State Equation Modeling of Untransposed Three-Phase Lines

Powerful simulation programs are available for large electric and electronic circuits with lumped parameter elements. State equation models are used for each component. This paper presents the methodology for obtaining a finite order state equation model for transmission lines, despite the distributed nature of their parameters. The lines considered are three-phase, untransposed, with full representation of frequency dependence. There is no requirement for constant (real) transformation matrices. All calculations are initially performed in the s-domain. The results are in the form of standard state equations with phase voltages at both line ends as inputs and corresponding currents as outputs. These equations can then be interfaced with those of linear or nonlinear connected components and integrated numerically using advanced numerical integration methods.