# Mitigation of Complex Non-Linear Dynamic Effects in Multiple Output Cascaded DC-DC Converters Major Electrical Projects

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.

FPL

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 fixed power load (FPL) under reasonable assumptions such as fixed frequency and input voltage.

MATLAB

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

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.

CURRENT

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.

CONVERTER

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.

REFERENCES:

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