# Modeling of Voltage Fluctuations Generated by Arc Furnaces
## 1 Introduction
The amplitude of voltage fluctuations \(\Delta\)U is presented as a percentage of the nominal voltage of the network--Figure 2.  
Due to the non-linear nature of the electric arc, it is very difficult to estimate the increase in voltage fluctuations with arc devices operating in parallel. Electric arc furnaces are classified as non-linear loads of electricity. Therefore, the superposition method cannot be used to calculate voltage fluctuations in the operation of several arc devices. Figure 3 shows comparatively the voltage fluctuations recorded with one and two operating arc devices. The standard deviation of voltage fluctuations for a different number of arc furnaces is also presented. The voltage fluctuations recorded in the networks supplying arc devices shows how disturbing arc furnaces are for the power quality--Figure 3. Switching the furnace causes voltage fluctuation whose amplitude can be determined by the standard deviation (SD \(\Delta\)U)1. Connecting another furnace causes an increase in voltage fluctuations, with the amplitude of fluctuations SD(\(\Delta\)U)2. The article is a continuation of the issues of the impact of electric arc furnaces on the supply network presented in publication [20]. Currently, the focus was mainly on the voltage fluctuations. The article presents a proposal of the arc furnace model with a power supply network. The proposed model is a compromise resulting from the adopted initial assumptions and the usefulness of the model in practical (engineering) applications. Publication [21] presents an analysis of harmonics generated by arc furnaces. The proposed DCMM (Data-driven Compartmental Modeling Method) considers the coupling relationship among different frequencies of harmonics to enhance the modeling accuracy, meanwhile, the dimensions of the harmonic dataset are reduced to improve computational efficiency [21]. However, harmonic disturbances are not related to other disturbances, for example, voltage fluctuations. Publication [22] discusses a method for selecting the elements of a C-type filter working with a conventional LC-type filter for compensating reactive power and filtering out higher harmonics generated by arc furnaces and ladle furnaces. The assessment of the parameters of the power supply network for arc furnaces based on the measurements of currents and voltages is presented in publication [23]. The single-phase equivalent diagram of the arc furnace supply network is being considered (similarly to the presented article). The disruptive influence of arc furnaces on the quality of energy in the power system is presented in the article [24]. The dependence of voltage fluctuations (characterized by flicker indicators) on the short-circuit power of the supply network was analyzed. The operation of arc furnaces is modeled with the use of simulation programs. These programs already have applications or blocks that simulate disturbances caused by arc devices. For example, in the article [25], to ensure sufficient dynamics and accuracy, the model predictive direct power control was applied using the MATLAB/Simulink Real Time Workshop environment implemented into the dSPACE(tm) control system DS1005. The article proposes a classical method of voltage fluctuation modeling. The adopted assumptions constitute a compromise between the (acceptable) accuracy of calculations and the possibility of using the model for practical applications. The disadvantage of the proposed method is the quasi-dynamic way of reflecting the phenomena occurring in the supply network during individual melts in the arc furnace. Using the proposed model, one can determine, among others, maximum values of voltage fluctuations that will occur for the given short-circuit power of the network and the power of the furnace transformer.