Balanced Models in Modelica 3.0 for Increased Model Quality

A Modelica model can only be simulated, if the number of unknowns and the number of equations are equal. In Modelica 3.0, restrictions have been introduced into the language, in order that every model must be “locally balanced”, which means that the number of unknowns and equations must match on every hierarchical level. It is then sufficient to check every model locally only once, e.g., all models in a library. Using these models (instantiating and connecting them, redeclaring replaceable models etc.) will then lead to a model where the total number of unknowns and equations are equal. Besides this strong guarantee, it is possible to precisely pinpoint which submodels have too many equations or lack equations in case of error. This paper gives the rationale behind the Modelica 3.0 design choices including proofs of the new guarantees, and discusses the limitations of this approach.