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39 results on '"Harb, Ahmad M."'

27. Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems

Author

Harb, Ahmad M., Electrical and Computer Engineering, Nayfeh, Ali H., VanLandingham, Hugh F., Phadke, Arun G., Mook, Dean T., and Mili, Lamine M.

Subjects
LD5655.V856 1996.H373, power systems, methods of multiple scales, bifurcation theory, subsynchronous resonance
Abstract

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 as the 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 bifurcation. Ph. D.

Published
1996

37. Galerkin-Based New Method for Analyzing Bifurcations in a Single Machine Infinite Busbar Power System.

Author

Harb, Ahmad M. and Harb, Bassam A.

Subjects
*GALERKIN methods, *BIFURCATION theory, *BUS conductors (Electricity), *ELECTRIC power, *ALGORITHMS, *NUMERICAL analysis
Abstract

In this paper, a Galerkin-based method is applied to a single machine infinite busbar (SMIB) power system. The method computes the separatrix cycle and the exact values for the input mechanical power at which a limit cycle bifurcates from the separatrix cycle. The first part of the algorithm approximates the limit cycle by a truncated Fourier series which employs N harmonics, where N is a user-specified. The second part of the algorithm finds the exact value of the input mechanical power by utilizing the fact that the separatrix cycle must approach the saddle point. The algorithm is applied to simple example with N = 3. Data is given which relates the damping coefficient to the input mechanical power. [ABSTRACT FROM AUTHOR]

Published
2004
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38. Nonlinear control of permanent magnet stepper motors

Author

Harb, Ahmad M. and Zaher, Ashraf A.

Subjects
*STEPPING motors, *BIFURCATION theory, *NUMERICAL solutions to nonlinear differential equations, *SERVOMECHANISMS, *ELECTRIC motors, *MATHEMATICAL models
Abstract

The nonlinear dynamics of a permanent magnet stepper motor is studied by means of modern nonlinear theories such as bifurcation and chaos. A three-phase stepper motor is considered as a case study in this paper. The study shows that the system experiences a dynamic bifurcation (Hopf bifurcation) at high frequencies. Since this kind of motors is widely used in some important applications such as printers, disk drives, process control systems, X–Y records, and robotics, controlling such instabilities is the main concern of this paper. A nonlinear robust model-reference controller is introduced. The study shows how to stabilize the system, while having a satisfactory performance, even in the case when some of the motor parameters were uncertain. [Copyright &y& Elsevier]

Published
2004
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39. Chaos and bifurcation in a third-order phase locked loop

Author

Harb, Bassam A. and Harb, Ahmad. M.

Subjects
*CHAOS theory, *PHASE-locked loops, *NONLINEAR theories
Abstract

The chaos induced in a new type of phase locked loop (PLL) having a second-order loop filter is investigated. The system under consideration is modeled as a third-order autonomous system with sinusoidal phase detector characteristics. The modern of nonlinear theory such as bifurcation and chaos is applied to a third-order of PLL. A method is developed to quantitatively study the type of bifurcations that occur in this type of PLL’s. The study showed that PLL experiencing a Hopf bifurcation point as well as chaotic behaviour. The method of multiple scales is used to find the normal form near the Hopf bifurcation point. The point is found to be supercritical one. [Copyright &y& Elsevier]

Published
2004
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