Inverter-based distributed generation (IBDG) sources are continually being connected to the grid. Such IBDG sources act as current sources that are unbalanced in either one or two phases. When connected to the grid, unbalanced IBDG sources inject the unbalanced current during an electric fault. Moreover, unbalanced load currents can also change the short-circuit current. Therefore, short-circuit analyses of power systems with either clustered or distributed IBDG sources should not ignore the contribution from unbalanced IBDG sources and load currents. Thus, the objective of this study is to present a method that calculates the short-circuit current flowing from unbalanced IBDG sources. For this purpose, zero- and negative-sequence networks are referred to the positive-sequence network, and new bus impedance matrices are defined for each sequence network. This study also proposes a hybrid method that combines Thevenin's equivalent circuit and the three-phase bus impedance matrix for distribution systems with untransposed lines. The method examines the effect of unbalanced loads on the short-circuit current. The proposed methods are verified by using well known IEEE test feeders.