CN111313467A - LCL inverter grid-connected device based on parameter joint design and control method - Google Patents

LCL inverter grid-connected device based on parameter joint design and control method Download PDF

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CN111313467A
CN111313467A CN202010176277.5A CN202010176277A CN111313467A CN 111313467 A CN111313467 A CN 111313467A CN 202010176277 A CN202010176277 A CN 202010176277A CN 111313467 A CN111313467 A CN 111313467A
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吕建国
阎亦然
徐炜基
胡文斌
孙状
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Nanjing 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • 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
    • 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
    • Y02E40/40—Arrangements for reducing harmonics

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Abstract

The invention discloses an LCL inverter grid-connected device based on parameter joint design and a control method. The device comprises a three-level inverter, a digital processing control module and a driving circuit, wherein the digital processing control module comprises a sampling unit, a closed-loop control unit, an active damping unit and a sine pulse width modulation unit. The method comprises the following steps: selecting capacitance values of capacitors of the LCL filter, network side inductors and inverter side inductor values; determining a feasible range of proportional parameters and an active damping feedback coefficient of the PR controller by Nyquist stability analysis and combining resonance suppression conditions; and selecting a proper proportional parameter and an active damping feedback coefficient of the PR controller by using a Lagrange multiplier method in the determined feasible domain, so that the control system obtains larger bandwidth and good dynamic performance. The invention has the characteristics of low hardware cost, accurate control and wide application range, can effectively inhibit the harmonic component of the resonant frequency of the LCL filter and reduce the distortion rate of the network access current.

Description

LCL inverter grid-connected device based on parameter joint design and control method
Technical Field
The invention belongs to the technical field of power electronic conversion, and particularly relates to an LCL inverter grid-connected device based on parameter joint design and a control method.
Background
The LCL filter has the advantages of simple structure, good high-frequency filtering performance, low output harmonic content and the like, and is widely applied to new energy distributed grid-connected power generation occasions. However, due to the inherent characteristics of the LCL filter, the resonance characteristics of the LCL filter can significantly degrade the power quality at the output side. At present, for the problem of the resonant frequency of the LCL filter, two solutions are mainly provided: (1) an additional hardware damping circuit is adopted to inhibit LCL resonance; (2) and a software control method is adopted to inhibit LCL resonance. The latter method is generally used because the first method increases hardware costs. Under ideal power grid conditions, the existing active damping control method is relatively mature, such as an active damping control method based on a wave trap, an active damping control method based on filter capacitor current feedback, an active damping control method based on multi-state quantity hybrid feedback, and the like. In practical situations, however, the power grid is not an ideal fundamental power grid, low-frequency harmonics exist in the power grid, and under non-ideal power grid conditions, a plurality of PR controllers are required to be controlled in parallel, so that the system is required to have enough open-loop bandwidth, and the difficulty is brought to the resonance suppression control of the LCL filter with active damping.
Disclosure of Invention
The invention aims to provide an LCL type inverter grid-connected device and a control method based on parameter joint design and suitable for non-ideal power grid conditions, so as to realize resonance suppression of an LCL filter under the non-ideal power grid conditions.
The technical solution for realizing the purpose of the invention is as follows: an LCL type inverter grid-connected device based on parameter joint design comprises a three-level inverter, a digital processing control module and a driving circuit, wherein the three-level inverter is an LCL type NPC three-level inverter, and the digital processing control module comprises a sampling unit, a closed-loop control unit, an active damping unit and a sine pulse width modulation unit;
the sampling unit respectively collects three-phase voltage signals at the network side of the LCL filter and three-phase current signals at the network side of the LCL filter and transmits the three-phase voltage signals and the three-phase current signals to the closed-loop control unit;
the closed-loop control unit transforms the network side voltage and the network side current under the static abc coordinate system to the static αβ coordinate system through Clarke transformation according to the collected signals, and transforms the α and β axial components i of the network side current under the static αβ coordinate systemα、iβAn input active damping unit;
and the output end of the sine pulse width modulation unit is connected to each switching tube of each phase bridge arm of the three-level inverter through a driving circuit.
Further, the digital processing control modules are TMS320F28377D and EPM1270T chips.
A LCL inverter grid-connected control method based on parameter joint design comprises the following steps:
step 1, in each switching period, a sampling unit of a digital processing control module respectively collects a network side voltage signal e of an LCL filtera、eb、ecAnd net side current signal ia、ib、ic；
Step 2, the closed-loop control unit transforms the network side voltage and the network side current under the stationary abc coordinate system to the stationary αβ coordinate system through Clarke transformation according to the signals collected in the step 1;
step 3, calculating an open-loop transfer function of the system after an active damping ring and a PR controller are added under a z-domain, and analyzing the stability of the system by utilizing a Nyquist criterion;
step 4, analyzing the harmonic suppression condition of the resonant frequency of the LCL filter;
and 5, selecting a proportionality coefficient K of the PR controller which enables the system bandwidth to be maximum by using a Lagrange multiplier method within the range of meeting the stability condition and the resonance suppression conditionpAnd an active damping feedback coefficient H to obtain an optimized closed-loop control system;
step 6, calculating current setting by taking current sine as a target, subtracting the obtained current setting quantity by taking the network side current as a feedback quantity, adding the obtained current setting quantity with the output of an active damping ring after passing through a proportional resonance regulator, and outputting a three-phase modulation wave signal through Clarke inverse transformation;
and 7, generating a pulse width modulation signal by the three-phase modulation signal obtained in the step 6 through a sine pulse width modulation unit, wherein the pulse width modulation signal controls the working state of a switching tube of the inverter through a driving circuit.
Further, the stability analysis of the system in step 3 is specifically as follows:
system open loop transfer function Gop(s) is:
Figure BDA0002410934650000021
wherein L is1Is inductance value, L, of inverter side of LCL filter2The inductance value of the LCL filter network side, C the capacitance value of the LCL filter capacitor, KpIs the proportionality coefficient of the PR controller, H is the active damping feedback coefficient, ωresIs the resonant frequency, T, of the LCL filtersFor system sampling time, omegaresThe expression of (a) is as follows:
Figure BDA0002410934650000022
converting z to sin (ω T)s)-jcos(ωTs) Substituting the formula into the formula, and settling to obtain the open-loop frequency response equation of the control system as follows:
Figure BDA0002410934650000031
wherein A (omega) is a coefficient of a numerator real part in a system open-loop frequency response equation, B (omega) is a coefficient of a numerator imaginary part in the system open-loop frequency response equation, C (omega) is a coefficient without H terms of a denominator real part in the system open-loop frequency response equation, D (omega) is a coefficient containing H terms of a denominator real part in the system open-loop frequency response equation, E (omega) is a coefficient without H terms of a denominator imaginary part in the system open-loop frequency response equation, and F (omega) is a coefficient containing H terms of a denominator imaginary part in the system open-loop frequency response equation;
A(ω)＝Ts 2[(ωresTs-sin(ωresTs))cos(ωTs)4-(2ωresTscos(ωresTs)-2sin(ωresTs))cos(ωTs)3-(6sin(ωTs)2-1)(ωresTs-sin(ωresTs))cos(ωTs)2+6sin(ωTs)2(ωresTscos(ωresTs)-sin(ωresTs))cos(ωTs)+sin(ωTs)2(sin(ωTs)2-1)(ωresTs-sin(ωresTs))]
B(ω)＝Ts 2sin(ωTs)[4(ωresTs-sin(ωresTs))cos(ωTs)3-6(ωresTscos(ωresTs)-sin(ωresTs))cos(ωTs)2-(4sin(ωTs)2-2)(ωresTs-sin(ωresTs))cos(ωTs)+2sin(ωTs)2(ωresTscos(ωresTs)-sin(ωresTs))]
Figure BDA0002410934650000032
D(ω)＝L1L2{(ωresTs-sin(ωresTs))cos(ωTs)4-2(ωresTs+ωresTscos(ωresTs)-2sin(ωresTs))cos(ωTs)3-2[3(ωresTs-sin(ωresTs))sin(ωTs)2-2ωresTscos(ωresTs)-ωresTs+3sin(ωresTs)]cos(ωTs)2+2(ωresTscos(ωresTs)+ωresTs-2sin(ωresTs))(3sin(ωTs)2-1)cos(ωTs)+(ωresTs-sin(ωresTs))sin(ωTs)4-2(2ωresTscos(ωresTs)+ωresTs-3sin(ωresTs))sin(ωTs)2+ωresTs-sin(ωresTs)}
Figure BDA0002410934650000033
F(ω)＝L1L2sin(ωTs){4(ωresTs-sin(ωresTs))cos(ωTs)3-6(ωresTscos(ωresTs)+ωresTs-2sin(ωresTs))cos(ωTs)2+4[(sin(ωTs)2-3)sin(ωresTs)-(sin(ωTs)2-2cos(ωresTs) When-1) ωresTs]cos(ωTs)-2(sin(ωTs)+1)[2sin(ωresTs)-ωresTs(cos(ωresTs)-1)](sin(ωTs)-1)}
ωres≤ωsAt/6:
Kpand H has the following value ranges:
Figure BDA0002410934650000041
wherein A (ω)h) When ω is equal to ωhCoefficient of real part of molecule, B (omega) in open-loop frequency response equation of time systemh) When ω is equal to ωhCoefficient of imaginary part of molecule, C (omega) in open-loop frequency response equation of time systemh) When ω is equal to ωhH-free coefficient, D (omega) of real part of denominator in open-loop frequency response equation of time systemh) When ω is equal to ωhCoefficient containing H term, E (omega) of mother real part in open-loop frequency response equation of time systemh) When ω is equal to ωhH-free coefficient F (omega) of mother imaginary part in open-loop frequency response equation of time systemh) When ω is equal to ωhThe H-term-containing coefficient of the mother imaginary part in the open-loop frequency response equation of the time system;
when ω iss/6<ωres<ωsAt the time of/2:
Kpand H has the following value ranges:
Figure BDA0002410934650000042
wherein KpIs the proportionality coefficient of the proportional resonant controller, H is the active damping feedback coefficient, TsFor sampling period, omega, of a digitally controlled systemsSampling angular frequency, omega, for a digitally controlled systemhFor the system cross-over frequency, Top(z) is the system open loop transfer function.
Further, the analyzing of the harmonic suppression condition of the resonant frequency of the LCL filter in step 4 is specifically as follows:
due to the presence of the zero-order keeper in the digital control, the actual resonance frequency ω of the LCL filterresThe shift can occur after the active damping control loop is used, and the resonance frequency after the shift is omegares', the resonance suppression analysis results are as follows:
Figure BDA0002410934650000043
wherein
a(ωres′)＝-(D(ωres′)2+F(ωres′)2)·((A(ωres′)2+B(ωres′)2)·(D(ωres′)2+F(ωres′)2)′-(D(ωres′)2+F(ωres′)2)·(A(ωres′)2+B(ωres′)2)′)
b(ωres′)＝4·(A(ωres′)2+B(ωres′)2)′·(C(ωres′)D(ωres′)3+C(ωres′)D(ωres′)F(ωres′)2+D(ωres′)2E(ωres′)F(ωres′)+E(ωres′)F(ωres′)3)-2·(A(ωres′)2+B(ωres′)2)·(C(ωres′)D(ωres′)3+C(ωres′)D(ωres′)F(ωres′)2+D(ωres′)2E(ωres′)F(ωres′)+E(ωres′)F(ωres′)3)′
c(ωres′)＝2(A(ωres′)2+B(ωres′)2)′·(3C(ωres′)2D(ωres′)2+C(ωres′)2F(ωres′)2+D(ωres′)2E(ωres′)2+3E(ωres′)F(ωres′)+4C(ωres′)D(ωres′)E(ωres′)F(ωres′))-(A(ωres′)2+B(ωres′)2)·(3C(ωres′)2D(ωres′)2+C(ωres′)2F(ωres′)2+D(ωres′)2E(ωres′)2+3E(ωres′)F(ωres′)+4C(ωres′)D(ωres′)E(ωres′)F(ωres′))′
d(ωres′)＝4·(A(ωres′)2+B(ωres′)2)′·(C(ωres′)3D(ωres′)+C(ωres′)D(ωres′)E(ωres′)2+C(ωres′)2E(ωres′)F(ωres′)+E(ωres′)3F(ωres′))-2·(A(ωres′)2+B(ωres′)2)·(C(ωres′)3D(ωres′)+C(ωres′)D(ωres′)E(ωres′)2+C(ωres′)2E(ωres′)F(ωres′)+E(ωres′)3F(ωres′))′
e(ωres′)＝-(C(ωres′)2+E(ωres′)2)·((A(ωres′)2+B(ωres′)2)·(C(ωres′)2+E(ωres′)2)′-(C(ωres′)2+E(ωres′)2)·(A(ωres′)2+B(ωres′)2)′)
Wherein a (ω)res') is when ω is ω ═ ωresIn the time constraint of H4Coefficient of term, b (ω)res') is when ω is ω ═ ωresIn the time constraint of H3Coefficient of term, c (ω)res') is when ω is ω ═ ωresIn the time constraint of H2Coefficient of term, d (ω)res') is when ω is ω ═ ωresCoefficient of the H term in the time constraint, e (ω)res') is when ω is ω ═ ωresCoefficient of constant term in the' time constraint, A (ω)res') is when ω is ω ═ ωresCoefficient of real part of molecule, B (omega) in open-loop frequency response equation of' time systemres') is when ω is ω ═ ωresCoefficient of imaginary part of molecule, C (omega) in open-loop frequency response equation of' time systemres') is when ω is ω ═ ωresH-free coefficient, D (omega) of real part of denominator in open-loop frequency response equation of time systemres') is when ω is ω ═ ωresCoefficient containing H term, E (omega) of mother real part in open-loop frequency response equation of time systemres') is when ω is ω ═ ωresH-free coefficient, F (omega) of the mother imaginary part in the open-loop frequency response equation of the' time systemres') is when ω is ω ═ ωresThe H term-containing coefficient of the imaginary part of the denominator in the open-loop frequency response equation of the time system.
Further, K in step 5pAnd H are selected as follows:
max Kp
s.t.
Figure BDA0002410934650000061
Figure BDA0002410934650000062
h2(Kp,H,ωh,ωres′)＝a(ωres′)H4+b(ωres′)H3+c(ωres′)H2+d(ωres′)H+e(ωres′)＝0
the above formula is KPAnd H, the final parameter of which is selected from the equation in which gi(kp,H,ωh,ωres') and i ═ 1,2,3, represent inequality constraints, hj(kp,H,ωh,ωres') denotes the equality constraint and j is 1, 2.
Compared with the prior art, the invention has the remarkable advantages that: (1) active damping is fed back through network side current, hardware cost is not increased, and LCL resonance suppression control is achieved; (2) and a control parameter which enables the system passband to be larger is selected, so that the distortion rate of the output current is reduced, and the waveform quality is improved.
Drawings
Fig. 1 is a schematic structural diagram of an LCL type inverter grid-connected device based on parameter joint design according to the present invention.
Fig. 2 is a control block diagram of an LCL type NPC three-level inverter grid-connected system.
Fig. 3 is a topology diagram of an NPC three-level grid-connected inverter.
FIG. 4 is ωres≤ωsSimulation waveform after adding active damping at/6.
FIG. 5 is ωs/6<ωres<ωsThe simulated waveform after adding active damping at/2.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
With reference to fig. 1, the LCL inverter grid-connected device based on parameter combination design comprises a three-level inverter, a digital processing control module and a driving circuit, wherein the three-level inverter is an LCL NPC three-level inverter, the digital processing control module comprises a sampling unit, a closed-loop control unit, an active damping unit and a sine pulse width modulation unit, the sampling unit is used for respectively acquiring three-phase voltage signals on the network side of an LCL filter and three-phase current signals on the network side of the LCL filter and transmitting the three-phase voltage signals and the three-phase current signals to the closed-loop control unit, the closed-loop control unit is used for transforming the network side voltage and the network side current under a static abc coordinate system to a static αβ coordinate system through Clarke transformation according to the acquired signals, and α and β axial components i of the network side currentα、iβAn input active damping unit; and the output end of the sine pulse width modulation unit is connected to each switching tube of each phase bridge arm of the three-level inverter through a driving circuit.
As a specific example, the digital processing control modules are TMS320F28377D and EPM1270T chips.
The invention relates to a control method of an LCL type inverter grid-connected device based on parameter joint design, which comprises the following steps:
step 1, in each switching period, a sampling unit of a digital control module respectively collects a network side voltage signal e of an LCL filtera、eb、ecNet side current signal ia、ib、icCapacitor voltage U on the DC sideC1And the capacitor voltage U under the DC sideC2；
Step 2, the closed-loop control unit transforms the network side voltage and the network side current under the stationary abc coordinate system to the stationary αβ coordinate system through Clarke transformation according to the signals collected in the step 1;
clarke transforms the transform matrix into Tabc/αβ：
Figure BDA0002410934650000071
After the steps, α and β axial components e of the grid side voltage under the static αβ coordinate system are obtainedα、eβAnd α, β axial components i of net side currentα、iβ；
And 3, calculating an open-loop transfer function of the system after the active damping ring and the PR controller are added in the z-domain, and analyzing the stability of the system by utilizing the Nyquist criterion.
A control block diagram of the LCL NPC three-level inverter grid-connected system is shown in fig. 2, wherein:
Gc(s) is a current controller whose transfer function is as follows:
Figure BDA0002410934650000072
Kpfor proportional controller gain, KrIs the fundamental resonant controller gain, omegaiFor fundamental harmonic control of angular frequency, Krh(h is 3, 5, 7 …) represents the gain of each resonant controller, h represents the harmonic order, ωih(h-3, 5, 7 …) is the angular frequency, ω, of each resonant controlleroIs the angular frequency of the fundamental voltage of the power grid. The PR controller can realize the static-error-free control of fundamental current, and the HC controller can restrain harmonic components generated by power grid background harmonic in grid-connected current.
Gad(s) is an active damping link, and the transfer function is as follows:
Gad(s)＝HL1L2s2
wherein H is the active damping coefficient, L1Is inductance value, L, of inverter side of LCL filter2The inductance value of the LCL filter network side is shown.
GZOH(s) is a zero order keeper with a transfer function of:
Figure BDA0002410934650000081
wherein T issThe system sample time.
G1(s) is the transfer function of inverter output voltage to network access current of the LCL inverter:
Figure BDA0002410934650000082
wherein C is the capacitance value of LCL filter capacitor, omegaresIs the resonant frequency, omega, of the LCL filterresThe expression of (a) is as follows:
Figure BDA0002410934650000083
system open loop transfer function Gop(s) is:
Figure BDA0002410934650000084
wherein L is1Is inductance value, L, of inverter side of LCL filter2The inductance value of the LCL filter network side, C the capacitance value of the LCL filter capacitor, KpIs the proportionality coefficient of the PR controller, H is the active damping feedback coefficient, TsThe system sample time.
Converting z to sin (ω T)s)-jcos(ωTs) Substituting the formula into the formula, and obtaining the open-loop frequency response equation of the control system by sorting:
Figure BDA0002410934650000085
wherein A (omega) is a coefficient of a numerator real part in the system open-loop frequency response equation, B (omega) is a coefficient of a numerator imaginary part in the system open-loop frequency response equation, C (omega) is a coefficient without H terms of a denominator real part in the system open-loop frequency response equation, D (omega) is a coefficient containing H terms of a denominator real part in the system open-loop frequency response equation, E (omega) is a coefficient without H terms of a denominator imaginary part in the system open-loop frequency response equation, and F (omega) is a coefficient containing H terms of a denominator imaginary part in the system open-loop frequency response equation.
A(ω)＝Ts 2[(ωresTs-sin(ωresTs))cos(ωTs)4-(2ωresTscos(ωresTs)-2sin(ωresTs))cos(ωTs)3-(6sin(ωTs)2-1)(ωresTs-sin(ωresTs))cos(ωTs)2+6sin(ωTs)2(ωresTscos(ωresTs)-sin(ωresTs))cos(ωTs)+sin(ωTs)2(sin(ωTs)2-1)(ωresTs-sin(ωresTs))]
B(ω)＝Ts 2sin(ωTs)[4(ωresTs-sin(ωresTs))cos(ωTs)3-6(ωresTscos(ωresTs)-sin(ωresTs))cos(ωTs)2-(4sin(ωTs)2-2)(ωresTs-sin(ωresTs))cos(ωTs)+2sin(ωTs)2(ωresTscos(ωresTs)-sin(ωresTs))]
Figure BDA0002410934650000091
D(ω)＝L1L2{(ωresTs-sin(ωresTs))cos(ωTs)4-2(ωresTs+ωresTscos(ωresTs)-2sin(ωresTs))cos(ωTs)3-2[3(ωresTs-sin(ωresTs))sin(ωTs)2-2ωresTscos(ωresTs)-ωresTs+3sin(ωresTs)]cos(ωTs)2+2(ωresTscos(ωresTs)+ωresTs-2sin(ωresTs))(3sin(ωTs)2-1)cos(ωTs)+(ωresTs-sin(ωresTs))sin(ωTs)4-2(2ωresTscos(ωresTs)+ωresTs-3sin(ωresTs))sin(ωTs)2+ωresTs-sin(ωresTs)}
Figure BDA0002410934650000092
F(ω)＝L1L2sin(ωTs){4(ωresTs-sin(ωresTs))cos(ωTs)3-6(ωresTscos(ωresTs)+ωresTs-2sin(ωresTs))cos(ωTs)2+4[(sin(ωTs)2-3)sin(ωresTs)-(sin(ωTs)2-2cos(ωresTs)-1)ωresTs]cos(ωTs)-2(sin(ωTs)+1)[2sin(ωresTs)-ωresTs(cos(ωresTs)-1)](sin(ωTs)-1)}
(1) When ω isres≤ωsAt time/6
When H <0, the stability condition cannot be satisfied;
when H is more than or equal to 0 and less than or equal to [2cos (omega) ]resTs)-1]ωres 3Ts 2C/[sin(ωresTs)-ωresTs(2cos(ωresTs)-1)]In time, G needs to be satisfied in order for the system to satisfy the Nyquist stability criterionop(z＝ejωhTs)|<1, i.e. KpAnd H needs to satisfy the following condition:
Figure BDA0002410934650000093
wherein A (ω)h) When ω is equal to ωhCoefficient of real part of molecule, B (omega) in open-loop frequency response equation of time systemh) When ω is equal to ωhCoefficient of imaginary part of molecule, C (omega) in open-loop frequency response equation of time systemh) When ω is equal to ωhH-free coefficient, D (omega) of real part of denominator in open-loop frequency response equation of time systemh) When ω is equal to ωhCoefficient containing H term, E (omega) of mother real part in open-loop frequency response equation of time systemh) When ω is equal to ωhH-free coefficient F (omega) of mother imaginary part in open-loop frequency response equation of time systemh) When ω is equal to ωhAnd H term-containing coefficients of the mother imaginary part in the open-loop frequency response equation of the time system.
When [2cos (ω)resTs)-1]ωres 3Ts 2C/[sin(ωresTs)-ωresTs(2cos(ωresTs)-1)]<H, the stability condition cannot be met;
(2) when ω iss/6<ωres<ωsAt 2 time
When H is present<[2cos(ωresTs)-1]ωres 3Ts 2C/[sin(ωresTs)-ωresTs(2cos(ωresTs)-1)]When it is, the stability condition cannot be satisfied;
when [2cos (ω)resTs)-1]ωres 3Ts 2C/[sin(ωresTs)-ωresTs(2cos(ωresTs)-1)]H is less than or equal to 0, and | G is required to be satisfied in order to make the system satisfy the Nyquist stability criterionop(z＝ejωhTs)|<1, Kp, needs to satisfy the following condition:
Figure BDA0002410934650000101
when 0< H, the stability condition cannot be satisfied;
step 4, analyzing the harmonic suppression condition of the resonant frequency of the LCL filter;
the harmonic suppression condition of the resonant frequency of the LCL filter is 20lgAωres'≤-3dB，ωres' is the resonant frequency of the LCL filter after adding active damping, Aωres'The expression of (a) is:
Figure BDA0002410934650000102
namely KpAnd H needs to satisfy the following condition:
Figure BDA0002410934650000103
wherein
a(ωres′)＝-(D(ωres′)2+F(ωres′)2)·((A(ωres′)2+B(ωres′)2)·(D(ωres′)2+F(ωres′)2)′-(D(ωres′)2+F(ωres′)2)·(A(ωres′)2+B(ωres′)2)′)
b(ωres′)＝4·(A(ωres′)2+B(ωres′)2)′·(C(ωres′)D(ωres′)3+C(ωres′)D(ωres′)F(ωres′)2+D(ωres′)2E(ωres′)F(ωres′)+E(ωres′)F(ωres′)3)-2·(A(ωres′)2+B(ωres′)2)·(C(ωres′)D(ωres′)3+C(ωres′)D(ωres′)F(ωres′)2+D(ωres′)2E(ωres′)F(ωres′)+E(ωres′)F(ωres′)3)′
c(ωres′)＝2(A(ωres′)2+B(ωres′)2)′·(3C(ωres′)2D(ωres′)2+C(ωres′)2F(ωres′)2+D(ωres′)2E(ωres′)2+3E(ωres′)F(ωres′)+4C(ωres′)D(ωres′)E(ωres′)F(ωres′))-(A(ωres′)2+B(ωres′)2)·(3C(ωres′)2D(ωres′)2+C(ωres′)2F(ωres′)2+D(ωres′)2E(ωres′)2+3E(ωres′)F(ωres′)+4C(ωres′)D(ωres′)E(ωres′)F(ωres′))′
d(ωres′)＝4·(A(ωres′)2+B(ωres′)2)′·(C(ωres′)3D(ωres′)+C(ωres′)D(ωres′)E(ωres′)2+C(ωres′)2E(ωres′)F(ωres′)+E(ωres′)3F(ωres′))-2·(A(ωres′)2+B(ωres′)2)·(C(ωres′)3D(ωres′)+C(ωres′)D(ωres′)E(ωres′)2+C(ωres′)2E(ωres′)F(ωres′)+E(ωres′)3F(ωres′))′
e(ωres′)＝-(C(ωres′)2+E(ωres′)2)·((A(ωres′)2+B(ωres′)2)·(C(ωres′)2+E(ωres′)2)′-(C(ωres′)2+E(ωres′)2)·(A(ωres′)2+B(ωres′)2)′)
Wherein a (ω)res') is when omega＝ωresIn the time constraint of H4Coefficient of term, b (ω)res') is when ω is ω ═ ωresIn the time constraint of H3Coefficient of term, c (ω)res') is when ω is ω ═ ωresIn the time constraint of H2Coefficient of term, d (ω)res') is when ω is ω ═ ωresCoefficient of the H term in the time constraint, e (ω)res') is when ω is ω ═ ωresCoefficient of constant term in the' time constraint, A (ω)res') is when ω is ω ═ ωresCoefficient of real part of molecule, B (omega) in open-loop frequency response equation of' time systemres') is when ω is ω ═ ωresCoefficient of imaginary part of molecule, C (omega) in open-loop frequency response equation of' time systemres') is when ω is ω ═ ωresH-free coefficient, D (omega) of real part of denominator in open-loop frequency response equation of time systemres') is when ω is ω ═ ωresCoefficient containing H term, E (omega) of mother real part in open-loop frequency response equation of time systemres') is when ω is ω ═ ωresH-free coefficient, F (omega) of the mother imaginary part in the open-loop frequency response equation of the' time systemres') is when ω is ω ═ ωresThe H term-containing coefficient of the imaginary part of the denominator in the open-loop frequency response equation of the time system.
And 5, selecting a proportional link coefficient K of the PR controller which enables the system bandwidth to be maximum by using a Lagrange multiplier method within the range of meeting the stability condition and the resonance inhibition conditionpAnd an active damping feedback coefficient H to obtain a closed-loop control system with good dynamic performance, i.e. to find K satisfying the following conditionpAnd H:
max Kp
s.t.
Figure BDA0002410934650000121
Figure BDA0002410934650000122
h2(Kp,H,ωh,ωres′)＝a(ωres′)H4+b(ωres′)H3+c(ωres′)H2+d(ωres′)H+e(ωres′)＝0
the above formula is KPAnd H, the final parameter of which is selected from the equation in which gi(kp,H,ωh,ωres') (i ═ 1,2,3) denotes an inequality constraint, hj(kp,H,ωh,ωres') (j ═ 1,2) represents an equality constraint.
Step 6, calculating current set by taking current sine as a target, subtracting the obtained current set quantity by taking the network side current as a feedback quantity, adding the obtained current set quantity and the obtained current set quantity with the output of an active damping ring after passing through a proportional resonance regulator, and outputting a three-phase modulation wave signal through Clarke inverse transformation;
step 6.1, obtaining 4 paths of modulation wave signals u under a static αβ coordinate system through the closed-loop control unit and the active damping unitαh、uαpr、uβh、uβprTwo modulated wave signals u under α axes under a stationary αβ coordinate systemαh、uαprAdding to obtain:
uα＝uαh+uαpr
β two modulated wave signals u under axisβh、uβprAdding to obtain:
uβ＝uβh+uβpr
through the steps, a modulation wave signal u under a static αβ coordinate system is obtainedα、uβ；
Step 6.2, placing the u under a stationary αβ coordinate systemα、uβConverting the matrix into T under the three-phase static coordinate systemαβ/abc：
Figure BDA0002410934650000123
Through the steps, a three-phase modulation wave signal u under a three-phase static coordinate system is obtaineda、ub、uc；
And 7, generating a pulse width modulation signal by the three-phase modulation signal obtained in the step 6 through a sine pulse width modulation unit, wherein the pulse width modulation signal controls the working state of a switching tube of the inverter through a driving circuit, and specifically comprises the following steps:
three-phase modulation wave signal u under three-phase static coordinate systema、ub、ucAnd the pulse width modulation signal is sent to a sine pulse width modulation unit to generate a pulse width modulation signal, and the pulse width modulation signal controls the working state of a switching tube of the three-level inverter through a driving circuit to realize the control of the resonance suppression of the LCL filter.
The modulation rule of the NPC three-phase three-level inverter is shown in FIG. 3, taking an a-phase bridge arm as an example, in uarefPositive half cycle of (d), when uarefWhen greater than the carrier, order Sa1、Sa2When the a-phase bridge arm is conducted, the a-phase bridge arm outputs high level when u isarefWhen smaller than the carrier, order Sa2、Sa3Conducting, and outputting zero level by the a-phase bridge arm; at uarefNegative half cycle of (d), when uarefWhen smaller than the carrier, order Sa3、Sa4When the a-phase bridge arm is conducted, the a-phase bridge arm outputs low level when u isarefWhen greater than the carrier, order Sa2、Sa3Conducting, and outputting zero level by the a-phase bridge arm; b. the modulation rules of the c-phase bridge arms are the same.
Example 1
In the embodiment, a three-level inverter circuit is built by using a Simulink tool in MATLAB, the direct current is inverted by the three-level inverter circuit to output three-phase voltage after passing through a direct current bus capacitor, and stable three-phase sinusoidal voltage is output through an LCL filter circuit.
The electrical parameter settings during the simulation are as in table 1:
TABLE 1
Figure BDA0002410934650000131
The lagrange function is defined as follows:
Figure BDA0002410934650000132
wherein ω isiIs an inequality constrained Lagrangian multiplier, vjIs an equality constrained Lagrangian multiplier, gi(Kp,H,ωh,ωres') denotes the inequality constraint, hj(Kp,H,ωh,ωres') denotes the equality constraint, gi(Kp,H,ωh,ωres') and hj(Kp,H,ωh,ωres') can be expressed as:
Figure BDA0002410934650000141
h2(Kp,H,ωh,ωres′)＝a(ωres′)H4+b(ωres′)H3+c(ωres′)H2+d(ωres′)H+e(ωres′)＝0
will be provided with
Figure BDA0002410934650000142
L(Kp,H,ωh,ωres',wi,vj) And
Figure BDA0002410934650000143
L(Kp,H,ωh,ωres',wi,vj) Are respectively defined as Lagrangian function L (K)p,H,ωh,ωres',wi,vj) The first and second order gradients, the requirements and sufficiency of the maximum are:
Figure BDA0002410934650000144
where d is the falling direction of the Lagrangian function, G (K)p,H,ωh,ωres') set of all possible descent directions, G (K)p,H,ωh,ωres') is:
Figure BDA0002410934650000145
according to the above solving process, the proportional gain of the current controller reaches a maximum value at the following points:
Figure BDA0002410934650000146
FIG. 4 is ωres≤ωsSimulation waveform after active damping is added at/6, and FIG. 5 is ωs/6<ωres<ωsAnd 2, adding a simulation oscillogram after active damping, and thus, the LCL type inverter grid-connected device and method based on parameter joint design effectively inhibit the harmonic of the resonant frequency in the grid side current and reduce the total harmonic distortion rate of the current.
In summary, the LCL type inverter grid-connected control method based on parameter joint design of the present invention utilizes nyquist criterion to analyze the stability of the system, calculates the conditions required to be satisfied for suppressing the resonance of the LCL filter, obtains the parameter that maximizes the cutoff frequency in the feasible domain through the parameter joint design method and the lagrangian multiplier method as the system parameter, adds the output of the active damping unit and the output of the closed-loop control unit, obtains a three-phase modulation wave after Clarke inverse transformation, generates a sinusoidal pulse width modulation signal through the sinusoidal pulse width modulation unit, and controls the working state of each switching tube of the three-level inverter through the driving circuit, thereby realizing the control of the resonance suppression of the LCL filter. According to the invention, the LCL resonant frequency subharmonic is suppressed through the current feedback active damping at the network side, the harmonic of the output current is reduced, the waveform quality is improved, the grid connection of a grid-connected inverter is facilitated, and the method has great engineering application value.

Claims (6)

1. An LCL type inverter grid-connected device based on parameter joint design is characterized by comprising a three-level inverter, a digital processing control module and a driving circuit, wherein the three-level inverter is an LCL type NPC three-level inverter, and the digital processing control module comprises a sampling unit, a closed-loop control unit, an active damping unit and a sine pulse width modulation unit;
the sampling unit respectively collects three-phase voltage signals at the network side of the LCL filter and three-phase current signals at the network side of the LCL filter and transmits the three-phase voltage signals and the three-phase current signals to the closed-loop control unit;
the closed-loop control unit transforms the network side voltage and the network side current under the static abc coordinate system to the static αβ coordinate system through Clarke transformation according to the collected signals, and transforms the α and β axial components i of the network side current under the static αβ coordinate systemα、iβAn input active damping unit;
and the output end of the sine pulse width modulation unit is connected to each switching tube of each phase bridge arm of the three-level inverter through a driving circuit.
2. The LCL type inverter grid-connected device based on parameter combination design according to claim 1, wherein the digital processing control module is TMS320F28377D and EPM1270T chips.
3. A LCL inverter grid-connected control method based on parameter joint design is characterized by comprising the following steps:
step 1, in each switching period, a sampling unit of a digital processing control module respectively collects a network side voltage signal e of an LCL filtera、eb、ecAnd net side current signal ia、ib、ic；
Step 2, the closed-loop control unit transforms the network side voltage and the network side current under the stationary abc coordinate system to the stationary αβ coordinate system through Clarke transformation according to the signals collected in the step 1;
step 3, calculating an open-loop transfer function of the system after an active damping ring and a PR controller are added under a z-domain, and analyzing the stability of the system by utilizing a Nyquist criterion;
step 4, analyzing the harmonic suppression condition of the resonant frequency of the LCL filter;
and 5, selecting a proportionality coefficient K of the PR controller which enables the system bandwidth to be maximum by using a Lagrange multiplier method within the range of meeting the stability condition and the resonance suppression conditionpAnd an active damping feedback coefficient H to obtain an optimized closed-loop control system;
step 6, calculating current setting by taking current sine as a target, subtracting the obtained current setting quantity by taking the network side current as a feedback quantity, adding the obtained current setting quantity with the output of an active damping ring after passing through a proportional resonance regulator, and outputting a three-phase modulation wave signal through Clarke inverse transformation;
and 7, generating a pulse width modulation signal by the three-phase modulation signal obtained in the step 6 through a sine pulse width modulation unit, wherein the pulse width modulation signal controls the working state of a switching tube of the inverter through a driving circuit.
4. The LCL type inverter grid-connected control method based on parameter combination design according to claim 3, wherein the stability analysis of the system in step 3 is specifically as follows:
system open loop transfer function Gop(s) is:
Figure FDA0002410934640000021
wherein L is1Is inductance value, L, of inverter side of LCL filter2The inductance value of the LCL filter network side, C the capacitance value of the LCL filter capacitor, KpIs the proportionality coefficient of the PR controller, H is the active damping feedback coefficient, ωresIs the resonant frequency, T, of the LCL filtersFor system sampling time, omegaresThe expression of (a) is as follows:
Figure FDA0002410934640000022
converting z to sin (ω T)s)-jcos(ωTs) Substituting the formula into the formula, and settling to obtain the open-loop frequency response equation of the control system as follows:
Figure FDA0002410934640000023
wherein A (omega) is a coefficient of a numerator real part in a system open-loop frequency response equation, B (omega) is a coefficient of a numerator imaginary part in the system open-loop frequency response equation, C (omega) is a coefficient without H terms of a denominator real part in the system open-loop frequency response equation, D (omega) is a coefficient containing H terms of a denominator real part in the system open-loop frequency response equation, E (omega) is a coefficient without H terms of a denominator imaginary part in the system open-loop frequency response equation, and F (omega) is a coefficient containing H terms of a denominator imaginary part in the system open-loop frequency response equation;
A(ω)＝Ts 2[(ωresTs-sin(ωresTs))cos(ωTs)4-(2ωresTscos(ωresTs)-2sin(ωresTs))cos(ωTs)3-(6sin(ωTs)2-1)(ωresTs-sin(ωresTs))cos(ωTs)2+6sin(ωTs)2(ωresTscos(ωresTs)-sin(ωresTs))cos(ωTs)+sin(ωTs)2(sin(ωTs)2-1)(ωresTs-sin(ωresTs))]
B(ω)＝Ts 2sin(ωTs)[4(ωresTs-sin(ωresTs))cos(ωTs)3-6(ωresTscos(ωresTs)-sin(ωresTs))cos(ωTs)2-(4sin(ωTs)2-2)(ωresTs-sin(ωresTs))cos(ωTs)+2sin(ωTs)2(ωresTscos(ωresTs)-sin(ωresTs))]
Figure FDA0002410934640000024
D(ω)＝L1L2{(ωresTs-sin(ωresTs))cos(ωTs)4-2(ωresTs+ωresTscos(ωresTs)-2sin(ωresTs))cos(ωTs)3-2[3(ωresTs-sin(ωresTs))sin(ωTs)2-2ωresTscos(ωresTs)-ωresTs+3sin(ωresTs)]cos(ωTs)2+2(ωresTscos(ωresTs)+ωresTs-2sin(ωresTs))(3sin(ωTs)2-1)cos(ωTs)+(ωresTs-sin(ωresTs))sin(ωTs)4-2(2ωresTscos(ωresTs)+ωresTs-3sin(ωresTs))sin(ωTs)2+ωresTs-sin(ωresTs)}
Figure FDA0002410934640000031
F(ω)＝L1L2sin(ωTs){4(ωresTs-sin(ωresTs))cos(ωTs)3-6(ωresTscos(ωresTs)+ωresTs-2sin(ωresTs))cos(ωTs)2+4[(sin(ωTs)2-3)sin(ωresTs)-(sin(ωTs)2-2cos(ωresTs)-1)ωresTs]cos(ωTs)-2(sin(ωTs)+1)[2sin(ωresTs)-ωresTs(cos(ωresTs)-1)](sin(ωTs)-1)}
when ω isres≤ωsAt/6:
Kpand H has the following value ranges:
Figure FDA0002410934640000032
wherein A (ω)h) When ω is equal to ωhCoefficient of real part of molecule, B (omega) in open-loop frequency response equation of time systemh) When ω is equal to ωhCoefficient of imaginary part of molecule, C (omega) in open-loop frequency response equation of time systemh) When ω is equal to ωhH-free coefficient, D (omega) of real part of denominator in open-loop frequency response equation of time systemh) When ω is equal to ωhCoefficient containing H term, E (omega) of mother real part in open-loop frequency response equation of time systemh) When ω is equal to ωhH-free coefficient F (omega) of mother imaginary part in open-loop frequency response equation of time systemh) When ω is equal to ωhThe H-term-containing coefficient of the mother imaginary part in the open-loop frequency response equation of the time system;
when ω iss/6<ωres<ωsAt the time of/2:
Kpand H has the following value ranges:
Figure FDA0002410934640000033
wherein KpIs the proportionality coefficient of the proportional resonant controller, H is the active damping feedback coefficient, TsFor sampling period, omega, of a digitally controlled systemsSampling angular frequency, omega, for a digitally controlled systemhFor the system cross-over frequency, Top(z) is the system open loop transfer function.
5. The LCL type inverter grid-connected control method based on parameter combination design according to claim 3, wherein the step 4 of analyzing the harmonic suppression condition of the resonant frequency of the LCL filter is as follows:
due to the presence of the zero-order keeper in the digital control, the actual resonance frequency ω of the LCL filterresThe shift can occur after the active damping control loop is used, and the resonance frequency after the shift is omegares', the resonance suppression analysis results are as follows:
Figure FDA0002410934640000041
wherein
a(ωres′)＝-(D(ωres′)2+F(ωres′)2)·((A(ωres′)2+B(ωres′)2)·(D(ωres′)2+F(ωres′)2)′-(D(ωres′)2+F(ωres′)2)·(A(ωres′)2+B(ωres′)2)′)
b(ωres′)＝4·(A(ωres′)2+B(ωres′)2)′·(C(ωres′)D(ωres′)3+C(ωres′)D(ωres′)F(ωres′)2+D(ωres′)2E(ωres′)F(ωres′)+E(ωres′)F(ωres′)3)-2·(A(ωres′)2+B(ωres′)2)·(C(ωres′)D(ωres′)3+C(ωres′)D(ωres′)F(ωres′)2+D(ωres′)2E(ωres′)F(ωres′)+E(ωres′)F(ωres′)3)′
c(ωres′)＝2(A(ωres′)2+B(ωres′)2)′·(3C(ωres′)2D(ωres′)2+C(ωres′)2F(ωres′)2+D(ωres′)2E(ωres′)2+3E(ωres′)F(ωres′)+4C(ωres′)D(ωres′)E(ωres′)F(ωres′))-(A(ωres′)2+B(ωres′)2)·(3C(ωres′)2D(ωres′)2+C(ωres′)2F(ωres′)2+D(ωres′)2E(ωres′)2+3E(ωres′)F(ωres′)+4C(ωres′)D(ωres′)E(ωres′)F(ωres′))′
d(ωres′)＝4·(A(ωres′)2+B(ωres′)2)′·(C(ωres′)3D(ωres′)+C(ωres′)D(ωres′)E(ωres′)2+C(ωres′)2E(ωres′)F(ωres′)+E(ωres′)3F(ωres′))-2·(A(ωres′)2+B(ωres′)2)·(C(ωres′)3D(ωres′)+C(ωres′)D(ωres′)E(ωres′)2+C(ωres′)2E(ωres′)F(ωres′)+E(ωres′)3F(ωres′))′
e(ωres′)＝-(C(ωres′)2+E(ωres′)2)·((A(ωres′)2+B(ωres′)2)·(C(ωres′)2+E(ωres′)2)′-(C(ωres′)2+E(ωres′)2)·(A(ωres′)2+B(ωres′)2)′)
Wherein a (ω)res') is when ω is ω ═ ωresIn the time constraint of H4Coefficient of term, b (ω)res') is when ω is ω ═ ωresIn the time constraint of H3Coefficient of term, c (ω)res') is when ω is ω ═ ωresIn the time constraint of H2Coefficient of term, d (ω)res') is when ω is ω ═ ωresCoefficient of the H term in the time constraint, e (ω)res') is when ω is ω ═ ωresCoefficient of constant term in the' time constraint, A (ω)res') is when ω is ω ═ ωresCoefficient of real part of molecule, B (omega) in open-loop frequency response equation of' time systemres') is when ω is ω ═ ωresCoefficient of imaginary part of molecule, C (omega) in open-loop frequency response equation of' time systemres') is when ω is ω ═ ωresH-free coefficient, D (omega) of real part of denominator in open-loop frequency response equation of time systemres') is when ω is ω ═ ωresCoefficient containing H term, E (omega) of mother real part in open-loop frequency response equation of time systemres') is when ω is ω ═ ωresH-free coefficient, F (omega) of the mother imaginary part in the open-loop frequency response equation of the' time systemres') is when ω is ω ═ ωresThe H term-containing coefficient of the imaginary part of the denominator in the open-loop frequency response equation of the time system.
6. The LCL inverter grid-connected control method based on parameter combination design according to claim 3, wherein K is in step 5pAnd H are selected as follows:
max Kp
Figure FDA0002410934640000051
Figure FDA0002410934640000052
Figure FDA0002410934640000053
Figure FDA0002410934640000054
h2(Kp,H,ωh,ωres′)＝a(ωres′)H4+b(ωres′)H3+c(ωres′)H2+d(ωres′)H+e(ωres′)＝0
the above formula is KPAnd H, the final parameter of which is selected from the equation in which gi(kp,H,ωh,ωres') and i ═ 1,2,3, represent inequality constraints, hj(kp,H,ωh,ωres') denotes the equality constraint and j is 1, 2.
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CN112532096A (en) * 2020-12-03 2021-03-19 南京理工大学 LCL inverter grid-connected device and method suitable for weak power grid
CN113258615A (en) * 2021-06-08 2021-08-13 西南石油大学 Grid-connected inverter frequency self-adaptive control method, device, equipment and storage medium
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CN114094802A (en) * 2021-12-06 2022-02-25 南京理工大学 LCL inverter grid-connected device and method for widening positive damping interval

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CN112532096A (en) * 2020-12-03 2021-03-19 南京理工大学 LCL inverter grid-connected device and method suitable for weak power grid
CN112532096B (en) * 2020-12-03 2022-09-23 南京理工大学 LCL inverter grid-connected device and method suitable for weak power grid
CN113258615A (en) * 2021-06-08 2021-08-13 西南石油大学 Grid-connected inverter frequency self-adaptive control method, device, equipment and storage medium
CN113258615B (en) * 2021-06-08 2021-10-08 西南石油大学 Grid-connected inverter frequency self-adaptive control method, device, equipment and storage medium
CN113629984A (en) * 2021-07-27 2021-11-09 浙江大学 Three-phase LCL type SAPF parameter design method based on double-loop current control strategy
CN113629984B (en) * 2021-07-27 2023-02-28 浙江大学 Three-phase LCL type SAPF parameter design method based on double-loop current control strategy
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