Analyzing the internal resonances and energy exchange between modes of power system considering Frequency – Energy dependence using Pseudo-Arclength and shooting algorithm

The power system nonlinearity and its profound impact on the individual states of power system is first evaluated and the interaction between their constituent modes during the occurrence of internal mode resonance (IMR) is discussed in this paper. A typical dynamical feature of nonlinear systems is the frequency-energy dependence of their states and their corresponding constituent modes which is also underlined in this paper. At first predominant state is identified which is defined as the one with highest energy level and the internal mode resonances and energy exchange between its constituent modes are explored accordingly. However, Perturbation Techniques such as Normal Form (NF) or Modal Series (MS) and several polynomial approximation are explored and it is demonstrated that such methodologies do not lead to the acceptable results and does not work well in near-resonant conditions. For this reason, the integrated algorithm consists of Shooting and Pseudo-Arclength is employed for obtaining Frequency-Energy Plot (FEP) to estimate and evaluate the involved modes behavior during the resonance and the energy level at which the internal resonance occurs. The studies are performed on 39-bus New England test power System and the final results prove the accuracy and effectiveness of the proposed methodology and algorithm.