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This paper provides the comprehensive development procedures and mathematical model of an adjustable speed drive (ASD) for steady-state solutions, transient trajectories, and local stability based on a Floquet multiplier theory. A complete representation of the ASD is employed, which includes the dynamic equation of the dc link capacitor and the detailed models of the diode rectifier and of the pulse width modulated inverter. The power electronic switches are efficiently represented through smooth functions that allow a larger integration step to be used without the loss of precision in the solution. An efficient technique in the time domain for the computation of the periodic steady-state solution of electric systems, including ASDs based on a discrete-exponential-expansion matrix and the Poincaré map, is used. The obtained results are validated against the solutions obtained with an implementation using the Power System Blockset of Simulink and against the response obtained by the measurements from a 1.5-kVA ASD experimental setup system.