ABSTRACT:
In the modern world of technology, the cascaded DC-DC converters with multiple output configurations are contributing a dominant part in the DC distribution systems and DC micro-grids. An individual DC-DC converter of any configuration exhibits complex non-linear dynamic behavior resulting in instability. This paper presents a cascaded system with one source boost converter and three load converters including buck, Cuk, and Single-Ended Primary Inductance Converter (SEPIC) that are analyzed for the complex non-linear bifurcation phenomena. An outer voltage feedback loop along with an inner current feedback loop control strategy is used for all the sub-converters in the cascaded system. To explain the complex non-linear dynamic behavior, a discrete mapping model is developed for the proposed cascaded system and the Jacobian matrix's eigenvalues are evaluated. For the simplification of the analysis, every load converter is regarded as a _xed power load (FPL) under reasonable assumptions such as _xed frequency and input voltage. The eigenvalues of period-1 and period-2 reveal that the source boost converter undergoes period-2 orbit and chaos whereas all the load converters operate in a stable period-1 orbit. The proposed configuration eliminates the period-2 and chaotic behavior from all the load converters and is also validated using simulation in MATLAB/Simulink and experimental results.
KEYWORDS:
1. Bifurcation
2. Chaos
3. DC-DC power converters
4. Non-linear dynamical systems
SOFTWARE: MATLAB/SIMULINK
BLOCK DIAGRAM:
Figure 1. Block Diagram Of The
Proposed Cascaded System.
EXPECTED SIMULATION RESULTS:
Figure 2. Inductor Current Ripple And Output
Voltage Ripple Waveforms Of Stable Period-1 Operation For
A)
Boost Converter At Vs D 35 V B) Buck Converter At Vs D 50 V C) Cuk Converter At
Vs D 50 V D)Sepic
Converter
At Vs D 50 V
Figure 3. Inductor Current Ripple And Output
Voltage Ripple Waveforms Of Period-2 Operation For A) Boost Converter At Vs D 25
V B) Buck Converter At Vs D 36 V C) Cuk Converter At Vs D 24 V D) Sepic
Converter At Vs D 40 V.
Figure 4. Inductor Current Waveforms Of All The
Converters Of The Cascaded System At Vs D 35 V.
Figure 5. Inductor Current Waveforms Of All The
Converters Of The Cascaded System At Vs D 25 V.
Figure 6. Inductor Current Waveform Of Source
Boost Converter For Step Change In The Input Voltage Verifying Non-Linear
Incident Effects.
CONCLUSION:
This
paper presents a configuration of the cascaded multiple output DC-DC converters
to eliminate complex non-linear dynamic behavior and improve the stability when
subjected to varying source voltage. The proposed cascaded DC-DC converter
system consists of one source boost converter, one load Buck converter, one
load Cuk converter, and a SEPIC converter. All the converters in the proposed
system are engaged with a current-mode controller with a compensation network
technique in which an outer voltage feedback loop and an inner inductor current
feedback loop are used along with an offset divided voltage protection circuit
and an RS-latch. The simulation and experimental results reveal that the source
boost converter undergoes period-2 orbit and ultimately chaos when the input
voltage of the source boost converter is decreased. However, it is verified
that all the converters that are acting as a load in the proposed system continue
to operate in the stable period-1 orbit and the input voltage of the source
boost converter does not affect their stability. The discrete mapping model is
developed by considering all the load converters as FPLs because of their stable
behavior which also generalizes it for other types of converters. The Jacobian
matrix is developed using the data of the discrete mapping model and the
eigenvalues are obtained which are close to 1. So, by decreasing the input source
voltage, the eigenvalues move out of the unit circle which results in period-2
behavior of the system that severely affects the stability of the whole
cascaded converter system. The proposed structure makes load converters in the
system insensitive towards input voltage variation which has been demonstrated
analytically and using experimental results.
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