Closing the Accuracy Gap in Electrical Model-Free OPF with Concurrent Voltage Estimation

In PV-rich low-voltage (LV) networks, rooftop solar can push voltages above their limits, which distribution companies manage by curtailing customers' PV generation with active power setpoints. Model-based optimal power flow (OPF) computes these setpoints but requires an accurate electrical model of the LV network, such as line impedances and topology, which distribution companies rarely have. Electrical model-free OPF instead embeds a machine-learning (ML) model, trained purely on smart meter data, that calculates each customer's voltage from their active and reactive power and the transformer voltage. However, an accurate voltage model does not translate into good optimization decisions: trained on normal operation, the ML model is evaluated by the optimization at operating points beyond its training distribution, so near-perfect accuracy on historical data does not guarantee accurate setpoints. The existing electrical model-free OPF worsens this by holding the transformer voltage fixed: it falls as PV is curtailed, so the ML model receives a value inconsistent with the current operating point. We address this gap and propose electrical model-free OPF with concurrent voltage estimation (CVE-OPF), which estimates the transformer voltage within the optimization using a linear-regression (LR) model. On a realistic three-phase Australian LV network (146 customers, 5-minute smart meter data, 60\% PV), we evaluate two CVE-OPF variants, with a neural-network (NN) or an LR customer-voltage model, and the existing electrical model-free OPF against model-based OPF and power-flow simulation, on voltages and setpoints. The customer-voltage models are near-perfect on historical data but lose accuracy inside the optimization. CVE-OPF narrows this loss, yielding more accurate setpoint decisions.