Fault current limiters (FCL) keep the fault current levels below equipment ratings in expanding power systems. Analyzing a faulted power system with FCL using symmetrical components becomes computationally intensive due to the coupling between FCL impedance and the need to recalculate the bus impedance matrix. This paper proposes a fault analysis method based on compensation currents to minimize the computation efforts. The paper presents the mathematical formulation for the compensation currents to model a fault and an FCL. This paper discusses the coupling between sequence networks for various FCL activation cases and identifies corresponding interconnections. The results of the proposed method for various fault types and FCL activation are validated with time-domain simulations. In addition, the computational efforts required by the proposed method are discussed with an application to a large power system. The results show that the proposed method requires minimum computations. The analysis of FCLs with non-linear impedances is beyond the scope of this paper.