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In this paper, a
powerful analytical method, called He’s homotopy perturbation method is applied
to obtaining the approximate periodic solutions for some nonlinear differential
equations in mathematical physics via Van der Pol damped non-linear oscillators
and heat transfer. Illustrative examples reveal that this method is very
effective and convenient for solving nonlinear differential equations.
Comparison of the obtained results with those of the exact solution, reveals
that homotopy perturbation method leads to accurate solutions.
Adequate damping is
necessary to maintain the security and the reliability of power systems. The
most-cost effective way to enhance the small-signal of a power system is to use
power system controllers known as power system stabilizers (PSSs). In
general, the parameters of these controllers are tuned using conventional
control techniques such as root locus, phase compensation techniques, etc.
However, with these methods, it is difficult to ensure adequate stability of
the system over a wide range of operating conditions. Recently, there have been
some attempts by researchers to use Evolutionary Algorithms (EAs) such as
Genetic Algorithms (GAs), Particle Swarm Optimization, Differential Evolution
(DE), etc., to optimally tune the parameters of the PSSs over a wide range of
operating conditions. In this paper, a self-adaptive Differential Evolution
(DE) is used to design a power system stabilizer for small-signal stability
enhancement of a power system. By using self-adaptive DE, the control
parameters of DE such as the mutation scale factor F and cross-over rate CR
are made adaptive as the population evolves. Simulation results are presented
to show the effectiveness of the proposed approach.
The advisability of the use of matrix methods of
equations rearrangement for the investigated system which allows writing a
secular equation is considered in this article. This approach greatly simplifies
the analysis of performance of transient response in complicated multi-coupled
electrical system at small perturbations.