CN113315126A - Specified subharmonic suppression secondary sampling method and system for active power filter - Google Patents

Specified subharmonic suppression secondary sampling method and system for active power filter Download PDF

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CN113315126A
CN113315126A CN202110599699.8A CN202110599699A CN113315126A CN 113315126 A CN113315126 A CN 113315126A CN 202110599699 A CN202110599699 A CN 202110599699A CN 113315126 A CN113315126 A CN 113315126A
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harmonic
frequency
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active power
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CN113315126B (en
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戴珂
杨兵圆
罗辉
杨朝伟
潘非
孙玉鸿
林海涛
张雨潇
徐宏伟
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Huazhong University of Science and Technology
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    • 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
    • H02J3/01—Arrangements for reducing harmonics or ripples
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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
    • Y02E40/20—Active power filtering [APF]

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Abstract

The invention discloses a specified subharmonic suppression secondary sampling method and system for an active power filter, and belongs to the field of power quality control. By analyzing the specified subharmonic instruction extraction method based on recursive discrete Fourier transform and combining the characteristic that the frequency spectrum of the nonlinear load harmonic is basically unchanged in a steady state, the method carries out secondary sampling on the load current according to the harmonic frequency, and then carries out discrete Fourier forward transform to obtain the amplitude information of each subharmonic. Wherein, the lower the harmonic frequency, the lower the secondary sampling frequency; the higher the harmonic order, the higher the subsampling frequency. Specifically, the k-th harmonic content eta of the network current before the device is put into operationkAnd k harmonic current distortion limit ε specified by power quality standardskDetermining the second sampling frequency of the k harmonic
Figure DDA0003092467540000011
By adopting the secondary sampling method disclosed by the invention, the controller can be reduced in a single switching periodThe internal calculation amount increases the number of harmonic waves which can be compensated by the active power filter, and the harmonic wave suppression effect is improved.

Description

Specified subharmonic suppression secondary sampling method and system for active power filter
Technical Field
The invention belongs to the field of power quality control, and particularly relates to a specified subharmonic suppression secondary sampling method and system for an active power filter.
Background
With the continuous improvement of the industrial modernization level in China, more and more nonlinear loads are connected to a power grid, so that a large amount of harmonic current flows into a public power grid, the voltage distortion at a Point of Common Coupling (PCC) is caused, and the power quality of the public power grid is greatly deteriorated.
The active power filter is used as a typical power quality control device, can effectively solve the harmonic problem existing in a power distribution network, and enables the power quality of a power distribution system to meet the national standard, so that the active power filter is practically applied to a plurality of industrial fields. The switching frequency of the active power filter widely applied at present is mostly between 10kHz and 20kHz, and due to the limitation of the switching frequency, the control bandwidth of a current inner loop is limited, so that when the high-order harmonic is compensated, the current tracking control capability is poor, and the compensation effect is not ideal. The switching frequency of the active power filter is improved, and the control bandwidth of the current inner loop of the active power filter can be correspondingly improved. Therefore, the adoption of an active power filter with high switching frequency to treat the higher harmonics in the power grid is a feasible scheme.
However, the higher the switching frequency, the shorter the control period, which causes the shortage of computing resources in a Digital Signal Processor (DSP), which brings a challenge to the application of the high-frequency active power filter. For example, when the switching frequency of the parallel active power filter is 10kHz, a corresponding control period is 100 μ s, during which the digital signal processor is enough to complete a series of calculations such as sampling, extraction of harmonic current commands within 50 times, voltage outer loop control, current inner loop control, phase locking, trigger pulse formation, and the like, thereby ensuring the normal operation of the active power filter. However, when the switching frequency is raised to 100kHz, one control cycle is only 10 μ s, which eliminates the necessary time for calculation such as sampling, voltage outer loop control, current inner loop control, phase locking, trigger pulse formation, etc., and the DSP may not complete the calculation of the harmonic current command within 50 times in the remaining time, which results in that the device cannot compensate partial harmonics and causes unsatisfactory harmonic suppression effect.
At present, in order to reduce the calculation amount during harmonic instruction extraction, a harmonic instruction extraction method based on recursive discrete Fourier transform is mostly adopted in practical application, so that accurate and rapid extraction of specified subharmonic instructions is realized. Taking the parallel active power filter as an example, the method only samples the load current once, and the sampling frequency f is oncepsEqual to the switching frequency fswAnd the controller is in each control period Tc＝1/fswThe amplitude of each harmonic needs to be recalculated in the time domain, and then the harmonic current instruction value in the time domain is obtained through calculation. However, the harmonic frequency spectrum corresponding to the nonlinear load is basically unchanged in a steady state, the controller does not need to recalculate the amplitude of each harmonic in each control period, and the amplitude of each harmonic can be updated every several control periods, so that the operand for extracting the harmonic instruction is reduced, and the possibility is provided for improving the extraction of the harmonic instruction of the active power filter.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a specified subharmonic suppression secondary sampling method and system for an active power filter, and solves the problems of large calculation amount, long operation time and the like of the conventional harmonic instruction extraction method.
The invention provides a specified subharmonic suppression secondary sampling method of an active power filter, the active power filter is connected in parallel between a power grid and a load, a common connection point is PCC, a control part of the active power filter is divided into a voltage control outer ring, a current control inner ring and SVPWM modulation, and the method comprises the following steps in a three-phase system:
s1, sampling frequency fpsSampling for one time to obtain load current iL[n]PCC voltage uTOutput current of active power filter, and direct-current side voltage u of active power filterdc；
S2, detecting load current iL[n]According to the harmonic order k of the specified subharmonic to be suppressed, at a sampling frequency
Figure BDA0003092467520000021
For load current iL[n]Performing secondary sampling, and calculating to obtain k-th harmonic current compensation instruction iLkSumming to obtain total harmonic current compensation command value iLh *；
S3, voltage outer ring adjustment is carried out to obtain an active current instruction idc；
S4, compensating the instruction i according to the total harmonic currentLh *Active power filter output current and active current instruction idcPCC voltage uTPerforming current inner loop regulation to obtain a pulse width modulation signal urα、urβ；
S5, according to the pulse width modulation signal urα、urβAnd controlling a switching tube in the active power filter, and adopting space voltage vector modulation to output compensation current to realize the specified subharmonic suppression of the power grid.
Further, the k-th harmonic content of the power grid current before the active power filter is put into operation
Figure BDA0003092467520000031
K-th harmonic current distortion limit epsilon specified in connection with specific power quality standardskAccording to the formula
Figure BDA0003092467520000032
Calculating to obtain the secondary sampling frequency of k-th harmonic
Figure BDA0003092467520000033
Wherein Ik(t) is the k-th harmonic effective value of the current of the power grid before the active power filter is put into operation, I1(t) is the effective value of the fundamental wave of the grid current, fkThe k harmonic frequency. Further, step S2 specifically includes:
s21, load current i obtained by primary samplingL[n]Filtering to output iLF；
S22, pair iLFPerforming secondary sampling to obtain iLssAt a sub-sampling frequency of
Figure BDA0003092467520000034
Will iLssAnd cosine factor
Figure BDA0003092467520000035
Multiply by plus Ak[n-1]To obtain Ak[n](ii) a Will iLssAnd sine factor
Figure BDA0003092467520000036
Multiply by and add Bk[n-1]To obtain Bk[n](ii) a Wherein A isk[n-1]、Bk[n-1]Respectively a cosine component and a sine component of the k harmonic current amplitude before a second sampling period, Ak[n]、Bk[n]Respectively a cosine component and a sine component of the current amplitude of the k-th harmonic wave at the current sampling time,
Figure BDA0003092467520000037
second sampling period, omega, of the order of k harmonics1Is the fundamental angular frequency;
s23, mixing Ak[n]Multiplied by a cosine factor cos (k ω)1nTps)，Bk[n]Multiplication by sine factor sin (k ω1nTps) After the two terms are added, the two terms are multiplied by a gain adjustment coefficient 2/NkObtaining the current k-th harmonic current instruction value i at the current momentLk(ii) a Wherein T isps＝1/fpsIs a sampling period;
Figure BDA0003092467520000038
second sampling frequency of k harmonics, f1Is the fundamental frequency;
s24, adding the specified subharmonic current instruction values to be compensated to obtain the sum of the harmonic current instructions to be compensated
Figure BDA0003092467520000041
Further, step S21 employs a comb filter, which outputs iLF＝iL[n]-iL[n-N]In the formula iL[n]Load current i obtained by one sampling corresponding to the current momentL[n-N]Corresponding to the load current sampled at the previous time of a fundamental wave period, wherein N is fps/f1，f1Is the fundamental frequency.
For convenient digital realization, the secondary sampling frequency in practical application is recorded as secondary sampling optimization frequency
Figure BDA0003092467520000042
The sub-sampling frequency obtained in step S21 can be higher than that
Figure BDA0003092467520000043
Below the primary sampling frequency fpsIs selected between so that
Figure BDA0003092467520000044
Can be sampled once at frequency fpsInteger division, also the fundamental frequency f1Multiples of (a).
On the premise of ensuring the harmonic suppression effect, in order to simplify the program design of the controller, the secondary sampling frequency of each harmonic can be consistent and is equal to the highest secondary sampling frequency in the harmonic needing to be compensated. For a three-phase system, in practical application, secondary sampling and harmonic instruction calculation can be performed under a three-phase stationary abc coordinate system, a synchronous rotation dq coordinate system or a two-phase stationary alpha beta coordinate system according to needs.
In addition, the secondary sampling method provided by the invention is not only suitable for a three-phase system, but also suitable for a single-phase system; the method is not only suitable for 50Hz and 60Hz power frequency power grids, but also suitable for 400Hz intermediate frequency power grids; the method is not only suitable for the harmonic instruction extraction method based on the recursive discrete Fourier transform, but also suitable for other methods capable of extracting the appointed subharmonic instruction.
According to a second aspect of the present invention, there is provided an active power filter specified subharmonic rejection subsampling system comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium, and execute the active power filter specified subharmonic suppression subsampling method according to the first aspect.
Through the technical scheme, compared with the prior art, the load current compensation method can perform secondary sampling and calculation on the load current according to the harmonic frequency to obtain the command value of the harmonic to be compensated. Wherein, the lower the harmonic frequency, the lower the secondary sampling frequency; conversely, the higher the number of harmonics, the higher the subsampling frequency. Compared with the conventional harmonic instruction extraction method, the secondary sampling method provided by the invention can reduce the operation amount of harmonic instruction extraction, increase the number of harmonics which can be compensated by the active power filter, and improve the harmonic suppression effect.
Drawings
Fig. 1 is a schematic structural diagram of an active power filter system according to an embodiment of the present invention: 101 is a system circuit structure, which is composed of a power grid, a load and a parallel active power filter; reference numeral 102 denotes a control block diagram of the parallel active power filter.
Fig. 2 is a schematic diagram of one-time sampling of a load current according to an embodiment of the present invention, which corresponds to sub-diagram 110 in fig. 1.
Fig. 3 is a schematic diagram of load current filtering according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of second-sampling harmonic extraction according to an embodiment of the present invention, which corresponds to sub-diagram 120 in fig. 1.
Fig. 5 is a block diagram of the sub-sampling and instruction calculation for the k-th harmonic according to the embodiment of the present invention, which corresponds to the sub-diagram 122 in fig. 3.
Fig. 6 is a block diagram of a controller according to an embodiment of the present invention, which corresponds to the sub-diagram 130 in fig. 1.
Fig. 7 is a schematic diagram of a phase-locked loop according to an embodiment of the present invention, which corresponds to sub-diagram 140 in fig. 1.
Fig. 8(a) is a graph showing a relationship between a first sampling frequency and a second sampling optimized frequency of each sub-harmonic after the second sampling method provided by the present invention is adopted in this embodiment; fig. 8(b) is a relative error curve calculated for each harmonic amplitude at different secondary sampling frequencies.
FIG. 9(a) is a graph of net side current waveform and spectrum when the active power filter is not in operation; FIG. 9(b) is a plot of net side current waveform versus spectrum when no subsampling is performed, compensating only for harmonics 5 to 19 times; fig. 9(c) is a graph of the current waveform and spectrum of the grid side when the second sampling is performed according to the second sampling method provided by the present invention to compensate all the characteristic sub-harmonics within 50 times according to the harmonic number k; FIG. 9(d) is a graph of the second sampling optimization frequency for each harmonic at 49 th harmonic
Figure BDA0003092467520000051
And performing secondary sampling to compensate the waveform and spectrogram of the current on the network side when all characteristic subharmonics within 50 times are obtained.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The active power filter is widely applied to industrial fields as a high-efficiency harmonic suppression device and is used for suppressing harmonic generated by nonlinear loads. The parallel active power filter corresponding to fig. 1 is connected to the common connection point in a parallel manner, and outputs a compensation current i having the same magnitude and the opposite direction as the harmonic current in the load current by detecting the harmonic current in the nonlinear loadcReducing the harmonic current of the nonlinear load injected into the power grid to electricityThe energy quality standard is below the limit value specified by the energy quality standard, so that the electric energy quality of the public power grid is improved.
Harmonic current command extraction is a key loop in the parallel type active power filter shown in fig. 1. The speed and accuracy of the harmonic current command extraction affect the effect of the device compensation. Among various harmonic instruction extraction methods, a harmonic instruction extraction method based on recursive discrete Fourier transform is widely adopted with advantages of small calculation amount, short dynamic time, and the like. However, in some application occasions, the switching frequency needs to be further improved, the current tracking effect is ensured, for example, the problem of harmonic wave of a 400Hz intermediate frequency power grid is solved, when a harmonic wave instruction extraction method based on recursive discrete Fourier transform is adopted, the problem of large calculation amount in a single switching period still exists due to the shortening of the switching period, and the device cannot compensate partial harmonic wave, so that the harmonic wave suppression effect is not ideal. The invention provides a method for restraining secondary sampling of appointed subharmonic of an active power filter by combining the condition that a nonlinear load harmonic spectrum is basically unchanged in a steady state according to the characteristics of a harmonic instruction extraction method based on recursive discrete Fourier transform. Wherein each subharmonic is at different secondary sampling frequency
Figure BDA0003092467520000061
Performing discrete Fourier forward transform, and calculating to obtain cosine component A of its amplitudekSinusoidal component Bk(ii) a At a sampling frequency fpsPerforming inverse discrete Fourier transform, and calculating to obtain the command value i of the subharmonic currentLk. Compared with the common sampling method, the secondary sampling method provided by the invention can be used for sampling at the frequency lower than the switching frequency f according to the difference of harmonic timesswIn a range of different subsampling frequencies
Figure BDA0003092467520000062
And calculating to reduce the calculation amount of harmonic instruction extraction, increase the total number of harmonics which can be compensated by the active power filter and improve the harmonic suppression effect.
The invention provides a specified subharmonic suppression secondary sampling method of an active power filter, which comprises the following steps in a three-phase system:
s1, sampling frequency fpsSampling for one time to obtain load current iL[n]PCC voltage uTOutput current of active power filter, and direct-current side voltage u of active power filterdc；
S2, detecting load current iL[n]According to the harmonic order k of the specified subharmonic to be suppressed, at a sampling frequency
Figure BDA0003092467520000071
For load current iL[n]Performing secondary sampling, and calculating to obtain k-th harmonic current compensation instruction iLkSumming to obtain total harmonic current compensation command value iLh *；
S3, voltage outer ring adjustment is carried out to obtain an active current instruction idc；
S4, compensating the instruction i according to the total harmonic currentLh *Active power filter output current and active current instruction idcPCC voltage uTPerforming current inner loop regulation to obtain a pulse width modulation signal urα、urβ；
S5, according to the pulse width modulation signal urα、urβAnd controlling a switching tube in the active power filter, and adopting space voltage vector modulation to output compensation current to realize the specified subharmonic suppression of the power grid.
Specifically, the k-th harmonic content of the grid current before the active power filter is put into operation
Figure BDA0003092467520000072
K-th harmonic current distortion limit epsilon specified in connection with specific power quality standardskAccording to the formula
Figure BDA0003092467520000073
Calculating to obtain the secondary sampling frequency of k-th harmonic
Figure BDA0003092467520000074
Wherein Ik(t) isK-th harmonic effective value, I, of the network current before the active power filter is put into operation1(t) is the effective value of the fundamental wave of the grid current, fkThe k harmonic frequency.
Specifically, step S2 includes:
s21, load current i obtained by primary samplingL[n]Filtering to output iLF；
S22, pair iLFPerforming secondary sampling to obtain iLssAt a sub-sampling frequency of
Figure BDA0003092467520000075
Will iLssAnd cosine factor
Figure BDA0003092467520000076
Multiply by plus Ak[n-1]To obtain Ak[n](ii) a Will iLssAnd sine factor
Figure BDA0003092467520000077
Multiply by and add Bk[n-1]To obtain Bk[n](ii) a Wherein A isk[n-1]、Bk[n-1]Respectively a cosine component and a sine component of the k harmonic current amplitude before a second sampling period, Ak[n]、Bk[n]Respectively a cosine component and a sine component of the current amplitude of the k-th harmonic wave at the current sampling time,
Figure BDA0003092467520000081
second sampling period, omega, of the order of k harmonics1Is the fundamental angular frequency;
s23, mixing Ak[n]Multiplied by a cosine factor cos (k ω)1nTps)，Bk[n]Multiplication by sine factor sin (k ω1nTps) After the two terms are added, the two terms are multiplied by a gain adjustment coefficient 2/NkObtaining the current k-th harmonic current instruction value i at the current momentLk(ii) a Wherein T isps＝1/fpsIs a sampling period;
Figure BDA0003092467520000082
sub-sampling for k-th harmonicFrequency, f1Is the fundamental frequency;
s24, adding the specified subharmonic current instruction values to be compensated to obtain the sum of the harmonic current instructions to be compensated
Figure BDA0003092467520000083
Wherein step S21 employs a comb filter, the output of which is iLF＝iL[n]-iL[n-N]In the formula iL[n]Load current i obtained by one sampling corresponding to the current momentL[n-N]Corresponding to the load current sampled at the previous time of a fundamental wave period, wherein N is fps/f1，f1Is the fundamental frequency.
For convenient digital realization, the secondary sampling frequency in practical application is recorded as secondary sampling optimization frequency
Figure BDA0003092467520000084
The sub-sampling frequency obtained in step S21 can be higher than that
Figure BDA0003092467520000085
Below the primary sampling frequency fpsIs selected between so that
Figure BDA0003092467520000086
Can be sampled once at frequency fpsInteger division, also the fundamental frequency f1Multiples of (a).
On the premise of ensuring the harmonic suppression effect, in order to simplify the program design of the controller, the secondary sampling frequency of each harmonic can be consistent and is equal to the highest secondary sampling frequency in the harmonic needing to be compensated. For a three-phase system, in practical application, secondary sampling and harmonic instruction calculation can be performed under a three-phase stationary abc coordinate system, a synchronous rotation dq coordinate system or a two-phase stationary alpha beta coordinate system according to needs.
In addition, the secondary sampling method provided by the invention is not only suitable for a three-phase system, but also suitable for a single-phase system; the method is not only suitable for 50Hz and 60Hz power frequency power grids, but also suitable for 400Hz intermediate frequency power grids; the method is not only suitable for the harmonic instruction extraction method based on the recursive discrete Fourier transform, but also suitable for other methods capable of extracting the appointed subharmonic instruction.
The present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 shows a system structure diagram of a three-phase three-wire parallel active power filter according to an embodiment of the present invention. Load current iL(t) obtaining a load current i by sampling with a one-time sampling switch and a zero-order keeperL[n]A sampling frequency of fpsAs shown in fig. 2. Since the harmonic instruction extraction method based on recursive discrete Fourier transform is adopted in the embodiment to obtain the harmonic current spectrum information, a device capable of storing N ═ f is neededps/f1And the buffer area of the data points is used for storing the sampling data between the current sampling moment and one fundamental wave period.
Before each harmonic is sampled and calculated twice, the load current i is measuredL[n]And (6) carrying out filtering processing. In this embodiment, the filter used is a comb filter with an output of iLF＝iL[n]-iL[n-N]The corresponding z-domain control block diagram is shown in FIG. 3.
Fig. 4 shows a block diagram of the sub-sampling and calculation provided by the embodiment of the present invention. Aiming at different harmonic times k, different secondary sampling frequencies are adopted
Figure BDA0003092467520000091
Sampling and calculating to obtain a command value i of the k-th harmonic currentLkThen summing the harmonic current commands to obtain a total harmonic current command iLh *. Wherein, the secondary sampling frequency of each harmonic is determined according to the following steps:
n1: measuring the content rate of k-th harmonic of the current of the power grid before the active power filter is put into operation
Figure BDA0003092467520000092
Wherein Ik(t) is the k-th harmonic effective value of the current of the power grid before the active power filter is put into operation, I1(t) is the effective value of the current fundamental wave of the power grid;
n2: aiming at specific application occasions, the k-th harmonic current distortion limit value epsilon is obtained according to related electric energy quality standardsk；
N3: according to the formula
Figure BDA0003092467520000093
Calculating to obtain the secondary sampling frequency of k-th harmonic
Figure BDA0003092467520000094
Wherein f iskThe k harmonic frequency.
For step N1, in this embodiment, under the condition that the voltage of the power grid line is 380V and the direct-current side resistance of the three-phase uncontrolled rectifier bridge is 18.75 Ω, the content η of each sub-harmonic in the power grid before the active power filter is put into operation is measuredk。
In step N2, different power quality standards have different regulations on the content of each harmonic current, and the same standard has different regulations on the content of each harmonic current in different application occasions. In practical application, the distortion limit value of each harmonic current specified by the corresponding power quality standard is consulted to obtain the required epsilonkAnd (4) finishing. In the embodiment, the voltage of a power grid in IEEE std.519-2014 is in the range of 120V-69 kV, and the system short-circuit ratio ISC/ILIf the current distortion is less than 20, the predetermined distortion limit of each harmonic current is calculated.
For step N3, the following formula is calculated for the subsampling frequency
Figure BDA0003092467520000101
Derivation and explanation are carried out:
according to Fourier transform theory, a periodic continuous-time signal iL(t) can be written as follows:
Figure BDA0003092467520000102
Figure BDA0003092467520000103
wherein A isk、BkCosine component, sine component, T of the amplitude of the k harmonic current1、ω1The fundamental wave period and the fundamental wave angular frequency are respectively.
In the calculation of Ak、BkIn time, a discretization form is adopted:
Figure BDA0003092467520000104
wherein A isk[n]、Bk[n]The cosine component and the sine component of the k-th harmonic current amplitude corresponding to the current sampling time, wherein N is fs/f1，TsIs a sampling period, fs、f1Respectively, a sampling frequency and a fundamental frequency.
When the nonlinear load is a three-phase uncontrolled rectifier bridge with inductive load, the current pulsation of the grid side is small in a steady state and can be approximate to 120-degree square wave. At this time, i in the above formulaL[m]Can be regarded as a constant I tending towards a steady state valueL. To calculate Ak[n]For example, according to the formula of summation of trigonometric series, and neglecting infinitesimal terms in the derivation process, there are:
Figure BDA0003092467520000111
in fact:
Figure BDA0003092467520000112
therefore, the discretization process has relative errors:
Figure BDA0003092467520000113
wherein A isk[n]、Ak(t) is the result of k-th harmonic amplitude cosine component under the operation of discretization calculation and continuous integration, fk、ωkIs the k harmonic frequency, angular frequency, fsIs the sampling frequency, t1、t2Respectively corresponding to the starting point time and the end point time of the phase change of the same switch tube of a certain phase inversion bridge arm.
Although the above results in a relative error expression for calculating the cosine component of the amplitude of the k-th harmonic, the k-th harmonic amplitude is due to the relative error expression
Figure BDA0003092467520000114
And A isk[n]、Bk[n]The principle of calculation is consistent, so δkI.e. calculating the k-th harmonic amplitude C in a discretization mannerkRelative error of (2). At the same time, deltakThe relative error of the k-th harmonic effective value is also calculated for the discretization.
From deltakIt can be seen that the sampling frequency f is the sampling frequency when the instruction extraction is performed for the specified subharmonicsThe larger the discretization process is, the smaller the relative error is, and the closer the discretization result is to the actual value.
In the high-frequency active power filter, the current loop has high control bandwidth and strong current tracking control capability, and the transfer function of the current loop can be approximate to 1, namely the output current i of the devicecCapable of fully tracking instruction value iLh *When the active power filter is put into use, the k-th harmonic content of the grid current is as follows:
Figure BDA0003092467520000115
wherein, Ik(t)、Ik' (t) is respectively the k-th harmonic effective value of the power grid current before and after the active power filter is put into operation, I1(t) is the effective value of the fundamental wave of the grid current, Ik[n]The k-th harmonic effective value of the power grid current is obtained by performing discrete Fourier transform calculation after secondary sampling.
When active powerThe k-th harmonic content of the grid current after the filter is put into operation is eta'kThe k-th harmonic current distortion limit value epsilon specified in the power quality standard should be satisfiedkThe requirements of (a), namely:
Figure BDA0003092467520000121
the above equation is modified:
Figure BDA0003092467520000122
the relative error of the discretization process obtained by combining the derivation
Figure BDA0003092467520000123
Obtaining:
Figure BDA0003092467520000124
subsampling frequency in the invention
Figure BDA0003092467520000125
To meet the minimum sampling frequency of the above inequality condition, i.e.:
Figure BDA0003092467520000126
under the conditions that the frequency of a power grid is 50Hz, the line voltage is 380V and the direct-current side resistance of the three-phase uncontrolled rectification nonlinear load is 18.75 omega, the k-th harmonic content eta of the power grid current before the active power filter is put into operation is measuredkCombined with the k harmonic current distortion limit epsilon specified in the standard IEEE std.519-2014kAccording to the formula
Figure BDA0003092467520000127
The second sampling frequency of the characteristic subharmonic within 50 times is obtained by calculation
Figure BDA0003092467520000128
As shown in table 1 below.
TABLE 1
Figure BDA0003092467520000129
Figure BDA0003092467520000131
Second sampling optimization frequency of each harmonic in table 1
Figure BDA0003092467520000132
The determination is made with a switching frequency equal to 100 kHz. As can be seen from Table 1, the second sampling frequency of each harmonic
Figure BDA0003092467520000133
With frequency optimisation by subsampling
Figure BDA0003092467520000134
All satisfy the Shannon sampling theorem fs≥2fkWherein f iss、fkRespectively, a sampling frequency and a k-th harmonic frequency.
The secondary sampling frequency of each harmonic is determined according to the secondary sampling method provided by the invention
Figure BDA0003092467520000135
Fig. 5 shows a block diagram of the calculation of each harmonic current command.
FIG. 5 shows the kth harmonic current command of FIG. 4 at a subsampling frequency
Figure BDA0003092467520000136
And performing secondary sampling and calculating block diagram. First, for iLFPerforming secondary sampling to obtain iLssAt a sub-sampling frequency of
Figure BDA0003092467520000137
Will iLssRespectively with the cosine factor after the secondary sampling
Figure BDA0003092467520000138
Sine factor
Figure BDA0003092467520000139
Multiplying, and adding the amplitude A before one secondary sampling periodk[n-1]、Bk[n-1]Obtaining the cosine component A of the current amplitude of the k-th harmonic wave at the current momentk[n]Sinusoidal component Bk[n]Wherein
Figure BDA00030924675200001310
The subsampling period for the k harmonic. At this time, the transformation of the load current signal from the time domain to the frequency domain, i.e., the discrete Fourier forward transformation, is completed. In the conversion process, the secondary sampling frequency
Figure BDA00030924675200001311
Below the switching frequency fsw(in this example f)sw＝fps100kHz) so that the controller need not be on every switching period Tsw＝1/fswAnd updating the harmonic frequency spectrum, thereby reducing the calculation time of the harmonic current instruction.
As shown in fig. 5, the cosine component a of the current amplitude of the k-th harmonic at the current time is calculatedk[n]Sinusoidal component Bk[n]Then, the two are multiplied by cosine factors cos (k ω)1nTps) Sin (k ω) sine factor1nTps) Adding the two terms and multiplying by a gain adjustment coefficient of 2/NkObtaining the command value i of the k-th harmonic current at the current momentLk(ii) a Wherein
Figure BDA0003092467520000141
Second sampling frequency of k harmonics, f1Is the fundamental frequency. The calculation process corresponds to the inverse discrete Fourier transform, and the transformation of the load current signal from the frequency domain to the time domain is completed. With the foregoing Fourier forward transform processIn contrast, in each switching period TswDiscrete Fourier inverse transformation is required to obtain the instruction value i of the k-th harmonic currentLk。
According to the harmonic current instruction extraction method provided by the embodiment of the invention in FIG. 5, the harmonic current instructions are added to obtain a total harmonic current instruction iLh *。
Table 2 shows the comparison between the computation required for extracting the k-th harmonic current command according to the flow shown in fig. 5 by the second sampling method of the present invention and the computation required for extracting the k-th harmonic current command by the harmonic command extraction method based on the discrete Fourier transform and the recursive discrete Fourier transform. As can be seen from table 2, compared with the currently common harmonic instruction extraction method based on recursive discrete Fourier transform, the secondary sampling method provided by the present invention can further reduce the computation amount of harmonic current instruction extraction.
TABLE 2
Harmonic instruction extraction method Number of multiplications Number of times of addition
Discrete Fourier transform 2(N+2) 2N-1
Recursive discrete Fourier transform 5 3
Recursive discrete Fourier transform based on subsampling 3+2/m 1+2/m
Wherein m is a primary sampling frequency fpsWith frequency optimisation by subsampling
Figure BDA0003092467520000142
The ratio of.
Combining Table 1, subsampling optimized frequencies
Figure BDA0003092467520000143
The highest of these is 12.5kHz, which is only 1/8 of the switching frequency. When each harmonic is sampled and calculated twice according to 12.5kHz, the controller only needs to calculate the current amplitude of each harmonic every 8 switching periods, namely, the controller only needs to carry out multiplication and addition operation for 3.25 times on average when carrying out single harmonic current instruction calculation in each switching period. Compared with a harmonic instruction extraction method based on recursive discrete Fourier transform, the operation amount is reduced by nearly half. When each harmonic is sub-sampled and calculated according to the respective sub-sampling optimized frequency, the operation amount can be further reduced. Taking the 5 th harmonic current command calculation as an example, according to table 1, the secondary sampling optimization frequency is 1.25kHz, which is only 1/80 of the switching frequency, and the controller only needs to calculate the 5 th harmonic current amplitude every 80 switching cycles.
Fig. 6 shows a block diagram of a controller in an embodiment of the invention. According to the PCC voltage phase theta obtained by phase locking of a phase-locked loop, a total harmonic current instruction i is obtainedLh *And transforming the coordinate system into a dq synchronous rotating coordinate system for tracking control, wherein:
Figure BDA0003092467520000151
the d-axis current command value id *Adding the active current i output by the voltage loopdcThen subtracting the d-axis component i of the compensation current output by the devicedAnd the harmonic current is sent to a PI regulator for tracking control of the harmonic current. Similarly, the q-axis current command value iq *Subtracting the q-axis component i of the compensating current output by the deviceqAnd sending the signal to a PI regulator for regulation. The signals regulated by the PI regulator are subjected to state feedback cross decoupling and power grid voltage feedforward, and then are subjected to dq/alpha beta conversion to obtain alpha and beta axis components u of the regulating signals output by the controllerrα、urβ. In three-phase systems according to urα、urβThe pulse trigger signal of each switch tube on the three-phase inverter bridge is formed by utilizing a space voltage vector modulation technology, and the pulse trigger signal is driven and amplified to control the on-off of each switch tube and output a compensation current ic. Wherein:
Figure BDA0003092467520000152
fig. 7 is a diagram showing a control structure of a phase-locked loop according to an embodiment of the present invention, which is a phase-locked loop based on dq synchronous rotation coordinate transformation. By making the q-axis voltage command 0, the fundamental angular frequency ω is adjusted by the PI regulator1And adjusting to ensure that the direction of the d axis is always consistent with the direction of the PCC voltage synthetic vector, thereby completing phase locking.
Fig. 8(a) is a graph showing a relationship between a first sampling frequency and a second sampling optimized frequency of each sub-harmonic after the second sampling method provided by the present invention is adopted in this embodiment; fig. 8(b) is a relative error curve calculated for each harmonic amplitude at different secondary sampling frequencies. As can be seen from FIG. 8(a), the second sampling of each harmonic optimizes the frequency
Figure BDA0003092467520000161
Much lower than the primary sampling frequency fpsNamely, the controller does not need to carry out discrete Fourier forward conversion in each switching period to calculate the amplitude of each harmonic current, thereby reducing the calculation time of the harmonic current instruction. As can be seen from fig. 8(b), for the k harmonics, the first sampling frequency f is taken when the second sampling frequency is respectively the first sampling frequencypsSecond sampling frequency optimization
Figure BDA0003092467520000162
Sub-sampling optimized frequency
Figure BDA0003092467520000163
When the error is larger, the relative error is increased continuously; when the second sampling frequency of each harmonic is the same, the relative error increases as the number of harmonics increases.
Fig. 9(a) -9 (d) show the simulation results of the subsampling method provided by the embodiment of the present invention under the conditions of the grid frequency of 50Hz, the grid line voltage of 380V, the three-phase uncontrolled rectifying load of 18.75 Ω, and the switching frequency of 100 kHz. FIG. 9(a) is a graph of net side current waveform and spectrum when the active power filter is not in operation; FIG. 9(b) is a plot of net side current waveform versus spectrum when no subsampling is performed, compensating only for harmonics 5 to 19 times; FIG. 9(c) is a graph of the sub-sampling optimized frequency provided in Table 1 of the example of the present invention based on the harmonic order k
Figure BDA0003092467520000164
Performing secondary sampling to compensate all characteristic subharmonics within 50 times of grid side current waveform and spectrogram; FIG. 9(d) is a graph of the second sampling optimization frequency for each harmonic at 49 th harmonic
Figure BDA0003092467520000165
And performing secondary sampling to compensate the waveform and spectrogram of the current on the network side when all characteristic subharmonics within 50 times are obtained.
In fig. 9(a), when the active power filter is not in use, the current Distortion on the network side is severe, and the Total Harmonic Distortion (THD) reaches 27.76%. In the present embodiment, the switching frequency fswThe control period is only 10 mus at 100kHz, so when the harmonic is treated by the conventional sampling method, the compensation of all characteristic subharmonics within 50 times may not be completed due to the limited number of the compensated harmonics. FIG. 9(b) shows the simulation results when the 5 th to 19 th harmonic currents are compensated by the conventional sampling method, and although the distortion phenomenon of the net side current is improved, the THD is reduced from 27.76% to 5.54%, but the single harmonic of 23 th order and above is reducedThe content is still high. As can be seen from fig. 9(c), after the secondary sampling method provided by the present invention is adopted, harmonics of 23 times and above are well suppressed, THD further decreases to 2.50%, and the grid-side current approaches sinusoidal. As can be seen from FIG. 9(d), the second-order sampling optimization frequency when the second-order sampling frequency of each harmonic is 49 second-order sampling optimization frequency
Figure BDA0003092467520000171
When the method is used, the THD can be further reduced to 1.08%, and the overall effect of harmonic suppression is better.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A specified subharmonic suppression secondary sampling method of an active power filter is characterized in that the active power filter is connected between a power grid and a load in parallel, a public connection point is PCC, and a control part of the active power filter is divided into a voltage control outer ring, a current control inner ring and SVPWM modulation, and the method is characterized by comprising the following steps:
s1, sampling frequency fpsSampling for one time to obtain load current iL[n]PCC voltage uTOutput current of active power filter, and direct-current side voltage u of active power filterdc；
S2, detecting load current iL[n]According to the harmonic order k of the specified subharmonic to be suppressed, at a sampling frequency
Figure FDA0003092467510000011
For load current iL[n]Performing secondary sampling, and calculating to obtain k-th harmonic current compensation instruction iLkSumming to obtain total harmonic current compensation command value iLh *；
S3, voltage outer ring adjustment is carried out to obtain an active current instruction idc；
S4, compensating the instruction i according to the total harmonic currentLh *Active power filter output current and active current instruction idcPCC voltage uTPerforming current inner loop regulation to obtain a pulse width modulation signal urα、urβ；
S5, according to the pulse width modulation signal urα、urβAnd controlling a switching tube in the active power filter, and adopting space voltage vector modulation to output compensation current to realize the specified subharmonic suppression of the power grid.
2. The active power filter specified subharmonic suppression subsampling method according to claim 1, wherein a sampling frequency at which k-th harmonics are subsampled
Figure FDA0003092467510000012
Comprises the following steps:
Figure FDA0003092467510000013
Figure FDA0003092467510000014
wherein eta iskContent of k-th harmonic current of grid current before active power filter is put into operation, Ik(t) is the effective value of the k-th harmonic current of the network current before the active power filter is put into operation, I1(t) is the fundamental effective value of the network current, fkIs the frequency of the k harmonic current, epsilonkDistortion limit of k-th harmonic current specified for power quality standards.
3. The active power filter specified subharmonic rejection subsampling method according to claim 2, wherein step S2 is specifically:
s21, load current i obtained by primary samplingL[n]Filtering is carried outProcess, output iLF；
S22, pair iLFPerforming secondary sampling to obtain iLssAt a sub-sampling frequency of
Figure FDA0003092467510000021
Will iLssAnd cosine factor
Figure FDA0003092467510000022
Multiply by plus Ak[n-1]To obtain Ak[n](ii) a Will iLssAnd sine factor
Figure FDA0003092467510000023
Multiply by and add Bk[n-1]To obtain Bk[n](ii) a Wherein A isk[n-1]、Bk[n-1]Respectively a cosine component and a sine component of the k harmonic current amplitude before a second sampling period, Ak[n]、Bk[n]Respectively a cosine component and a sine component of the current amplitude of the k-th harmonic wave at the current sampling time,
Figure FDA0003092467510000024
second sampling period, omega, of the order of k harmonics1Is the fundamental angular frequency;
s23, mixing Ak[n]Multiplied by a cosine factor cos (k ω)1nTps)，Bk[n]Multiplication by sine factor sin (k ω1nTps) After the two terms are added, the two terms are multiplied by a gain adjustment coefficient 2/NkObtaining the current k-th harmonic current instruction value i at the current momentLk(ii) a Wherein T isps＝1/fpsIs a sampling period;
Figure FDA0003092467510000025
Figure FDA0003092467510000026
second sampling frequency of k harmonics, f1Is the fundamental frequency;
s24, specified subharmonic electricity to be compensatedAdding the current command values to obtain the sum of the harmonic current commands to be compensated
Figure FDA0003092467510000027
4. The active power filter specified subharmonic suppression subsampling method according to claim 3, wherein the output i in step S21LF＝iL[n]-iL[n-N](ii) a Wherein iL[n]Load current i obtained by one sampling corresponding to the current momentL[n-N]Corresponding to the load current sampled at the previous time of a fundamental wave period, wherein N is fps/f1，f1Is the fundamental frequency.
5. The active power filter specified subharmonic rejection subsampling method according to claim 2, wherein the primary sampling frequency fpsAnd a sub-sampling frequency
Figure FDA0003092467510000028
The following relationship is satisfied:
Figure FDA0003092467510000029
wherein the secondary sampling frequency
Figure FDA00030924675100000210
Can be sampled once at frequency fpsInteger division, also the fundamental frequency f1Multiples of (a).
6. The active power filter specified subharmonic suppression subsampling method according to claim 5, wherein the subsampling frequency of each harmonic is identical and equal to the highest subsampling frequency of the harmonics to be compensated.
7. An active power filter specified subharmonic rejection subsampling system, comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium, and execute the active power filter specified subharmonic suppression subsampling method of any of claims 1 to 6.
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