Circuit-Embedded Feeder-State Reconstruction for Low-Voltage Distribution Networks under Extreme Measurement Sparsity
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 AC circuit-embedding 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. The resulting AC equilibrium enforces the assigned virtual-element powers, while weighted least squares (WLS) reconciles measurements and pseudo-measurements 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. The proposed method converged for all 672 snapshots and achieved voltage RMSE, MAE, and maximum absolute error of 0.0033, 0.0014, and 0.0337 p.u., respectively, outperforming both static-prior WLS baselines. Under the same constructed priors, matched-prior WLS achieved a lower RMSE of 0.0029 p.u., while the proposed circuit embedding reconstructs the feeder state by solving the nonlinear AC equilibrium, bypassing WLS residual fitting entirely and requiring no specification or tuning of pseudo-measurement variances.