Microgrids are a possible solution to mitigate the extensive interruptions in service to end-use customers caused by abnormal events, such as major natural disasters. Microgrids can be formed by energizing portions of the distribution system to interconnect generators and critical loads. In this scenario, inrush dynamic currents can present a barrier for forming microgrids by preventing the necessary switching operations and/or damaging equipment. Modeling inrush dynamics, through electromagnetic transient tools, presents a challenge when the microgrid represents a large portion of a distribution feeder. This paper uses a dynamic-phasor approach to approximate the envelope of inrush dynamics; thus, allowing simulations of large systems. The two main contributions of this paper are: a) a new formulation to solve a set of dynamic-phasor differential equations representing an unbalanced distribution system; and b) modeling of transformer saturation in the dynamic-phasor frame. These two contributions allow the inrush phenomena to be simulated on full-size microgrid and/or distribution feeder models. The new formulation and model are implemented in GridLAB-D, and tested on IEEE test systems. The simulations showed good approximation as compared with a more accurate electromagnetic transient simulation in PSCAD software.