Comparative Time-Series Modeling and Short-Term Forecasting of Electric Arc Furnace Voltage Using Hybrid and Deep Learning Approaches

Accurate modeling and short-term forecasting of electric arc furnace (EAF) voltage are important for power quality analysis, process monitoring, and the development of data-driven compensation and control strategies. The strongly nonlinear and time-varying behavior of the electric arc makes its voltage difficult to represent using simplified analytical or low-order parametric models. This study compares several modeling approaches using industrial voltage and current measurements acquired on the secondary side of a three-phase furnace transformer. The investigated methods include a hybrid Fourier–polynomial model optimized by a genetic algorithm, a CNN–GRU model, LSTM and BiLSTM networks, and a Dilated CNN–BiLSTM architecture. The models are first evaluated for same-interval voltage estimation over a common measurement interval using RMSE, MAE, R2, and a current-interval V–I RMSE. A separate direct multi-horizon forecasting experiment is then performed using a 40 ms historical voltage–current window and prediction horizons of 1, 2, 5, 10, 20, 40, and 60 ms. Persistence and one-period predictors are used as reference baselines. For same-interval estimation, the Dilated CNN–BiLSTM achieves the lowest mean errors across three independent runs, with an RMSE of 5.33 ± 0.59 V, an MAE of 4.13 ± 0.44 V, an R2 of 0.99986 ± 0.00003, and a current-interval V–I RMSE of 1.70 ± 0.41 V. The BiLSTM obtains the next-lowest mean RMSE, 9.26 ± 4.25 V. In the forecasting task, no single neural architecture achieves the lowest RMSE at all prediction horizons. The BiLSTM provides the lowest neural model RMSE at 5 and 20 ms, the LSTM at 2, 10, and 60 ms, while the BiLSTM and Dilated CNN–BiLSTM yield nearly identical RMSE values at 1 ms. At 40 ms, the one-period baseline produces a lower RMSE than the neural models. The results show that forecasting performance is strongly horizon-dependent and that increased architectural complexity does not necessarily guarantee lower forecasting error. This study also demonstrates the importance of distinguishing same-interval voltage estimation from true future forecasting when evaluating EAF voltage models.