CN106126833A - A kind of novel bifurcation graphs method for drafting being applicable to Sliding mode variable structure control inverter - Google Patents

Abstract

The invention discloses a kind of novel bifurcation graphs method for drafting being applicable to Sliding mode variable structure control inverter, comprise the steps: 1, set up Sliding mode variable structure control discrete iteration mapping model；2, analyze existing bifurcation graphs method for drafting, determine that it judges stable region and the inaccurate reason of forked tunnel, find one's way out with this；3, the mechanism of research state jumping phenomenon；4, according to state mutation mechanism, the method deriving Variable sampling point-rendering inverter bifurcation graphs, and draw corresponding figure.The present invention proposes a kind of Variable sampling point bifurcation graphs method for drafting, the bifurcation graphs that empirical tests the method is drawn can not only accurately determine system stability working field, and the forked tunnel of system of analyzing can be used for, demonstrate the correctness of theory analysis finally by Experiment of Electrical Circuits, result of study provides reference for the non-linear behavior of research Sliding mode variable structure control inverter and the drafting of bifurcation graphs thereof.

Description

A kind of novel bifurcation graphs method for drafting being applicable to Sliding mode variable structure control inverter

Technical field

The present invention relates to control technical field in stability of power system, be applicable to sliding moding structure control particularly to one The novel bifurcation graphs method for drafting of inverter processed.

Background technology

As the important component part of solar electrical energy generation, combining inverter (Grid-connected Inverter, GI) Effect is to be that alternating current imports bulk power grid by DC inverter.Owing to GI is joined directly together with bulk power grid, large-scale distributed light The instability of volt GI is likely to result in bulk power grid fluctuation, even causes system to collapse the most suddenly.GI be one strong , there is period doubling bifurcation, fast change and become the non-linear phenomena such as wild effect, Holf fork slowly in nonlinear and time-varying system.Future New forms of energy part replaces or replaces completely traditional energy generating, and it is essential therefore to study GI stability and bifurcation, To solving, Practical Project problem is significant.

Bo Lei etc. establishes numerical scale and controls the inherent mechanism that single-phase H bridge GI occurs to shake, with the side of characteristic locus Method demonstrates and there is Holf fork in system.Xie Ruiliang etc. control the discrete iteration model of single-phase H bridge GI by setting up ratio, Research considers the forked tunnel of dead-time voltage GI, chooses for proportional controller parameter designing and Dead Time and provides well Theoretical foundation.Liao Zhixian etc. are by setting up booster converter (BOOST) and proportional plus integral control single-phase H bridge inverter combines The discrete model of two-stage type GI, in the case of research cascade, the selection of circuit and proportional plus integral control parameter is to GI nonlinear kinetics The impact of behavior, has some reference value to the efficiency improving photovoltaic generating system with stability.But above-mentioned document is the most only visited Beg for H bridge GI dynamic behavior of combining inverter under Linear Control.H bridge GI is connected to the grid and needs isolating transformer, to solve Its leakage problem being usually present.Ji Baojian etc. propose a kind of high efficiency H6 structure the most isolated grid-connected inverter (Non- Isolated Grid-connected Inverter with H6-type, NGI-H6), in the case of system is without transformator, Solve its leakage problem being usually present.This circuit structure is by embedding two high-performance diodes in H6 bridge midpoint, both Can be that inverter provides freewheeling path, may be implemented in again freewheeling period and DC source and AC network are isolated, and have Unipolarity modulation and H6 bridge midpoint still export the feature of three level voltages, and these features are conducive to improving efficiency and the power of GI Grade.Research show that this circuit structure has low common-mode voltage, high efficiency feature, in being more applicable for, high-power photovoltaic also In net electricity generation system.But NGI-H6 operation principle and pi controller are only designed and are verified, not to it by document Dynamic behavior and fork are studied.Sliding mode variable structure control is as a kind of rapid dynamic response speed, strong robustness and realization Simple typical case's Sliding mode variable structure control is widely used in inverter control system.It is online that above-mentioned document only discusses GI Property control lower discrete model and bifurcation, and there is the non-linear one-tenth that can not lead in inverter under Sliding mode variable structure control mode Point, Jacobi matrix exgenvalue method, maximum lyapunov index (Lyapunov exponents) etc. need system iteration The analytic method of equation derivation is the most inapplicable, therefore Sliding mode variable structure control GI kinetics and the analytic method of bifurcation and line Property control have significantly different, it would be highly desirable to study further.Existing method is according on Fault slip rate to SMC control stability research Motor point must be all this requirement of terminating point, when motor point arrives near diverter surface s (x)=0, must haveBecome Vertical, determine that sliding formwork controls the stable region of parameter with this.Hao Xiang etc. have studied Sliding mode variable structure control (Sliding Mode Controlled, SMC) stability of H bridge inverter and forked tunnel, based on Sinusoidal Pulse Width Modulation (Sinusoidal Pulse-Width-Modulated, SPWM) inverter duty cycle monotonicity principle proposition one stabilizing property criterion soon, research Result shows that this criterion can judge whether system is in steady operational status exactly, provides for SMC control stability research Important references.Existing method and soon stabilizing property criterion are simply possible to use in the stability judging SMC nonlinear Control inverter system, But can not response system dynamic behavior and bifurcation, more cannot well rely on it to draw out precise and stable bifurcation graphs.

Summary of the invention

For the problems referred to above, it is an object of the invention to overcome prior art not enough, it is provided that one is applicable to sliding formwork and becomes knot Structure controls the novel bifurcation graphs method for drafting of inverter, is illustrated based on Sliding mode variable structure control H6 bridge.

Technical scheme is as follows:

Step one, discrete iteration mapping, modeling:

ε is sliding formwork control coefrficient；I is grid-connected current, i_refFor grid-connected reference current, wherein i_ref(t)=I_ref×sin(2π f₁T), I_refFor i_refAmplitude；Control, in order to eliminate SMC, the chattering phenomenon that discontinuity is brought, introduce in SMC controller (proportionality coefficient is k to proportional component_p), obtain modulated signal (u_control) it is:

u_control=ε × sign (i_ref-i)+k_p×(i_ref-i) (1)；

By u_controlWith unipolarity triangular wave carrier u_carrierCompare, produce PWM drive signal, and generate S₁～S₄ PWM drive signal figure；u_controlCompare with zero-signal, produce S₅And S₆PWM drive signal.

Wherein i_ref(t)=I_ref*sin(2πf₁T), I_refFor i_refAmplitude, f₁For i_refFrequency；Reference by the n moment Electric current i_refN () compares with load current i (n) in n moment after, control to obtain dutycycle d in the n-th moment of system through SMC_n, its meter Calculation method is as follows:

$d_n=\left\{\begin{array}{cc}-\mathrm{\&epsiv;}\&times;sign\left(i_{ref}\right(n)-i(n\left)\right)-k_p\&times;\left(i_{ref}\right(n)-i(n\left)\right)& \left(i_{ref}\right(n)-i(n)\&GreaterEqual;0)\\ -\mathrm{\&epsiv;}\&times;sign\left(i\right(n)-i_{ref}(n\left)\right)-k_p\&times;\left(i\right(n)-i_{ref}(n\left)\right)& \left(i_{ref}\right(n)-i(n)<0)\end{array}\right.---\left(2\right);$

If inverter two brachium pontis midpoint A, the voltage between B is U_AB；Work as U_ABBe output as ± E and 0 time be respectively defined as 1 and 0 electricity Flat, and define when i flows to B from A as just；Conduction status according to switching tube can be classified as multiple switch mode, further according to Load inductance electric current i direction difference is divided into multiple duty, and forms respective state equation；

System discrete iteration mapping, modeling uses stroboscopic map thought, by i in n+1 moment value i_n+1By n moment value i_nCarry out table Show；Within the different time periods, stroboscopic map model is different；

L and R is load inductance, load resistance, makes a=E/R, b=L/R, u_grid=U_m* sin (ω t), U_mFor u_gridWidth Value, T_s=1/f_sFor carrier cycle；

Work as i_ref> 0 time, U_ABFor+E and 0, with T_sAs the stroboscopic sampling period, the state equation of a kind of mode can obtain i's Stroboscopic sampling model is:

$i_{n+1}=e^{-\frac{T_s}{b}}{i}_n-0.5a(e^{-\frac{T_s}{b}}-e^{(d_n-1)\&times;\frac{T_s}{b}})+U_{m}sin\left({\mathrm{\&omega;nT}}_s\right)(e^{-\frac{T_s}{b}}-1)/\left(2R\right)---\left(3\right);$

Work as i_ref< 0, U_ABFor-E and 0, the state equation of another kind of mode the stroboscopic sampling model obtaining i is:

$i_{n+1}=e^{-\frac{T_s}{b}}{i}_n-0.5a(e^{-\frac{T_s}{b}}-e^{(d_n-1)\&times;\frac{T_s}{b}})+U_{m}sin\left({\mathrm{\&omega;nT}}_s\right)(e^{-\frac{T_s}{b}}-1)/\left(2R\right)---\left(4\right);$

The principle that step 2, Sliding mode variable structure control inverter state mutated site produce:

According to a kind of structure obtained of step, the principle that Sliding mode variable structure control inverter state mutated site produces is: Error signal e=i_ref-i, when systematic error signal e e (n)=i occurs in the n-th switch periods_refThe situation of (n)-i (n) < 0 Time, u_control(n)=-ε+k_p× e (n) < 0, u_control(n)<u_carrier(n), therefore dutycycle d_n0 will be sported, inductive current To drastically decline, cause, n+1 switch periods, e (n+1)=i occurs_ref(n+1)-i (n+1) > 0, u_control(n)=-ε+k_p× E (n) > 0, u_carrierAnd u (n+1)_control(n+1) must there be two intersection points, the duty d of (n+1)th switch periods_n+1>0；Therefore exist Inductive current positive half period descending branch, the dutycycle of pulse-width modulation PWM control signal occurs in that d_n<d_n+1The feelings of non-monotonic decline Condition, causes system to occur in that the wild effect of state mutation；

Step 3, the determination of mutated site:

At each sinusoidal cycles N number of point of sampling, wherein N=f_s/f₁, f_sFor sample rate, f₁For i_refFrequency；By step In the dutycycle that obtains substitute into, select from N₀Time (N₀For more than the arbitrarily selected value of pi/2) sampled point start under obtaining current waveform Dutycycle d of fall continuous two switch periods of section M switch periods_nAnd d_n+1Make difference again divided by the absolute value of both differences, calculating The M number gone out is added and obtains P_MCan be expressed as follows:

$P_M=\underset{n=N_0}{\overset{N_0+M-1}{\&Sigma;}}\frac{d_{n+1}-d_n}{|d_{n+1}-d_n|}---\left(5\right);$

If dutycycle is always maintained at monotone variation, P in M switch periods_MDuring=M, system is i.e. in steady operation shape State；If P_M+1< M+1, system is in fork labile state, and Continuous plus goes out the P of front M and M+1 switch periods_MAnd P_M+1's Value, if P_M=M and P_M+1< M+1, it is determined that the state mutation cycle is N₀+ M switch periods；

Step 4, bifurcation graphs method for drafting:

The catastrophe point data obtained according to step 3 draw bifurcation graphs, in the reasonable scope, take fork parameter ε at the beginning of any Initial value substitutes in discrete iteration equation, works as P_MDuring=M, system is in steady-working state, and optional any sampled point is multiple Bifurcation graphs is drawn in the sampling location of power cycle；Work as P_M=M and P_M+1< M+1, then it represents that system occurs in that fork wild effect, Can determine whether that the state mutation cycle is N by state mutation cycle criterion₀+ M, then with N₀+ M sampled point is multiple power cycle Fixed sample position draw bifurcation graphs.

Further, described inverter is NGI-H6 system, wherein, D₁, D₂For high-performance diode, E is solaode VD, L₁、L₂, for load inductance, R₁、R₂For load resistance.

Further, in described step one, owing to dutycycle has saturated characteristic, need to be to d_nCarry out amplitude limit:

$d_n=\left\{\begin{array}{cc}0& (d_n\&le;0)\\ d_n& (0<d_n<1)\\ 1& (d_n\&GreaterEqual;1)\end{array}\right.---\left(6\right).$

The invention have benefit that:

Establish SMC herein and control the Discrete Mapping iterative model of NGI-H6, its state mutation phenomenon and fork are carried out Research.The mechanism that labor state mutation phenomenon produces, relies on state mutation point to obtain the bifurcation graphs of Variable sampling point, this The period doubling bifurcation labile state that bifurcation graphs energy correct response system occurs；Result of study can be Sliding mode variable structure control inversion Device dynamic behavior and STUDY OF BIFURCATION provide reference.

Accompanying drawing explanation

Fig. 1 is that the SMC of the embodiment of the present invention controls NGI-H6 system structure schematic diagram；

Fig. 2 is the S of the embodiment of the present invention₁～S₆Driving signal graph；

(n=25) conventional inverter bifurcation graphs when Fig. 3 is that in the embodiment of the present invention, fixed sample position is pi/2；

Fig. 4 is pwm control signal in the embodiment of the present invention, reference current i_refWaveform with inductive current i；

Fig. 5 is embodiment of the present invention intermediate cam carrier wave (u_carrier) and modulating wave (u_control) signal；

Fig. 6 is the big logotype of PWM control signal duty cycle in the embodiment of the present invention；

Conventional inverter bifurcation graphs when Fig. 7 is that in the embodiment of the present invention, fixed sample position is pi/2；

Conventional inverter bifurcation graphs when Fig. 8 is that in the embodiment of the present invention, fixed sample position is 3 π/10；

Fig. 9 is Variable sampling point bifurcation graphs in the embodiment of the present invention；

The time domain beamformer of i when Figure 10 is ε=0.13；

The positive half period descending branch time domain beamformer of i when Figure 11 is ε=0.13；

The spectrogram of i when Figure 12 is ε=0.13；

The time domain beamformer of i when Figure 13 is ε=0.2；

The positive half period descending branch time domain beamformer of i when Figure 14 is ε=0.2；

The spectrogram of i when Figure 15 is ε=0.2.

Detailed description of the invention

In order to be clearly understood from the technical characteristic of the present invention, purpose and effect, now comparison accompanying drawing illustrates the present invention's Detailed description of the invention.

The present embodiment combines SMC and controls NGI-H6 system, the method for drafting to Sliding mode variable structure control inverter bifurcation graphs It is described, comprises the following steps:

S1, Fig. 1 are that SMC controls NGI-H6 systematic schematic diagram, wherein: S₁～S₆For switching tube, D₁, D₂For high-performance two pole Pipe, E is solaode VD, L₁、R₁、L₂、R₂For load inductance, load resistance, u_gridFor line voltage, i is Grid-connected current, i_refFor grid-connected reference current.

According to the principle of Sliding mode variable structure control, export controlled quentity controlled variable u=ε × sign (e), wherein error signal e=i_ref- I, ε are sliding formwork control coefrficient.In order to eliminate the chattering phenomenon that Sliding mode variable structure control discontinuity is brought, in sliding mode controller (proportionality coefficient is k to introduce proportional component_p), obtain modulated signal (u_control) it is

u_control=ε × sign (i_ref-i)+k_p×(i_ref-i) (9)；

The u that will try to achieve_controlWith known unipolarity triangular wave carrier u_carrierCompare, produce PWM drive signal； S₁～S₄For switching tube, u_controlPositive half cycle and u_carrierRelatively produce S₁And S₄Driving signal；u_controlNegative half period with u_carrierRelatively produce S₂And S₃Driving signal；By i_refGeneration S is compared with zero-signal₅And S₆Driving signal, and drawn Become and drive signal graph, as shown in Figure 2；

According to the driving signal graph obtained, analyze the reference current i in n moment_refLoad current i (n) ratio in (n) and n moment After relatively, control to obtain dutycycle d in the n-th moment of system through SMC_n, its computational methods are as follows:

$d_n=\left\{\begin{array}{cc}-\mathrm{\&epsiv;}\&times;sign\left(i_{ref}\right(n)-i(n\left)\right)-k_p\&times;\left(i_{ref}\right(n)-i(n\left)\right)& \left(i_{ref}\right(n)-i(n)\&GreaterEqual;0)\\ -\mathrm{\&epsiv;}\&times;sign\left(i\right(n)-i_{ref}(n\left)\right)-k_p\&times;\left(i\right(n)-i_{ref}(n\left)\right)& \left(i_{ref}\right(n)-i(n)<0)\end{array}\right.---\left(10\right);$

If H6 bridge inverter two brachium pontis midpoint A, the voltage between B is U_AB.Work as U_ABIt is output as ± E, when 0, is respectively defined as 1,0 Level, and define when i flows to B from A as just.Conduction status according to switching tube can be classified as 4 kinds of switch mode, further according to Load inductance electric current i direction difference is divided into 4 kinds of duties.

Mode 1: as i > 0 time, S₁, S₄, S₅Conducting；S₂, S₃, S₆For switch mode 1 during shutoff.As it is shown in figure 1, E is through S₁、L₁、 R₁、u_grid、L₂、R₂Constitute closed-loop path to power to electrical network, wherein u_grid=U_m× sin (ω t), U_mFor u_gridAmplitude, then U_AB For

U_AB=+E (11)；

Make L₁=L₂=L, R₁=R₂=R, then the state equation of mode 1 can be written as:

$\frac{di}{dt}=-\frac{R}{L}i+\frac{E}{2L}-\frac{U_{m}sin\left(\mathrm{\&omega;}t\right)}{2L}---\left(12\right);$

Mode 2: work as i > 0, S₅And D₂Conducting；S₁, S₄, S₃, S₆For switch mode 2 during shutoff.I is through S₅、L₁、R₁、u_grid、L₂、 R₂、D₂Constitute the continuous current circuit of Circuits System, then U_ABFormula (13) and formula (14) can be expressed as with the state equation of mode 2:

U_AB=0 (13)；

$\frac{di}{dt}=-\frac{R}{L}i-\frac{U_{m}sin\left(\mathrm{\&omega;}t\right)}{2L}---\left(14\right);$

Mode 3 is analyzed similar with mode 4, and therefore 4 operation modes can represent, as shown in table 1 with 4 differential equations.

Table 1NGI-H6 operation mode and state equation

Work as i_ref> 0 time, U_AB> 0, S as shown in Table 1₅It is constantly in open-minded, works as i_ref< when 0, S₆Turn off always.SMC controls NGI-H6 system discrete iteration mapping, modeling uses stroboscopic map thought, by i in n+1 moment value i_n+1By n moment value i_nCome Represent.Within the different time periods, stroboscopic map model is different, can be divided into four sections as shown in Figure 3.

Make a=E/R, b=L/R, u_grid=U_m×Sin (ω t), U_mFor u_gridAmplitude, T_s=1/f_sFor carrier cycle.

Work as i_ref> 0 time, U_ABFor+E and 0, with T_sAs the stroboscopic sampling period, the state equation of mode 1 and 2 can obtain

Switch periods T_sIn, state equation during i > 0 can be expressed as:

$\left\{\begin{array}{c}\frac{di}{dt}=-\frac{R}{L}i+\frac{E}{2L}-\frac{U_{m}sin\left(\mathrm{\&omega;}t\right)}{2L}({\mathrm{nT}}_s\&le;t<(n+d_n\left)T_s\right)\\ \frac{di}{dt}=-\frac{R}{L}i-\frac{U_{m}sin\left(\mathrm{\&omega;}t\right)}{2L}\left(\right(n+d_n)T_s\&le;t<(n+1\left)T_s\right)\end{array}\right.---\left(15\right);$

Therefore the stroboscopic sampling model of i is:

$i_{n+1}=e^{-\frac{T_s}{b}}{i}_n-0.5a(e^{-\frac{T_s}{b}}-e^{(d_n-1)\&times;\frac{T_s}{b}})+U_{m}sin\left({\mathrm{\&omega;nT}}_s\right)(e^{-\frac{T_s}{b}}-1)/\left(2R\right)---\left(16\right);$

In like manner, it is known that work as i_ref< 0, U_ABFor-E and 0, the state equation of mode 3 and 4 the stroboscopic sampling model obtaining i is:

$i_{n+1}=e^{-\frac{T_s}{b}}{i}_n-0.5a(e^{-\frac{T_s}{b}}-e^{(d_n-1)\&times;\frac{T_s}{b}})+U_{m}sin\left({\mathrm{\&omega;nT}}_s\right)(e^{-\frac{T_s}{b}}-1)/\left(2R\right)---\left(17\right);$

S2, when inverter is in steady-working state, the dutycycle in each switch periods will be in strict accordance with sinusoidal bent The monotonicity of line is changed.Selection system occurred when cycle 1 state to period doubling bifurcation is suddenlyd change, and i positive half period descending branch is even The coherent signal of continuous 5 switch periods.Fig. 4 is PWM control, i_refWith i signal, Fig. 5 is triangular carrier (u_carrier) and modulating wave (u_control) signal, Fig. 6 is the big logotype of PWM control signal duty cycle.Owing to sliding mode controller contains sign function sign (e), when e polarity difference, u_controlIt is represented by:

$u_{control}=\left\{\begin{array}{cc}{k}_e+k_p\&times;e& (e>0)\\ -k_e+k_p\&times;e& (e<0)\end{array}\right.---\left(18\right);$

As shown in Figure 4, at (n-1)th switch periods e (n-1)=i_ref(n-1)-i (n-1) > 0, u_control(n-1)=ε+k_p ×e(n-1).As shown in Figure 5, u_carrierWith u_controlHaving two intersection points, there is twice saltus step, is classified as in pwm control signal Three phases.t₀-t₁And t₂-t₃Period: control signal is high level, system is operated in mode 1, and inductive current rises.According to number Word controls symmetric sampling SPWM modulation principle, if dutycycle is d_n-1, then high level time is d_n-1T_s。t₁-t₂Period: control letter Number being low level, system is operated in mode 2, and the low level working time is (1-d_n-1)T_s。

When in the n-th switch periods, i occurring_ref(n) < i (n), e (n)=i_refDuring the situation of (n)-i (n) < 0.By formula (11) Understand u_control(n)=-ε+k_p× e (n) < 0, u_control(n)<u_carrier(n), u_carrier(n) and u_controlN () is without intersection point, PWM Control signal is always maintained at low level, i.e. d_n=0.Due to numerically controlled hysteresis, the change delayed PWM control of inductive current One switch periods of signal processed, therefore inductive current i is (n+1)th cycle continuous discharge so that (n+1)th switch periods i_ref(n+ 1) > i (n+1), then e (n+1)=i_ref(n+1)-i (n+1) > 0, u_control(n+1)=ε+k_p× e (n+1) > 0, works as u_control(n+ 1)=u_carrier(n+1) time, u_carrierAnd u (n+1)_control(n+1) there are two intersection points.As shown in Figure 4, if dutycycle is d_n+1, Then the working time of mode 1 is d_n+1T_s；The working time of mode 2 is (1-d_n+1)T_s.In like manner can analyze n-th+2 and n+3 to open The work process in pass cycle.

It will be appreciated from fig. 6 that the dutycycle of continuous several switch periods no longer keeps monotonicity, wherein d_n-1>d_n, d_n<d_n+1, d_n+1 >d_n+2, d_n+2<d_n+3.Understand in conjunction with the driving of PWM in Fig. 4, the appearance of PWM drive signal doubling time, cause inductive current to occur State stable period 1 from (n-1)th switch periods sports the state mutation phenomenon of doubling time to the n-th switch periods.

Understand SMCI-H6 system inductance electric current from above-mentioned analysis and the root of state mutation phenomenon occurs in positive half period descending branch This reason is: when systematic error signal e e (n)=i occurs in the n-th switch periods_refDuring the situation of (n)-i (n) < 0, u_control (n)=-ε+k_p× e (n) < 0, u_control(n)<u_carrier(n), therefore dutycycle d_n0 will be sported, inductive current will drastically under Fall, causes e (n+1)=i occur in (n+1) individual switch periods_ref(n+1)-i (n+1) > 0, u_control(n)=-ε+k_p×e(n)> 0, u_carrierAnd u (n+1)_control(n+1) must there be two intersection points, the duty d of (n+1)th switch periods_n+1>0.Therefore at inductance electricity Stream positive half period descending branch, the dutycycle of pwm control signal occurs in that d_n<d_n+1The situation of non-monotonic decline, causes system to occur The wild effect of state mutation.

S3, selection are from N₀Sampled point during=pi/2 starts continuous two switches of obtaining current waveform descending branch M switch periods Dutycycle d in cycle_nAnd d_n+1Make difference again divided by the absolute value of both differences, the M number calculated is added and obtains P_MCan represent such as Under

$P_M=\underset{n=N_0}{\overset{N_0+M-1}{\&Sigma;}}\frac{d_{n+1}-d_n}{|d_{n+1}-d_n|}---\left(19\right);$

If dutycycle is always maintained at monotone variation, P in M switch periods_MDuring=M, system is i.e. in steady operation shape State.If P_M+1< M+1, system is in fork labile state, and Continuous plus goes out the P of front M and M+1 switch periods_MAnd P_M+1's Value, if P_M=M and P_M+1< M+1 then can determine that the state mutation cycle is N₀+ M switch periods.

S4, work as P_MDuring=M, system is in steady-working state, and optional any sampled point is adopting of multiple power cycle Bifurcation graphs is drawn in sample position；Work as P_M=M and P_M+1< M+1, then it represents that system occurs in that fork wild effect, passes through state mutation Cycle criterion can determine whether that the state mutation cycle is N₀+ M, then with N₀+ M sampled point is the fixed sample position of multiple power cycle Put drafting bifurcation graphs.

Embodiment 1,

Use conventional inverter bifurcation graphs method for drafting: first select certain parameter for fork parameter, join at certain fork In the case of number, an initial value of optional inverter state amount inductive current i substitutes into and starts iteration in discrete iteration equation；Remove Transient process, the value of the same fixed sample location status amount of the multiple sinusoidal cycles of continuous sampling, obtain one group of steady state value. With fork parameter as transverse axis, draw with this group steady statue value under this fork parameter for the longitudinal axis and i.e. can get inverter Bifurcation graphs.

Selecting circuit parameter is as follows: E=400V, R₁=R₂=R=2 Ω, L₁=L₂=L=6.85mH, f₁=50Hz, i_ref =I_ref× sin (100 π t) A, I_ref=5A, f_s=5kHz, k_p=0.2.Each sinusoidal cycles N number of point of sampling, wherein N=f_s/f₁ =5000/50=100；Continue with the same fixed position of 20 sinusoidal cycles, the and (n when fixed sample position is at pi/2 =25), with ε for fork parameter, from the conventional inverter bifurcation graphs of 0.01 to 1 change as shown in Figure 7.

The same fixed position of 20 sinusoidal cycles of continuous sampling, as can be seen from Figure 7, when ε=0.4, and chooses fixed sample When position is n=25, the sampled point of 20 power cycles overlaps, and all sampled points of bifurcation graphs overlap, and show as cycle 1 state.If When the fixing employing point selected is in 36 < n, < during 50 scope, now system is in fork labile state, the fork as n=40 Figure is as shown in Figure 8.

Comparison diagram 7 and Fig. 8 can be seen that inverter system under identical initial value and parameter, when selecting different sample bits When putting, drawing entirely different bifurcation graphs, the stable operation range and the bifurcation that therefore draw are the most different, and therefore, traditional divides , there is the biggest uncertainty in trouble figure drafting mode.

Embodiment 2,

Using SMC to control NGI-H6 system experimentation model machine, model machine parameter is: E=400V, u_gridFrequency f_ac=50Hz, R₁=R₂=R=10 Ω, L₁=L₂=L=6.85mH, numerical control chip: DSP2812, switching frequency f_s=5kHz, electrical network uses Chroma AC source simulates.As a example by different ε, obtain the experimental waveform of i.

The principle that inverter state catastrophe point produces is: error signal e=i_ref-i, when systematic error signal e is n-th There is e (n)=i in switch periods_refDuring the situation of (n)-i (n) < 0, u_control(n)=-ε+k_p× e (n) < 0, u_control(n)< u_carrier(n), therefore dutycycle d_nTo sport 0, inductive current will drastically decline, and cause e occur in (n+1) individual switch periods (n+1)=i_ref(n+1)-i (n+1) > 0, u_control(n)=-ε+k_p× e (n) > 0, u_carrierAnd u (n+1)_control(n+1) must have Two intersection points, the duty d of (n+1)th switch periods_n+1>0；Therefore at inductive current positive half period descending branch, pwm control signal Dutycycle occur in that d_n<d_n+1The situation of non-monotonic decline, causes system to occur in that the wild effect of state mutation；

Being analyzed for inverter state catastrophe point, step is as follows:

Selecting with ε for fork parameter, an optional initial value substitutes in discrete iteration equation, each power cycle sampling N Individual, wherein N=f_s/f₁=5000/50=100, calculates 20 power cycles.Work as P_M=M and P_M+1During=M+1, with N₀=25 It it is the sampled point of 20 power cycles.Work as P_M+1=M+1 and P_M+1< M+1, with N=N₀+ M is the fixed sample of 20 power cycles The bifurcation graphs of point-rendering is as shown in Figure 9.As can be seen from Figure 9 when 0.01 < ε < when 0.15, all sampled points of bifurcation graphs overlap, System is in steady statue, and therefore system stability territory is [0.01,0.15].Along with ε increases, Variable sampling point bifurcation graphs presents two Bar or a plurality of curve, illustrate to there occurs doubling time and multiple bifurcation phenomena near selected sampling location.

The time domain beamformer of i when Figure 10 is ε=0.13, Figure 11 is the time domain beamformer of the positive half period descending branch of i, from figure Can be seen that in 10 and Figure 11 that the ripple cycle of inverter is equal to switch periods.Figure 12 is the spectrogram of i, as can be known from Fig. 12 electricity The frequency of stream i mainly comprises fundamental frequency and switching frequency composition, and therefore system is now in steady-working state, becomes with Fig. 9 The analysis result of sampled point bifurcation graphs is consistent, and system is in steady-working state.

The time domain beamformer of i and spectrogram when Figure 13 is ε=0.2.From Figure 13 and Figure 14 can be seen that i at t about 0.288 Bifurcation phenomena is occurred in that near crossing.Figure 15 is the spectrogram of i, mainly contains fundamental frequency components, switch from Figure 15 Frequency content and a small amount of two divided-frequency composition.When ε=0.2, the sampled point of 20 power cycles shows as two paths, therefore becomes The period doubling bifurcation labile state that the bifurcation graphs energy correct response system of sampled point occurs.Therefore time domain waveform and spectrogram are again The secondary effectiveness demonstrating Variable sampling point bifurcation graphs.

The above, be only presently preferred embodiments of the present invention, and the present invention not makees any pro forma restriction, though So the present invention is disclosed above with preferred embodiment, but is not limited to the present invention, any technology people being familiar with this specialty Member, in the range of without departing from technical solution of the present invention, when the technology contents of available the disclosure above makes a little change or modification For the Equivalent embodiments of equivalent variations, as long as being the content without departing from technical solution of the present invention, the technical spirit of the foundation present invention Any simple modification, equivalent variations and the modification being made above example, all still falls within the range of technical solution of the present invention.

Claims (3)

1. the novel bifurcation graphs method for drafting being applicable to Sliding mode variable structure control inverter, it is characterised in that

Step one, discrete iteration mapping, modeling:

ε is sliding formwork control coefrficient；I is grid-connected current, i_refFor grid-connected reference current, wherein i_ref(t)=I_ref×sin(2πf₁T), I_refFor i_refAmplitude；Control, in order to eliminate SMC, the chattering phenomenon that discontinuity is brought, in SMC controller, introduce ratio Link, proportionality coefficient k_p, obtain modulated signal (u_control) it is:

u_control=ε × sign (i_ref-i)+k_p×(i_ref-i) (1)；

By u_controlWith unipolarity triangular wave carrier u_carrierCompare, produce PWM drive signal, and generate S₁～S₄PWM Drive signal graph；u_controlCompare with zero-signal, produce S₅And S₆PWM drive signal；

Wherein i_ref(t)=I_ref*sin(2πf₁T), I_refFor i_refAmplitude, f₁For i_refFrequency；Reference current by the n moment i_refN () compares with load current i (n) in n moment after, control to obtain dutycycle d in the n-th moment of system through SMC_n, its calculating side Method is as follows:

$d_n=\left\{\begin{array}{cc}-\mathrm{\&epsiv;}\&times;sign\left(i_{ref}\right(n)-i(n\left)\right)-k_p\&times;\left(i_{ref}\right(n)-i(n\left)\right)& \left(i_{ref}\right(n)-i(n)\&GreaterEqual;0)\\ -\mathrm{\&epsiv;}\&times;sign\left(i\right(n)-i_{ref}(n\left)\right)-k_p\&times;\left(i\right(n)-i_{ref}(n\left)\right)& \left(i_{ref}\right(n)-i(n)<0)\end{array}\right.---\left(2\right);$

If inverter two brachium pontis midpoint A, the voltage between B is U_AB；Work as U_ABBe output as ± E and 0 time be respectively defined as 1 and 0 level, and Definition is just when i flows to B from A；Conduction status according to switching tube can be classified as multiple switch mode, further according to load electricity Inducing current i direction difference is divided into multiple duty, and forms respective state equation；

System discrete iteration mapping, modeling uses stroboscopic map thought, by i in n+1 moment value i_n+1By n moment value i_nRepresent；? In the different time periods, stroboscopic map model is different；

L and R is load inductance, load resistance, makes a=E/R, b=L/R, u_grid=U_m× sin (ω t), U_mFor u_gridAmplitude, T_s=1/f_sFor carrier cycle；

Work as i_ref> 0 time, U_ABFor+E and 0, with T_sAs the stroboscopic sampling period, the state equation of a kind of mode can obtain the stroboscopic of i Sampling model is:

$i_{n+1}=e^{-\frac{T_s}{b}}{i}_n-0.5a(e^{-\frac{T_s}{b}}-e^{(d_n-1)\&times;\frac{T_s}{b}})+U_{m}sin\left({\mathrm{\&omega;nT}}_s\right)(e^{-\frac{T_s}{b}}-1)/\left(2R\right)---\left(3\right);$

Work as i_ref< 0, U_ABFor-E and 0, the state equation of another kind of mode the stroboscopic sampling model obtaining i is

$i_{n+1}=e^{-\frac{T_s}{b}}{i}_n-0.5a(e^{-\frac{T_s}{b}}-e^{(d_n-1)\&times;\frac{T_s}{b}})+U_{m}sin\left({\mathrm{\&omega;nT}}_s\right)(e^{-\frac{T_s}{b}}-1)/\left(2R\right)---\left(4\right);$

The principle that step 2, Sliding mode variable structure control inverter state mutated site produce:

According to a kind of structure obtained of step, the principle that Sliding mode variable structure control inverter state mutated site produces is: error Signal e=i_ref-i, when systematic error signal e e (n)=i occurs in the n-th switch periods_refDuring the situation of (n)-i (n) < 0, u_control(n)=-ε+k_p× e (n) < 0, u_control(n)<u_carrier(n), therefore dutycycle d_nTo sport 0, inductive current will be anxious Acute decline, causes e (n+1)=i occur n+1 switch periods_ref(n+1)-i (n+1) > 0, u_control(n)=-ε+k_p×e(n) > 0, u_carrierAnd u (n+1)_control(n+1) must there be two intersection points, the duty d of (n+1)th switch periods_n+1>0；Therefore at inductance Electric current positive half period descending branch, the dutycycle of pulse-width modulation PWM control signal occurs in that d_n<d_n+1The situation of non-monotonic decline, leads Cause system occurs in that the wild effect of state mutation；

Step 3, the determination of mutated site:

At each sinusoidal cycles N number of point of sampling, wherein N=f_s/f₁, f_sFor sample rate, f₁For i_refFrequency；Step 2 will be obtained The dutycycle arrived substitutes into, and selects from N₀Time (N₀For more than the arbitrarily selected value of pi/2) sampled point start obtaining current waveform descending branch Dutycycle d of M continuous two switch periods of switch periods_nAnd d_n+1Make difference again divided by the absolute value of both differences, calculate M number is added and obtains P_MCan be expressed as follows:

$P_M=\underset{n=N_0}{\overset{N_0+M-1}{\&Sigma;}}\frac{d_{n+1}-d_n}{|d_{n+1}-d_n|}---\left(5\right);$

If dutycycle is always maintained at monotone variation, P in M switch periods_MDuring=M, system is i.e. in steady-working state；If P_M+1< M+1, system is in fork labile state, and Continuous plus goes out the P of front M and M+1 switch periods_MAnd P_M+1Value, if P_M =M and P_M+1< M+1, it is determined that the state mutation cycle is N₀+ M switch periods；

Step 4, bifurcation graphs method for drafting:

The catastrophe point data obtained according to step 3 draw bifurcation graphs, and in the reasonable scope, taking fork parameter ε is arbitrary initial value Substitute in discrete iteration equation, work as P_MDuring=M, system is in steady-working state, and optional any sampled point is multiple power supply Bifurcation graphs is drawn in the sampling location in cycle；Work as P_M=M and P_M+1< M+1, then it represents that system occurs in that fork wild effect, passes through State mutation cycle criterion can determine whether that the state mutation cycle is N₀+ M, then with N₀+ M sampled point is consolidating of multiple power cycle Determine sampling location and draw bifurcation graphs.

A kind of novel bifurcation graphs method for drafting being applicable to Sliding mode variable structure control inverter the most according to claim 1, It is characterized in that, in described step one, owing to dutycycle has saturated characteristic, need to be to d_nCarry out amplitude limit:

$d_n=\left\{\begin{array}{cc}0& (d_n\&le;0)\\ d_n& (0<d_n<1)\\ 1& (d_n\&GreaterEqual;1)\end{array}\right.---\left(6\right).$

A kind of novel bifurcation graphs method for drafting being applicable to Sliding mode variable structure control inverter the most according to claim 1, It is characterized in that, described inverter is NGI-H6 system, wherein, D₁, D₂For high-performance diode, E is that solaode direct current is defeated Go out voltage, L₁、L₂, for load inductance, R₁、R₂For load resistance.