J Nathan Kutz

Andrea Pomarico, Yuxuan Bao, Liyao Mars Gao et al.

Monitoring electromechanical oscillations is crucial for maintaining the stability of modern power systems, particularly in the presence of increasing penetrations of inverter-based resources (IBRs), which introduce new dynamic behaviors. In this work, we propose a hierarchical multiscale framework based on the SINDy-SENDAI algorithm to characterize the transient dynamics captured by wide-area measurements. The proposed deep learning architecture robustly separates low- and high-frequency components embedded in sensor data and incorporates a Sparse Identification of Nonlinear Dynamical Systems (SINDy) module in the latent space to identify parsimonious governing equations. In contrast to conventional deep learning approaches that often produce black-box models with limited interpretability, the proposed framework learns an explicit dynamical representation, enabling physical interpretation, stability assessment, and forecasting of electromechanical oscillations. Given the societal importance of modern power systems, the proposed approach is specifically designed to satisfy key requirements for practical deployment, namely robustness, interpretability, and stable performance under diverse operating conditions. The framework is first validated on the two-area Kundur test system using conventional modal analysis as ground truth and subsequently demonstrated on two real-world datasets: the 2016 Iberian oscillatory event and the 2021 ambient measurements from the southern Italian power grid. The results show that SINDy-SENDAI consistently outperforms the state-of-the-art Hankel-DMD method and that the learned latent dynamics are sufficiently informative to accurately reconstruct and predict the behavior of the full system in the original state space.

Andrea Pomarico, Alberto Berizzi, J. Nathan Kutz

Dynamic State Estimation (DSE) will play a fundamental role in future power system operation by providing real-time estimates of the system state and enabling enhanced situational awareness. Existing DSE approaches are primarily based on Kalman filter variants or Machine Learning (ML) techniques. However, Kalman-based methods often suffer from high computational complexity, sensitivity to model inaccuracies, and performance degradation under strongly nonlinear operating conditions. Moreover, their effectiveness critically depends on the number and placement of measurements, since suboptimal PMU locations can reduce observability and even render state estimation infeasible. Machine learning approaches alleviate some of these limitations but typically require large amounts of training data and may struggle to generalize. To address these challenges, this paper proposes a SHallow REcurrent Decoder (SHRED) architecture for full-state reconstruction of power systems from sparse measurements. Unlike conventional model-based estimators, the proposed approach does not rely on an accurate physical model and is largely insensitive to PMU placement, making it particularly attractive for practical deployment in existing Wide Area Measurement Systems (WAMS). The method is validated on the IEEE 39-bus system under strongly nonlinear conditions, including short-circuit disturbances. The results demonstrate that SHRED can accurately reconstruct the complete system state using only a limited number of PMU measurements, consistently outperforming a state-of-the-art shallow decoder benchmark in sparse-measurement scenarios. Furthermore, the proposed framework exhibits strong robustness to measurement noise and maintains high reconstruction accuracy even under severe disturbances, highlighting its potential as a scalable and reliable alternative to conventional DSE techniques.