Search

We consider the Signature Method ( Σ -method) for the structural analysis of differential–algebraic equations (DAEs) that arise in the modeling and simulation of electrical circuits. Different formulations of the set of model equations are considered. We show that for some formulations the structural approach may fail for certain circuit topologies, while other formulations are better suited for a structural analysis. In particular, we show that for the branch-oriented model equations the Signature Method always succeeds with a structural index that corresponds to the differentiation index of the system. The results are illustrated by a number of examples. [ABSTRACT FROM AUTHOR]

Using polynomial interpolation, along with structural properties of the family of rational positive real functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the complex plane by rational positive real functions whose degree is at most m . Moreover we introduce an easy-to-find parametrization in R 2 m + 3 of a large subset of these interpolating functions. [ABSTRACT FROM AUTHOR]

This paper deals with the application of fractional derivatives in the modeling of electrical circuits RC, RL, RLC, power electronic devices and nonlinear loads, the equations are obtained by replacing the time derivative by fractional derivatives of type Riemann–Liouville, Grünwald–Letnikov, Liouville–Caputo and the fractional definition recently introduced by Caputo and Fabrizio. The fractional equations in the time domain considers derivatives in the range of α ∈ (0; 1], analytical and numerical results are presented considering different source terms introduced in the fractional equation. The resulting solutions modified the capacitance, inductance, also, the resistance exhibits fluctuations or fractality of time in different scales. Furthermore, the results showed the existence of heterogeneities in the electrical components causing irreversible dissipative effects. The classical models are recovered when the order of the fractional derivatives are equal to 1. [ABSTRACT FROM AUTHOR]