Maximum efficiency of an induction machine operating in a wide range of speed and torque - part 1 (theoretical analysis)

A set of unique equations usable to calculate directly the optimum slip frequency and line voltage of a 3phase squirrel-cage induction machine with respect to maximum efficiency is deduced in this article. An operation in steady state at any requested speed and torque in a wide range is taken into consideration. The proposed calculation is especially useful for independent traction purposes. The requested torque, speed and an extended mathematical model of the machine based on a Γ-network are the inputs of the calculation. The optimum slip frequency and line voltage are the outputs. The calculation results using the deduced analytical formulas were verified with a practical measurement and with a MATLAB simulation. Due to the extensiveness of the problems the correspondence of the theoretical calculation with the practical results will be presented in a separate 2nd part of the article.