Approximate Solutions of a Class of Cubic Characteristic Equations in One Variable in Asymmetric Transient Analysis of Induction Machines

In order to limit currents, a two phase voltage is applied to an induction machine in rotating state after a brief power outage before full voltages are gradually provided via thyristor switch. The asymmetric electromagnetic transient process after switching-on two phase supply is studied in the paper. Firstly, a cubic characteristic equation in one variable is obtained via Laplace transforms on corresponding differential equations. Secondly, the cubic equation is solved via Newton’s method, and then applied to asymmetric transient process analysis of induction machines. Lastly an approximate formula of time constant are derived and compared to the accurate but complicated Cadarno formula. The suggested formula is simple and easily applicable, with an error less than 5% in application to general induction machines of power over 5.5 kW.