On a stochastic arc furnace model
DOI:
https://doi.org/10.24193/subbmath.2019.2.02Keywords:
Electric arc furnace, random differential equation, Ornstein-Uhlenbeck process, Monte Carlo method, polynomial chaos expansion.Abstract
One of the approaches in modeling of electric arc furnace is based on the power balance equation and results in a nonlinear ordinary differential equation. In reality it can be observed that the graph of the arc voltage varies randomly in time, in fact it oscillate with a random time-varying amplitude and a slight shiver. To get a more realistic model, at least one of the model parameters should be modeled as a stochastic process, which leads to a random differential equation. We propose a stochastic model using the stationary Ornstein-Uhlenbeck process for modeling stochastic influences. Results, gained by applying Monte Carlo method and polynomial chaos expansion, are given here.
Mathematics Subject Classification (2010): 34F05.
References
Acha, E., Semlyen, A., Rajakovi´c, N., A harmonic domain computational package for nonlinear problems and its application to electric arcs, IEEE Transactions on Power Delivery, 5(1990), no. 3, 1390-1397.
Adler, R.J., Taylor, J.E., Random Fields and Geometry, Springer, New York, 2007.
Corlay, S., Pag`es, G., Functional quantization-based stratified sampling methods, Monte Carlo Methods Appl., De Gruyter, 21(2015), no. 1, 1-32.
Grabowski, D., Selected Applications of stochastic approach in circuit theory, Wydawnictwo Politechniki S´laskiej, Gliwice, 2015.
Grabowski, D., Walczak, J., Analysis of deterministic model of electric arc furnace, 10th International Conference on Environment and Electrical Engineering, 1-4.
Grabowski, D., Walczak, J., Klimas, M., Electric arc furnace power quality analysis based on stochastic arc model, 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE Industrial and Commercial Power Systems Europe, 1-6.
Sullivan, T.J., Introduction to Uncertainty Quantification, Springer, Cham, 2012.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
