Circuit-Embedded Feeder-State Reconstruction for Low-Voltage Distribution Networks under Extreme Measurement Sparsity

RESUMO

Low-voltage (LV) distribution feeders increasingly require internal state information, yet real-time telemetry is often limited to feeder-head active and reactive power, while downstream demand and production are described only by static contract metadata. This paper proposes a physics-based augmented-circuit reconstruction framework for this extreme-sparsity regime. Feeder-head measurements, matched metadata, and class-level profiles first determine bus-level load and production priors. These priors parameterize auxiliary constant-power elements coupled to the physical feeder through impedance branches, and the feeder state is reconstructed by solving the resulting nonlinear AC circuit equilibrium. Thus, the augmented-network physics maps the sparse information set into Kirchhoff-consistent physical-bus voltages, angles, and flows, whereas weighted least squares (WLS) reconstructs the state through weighted residual fitting. The method is evaluated on a real 459-bus Portuguese LV feeder model using an in-sample-calibrated synthetic benchmark of 672 fifteen-minute snapshots. It converged for every snapshot and achieved voltage RMSE, MAE, and maximum absolute error of 0.0033, 0.0014, and 0.0337 p.u., respectively. Its RMSE was lower than those of two independently specified static-prior WLS baselines. A direct-prior AC power-flow check produced closely matching voltage magnitudes, confirming that the augmented circuit faithfully realizes the constructed priors.