Electric Arc Furnace Power Quality Analysis Based on a Stochastic Arc Model

Abstract

Electric arc furnaces (EAF) are commonly used in steel industry. Unfortunately, nonlinear characteristic of the arc furnace and its stochastic behavior bring about many problems, e.g. voltage flicker and waveform distortions. The AC furnaces are usually modelled using combined models which divide the phenomenon taking place in real objects into a deterministic and a stochastic or chaotic parts. The former can be expressed by a nonlinear differential equations. The paper goal was to take advantage of the earlier results, i.e. a closed form of the solution to one of the most popular nonlinear differential equations used for the AC electric arc modelling, and start research towards a complete EAC model which covers not only the deterministic but also the time-varying nature of the arc waveforms. Such a model can be helpful, among others, in solution to power quality problems in EAF supplying networks. Theoretical considerations have been illustrated by some examples and the results have been compared with measurements.

On a stochastic arc furnace model

“…Figure 2(b) shows a random time varying amplitude of the arc voltage, similar as it can be observed in reality (see, e.g. [4] or [6]).…”

“…We get a formula of this p-periodic solution y per also by applying the pullback limit of t 0 on the initial value solution (2.3). It holds In [6] this periodic solution is referred to as a steady state solution of the system. Sometimes it is also called the equilibrium solution.…”

“…In reality it can be observed that the arc voltage varies randomly in time, it oscillates with a random time-varying amplitude and the graph of the function shows a slight shivering (cf. [4] or [6]). To take this into account, it is better to model the arc voltage as a stochastic process.…”

“…The stochastic model is based on a deterministic one, for which for certain parameters explicit solutions of (1.1) can be given. This deterministic model was investigated for example in [6] and is recapped here in section 2.…”

Inter‐harmonics analysis and parameter estimation based on H2R6 window and constructing low‐interference zone

“…In addition, according to IEC Std 3002-2018, EAF is also a kind of typically unilinear load, which should be considered in DG. Its dynamic v-i characteristic [17,18] is given in (28), and corresponding curve is shown in Fig. 11…”