A unified methodology for the power efficiency analysis of physical systems

In this paper, the problem of power efficiency evaluation for n-ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class.