No More Blackouts for Meter Checks: Kirchhoff and Cable-Heat Constraints Let Voltage Transformers Be Scored Online
Synopsis
Distribution-network voltage transformers have been checked mainly by de-energizing and comparing them against standard units, which is slow and interrupts supply. A State Grid Wuhan team embedded switching-station Kirchhoff voltage constraints and a cable thermal-balance equation as soft loss terms in a neural network, added radial-basis multi-scale time features and residual attention weighting, and estimated transformer error online. On a laboratory physical simulation platform the method cut RMSE by 35.2% and MAE by 36.4% and raised R² by 2.63 points over the runner-up MRSA-DGCN; in a field pilot in a 10 kV Wuhan area it flagged one out-of-tolerance transformer, matching the de-energized check.
Interpretation
Error evaluation of distribution-network voltage transformers moves from off-line comparison to online estimation, judged from the voltage transfer relation between adjacent distribution rooms fed by the same switching-station busbar. Regulations require periodic de-energization, disassembly and comparison against standard transformers, a mode that consumes manpower and materials, runs at low efficiency and causes frequent supply interruptions. A laboratory physical simulation platform reproduces a typical 10 kV Wuhan distribution topology, covering the substation feeder, switching station, line modules and error-adjustable transformers whose injected errors are precisely controlled.
Physical laws enter training as soft constraints rather than being solved first to recover exact line parameters and then invert for error. Physics-based methods depend on precise line parameters that are hard to obtain in complex distribution-room electromagnetic environments with strongly time-varying lines, while purely data-driven models struggle to separate error drift from external disturbance. The loss combines a data-fitting term, a switching-station busbar voltage consistency term and a cable thermal-balance differential term; the time derivative of cable core temperature is obtained by automatic differentiation through the radial-basis network instead of numerical differencing.
Under the same data split, adding the physical constraints and the two data-side modules gives higher ratio-error accuracy than six comparison models. The runner-up MRSA-DGCN reached R² of 0.9547, plain PINN reached 0.9065, and single-structure MLP and TCN stayed below 0.88. On 10,800 valid records, with the first 90% split 8:1 into training and validation and the last 10% held out, the method reached RMSE 0.001662, MAE 0.000757 and R² 0.9810, reducing RMSE by 35.2% and MAE by 36.4% relative to MRSA-DGCN.
Online evaluation in the field pilot agreed with the de-energized verification transformer by transformer. The pilot deployed synchronous acquisition and online evaluation on phase A of one substation feeder and three distribution-room incoming lines in a 10 kV Wuhan area, training on the first 3000 records and evaluating the remaining 375. VT3 exceeded the 0.2-class ratio-error limit and was judged abnormal, as was the de-energized check; the largest absolute deviation between online and off-line results was 0.11% in ratio error and 1.3′ in phase error.
Perspective
The model is single-phase only, and the field pilot evaluated phase A of four transformers. Evaluation depends on synchronously acquired voltage and current data, and on the laboratory platform it identified a 0.2% abrupt error and a 0 to 0.4% gradual drift with absolute deviation not exceeding 0.05%. The field portion covers one 10 kV area, four transformers and 375 evaluation records, for distribution rooms that have synchronized acquisition and known topology.
Single-phase modeling leaves three-phase unbalanced scenarios uncovered, and sensor faults, missing data and environmental noise may affect evaluation accuracy. The largest online-versus-off-line deviation, 0.11% in ratio error and 1.3′ in phase error, comes from four transformers in one area.