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.

翻译：时间序列模体用于挖掘时间序列数据的高阶结构。基于时间序列模体，提出模体嵌入相关场以刻画动力系统时间序列的高阶时间结构。将基于MECF的无监督学习方法应用于定位强迫振荡源——一种对电网产生有害影响的周期性扰动。定位FO源对系统稳定性至关重要。与傅里叶分析相比，基于MECF的无监督学习适用于多种FO场景，包括单一FO、共振FO及多源FO。该方法是数据驱动方法，无需任何系统模型或拓扑的先验知识。在英国高压输电网上的测试验证了基于MECF的无监督学习的有效性。此外，研究了耦合强度与测量噪声对基于MECF的无监督学习定位FO源的影响。