The Theory of Bond Graphs in Distributed Systems and Simulations

The bond graph theory provides a firm and complete strategy for making mathematical models and are used in this work to obtain a good relation between connectivity, causality and model fidelity in distributed systems. By distributing a system more computational power is available which makes it possible to increase the model fidelity in large systems without increasing the time to solve the total system. Also, more complex models with causality switching properties may be used for simplifying the connectivity problem between distributed models and for representing changing dynamics that also affects the model causality. Stability of distributed systems are dependent on both solver stability and dynamical stability, when neglecting the stability results based on cascaded systems with certain passivity properties. For linear distributed systems solver with fixed step size solvers a stability criterion involving the system dynamics, local solver time step and global synchronization time step can be formulated. In this work a stability criterion for linear distributed systems solved with the Euler integration method will be derived and a hybrid causality model, representing a small power plant, will be used to test the stability criterion