8 a generator 9 and an ac ac converter 10 the principle schematics of a standard doubly fed induction generator 9 is illustrated in fig3 where the stator 11 is connected to the grid 15 via a grid transformer 14 and the rotor 12 is connected to the grid 15 via slip rings 13 an ac ac converter 10 and the grid transformer 14 fig4 illustrates the standard steady state t equivalent diagram for a doubly fed induction generator where u s i s r s and l sl are the stator voltage stator current stator resistance and stator leakage inductance respectively similarly u r i r r r and l rl are the rotor voltage rotor current rotor resistance and rotor leakage inductance respectively l sr is the magnetizing inductance all generator parameters are transferred to fixed stator voltage reference frame in the following the currents and voltages will all be referred to in a balanced orthogonal two phase rotating reference frame namely the so called dq system of coordinates fig5 a and 5 b illustrates the two steps of transformation of the quantities from a balanced three phase system into the dq system the first step which is known as the clarke transformation converts balanced three phase quantities into balanced two phase quadrature quantities as illustrated in fig5 a the relations between the three phase quantities a b and c.