On a stochastic arc furnace model

Hans-Jörg Starkloff; Markus Dietz; Ganna Chekhanova

doi:10.24193/subbmath.2019.2.02

Authors

Hans-Jörg Starkloff Technische Universität Bergakademie Freiberg
Markus Dietz Technische Universität Bergakademie Freiberg
Ganna Chekhanova Technische Universität Bergakademie Freiberg

DOI:

https://doi.org/10.24193/subbmath.2019.2.02

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.

References

Acha, E.; Semlyen, A.; Rajakovic, 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 (DOI: 10.1109/61.57981).

Adler, R. J.; Taylor, J. E., Random fields and geometry, Springer, New York, 2007.

Corlay, S.; Pages, G., Functional quantization-based stratified sampling methods, Monte Carlo Methods and Applications, De Gruyter, 21(2015), no. 1, 1-32;

arXiv:1008.4441v2, 2015 (DOI: 10.1515/mcma-2014-0010).

Grabowski, D., Selected Applications of stochastic approach in circuit theory, Wydawnictwo Politechniki Slaskiej, Gliwice, 2015.

Grabowski, D.; Walczak, J., Analysis of deterministic model of electric arc furnace, 10th International Conference on Environment and Electrical Engineering, DOI: 10.1109/EEEIC.2011.5874805, 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 Com-

mercial Power Systems Europe, DOI: 10.1109/EEEIC.2018.8494547, 1-6.

Sullivan, T. J., Introduction to Uncertainty Quantification, Springer, Cham, 2012 (DOI: 10.1007/978-3-319-23395-6).