A Closed Normal Form Solution Under Near-Resonant Modal Interaction in Power Systems.

Normal form (NF) is an effective tool to quantitatively analyze nonlinear modal interaction, which is believed to contribute to the complex nonlinear dynamics in power systems. However, in conventional NF analysis, the solution under resonance condition cannot be expressed in a closed form. Hence the NF analysis of power system higher order modal interaction was limited to nonresonant cases, or directly neglecting the resonant terms. In this paper, the NF solutions under modal resonance are derived, by means of the polynomial vector space decomposition. The obtained solution is in a simple closed form, including both the nonresonant part and the resonant part. Numerical simulations are performed to verify the effectiveness of the proposed approach. The results show that, under modal resonant conditions, neglecting the resonant terms may cause significant errors to the obtained numerical solutions, whereas including modal resonant terms in NF may increase the accuracy of the analysis. Finally, the approach proposed in this paper is compared with the modal series method, which, unlike NF method, is not limited by resonant condition. The results show that the proposed method in this paper has better performance in both accuracy and computing time. [ABSTRACT FROM PUBLISHER]