Analytical solution for no-load induction machine speed calculation during direct start-up

This paper deals with the investigation into mathematical modeling of induction machine speed-time and time-speed dependencies during no-load direct start-up. Namely, a precise analytical formula for induction machine speed calculation during no-load direct start-up is given and solved in the form of the Lambert W function. The results obtained by using developed analytical solution are compared with corresponding results obtained by using methods based on numerical time-domain computation (NTDC) that have been realized in two different program packages. Furthermore, the results obtained by using developed analytical solution are compared with corresponding experimental results. The findings showed good agreement between the obtained results. All developed MATLAB programs for speed-time and time-speed curve determination are given in the paper. The Mathematica program developed for solving the Lambert W equation is also provided.