Simplification of Mathematical Model of Double Fed Asynchronous Machine

Abstract

Double Fed Asynchronous Machines in (DFAM) recent years have found wide application both as generators mainly in renewable energy sources (wind power, small hydropower), and as a motors embedded in various electric drives. In order to study the static and dynamic modes of operation of these machines as one of the most effective methods - the method of mathematical modeling is widely used. It was found that the algebraic-differential equations that make up the mathematical model of double fed induction machine are expediently represented in the d and q axes rotating with the rotor speed of the machine. Particularly this form allows relatively simple reproduction of control coordinates - amplitude and frequency converted to the rotor winding voltage. This mathematical model is based on the well-known Park equations for synchronous machines. It is proposed to simplify the algebraic-differential equations of the double-fed induction machine by reducing the transformer emf, the slip emf and the voltage drop on the stator winding of the machine. The results of calculations for the complete equations of the machine having the 6th order and on the simplified equations having the 4th order showed that the error in determining the regime parameters of the machine in steady-state conditions is in the range 0-7%, i.e. does not exceed 7 percent. The error in dynamic modes is also within acceptable limits. In the dynamics of the change in the regime parameters of DFIM with a sharp change in the disturbing influences slightly differ from each other, and with a sharp change in the control actions they make up 20-30%. This allows to recommend the proposed simplification for engineering calculations, especially when these machines operate in a group or in parallel with other machines and components of power systems.Â