paper title - IRD India

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International Journal of Recent Advances in Engineering & Technology (IJRAET)

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ISSN (Online): 2347 - 2812, Volume-3, Issue -6, 2015 38

Study of Chaos in Voltage Controlled DC-DC Buck Converter

1Aswini C V, ²K I Ramachandran, ³T B Isha

Email: ¹[email protected], ²[email protected], ³[email protected] Abstract—Power electronics as an application oriented

discipline, has been employed in industrial, commercial, residential and aerospace environments. Since power electronic circuits containing pulse width modulation, are nonlinear systems, it exhibits complex behaviors such as bifurcation and chaos. In this paper, a simulation study of chaos in voltage controlled buck converter is done by varying the load resistances.

Index Terms—Chaos, Bifurcation, DC-DC buck converter.

I. INTRODUCTION

A DC-DC buck converter consists of controlled switch and uncontrolled switch which are turned on and off in a complementary and cyclic manner. The toggling of circuit topologies introduces non linearity in the operation of DC-DC converter. Being non-linear it is prone to a variety of complex behaviors like bifurcation, sudden change of operating regime, chaotic operation and occasional instability.

Bifurcation means splitting of system behavior into two qualitatively different behaviors corresponding to the parameter variations below and above a threshold value.

The main types of bifurcation are saddle node bifurcation, transcritical bifurcation, period doubling bifurcation, super critical bifurcation etc. It has been observed that period doubling bifurcation is common in voltage controlled buck and boost converters .Series of bifurcation leads to chaos .Period doubling may persist if the parameter is varied in same direction, which leads to chaos. Chaos can be regarded as a qualitative behavior of non-linear system. Chaotic systems are aperiodic and random in nature. Chaos is deterministic though it seems random in nature. Sensitive dependence on the initial conditions and parameter variations are the key properties of a chaotic system.

A DC-DC buck converter is mainly used for conversion of voltage from higher to lower voltage levels. This step down property of the converter is extensively employed in many industrial and electronic circuit applications such as spacecraft , mobile telephone , solar array etc.

These applications demands the efficient working of the power converter system. So it should be designed in such way so that it results in satisfactory operation under all

conditions. It requires in depth analysis of the operation of power converter system.

The main objective of this paper is to discuss some basic results regarding the qualitative study of dynamic behavior of power converters. Section II of this paper discusses the basic concepts about voltage controlled buck converter. Section III presents the simulation results of closed loop buck converter in Or Cad software.

II. THE BUCK CONVERTER

A buck converter is used for stepping down higher dc voltages to lower dc voltage levels as shown in Fig.1. It consists of an uncontrolled switch (diode), a controlled switch (MOSFET) , an inductor L , a load resistance R and a capacitor. Switching of MOSFET is controlled through a feedback loop inorder to get a constant output voltage. The output of the buck converter is compared with the desired voltage value to obtain the error voltage . This error voltage is compared with a saw tooth wave of frequency f. When the error voltage is greater than saw tooth wave the switch is turned on. Switch will remain turned off when the error voltage is less than the saw tooth wave.

When the switch is turned on, the diode becomes reverse biased and the inductor current increases. When the swith is open diode becomes forward biased and the inductor current decreases. The energy stored in the inductor is transferred to the capacitor. If the inductor current falls to zero or negative value during turn off period, then the mode of operation is termed as discontinuous conduction mode. In case of continuous conduction mode the inductor current does not fall to zero , and the converter toggles between on and off topologies.

Fig.1. Circuit diagram of buck converter

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Fig. 2. The complete closed loop simulation diagram of buck converter

III. CIRCUIT REALISATION OF BUCK CONVERTER IN ORCAD SOFTWARE

An OrCad simulation study is carried out in order to analyse the chaotic phenomena of buck converter. The circuit diagram of closed loop buck converter is shown in Fig.2. The control circuit is implemented using analog op amps .

The power circuit consists of n channel MOSFET IRF 530 and a high switching frequency diode MUR 160. A DC voltage of 10V is given as input. The system is implemented in such a way to get a constant output voltage of 5V.

The control circuit consists of one error amplifier , saw tooth generator and a comparator . The output voltage is compared with the reference voltage using error amplifier TL082. The output from error amplifier is compared with saw tooth wave of time period T , using comparator LM311 and the switching pulses are obtained.The pulses are fed to the switch through a driver circuit.

The plot between current through inductor and voltage across capacitor is observed by varying the load resistance values.

IV. CHAOTIC PHENOMENA OBSERVED IN SIMULATION

Chaotic study in the circuit is carried by varying the parameters in the closed loop buck converter. There are mainly seven parameters in the system where we can introduce changes to analyze the chaotic behavior : input voltage, load resistance, reference voltage , inductance, capacitance , gain of error amplifier and the time period . Since time period , inductance, capacitance and error amplifier gain are the designed parameters, the system is analysed by varying the load resistance.

Fig. 3 shows current through inductor and voltage across capacitor versus time plot for a load resistance , equal to 10Ω. The phase plot corresponding to the same load resistance value is shown in Fig.4. From Fig.3 , it is clear that all waveform repeat at the same rate as switching frequency . This kind of operation is termed as period one operation.

Fig.5 shows inductor current versus time plot of buck converter operating with load resistance equal to 20Ω.

Capacitor voltage versus time plot corresponding to the same load resistance is shown in Fig.6. Fig.7. shows the phase plot between inductor current and capacitor voltage. It is clear that the system exhibits a period two operation for load resistance equal to 20Ω.

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Fig.3. The fundamental waveforms of inductor current and capacitor voltage corresponding to load resistance

R=10Ω

Fig.4. Phase plot of the buck converter corresponding to load resistance R=10 Ω

Fig.5. Inductor current versus time plot for the buck converter with loa resistance R=20Ω

Fig.5 shows inductor current versus time plot of buck converter operating with load resistance equal to 20Ω.

Capacitor voltage versus time plot corresponding to the same load resistance is shown in Fig.6. Fig.7. shows the phase plot between inductor current and capacitor voltage. It is clear that the system exhibits a period two operation for load resistance equql to 20Ω.

The inductor current versus time plot of buck converter with load resistance equal to 50Ω is shown in Fig.8.Fig.

9 shows the capacitor voltage versus time plot corresponding to the same load resistance. The phase plot between inductor current and capacitor voltage is shown

in Fig. 10. From the Fig. 8,9 ,10 it is clear that the system becomes chaotic for a load resistance equal to 50Ω.

From the simulation study , it is inferred that voltage controlled buck converter exibhits period one operation for a load resistance equal to 10Ω.The mode of operation changes to period two for an increase of resistance to 20 Ω. When the resistance value is further increased the system becomes chaotic.

Fig.6. Capacitor voltage versus time plot of buck converter with load resistance R=20Ω

Fig.7. Phase plot of buck converter with load resistance R=20Ω

Fig.8. Inductor current versus time plot of buck converter with load resistance R=50Ω

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Fig.9. Capacitor voltage versus time plot of buck converter with load resistance R=50Ω

Fig.10. Phase plot of buck converter with load resistance R=50Ω

V. CONCLUSION

The presence of switching elements makes power electronic circuits nonlinear. Being nonlinear they are potentially chaotic. Since power electronic circuits has widely employed in industrial, commercial and aerospace environments, it is necessary to have a

knowledge about the behavior of the system by varying the parameters. This paper analyses the chaotic behavior of the voltage controlled buck converter system by varying the load resistance. It is observed that the system becomes chaotic with increasing load resistance value.

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