Geometry-Conditioned Conformal Calibration for Guaranteed False-Alarm Control in Uncertain Nonlinear Photovoltaic Systems

Abstract

A fault detector inside an active fault-tolerant loop drives an automatic action, so every false alarm commands a reconfiguration for a fault that is absent. In a photovoltaic (PV) plant the false-alarm rate has to be controlled within each operating regime, because the healthy uncertainty changes with the position of the sun as inter-row shading switches bypass diodes into conduction. Monitoring limits, including kernel-density ones, fix one threshold over the whole fault-free record, and conformal calibration guarantees the rate only on average across regimes. This work analyses 33 measured days from a 100.44 kWp sub-array near Madrid (Spain) at the inverter’s native 5 min resolution. Conformal calibration is conditioned on a solar-elevation partition frozen before any evaluation and compared with three alternative calibrations of the same anomaly score, on measured healthy data and on 148 injected fault events. The standard deviation of the healthy voltage residual grows by a factor of 5.15 from high to low sun, and normality is rejected in every regime. At a significance level of 0.05 the conditioned calibration keeps the realised false-alarm rate between 5.4% and 6.2% in all four regimes, while pooled calibration diverges across them by a factor of 58.3. At a level of 0.01 a healthy string requests a spurious reconfiguration at worst every 6.3 h, against every 66 to 87 min under the alternatives. The guarantee has a price, as event detection at the 0.05 level falls from 98.0% to 90.5%, with the loss in the low-sun regime that a deterministic bound on the same uncertainty predicts. The partition needs only the site coordinates and the timestamp, so the construction transfers to other plants.