The modified nodal analysis (MNA) is probably the most widely used formulation for the modeling and simulation of electric circuits. Its conventional form uses electric node potentials and currents across inductors and voltage sources as unknowns, thus taking an electric viewpoint. In this paper, we propose a magnetic oriented nodal analysis (MONA) for electric circuits, which is based on magnetic node potentials and charges across capacitors and voltage sources as the primary degrees of freedom, thus giving direct access to these quantities. The resulting system has the structure of a generalized gradient system which immediately ensures passivity in the absence of sources. A complete index analysis is presented showing regularity of the magnetic oriented formulation under standard topological conditions on the network interconnection. In comparison to conventional MNA, the differential-algebraic index is reduced by one in most cases which facilitates the numerical solution. Some preliminary numerical experiments are presented for illustration of the feasibility and stability of the new approach.
翻译:修改的节点分析(MNA)可能是用于电路建模和模拟的最广泛使用的配方,其常规形式是将电导和电压源之间的电节点潜能和电流作为未知物使用,因此采用了电动观点,在本文中,我们提议对电路进行磁定向节点分析(MONA),该分析以电容器和电压源之间的磁节点潜能和电荷为主自由度,从而可以直接接触这些电路的数量,由此形成的系统具有普遍梯度系统的结构,在没有电源的情况下可以立即确保被动性。