Bifurcation diagram with Electromagnetic Transient Program (EMTP) for ferroresonance analysis

Bifurcation diagram presents the steady state behavior of a nonlinear system with respect to important parameters and initial conditions. The most popular method for generating bifurcation diagram is based on the simulation of ferroresonant circuit with Ordinary Differential Equation (ODE) and XPPAUT. However, this method is limited only to single phase equivalent circuit with many assumptions for simplification. The Electro-Magnetic Transient Program (EMTP) is popular for providing time domain solutions to the ferroresonant circuit in single phase and three phase systems. PSCAD/EMTDC, which is developed from EMTP, offers simple modeling of individual physical component without the need to simplify the system to accommodate the analytical expression. For single phase ferroresonant circuit, ODE with XPPAUT and PSCAD/EMTDC give similar results based on phase trajectories, Poincaré sections, and Lyapunov exponents. Application of brute force technique and Poincaré sections on steady state solutions, can generate bifurcation diagrams for three phase power system. Generation of bifurcation diagram with EMTP method combines the simplicity in circuit modeling with practical features of the three phase power system and the simplicity in investigation of ferroresonance with respect to different operating conditions.