Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models

5 Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models 

Here Vuct is the voltage across resistor Ra is the linearized value obtained from the fit of impedance spectra K is RTIF and P is the transfer coefficient that can be assumed to have a value of 0.5. A more exact treatment allows one to derive a similar relationship using the Framkin isotherm (Levi and Aurbach [1999]). 

Methods to calculate time dependent current/voltage response for circuits whose parameters depend on voltage or current are well developed in theoretical electronics and free open source tools for numerical calculations are available, such as general electronic circuit simulator SPICE (Hageman [1993]). 

6 Special Kinds of Impedance Measurement Possible with Power Sources—Passive Load Excitation and Load Interrupt 

To obtain impedance spectra, acquired arrays v[t], t[/] are used to estimate parameters of a differentiable interpolation function v(t). These parameter values are then snbstitnted into Laplace transform of this function, V(5). To achieve maximum possible noise rejection, it is useful to employ a physically meaningful interpolation function for the particnlar system nnder test and to fit v[j], t[j] data to the function to find its parameters. For most electric systems, such a function would be a sum of exponentials, as proposed to be use in such conversion by Macdonald [1993]. In this case v(t) and its Laplace transform V(s) are shown below. 

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