CN103516249A - Single-phase inverter and waveform control method thereof - Google Patents

Abstract

The invention relates to the technical field of electric power and electronics, and in particular relates to a single-phase inverter and a waveform control method thereof. The single-phase inverter comprises an input direct current power supply Vdc, a single-phase full bridge inverter circuit which is composed of 4 power switch tubes and 4 freewheeling diodes which are in antiparallel connection with 4 power switch tubes, a filter inductor L, a filter capacitor C, a load Z, a voltage sensor VSEN, a current sensor ISEN, an A/D conversion circuit, a digital controller and a driver circuit. According to the invention, when the harmonic content is large, the parameter K of an adjustable system is adjusted, so that a repetitive controller plays the main role and the system is stable; when the harmonic content is small, the parameter K of the adjustable system is adjusted, so that a PI controller plays the main role and the system has fast response speed; and the control scheme integrates the characteristics of repetitive control and PI control and gives full play to the advantages of compound control, so that the system has the advantages of good output waveform, fast dynamic response, strong adaptability to the load and the like.

Description

A kind of single-phase inverter and waveform controlling method thereof

Technical field

The present invention relates to electric and electronic technical field, be specifically related to a kind of single-phase inverter and waveform controlling method thereof.

Background technology

In various power electronic equipments, the range of application of inverter is the most widely, but is faced with a lot of nonlinear problems in the application of inverter, thereby has affected inverter output voltage waveform quality.In these non-linear factors, rectified load occupies suitable proportion.These non-linear rectified loads are due to the periodic turn-on and turn-off of diode, the topological structure of whole circuit is cyclic variation, the output current distortion that makes inverter is a series of pinnacle burst pulse, because near the output impedance value non-vanishing and resonance frequency of inverter is very large, load current will form pressure drop in output impedance, its harmonic components will cause the wave distortion of power output end voltage, voltage THD value can surpass 5%, when serious, can reach more than 10%, far beyond power supply quality standard, other power consumption equipment that also can be docked in inverter electric power system impacts simultaneously, thereby when serious, can in circuit, produce concussion causes components and parts to damage.For voltage source inverter system, the dead band time delay arranging in order to prevent bridge arm direct pass also can impact output voltage waveforms.

In order to solve the distortion of inverter output waveform, can by closed loop control method, reduce the harmonic wave of output voltage, existing control method comprises: repeat to control, PI controls, STATE FEEDBACK CONTROL, sliding formwork is controlled, dead beat control etc., there are various weak points in single control, in order to solve the deficiency of single control mode, can adopt compound control, at present the most frequently used compound control is two closed loops of PI+repeat to control, but mention the ability that this compound control scheme does not have effectively to bring into play instantaneous value adjuster in paper " the PV system interconnection technology based on voltage mode control ", dynamic response is still undesirable, its reason is, under this compound scheme, the input that repeats control and PID adjuster is the tracking error of system, two adjusters regulate same error, the mutual interference of two regulated quantity phases of result.Owing to also there is no a kind of perfect composite controller design method at present, and two controllers cannot be considered the impact that introducing each other produces original control model during independent design separately exactly, so the performance of system can not be guaranteed; From another perspective, the effect of only using repetitive controller is to make to export tracing preset completely, output voltage and given instruction are without differing, and while only adopting PID adjuster, system output and given normally have differ, both regulating characteristicss are different, if directly it is also arrived together by force, may cause the confusion of regulating effect.Existence due to above two factors, in order to guarantee stability and the stable state output-index of system, normally P, I parameter are got littlely, but just directly sacrificed like this dynamic response capability of instantaneous value adjuster, finally often do not reached and introduced the original intention that instantaneous value is controlled.

Summary of the invention

The object of the present invention is to provide a kind of single-phase inverter with better dynamic and static performance, the present invention also aims to provide a kind of waveform controlling method of single-phase inverter.

The object of the present invention is achieved like this:

, comprise input DC power V _dc, by 4 power switch pipes and 4 fly-wheel diodes antiparallel with it, form single-phase full bridge inverter circuit, filter inductance L, filter capacitor C, load Z, voltage sensor VSEN, current sensor ISEN, A/D change-over circuit, digitial controller and drive circuit, the collector electrode C end that the emitter E of the first power switch pipe VT1 is connected to the second power switch pipe VT2 forms a brachium pontis 1, the collector electrode C end that the emitter E of the 3rd power switch pipe VT3 is connected to the 4th power switch pipe VT4 forms brachium pontis 2, the collector electrode C end of the first power switch pipe VT1 of brachium pontis 1 is connected with the collector electrode C end of the 3rd power switch pipe VT3 of brachium pontis 2, the emitter E end of the second power switch pipe VT2 of brachium pontis 1 is connected with the collector electrode E end of the 4th power switch pipe VT4 of brachium pontis 2, DC power supply V _dcpositive pole be connected to the collector electrode C end of the first power switch pipe VT1 and the 3rd power switch pipe VT3, V _dcnegative pole be connected to the emitter E end of the second power switch pipe VT2 and the 4th power switch pipe VT4, filter inductance L one end is connected with the mid point A of brachium pontis 1, and the filter inductance L other end is connected with filter capacitor C, and the other end of filter capacitor C is connected on the mid point B of brachium pontis 2, load Z is connected in parallel on the two ends of capacitor C, the two ends of voltage sensor VSEN are also connected to the two ends of capacitor C, and current sensor ISEN is connected in series on the circuit that inductance L is connected with capacitor C, the output voltage signal u that voltage sensor VSEN is detected _cthe current signal i detecting with current sensor ISEN _lfeed-in A/D change-over circuit, A/D change-over circuit is by u _cand i _lconvert digital signal to and give digitial controller, in digitial controller to output sinusoidal voltage u _ccarry out harmonic spectrum calculating, extract in real time u _cthe frequency spectrum of the harmonic wave of characteristic frequency calculates according to these harmonic spectrums the parameter K that power spectrum regulates adjustable system in real time in adaptive mechanism, meanwhile by output voltage u _cwith reference voltage u _refsend into error e that subtracter A1 obtains and send into harmonic wave and extract link, extract error e harmonic components and give and repeat to control G _rpcompensate adjusted value u ₂, by u ₂as product, be compensated signal u with adjustable system K ₃=Ku ₂, meanwhile by error e, give G _vadjusting obtains i _r, then by i _land i _rsend into subtracter A2, the signal obtaining is sent into G _cregulate adjusted value u ₁, finally by signal u ₂and u ₃give adder A3 and be compensated signal u _m=u ₁+ u ₃, by u _mgive SPWM modulator and generate pwm signal, then give drive circuit formation drive pulse signal by pwm signal, finally drive pulse signal is given to the gate pole G end of 4 power switch pipe VT1～VT4.

Load Z is linear load or nonlinear load.

The waveform controlling method of single-phase inverter comprises: direct-current input power supplying V _dcafter single-phase full bridge inverter circuit, inversion is alternating current, then after LC filter circuit, output sinusoidal voltage u _cwith sinusoidal current i _lgive load Z, use voltage sensor VSEN and current sensor ISEN to detect respectively output sinusoidal voltage u _cwith sinusoidal current i _l, then by u _cand i _lsend into A/D change-over circuit and convert digital signal to, finally by this digital signal, give digitial controller, in digitial controller, by the output voltage u detecting _cwith given reference voltage u _refsend into subtracter A1 and make comparisons and obtain error e, meanwhile to output voltage u _ccarry out harmonic spectrum calculating, to output voltage signal u _ccarry out Fourier series decomposition, extract in real time output voltage signal u _cthe frequency spectrum of the harmonic wave of characteristic frequency, then the harmonic spectrum obtaining is sent in adaptive mechanism, in adaptive mechanism, these harmonic spectrums are calculated to power spectrum S (ω), utilize least-squares algorithm so that harmonic signal power spectrum S (ω) minimum is the parameter K that principle regulates adjustable system in real time:

$u_c=c_0+\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{a}_n\cos \mathrm{n\ωt}+b_n\sin \mathrm{n\ωt},$

U in formula _cbe output voltage signal, ω=2 π/T is first-harmonic angular frequency, and T is the cycle of signal, c ₀dC component, a _n, b _nthe amplitude of mutually orthogonal trigonometric function,

$c_0=\frac{1}{T}\underset{0}{\overset{T}{\∫}}{u}_c\mathrm{dt};$

$\left\{\begin{array}{c}{a}_n=\frac{2}{T}\underset{0}{\overset{T}{\∫}}{u}_c\cos \mathrm{n\ωtdt}\\ b_n=\frac{2}{T}\underset{0}{\overset{T}{\∫}}{u}_c\sin \mathrm{n\ωtdt}\end{array}\right.;$

$S\left(\mathrm{\ω}\right)=\underset{T\→\∞}{\lim }\frac{1}{2T}{\left|U\left(\mathrm{j\ω}\right)\right|}^2;$

U in formula (j ω) is u _cfourier transform,

s (ω) is u _cpower spectrum;

By obtaining error e, send into respectively in the two closed loop controllers of two PI in parallel and repetitive controller, in repetitive controller, first error e is sent into harmonic wave and extracted link, extract the harmonic components of error e, the harmonic components of the error e of extracting is sent into repetitive control G _rpmiddle adjusting obtains voltage signal u ₂, u ₂as product, obtain signal u with the parameter K of adjustable system ₃=Ku ₂:

u _c＝u _f(t)+u _h(t)

$u_f\left(t\right)=\sin \mathrm{\ωt}\·\frac{4}{T}\underset{t-\frac{T}{2}}{\overset{t}{\∫}}{u}_c\sin \mathrm{\ωtdt}+\cos \mathrm{\ωt}\·\frac{4}{T}\underset{t-\frac{T}{2}}{\overset{t}{\∫}}{u}_c\cos \mathrm{\ωtdt}$

U in formula _coutput voltage signal, u _f(t) be the fundametal compoment instantaneous value of output voltage signal, u _h(t) be the harmonic component instantaneous value of output voltage signal;

In the two closed loop controllers of PI, error e is sent into Voltage loop PI controller G _vregulate and obtain given value of current signal i _r, then by the output current i detecting _lwith i _rsend into subtracter A2, then the signal obtaining is sent into electric current loop PI controller G _cmiddle adjusting, obtains the regulated value u of the two closed loop controllers of PI ₁, finally two controllers in parallel are obtained to signal u ₁and u ₃adder A3, is finally compensated signal u _m=u ₁+ u ₃, then compensating signal u _mgive SPWM modulator and generate pwm pulse signal, pwm pulse signal is given to drive circuit again and formed drive pulse signal, 4 power switch pipe VT1, VT2, VT3, VT4 finally drive pulse signal being given in single-phase full bridge inverter circuit make system normal operation.

Beneficial effect of the present invention is:

In single-phase inverter Waveform Control system, compare with the compound control of two closed loops of conventional PI+repeat to control, the control method that the present invention proposes is utilized repetitive controller only to regulate harmonic wave, is not affected the characteristic of first-harmonic, pi regulator is mainly used in the quick tracking to first-harmonic instruction, and utilize adaptive mechanism to detect in real time the harmonic content of output voltage, according to the content of harmonic wave, the output of repetitive controller is weighted to adjusting.When harmonic content is large, adjust the parameter K of adjustable system, repetitive controller is played a major role, make system there is better stability; When harmonic content hour, adjust the parameter K of adjustable system, PI controller is played a major role, make system there is response speed faster.Repeat to control and PI controls coupling and the phase mutual interference of regulated quantity each other and greatly weakened, controller can be respectively according to needing separately independent design in the design phase, and PI parameter is also without deliberately reduction again.The advantages such as this control program merges and repeats to control and PI controls feature separately, gives full play to the advantage of compound control, makes system have good output waveform, and dynamic response is fast, and the ability of adaptation load is strong.

Accompanying drawing explanation

Fig. 1 is single-phase inverter main circuit of the present invention and control structure figure thereof;

Fig. 2 is the control flow chart of the digitial controller of Fig. 1.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be described in more detail:

The present invention proposes the separated method of controlling in inverter Waveform Control, utilize repetitive controller and PI controller respectively the harmonic wave of inverter output voltage and first-harmonic independently to be regulated separately, and adopt the self-adaptive controlled harmonic wave that harmonic wave of output voltage content detection module constantly detects output voltage that arranges in control system, according to harmonic content, the output of repetitive controller being carried out to weighting in real time controls, giving full play to repetitive controller and PI controller feature separately, is a kind of control method that makes inverter system have good dynamic and static performance.

As shown in Figure 1, single-phase inverter main circuit comprises input DC power V _dc, V _dccan be understood as batteries or other feasible DC power supply (as rectifier power source); Four power switch pipes (as IGTB, MOSFET etc.) VT1, VT2, VT3, VT4 and four fly-wheel diode VD1s antiparallel with it, VD2, VD3, VD4; The collector electrode that the emitter of VT1 is connected to VT2 forms a brachium pontis 1, and the collector electrode that the emitter of VT3 is connected to VT4 forms 2, two brachium pontis of brachium pontis formation in parallel single-phase full bridge inverter circuit, DC power supply V _dcpositive pole be connected to the collector electrode of VT1, negative pole is connected to the emitter of VT2; Single-phase inverter adopts LC mode filter, and filter inductance L one end is connected with the VT1 of inverter circuit brachium pontis 1 and the mid point A of VT2, and the other end is connected with filter capacitor C, and the other end of capacitor C is connected to the VT3 of brachium pontis 2 and the mid point B of VT4; Load Z(linear load or nonlinear load) be connected in parallel on the two ends of capacitor C.

Control system comprises digitial controller, and current detection circuit consists of current sensor ISEN, and voltage detecting circuit consists of voltage sensor VSEN, A/D change-over circuit and drive circuit.Digitial controller comprises the two closed loop controllers of PI, Voltage loop PI controller G _v, electric current loop PI controller G _c; Harmonic wave extracts link; Repetitive controller G _rp; Adjustable system K; Voltage harmonic frequency spectrum calculates; Adaptive mechanism, SPWM modulator.Current sensor ISEN is connected on the circuit of inductance L, and voltage sensor VSEN is connected in parallel on the two ends of electric capacity R.The output voltage signal u being detected by voltage detecting circuit _cfeed-in A/D change-over circuit, the inductive current i being detected by current detection circuit _lfeed-in A/D change-over circuit; By A/D change-over circuit by u _c, i _lconvert digital signal to, then send into digitial controller.In digitial controller, by output voltage u _ccarry out harmonic spectrum calculating, extract in real time output voltage signal u _cthe harmonic spectrum of characteristic frequency (for example 3,5,7,9,11 subharmonic), in adaptive mechanism, according to these harmonic signals, calculate its power spectrumanalysis and go out harmonic content, utilize least-squares algorithm so that harmonic signal power spectrum minimum regulates the parameter K of adjustable system in real time for principle.By the voltage signal u feeding back _cwith reference voltage u _refsend into subtracter A1 and obtain error e, e is sent into harmonic wave and extract link, extract its harmonic components, then pass through repetitive controller Gr _pthe adjusted value of compensation u ₂, then by u ₂as product, obtain signal u with K ₃; In the two closed loop controllers of PI, e is sent into Voltage loop PI controller G _vregulate and obtain given value of current i _r, then by current signal i _land i _rsend into subtracter A2, then the signal obtaining is sent into electric current loop PI controller G _cadjusting obtains the regulated value u of the two closed loop controllers of PI ₁.The signal u after the two closed loop controller compensation of PI ₁with the signal u after repetitive controller and adjustable system K compensation ₃give adder A3, obtain final compensating signal u _m=u ₁+ u ₃, then compensating signal u _mgive SPWM modulator and generate pwm signal, given drive circuit and form drive pulse signal, finally pulse signal, give the power switch pipe in full bridge inverter.

Shown in Fig. 1 and Fig. 2, DC power supply V _dcdirect current inversion after single-phase full bridge inverter circuit of input is alternating current, and after LC filtering, output sinusoidal voltage is given load Z.Current detection circuit and voltage detecting circuit consist of current sensor ISEN and voltage sensor VSEN respectively, for example: Hall current sensor and Hall voltage transducer, voltage sensor VSEN is also connected to the two ends of filter capacitor C, output voltage u detected _c, current sensor ISEN is connected in series on the circuit that inductance is connected with electric capacity, inductive current i detected _l.In inversion process by the inductive current i detecting _lwith output voltage u _csignal is sent into A/D change-over circuit and is converted digital signal to, then gives digitial controller this digital signal.

In digitial controller, harmonic spectrum calculates according to (1) formula output voltage signal u _ccarry out Fourier series decomposition, extract in real time output voltage signal u _cthe frequency spectrum of the harmonic wave of characteristic frequency (for example n=3,5,7,9,11 subharmonic), in adaptive mechanism, these harmonic spectrums are calculated to power spectrum according to (4) formula, utilize least-squares algorithm so that harmonic signal power spectrum minimum regulates the parameter K of adjustable system in real time for principle.

$u_c=c_0+\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{a}_n\cos \mathrm{n\ωt}+b_n\sin \mathrm{n\ωt}---\left(1\right)$

(1) u in formula _cbe output voltage signal, ω=2 π/T is first-harmonic angular frequency, and T is the cycle of signal, c ₀that DC component can be tried to achieve by (2) formula, a _n, b _nbe the amplitude of mutually orthogonal trigonometric function, (3) formula utilizes the orthogonal property of trigonometric function can derive a _n, b _n.

$c_0=\frac{1}{T}\underset{0}{\overset{T}{\∫}}{u}_c\mathrm{dt}---\left(2\right)$

$\left\{\begin{array}{c}{a}_n=\frac{2}{T}\underset{0}{\overset{T}{\∫}}{u}_c\cos \mathrm{n\ωtdt}\\ b_n=\frac{2}{T}\underset{0}{\overset{T}{\∫}}{u}_c\sin \mathrm{n\ωtdt}\end{array}\right.---\left(3\right)$

$S\left(\mathrm{\ω}\right)=\underset{T\→\∞}{\lim }\frac{1}{2T}{\left|U\left(\mathrm{j\ω}\right)\right|}^2---\left(4\right)$

(4) in formula, U (j ω) is u _cfourier transform,

s (ω) is u _cpower spectrum.

By output voltage u _cwith reference voltage u _refsend into subtracter A1 and obtain departure e, then e is sent into harmonic wave and extract link, harmonic wave extracts link and uses the Harmonic detection based on instantaneous reactive power theory, and by formula (5), (6) can extract departure e harmonic components, then pass through repetitive controller G _rpadjusting, repeating to control is the control method based on internal model principle, makes system can overcome the error effect that PERIODIC INTERFERENCE is brought, and makes input and output signal consistent, finally obtains the regulated value u of repetition control and compensation ₂.

u _c＝u _f(t)+u _h(t) (5)

$u_f\left(t\right)=\sin \mathrm{\ωt}\·\frac{4}{T}\underset{t-\frac{T}{2}}{\overset{t}{\∫}}{u}_c\sin \mathrm{\ωtdt}+\cos \mathrm{\ωt}\·\frac{4}{T}\underset{t-\frac{T}{2}}{\overset{t}{\∫}}{u}_c\cos \mathrm{\ωtdt}---\left(6\right)$

(5) u in formula _coutput voltage signal, u _f(t) be the fundametal compoment instantaneous value of output voltage signal, u _h(t) be the harmonic component instantaneous value of output voltage signal.

The two closed loop controllers of PI mainly play quick adjustment effect, in the two closed loop controllers of PI, and Voltage loop PI controller G _vemploying capacitance voltage feedback, electric current loop PI controller G _cadopt the mode of inductor current feedback.Error e is sent into Voltage loop PI controller G _vregulate and obtain given value of current i _r, then by inductive current i _land i _rsend into subtracter A2, then the signal obtaining is sent into electric current loop PI controller G _cregulate, obtain the regulated value u of the two closed loop controllers of PI ₁.

The harmonic content of the output voltage detecting according to adaptive mechanism regulates adjustable system K, when harmonic content is large, adjusts the parameter K of adjustable system, and repetitive controller is played a major role, and makes system have better stability; When harmonic content hour, adjust the parameter K of adjustable system, PI controller is played a major role, make system there is response speed faster.To the output u that repeats to control ₂be weighted control, be compensated signal Ku ₂, the signal of the repetitive controller compensation of the signal after the two closed loop controller compensation of PI and weighting control, give adder A3 and superpose, obtain final compensating signal u _m=u ₁+ Ku ₂, then compensating signal u _mgive SPWM modulator and generate pwm pulse signal, then given drive circuit formation drive pulse signal, the power switch pipe of finally drive pulse signal being given in single-phase full bridge inverter circuit makes circuit normal operation.

Claims (3)

1. a single-phase inverter, comprises input DC power V _dc, by 4 power switch pipes and 4 fly-wheel diodes antiparallel with it, form single-phase full bridge inverter circuit, filter inductance L, filter capacitor C, load Z, voltage sensor VSEN, current sensor ISEN, A/D change-over circuit, digitial controller and drive circuit, it is characterized in that: the collector electrode C end that the emitter E of the first power switch pipe VT1 is connected to the second power switch pipe VT2 forms a brachium pontis 1, the collector electrode C end that the emitter E of the 3rd power switch pipe VT3 is connected to the 4th power switch pipe VT4 forms brachium pontis 2, the collector electrode C end of the first power switch pipe VT1 of brachium pontis 1 is connected with the collector electrode C end of the 3rd power switch pipe VT3 of brachium pontis 2, the emitter E end of the second power switch pipe VT2 of brachium pontis 1 is connected with the collector electrode E end of the 4th power switch pipe VT4 of brachium pontis 2, DC power supply V _dcpositive pole be connected to the collector electrode C end of the first power switch pipe VT1 and the 3rd power switch pipe VT3, V _dcnegative pole be connected to the emitter E end of the second power switch pipe VT2 and the 4th power switch pipe VT4, filter inductance L one end is connected with the mid point A of brachium pontis 1, and the filter inductance L other end is connected with filter capacitor C, and the other end of filter capacitor C is connected on the mid point B of brachium pontis 2, load Z is connected in parallel on the two ends of capacitor C, the two ends of voltage sensor VSEN are also connected to the two ends of capacitor C, and current sensor ISEN is connected in series on the circuit that inductance L is connected with capacitor C, the output voltage signal u that voltage sensor VSEN is detected _cthe current signal i detecting with current sensor ISEN _lfeed-in A/D change-over circuit, A/D change-over circuit is by u _cand i _lconvert digital signal to and give digitial controller, in digitial controller to output sinusoidal voltage u _ccarry out harmonic spectrum calculating, extract in real time u _cthe frequency spectrum of the harmonic wave of characteristic frequency calculates according to these harmonic spectrums the parameter K that power spectrum regulates adjustable system in real time in adaptive mechanism, meanwhile by output voltage u _cwith reference voltage u _refsend into error e that subtracter A1 obtains and send into harmonic wave and extract link, extract error e harmonic components and give and repeat to control G _rpcompensate adjusted value u ₂, by u ₂as product, be compensated signal u with adjustable system K ₃=Ku ₂, meanwhile by error e, give G _vadjusting obtains i _r, then by i _land i _rsend into subtracter A2, the signal obtaining is sent into G _cregulate adjusted value u ₁, finally by signal u ₂and u ₃give adder A3 and be compensated signal u _m=u ₁+ u ₃, by u _mgive SPWM modulator and generate pwm signal, then give drive circuit formation drive pulse signal by pwm signal, finally drive pulse signal is given to the gate pole G end of 4 power switch pipe VT1～VT4.

2. a kind of single-phase inverter according to claim 1, is characterized in that: described load Z linear load or nonlinear load.

3. a waveform controlling method for single-phase inverter, is characterized in that: direct-current input power supplying V _dcafter single-phase full bridge inverter circuit, inversion is alternating current, then after LC filter circuit, output sinusoidal voltage u _cwith sinusoidal current i _lgive load Z, use voltage sensor VSEN and current sensor ISEN to detect respectively output sinusoidal voltage u _cwith sinusoidal current i _l, then by u _cand i _lsend into A/D change-over circuit and convert digital signal to, finally by this digital signal, give digitial controller, in digitial controller, by the output voltage u detecting _cwith given reference voltage u _refsend into subtracter A1 and make comparisons and obtain error e, meanwhile to output voltage u _ccarry out harmonic spectrum calculating, to output voltage signal u _ccarry out Fourier series decomposition, extract in real time output voltage signal u _cthe frequency spectrum of the harmonic wave of characteristic frequency, then the harmonic spectrum obtaining is sent in adaptive mechanism, in adaptive mechanism, these harmonic spectrums are calculated to power spectrum S (ω), utilize least-squares algorithm so that harmonic signal power spectrum S (ω) minimum is the parameter K that principle regulates adjustable system in real time:

$u_c=c_0+\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{a}_n\cos \mathrm{n\ωt}+b_n\sin \mathrm{n\ωt},$

U in formula _cbe output voltage signal, ω=2 π/T is first-harmonic angular frequency, and T is the cycle of signal, c ₀dC component, a _n, b _nthe amplitude of mutually orthogonal trigonometric function,

$c_0=\frac{1}{T}\underset{0}{\overset{T}{\∫}}{u}_c\mathrm{dt};$

$\left\{\begin{array}{c}{a}_n=\frac{2}{T}\underset{0}{\overset{T}{\∫}}{u}_c\cos \mathrm{n\ωtdt}\\ b_n=\frac{2}{T}\underset{0}{\overset{T}{\∫}}{u}_c\sin \mathrm{n\ωtdt}\end{array}\right.;$

$S\left(\mathrm{\ω}\right)=\underset{T\→\∞}{\lim }\frac{1}{2T}{\left|U\left(\mathrm{j\ω}\right)\right|}^2;$

U in formula (j ω) is u _cfourier transform,

s (ω) is u _cpower spectrum;

By obtaining error e, send into respectively in the two closed loop controllers of two PI in parallel and repetitive controller, in repetitive controller, first error e is sent into harmonic wave and extracted link, extract the harmonic components of error e, the harmonic components of the error e of extracting is sent into repetitive control G _rpmiddle adjusting obtains voltage signal u ₂, u ₂as product, obtain signal u with the parameter K of adjustable system ₃=Ku ₂:

u _c＝u _f(t)+u _h(t)

$u_f\left(t\right)=\sin \mathrm{\ωt}\·\frac{4}{T}\underset{t-\frac{T}{2}}{\overset{t}{\∫}}{u}_c\sin \mathrm{\ωtdt}+\cos \mathrm{\ωt}\·\frac{4}{T}\underset{t-\frac{T}{2}}{\overset{t}{\∫}}{u}_c\cos \mathrm{\ωtdt}$

U in formula _coutput voltage signal, u _f(t) be the fundametal compoment instantaneous value of output voltage signal, u _h(t) be the harmonic component instantaneous value of output voltage signal;

In the two closed loop controllers of PI, error e is sent into Voltage loop PI controller G _vregulate and obtain given value of current signal i _r, then by the output current i detecting _lwith i _rsend into subtracter A2, then the signal obtaining is sent into electric current loop PI controller G _cmiddle adjusting, obtains the regulated value u of the two closed loop controllers of PI ₁, finally two controllers in parallel are obtained to signal u ₁and u ₃adder A3, is finally compensated signal u _m=u ₁+ u ₃, then compensating signal u _mgive SPWM modulator and generate pwm pulse signal, pwm pulse signal is given to drive circuit again and formed drive pulse signal, 4 power switch pipe VT1, VT2, VT3, VT4 finally drive pulse signal being given in single-phase full bridge inverter circuit make system normal operation.

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