###### Abstract  
State estimation in distribution power systems is increasingly challenged by the proliferation of distributed energy resources (DERs), bidirectional power flows, and the growing complexity of unbalanced network topologies. Physics-Informed Neural Networks (PINNs) offer a compelling solution by integrating machine learning with the physical laws that govern power system behavior. This paper introduces a PINN-based framework for state estimation in unbalanced distribution systems, leveraging available data and embedded physical knowledge to improve accuracy, computational efficiency, and robustness across diverse operating scenarios. The proposed method is evaluated on four IEEE test feeders--IEEE 13, 34, 37, and 123--using synthetic datasets generated via OpenDSS to emulate realistic operating scenarios, and demonstrates significant improvements over baseline models. Notably, the PINN achieves up to a 97% reduction in current estimation errors while maintaining high voltage prediction accuracy. Extensive simulations further assess model performance under noisy inputs and partial observability, where the PINN consistently outperforms conventional data-driven approaches. These results highlight the method's ability to generalize under uncertainty, accelerate convergence, and preserve physical consistency in simulated real-world conditions without requiring large volumes of labeled training data. p 2025 2  
arise from characteristics unique to distribution networks, such as radial or weakly meshed topologies, lack of real-time measurements, low resistance-to-reactance (R/X) ratios, and sparse measurement infrastructure [4; 5]. Additionally, distribution systems are typically unbalanced and require full three-phase modeling to capture their operating conditions accurately. Conventional SE approaches, which often assume balanced conditions, can produce inaccurate results when applied to these networks. The increasing integration of distributed energy resources (DERs) further complicates observability and introduces higher variability into the system [6; 7]. These challenges have led to the development of specialized DSSE methods, including branch current-based state estimation, node voltage-based approaches, and methods leveraging pseudo-measurements derived from historical load data or load forecasts [8]. Despite these efforts, conventional DSSE methods frequently suffer from reduced accuracy and increased computational burden as network complexity scales. In response, researchers have turned to machine learning (ML) approaches that can directly learn the mapping from measurements to system states. Enabled by advances in smart meters and phasor measurement units (PMUs), ML models offer faster inference and adaptability [9]. In response, researchers have turned to machine learning (ML) approaches that can directly learn the mapping from measurements to system states. Enabled by advances in smart meters and phasor measurement units (PMUs), ML models offer faster inference and adaptability [10]. However, purely data-driven methods often fail to incorporate the underlying physical principles of power systems, potentially leading to physically implausible results, especially when confronted with scenarios outside their training distributions [11]. Moreover, they require large volumes of labeled training data, which may not be available across diverse distribution network configurations. Physics-Informed Neural Networks (PINNs) present a promising alternative that bridges the gap between purely data-driven and physics-based methods [12]. PINNs incorporate the governing equations of physical systems--such as the power flow equations--directly into the training objective of a neural network. This is achieved by augmenting the loss function with residuals of these equations, penalizing deviations from physical laws during training.