Thermodynamic optimization of an electric circuit as a non-steady energy converter

TL;DR

This paper models a non-steady electric circuit as an energy converter using thermodynamic principles, deriving equations in frequency space to analyze and optimize its energetic performance.

Contribution

It introduces a thermodynamic framework for analyzing transient electric circuits as energy converters, including the derivation of algebraic equations in frequency space and the identification of optimal operation regimes.

Findings

Derived algebraic equations in frequency space for the circuit

Identified symmetry and cross effects similar to steady states

Established conditions for maximum efficient power regime

Abstract

Electrical circuits with transient elements can be good examples of systems where non--steady irreversible processes occur, so in the same way as a steady state energy converter, we use the formal construction of the first order irreversible thermodynamic (FOIT) to describe the energetics of these circuits. In this case, we propose an isothermic model of two meshes with transient and passive elements, besides containing two voltage sources (which can be functions of time); this is a non--steady energy converter model. Through the Kirchhoff equations, we can write the circuit phenomenological equations. Then, we apply an integral transformation to linearise the dynamic equations and rewrite them in algebraic form, but in the frequency space. However, the same symmetry for steady states appears (cross effects). Thus, we can study the energetic performance of this converter model by means of two parameters: the "force ratio" and the "coupling degre". Furthermore, it is possible to obtain the characteristic functions (dissipation function, power output, efficiency, etc.). They allow us to establish a simple optimal operation regime of this energy converter. As an example, we obtain the converter behavior for the maximum efficient power regime (MPE).