Question 5.3: An open-circuit test performed on a three-phase, 60-Hz synch......
An open-circuit test performed on a three-phase, 60-Hz synchronous generator shows that the rated open-circuit voltage of 13.8 kV is produced by a field current of 318 A. Extrapolation of the air-gap line from a complete set of measurements on the machine shows that the field- current corresponding to 13.8 kV on the air-gap line is 263 A. Calculate the saturated and unsaturated values of L_{af}.
From Eq. 5.21, L_{af} is found from
E_{af}=\frac{ω_eL_{af}I_f}{\sqrt{2}} (5.21)
L_{af}=\frac{\sqrt{2} E_{af}}{ω_e I_f}
Here, E_{af} = 13.8 kV/\sqrt{3} = 7.97 kV. Hence the saturated value of L_{af} is given by
(L_{af})_{sat}=\frac{\sqrt{2}(7.97 × 10^3)}{377 × 318}=94 mH
and the unsaturated value is
(L_{af})_{unsat}=\frac{\sqrt{2}(7.97 × 10^3)}{377 × 263}=114 mH
In this case, we see that saturation reduces the magnetic coupling between the field and armature windings by approximately 18 percent.