Modeling DFIG Using General Vector Representation in the Presence of Harmonics

Abstract

In this paper, a doubly-fed induction generator (DFIG) wind turbine is modeled by using the general vector representation of voltage, current and magnetic flux in the presence of harmonics. The general vector representation provides insights into how harmonics are injected to the rotor side because of the DC/AC inverter, and how rotor current is modulated with the rotor's mechanical speed before it goes into the stator side through the air gap. Repetitive rectangular pulses have also been applied to account for the area changing of interface between the stator's poles and the rotor's poles caused by mechanical rotation. For a 6-pole DFIG, periodicity of rectangular pulse creates multiples of the sixth harmonics of the induced magnetic flux which is modulated with the flux of the synchronous speed and it produces multiples of (6n±1)ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> . Our simulation results show that in the stator side of the 6-pole DFIG wind turbine, 5th, 7th and 11th harmonics in addition to a sub fundamental frequency are injected into the grid. Hence, the general vector representation model could be used to design optimal controller that would also minimize harmonics of the stator current.