This paper concentrates on the implementation of an analytically-based identification procedure of three phase induction motor models, for steady-state and quasi-steady-state analysis. The mathematical model of the motor is based on the use of linear and quadratic equations, reducing therefore the system nonlinearity to at most second degree. The model optionally includes slip-dependent rotor parameters, allowing therefore a unified and accurate representation of every possible motor design (NEMA designs A, B, C and D). The parameter estimation methodology allows the motor model identification using the slip-torque and slip-current motor characteristic. The estimation procedure is demonstrated with some simple numerical examples.