Saturation in the ferromagnetic core significantly affects the performance of electrical machines. In the performance analysis of electrical machines, an accurate representation of the saturation characteristics in the machine model is important. In this paper, a new trigonometric algorithm is proposed to represent the saturation characteristics of electrical machines based on the measured saturation characteristics data points. This model can be applied to various kinds and sizes of electrical machines. The calculated results demonstrate the effectiveness of the proposed model. This trigonometric model has been applied to a conventional synchronous machine model and extensive stability performance analysis has been carried out. This further reveals the usefulness of the proposed trigonometric saturation model and the importance of the inclusion of saturation in stability analysis.