Wide-area wave motion analysis using complex empirical orthogonal functions

In this paper, a method for detection of propagating features in wide-area system measurements through its traveling and standing parts is proposed, where the relationship between complex modes and wave motion is explored. From an ensemble of complex signals, a complex correlation matrix is formed, and its real and complex eigensolutions are the basis of the decomposition. The real and complex eigenvectors contain standing and traveling characteristics. The basic idea is a complex generalization of proper orthogonal decomposition (POD). The method developed is general and could be applied without loss of generality to measured or simulated data. As illustrative case, the method is applied to a synthetic example; additionally, data obtained from global positioning system (GPS)-based multiple phasor measurement units (PMUs) from a real event in power systems are used to study the practical applicability of the method.