An invertible dependence of the speed and time of the induction machine during no-load direct start-up

In this paper, an invertible dependence of the speed and time of the induction machine during no-load direct start-up is presented. Namely, based on the parameters of the induction machine equivalent circuit as well as on the basic, well-known, equation for machine torque, the analytical expression for the induction machine time-speed dependence during direct start-up is derived. On the other hand, in order to obtain inverse i.e. speed-time dependence, the derived time-speed expression is rearranged in one nonlinear equation. As the derived nonlinear equation does not have an analytical solution, a novel iterative procedure, based on the usage of Lambert W function, is proposed for its solving. The results obtained by using the developed expressions for speed-time or time-speed curves are compared with the corresponding results obtained by using expressions known in the literature as well as with the results obtained by using a numerical time-domain computation method. Moreover, the results obtained by using the developed expressions have been compared with the corresponding experimental results to demonstrate the accuracy of the derived expressions. The Matlab code developed for solving the presented iterative procedure, as well as the Matlab code for induction machine speed-time curve determination, is also provided.