Several challenges hinder accurate and physically consistent dynamic parameter estimation in power systems, particularly under scenarios involving limited measurements, strong system nonlinearity, and high variability introduced by renewable integration. Although data-driven methods such as Physics-Informed Neural Networks (PINNs) provide a promising direction, they often suffer from poor generalization and training instability when faced with complex dynamic regimes. To address these challenges, we propose a Residual Physics-Informed Neural Network (Res-PINN) framework, which integrates a residual neural architecture with the swing equation to enhance estimation robustness and precision. By replacing the traditional multilayer perceptron (MLP) in PINN with residual connections and injecting normalized time into each network layer, the proposed model improves temporal awareness and enables stable training of deep networks. A physics-constrained loss formulation is employed to estimate inertia and damping parameters without relying on large-scale labeled datasets. Extensive experiments on a 4-bus, 2-generator power system demonstrate that Res-PINN achieves high parameter estimation accuracy across various dynamic conditions and outperforms traditional PINN and Unscented Kalman Filter (UKF) methods. It also exhibits strong robustness to noise and low sensitivity to hyperparameter variations. These results show the potential of Res-PINN to bridge the gap between physics-guided learning and practical power system modeling and parameter identification.

Non-intrusive load monitoring (NILM) is a key enabler for smart-grid applications, yet practical deployment is often hindered by limited appliance-level labels and severe distribution shifts across households and operating conditions. As a result, many deep learning approaches become unreliable in small-sample and out-of-distribution (OOD) settings. In this paper, we propose CR-MAT, a causality-driven representation learning framework for few-shot NILM classification. Instead of relying on large-scale training or heavy data augmentation, CR-MAT injects causal representation learning into multi-appliance task modeling, encouraging the network to learn appliance-discriminative features that are stable across environments while suppressing spurious, domain-specific correlations. We conduct extensive experiments under multiple OOD scenarios and consistently observe improved classification robustness compared with deep NILM baselines. Further analysis indicates that causal representation learning enhances resilience to non-stationary consumption patterns and improves generalization under OOD scenarios. The proposed framework provides a practical route toward reliable NILM classification and supports downstream smart-grid applications such as flexible load control and demand response.