The effects of interphase coupling in a multiphase power system become important in the presence of network imbalances and unbalanced phase loadings. In grounded-wye systems, currents that flow in the earth can have significant effects on the system's behavior. Both these effects must be considered in an accurate multiphase power system model. A new treatment of multiphase power system modeling is presented. The treatment relies upon linear graph theory and produces a system multiport model. Mutual coupling effects, the effects of neutral and static conductors, the finite conductivity of earth, and various component models are considered. A reduction in the order of the multiport model also is presented. Multiphase load flow analysis is introduced. Special considerations that arise in multiphase analyses are discussed. Example solutions are presented. A convenient method of representing multiple slack ports is described which results from an application of the principle of superposition. Circulating power flow in multiphase loops is discussed. A procedure is proposed for conveniently representing common shunt and series faults that occur in power systems. The procedure is constructed for efficient computer modeling of multiple cases of various fault combinations in a particular system. / Doctor of Philosophy