Figure GDA00021429109300000318
(5) Application of C0To i0Transforming to obtain:
Figure GDA0002142910930000041
using LPF to filter i0qIn (b) to obtain i0qThe DC value of (1) is defined as I0q1：
Figure GDA0002142910930000042
(6) Calculating A-phase reactive current
Figure GDA0002142910930000043
The B-phase reactive current detection method comprises the following steps:
(1) the three-phase load current i is reordered as:
Figure GDA0002142910930000044
(2) taking B-phase power grid voltage as a synchronous reference signal, and converting a matrix in positive sequenceNegative sequence transformation matrix
Figure GDA0002142910930000046
And zero sequence transformation matrix C0The evolution becomes:
Figure GDA0002142910930000047
Figure GDA0002142910930000048
Figure GDA0002142910930000049
(3) application of
Figure GDA00021429109300000410
Converting the three-phase current i in the abc coordinate system into a fundamental wave positive sequence SRF to obtain
Figure GDA00021429109300000411
Figure GDA0002142910930000051
Wherein:
filtering by LPF
Figure GDA0002142910930000054
Traffic in (1) to obtainMedium direct current value
Figure GDA0002142910930000056
Figure GDA0002142910930000057
(4) Application of
Figure GDA0002142910930000058
Converting three-phase current i in the abc coordinate system into a fundamental wave negative sequence SRF to obtain current
Figure GDA0002142910930000059
Figure GDA00021429109300000510
Wherein:
Figure GDA00021429109300000511
Figure GDA00021429109300000512
filtering by LPF
Figure GDA00021429109300000513
Traffic in (1) to obtain
Figure GDA00021429109300000514
Medium direct current value
Figure GDA00021429109300000515
Figure GDA00021429109300000516
(5) Application of C0To i0Transforming to obtain:
Figure GDA00021429109300000517
using LPF to filter i0qIn (b) to obtain i0qD.c. value of0q1：
Figure GDA0002142910930000061
(6) Calculating B-phase reactive current
Figure GDA0002142910930000062
The C-phase reactive current detection method comprises the following steps:
(1) the three-phase load current i is reordered as:
Figure GDA0002142910930000063
(2) taking C-phase power grid voltage as synchronous reference signal, positive sequence transformation matrix
Figure GDA0002142910930000064
Negative sequence transformation matrix
Figure GDA0002142910930000065
And zero sequence transformation matrix C0The evolution becomes:
Figure GDA0002142910930000066
Figure GDA0002142910930000068
(3) application of
Figure GDA0002142910930000069
Converting the three-phase current i in the abc coordinate system into a fundamental wave positive sequence SRF to obtain
Figure GDA00021429109300000610
Wherein:
Figure GDA00021429109300000612
Figure GDA0002142910930000071
filtering by LPF
Figure GDA0002142910930000072
Traffic in (1) to obtain
Figure GDA0002142910930000073
Medium direct current value
Figure GDA0002142910930000075
(4) Application of
Figure GDA0002142910930000076
Converting three-phase current i in the abc coordinate system into a fundamental wave negative sequence SRF to obtain current
Figure GDA0002142910930000077
Figure GDA0002142910930000078
Wherein:
Figure GDA0002142910930000079
Figure GDA00021429109300000710
filtering by LPF
Figure GDA00021429109300000711
Traffic in (1) to obtain
Figure GDA00021429109300000712
Medium direct current value
Figure GDA00021429109300000713
Figure GDA00021429109300000714
(5) Application of C0To i0Transforming to obtain:
Figure GDA00021429109300000715
using LPF to filter i0qIn (b) to obtain i0qD.c. value of0q1：
Figure GDA00021429109300000716
(6) Calculating C-phase reactive current
Figure GDA00021429109300000717
The invention has the beneficial effects that: on one hand, the reactive current fast detection method based on voltage reference split-phase synchronization has fast detection speed and stronger real-time performance compared with a Fast Fourier Transform (FFT) equal frequency domain detection method based on an instantaneous reactive power theory; on the other hand, the method overcomes the defect that the existing reactive current detection method based on the instantaneous reactive power theory cannot realize split-phase reactive current detection, and particularly under the condition of unbalanced load, the method can accurately detect the reactive current of each phase load, while the existing reactive current detection method based on the instantaneous reactive power theory cannot realize the accurate detection of the reactive current of the unbalanced load.
Drawings
Fig. 1 is a schematic diagram of a-phase fundamental wave reactive current detection.
Fig. 2 is a simplified schematic diagram of a-phase fundamental wave reactive current detection.
Fig. 3 is a schematic diagram of B-phase fundamental wave reactive current detection.
Fig. 4 is a simplified schematic diagram of B-phase fundamental wave reactive current detection.
Fig. 5 is a schematic diagram of C-phase fundamental wave reactive current detection.
Fig. 6 is a simplified schematic diagram of C-phase fundamental wave reactive current detection.
FIG. 7 is a typical three-phase unbalanced load wiring diagram for a three-phase four-wire system
Fig. 8 is a three-phase voltage current vector diagram.
Fig. 9 is an a-phase reactive current operation vector diagram.
Fig. 10 is a vector diagram of B-phase and C-phase reactive current operations based on the a-phase voltage.
Fig. 11 is a three-phase voltage-current vector diagram based on the B-phase voltage.
Fig. 12 is a B-phase reactive current operation vector diagram.
Fig. 13 is a three-phase voltage-current vector diagram based on the C-phase voltage.
Fig. 14 is a vector diagram of a C-phase reactive current operation.
Detailed Description
For the purpose of enhancing the understanding of the present invention, the present invention will be described in further detail with reference to the following examples and the accompanying drawings, which are provided for the purpose of illustration only and are not intended to limit the scope of the present invention.
The invention defines the three-phase power grid voltage as:
Figure GDA0002142910930000081
defining a three-phase arbitrary load current matrix as i:
Figure GDA0002142910930000091
wherein:
Figure GDA0002142910930000092
Figure GDA0002142910930000094
defining the zero sequence current of any three-phase load as i0:
Figure GDA0002142910930000095
The novel reactive current detection method of the present invention is described in detail below:
detection of A-phase reactive current
The detection principle of A-phase fundamental wave reactive current is as followsShown in FIG. 1, in which θeFor phase signals synchronized with the mains A-phase voltage, i.e. thetae＝ωt，Respectively are transformation matrixes from an abc coordinate system to a fundamental wave positive sequence SRF coordinate system and a fundamental wave negative sequence SRF coordinate system;
Figure GDA0002142910930000097
respectively are transformation matrixes from a fundamental positive sequence SRF coordinate system and a fundamental negative sequence SRF coordinate system to an abc coordinate system; c0、
Figure GDA0002142910930000098
Respectively, a zero-sequence current transformation matrix:
Figure GDA0002142910930000099
Figure GDA00021429109300000910
Figure GDA00021429109300000911
Figure GDA0002142910930000101
Figure GDA0002142910930000102
step one, detecting positive sequence component
Application of
Figure GDA0002142910930000103
The three-phase current positive and negative sequence components expressed by the formulas (3) and (4) are converted into a fundamental wave positive sequence SRF coordinate system, so that the three-phase current SRF coordinate system can be obtained:
Figure GDA0002142910930000104
and filtering the alternating current component on the dq axis by using an LPF (low pass filter), so that the direct current component on the dq axis can be obtained:
Figure GDA0002142910930000106
let the d-axis component of equation (14)
Figure GDA0002142910930000107
To zero, applying a transformation matrixThe matrix of the formula (14) is transformed into a three-phase abc coordinate system to obtain three-phase fundamental wave positive sequence reactive current
Figure GDA0002142910930000109
Figure GDA00021429109300001010
Step two, detecting the negative sequence component
Application of
Figure GDA00021429109300001011
Converting the three-phase current positive and negative sequence components expressed by the formulas (3) and (4) into a fundamental negative sequence SRF coordinate system to obtain:
Figure GDA00021429109300001012
Figure GDA00021429109300001013
and filtering the alternating current component on the dq axis by using an LPF (low pass filter), so that the direct current component on the dq axis can be obtained:
let the d-axis component of equation (18)To zero, applying a transformation matrix
Figure GDA0002142910930000113
Transformation of equation (18) into the three-phase abc coordinate system yields a three-phase fundamental negative-sequence q-axis current, defined as
Figure GDA0002142910930000114
Step three, zero sequence component
Using transformation matrices C0To formula (6) i0And (3) carrying out transformation:
Figure GDA0002142910930000116
filtering an alternating current component on the equivalent dq axis by using an LPF (low pass filter), and obtaining a direct current component on the equivalent dq axis:
Figure GDA0002142910930000117
let I0d1Is zero, use formula (11)
Figure GDA0002142910930000118
And (3) transforming to solve fundamental wave zero sequence reactive current:
Figure GDA0002142910930000119
according to equations (15), (19), (22), the fundamental reactive current of the a-phase arbitrary load current is obtained:
Figure GDA00021429109300001110
it can be seen that the a-phase reactive current detection principle shown in fig. 1 can be further simplified as shown in fig. 2.
Detection of B-phase fundamental wave reactive current
And (3) carrying out a reactive current detection process by taking the phase B as a reference, wherein the specific implementation process is analyzed as follows:
an arbitrary load current i represented by the formula (2)a、ib、icReordering to ib、ic、ia：
Figure GDA0002142910930000121
Accordingly, the positive and negative sequence currents are:
Figure GDA0002142910930000123
using B-phase mains voltage as a synchronous reference signal, i.e. thetaeω t-120 °. At this time, the relevant positive and negative sequence and zero sequence current transformation matrix correspondingly evolves as:
Figure GDA0002142910930000124
Figure GDA0002142910930000126
Figure GDA0002142910930000127
Figure GDA0002142910930000128
step one, detecting positive sequence component
Using matrices of the formula (27)
Figure GDA0002142910930000129
The three-phase current components represented by equations (25) and (26) are transformed into the fundamental positive sequence SRF coordinate system, and it is possible to obtain:
Figure GDA00021429109300001210
Figure GDA0002142910930000131
and filtering the alternating current component on the dq axis by using an LPF (low pass filter), so that the direct current component on the dq axis can be obtained:
Figure GDA0002142910930000132
let the d-axis component of equation (34)
Figure GDA0002142910930000133
To zero, applying the transform matrix of equation (28)
Figure GDA0002142910930000134
The matrix of the formula (34) is transformed into a three-phase abc coordinate system, so that three-phase fundamental wave positive sequence reactive current can be obtained
Figure GDA0002142910930000135
Figure GDA0002142910930000136
Step two, detecting the negative sequence component
Using a transformation matrix of the formula (29)The three-phase current components represented by equations (25) and (26) are transformed into the fundamental negative sequence SRF coordinate system, and it is possible to obtain:
Figure GDA0002142910930000138
Figure GDA0002142910930000139
and filtering the alternating current component on the dq axis by using an LPF (low pass filter), so that the direct current component on the dq axis can be obtained:
Figure GDA00021429109300001310
let the d-axis component of equation (38)
Figure GDA00021429109300001311
To zero, applying the transform matrix of equation (30)
Figure GDA00021429109300001312
The three-phase fundamental wave negative sequence q-axis current can be obtained by transforming the matrix of the formula (38) into a three-phase abc coordinate system and is defined as
Figure GDA00021429109300001313
Figure GDA00021429109300001314
Figure GDA00021429109300001315
(3) Zero sequence component detection
Transformation matrix C using equation (31)0To i0And (3) carrying out transformation:
Figure GDA0002142910930000141
filtering an alternating current component on the equivalent dq axis by using an LPF (low pass filter), and obtaining a direct current component on the equivalent dq axis:
Figure GDA0002142910930000142
let I0d1Is zero, use formula (31)
Figure GDA0002142910930000143
And (3) transforming to solve fundamental wave zero sequence reactive current:
Figure GDA0002142910930000144
a fundamental wave reactive current of the B-phase arbitrary load current is obtained from equations (35), (39), and (42):
Figure GDA0002142910930000145
the above-mentioned B-phase fundamental wave reactive current detection principle and its simplified principle are shown in fig. 3 and 4, respectively.
Detection of C-phase fundamental wave reactive current
Similarly, to correctly detect the C-phase fundamental wave reactive current, the reactive current detection process must be implemented with the C-phase as a reference, and the specific implementation process analysis is as follows:
an arbitrary load current i represented by the formula (2)a、ib、icReordering to ic、ia、ib：
Accordingly, the positive and negative sequence currents are:
Figure GDA0002142910930000151
Figure GDA0002142910930000152
using C-phase mains voltage as synchronous reference signal, i.e. thetaeω t +120 °. At this time, the relevant positive and negative sequence and zero sequence current transformation matrix correspondingly evolves as:
Figure GDA0002142910930000153
Figure GDA0002142910930000154
Figure GDA0002142910930000155
Figure GDA0002142910930000156
Figure GDA0002142910930000157
step one, detecting positive sequence component
Using a matrix of the formula (47)
Figure GDA0002142910930000158
The three-phase current components represented by equations (45) and (46) are transformed into the fundamental positive sequence SRF coordinate system, which can be obtained:
Figure GDA0002142910930000159
and filtering the alternating current component on the dq axis by using an LPF (low pass filter), so that the direct current component on the dq axis can be obtained:
Figure GDA00021429109300001511
let equation (54) d-axis component
Figure GDA0002142910930000161
To zero, applying the transform matrix of equation (48)
Figure GDA0002142910930000162
The three-phase fundamental wave positive sequence reactive current can be obtained by transforming the matrix of the formula (54) into a three-phase abc coordinate system
Figure GDA0002142910930000163
Figure GDA0002142910930000164
Step two, negative sequence component
Using transformation matrices of the formula (49)
Figure GDA0002142910930000165
The three-phase current components represented by equations (45) and (46) are transformed into the fundamental negative sequence SRF coordinate system, which can be obtained:
Figure GDA0002142910930000166
Figure GDA0002142910930000167
and filtering the alternating current component on the dq axis by using an LPF (low pass filter), so that the direct current component on the dq axis can be obtained:
Figure GDA0002142910930000168
let equation (58) d-axis component
Figure GDA0002142910930000169
To zero, applying the transform matrix of formula (3-50)
Figure GDA00021429109300001610
The matrix of the formula (58) is transformed into a three-phase abc coordinate system, and three-phase fundamental wave negative sequence q-axis current can be obtained and fixedIs defined as
Figure GDA00021429109300001611
Figure GDA00021429109300001612
Figure GDA00021429109300001613
Step three, zero sequence component
Using the transformation matrix C of formula (51)0To formula i0And (3) carrying out transformation:
filtering an alternating current component on the equivalent dq axis by using an LPF (low pass filter), and obtaining a direct current component on the equivalent dq axis:
Figure GDA0002142910930000171
let I0d1Zero, operational type (51)
Figure GDA0002142910930000172
And (3) transforming to solve fundamental wave zero sequence reactive current:
a fundamental reactive current of the C-phase arbitrary load current is obtained from equations (55), (59), and (62):
the above-mentioned principle of detecting the C-phase fundamental wave reactive current and the simplified principle thereof are shown in fig. 5 and 6, respectively.
The three-phase four-wire system unbalanced typical load is used for further verifying the correctness of the method.
Setting three-phase four-wire system unbalanced load: the A phase and the B phase are connected in series with a resistor load, and the C phase is open-circuited, as shown in FIG. 7.
In the figure, R is a resistive load; e.g. of the typea、eb、ecFor the system three-phase voltage, the same formula (1) is defined, expressed in vector form as:
Figure GDA0002142910930000175
then according to fig. 7, the three-phase load current vector can be represented as:
Figure GDA0002142910930000176
in the formula, the current vector magnitude I is E/R.
Fig. 8 is a voltage-current vector diagram, and it is apparent that the a-phase reactive current, the B-phase reactive current, and the C-phase reactive current are all zero, and are sequentially set to Iaq、Ibq、Icq。
The correctness of the provided novel fundamental wave reactive current detection method is verified by using a symmetric component method according to the reactive current detection principle of the invention. The symmetric component method is defined as follows:
wherein α is 1 ∠ 120 DEG is complex operator, I+、I-、I0Positive sequence, negative sequence and zero sequence currents, respectively.
The three-phase current vector of the unbalanced load can also be expressed by a symmetrical component method according to the formula (66):
Figure GDA0002142910930000182
the active and reactive current components of the three-phase load are represented in the form of subscripts p, q, then equation (67) represents the transformation:
Figure GDA0002142910930000183
(1) a-phase reactive current calculation
With the a-phase voltage as a reference, positive, negative and zero sequence currents are calculated, respectively, according to equation (66):
definition of lead EaThe vector axis of (a) is the q axis, and I is calculated separately+、I-、I0Projection on the q-axis, in turn, is defined as
Figure GDA0002142910930000185
I0qReferring to fig. 9, then:
Figure GDA0002142910930000186
then, according to equations (68) to (70), the fundamental reactive current a is obtained as:
Figure GDA0002142910930000191
equation (69) is consistent with the reactive current conclusion of the typical load shown in fig. 8, and the correctness of the detection of the reactive current of the phase a is verified.
For the detection of the B-phase and C-phase reactive currents, it is analyzed below what results would be obtained if the a-phase voltage is still referenced?
The following equations (68) to (70) can be obtained:
Figure GDA0002142910930000192
obviously, this conclusion does not correspond to the conclusion that the reactive current of the B-phase and C-phase of the typical load shown in fig. 8 is zero, and the corresponding vector diagram is shown in fig. 10.
That is, for the phase a current, the detection of the fundamental reactive current can be obtained by superposing three alternating current components corresponding to q-axis channels of three-phase fundamental positive sequence, negative sequence and zero sequence currents. While for phase B and phase C currents, the reactive current does not have a direct superposition of the three components.
(2) B-phase reactive current calculation
The following analysis detects the B-phase fundamental wave reactive current with the B-phase voltage as a reference.
For the convenience of analysis, the three-phase voltage current vector diagram shown in fig. 8 is rotated counterclockwise by 120 degrees as shown in fig. 11.
Based on fig. 11, the three-phase voltage-current vector after rotation is defined as:
then, the three-phase load current vector can be expressed as:
Figure GDA0002142910930000195
and, the order component transformation formula evolves to:
Figure GDA0002142910930000201
the positive, negative and zero sequence currents are calculated respectively according to equation (72):
Figure GDA0002142910930000202
definition of lead EbThe vector axis of (a) is the q axis, and I is calculated separately+、I-、I0Projection on the q-axis, in turn, is defined asI0qReferring to fig. 12, then:
Figure GDA0002142910930000204
the unbalanced load three-phase current vector is expressed by a symmetrical component method, wherein only B phase is expressed:
Ib＝I++I-+I0(75)
similarly, if the active and reactive current components of the three-phase load are expressed in the form of the symbols p and q, the transformation is expressed by the equation (75):
Figure GDA0002142910930000205
by combining formulae (74) and (76), the following can be obtained:
equation (77) is consistent with the reactive current conclusion of the typical load shown in fig. 8, and the correctness of the B-phase reactive current detection is verified.
(3) C-phase reactive current calculation
According to the reactive current detection principle of the invention, the C-phase fundamental wave reactive current is detected by analyzing and taking the C-phase voltage as a reference.
The three-phase voltage current vector diagram shown in fig. 8 is rotated 120 degrees clockwise as shown in fig. 13.
Based on fig. 13, the rotated three-phase voltage-current vector phase is converted into:
Figure GDA0002142910930000211
then, the three-phase load current vector can be expressed as:
Figure GDA0002142910930000212
and, the order component transformation formula evolves to:
Figure GDA0002142910930000213
the positive, negative and zero sequence currents are calculated respectively according to equation (80):
definition of lead EcThe vector axis with 90 degrees of phase is the q axis, and I is respectively calculated+、I-、I0Projection on the q-axis, in turn, is defined as
Figure GDA0002142910930000215
I0qReferring to fig. 14, then:
Figure GDA0002142910930000216
according to the equation (80), the asymmetric system C current vector is expressed by a symmetric component method:
Ic＝I++I-+I0(83)
similarly, when the active and reactive current components of the three-phase load are expressed in the form of the following labels p and q, the transformation is expressed by the formula (83):
Figure GDA0002142910930000217
by combining formulae (81) and (84), the following can be obtained:
Figure GDA0002142910930000218
equation (85) is consistent with the reactive current conclusion of the typical load shown in fig. 8, and the correctness of the detection of the C-phase reactive current is verified.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (1)

1. A reactive current rapid detection method based on voltage reference split-phase synchronization is characterized by comprising A-phase reactive current detection, B-phase reactive current detection and C-phase reactive current detection,
the A-phase reactive current detection method comprises the following steps of:
(1) defining a three-phase arbitrary load current matrix as i:
Figure FDA0002142910920000011
wherein:
Figure FDA0002142910920000012
Figure FDA0002142910920000013
Figure FDA0002142910920000014
defining the zero sequence current of any three-phase load as i0:
(2) Defining positive sequence transformation matrix by using A-phase power grid voltage as synchronous reference signal
Figure FDA0002142910920000016
Negative sequence transformation matrix
Figure FDA0002142910920000017
And zero sequence transformation matrix C0Comprises the following steps:
Figure FDA0002142910920000018
Figure FDA0002142910920000019
Figure FDA00021429109200000110
(3) application of
Figure FDA00021429109200000111
Converting three-phase current i in the abc coordinate system into a fundamental wave positive sequence Synchronous Rotating coordinate System (SRF), wherein the current on the converted fundamental wave positive sequence SRF is defined as
Figure FDA0002142910920000021
Figure FDA0002142910920000022
Wherein:
Figure FDA0002142910920000023
Figure FDA0002142910920000024
using a Low Pass Filter (LPF) to Filter outTraffic in (1) to obtain
Figure FDA0002142910920000026
Is defined as the DC value
Figure FDA0002142910920000027
(4) Application of
Figure FDA0002142910920000029
Three-phase current i in the abc coordinate system is converted into a fundamental wave negative sequence SRF, and the current on the converted fundamental wave negative sequence SRF is defined as
Wherein:
Figure FDA00021429109200000212
Figure FDA00021429109200000213
filtering by LPFTraffic in (1) to obtain
Figure FDA00021429109200000215
Is defined as the DC value
Figure FDA00021429109200000217
(5) Application of C0To i0Transforming to obtain:
Figure FDA0002142910920000031
using LPF to filter i0qIn (b) to obtain i0qThe DC value of (1) is defined as I0q1：
Figure FDA0002142910920000032
(6) Calculating A-phase reactive current
The B-phase reactive current detection method comprises the following steps:
(1) the three-phase load current i is reordered as:
Figure FDA0002142910920000034
(2) taking B-phase power grid voltage as a synchronous reference signal, and converting a matrix in positive sequence
Figure FDA0002142910920000035
Negative sequence transformation matrix
Figure FDA0002142910920000036
And zero sequence transformation matrix C0The evolution becomes:
Figure FDA0002142910920000037
Figure FDA0002142910920000038
Figure FDA0002142910920000039
(3) application of
Figure FDA00021429109200000310
Converting the three-phase current i in the abc coordinate system into a fundamental wave positive sequence SRF to obtain
Figure FDA00021429109200000311
Figure FDA0002142910920000041
Wherein:
Figure FDA0002142910920000042
filtering by LPF
Figure FDA0002142910920000044
Traffic in (1) to obtain
Figure FDA0002142910920000045
Medium direct current value
Figure FDA0002142910920000047
(4) Application of
Figure FDA0002142910920000048
Converting three-phase current i in the abc coordinate system into a fundamental wave negative sequence SRF to obtain current
Figure FDA00021429109200000410
Wherein:
Figure FDA00021429109200000412
filtering by LPFTraffic in (1) to obtain
Figure FDA00021429109200000414
Medium direct current value
Figure FDA00021429109200000415
(5) Application of C0To i0Transforming to obtain:
Figure FDA00021429109200000417
using LPF to filter i0qIn (b) to obtain i0qD.c. value of0q1：
Figure FDA0002142910920000051
(6) Calculating B-phase reactive current
Figure FDA0002142910920000052
The C-phase reactive current detection method comprises the following steps:
(1) the three-phase load current i is reordered as:
Figure FDA0002142910920000053
(2) taking C-phase power grid voltage as synchronous reference signal, positive sequence transformation matrix
Figure FDA0002142910920000054
Negative sequence transformation matrix
Figure FDA0002142910920000055
And zero sequence transformation matrix C0The evolution becomes:
Figure FDA0002142910920000056
Figure FDA0002142910920000057
Figure FDA0002142910920000058
(3) application of
Figure FDA0002142910920000059
Converting the three-phase current i in the abc coordinate system into a fundamental wave positive sequence SRF to obtain
Figure FDA00021429109200000510
Figure FDA00021429109200000511
Wherein:
Figure FDA00021429109200000512
filtering by LPF
Figure FDA0002142910920000062
Traffic in (1) to obtain
Figure FDA0002142910920000063
Medium direct current value
Figure FDA0002142910920000064
(4) Application of
Figure FDA0002142910920000066
Converting three-phase current i in the abc coordinate system into a fundamental wave negative sequence SRF to obtain current
Figure FDA0002142910920000067
Wherein:
Figure FDA0002142910920000069
Figure FDA00021429109200000610
filtering by LPFTraffic in (1) to obtain
Figure FDA00021429109200000612
Medium direct current value
Figure FDA00021429109200000613
(5) Application of C0To i0Transforming to obtain:
Figure FDA00021429109200000615
using LPF to filter i0qIn (b) to obtain i0qD.c. value of0q1：
(6) Calculating C-phase reactive current
Figure FDA00021429109200000617
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