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A fast and stable approach for the simulation of transformer nonlinearities during transient and unbalanced operating conditions is given. The proposed scheme implements separate magnetic and electric equivalent circuits. The solution of the transformer nonlinear mathematical model is carried out using the Newton-Raphson iterative method. Introducing the magnetic circuit nonlinearities into the model as either continuous or piecewise functions eliminated the difficulty of the Jacobian formation. The method was verified against experimental and computed results. The application of the Jacobian iterative method increased the stability and convergence of the solution as compared to a predictor corrector scheme. The proposed method was able to accurately simulate the transformer behaviour under switching and no-load conditions.