Title page for ETD etd-35541228119663620

Type of Document Dissertation
Author Harb, Ahmad M.
URN etd-35541228119663620
Title Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems
Degree PhD
Department Electrical and Computer Engineering
Advisory Committee
Advisor Name Title
Mook, Dean T.
Phadke, Arun G.
VanLandingham, Hugh F.
Nayfeh, Ali H. Committee Chair
Mili, Lamine M. Committee Co-Chair
  • subsynchronous resonance
  • bifurcation theory
  • power systems
  • methods of multiple scales
Date of Defense 1996-12-16
Availability unrestricted
A bifurcation analysis is used to investigate the

complex dynamics of two heavily loaded

single-machine-infinite-busbar power systems

modeling the characteristics of the

BOARDMAN generator with respect to the

rest of the North-Western American Power

System and the CHOLLA$#$ generator with

respect to the SOWARO station. In the

BOARDMAN system, we show that there are

three Hopf bifurcations at practical

compensation values, while in the

CHOLLA$#4$ system, we show that there is

only one Hopf bifurcation. The results show that

asthe compensation level increases, the

operating condition loses stability with a

complex conjugate pair of eigenvalues of the

Jacobian matrix crossing transversely from the

left- to the right-half of the complex plane,

signifying a Hopf bifurcation. As a result, the

power system oscillates subsynchronously with

a small limit-cycle attractor. As the

compensation level increases, the limit cycle

grows and then loses stability via a secondary

Hopf bifurcation, resulting in the creation of a

two-period quasiperiodic subsynchronous

oscillation, a two-torus attractor. On further

increases of the compensation level, the

quasiperiodic attractor collides with its basin

boundary, resulting in the destruction of the

attractor and its basin boundary in a bluesky

catastrophe. Consequently, there are no

bounded motions. When a damper winding is

placed either along the q-axis, or d-axis, or both

axes of the BOARDMAN system and the

machine saturation is considered in the

CHOLLA$#4$ system, the study shows

that,there is only one Hopf bifurcation and it

occurs at a much lower level of compensation,

indicating that the damper windings and the

machine saturation destabilize the system by

inducing subsynchronous resonance. Finally, we

investigate the effect of linear and nonlinear

controllers on mitigating subsynchronous

resonance in the CHOLLA$#4$ system . The

study shows that the linear controller increases

the compensation level at which subsynchronous

resonance occurs and the nonlinear controller

does not affect the location and type of the

Hopf bifurcation, but it reduces the amplitude of

the limit cycle born as a result of the Hopf


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