Title page for ETD etd-08172001-124400

Type of Document Dissertation
Author Mazumder, Sudip K
Author's Email Address sumazumd@vt.edu
URN etd-08172001-124400
Title Nonlinear Analysis and Control of Standalone, Parallel DC-DC, and Parallel Multi-Phase PWM Converters
Degree PhD
Department Electrical and Computer Engineering
Advisory Committee
Advisor Name Title
Boroyevich, Dushan Committee Co-Chair
Nayfeh, Ali H. Committee Co-Chair
Baumann, William T. Committee Member
Lai, Jih-Sheng Jason Committee Member
VanLandingham, Hugo L. Committee Member
  • Lyapunov's Method
  • Sliding Surface
  • Bifurcation Theory
  • Modeling
  • Nonlinear Control
  • Parallel Converters
  • Multi-Phase Converters
  • Differential Inclusion
  • DC-DC Converters
  • Stability Analysis
  • Power Electronics
  • Floquet Theory
Date of Defense 2001-07-30
Availability unrestricted
Applications of distributed-power systems are on the rise. They are

already used in telecommunication power supplies, aircraft and shipboard

power-distribution systems, motor drives, plasma applications, and

they are being considered for numerous other applications. The successful

operation of these multi-converter systems relies heavily on a stable

design. Conventional analyses of power converters are based

on averaged models, which ignore the fast-scale instability and analyze

the stability on a reduced-order manifold. As such, validity of the averaged

models varies with the switching frequency even for the same topological structure.

The prevalent procedure for analyzing the stability of switching converters

is based on linearized smooth averaged (small-signal) models. Yet there are

systems (in active use) that yield a non-smooth averaged model. Even for

systems for which smooth averaged models are realizable, small-signal analyses

of the nominal solution/orbit do not provide anything

about three important characteristics: region of attraction of the nominal

solution, dependence of the converter dynamics on the initial conditions of the

states, and the post-instability dynamics. As such, converters designed based on

small-signal analyses may be conservative. In addition, linear controllers

based on such analysis may not be robust and optimal. Clearly, there is a need to

analyze the stability of power converters from a different perspective and

design nonlinear controllers for such hybrid systems.

In this Dissertation, using bifurcation analysis and Lyapunov's method, we

analyze the stability and dynamics of some of the building blocks of

distributed-power systems, namely standalone, integrated, and parallel

converters. Using analytical and experimental results, we show some of

the differences between the conventional and new approaches for stability

analyses of switching converters and demonstrate the shortcomings of some of

the existing results. Furthermore, using nonlinear analyses we attempt to answer

three fundamental questions: when does an instability occur, what is the mechanism

of the instability, and what happens after the instability?

Subsequently, we develop nonlinear controllers to stabilize parallel

dc-dc and parallel multi-phase converters. The proposed controllers

for parallel dc-dc converters combine the concepts of multiple-sliding-surface

and integral-variable-structure control. They are easy to design, robust, and have

good transient and steady-state performances. Furthermore, they achieve a constant

switching frequency within the boundary layer and hence can be operated

in interleaving or synchronicity modes. The controllers developed for

parallel multi-phase converters retain many of the above features. In addition,

they do not require any communication between the modules; as such, they

have high redundancy. One of these control schemes combines space-vector modulation

and variable-structure control. It achieves constant switching frequency within

the boundary layer and a good compromise between the transient and steady-state


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