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Power system oscillations under a large disturbance often exhibit distorted waveforms as captured by increasingly deployed phasor measurement units. One cause is the occurrence of a near-resonance condition among several dominant modes that are influenced by nonlinear transient dynamics of generators. This paper proposes an Extended Prony Analysis method for measurement-based modal analysis. Based on the normal form theory, it compares analyses on transient and post-transient waveforms to distinguish a resonance mode caused by a nearresonance condition from natural modes so that the method can give more accurate modal properties than a traditional Prony Analysis method, especially for large disturbances. The new method is first demonstrated in detail on Kundur's two-area system and then tested on the IEEE 39-bus system to show its performance under a near-resonance condition.

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In a power system, the conventional method for computing participation factors of generators associated with an oscillatory mode involves using linearized system models and element-by-element products of corresponding right and left eigenvectors. Unlike traditional modal analysis methods, this paper proposes a new approach for estimating participation factors from measurements on generator responses under a range of disturbances. This method computes extended participation factors that coincide with accurate model-based participation factors, provided that the measured responses satisfy an ideally symmetric condition. This paper further relaxes the symmetric condition by identifying a coordinate transformation from the original measurement space to an optimal new space for the best symmetry. Consequently, the optimal estimation of participation factors solely from measurements is achieved, and the factors influencing accuracy are discussed. The proposed approach is comprehensively demonstrated using a two-area system and then tested on an NPCC 48-machine power system.