Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters

Viktor Avrutin, Zhanybai T. Zhusubaliyev, Erik Mosekilde

Research output: Contribution to journalJournal articleResearchpeer-review

1 Downloads (Pure)

Abstract

Power electronic DC/AC converters (inverters) play an important role in modern power engineering. These systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies. As a consequence, inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation.
Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
Volume345
Pages (from-to)27-39
Number of pages13
ISSN0167-2789
DOIs
Publication statusPublished - 2017

Keywords

  • Power electronic inverter
  • Piecewise-smooth map
  • Local bifurcations
  • Border-collision bifurcations

Cite this

Avrutin, Viktor ; Zhusubaliyev, Zhanybai T. ; Mosekilde, Erik. / Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters. In: Physica D: Nonlinear Phenomena. 2017 ; Vol. 345. pp. 27-39.
@article{6b282e87bbcb457ab02fac1a9e9afd8d,
title = "Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters",
abstract = "Power electronic DC/AC converters (inverters) play an important role in modern power engineering. These systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies. As a consequence, inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation.",
keywords = "Power electronic inverter, Piecewise-smooth map, Local bifurcations, Border-collision bifurcations",
author = "Viktor Avrutin and Zhusubaliyev, {Zhanybai T.} and Erik Mosekilde",
year = "2017",
doi = "10.1016/j.physd.2016.12.008",
language = "English",
volume = "345",
pages = "27--39",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",

}

Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters. / Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik.

In: Physica D: Nonlinear Phenomena, Vol. 345, 2017, p. 27-39.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters

AU - Avrutin, Viktor

AU - Zhusubaliyev, Zhanybai T.

AU - Mosekilde, Erik

PY - 2017

Y1 - 2017

N2 - Power electronic DC/AC converters (inverters) play an important role in modern power engineering. These systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies. As a consequence, inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation.

AB - Power electronic DC/AC converters (inverters) play an important role in modern power engineering. These systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies. As a consequence, inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation.

KW - Power electronic inverter

KW - Piecewise-smooth map

KW - Local bifurcations

KW - Border-collision bifurcations

U2 - 10.1016/j.physd.2016.12.008

DO - 10.1016/j.physd.2016.12.008

M3 - Journal article

VL - 345

SP - 27

EP - 39

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -