The mechanism of eliminating harmonic resonance with controllers by over-voltage in the power systems

Abstract

The phenomenon of anti-symmetrical bifurcation of periodic solutions occurring near an integral manifold is the intrinsic cause resulting in harmonic resonance over-voltage in power systems. On the basis of this conclusion, the principle of eliminating harmonic resonance by using an anti-bifurcation approach is presented, which means that the theoretical basis of every measure to eliminate resonance is unified firstly from a point of view of basic theory. Our discussion models depend on a class of non-linear control model produced by over-voltage in the power systems. Using the direct Lyapunov technique, a complete theoretical proof is given in accordance with the measure of eliminating resonance by connecting non-linear resistors in series to the neutral point of PT and applying the feedback control law. It comprises the action of the parameters of the resistors to eliminate resonance and the actual process of eliminating resonance, that is, to go against the bifurcation process which forces the big harmonic solutions to retreat to the integral manifold gradually and disappear eventually, by using the non-linear controllers. This ensures that the intrinsic cause of resonance is eliminated thoroughly.