Alternative modes of operation for Wind Energy Conversion Systems and the Generalised Lambert W-function.

When a wind energy conversion system (WECS) based on a doubly fed induction generator is operating in a different mode than maximum power tracking, there exist two different modes of operation. Here, it is shown that such modes satisfy the torque balance condition between the WECS and the electric network, which is described by a transcendental equation in terms of the desired angular velocities. The analytic solution to such equation is the newly found generalised Lambert W-function. Using a real WECS, the authors make an analysis of the lower and upper torque modes of operation. Finally, the authors propose an effective formula to estimate the upper solution which is universally applicable to this class of WECS.