Since steady state operation of IM is considered, the time derivative term of flux linkage in equation 2 will vanish. Hence, the rotor currents are:
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(3)
(4)
(5) |
Form equation 5 it can be seen that the dot product between the rotor flux and rotor current vectors is zero in case of singly excited IM. Hence, it can be concluded that the rotor flux and rotor current vectors are perpendicular to each other in steady state operation. The defining feature of FOC is that this characteristic (that the rotor flux and rotor current vectors are perpendicular to each other) is maintained during transient conditions as well.
In both direct and indirect FOC, the 90° shift between the rotor flux and rotor current vector can be achieved in two steps:
- The first step is to ensure that
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(6) |
- The second step is to ensure that
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(7) |
By suitable choice of θs on an instantaneous basis, equation 6 can be achieved. Satisfying equation 7 can be accomplished by forcing d -axis stator current to remain constant. To see this, consider the d- axis rotor voltage equation
 |
(8)
(9)
(10)
(11)
(12) |