An algorithm for solving piecewise-linear networks that include elements with discontinuous characteristics

In this paper, an algorithm for solving piecewise-linear networks that include elements with discontinuous characteristics is presented. The algorithm is based on modifications of the Katzenelson algorithm that traces the solution curve through regions where boundary conditions are satisfied. Jumps in the network output variables, caused by state changes of elements with discontinuous characteristics, may in turn result in additional state changes of piecewise-linear elements. To resolve these state changes, the network solution point is dragged over the line segment that connects the solution points at the discontinuity, and the network state is changed whenever boundary conditions are violated. Since the algorithm traces cause and effect sequence of state changes, it is well suited for application in time-domain simulations. The algorithm has been implemented in a simulator for piecewise linear networks, and extensively tested on networks encountered in power electronics. An example of such application is presented.