Time discretization issues in induction machine model solving for real-time applications

The Euler numerical integration method is used very commonly to solve the dynamic equations of the induction machine in real-time on digital processors. The need to solve the machine model also arises in real-time hardware-in-loop simulations, and in electric load emulation. The Euler method is often preferred in such applications due to its fast, simple single-step, explicit nature. However, Euler integration can result in large errors in transient and steady state response calculations, even with practical integration time steps. This paper aims at providing an analytical approach to studying the steady state errors caused by the Euler method in solving the induction machine model. It is shown analytically that the least error occurs when the machine model is solved in the synchronous reference frame. The effect of these errors on the closed loop decoupled control of induction machines is analysed in detail. The paper also gives a new formulation of Feedback Linearization Control (FLC) in the synchronous reference frame to reduce the effect of the discretization error. Analyses and simulations are validated through experiments.