Non-transposed three-phase line analyses with a single real transformation matrix

In transmission line transient analyses, a single real transformation matrix can obtain exact modes when the analyzed line is transposed. For non-transposed lines, the results are not exact. In this paper, non-symmetrical and non transposed three-phase line samples are analyzed with a single real transformation matrix application (Clarke´s matrix). Some interesting characteristics of this matrix application are: single, real, frequency independent, line parameter independent, identical for voltage and current determination. With Clarke´s matrix use, mathematical simplifications are obtained and the developed model can be applied directly in programs based on time domain. This model works without convolution procedures to deal with phase-mode transformation. In EMTP programs, Clarke´s matrix can be represented by ideal transformers and the frequency dependent line parameters can be represented by modified circuits. With these representations, the electrical values at any line point can be accessed for phase domain or mode domain using the Clarke matrix or its inverse matrix. For symmetrical and non-transposed lines, the model originates quite small errors. In addition, the application of the proposed model to the nonsymmetrical and non-transposed three phase transmission lines is investigated.