Accelerated state estimation and voltage-magnitude monitoring in transmission networks using multi-output regressor chains
Abstract
State estimation is essential for the safe and efficient operation of power systems. Real-time voltage-magnitude estimation requires a fast and computationally efficient algorithm. Although conventional power-flow algorithms provide accurate results, their computational requirements may limit their suitability for real-time applications. To address this limitation, this study proposes a voltage-magnitude estimation method based on a multi-output regressor chain (RC) with random forest (RF) as the base learner, hereafter referred to as the RF-RC model. The proposed approach was evaluated through extensive experiments on the IEEE 39-bus New England transmission system under different operating conditions, including N-1 contingencies and load variations of ±40% from the baseline. It was further assessed through hyperparameter-sensitivity analysis, chain-ordering analysis, five-fold cross-validation, bootstrap-ensemble uncertainty analysis, and statistical significance testing using the IEEE 14-bus, 39-bus, and 118-bus systems. Under normal operating conditions, the proposed RF-RC model achieved an R2 value greater than 0.99 and a root mean square error (RMSE) below 4×10-4 p.u. It also maintained high predictive accuracy under heavy loading conditions but exhibited reduced performance for extreme out-of-distribution loading scenarios. Further analysis demonstrated low predictive uncertainty, strong physical consistency with voltage constraints, and statistically significant performance differences between the proposed model and the baseline models. Moreover, the interpretability of the proposed model was evaluated using permutation importance to identify the input features that most strongly influence voltage-magnitude estimates. Overall, the results demonstrate the potential of the RF–RC model for accurate voltage-magnitude estimation in standard transmission systems. However, the proposed model is dependency-aware rather than topology-aware, and its scalability has been evaluated only on standard IEEE test systems.