Time series motifs are used for discovering higher-order structures of time series data. Based on time series motifs, the motif embedding correlation field (MECF) is proposed to characterize higher-order temporal structures of dynamical system time series. A MECF-based unsupervised learning approach is applied in locating the source of the forced oscillation (FO), a periodic disturbance that detrimentally impacts power grids. Locating the FO source is imperative for system stability. Compared with the Fourier analysis, the MECF-based unsupervised learning is applicable under various FO situations, including the single FO, FO with resonance, and multiple sources FOs. The MECF-based unsupervised learning is a data-driven approach without any prior knowledge requirement of system models or typologies. Tests on the UK high-voltage transmission grid illustrate the effectiveness of MECF-based unsupervised learning. In addition, the impacts of coupling strength and measurement noise on locating the FO source by the MECF-based unsupervised learning are investigated.

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