Parameter Study of Ferro-Resonance with Harmonic Balance Method

Ferro‐resonance is an electrical phenomenon which can cause damage to electrical equipments of power systems by its characteristic steady state over voltages and over currents. Configurations where ferro‐resonance is possible has more than one steady state operation. With time domain simulations, different dangerous steady state operations are hard to find due to the fact of dependancy of initial conditions and parameters of the system. Determination of risk of ferro‐resonance needs special studies involving frequency domain and Fourier series based harmonic balance method. Two different types of harmonic balance method are used; namely analytical and numerical method. In order to draw twoparameter continuous curves, harmonic balance with hyper‐sphere continuation method algorithm is created in MATHCAD environment. Work of two case studies in academic literature are extended by comparing different system parameter curves and calculating stability domain risk zones for fundamental ferro‐resonance, subharmonic‐1/2 and subharmonic ‐1/3 ferro‐resonance. Alstom’s test system is also investigated with approximations. Application of numerical harmonic balance method is more superior than analytical method since it is ease of use with thevenin equivalents rather than deriving system equation by hand and possibility to study subharmonic ferro‐resonance. Hypersphere continuation method worked well enough to turn limit points on parameter curves depending on considered Fourier components. Critical values for system parameters have been found for each type of ferro‐resonance allowing to analyse normal operation and ferroresonance operation regimes. Critical values of static damping resistor in the system can be calculated by harmonic balance method without using empirical formula. Damping resistor calculated by harmonic balance method showed difference than the one calculated by empirical formula. Fundamental and subharmonic ferro‐resonance solutions existence zones are co‐existant and sensitive to parameter changes therefore same attention should be given to subharmonic as in fundamental ferro‐resonance. For future studies, three‐phase models for harmonic balance method should be developed in order to study neutral isolated networks and a more customized method of solving non‐linear harmonic balance equations for faster computation can also be developed in MATLAB environment