TY - GEN
T1 - A Stochastic Arc Furnace Model With Exponential Ornstein-Uhlenbeck Fluctuations
AU - Chekhanova, Anna
AU - Dietz, Markus
AU - Grabowski, Dariusz
AU - Klimas, MacIej
AU - Starkloff, Hans Jörg
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025
Y1 - 2025
N2 - Many developed electric arc furnace models are still deterministic. One of the most important ones is based on the power balance equation and results in a nonlinear ordinary differential equation. The stochastic and nonlinear nature of the electric arc phenomenon leads to a randomly time-varying arc voltage-current characteristic. A stochastic model is required to adequately describe these random effects. We propose an extension of the deterministic model mentioned above by using an exponential stationary Ornstein-Uhlenbeck process for modeling stochastic influences. Based on the Karhunen-Loève expansion of the Ornstein-Uhlenbeck process, approximate polynomial chaos expansions for some quantities of interest, such as the arc radius or the arc voltage, are derived. These results are compared with Monte Carlo simulations.
AB - Many developed electric arc furnace models are still deterministic. One of the most important ones is based on the power balance equation and results in a nonlinear ordinary differential equation. The stochastic and nonlinear nature of the electric arc phenomenon leads to a randomly time-varying arc voltage-current characteristic. A stochastic model is required to adequately describe these random effects. We propose an extension of the deterministic model mentioned above by using an exponential stationary Ornstein-Uhlenbeck process for modeling stochastic influences. Based on the Karhunen-Loève expansion of the Ornstein-Uhlenbeck process, approximate polynomial chaos expansions for some quantities of interest, such as the arc radius or the arc voltage, are derived. These results are compared with Monte Carlo simulations.
KW - Electric arc furnace
KW - Karhunen-Loève polynomial chaos expansion
KW - Ornstein-Uhlenbeck process
KW - random differential equation
KW - voltage-current characteristic
UR - https://www.scopus.com/pages/publications/105019048770
U2 - 10.1109/EEEIC/ICPSEurope64998.2025.11169287
DO - 10.1109/EEEIC/ICPSEurope64998.2025.11169287
M3 - Conference contribution
AN - SCOPUS:105019048770
T3 - Conference Proceedings - 2025 IEEE International Conference on Environment and Electrical Engineering and 2025 IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2025
BT - Conference Proceedings - 2025 IEEE International Conference on Environment and Electrical Engineering and 2025 IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2025
A2 - Leonowicz, Zbigniew
A2 - Stracqualursi, Erika
A2 - Jasinski, Michal
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2025 IEEE International Conference on Environment and Electrical Engineering and 2025 IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2025
Y2 - 15 July 2025 through 18 July 2025
ER -