# Modeling of Voltage Fluctuations Generated by Arc Furnaces
## 2 Modeling of Voltage Fluctuations in the Operation of a Single Arc Furnace
The factors determining the short-circuit power of the network (e.g., at the point of connecting the arc furnaces) are supply voltage and line impedance. In the proposed model, the short-circuit power is determined by the parameters of the supply network, resistance-\(\text{R}_{\text{L}}\) and reactance-\(\text{X}_{\text{L}}\). The electrical parameters of the electric arc furnace installation are defined by resistance-\(\text{R}_{\text{T}}\) and reactance-\(\text{X}_{\text{L}}\). The electric arc is represented by the voltage \(\text{U}_{\text{Arc}}\). The following ratios of the short-circuit power of the network to the power of the furnace transformer were proposed for model tests, \(\text{S}_{\text{cc}}/\text{S}_{\text{intr}}\)--20, 50, 80, 120, which takes into account the different electrical parameters of the power supply line--Figure 4:5  
* \(\text{S}_{\text{cc}}/\text{S}_{\text{intr}}\): 20, 50--correspond to the worst electrical conditions for powering the steel-works. With such low short-circuit power of the network, voltage fluctuations generated by arc furnaces will cause excessive disturbances, perceived, for example, as flickering light caused by lighting receivers. * \(\text{S}_{\text{cc}}/\text{S}_{\text{intr}}=80\) is the minimum power requirement for arc furnaces specified in [43]. In publication [44] it is recommended to take \(\text{S}_{\text{cc}}/\text{S}_{\text{intr}}\) above 120. Figure 4:6 Voltage fluctuations for different histograms of arc furnace current changes. According to the UIE recommendations given in publication [44], it is recommended that the minimum ratio of the short-circuit power of the \(\mathrm{S_{CC}}\) network to the power of the furnace transformer \(\mathrm{S_{ntr}}\) should be 120. When these power conditions are provided for the steel plant, the voltage fluctuations generated by arc furnaces will not cause an annoying flicker of light. Due to the recommendations presented in [43; 44], such \(\mathrm{S_{cc}}/\mathrm{S_{ntr}}\) values were adopted in the presented research. It was assumed that the greatest changes in current are \(\mathrm{D(I)}=3\), which corresponds to the beginning of melting the scrap. Current variations from \(\mathrm{I_{A}}\) to \(\mathrm{I_{B}}\) cause voltage fluctuations in the \(\mathrm{\Delta U_{AB}}\). They are marked with different colors for different short-circuit powers of the supply network--Figure 4:7  
Figure 10 compares the graphs with and without the resistance in the electric arc supply line. For a sufficiently high short-circuit power of the supply network \(\mathrm{S_{cc}}/\mathrm{S_{ntr}}=120\), omitting the resistance does not cause significant errors in determining voltage fluctuations --Figure 4:8  
For the range of furnace current changes between the extreme values of \(\mathrm{I_{A}}\) and \(\mathrm{I_{B}}\) (\(\mathrm{\Delta I_{AB}}\)), a voltage fluctuation \(\mathrm{\Delta U_{AB}}\) is generated. In the case of a sufficiently high short-circuit power of the network in relation to the power of the furnace transformer (\(\mathrm{S_{cc}}/\mathrm{S_{ntr}}=120\)), omitting the resistance causes a difference in the calculated voltage fluctuation \(\mathrm{\Delta U_{AB}}\) of 0.051% (in relation to the rated voltage \(\mathrm{U_{n}}=100\%\)). For \(\mathrm{S_{cc}}/\mathrm{S_{ntr}}=50\), the resistance omission has an error of 0.107% and for \(\mathrm{S_{cc}}/\mathrm{S_{ntr}}=20\) it is 0.19%. Based on the analysis of the curves shown in Figure 10 and the analysis of the data in Table 1, it was found that the neglect of the resistance \(\mathrm{R_{L}}\) and \(\mathrm{R_{T}}\) has a negligible effect on the value of the determined voltage fluctuations. Taking into account only the resistances \(\mathrm{X_{L}}\) and \(\mathrm{X_{T}}\) in the electric arc supply circuit greatly simplifies the model calculations. The results of the calculations for the cases with and without resistance are presented in the further part of the article.