By Petersson Andreas

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9). For small bandwidths the rejection is twice as good. 4 Internal Model Control (IMC) Due to the simplicity of IMC for designing controllers, this method will be used throughout this thesis. IMC can, for instance, be used for designing current or speed control laws of any ac machine [40, 44, 102]. The idea behind IMC is to augment the error between the process, ˆ G(p) and a process model, G(p), by a transfer function C(p), see Fig. 2. Controller design is then just a matter of choosing the “right” transfer function C(p).

10. Gain in energy production by lowering the magnetizing losses for a DFIG system as a function of the average wind speed. Solid line is the Y-Δ-connected DFIG and dashed line is short-circuited DFIG. system (VSIG), one-speed system (FSIG 1), two-speed system (FSIG 2), and, a variablespeed system equipped with a permanent magnet synchronous generator (PMSG). The average efficiency for the PMSG is taken from [34]. The converter losses of the PMSG system are assumed equal to that of the VSIG system.

9) where ε = sin(θ1 − θˆ1 ) and θ1 − θˆ1 is the error in the estimated angle. In the above equations γ1 and γ2 are gain parameters. The notation “ˆ” indicates an estimated variable or parameter. If the true frequency and position are given by dω1 /dt = 0 and dθ1 /dt = ω1 , then it is ˆ 1 and θ˜1 = θ1 − θˆ1 are shown in [37] that the estimation error equations for ω ˜ 1 = ω1 − ω ˆ 1 and θˆ1 will converge to ω1 and θ1 asymptotically stable if {γ1 , γ2 } > 0. This implies that ω ˆ respectively, asymptotically.