Dynamic iteration schemes and port‐Hamiltonian formulation in coupled differential‐algebraic equation circuit simulation. (4th October 2020) - Günther, Michael; Bartel, Andreas; Jacob, Birgit; Reis, Timo
Summary: Electric circuits are usually described by charge/flux‐oriented modified nodal analysis. Here, we derive models as port‐Hamiltonian systems on several levels: overall systems, multiply coupled systems, and systems within dynamic iteration procedures. To this end, we introduce new classes of port‐Hamiltonian differential‐algebraic equations. Thereby, we additionally allow for nonlinear dissipation on a subspace of the state space. Both, each subsystem and the overall system possess a port‐Hamiltonian structure. A structural analysis is performed for the new setups. Dynamic iteration schemes are investigated, and we show that the Jacobi approach as well as an adapted Gauss‐Seidel approach lead to port‐Hamiltonian differential‐algebraic equations. Abstract : We derive models as port‐Hamiltonian systems on several levels: overall systems, multiply coupled systems, and systems within dynamic iteration procedures. To this end, we introduce new classes of port‐Hamiltonian differential‐algebraic equations. Additionally, we allow for nonlinear dissipation on a subspace of the state space. Both, each subsystem and the overall system, possess a port‐Hamiltonian structure. A structural analysis is performed for the new setups. Dynamic iteration schemes are investigated, and we show that the Jacobi approach as well as an adapted Gauss‐Seidel approach lead to port‐Hamiltonian differential‐algebraic equations.