Exploiting model graph analysis for simplified modeling and improved diagnostics

In systems modeling, the dynamic behavior is approximated by considering certain properties to be constant in space in each physical component of the system. Such models are called lumped element models and are composed of connected components. Each component is described by ordinary differential equations and algebraic equations. The theory of linear graphs or model graphs can be helpful for analysis of such models. This paper presents a unified methodology for describing and analyzing network topology, using both linear graphs and the underlying algebraic equations, i.e. to take advantage of linear graph methods to enhance symbolic manipulation of model equations in order to handle underdetermined sets of potential variables and overdetermined sets of flow variables. The methodology is extended to handle overdetermined potential variables which arise, for example, when dealing with 3D rotations in multi body systems. It also allows handling of planar loops without any special attention by the user. This methodology for treating lumped models is in particular applicable to Modelica tools and would in certain cases allow simulation of ungrounded circuits and otherwise enable better diagnostics, for example when forgetting to ground an electrical circuit. It will also simplify the Multibody library of Modelica Standard Library.