Abstract The aim of this paper is to present a systematic approach of calculating fault currents due to the switching of elements or fault impedances that involve two buses and ground. Traditionally, Thevenin’s equivalent circuits are made up of two terminals suitable for calculating the current into an element connected between both terminals of the equivalent circuit. In such cases, the current entering the element is equal to the current leaving the element. So many practical cases involve elements that have a third terminal connected to ground. Tee and pi models of transmission lines are examples of such cases. Traditionally, the two terminals Thevenin’s equivalent circuit is used to tackle such problems by decomposing the three terminal element into its basic elements. The problem is then transferred to a multi element application where each element is processed once a time. This approach is cumbersome and time consuming. In this paper, a systematic approach to applying the three terminal Thevenin’s equivalent circuit to three terminal elements is proposed.