Electromechanical spring stiffness from the small perturbation linearized equations of generalized machine theory

The authors derive the static electromechanical spring stiffness coefficient of the class of balanced polyphase electric machines which are amenable to the generalized machine reference-frame transformation. The stiffness coefficient derived from the torque equation of the original unprimed frame expressed in the linearized small-perturbation form is given. The spring stiffness, which is physically present but suppressed in the reference-frame transformation, is then modeled and can be used effectively for transient analysis and the analysis of the dynamics of motion control systems. A procedure for the calculation of the stiffness coefficient is described and the electromechanical spring stiffness coefficients of synchronous machines and the induction machine are derived