Transient Step Response Specification of Z-Source DC-DC Converter

Transcription

1 459 Transient Step Response Specification of Z-Source DC-DC Converter Shilpa P.Ashtankar 1 1 Department of Electrical Engg, KITS, Ramtek, RTM Nagpur university, Nagpur, India ABSTRACT Z-Source dc-dc converter is alternative power conversion topology that can buck/boost the input voltage using passive components. It allows shoot through state which is forbidden in traditional converter avoiding the risk of damaging switches in converter circuit to make circuit more reliable. A steady state dc value of capacitor voltage V Cz,output voltage V 0 & dc link voltage Vdc are calculated theoretically & results are verified by using simulation. Simulation results for open loop & close loop ZSC with PID controller are obtained for step change in input voltage, duty cycle & load resistance by using MATLAB/SIMULINK. The transient step responses are also obtained for step disturbance in input voltage & load. Keywords Buck/boost, dc link voltage, MATLAB/SIMULINK, steady state dc value of capacitor voltage, transient step responses, Z-source dc-dc converter(zsc),. I. INTRODUCTION In power electronics literature, the level and characteristics of source voltage have been changed by using various converter topologies. Each converter topology has its own barrier regarding different aspects like number of components used, stress on semiconductor switches, cost and converter efficiency. Today, efficient power conversion is more important because of alternative energy sources like photovoltaic system, fuel cell, solar energy, wind energy and ocean wave energy that require proper power conditioning to adapt to different loads. Also hybrid vehicles are also very promising new applications of power converters. The Z-source converter is a newly proposed power conversion concept that is very promising in the above mentioned areas of power conditioning especially in alternative energy sources,hybrid electric vehicles and distributed generation. Higher Efficiency, lower cost & more reliability are major objective for power electronics designers. New topologies in power conversion like Z- source converter (ZSC) are given in detail with ac small signal modeling & analysis in continuous conduction mode[1].the open loop duty factor to output voltage transfer function, Gvd is derived based on the detailed mathematical modeling of ZSC by using state space averaging method in continuous conduction mode []. Unique buck- boost capability of Z-Source Inverter allows a wider input voltage range & eliminates the usage of traditional converter [3].Maximum boost control method is presented to produce maximum voltage boost under given modulation index[4]. A novel bidirectional Z-source dc-dc converter buck-boost topology is used for electric vehicle application [5-6].The algorithm to control both dc boost and ac output voltage of Z-source inverter [7].. ZSC can be implemented as a 3-phase dc/ac converter known as Z-source inverter (ZSI).It can also be applied to ac/dc & ac/ac power conversion. ZSI topology is developed continuously & successfully utilized in various applications like motor drives, Adjustable speed drives, Hybrid Electric Vehicles & Photovoltaic applications [8-11]. Operating principle of Z-source dc-dc converter is explained []. In operating principle, two operating modes of ZSC Shoot through & Non-shoot through state is explained with mathematical equations. Further the steady state model of ZSC is obtained for continuous conduction mode to study the dynamics introduced by inductors & capacitors uniquely contained in the circuit. It also gives the design of close loop controller along with design component of ZSC. Detailed mathematical modeling along with transfer function of ZSC is given in reference []. This paper gives the transient step responses of ZSC obtained for step disturbance in input voltage & load. The paper is organized as follows. The review of Z-Source dc-dc converter is presented in section II. The mathematical analysis of steady state dc value of capacitor voltage V Cz,output voltage V 0, & dc link voltage Vdc are given in section III. Section IV gives the theoretical calculation of V Cz & Vdc is given along with its simulation similarly simulation results for open loop & close loop ZSC with PID controller are obtained by using MATLAB/SIMULINK. The transient responses are also obtained for step disturbance in input voltage Vs & load RL followed by summery of the work presented in last section V.

2 460 II. REVIEW OF Z-SOURCE DC-DC CONVERTER Fig.1: Open loop system configuration of zsc converter Z-source converter is new promising topology in power conversion. It consist of X shaped impedance which is composed of two split inductors & two capacitors to provide coupling between dc source & load. Unique buck/boost capability of ZSC allows a wider input voltage range & eliminates the usage of traditional converter [-3].Also the ZSC has the unique ability to allow dc link to be shorted which is called shoot through state. In ZSC only one switch MOSFET connected across dc link, hence when switch get turn on shoot through state takes place & when it is switched off non shoot through state takes place [1-3].Shoot through state improves the reliability of the circuit. ZSI at the non-shoot through mode and shoot through mode respectively. In non shoot through mode as shown in Fig. switch S is off state. In this mode, Z-source inductor L Z, transfer the stored energies on them to load also the input current is transferred to Z- source capacitor C Z and load. Inductor L o is energized during this mode. In this mode as diode is forward biased switch S 1 is closed. In shoot-through mode as shown in Fig. switch S is switched on. In this mode L z are energized by C Z. By applying Kirchhoff s voltage law to fig voltage across diode (switch S 1 ) comes out to be negative value. Diode becomes reversed biased and hence switch S 1 becomes open.the load is meanwhile fed by filter inductor L o and C o. The detailed mathematical modeling of ZSC is given in reference [].ZSC can be operated in buck/boost mode depending upon the operating region of duty cycle. When D < 0.5, converter operates in boost mode & when D > 0.5, it operates in buck-boost mode. V S D closed S 1 L Z1 L o V R L dc S V o C C o z1 open C z Fig. 3: boost and buck-boost nature of z-source converter V S D Open S 1 LZ1 C z1 C z L z L z L o S Closed Fig. : Equivalent circuit of zsc non-shoot through mode shoot through mode. Fig. 1 shows the simplified circuit of open loop Z- source dc-dc converter. The ZSC has two operating modes: Non shoot through mode and Shoot through mode [1]. Fig. & shows the equivalent circuit of C o V o R L III. STEADY STATE EQUATION OF CAPACITOR & DC LINK Assume the Z-source inductors (L Z1 & L Z) & capacitors (C Z1 & C Z) respectively. From the equivalent circuit, we have VLz1 VLz VLz, VCz1 VCz VCz (1) When the ZSC is in the non-shoot through state for a period T 1 from Fig. the inductor voltage and input voltage of the inverter can be expressed as VLz VCz, Vdc VCz VLz VCz Vs () When the ZSC is in the shoot through state for a period T o from Fig, the voltage Vdc becomes zero. The inductor voltage can be expressed as V (3) Lz V Cz

3 461 As the average of the inductor voltage over one switching period T becomes zero in steady state, the capacitor voltage can be derived as T1 D VCz Vo V T1 To D V s (4) S Where T T 1 T is the switching period & o D To / T is the shoot through time duty ratio. Above equation shows that steady state dc value of capacitor voltage V Cz is equal to output voltage V o & V s is the steady state value of the input voltage. The peak value (Vdc) of the capacitor voltage is dependent on shoot through time & can be stepped up by increasing the shoot- through time. The peak value of the pulsating dc link voltage (Vdc) is given as T 1 Vdc V cz Vs T1 To D (5) Fig. 5 : Simulation waveform of dc link voltage in steady state. The close loop simulation results are obtained by applying close loop PID controller as shown in fig below. REFERENCE + _ PID CONTROLLER Z-SOURCE DC-DC CONVERTER OUTPUT IV. SIMULATION RESULTS The simulation results are obtained for ZSC input voltage Vs=30V, shoot through duty cycle=0., R L =8Ω, Z source input inductor & input capacitor are Lz 1 =Lz =300µH, Cz 1 =Cz =360µF respectively. ZSC output inductor & output capacitor values are taken as Lo=100µH & Co=500µF respectively. The Z-source circuit parameter is considered as ideal circuit parameter and simulation is performed by using MATLAB/SIMULINK. From above design analysis, the output voltage Vo are obtained as 40V.Similarly capacitor voltage VCz, are obtained theoretically as Vo=Vcz=40V which is verified by simulation result. Fig. 6: Block diagram of the z-source dc-dc converter with close loop PID controller. ZSC open loop & close loop simulation waveforms is obtained for output voltage & load current for step disturbance in input voltage, load and duty cycle as follows. Transient responses are also obtained for step disturbance in input voltage & load. Fig. 4: Simulation waveform of capacitor voltage in steady state. The simulation of peak V dc based on the ideal circuit agrees well with the theoretical results (1/(1-D) V s =50 V,where D=0. and V s =30V. ( b) Fig. 7 : Open loop simulation waveform obtained from z-source dc-dc converter model Output voltage load current for 0% step change in input voltage.

4 46 Fig. 8: open loop simulation waveform obtained from z-source dc-dc converter model Output voltage load current for step change in duty cycle from 0. to 0.3. Table I Obtained Transient Parameter from open loop ZSC Step Responses T.R. S.R. Rise time,tr Settling time,ts time,tp overshoot (%) Fig Fig Fig Fig Fig Fig Transient responses are obtained from open loop simulation waveform for step changes in input voltage, duty cycle & load are given in table I. Fig. 9: Open loop simulation waveform obtained from z-source dc-dc converter model output voltage load current for step change in RL from 10Ω to 5 Ω. Figure 10: close loop simulation waveform obtained for output voltage load current for change in input voltage from 30V to 36V.

5 463 VI. REFERENCES Figure 11: close loop simulation waveform obtained for output voltage load current for step change in load from 10 ohm to 5 ohm. Table II Obtained Transient Parameter from close loop ZSC Step Responses T.R. S.R. Rise time,tr Settlin g time,ts time,tp overshoot (%) Fig Fig Fig Fig Transient responses are obtained from close loop simulation waveform for step changes in input voltage, duty cycle & load are given in table II. V. CONCLUSION This paper shows that ZSC can be operated in buck/boost mode depending upon the operating region of duty cycle. The theoretical calculation results of steady state dc value of capacitor voltage V Cz,output voltage V 0, & dc link voltage Vdc are well agree with its simulation results. In this paper transient specification obtained from close loop ZSC step response shown in table II are compared with open loop transient responses given in table I for change in input voltage & change in load resistance which is obtained from simulation results. The comparison shows that with close loop PID controller rise time is reduced by ( ) msec, settling time reduced by (0.3-1) msec, peak time reduced by (5-11 msec) & peak overshoot is reduced by (1%-34.5%). By using close loop PID controller, desired transient specifications. [1] J.liu,J.Hu and L. Xu, Dynamic Modeling & Analysis of Z-Source converter Derivation of AC Small Signal Model and Design Oriented Analysis, IEEE Transaction on Power Electronics,vol., no.5, sept.007,pp [] Shilpa B.Sarode & Dr.S.G.Kadwane, Dynamic Modeling & Controller Design for Z-source DC-DC converter, Internation journal of Scientific Engineering, and Applied sciences,15-16march 013. [3] F.Z.Peng, Z-source inverter, IEEE Trans. Ind.Appl., vol.39, No., pp , Mar./Apr.003. [4] F.Z.Peng, M.Shen, and Z.Qian, Maximum boost control of the Z-source inverter, IEEE Trans. Power Electron., vol.0, no.4, pp , Jul.005. [5] Y.Xie,Z.Qian,X.Ding,F.Peng, A Novel Buck-Boost Z-Source Rectifier,37 th IEEE Power Electronics Specialists Conference,PESC, Jeju,Korea,pp. 18-, June 006. [6 ] Xupeng Fang & Xingquan Ji, Bidirectional Power Flow Z-source DC-DC Converter Proc. On IEEE vehicle power & Propulsion Conference (VPPC),September 3-5, 008,Harbin,China. [7] Q.Tran, T.Chun, J.Ahn, and H.Lee, Algorithms for controlling both the DC boost and AC output voltage of Z-sourceinverter, IEEE Trans. Ind. Electron., vol.54, no.5, pp ,Oct.007. [8] Fang Zheng Peng, Z-Source Inverter for Motor Drives, IEEE Transactions on Power Electronics, Vol.0, No.4, pp ,july 005. [9] Fang Z. Peng, Xiaoming Yuan, Z-Source inverter for adjustable Speed Drives,IEEE Power Electronics Letters,Vol.1,No.,pp.33-35,June 003. [10] Fang Zheng Peng, Miaosen Shen,and Kent Holland, Application of Z-Source Inverter for Traction Drive of Fuel Cell-Battery Hybrid Electric vehicles, IEEE transaction on Power Electronics,Vol., No.3, pp , may 007. [11] Dong Cao,Shuai Jiang,Xianhao Yu,and Fang Zheng Peng, Low- Cost Semi ZSource Inverter for Single Phase Photovoltaic systems, IEEE Transactions on Power Electronics, Vol.6,No.1, pp , December. Book: [1] R.W.Ericson, D.Maksimovic, Fundamentals of Power Electronics, Norwell,MA:Kluwer, nd Edition, 001.