胡乃紅，周宇飛，陳信懷

(1.安徽水利水電職業(yè)技術(shù)學(xué)院，安徽合肥231603；2.安徽大學(xué)電子科學(xué)與技術(shù)學(xué)院，安徽合肥230039；3.杭州利爾達(dá)科技集團(tuán)有限公司，浙江杭州311121)

多級(jí)并聯(lián)Boost變換器中的快標(biāo)分叉控制研究

胡乃紅1，周宇飛2，陳信懷3

(1.安徽水利水電職業(yè)技術(shù)學(xué)院，安徽合肥231603；2.安徽大學(xué)電子科學(xué)與技術(shù)學(xué)院，安徽合肥230039；3.杭州利爾達(dá)科技集團(tuán)有限公司，浙江杭州311121)

峰值電流控制模式多級(jí)并聯(lián)Boost變換器是一種時(shí)變參數(shù)非線性系統(tǒng)，極易產(chǎn)生時(shí)域上的快標(biāo)不穩(wěn)定現(xiàn)象。本文基于非線性系統(tǒng)的分叉理論，采用斜坡補(bǔ)償法對(duì)其進(jìn)行了分叉控制，給出了斜坡信號(hào)補(bǔ)償幅度的理論要求，并分析了不同參數(shù)對(duì)補(bǔ)償幅度的影響。數(shù)值仿真與理論計(jì)算結(jié)果一致表明分叉控制的有效性。

多級(jí)并聯(lián)Boost變換器；峰值電流模式控制；斜坡補(bǔ)償；快標(biāo)分叉；分叉控制

Modern power technology is a kind of power transform technique,and is extensively used in practice.Its core part is DC converter[1-3].In recent years, strong nonlinearity had been found in DC converter, such as attractor coexistence,the period-doubling bifurcation,border collision bifurcation and chaos[4-8]. Peak current controlled Boost converter is widely used in industry,and its nonlinear phenomenon is one of the early research object.A single Boost converter technology is very mature,and it has some restrictions.In order to reduce the instantaneous high voltage or current of the semiconductor switch,afew Boost converter modules can be used in parallel.But it will appear from bifurcate to chaos due to the variation of the system parameters,and the voltage and current ripple will increase,and working performance of the converter will be worsened[9-10]. So it is important to look for an effective way to restrain the chaotic behavior.

Slope compensation is a simple and effective method to control chaos.Experience plays the leading role in the actual engineering design,which lacks necessary design criteria.Therefore,this paper studies the slope compensation of the parallel Boost converters under peak current controlled mode, which is based on the bifurcation theory of nonlinear system.This method can control the bifurcate and chaos and make output current ripple be improved obviously.It provides some theoretical guidance for the stable operation of the circuit.

1 Multi-parallelBoostconvertorunderpeakcurrentcontrolledmode

The basic circuit topology of the multi-parallel Boost Convertors is shown in Figure 1(a).The circuit closed loop control system includes two parts,i. e.,external voltage loop and internal current loop. The voltage loop provides Ireffor the current loop. The voltage vois more stable after PI adjustment in the external voltage loop and can be seen as a constant.Duty cycle D is big in the convertor,and can bring about unstable fast-scale phenomenon.For eliminating the instability,the circuit provides compensation current icwhich is a sawtooth wave signal.The reference currentis compared to the inductance current iL,which can drive and trigger the switch tube G through the RS flip-flops and PWM circuit.

In multi-parallel Boost converters,each of them contains an inductor L,a capacitance C,a switch tube G,a diode Gdand a load resistance R. According to the different conditions of switch tube G,there are differential equations[11]:

where x is the state vector,x=[iL1,vo,iL2, vo,……iLm,vo]T,the coefficient matrixes are:

Figure 1Multi-parallel Boost convertor under peak current controlled mode

Based on the equations(1)and(2),with the circuit shown in Figure 1(a),simulate the system with accurte Simulink models,the parameters are:input voltage E=5 V,inductance L=1 mH,capacitance C=20 μF,load R=20Ω,switch cycle Ts=0.1 ms, reference voltageVref=15 V,P for proportion coefficient,Tifor inte,we can see that eagral constants.Inductance current of each convertor and its sampling waveform is shown in Figure 1(b)and(c), which indicate that the converter operates chaotically and the switch tube is working in irregular state. If the condition is serious,the converter will stop working.

2 Stabilityanalysis

In the past 20 years,with the deep study of the nonlinear phenomena in the DC-DC converter,it is found that slope compensation can inhibite the fastscale instability well and it is a simple and effective bifurcate control method[12-13].We construct discrete iterative map of the multi-parallel Boost convertor, with the bifurcation theory of nonlinear systems, can deduce the theoretical basis of slope compensation method.

Figure 2Operating waveform with slope compensation

The circuit operating waveform is shown in Figure 2.In one switching cycle,the arriving of clock pulse drives switch tude on,the inductor current increases;when the inductor current reaches the reference current compensationref,the inductor current begins to decline.So the discrete iteration mapping function of inductor current is:

The perturbation equations for above is:

Decompose the equations above to steady component and small perturbation component,and only consider the steady component,we will get

According to the equations above,we can get perturbation equation of the inductance current:

The characteristic root λ of the equation is

When λ is located in the interval(-1,1),the cycle of the converter is regular 1;when λ is out of the interval and smaller than-1,the converter produces doubled-cycle bifurcate,the cycle becomes 2.So λ＝-1 is the critical point,from this we can get the slope expression of the compensation signal is:

From(9),the critical magnitude requirement for slope compensation is:

The above equation is the design criteria for slope compensation.

3 Factorsofthecompensation

From the previous analysis,we can see that Vref, E,Ts,L are the parameters which affect the slope compensation magnitude.This paper gives their effect on the circuit after lots of simulation and theo-retical calculation as shown in Figure 3,from which we can know that the critical magnitude of slope compensation increases when Vrefand Tsincrease, while it reduces when E and L increase.The theoretical results and simulation results are completely con sistent and they can provide good guidance for stability design of converter systems.

Figure 3Influences of circuit parameters onAramp

4 Controlperformanceanalysis

Figure 4 shows the inductance current waveforms before and after control,from which we can see that the ripple is different in bifurcate state and in bifurcation-controlled state.The ripple can reach 1.12 A in bifurcate state,but only 0.34 A in bifurcation-controlled state.It is because the bifurcation makes switch irregular and ripple increases.The excessive ripple increases the current stress of the switching devices and effects the operating of the system.After the bifurcation is controlled,the system works steadily in period 1 and far from the bifurcation and chaos.

Figure 4Inductance current waveforms before and after control

Slope compensation is a simple and effective method to control chaos.Experience plays the leading role in the actual engineering design and lacks necessary design criteria.Therefore,this paper invetigates the slope compensation of multi-parallel Boost convertors under peak current controlled mode based on the bifurcate theory of nonlinear systems,and gives precise magnitude requirements of the slope signal compensation.Lots of Accurate simulation results verify the validity of the theoretical analysis.This method is also applicable to other converter stability analysis.

Reference

[1]Aroudi A E,Leyvar R.Quasi-periodic route to chaos in a PWM voltage-controlled DC-DC boost converter [J].IEEE Trans.Circuits and Systems-I,2001,48(8): 967-978.

[2]Tse C K,Bernardo M D.Complex behavior in switching power converter[J].Proceedings of IEEE,2002,90 (5):768-781.

[3]Deane J B,Hamill D C.Instability,subharmonics,and chaos in power electronic systems[J].IEEE Trans. Power Electron,1990,5(3):260-268.

[4]Baillieul J,Brockett R W,Washburn R B.Chaotic motion in nonlinear feedback systems[J].IEEE Trans.Circuit System-I,1980,27(11):990-997.

[5]Hamill D C,Jefferies D J.Subharmonics and chaos in controlled switched-mode power converter[J].IEEE Trans.Circuits Systems-I,1988,35(8):1059-1061.

[6]Ma X K,Li M,Dai D,et al.Reviews of research on complex behavior of power electronic circuits and system[J].Transactions of China Electrotechnical Society, 2006,21(12):1-11.

[7]Zhou Y F,Qiu S S,Chen J N.Nonlinear phenomena in hysteretic current-controlled Cuk converters[J].Proceedings of the CSEE,2004,25(21):30-33.

[8]Zhou Y F,Chen J N,Xu C.Simulation and experimental studies on coexising attractors in DC-DC switching converter[J].Proceedings of the CSEE,2004,25(21): 30-33.

[9]Lu W G,Zhou L W,Luo Q M,et al.Time-delayed feedback control of chaos in BOOST converter and its optimization[J].Acta Physica Sinica,2007,56(11): 6275-6281.

[10]Zhou Y F,Chen J N,Tse C K,et al.Application of resonant parametric perturbation to the chaos control in Boost converter and its optimization[J].Acta Physica Sinica,2004,53(11):3676-3683.

[11]Chen M L,Ma W M.Bifurcation and chaos in mutiparallel-connected current mode controlled Boost DCDC converters[J].Proceedings of the CSEE,2005,25 (6):67-70.

[12]Zhou Y F,Jiang X E,Chen J N.Analysis of complex intermittency in Boost converter from a bifurcation control viewpoint[J].Science in China Series F:Information Sciences,2008,51(12):2135-2149.

[13]Tse C K and Lai Y M.Controlling Bifurcation in Power Electronics:a Conventional Practice Re-visited[J]. LatinAmericanApplied Research,1994,31(3):51-52．

Study of fast-scale bifurcation control in multi-connected Boost converter

HU Nai-hong1,ZHOU Yu-fei2,CHEN Xin-huai3
(1.Anhui Water Conservancy Technical College,Hefei Anhui231603,China;2.School of Electronic Science and Technology,Anhui University,Hefei Anhui230039,China;3.Hangzhou Lierda Science&Technology Group Co.,Ltd,Hangzhou Zhejiang311121,China)

Multi-connected Boost Converter,under peak current controlled mode,is a time-varying parameter system, which is very easy to generate fast-scale instability phenomena.Based on the bifurcation theory of nonlinear system,this paper uses the slope compensation method to control bifurcation,presents the theoretical amplitude requirement of the slope signal, and analyses the influence of different parameters on the amplitude.The numerical simulation results and the theoretical calculation results are consistent to verify the effectiveness of the proposed bifurcation control method.

multi-connected Boost converter;peak current control mode;slope compensation;fast-scale bifurcation;bifurcation control

TM17

A

1004-4329（2017）01-033-05

10.14096/j.cnki.cn34-1069/n/1004-4329（2017）01-033-05

2016-08-10

國(guó)家自然科學(xué)基金項(xiàng)目（61071023）；安徽省教育廳自然科學(xué)研究重點(diǎn)項(xiàng)目（KJ2015A416）資助。

胡乃紅（1970-），男，博士，講師，研究方向：非線性電路與系統(tǒng)。