Overdetermined Steady-State Initialization Problems in Object-Oriented Fluid System Models

The formulation of steady-state initialization problems for fluid systems is a non-trivial task. If steady-state equations are specified at the component level, the corresponding system of initial equations at the system level might be overdetermined, if index reduction eliminates some states. On the other hand, steady-state equations are not sufficient to uniquely identify one equilibrium state in the case of closed systems, so additional equations are required. The paper shows how these problems might be solved in an elegant way by formulating overdetermined initialization problems, which have more equations than unknowns and a unique solution, then solving them using a least-squares minimization algorithm. The concept is tested on a representative test case using the OpenModelica compiler.