Mathematical models for calculating the performance characteristics of controlled asynchronous motors based on equivalent substitution schemes with parameters changing with frequency control are generated. We use circuits with and without the activation of the active resistance of the magnetization branch. To study transient electromagnetic and electromechanical processes, a mathematical model is constructed, based on a set of differential equations for the equilibrium of voltages and currents in a system of transformed coordinates. The active power consumed by the engine is determined taking into account losses in the magnetic circuit, additional and mechanical. The experimental and theoretical characteristics of regulated induction motors in static and dynamic modes are compared. Errors in the calculation of the active power consumed by the engine, the efficiency of the engine as determined by taking into account the active resistance of the magnetization branch of the equivalent replacement circuit, and without taking into account are determined. The necessity of using an equivalent replacement circuit with the active resistance of the magnetization branch is substantiated for finding the efficiency of regulated asynchronous motors.