CN103887822A - LCL-type single-phase grid-connected inverter power control and active damping optimization method - Google Patents

LCL-type single-phase grid-connected inverter power control and active damping optimization method Download PDF

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CN103887822A
CN103887822A CN201410133468.8A CN201410133468A CN103887822A CN 103887822 A CN103887822 A CN 103887822A CN 201410133468 A CN201410133468 A CN 201410133468A CN 103887822 A CN103887822 A CN 103887822A
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grid
current
omega
phase
lcl
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CN103887822B (en
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罗安
周乐明
陈燕东
陈智勇
龙际根
王明玥
王华军
李明飞
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CHANGSHA BOLI ELECTRIC Co Ltd
Hunan University
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CHANGSHA BOLI ELECTRIC Co Ltd
Hunan University
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    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30Reactive power compensation
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40Arrangements for reducing harmonics

Abstract

The invention discloses an LCL-type single-phase grid-connected inverter power control and active damping optimization method. An equivalent synchronous coordinate PI controller is adopted, a two-phase virtual orthogonal system is constructed by adopting an all-pass filter, the problem that data used in previous construction methods have asynchrony or noise interference is introduced is solved, regulation of grid-connected currents at fundamental frequency in a zero steady state error is achieved, and the stability of the system is improved. According to the LCL-type single-phase grid-connected inverter power control and active damping optimization method, the primary differential and the high-frequency components of the grid-connected currents are fed back in real time, the damping of the system is increased, the resonance peak of the LCL filter is restrained, an optimized parameter selection method is given, single-current feedback factors are reduced to a variable, the defect that parameters are difficult to select in single current high-frequency component feedback is overcome, and the reliability and the dynamic nature of the system are improved.

Description

A kind of LCL type single-phase grid-connected inverter power control and active damping optimization method
Technical field
The present invention relates to PWM inversion control and new energy field thereof, specifically the power control of a kind of LCL type single-phase grid-connected inverter and active damping optimization method.
Background technology
The shortage of fossil energy and the environmental pollution causing make photovoltaic generation become one of study hotspot, at the tip of electrical network, a large amount of accesses of non-resistive load can produce reactive current, this requires distributed photovoltaic grid-connected system that the active current of low harmonics distortion can be provided, and also needing provides reactive current to load.The grid-connected control strategy that has no-power compensation function concurrently is carried out to corresponding research both at home and abroad, its under synchronous rotating frame to meritorious and idle carry out respectively that PI regulates can the equivalence ratio resonance control of grid-connected current in pairs, realize floating and the power factor of grid-connected electric current, and the detection of load reactive current is the key that realizes Active Generation and reactive power compensation, conventionally adopt structure three-phase system or two-phase orthogonal system and obtain virtual three-phase or the biphase current under different coordinates, but all introduce so undoubtedly latency issue in various degree, the stability of system is had to larger impact.
The orthogonal system of structure is only realized power adjustments at first-harmonic, does not consider humorous wave zone, and this will be with the harm of dealing public electric wire net harmonic.In order to reduce the harm of harmonic wave to public electric wire net, require it to there is extremely low total harmonic distortion.In grid-connected system, by HC(Harmonic compensator) strategy can realize the inhibition to low-order harmonic, adopts LCL filter, and can better suppress high order harmonic component, and reduce total inductance amount.But LCL filter is a third-order system has a resonance spikes that damping coefficient is very low, easily occur vibrate and cause system unstable, therefore the control of system is had higher requirement.Conventionally adopt the method for active damping to suppress resonance spikes, capacitance current in sampling LCL filter also carries out FEEDBACK CONTROL or adopts net side inductive drop micro component to replace capacitance current suppressing resonance spikes, but all can introduce extra current sensor, the hardware cost that has increased system, has reduced system reliability.Therefore, reducing the extra transducer of introducing adopts single current feedback to become study hotspot, there is at present the strategy adopting twice Derivative Feedback of grid-connected current and the current capacitance current value of estimation feedback, but the coefficient of two subdifferentials is difficult for choosing and the comparatively complicated and time consumption of evaluation method of capacitance current, and easily introduces error.
Summary of the invention
Technical problem to be solved by this invention is, for prior art deficiency, the power control of a kind of LCL type single-phase grid-connected inverter and active damping optimization method are provided, solve the problem that the idle detection of traditional single phase exists larger time delay or introduces interference signal, solve current single-phase LCL type combining inverter needs additional sensors or introduces the problem that single current feedback parameter is difficult for choosing simultaneously.
For solving the problems of the technologies described above, the technical solution adopted in the present invention is: the power control of a kind of LCL type single-phase grid-connected inverter and active damping optimization method, and the method is:
1) in the starting point in each sampling period, the A/D sample circuit of LCL type single-phase grid-connected inverter is to line voltage u swith grid-connected current i gand the inverter circuit DC capacitor voltage U of LCL type single-phase grid-connected inverter dcsample respectively, and sampled data is given to the control module processing of LCL type single-phase grid-connected inverter;
2) to grid-connected current i gobtain β phase virtual orthographic signal i by all-pass filter β, construct two-phase virtual orthographic system, obtain two-phase quadrature current i α, i β:
i α = i g i β = ω 0 - s ω 0 + s i g ;
Wherein, ω 0for power frequency angular frequency; S=j ω, j is imaginary part unit symbol;
3) to i α, i βdo α β/dq coordinate transform and obtain single-phase grid-connected active current value i dwith grid-connected reactive current value i q;
4) to DC side reference voltage U dc *with inverter circuit DC capacitor voltage U dcbe PI and regulate, obtain the grid-connected current active current command value i of DC side voltage stabilizing link d *, according to the reactive power Q of need compensation sdetermine the command value i of reactive current q *:
I q * = 2 Q s * / U s ;
5) to single-phase grid-connected active current i d, grid-connected current active current command value i d *and grid-connected reactive current i q, reactive current command value i q *carry out respectively PI adjusting, and adjusted value after PI is regulated does dq/ α β coordinate transform and obtains command signal i 1 α, i 1 β; Its control effect to grid-connected current can be equivalent to synchronous coordinate system PI controller, grid-connected current i gwith grid-connected current command value i g *equivalent difference E at α under mutually αto inverter control signal i 1 αtransfer function G c(s) be:
G c ( s ) = K p s 3 + ( K p ω 0 + K i ) s 2 + ( K p ω 0 2 + 2 ω 0 K i ) s + K p ω 0 3 - K i ω 0 2 s 3 + ω 0 s 2 + ω 0 2 s + ω 0 3 ,
G c(s) infinitely great in the gain of fundamental frequency place, gain at non-fundamental frequency place very little, zero steady-state error that realizes grid-connected current regulates.Wherein K p, K ifor PI parameter in grid-connected meritorious and reactive current PI controller.
6) to grid-connected current i gintroduce 3,5,7 subharmonic compensators, obtain offset current i 3, and by command signal i 1 αwith offset current i 3make the poor current signal i that obtains 0;
7) to grid-connected current i gintroducing feedback increases system damping, obtains grid-connected current value of feedback; Wherein feedback factor is H 1(s):
H 1 ( s ) = K d s + K c s + ω d s ;
Wherein K d, K cbe respectively grid-connected current differential, high fdrequency component coefficient; ω is electrical network angular frequency;
8) by current signal i 0poor with grid-connected current value of feedback, obtain SPWM modulation wave signal d;
9) SPWM modulating wave and triangular carrier are carried out to bipolarity modulation, obtain the duty cycle signals of inverter circuit switching tube, through the Drive Protecting Circuit of LCL type single-phase grid-connected inverter, control opening and turn-offing of inverter circuit switching tube.
In described step 7), K cwith K dpass be:
K c=(1-T sω d)K d/T s
ω dand K dvalue be:
ω d = 4 ξ 2 / ( 4 ξ 2 + 1 ) ω res K d = 2 T s ξ K inv ( 4 ξ 2 + 1 ) ω res [ 2 ( L + L g ) - LL g C 4 ξ 2 + 1 ω res 2 ] ;
Wherein, ω resfor the resonance frequency of LCL filter, ξ is the target damping coefficient of LCL type inverter in grid-connected current feedback, ω nfor grid-connected current is introduced the resonance frequency after feedback, K invfor the equivalent gain of LCL type inverter, L, Lg are the inductance sense value in LCL filter, and C is the capacitor's capacity of LCL filter, T sfor the sampling period.
Compared with prior art, the beneficial effect that the present invention has is: for single phase system directly application of synchronized rotating coordinate system realize the problem of grid-connected power control, the present invention adopts equivalent synchronous coordinate system PI controller, adopt all-pass filter structure two-phase virtual orthographic system, overcome the problem that building method data used in the past have asynchronism or introduce noise jamming, realize grid-connected current and regulate at fundamental frequency zero steady state error, improve the stability of a system.One subdifferential and the high fdrequency component of Real-time Feedback grid-connected current of the present invention, increase system damping, suppress the resonance spikes of LCL filter, and provide the parameter selection method of optimizing, single current feedback coefficient is reduced to unitary variant, overcome the shortcoming that in single electric current high fdrequency component feedback, parameter is difficult for choosing, improved system reliability and dynamic.
Brief description of the drawings
Fig. 1 is the combining inverter power control of one embodiment of the invention LCL type and active damping optimization method structure chart thereof;
Fig. 2 is the combining inverter power control of one embodiment of the invention LCL type and active damping optimization method control block diagram thereof;
Fig. 3 is single current feedback active damping Optimal Control Strategy control block diagram schematic diagram of one embodiment of the invention LCL type combining inverter;
Fig. 4 is one embodiment of the invention K 1transfer function during from the different ratio of ζ
Figure BDA0000486845050000051
bode diagram;
Fig. 5 is one embodiment of the invention line voltage u ssurvey current i with net gsimulation waveform.
Embodiment
As shown in Figure 1, one embodiment of the invention single-phase photovoltaic grid-connected inverter comprises inverter circuit, LCL filter circuit, A/D sample circuit, phase-locked loop circuit, controller DSP 2812, Drive Protecting Circuit, and described photovoltaic array, boost chopper, inverter circuit, LCL filter circuit, electrical network connect successively; Described A/D sample circuit input is connected with described LCL filter circuit; Described controller DSP 2812 is connected with described Drive Protecting Circuit input, A/D sample circuit output, phase-locked loop circuit output; Described phase-locked loop circuit input is connected with electrical network; Described Drive Protecting Circuit drives described inverter circuit.Inverter circuit is connected with LCL filter circuit, and dsp controller is connected with A/D sample circuit, phase-locked loop pll circuit, Drive Protecting Circuit respectively, and Drive Protecting Circuit is connected with the switching tube of rectification circuit.The break-make of switching tube in the output control inverter circuit of Drive Protecting Circuit.Inductance L and inductance L g, and capacitor C forms the filter circuit of single-phase photovoltaic grid-connected inverter, is used for the high order harmonic component of filtering grid-connected current, has significant attenuation.U dcfor inverter circuit DC capacitor voltage, i gfor grid-connected current, u sfor line voltage.
LCL type combining inverter of the present invention power control and active damping optimization method thereof are as follows:
1) in the starting point in each sampling period, A/D sample circuit is to line voltage u swith grid-connected current i gand inverter circuit DC capacitor voltage U dcsample respectively, and give control module processing by sampled data;
2) to grid-connected current i gobtain β phase virtual orthographic signal i by all-pass filter β, construct two-phase virtual orthographic system, do α β/dq coordinate transform and obtain single-phase grid-connected active current i dwith grid-connected reactive current i q;
3) to grid-connected active current i dwith grid-connected reactive current i qvalue and grid-connected current active current command value i d *, reactive current command value i q *carry out PI adjusting, do dq/ α β coordinate transform and obtain command signal i 1 α, i 1 β, wherein i 1 αit is the signal of control inverter;
4) introduce 3,5,7 subharmonic compensators, obtain offset current i 3, instruction current i 1 αwith offset current i 3make the poor current signal i that obtains 0;
5) grid-connected current being introduced to feedback increases system damping, and feedback factor is H 1(s), current signal i 0poor with value of feedback, obtain SPWM modulation wave signal d;
6) SPWM modulating wave and triangular carrier carry out bipolarity modulation, draw the duty cycle signals of inverter circuit switching tube, through Drive Protecting Circuit, control opening and turn-offing of inverter circuit switching tube.
Fig. 2 is the power control of LCL type combining inverter and the active damping optimization method control block diagram thereof of invention.
By single order all-pass filter, construct i β, sampling period T of its time delay s, it is followed the tracks of that load dynamic change response is fast, and stability and real-time are high, have solved building method data used in the past and have the problem of asynchronism.
i β ( s ) = ω 0 - s ω 0 + s i g ( s )
By moment reactive power theory can obtain, through C α β-pqafter coordinate transform, under p-q rotating coordinate system, can obtain grid-connected current active current and reactive current component, both obtain DC component I by low pass filter filtering of ac pand I q, be expressed as:
I p I q = 2 I g 1 cos θ 1 2 I g 1 sin θ 1
Wherein, I g1for the effective value of fundamental current, θ 1for the phase deviation of fundamental current.
Under p-q two-phase rotating coordinate system, grid-connected gaining merit subtracted each other to obtain difference E with its command value respectively with reactive current component p, E qfor:
E p = I sp * - I p E q = I sq * - I q
E pand E qbe E at α β two-phase rest frame down conversion αand E β, wherein E αand E βbe respectively i αand i βwith the difference of its set-point, and E αbe grid-connected current i simultaneously swith grid-connected current command value i s *difference, thereby realize closed-loop control to grid-connected current.It regulates grid-connected PI meritorious and reactive current under p-q two-phase rotating coordinate system, converts under α β two-phase static coordinate.This is controlled under frequency domain and can be expressed as:
i 1 α ( s ) i 1 β ( s ) = 1 2 G PI ( s + j ω 0 ) + G PI ( s - j ω 0 ) - j G PI ( s + j ω 0 ) + j G PI ( s - j ω 0 ) j G PI ( s + j ω 0 ) - j G PI ( s - j ω 0 ) G PI ( s + j ω 0 ) + G PI ( s - j ω 0 ) E α ( s ) E β ( s )
Wherein, i 1 αand i 1 βfor the control signal of this controller output.
Have:
i 1 α ( s ) i 1 β ( s ) = 1 2 K p + K i s s 2 + ω 0 2 - K i ω 0 s 2 + ω 0 2 K i ω 0 s 2 + ω 0 2 K p + K i s s 2 + ω 0 2 E α ( s ) E β ( s )
Wherein
E β(s)=((ω 0-s)/(ω 0+s))E α(s)
Grid-connected current difference E αto inverter control command value i 2transfer function G c(s) be:
G c ( s ) = K p s 3 + ( K p ω 0 + K i ) s 2 + ( K p ω 0 2 + 2 ω 0 K i ) s + K p ω 0 3 - K i ω 0 2 s 3 + ω 0 s 2 + ω 0 2 s + ω 0 3
From the viewpoint of controlling, G c(s) under rest frame, can equivalence become wherein K of synchronous coordinate system PI p=0.05, K i=10, ω 0=2 π * 50, transfer function G c(s) infinitely great in the gain of fundamental frequency place, at non-fundamental frequency place, gain is very little, the zero steady-state error control that realizes grid-connected current is identical with ratio resonance control (PR) control effect, but near ratio of gains PR fundamental frequency controls and wants high, can reduce mains frequency skew time, on the impact of harmonic suppression effect.
Its single current feedback active damping control strategy elaborates in Fig. 3.
Fig. 3 is single current feedback active damping Optimal Control Strategy control block diagram of LCL type combining inverter.
Introduce this list current feedback, ignore the dead resistance of filter, now inverter output voltage u invto current on line side i gclosed loop transfer function, be:
G u inv i g ( s ) = s + ω d s ( LL g C s 3 + LL g C ω d s 2 + ( L + L g ) s + ( L + L g ) ω d - K d K inv / T s )
Its characteristic equation can be expressed as:
D ( s ) = LL g Cs ( s + K 1 ω n ) ( s 2 + 2 ξ ω n + ω n 2 )
Wherein ξ is the target damping coefficient of system under this strategy, ω nfor introducing the resonance frequency after feedback, K 1for the limit of introducing arrives the coefficient ratio of imaginary axis distance to the distance of the imaginary axis and complex-conjugate poles.
Obtain according to the coefficient of homogeneous power is identical:
ω n = 1 / ( 2 K 1 ξ + 1 ) ω res ω d = ( K 1 + 2 ξ ) ω n K d = T s [ ( L + L g ) ω d - K 1 ω n 3 LL g C ] / K inv
From above formula, ω ndepart from the resonance frequency omega of LCL filter res, and ω nthan ω reslittle.When selecting ω nduring for certain value, K 1the value of ζ is constant, if K 1what become is increasing, and what ζ became so is more and more less, the inhibition ability of LCL resonance spikes is died down; If it is increasing that ξ becomes, K so 1what become is more and more less, is difficult to maintain a higher dynamic responding speed.Therefore K 1, ζ must ensure that system has the prerequisite that good resonance spikes suppresses ability and very fast response speed and gets off to design.
Can be obtained fom the above equation:
ω d = ( K 1 ξ + 2 / K 1 ξ ) K 1 ξ / ( 2 K 1 ξ + 1 ) ω res
Work as K 1=2 ζ, ω dthere is minimum to make the stability of system and the inhibition of response speed and resonance spikes have optimal value, have:
ω d = 4 ξ 2 / ( 4 ξ 2 + 1 ) ω res K d = 2 T s ξ K inv ( 4 ξ 2 + 1 ) ω res [ 2 ( L + L g ) - LL g C 4 ξ 2 + 1 ω res 2 ]
ω d, K dvalue can be determined by ζ, therefore two variablees of feedback factor are reduced to a variable in single current feedback, and the resonance inhibition of ζ and system is proportionate, and only just can change system damping by ζ, simultaneously ζ variable effect stability margin and the response speed of system.As shown in table 1, along with the increase of ζ, steady state error and the Phase margin of system first increase afterwards and diminish; And ω nsuccessively decrease always.For system has good transient process, conventionally require Phase margin to reach 45 °~70 °.System has identical ζ, ω nlarger, response speed is faster, in order to have good dynamic property, ω ncan not be too small.
Get ζ=0.5~0.6, ω n/ ω resratio be 0.64~0.7, now system overshoot appropriateness, the adjusting time is shorter, and LCL resonance spikes is had to good inhibition, system has dynamic property faster.
The present invention has provided the method for designing of this list current feedback.When system parameters has certain optional scope, can meet increase system damping, improve under the prerequisite of the stability of a system and response speed requirement, its feedback parameter is further optimized: (1), first according to the parameter of inverter, determines K cand K drelation, and use K drepresent K c; (2) the later resonance frequency of supposition skew is determined, suppresses ability angle analysis from stability and resonance, works as K 1when=2 ζ, can obtain minimum ω dmake systematic function the best; (3) stability margin and the response speed of system while variation according to ζ, determine the span of ζ; (4) adjust the value of ζ, make system there is good stability and response speed faster.
Fig. 4 is K 1transfer function during from the different ratio of ζ
Figure BDA0000486845050000091
bode diagram.Work as K 1>2 ζ, along with K 1increase K with the ratio of ζ 1ω nvalue become large, real pole departs from the imaginary axis, dynamic performance strengthens, but it is to the inhibition of system damping variation gradually, works as K 1<2 ζ, resonance spikes suppresses ability and K 1=2 ζ are suitable, but along with K 1successively decrease with the ratio of ζ, the dynamic property variation of system, Phase margin diminishes, and magnitude margin increases, the stability variation of system, and work as K 1when=0.6 ζ, its phase frequency curve passes through the frequency of 0dB lower than amplitude frequency curve through the frequency of-180 °, and system is unstable.Therefore work as K 1=2 ζ, system has optimum performance.
Fig. 5 is line voltage u ssurvey current i with net gsimulation waveform.Set up system simulation model with Matlab/Simulink, emulation initial condition is 500W/m 2, 25 ° of ambient temperatures.T=0s moment grid-connected inverters, the not access of local load, when 0.085s, illumination Intensity Abrupt is 1000W/m 2, when 0.18s, accessing load (3+j2) kVA, when 0.265s, combining inverter provides reactive power.For the ease of observing, the line voltage u in figure samplitude is 0.1 times of actual value.The system that can obtain has response speed fast.In the time of the local load of access, inverter can be adjusted power coefficient, when providing active power to load, can cross the object that realizes reactive power compensation, thereby reach the quality of power supply that improves electrical network tip, entirety is controlled and has been reduced grid-connected aberration rate, has improved the quality of power supply and the antijamming capability of photovoltaic parallel in system.

Claims (2)

1. the power control of LCL type single-phase grid-connected inverter and an active damping optimization method, is characterized in that, the method is:
1) in the starting point in each sampling period, the A/D sample circuit of LCL type single-phase grid-connected inverter is to line voltage u swith grid-connected current i gand the inverter circuit DC capacitor voltage U of LCL type single-phase grid-connected inverter dcsample respectively, and sampled data is given to the control module processing of LCL type single-phase grid-connected inverter;
2) to grid-connected current i gobtain β phase virtual orthographic signal i by all-pass filter β, construct two-phase virtual orthographic system, obtain two-phase quadrature current i α, i β:
i &alpha; = i g i &beta; = &omega; 0 - s &omega; 0 + s i g ;
Wherein, ω 0for power frequency angular frequency; S=j ω, j is imaginary part unit symbol, ω is electrical network angular frequency;
3) to i α, i βdo α β/dq coordinate transform and obtain single-phase grid-connected active current value i dwith grid-connected reactive current value i q;
4) to DC side reference voltage U dc *with inverter circuit DC capacitor voltage U dcbe PI and regulate, obtain the grid-connected current active current command value i of DC side voltage stabilizing link d *, according to the reactive power Q of need compensation sdetermine the command value i of reactive current q *:
I q * = 2 Q s * / U s ;
5) to single-phase grid-connected active current i d, grid-connected current active current command value i d *and grid-connected reactive current i q, reactive current command value i q *carry out respectively PI adjusting, and adjusted value after PI is regulated does dq/ α β coordinate transform and obtains command signal i 1 α, i 1 β;
6) to grid-connected current i gintroduce 3,5,7 subharmonic compensators, obtain offset current i 3, and by command signal i 1 αwith offset current i 3make the poor current signal i that obtains 0;
7) to grid-connected current i gintroducing feedback increases system damping, obtains grid-connected current value of feedback; Wherein feedback factor is H 1(s):
H 1 ( s ) = K d s + K c s + &omega; d s ;
Wherein K d, K cbe respectively grid-connected current differential, high fdrequency component coefficient;
8) by current signal i 0poor with grid-connected current value of feedback, obtain SPWM modulation wave signal d;
9) SPWM modulating wave and triangular carrier are carried out to bipolarity modulation, obtain the duty cycle signals of inverter circuit switching tube, through the Drive Protecting Circuit of LCL type single-phase grid-connected inverter, control opening and turn-offing of inverter circuit switching tube.
2. LCL type single-phase grid-connected inverter according to claim 1 power control and active damping optimization method, is characterized in that, in described step 7), and K cwith K dpass be:
K c=(1-T sω d)K d/T s
ω dand K dvalue be:
&omega; d = 4 &xi; 2 / ( 4 &xi; 2 + 1 ) &omega; res K d = 2 T s &xi; K inv ( 4 &xi; 2 + 1 ) &omega; res [ 2 ( L + L g ) - LL g C 4 &xi; 2 + 1 &omega; res 2 ] ;
Wherein, ω resfor the resonance frequency of LCL filter, ξ is the target damping coefficient of LCL type inverter in grid-connected current feedback, ω nfor grid-connected current is introduced the resonance frequency after feedback, K invfor the equivalent gain of LCL type inverter, L, Lg are the inductance sense value in LCL filter, and C is the capacitor's capacity of LCL filter, T sfor the sampling period.
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