Electric Arc Furnaces (EAFs) are loads that are characterized by non-linear, time-varying and stochastic behavior. Furthermore, EAFs injects large amount of harmonics to the grid besides having poor and varying power factor in different operating conditions. Large variation of reactive power consumed by an EAF leads to voltage flicker in the Point of Common Coupling (PCC), and therefore these loads are almost invariably accompanied by a Static Var Compensator (SVC). To prevent excessive harmonic injection to the grid (associated with EAF and the Thyristor Controlled Reactor (TCR) of the SVC), the capacitive part of SVC is normally implemented by means of notch filters. To perform studies for the design of these filters, the whole system, including EAF, SVC and the rest of system must be accurately modeled in the frequency domain. Any error in modeling results in improper filter design and consequently inadequate performance. In this thesis, different EAF and TCR models in frequency domain are examined. A new model is proposed for EAF to cover its behavior in all operating conditions. Different notch filters, including Pi-type and C-type filter are studied. Design criteria for designing Pi-type filters are mentioned. All the above analyses are applied to a case study regarding upgrading EAFs in Mobarakeh Steel Complex in Isfahan . Various simulations are carried out to compare the performance of different topologies.