CN109444515B - Reactive power, imbalance and harmonic detection method based on SDFT algorithm - Google Patents

Reactive power, imbalance and harmonic detection method based on SDFT algorithm Download PDF

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CN109444515B
CN109444515B CN201811121257.7A CN201811121257A CN109444515B CN 109444515 B CN109444515 B CN 109444515B CN 201811121257 A CN201811121257 A CN 201811121257A CN 109444515 B CN109444515 B CN 109444515B
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徐文涛
王思敏
牛轲
张鹏程
郭志强
宁振
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Qingdao Topscomm Communication Co Ltd
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Abstract

The application discloses a fundamental wave reactive power, unbalance and harmonic detection method based on an SDFT algorithm, which comprises the steps of sampling a three-phase alternating current signal in a fixed sampling period to obtain discrete sampling data; solving a zero sequence component and simultaneously obtaining a result of removing the zero sequence component; carrying out SDFT conversion on the sampling data to obtain an integral result of each current magnitude under the number of fundamental wave period points; according to the calculation formula of DFT, correcting the integral value of each current quantity, and replacing the result of SDFT operation; combining a grid voltage phase locking result, obtaining fundamental wave reactive and unbalanced components according to a calculation formula, and obtaining an instantaneous value of a harmonic component according to a phase relation; the twiddle factors are obtained by a table look-up method, only a sine value table is saved, and the use of a memory can be reduced; the stability problem caused by the iterative accumulated error can be eliminated.

Description

Reactive power, imbalance and harmonic detection method based on SDFT algorithm
Technical Field
The invention relates to the field of electric energy quality, and mainly aims at detecting reactive, unbalanced and harmonic signals in the electric energy quality.
Background
With the rapid development of power electronic technology and information technology, the wide application of various nonlinear devices, the enlargement of the scale of a power grid and the improvement of complexity, the problem of power quality becomes more and more the key points of increasing attention of power supply enterprises and users. The detection and treatment of reactive power consumption, three-phase imbalance phenomenon, harmonic interference and the like are the most concerned problems of the quality of the electric energy nowadays.
For the detection of fundamental wave reactive power and harmonic wave problems, common modes comprise algorithms such as Fourier transform, instantaneous reactive power method, synchronous measurement method and the like, and for the detection of three-phase unbalance, a common method is a symmetric component method. The SDFT algorithm has the characteristics of Fourier transform, small operand and the like, and has obvious advantages for harmonic detection. Also, because of the flexibility of the SDFT, it is equally applicable in fundamental reactive and three-phase imbalance detection.
The SDFT algorithm is the same as the DFT principle, is a fast calculation mode of DFT, and searches the DFT result X of the signal at the previous momentn-1(k) DFT result X with signal of later timen(k) By calculating X in an iterative mannern(k) In that respect Two SDFT algorithms exist according to different coordinate axes of the SDFT.
In the first algorithm, if all time signals are placed on the same time axis, the twiddle factor changes after each sliding, that is, the time factor is considered, as shown in fig. 1, the expression is:
Xm+1(k)＝Xm(k)+(x(N+m)-x(m))e-j2πmk/N (1)
wherein, the initial values of X (0) -X (N-1) can be all set to 0, in this case, Xm(k) Is 0; m is the number of SDFT slips, and the initial value m is 0; k is the harmonic number; x (N + m) is the last sample point for the current SDFT, and x (m) is the first sample point for the last cycle SDFT.
The twiddle factor varies periodically with time, and as the data moves, x (0) → x (n) its base's initial phase also rotates at the same angular velocity e-j2π0k/N→e-j2πnk/NThe data phase angle is always a constant angle with the base phase of the twiddle factor, so the value obtained in (1) is a relative value, which results in a constant value when the signal is stationary.
Second algorithm, if all signals have the same initial position, X is obtained every timem+1(k) All results are obtained by using a DFT operation formula, that is, without considering a time factor, as shown in fig. 2, the expression is:
Xm+1(k)＝(Xm(k)+x(N+m)-x(m))ej2πk/N (2)
the twiddle factor is constant throughout, x (0) → x (n) when the data moves, and the initial phase of its basis is constant e-j2π0k/N→e-j2π0k/NThe phase of the data is constantly changing and the basis is kept constant, so that the result obtained by equation (2) is an absolute value, i.e. the instantaneous value of the signal.
For the twiddle factors obtained by using the table look-up method, the existing quantization error cannot be avoided. There is a difference in the cumulative effect of both on quantization error.
For equation (1), the following recursion equation is obtained:
Figure GDA0002793272590000021
it can be seen that when the number of points of sliding m exceeds one sampling period N, the reduction calculation can be performed. The summation is spread internally as shown in figure 3.
Wherein the left, middle and right parts respectively represent x (N + N), x (N) and e-j2πnk/N。
When the number of the sliding points exceeds one period, the calculation result only keeps the error accumulation of N points, and higher operation errors cannot be caused by the increase of the sliding points.
For equation (2), the following recursion equation can be obtained:
Figure GDA0002793272590000022
each time the sliding operation is performed, the twiddle factors are multiplied, and the operation errors cannot be mutually offset, so that the errors are accumulated continuously.
In consideration of the advantages and disadvantages of the two algorithms, the stability of the first SDFT algorithm is higher than that of the second SDFT algorithm from the stability point of view, so that the first SDFT algorithm is adopted for detecting reactive power, imbalance and harmonic signals.
Disclosure of Invention
The invention aims to provide a detection method of fundamental wave positive sequence reactive signals, fundamental wave negative sequence signals and harmonic signals based on an SDFT algorithm.
The invention provides a method for detecting reactive and unbalanced components of a current signal based on an SDFT algorithm, which comprises the following steps:
sampling the three-phase current signals to obtain zero sequence components of the three-phase signals, and subtracting the zero sequence components from the three-phase sampling signals to obtain three-phase zero-removed current signals;
according to the sampling sequence and the number N of the periodic points, carrying out SDFT operation on three-phase zero-removed current signals and zero-sequence component signals with different phase shifts k equal to 1 according to the recursion rule of the SDFT algorithm;
after SDFT operation, one of sine terms and cosine terms in SDFT results of three-phase zero-removing current signals and zero sequence component signals is corrected in sequence by single-point DFT operation, and the corrected result in each period is used as the output of the current period and is also used as the input of the next period;
after 8 fundamental wave periods, each item of the SDFT result of the three-phase zero-removed current signal and the zero-sequence component signal is corrected, and then the correction of the next cycle is carried out;
and combining the phase-locked voltage, and performing fundamental positive sequence reactive component, negative sequence reactive/active component and zero sequence reactive/active component, namely fundamental reactive and unbalanced components by using a formula.
Wherein, still include:
and caching and replacing the input three-phase current sampling signals by utilizing an annular buffer.
The twiddle factor of each phase is obtained by a table look-up method, the sine term sin (2 pi i/N) of the twiddle factor, i-0, 1, N-1, is stored in a look-up table, and the value of the twiddle factor is obtained by the table look-up method.
Wherein, N is the point number of a fundamental wave period and is the point number of making SDFT. The stored lookup table is a sine item of the A-phase twiddle factor, and the A-phase twiddle factor cosine item and the BC two-phase twiddle factor are obtained by changing the way of the subscript of the lookup table.
The invention provides a harmonic detection method based on an SDFT algorithm, which comprises the following steps:
the number of harmonics to be solved kiStoring K into a table, and carrying out different harmonic times K-K on the three-phase input signal according to a sampling sequence and the number N of fundamental wave period points and a recursion rule of an SDFT algorithmiObtaining the SDFT result of each harmonic three-phase current signal by the SDFT operation;
after SDFT operation of all harmonic signals is completed, each harmonic signal is corrected, the correction period depends on the total times of the harmonic, the correction mode is the same as that of the fundamental wave signal, and the correction result is used as the output of the current period and is also the input of the next period;
after obtaining the SDFT result, amplitude information can be obtained, and an instantaneous value can also be obtained through phase transformation and selected according to requirements.
Wherein, still include:
the twiddle factors for the SDFT operation are obtained by a table look-up method by using a stored sine table.
For k harmonics, the index interval of the lookup table is k, which avoids multiplication of the twiddle factors.
The invention provides a detection method of fundamental current reactive and unbalanced components based on an SDFT algorithm, which comprises the steps of sampling and caching three-phase current, calculating a zero-sequence current signal, carrying out SDFT operation with k equal to 1 on the zero-sequence current signal and a three-phase zero-removed current signal, and then combining a result obtained by phase locking to calculate an active value and an passive value of the positive-sequence reactive and unbalanced components; the SDFT operation result needs to be corrected item by item, each interruption period carries out single-point correction, N interruption periods complete single-item correction, and the corrected value is used as the SDFT operation value of the period; the harmonic detection method based on the SDFT algorithm comprises the steps of sampling and caching three-phase current signals, and determining the number k of harmonic times to be detectediExecute k ═ kiPerforming SDFT operation, and obtaining a harmonic signal instantaneous value according to phase transformation; the harmonic detection algorithm also comprises a correction link, and the correction mode is the same as the fundamental wave.
The method relates to the extraction of three-phase current fundamental wave positive sequence, negative sequence, zero sequence component and harmonic component, and the real-time detection is carried out aiming at the situations of reactive current, unbalanced current and harmonic current. In order to eliminate the stability problem caused by interference and iteration errors, the method carries out correction once at a plurality of fundamental wave periodic points, and ensures the accuracy of operation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic diagram of a first SDFT algorithm provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a second SDFT algorithm provided by an embodiment of the present invention;
FIG. 3 is a diagram illustrating accumulated error of a first SDFT algorithm according to an embodiment of the present invention;
FIG. 4 is a flow chart of a fundamental reactive and unbalanced current detection method provided by an embodiment of the present invention;
FIG. 5 is a flow chart of a method for detecting harmonic current according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a fundamental reactive component detection simulation result provided by the embodiment of the present invention;
fig. 7 is a schematic diagram of an unbalanced component detection simulation result according to an embodiment of the present invention;
fig. 8 is a schematic diagram of a simulation result of the detection of the 3 rd harmonic component according to the embodiment of the present invention;
fig. 9 is a block diagram of a structure of a system for detecting reactive power, imbalance and harmonics based on an SDFT algorithm according to an embodiment of the present invention;
Detailed Description
The core of the invention is to provide a method for detecting fundamental wave reactive power, three-phase imbalance and harmonic wave based on an SDFT algorithm, which has the advantages of simple operation, less resource occupation and short execution time, and can eliminate accumulated errors caused by interference and iterative operation.
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 4 is a flowchart of a fundamental reactive and unbalanced current detection method according to an embodiment of the present invention, where the method includes:
s100, sampling the three-phase current signals according to sampling frequency adaptive to a fundamental wave period, and performing quantization processing to obtain three-phase sampling signals;
the sampling frequency is determined according to the voltage frequency of the power grid, and a fixed sampling point number is ensured in one fundamental wave period. In general, the grid voltage frequency fluctuation is small, so the sampling frequency is slightly adjusted.
S110, solving the zero sequence component of the three-phase current, namely the average value of the three-phase current data, and simultaneously obtaining a three-phase zero-removing current signal.
And S120, carrying out SDFT operation with k being 1 on the obtained zero sequence component and the three-phase zero-removed current signal on a fundamental wave period, wherein the formula is as follows:
sumix_n+1＝sumix_n+(iin-iout)e-j2πn/N
wherein iinAnd ioutThe input current and the eliminated current are of the current category (A phase zero removal/B phase zero removal/C phase zero removal/zero sequence), and N is the number of sampling points in one fundamental wave period.
According to different current types and sine terms and cosine terms of the current, 8 integral values can be obtained, and the obtained integral results are used for calculating the fundamental wave reactive current and the unbalanced current.
To reduce the amount of computation, the rotation factor e is used-j2πn/NSine item sin (2 pi i/N) is stored in a lookup table, cosine items can be obtained by modifying table lookup subscripts, and table multiplexing can reduce storage space.
The results of the calculation by using the SDFT are all intermediate variables, and the variables of the zero sequence current and the variables of the ABC three-phase current have different meanings.
And S130, in each interrupt cycle, calculating and correcting one integral term by using a DFT formula.
Such as: and starting from the first interrupt period, carrying out single-point correction and summation on the phase-A zero-removed current signal, finishing the correction of the phase-A zero-removed current signal DFT result after N interrupt periods, replacing the result with the current SDFT result of the phase-A zero-removed current data, and using the result for the SDFT operation of the next interrupt period.
And S140, after the previous integral term is corrected, correcting the next integral term by using the correction process from the next interrupt cycle until the 8-term correction is finished, and then performing the next round of correction.
S150, by using the obtained 8 integral values and combining with the grid voltage, fundamental positive sequence reactive power, negative sequence active/reactive power and zero sequence active/reactive power components can be obtained according to a formula, wherein the specific formula is as follows:
Figure GDA0002793272590000061
the unlabeled formula is an intermediate variable, which contains current amplitude and phase information. The actual current value can be obtained by the above equation.
Based on the technical scheme, the fundamental wave reactive power and unbalance detection method based on the SDFT provided by the embodiment of the invention realizes reactive power and unbalance detection in an ABC three-phase coordinate system, introduces a correction process, and can eliminate the stability problem caused by accumulated errors by using a small amount of calculation.
Fig. 5 is a flowchart of a harmonic detection method according to an embodiment of the present invention, where the method includes:
s200, sampling and quantizing the input current signal at a sampling frequency suitable for the fundamental wave period to obtain discrete sampling points, wherein the result is also a cache result after S100;
s210, specifying the number k of harmonics to be detectediProceed k to kiThe SDFT operation of (1); after one harmonic operation is finished, performing the operation of the next harmonic until all the harmonic operations of the times to be detected are finished;
k＝kithe second SDFT operation formula is:
Figure GDA0002793272590000062
wherein the content of the first and second substances,
Figure GDA0002793272590000071
is the k-thiSDFT operation result i after subharmonic sliding n pointsinIs the current signal sample value, i, input for the interrupt periodoutIs the current signal sampling value input before N interruption periods;
the twiddle factor is obtained by a table look-up method, the sine item sin (2 pi i/N) of the twiddle factor is stored in the look-up table, and the storage space can be reduced by multiplexing the sine part and the cosine part of the twiddle factor.
S220, after the operation of each subharmonic is finished, correcting the subharmonic by using single-point DFT operation, wherein the correction formula is as follows:
Figure GDA0002793272590000072
after N interruption periods, completing a complete DFT operation, replacing the SDFT detection result of the item with the operation result at the moment, and correcting the next correction item in the next interruption period;
the correction term comprises an ABC three-phase signal, each phase comprises the number of harmonics to be detected, and each harmonic comprises the integral of a sine term and the integral of a cosine term as the rotation factor consists of a sine term and a cosine term.
S230, after the correction of a certain integral term is finished, the corrected value is used for the current period of the term, the correction of the next integral term is started in the next interrupt period, and the correction formula refers to the operation formula of DFT:
Figure GDA0002793272590000073
s240, the SDFT algorithm is used to obtain a relative phase signal, so when converting the relative phase signal into an instantaneous phase, phase conversion is required, and the relative phase signal can be obtained by using the following formula:
Figure GDA0002793272590000074
wherein the content of the first and second substances,
Figure GDA0002793272590000075
including a certain phase kiOf the sine term of subharmonic currents
Figure GDA0002793272590000076
And cosine term
Figure GDA0002793272590000077
The obtained real part result is the harmonic current instantaneous value;
phase shift factor
Figure GDA0002793272590000078
The same needs to be decomposed into sine items and cosine items, and the stored sine table is obtained by using a table look-up mode.
Based on the technical scheme, the harmonic detection method based on the SDFT provided by the embodiment of the invention performs the SDFT analysis on the three-phase current signal in the ABC coordinate system, corrects each harmonic in a time-sharing manner in order to eliminate the stability problem caused by accumulated errors, the correction period depends on the number of harmonics and the total number of harmonics corrected each time, the calculation amount is small, the operation is simple, the precision is high, and the method is suitable for the implementation of an embedded platform.
To illustrate the above embodiments in detail, an embodiment simulation verification is presented herein. Compiling S functions of fundamental wave reactive power, unbalance and harmonic detection, building a Simulink simulation model, setting the sampling frequency to be 20kHz, setting the number of SDFT points to be 400, and referring to the specific simulation results to fig. 6-8.
The embodiment of the invention provides a method for detecting fundamental positive sequence reactive, unbalanced and harmonic signals based on SDFT, which can accurately eliminate accumulated errors in real time.
In the following, the detection algorithm of the fundamental wave reactive power, the imbalance and the harmonic signals based on the SDFT algorithm provided by the embodiment of the present invention is introduced, and the detection system of the fundamental wave reactive power, the imbalance and the harmonic signals based on the SDFT algorithm described below and the detection algorithm of the fundamental wave reactive power, the imbalance and the harmonic signals based on the SDFT algorithm described above may be referred to correspondingly.
Referring to fig. 9, fig. 9 is a block diagram of a system for detecting fundamental reactive, unbalanced and harmonic signals based on an SDFT algorithm according to an embodiment of the present invention, where the system may include:
the signal generating module 100 is configured to generate a power grid voltage phase locking result and a three-phase alternating-current signal, and add harmonic signals with different times and amplitude phase information to the three-phase signal;
the signal sampling module 200 is used for sampling three-phase continuous signals, and in the system, the sampling frequency is 20kHz, so that the number of sampling points in one fundamental wave period is 400;
the signal processing module 300, namely the operation and correction part of the invention, is used for caching and processing the sampling signal, obtaining the integral value of the signal by using the SDFT algorithm, obtaining the fundamental wave reactive power and unbalanced component by combining the grid voltage phase locking result, and obtaining the harmonic signal instantaneous value according to the phase transformation;
and the result display module 400 displays the obtained detection result of the reactive power and the unbalance of the fundamental wave in real time and can perform real-time observation by using a simulation oscilloscope.
Based on the above technical solution, the simulation system further includes:
the buffer module is used for carrying out buffer processing on the three-phase sampling data by utilizing the annular buffer;
and the table look-up module is used for obtaining the sine value and the cosine value of the twiddle factor and storing the sine value in a look-up table.
In the description, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same parts among the embodiments are referred to each other.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or the like. While the foregoing description has generally described various example compositions and steps in terms of their functionality, the manner in which such functionality is implemented should not be construed as exceeding the scope of the invention.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (6)

1. A method for detecting reactive and unbalanced components based on an SDFT algorithm is characterized by comprising the following steps:
sampling the three-phase current signal at a certain sampling frequency to obtain discrete sampling values, wherein the number of sampling points in each period is N, and the sampling values are in an ABC coordinate system;
solving zero sequence components and three-phase zero-removing current signals of the three-phase zero-removing current signals, and obtaining integral values of all current items in a fundamental wave period by using an SDFT algorithm;
performing single-period DFT calculation on the SDFT operation items parameter by parameter according to the sampling sequence and the superposition period to serve as correction, wherein in the DFT calculation, the operation result from the ith point is the accumulated value of the operation result from the ith-1 point and the real-time operation result from the ith point;
when i is less than N, outputting the SDFT result of the current period;
when i is equal to N, outputting the current correction result as the SDFT operation result of the current period;
and (4) calculating the results of the fundamental wave reactive power and the unbalanced component according to the SDFT operation result and the grid voltage phase locking result.
2. The SDFT algorithm-based reactive and unbalanced component detection method of claim 1, wherein a circular buffer is used for buffering the three-phase sampled current data, and the size of the buffer area only needs one period of the number of the three-phase sampled current data.
3. The method for detecting reactive and unbalanced components based on the SDFT algorithm as claimed in claim 2, wherein the sine term sin (2 pi i/N) of the twiddle factor is calculated and stored in a look-up table, and the sine term sin and the cosine term sin of the twiddle factor are obtained by using a table look-up method.
4. A harmonic detection method based on an SDFT algorithm is characterized by comprising the following steps:
sampling the three-phase current signal at a certain sampling frequency to obtain a discrete sampling value, wherein the sampling value is in an ABC coordinate system;
obtaining the integral value of each harmonic current on a fundamental wave period by using the SDFT algorithm on the sampled signal;
correcting each SDFT operation item by single-point DFT calculation according to the sampling sequence and the superposition period, wherein the correction result of the ith point is the accumulated value of the DFT result of the ith point and the correction result of the (i-1) th point;
when i is less than N, outputting the SDFT result of the current period;
when i is equal to N, outputting the current correction result as the SDFT operation result of the current period;
and solving the instantaneous result of the harmonic component of the obtained SDFT operation result according to the phase shift transformation relation.
5. The harmonic detection method based on the SDFT algorithm as recited in claim 4, wherein the three-phase sampled current data is buffered by a circular buffer, and the size of the buffer area only needs one period of the number of the three-phase sampled current data.
6. The SDFT algorithm-based harmonic detection method of claim 5, wherein sine terms sin (2 pi i/N) of the twiddle factors are calculated and stored in a lookup table, and sine terms and cosine terms of the twiddle factors are obtained by a lookup table method.
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