Dynamic iteration schemes and port‐Hamiltonian formulation in coupled differential‐algebraic equation circuit simulation,International Journal of Circuit Theory and Applications

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Dynamic iteration schemes and port‐Hamiltonian formulation in coupled differential‐algebraic equation circuit simulation
International Journal of Circuit Theory and Applications ( IF 1.8 ) Pub Date : 2020-10-04 , DOI: 10.1002/cta.2870
Michael Günther ₁ , Andreas Bartel ₁ , Birgit Jacob ₁ , Timo Reis ₂

Affiliation

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.

中文翻译：

耦合微分-代数方程电路仿真中的动态迭代方案和端口哈密顿公式

电路通常通过电荷/通量导向的改进节点分析来描述。在这里，我们在多个层次上将模型推导为汉密尔顿港口系统：整体系统，多重耦合系统和动态迭代过程中的系统。为此，我们引入了新的端口哈密顿型微分代数方程组。因此，我们还允许在状态空间的子空间上进行非线性耗散。每个子系统和整个系统都具有哈密尔顿港结构。对新设置执行结构分析。对动态迭代方案进行了研究，结果表明，雅可比（Jacobi）方法以及经过改编的高斯-赛德尔（Gauss-Seidel）方法导致了Port-Hamiltonian微分-代数方程。

更新日期：2020-10-04

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