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Catastrophic equipment failures continue to occur today due to ferroresonance even though this phenomenon has been extensively studied over the past 90 years. This paper is concerned with comparing analytical nonlinear dynamics methods with a two-dimensional (2-D) brute-force bifurcation diagram for displaying safety margins in a 2-D parameter space. A simplified single-phase model is used to represent the case of ferroresonance between a transformer and circuit breaker grading capacitor. Comparisons are made between the analytical method and EMTP simulations of an actual ferroresonant event.