Applying an iterative-decomposed piecewise-linear model to find multiple operating points

This paper presents a new methodology for obtaining all the operating points in piecewise-linear (PWL) electrical networks. The networks can include independent and controlled voltage or current sources, resistors or conductances, and PWL elements. The nonlinear behavior of the PWL elements is graphically described by one-dimensional PWL curves. The mathematical representation of every PWL curve is given by an iterative and decomposed PWL model. The model is denominated as iterative because the representation of the segments belonging to the PWL curve depends on the value of one parameter included in the formulation. It is also denoted as decomposed because the two axis variables (x and y), in the PWL curve, are included separately in a system of linear equations. In order to optimize the process of searching 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 a numerical example here presented, it is possible to confirm the efficiency of the methodology.