# Modeling of Voltage Fluctuations Generated by Arc Furnaces
## 4 Verification of the Proposed Furnace Power Supply System with the Electric Arc Model  
The proposed method of determining voltage fluctuations along with the adopted assumptions has been verified in industrial conditions. A series of measurements of indicators characterizing the power quality in the supply lines of arc furnaces were carried out. The measurements included weekly data logging cycles and periods for individual heats in electric arc furnaces. Steel plants with different supply conditions (different short-circuit power of the network) and different rated powers of furnace transformers were selected for the tests. Depending on the research problem under consideration, the following are accepted--three-phase [45,46] or single-phase equivalent diagrams of the arc device with the power  
Figure 14: Vector diagram of the arc furnace currents and voltages taking into account the resistance (**a**), marked area with a circle in the magnification (**b**). supply system [47; 48; 49; 50]. In model studies of voltage fluctuations generated by arc furnaces, a single-phase equivalent diagram was adopted--Figure 4.  
This is due to the high correlation of indicators characterizing voltage fluctuations in individual phases (\(\Delta\)U, P\({}_{\text{st}}\)). Figure 15 shows the voltage fluctuations recorded in all phases during one smelting in the arc furnace, where \(\Delta\)U\({}_{\text{L1}}\), \(\Delta\)U\({}_{\text{L2}}\), and \(\Delta\)U\({}_{\text{L3}}\) are the voltage fluctuations in the phases of the arc furnace supply line. The correlation coefficients between voltage fluctuations recorded in individual phases are as follows:  
\[\tau_{\Delta\text{U}_{\text{L1}}\Delta\text{U}_{\text{L2}}}=0.911,\ \tau_{\Delta\text{U}_{\text{L2}}\Delta\text{U}_{\text{L3}}}=0.917,\ \tau_{\Delta\text{U}_{\text{L3}}\Delta\text{U}_{\text{L1}}}=0.919 \tag{37}\]  
Another indicator, the changes of which registered in particular phases were analyzed, is the short-term flicker severity P\({}_{\text{st}}\). The short-term flicker severity P\({}_{\text{st}}\) is directly related to voltage fluctuations, which result in the flicker phenomenon generated by lighting receivers. The statistical analysis of the short-term flicker severity P\({}_{\text{st}}\) was based on the data recorded during individual melts. Figure 16 shows the change of the P\({}_{\text{st}}\) coefficient measured in the three phases of the steelworks supply network during one melt carried out in the arc furnace. A short analysis of the obtained measurement results in three phases is presented below. The relationships between the indicators recorded in individual phases are shown in Figure 17.  
The correlation coefficients between the indicators recorded in individual phases are as follows:  
\[\text{r}_{\text{P}_{\text{st}(\text{L1})}\text{P}_{\text{st}(\text{L2})}}=0.876, \ \text{r}_{\text{P}_{\text{st}(\text{L1})}\text{P}_{\text{st}(\text{L3})}}=0.905, \ \text{r}_{\text{P}_{\text{st}(\text{L2})}\text{P}_{\text{st}(\text{L3})}}=0.889 \tag{38}\]  
The correlation coefficients between the indicators measured in individual phases and their average value are slightly higher and amount to  
\[\text{r}_{\text{P}_{\text{st}(\text{L1})}\text{P}_{\text{st}_{\text{mean}}}}=0.963,\ \text{r}_{\text{P}_{\text{st}(\text{L2})}\text{P}_{\text{st}_{\text{mean}}}} =0.955,\ \text{r}_{\text{P}_{\text{st}(\text{L1})}\text{P}_{\text{st}_{\text{mean}}}} =0.969 \tag{39}\]  
Figure 15: Changes of voltage fluctuations \(\Delta\)U(a) measured during one melt. It was limited to taking into account the results of measurements in the phase with the greatest voltage fluctuations, as it is adopted in Electricite de France [51]. Based on the determined correlation coefficients between voltage fluctuations in individual phases and a very large correlation of the short-term flicker severity, it was limited to model studies based on a single-phase scheme.