Finding all the operating points in piecewise-linear electrical networks: An iterative-decomposed approach

In this work is presented a methodology for obtaining all the operating points in piecewise-linear (PWL) electrical networks. The networks can include independent and controlled voltage or currents sources, resistors or conductances and PWL elements. The PWL elements are described by an iterative and decomposed one-dimensional PWL model. The model is denominated as iterative, because the particular representation of each segment depends on the value of one parameter included in the formulation. In order to optimize the search of all the operating points, the methodology is aided by a graphical procedure for identifying such constitutive element segments involved into the existence of any DC solution. By numerical examples here presented, it is possible to confirm the efficiency of the methodology.