CN108899907B - LCLCL type active power filter control method based on repeated sliding mode control - Google Patents

LCLCL type active power filter control method based on repeated sliding mode control Download PDF

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CN108899907B
CN108899907B CN201810758060.8A CN201810758060A CN108899907B CN 108899907 B CN108899907 B CN 108899907B CN 201810758060 A CN201810758060 A CN 201810758060A CN 108899907 B CN108899907 B CN 108899907B
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sliding mode
phase
control
error
sapf
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CN108899907A (en
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高云广
武迎春
智泽英
左龙
丁伟
贺玫璐
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Taiyuan 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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • 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
    • Y02E40/20—Active power filtering [APF]

Abstract

LCLCL type active power filter control method based on repeated sliding mode controlThe invention belongs to the field of active power filter control, and establishes a sliding mode switching function by linear combination of 3 error variables of an inverter output current error, a filter capacitor voltage error and a grid-connected harmonic current error, solves the sliding mode control effect through an exponential approximation law, adds repeated control to a sliding mode surface instead of multi-proportion resonance control aiming at the sliding mode surface drift problem caused by the incompleteness of system modeling and the uncertainty of system parameters, and adds a harmonic current error term x to the sliding mode surface3aCompensation is carried out, a repeated sliding mode composite control strategy is provided, full harmonic compensation is realized, steady-state errors are further reduced, and frequency adaptability is enhanced.

Description

LCLCL type active power filter control method based on repeated sliding mode control
Technical Field
The invention belongs to the field of active power filter control, and particularly relates to a control method of an LCLCLCL type active power filter based on repeated sliding mode control.
Background
The sliding mode control is variable structure control, and the essence of the variable structure control is that in the vicinity of a specified sliding manifold (sliding mode surface), a controlled state motion track vector always points to the sliding manifold, and the motion is guided and realized by discontinuous control action applied by a switch control strategy, so that the trajectory of a controlled object is finally driven to a desired balance point. In the sliding mode switching process, the system running track is only influenced by the sliding mode surface and is irrelevant to the parameters and disturbance of a control object, so the system has high dynamic response speed and strong robustness [39 ]. The ideal sliding mode control method requires that the switch can be infinitely switched, so that the system state always meets the sliding mode, the sliding mode motion is ensured, and accurate tracking, zero-error regulation and quick dynamic response are realized. However, in practical application, the sliding mode control method is realized by a digital system, and the method needs to detect intermediate variables by a plurality of sensors, construct a state equation, further establish a sliding mode surface, and realize the approach and the following of the sliding mode surface through high switching frequency switching. Although the robustness of the control system is enhanced, the non-ideal infinite switching of the switch in the control process can cause buffeting to occur, and the problems of unmodeled dynamic influence, parameter uncertainty, adaptive learning and the like exist in the presence of time lag and discrete system delay, so that the steady-state compensation precision of the control system is influenced. In the existing research, the steady-state performance of sliding mode control is improved through the approach law design and the sliding mode surface modification. The conventional linear sliding surface is composed of a linear combination of system state variables, and when system parameter changes or external interference exists, the sliding surface can drift, which influences the output tracking error of the system. Integral sliding mode control and intelligent sliding mode control integrated with technologies such as fuzzy logic, artificial neural networks and the like become research hotspots for improving sliding mode control performance.
The prior art proposes a multiple-integration smc (ismc) method for DC-DC converters and DC-AC inverters, which utilizes sequential integration to smooth buffeting and improve system steady-state accuracy. In addition, a new SMC with a double integral sliding surface is provided on the basis of the ISMC for a direct current tracking system, and the control scheme can effectively reduce the steady-state error of the DC-DC converter. Or an integral sliding mode surface is obtained by introducing the difference integral of the equivalent control rate and the actual control rate, so that buffeting in sliding mode movement is effectively reduced, and the steady-state precision of the active power filter is improved. However, for the ac tracking system, the steady-state error can be reduced by using these methods, but the sinusoidal tracking error of the inverter cannot be completely reduced, and for the active power filter, the tracking capability for the harmonic is limited, and the integration sliding mode control is easy to cause the problems of large overshoot and long adjustment time, thereby deteriorating the transient performance. In order to solve the defects, a multi-resonance item of grid-connected current errors is introduced into a sliding mode surface, and the grid-connected current tracking errors are eliminated by utilizing the high loop gain characteristic of resonance control on periodic signals.
Disclosure of Invention
The invention provides a control method of an LCLCLCL type active power filter based on repeated sliding mode control aiming at adverse effects of mine power grid impedance changes on robustness of a traditional feedforward repeated control system, and solves the problem of robustness of the LCLCL filter when a transfer function of a controlled object is changed. The method has the advantages of quick dynamic response, strong robustness and simple execution, and can eliminate the influence of the disturbance of the impedance of the power grid on the system. The sliding mode surface is reformed by using the advantages of gain amplification of harmonic waves by repeated control and no-static-error tracking of periodic signals, a repeated sliding mode control strategy for the active power filter is provided, and the steady-state precision of the sliding mode control system is improved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the LCLCL type active power filter control method based on repeated sliding mode control comprises the following design steps:
step 1) establishing a continuous time dynamic model of a three-phase LCLCL type SAPF according to a main circuit structure of the LCLCLCL active power filter;
step 2) defining an error variable x according to the time dynamic model of the active power filter established in the step 1)1a，x2aAnd x3aEstablishing a system state space equation of sliding mode control, and solving a coefficient of the system state space equation;
step 3) solving a sliding mode switching function, a sliding mode surface and a control action u according to the system state space equation established in the step 2), wherein the control action u is a duty ratio d;
step 4) carrying out Laplace transformation on the obtained sliding mode switching function to convert the sliding mode switching function into a sliding mode form in a frequency domain, and switching harmonic current error x in the function to the sliding mode3aInserting a repeated control condition, modifying a sliding mode switching function, and determining a control block diagram of the SAPF control system based on the repeated sliding mode according to the sliding mode switching function.
Further, the establishment process of the continuous time dynamic model of the three-phase LCLCLCL type SAPF is as follows:
the continuous time dynamic model of the three-phase LCLCLCL type SAPF is
Figure BDA0001727219340000021
Wherein the content of the first and second substances,
Figure BDA0001727219340000022
for the phase voltage of the grid to the neutral point n,
Figure BDA0001727219340000023
the phase voltage at the output side of the PWM inverter to the dc side midpoint o,
Figure BDA0001727219340000024
the phase voltage of the filter capacitor branch to the neutral point o 'is considered, and when the three phases are balanced, n, o and o' are considered as equal potential points; i.e. ishAnd iinvRespectively, the grid-connected current and the inverter output current of the SAPF.
Wherein the inverter outputs a voltage vector
Figure BDA0001727219340000025
Can be based on the voltage u on the DC sidedcThe relationship (c) is expressed as follows:
Figure BDA0001727219340000031
in the formula (I), the compound is shown in the specification,
Figure BDA0001727219340000032
when the frequency is high enough, neglecting PWM high frequency component to switch in one period skVarying mean value, i.e. PWM duty cycle dkTo replace skThe above formula can be rewritten as:
Figure BDA0001727219340000033
for a three-phase symmetric system, three phases can be independently controlled, and the analysis is performed by taking the phase A as an example,
wherein the A-phase continuous time dynamic model is as follows:
Figure BDA0001727219340000034
usafor the A-phase voltage of the network, ucaIs the A-phase capacitance branch voltage, ishaAnd iinvaThe phase A grid-connected current of the SAPF and the phase A output current of the inverter are respectively. daIs the a phase duty cycle.
Further, the establishment process of the system state space equation of sliding mode control is as follows:
define 3 error variables: error x of output current1aFilter capacitor voltage error x2aAnd grid-connected harmonic current error x3a，，
Figure BDA0001727219340000035
In the formula (I), the compound is shown in the specification,
Figure BDA0001727219340000036
and
Figure BDA0001727219340000037
respectively is an inverter output current A-phase reference value, an A-phase capacitance voltage reference value and an SAPF grid-connected current A-phase reference value,
Figure BDA0001727219340000038
the harmonic current is obtained by d-q method detection based on instantaneous reactive power theory, namely, A phase harmonic command current,
Figure BDA0001727219340000039
and
Figure BDA00017272193400000310
satisfies the formula (1), and therefore
Figure BDA00017272193400000311
And
Figure BDA00017272193400000312
the derivation can be as follows:
Figure BDA00017272193400000313
Figure BDA00017272193400000314
state variable x1a，x2aAnd x3aRespectively, the 3 error variables of interest, and if the 3 error variables are made to be 0 through the control action, the SAPF achieves perfect harmonic compensation, and therefore, a state space equation is constructed:
Figure BDA0001727219340000041
in the formula (I), the compound is shown in the specification,
Figure BDA0001727219340000042
Figure BDA0001727219340000043
Figure BDA0001727219340000044
Figure BDA0001727219340000045
the coefficients and state inputs of the system state space equation can be described as:
Figure BDA0001727219340000046
further, the specific process of step 3) is as follows:
defining a linear sliding-mode switching function sigmaa
σa＝CX＝[α1 α2 α3]X (6)
In the formula, alpha1，α2And alpha3Is a real constant to achieve system stability.
The exponential approach rate is selected so that the system meets the arrival conditions while being stable.
Figure BDA0001727219340000047
The compounds represented by the formulae (4), (5) and (6) can be obtained by substituting the compounds represented by the formula (7):
Figure BDA0001727219340000048
the control action u of the system, i.e. the A-phase duty cycle d, can be obtained by solving the formula (8)a
Figure BDA0001727219340000049
In the formula (I), the compound is shown in the specification,
Figure BDA00017272193400000410
Figure BDA0001727219340000051
Figure BDA0001727219340000052
as can be seen from the equation (9), d is a control action of the modulated waveaCan be divided into three parts: equivalent part da_eqLinear part da_lAnd a non-linear part da_nWherein the equivalent part da_eqIs composed of
Figure BDA0001727219340000053
Equivalent control action, linear part d, which can be obtaineda_lAnd a non-linear part da_nThe control effect of B phase and C phase is consistent with that of A phase, wherein K is the compensation effect of exponential approach ratePWMFor inverter output gain udc/2。
Further, the sliding mode form in the frequency domain:
σa(s)＝α1x1a(s)+α2x2a(s)+α3x3a(s) (13)
the internal model structural form of the time domain repetitive control can be expressed as:
Figure BDA0001727219340000054
in the formula, kRCFor repeated control gain, T is the fundamental wave period of the input signal, omega is the fundamental wave frequency, and n is the harmonic frequency;
when Q takes a constant, equation (14) can be rewritten as:
Figure BDA0001727219340000055
in the formula, ωcIs a resonant frequency, and
Figure BDA0001727219340000056
harmonic current error x in function switching to sliding mode3aThe term is inserted into the repetitive control condition (15), then the sliding mode switching function can be modified to:
σa(s)＝α1x1a(s)+α2x2a(s)+α3x3a(s)+GRC(s)x3a(s) (16)
the repetitive control can be directly applied to the harmonic current error x by equation (16)3aThe a-phase control block diagram of the repetitive sliding mode control based SAPF system is determined according to equation (16).
The invention establishes a sliding mode switching function by linear combination of 3 error variables of inverter output current error, filter capacitor voltage error and grid-connected harmonic current error, obtains the sliding mode control action through an exponential approximation law, adds repeated control to a sliding mode surface instead of multi-proportion resonance control, and adds a harmonic current error term x3aCompensation is carried out, a repeated sliding mode composite control strategy is provided, full harmonic compensation is realized, steady-state errors are further reduced, and frequency adaptability is enhanced.
The repeated sliding mode control strategy can realize high-precision compensation of power grid harmonic waves, has good dynamic response capability and robustness against power grid impedance disturbance, has smaller tracking error, and has more advantages in the aspects of discrete implementation, frequency adaptability and the like.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings.
Fig. 1 shows a main circuit structure of an lclclcl active power filter.
FIG. 2 is a control block diagram of an A-phase of a SAPF control system based on a repeated sliding mode.
FIG. 3 shows the error x in repetitive sliding mode control3a(s) Bode diagram.
FIG. 4 shows the A-phase load current i based on the repetitive sliding mode controlLaWith the current i of the gridsaA steady state waveform is simulated.
Fig. 5 is a graph of a-phase harmonic current spectrum based on repetitive sliding mode control.
FIG. 6 shows the phase-A harmonic current error x under different control strategies3a(t) waveform.
Fig. 7 is a phase a dynamic simulation waveform of a repetitive sliding mode control SAPF when the load changes.
Fig. 8 is a steady-state simulation waveform of the phase a of the SAPF when the grid impedance changes.
Fig. 9 is a phase a dynamic simulation waveform of SAPF when the grid impedance changes.
Fig. 10 is a waveform of a power grid current and harmonic error experiment in sliding mode control.
Fig. 11 shows experimental waveforms of the grid current and the harmonic error in the multi-scale resonant sliding mode control.
Fig. 12 shows the experimental waveform of the grid current and the harmonic error when the sliding mode control is repeated.
Fig. 13 is a power grid current spectrum under multi-scale resonant sliding mode control.
Fig. 14 shows the grid current spectrum when sliding mode control is repeated.
FIG. 15 is a waveform of a dynamic response experiment in multi-scale resonant sliding mode control.
Fig. 16 is a waveform of a dynamic response experiment when sliding mode control is repeated.
Detailed Description
In order to make the objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
The LCLCL type active power filter control method based on repeated sliding mode control comprises the following design steps:
step 1) establishing a continuous time dynamic model of a three-phase LCLCL type SAPF according to a main circuit structure of the LCLCLCL active power filter;
step 2) defining an error variable x according to the time dynamic model of the active power filter established in the step 1)1a，x2aAnd x3aEstablishing a system state space equation of sliding mode control, and solving a coefficient of the system state space equation;
step 3) solving a sliding mode switching function, a sliding mode surface and a control action u according to the system state space equation established in the step 2), wherein the control action u is a duty ratio d;
step 4) carrying out Laplace transformation on the obtained sliding mode switching function to convert the sliding mode switching function into a sliding mode form in a frequency domain, and switching harmonic current error x in the function to the sliding mode3aInserting a repeated control condition, modifying a sliding mode switching function, and determining a control block diagram of the SAPF control system based on the repeated sliding mode according to the sliding mode switching function.
The specific process is as follows:
step 1) according to the main circuit structure of the lclclcl active power filter of fig. 1, the process of establishing the continuous time dynamic model of the three-phase lclclclcl type SAPF is:
the continuous time dynamic model of the three-phase LCLCLCL type SAPF is:
Figure BDA0001727219340000071
wherein the content of the first and second substances,
Figure BDA0001727219340000072
for the phase voltage of the grid to the neutral point n,
Figure BDA0001727219340000073
the phase voltage at the output side of the PWM inverter to the dc side midpoint o,
Figure BDA0001727219340000074
the phase voltage of the filter capacitor branch to the neutral point o 'is considered, and when the three phases are balanced, n, o and o' are considered as equal potential points; i.e. ishAnd iinvRespectively, the grid-connected current and the inverter output current of the SAPF.
Wherein the inverter outputs a voltage vector
Figure BDA0001727219340000075
Can be based on the voltage u on the DC sidedcThe relationship (c) is expressed as follows:
Figure BDA0001727219340000076
in the formula (I), the compound is shown in the specification,
Figure BDA0001727219340000077
when the frequency is high enough, neglecting PWM high frequency component to switch in one period skVarying mean value, i.e. PWM duty cycle dkTo replace skThe above formula can be rewritten as:
Figure BDA0001727219340000078
for a three-phase symmetric system, three phases can be independently controlled, and the analysis is performed by taking the phase A as an example,
wherein the A-phase continuous time dynamic model is as follows:
Figure BDA0001727219340000081
usafor the A-phase voltage of the network, ucaIs the A-phase capacitance branch voltage, ishaAnd iinvaThe phase A grid-connected current of the SAPF and the phase A output current of the inverter are respectively. daIs the a phase duty cycle.
Step 2) define 3 error variable inverters: error x of output current1aFilter capacitor voltage error x2aAnd grid-connected harmonic current error x3a，
Figure BDA0001727219340000082
In the formula (I), the compound is shown in the specification,
Figure BDA0001727219340000083
and
Figure BDA0001727219340000084
respectively is an inverter output current A-phase reference value, an A-phase capacitance voltage reference value and an SAPF grid-connected current A-phase reference value,
Figure BDA0001727219340000085
the harmonic current is obtained by d-q method detection based on instantaneous reactive power theory, namely, A phase harmonic command current,
Figure BDA0001727219340000086
and
Figure BDA0001727219340000087
satisfies the formula (1), and therefore
Figure BDA0001727219340000088
And
Figure BDA0001727219340000089
the derivation can be as follows:
Figure BDA00017272193400000810
Figure BDA00017272193400000811
state variable x1a，x2aAnd x3aRespectively, the 3 error variables of interest, and if the 3 error variables are made to be 0 through the control action, the SAPF achieves perfect harmonic compensation, and therefore, a state space equation is constructed:
Figure BDA00017272193400000816
in the formula (I), the compound is shown in the specification,
Figure BDA00017272193400000812
Figure BDA00017272193400000813
Figure BDA00017272193400000814
Figure BDA00017272193400000815
the coefficients and state inputs of the system state space equation can be described as:
Figure BDA0001727219340000091
the specific process of the step 3) is as follows: defining a linear sliding-mode switching function sigmaa
σa＝CX＝[α1 α2 α3]X (6)
In the formula, alpha1，α2And alpha3Is a real constant to achieve system stability.
The exponential approach rate is selected so that the system meets the arrival conditions while being stable.
Figure BDA0001727219340000098
The compounds represented by the formulae (4), (5) and (6) can be obtained by substituting the compounds represented by the formula (7):
Figure BDA0001727219340000092
the control action u of the system, i.e. the A-phase duty cycle d, can be obtained by solving the formula (8)a
Figure BDA0001727219340000093
In the formula (I), the compound is shown in the specification,
Figure BDA0001727219340000094
Figure BDA0001727219340000095
Figure BDA0001727219340000096
as can be seen from the equation (9), d is a control action of the modulated waveaCan be divided into three parts: equivalent part da_eqLinear part da_lAnd a non-linear part da_nWherein the equivalent part da_eqIs composed of
Figure BDA0001727219340000097
Equivalent control action, linear part d, which can be obtaineda_lAnd a non-linear part da_nThe control effect of B phase and C phase is consistent with that of A phase, wherein K is the compensation effect of exponential approach ratePWMFor inverter output gain udc/2。
Step 4), sliding mode form in frequency domain:
σa(s)＝α1x1a(s)+α2x2a(s)+α3x3a(s) (13)
the internal model structural form of the time domain repetitive control can be expressed as:
Figure BDA0001727219340000101
in the formula, kRCFor repeated control gain, T is the fundamental wave period of the input signal, omega is the fundamental wave frequency, and n is the harmonic frequency;
when Q takes a constant, equation (14) can be rewritten as:
Figure BDA0001727219340000102
in the formula, ωcIs a resonant frequency, and
Figure BDA0001727219340000103
harmonic current error x in function switching to sliding mode3aThe term is inserted into the repetitive control condition (15), then the sliding mode switching function can be modified to:
σa(s)＝α1x1a(s)+α2x2a(s)+α3x3a(s)+GRC(s)x3a(s) (16)
the repetitive control can be directly applied to the harmonic current error x by equation (16)3aDetermining an A-phase control frame based on a repetitive sliding mode control SAPF system according to equation (16)Figure (a).
The following analysis takes the compensation of the error introduced by the 7 th harmonic current and the fundamental voltage as an example to analyze the effect of the present invention.
Figure BDA0001727219340000104
When k isRCWhen 1, x3aThe(s) frequency domain bode plot is shown in fig. 3.
As can be seen from FIG. 3, the error x3a(s) has a significant attenuation at both fundamental and harmonic frequencies, with a gain of less than-200 dB. Therefore, errors caused by any harmonic wave can be attenuated when the parameters of the filter are changed, and the fact that the repeated control is added to the sliding mode surface can replace a plurality of resonance conditions is proved to play the same error correction role.
The control block diagram of the A phase based on the repeated sliding mode control system is shown in figure 2. Harmonic current error x in fig. 23aAfter repeated control, adding a sliding mode surface, and repeating a transfer function G of the controllerRCAnd(s) in discrete implementation, the influence of power grid fluctuation can be considered, a fractional delay repetitive controller is adopted, and meanwhile, a compensator C (z) consisting of a low-pass filter and a phase lead link can be reasonably added to enable the harmonic compensation effect to be optimal. Compared with a multi-proportion resonance sliding mode control system, the SAPF system based on repeated sliding mode control has the advantages that full harmonic compensation can be realized by using a repeated control strategy, steady-state errors are further reduced, the SAPF system has frequency adaptability by combining a fractional delay filter, and transient characteristics and robustness are enhanced by using sliding mode control.
And (3) building an LCLCLCL type SAPF model based on repeated sliding mode control in the simulation environment of MATLAB, respectively performing steady-state simulation and dynamic simulation, and comparing the performance with the performance of the traditional sliding mode control and the multi-resonance sliding mode control.
1. Steady state characteristic
Fig. 4 and fig. 5 respectively show a phase-a current simulation waveform and a phase-a harmonic current spectrogram of the SAPF during repeated sliding mode control, and it can be seen from the graphs that after a repeated control action is added on the sliding mode surface, the harmonic content of the grid current is further reduced and is lower than 0.8%, which indicates that the repeated control attenuates the harmonic, the grid current THD is reduced to 1.58%, and the harmonic compensation accuracy of the system is obviously better than that of the multi-ratio resonance sliding mode control.
FIG. 6 shows A-phase harmonic current error x under sliding mode control, multi-proportion resonance sliding mode control and repeated sliding mode control strategies3a(t) waveform. Wherein FIG. 6(a) is x for pure sliding mode control3a(t) because uncertainty of system modeling and parameters is not considered, the slip form surface deviates, and the error is large; harmonic current error x by multi-ratio resonant sliding mode control3a(t) is greatly reduced, as shown in FIG. 6(b), x3a(t) the waveform is similar to the harmonic reference, but the multi-proportion resonance sliding mode control strategy cannot realize gain amplification on all harmonics, and still has small errors; FIG. 6(c) shows x in repeating sliding mode control3aAnd (t) the waveform further reduces the harmonic current error compared with the other two cases, and high-precision compensation of the power grid harmonic is realized, but the bandwidth of the internal model filter Q (z) and the compensator C (z) are repeatedly controlled based on stability consideration to influence the harmonic compensation effect.
2. Dynamic characteristics
FIG. 7 is a dynamic simulation waveform of a repetitive sliding mode control SAPF during a load step change, and it can be seen that the A-phase grid current i is during a nonlinear load step changesaThe method has the advantages of good tracking capability and high waveform sine degree, and compared with the waveform in multi-proportion resonant sliding mode control, the method has the advantages that due to the fact that the transient process of repeated control is slightly changed, a small distortion point appears at the current peak value, and still has good dynamic response.
3. Robust analysis
The sliding mode control has the important characteristic of strong robustness, and is reflected in insensitivity of the SAPF control system to power grid parameters, SAPF parameter changes and external interference. When the parameters of the power grid change or disturbance exists, the system can be kept stable and has ideal steady-state accuracy. The invention changes the reactance L of the power grid by changing the resistance L of the power grid under the condition of the same nonlinear load (the resistance on the direct current side is 30 omega)s(0.1mH to 0.8mH) before each testAnd the anti-disturbance capability of the SAPF system during the feedback repetition control and the repetition sliding mode control.
FIG. 8 shows the grid reactance LsAnd (5) steady state simulation results in the change. It can be seen from the figure that when the grid reactance LsWhen the current is changed from 0.1mH to 0.8mH, under the feedforward repeated control, the compensation current i changes due to the change of the control modelshaSignificant deviation, grid current isaThe compensation effect is poor, and the THD is increased to 5.59 percent from 3.09 percent before change; under the control of repeated sliding modes, the approach of the sliding mode surface is independent of the parameters of the power grid, so that the current THD is changed into 1.74% from 1.58% before change, and the waveform of the current of the power grid is close to a standard sine wave.
FIG. 9 shows the grid reactance LsAnd (5) dynamic simulation results in the change. It can be seen from the figure that when the grid reactance LsWhen 0.8s is changed from 0.1mH to 0.8mH, under the feedforward repetitive control, the harmonic current error eaPlus or minus 1A, the current i of the power gridsaThe compensation effect is obviously poor, and the THD is increased from 3.09% to 5.65%; harmonic current error x under repeated sliding mode control3aThe fluctuation of +/-0.5A is increased, the fluctuation is gradually reduced and tends to be stable, the current THD is only changed from 1.58% to 1.63%, and the waveform of the current of the power grid is basically unchanged. Simulation results show that under the condition of power grid impedance change, compensation of the SAPF system is deteriorated due to the fact that a feedforward repetitive control strategy is influenced by disturbance, and the SAPF system can obtain stable harmonic compensation through a repetitive sliding mode control method, so that the SAPF system has strong robustness.
The invention performs experimental simulation of a composite sliding mode control strategy based on a 380V three-phase LCLCLCL type SAPF system experimental platform. Specific parameters of the SAPF system are given in tables 1 and 2. The experimental platform is connected with a 10kW three-phase uncontrolled rectification nonlinear load, and the total direct current capacitance is 3300 muF (Cd1 and Cd2 are respectively formed by connecting two 3300 muF in parallel).
Figure BDA0001727219340000121
TABLE 1SAPF System parameters
Figure BDA0001727219340000122
TABLE 2 sliding mode control system and main circuit parameters
1. Results of steady state experiments
In a steady-state experiment, 40 omega resistors are connected on the direct current side, the harmonic steady-state compensation performance of the system is verified by adopting pure sliding mode control, multi-proportion resonance sliding mode control and repeated sliding mode control methods, the experimental waveforms of the three control methods are respectively shown in figures 10, 11 and 12, and i in the figures issa、isbAnd iscFor three-phase currents of the grid, x3aIs the phase a harmonic current error.
As can be seen from fig. 10, when the pure sliding mode control method is adopted, the harmonic current mutation caused by the non-linear load current discontinuity may cause poor harmonic compensation effect, the sine degree of the grid current is not high, and the compensated grid current THD is 4.3%. This is due to the fact that the sliding mode surface is shifted due to the imperfection of system modeling and system control and sampling delay, and the compensation current has a periodic error of about +/-1A. Fig. 11 shows the power grid current and harmonic error waveforms during the multi-scale resonant sliding mode control, and the compensation effect is obviously improved. It can be seen that the multi-ratio resonance control exerts an influence on the sliding mode surface in view of the sliding mode surface offset problem, the compensation is realized for the specified low-order harmonic, the system steady-state precision is high, and the grid current THD is reduced to 2.4%, as shown in fig. 13.
As shown in fig. 13. In order to obtain a power grid current with better characteristics, repetitive control is introduced into a sliding mode surface to form a composite repetitive sliding mode control system, the experimental waveform of which is shown as 12, and as can be seen from the figure, the repetitive control introduces a great gain at a harmonic frequency, so that the tracking capability of a periodic harmonic error of the SAPF system is enhanced, full harmonic compensation is realized, the steady-state performance of the system is further improved, and the power grid current THD is reduced to 1.7%, as shown in FIG. 14.
2. Results of dynamic experiments
Fig. 15 and 16 show dynamic response waveforms of different control strategies when the system is switched from half-load (dc-side resistance of 60 Ω) to full-load (dc-side resistance of 30 Ω).
It can be seen from the figure that both the multi-ratio resonant sliding mode control and the repetitive sliding mode control have good dynamic response characteristics in the application of the SAPF. The accumulated error of repeated control when the load changes can cause the system to generate an overcompensation phenomenon in the next period, and a small distortion point appears as shown in the figure. But the system state quantity can be stabilized near the sliding mode surface within a limited time by the aid of the sliding mode control index approach rate and the effect of the equivalent control part, so that good sliding mode motion quality of sliding mode control is guaranteed.
The invention adds repeated control to the sliding mode surface instead of multi-proportion resonance control, and the error term x of the harmonic current is corrected3aCompensation is carried out, a repeated sliding mode composite control strategy is provided, full harmonic compensation is realized, steady-state errors are further reduced, and frequency adaptability is enhanced. Through simulation and experimental comparison, the result shows that the method can realize high-precision compensation of power grid harmonic waves, has good dynamic response capability and robustness against power grid impedance disturbance, has smaller tracking error in a repeated sliding mode control strategy compared with multi-proportion resonance sliding mode control, and has more advantages in the aspects of discrete implementation, frequency adaptability and the like in repeated control.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (4)

1. The LCLCL type active power filter control method based on repeated sliding mode control is characterized by comprising the following design steps:
step 1) establishing a continuous time dynamic model of a three-phase LCLCL type SAPF according to a main circuit structure of the LCLCLCL active power filter; the establishment process of the continuous time dynamic model of the three-phase LCLCLCL type SAPF comprises the following steps:
the continuous time dynamic model of the three-phase LCLCLCL type SAPF is
Figure FDA0003008373500000011
Wherein L is1Is a grid side inductance, L2Is an inverter-side inductance, CfIs the filter capacitance of the LCLCLCL filter;
Figure FDA0003008373500000012
for the phase voltage of the grid to the neutral point n,
Figure FDA0003008373500000013
the phase voltage at the output side of the PWM inverter to the dc side midpoint o,
Figure FDA0003008373500000014
the phase voltage of the filter capacitor branch to the neutral point o 'is considered, and when the three phases are balanced, n, o and o' are considered as equal potential points;
Figure FDA0003008373500000015
and
Figure FDA0003008373500000016
respectively the grid-connected current of the SAPF and the output current of the inverter;
wherein, the phase voltage of the output side of the PWM inverter to the midpoint o of the direct current side
Figure FDA0003008373500000017
The vector comprises a three-phase voltage u of a, b and cia、uib、uicPhase voltage of output side of PWM inverter to DC side midpoint o
Figure FDA0003008373500000018
Can be based on the voltage u on the DC sidedcThe relationship (c) is expressed as follows:
Figure FDA0003008373500000019
in the formula (I), the compound is shown in the specification,
Figure FDA00030083735000000110
when the frequency is high enough, neglecting PWM high frequency component to switch in one period skVarying mean value, i.e. PWM duty cycle dkTo replace skThe above formula can be rewritten as:
Figure FDA0003008373500000021
for a three-phase symmetric system, three phases can be independently controlled, the A phase is analyzed,
wherein the A-phase continuous time dynamic model is as follows:
Figure FDA0003008373500000022
usafor the A-phase voltage of the network, ucaIs the A-phase capacitance branch voltage, ishaAnd iinvaA-phase grid-connected current of SAPF and A-phase output current of inverter, daIs the duty cycle of phase A;
step 2) defining an error variable x according to the continuous time dynamic model of the three-phase LCLCLCL type SAPF established in the step 1)1a，x2aAnd x3aEstablishing a system state space equation of sliding mode control, and solving a coefficient of the system state space equation;
step 3) solving a sliding mode switching function, a sliding mode surface and a control action u according to the system state space equation established in the step 2), wherein the control action u is a duty ratio d;
step 4) carrying out Laplace transformation on the obtained sliding mode switching function to convert the sliding mode switching function into a sliding mode form in a frequency domain, and switching harmonic current error x in the function to the sliding mode3aInserting a repeated control condition, modifying a sliding mode switching function, and determining a control block diagram of the SAPF control system based on the repeated sliding mode according to the sliding mode switching function.
2. The lclclclcl type active power filter control method based on repetitive sliding mode control according to claim 1, characterized in that: the establishment process of the system state space equation controlled by the sliding mode comprises the following steps:
define 3 error variables: error x of output current1aFilter capacitor voltage error x2aAnd harmonic current error x3a，
Figure FDA0003008373500000023
In the formula (I), the compound is shown in the specification,
Figure FDA0003008373500000024
and
Figure FDA0003008373500000025
respectively an A-phase output current reference value of the inverter, an A-phase capacitance branch voltage reference value and an A-phase grid current reference value of the SAPF,
Figure FDA0003008373500000026
the harmonic current is obtained by d-q method detection based on instantaneous reactive power theory, namely, A phase harmonic command current,
Figure FDA0003008373500000027
and
Figure FDA0003008373500000028
satisfies the formula (1), and therefore
Figure FDA0003008373500000029
And
Figure FDA00030083735000000210
the derivation can be as follows:
Figure FDA00030083735000000211
Figure FDA00030083735000000212
state variable x1a，x2aAnd x3aRespectively, the 3 error variables of interest, and if the 3 error variables are made to be 0 through the control action, the SAPF achieves perfect harmonic compensation, and therefore, a state space equation is constructed:
Figure FDA0003008373500000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003008373500000032
X＝[x1a x2a x3a]T；
Figure FDA0003008373500000033
Figure FDA0003008373500000034
Figure FDA0003008373500000035
assuming that the grid voltage is constant, the coefficients and state inputs of the system state space equation can be described as:
Figure FDA0003008373500000036
3. the LCLCLCL type active power filter control method based on repeated sliding mode control according to claim 2, wherein the specific process of step 3) is as follows:
defining a linear sliding-mode switching function sigmaa
σa＝CX＝[α1 α2 α3]X (6)
In the formula, alpha1，α2And alpha3Is a real constant that achieves system stability,
the exponential approach rate is selected to make the system meet the reaching conditions and make the system stable,
Figure FDA0003008373500000037
wherein k and ε are real positive constants greater than 0;
the compounds represented by the formulae (4), (5) and (6) can be obtained by substituting the compounds represented by the formula (7):
Figure FDA0003008373500000038
the control action u of the system, i.e. the A-phase duty cycle d, can be obtained by solving the formula (8)a
Figure FDA0003008373500000039
In the formula (I), the compound is shown in the specification,
Figure FDA0003008373500000041
Figure FDA0003008373500000042
Figure FDA0003008373500000043
as can be seen from the equation (9), d is a control action of the modulated waveaCan be divided into three parts: equivalent part da_eqLinear part da_lAnd a non-linear part da_nWherein the equivalent part da_eqIs composed of
Figure FDA0003008373500000044
Equivalent control action, linear part d, which can be obtaineda_lAnd a non-linear part da_nThe control effect of the B phase and the C phase is consistent with that of the A phase for compensating the exponential approach rate.
4. The LCLCLCL type active power filter control method based on repeated sliding mode control according to claim 3, wherein the sliding mode form in frequency domain:
σa(s)＝α1x1a(s)+α2x2a(s)+α3x3a(s) (13)
the internal model structural form of the time domain repetitive control can be expressed as:
Figure FDA0003008373500000045
in the formula, kRCFor repeated control gain, T is the fundamental wave period of the input signal, omega is the fundamental wave frequency, and n is the harmonic frequency;
when Q takes a constant, equation (14) can be rewritten as:
Figure FDA0003008373500000046
in the formula, ωcIs a resonant frequency, and
Figure FDA0003008373500000047
harmonic current error x in function switching to sliding mode3aThe term is inserted into a repetitive control condition (15), the sliding mode switching function can be modifiedComprises the following steps:
σa(s)＝α1x1a(s)+α2x2a(s)+α3x3a(s)+GRC(s)x3a(s) (16)
the repetitive control can be directly applied to the harmonic current error x by equation (16)3aThe a-phase control block diagram of the repetitive sliding mode control based SAPF system is determined according to equation (16).
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