A type $1$ wind turbine with a six$-$pole, $60$ Hz three$-$phase, Y$-$connected induction generator is spinning the generator

at $1250$ r$/$min$.$ The terminal voltage of the generator is $690$ V$.$ The parameters of the machine are r$1=$r$2=10$m$$ ;

x$1=$x$2=100$m$,$ and Xm$=2.$ Ignore the core losses and the rotational losses of the generator. Compute the

following:

$$ Current in the rotor circuit referred to stator

$$ Developed power

$$ Airgap power

$$ Power delivered to the grid

$$ compute the reactive power of the generator and the power factor at the terminals of the generator.

$$ compute the rotor inrush current at starting. Assume the turbine is spinning the generator at $1350$ r$/$min when the

connecting switch isclosed.

$$ the speed of the generator is $1350$ rpm when it is connected to the grid. Compute the terminal voltage of the

generator that reduces the inrush current to $1$ kA$.$ And compute the triggering angle of the SCRs