Linear transformations are commonly utilized in the analysis of three-phase systems, as they help simplify the mathematical representation of system behavior. Notable among these are the Fortescue, Clarke, and Park transformations, which are extensively used in practice. In particular, the last one leads to the formulation of the Space-Vector theory that is currently employed in the fields of AC machine theory. In this paper, the Space - Vector theory is expanded, being used to modeling of the other components of the electrical system: power source, transformer, transmission line and load. The proposed methodology can also be employed to analyze both steady-state and transient behavior of power systems. The resulting models are as straightforward as those derived using the per-phase approach. Furthermore, by applying the space-vector transformation, the concepts of instantaneous active where reactive power will be generalized, creating a more complete assessment of the performance of the power system as a whole or in its specific components. The proposed models are implemented in some examples, which have been tested in simulation programs for steady-state and transients.