Comparative Time-Series Modeling and Short-Term Forecasting of Electric Arc Furnace Voltage Using Hybrid and Deep Learning Approaches
- 1Department of Electrical Engineering and Industrial Informatics, University Politechnica Timisoara, 300006 Timisoara, Romania
Abstract
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.
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BibTeX
@article{panoiu2026comparative,
title = {{Comparative Time-Series Modeling and Short-Term Forecasting of Electric Arc Furnace Voltage Using Hybrid and Deep Learning Approaches}},
author = {Manuela Panoiu and Caius Panoiu and Loredana Ghiormez},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203710},
url = {https://www.mdpi.com/2227-7390/14/20/3710},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Comparative Time-Series Modeling and Short-Term Forecasting of Electric Arc Furnace Voltage Using Hybrid and Deep Learning Approaches
AU - Manuela Panoiu
AU - Caius Panoiu
AU - Loredana Ghiormez
PY - 2026
DA - 2026/10/13
JO - Mathematics
DO - 10.3390/math14203710
UR - https://www.mdpi.com/2227-7390/14/20/3710
AB - 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.
SN - 2227-7390
ER -