Mathematical Simulation Model of Doubly-Fed Induction Machines

Doubly-fed induction machines (DFIM) are widely used in wind power generation and industrial drive systems. Their mathematical simulation models are crucial for system design and control strategy validation.

The dynamic behavior of DFIMs is typically described by voltage equations and torque equations. Voltage equations are based on equivalent circuits of stator and rotor, considering induced electromotive force and resistive voltage drops. Torque equations reflect the balance between electromagnetic torque and mechanical torque.

During simulation modeling, the dq-reference frame is commonly employed to simplify analysis by eliminating time-varying inductance effects. The model must include voltage balance equations for both stator and rotor sides, flux linkage equations, and motion equations.

Simulation requires accurate machine parameters such as stator/rotor resistances, inductances, and moment of inertia. Additionally, the impact of converter control strategies on machine dynamics must be considered, with common control methods including vector control and direct torque control. From an implementation perspective, these controllers typically involve Park/Clarke transformations and PI regulators for decoupled control of active and reactive power.

Mathematical simulation enables performance evaluation under various operating conditions, including startup, variable-speed operation, and fault scenarios. This provides critical reference for practical system design and commissioning, where simulation code often implements numerical integration methods like Runge-Kutta for solving differential equations and includes saturation effects for improved accuracy.