Question 5.2: Assuming the input power and terminal voltage for the motor ......
Assuming the input power and terminal voltage for the motor of Example 5.1 remain constant, calculate (a) the phase angle δ of the generated voltage and (b) the field current required to achieve unity power factor at the motor terminals.
a. For unity power factor at the motor terminals, the phase-a terminal current will be in phase with the phase-a line-to-neutral voltage \hat{V}_a. Thus
\hat{I}_a=\frac{P_{in}}{3V_a} = \frac{90.6 kW}{3×265.6 V} = 114 A
From Eq. 5.23,
\hat{V}_a=R_a \hat{I}_a+ jX_s \hat{I}_a+ \hat{E}_{af} (5.23)
\begin{aligned}\hat{E}_{af}&= \hat{V}_a – jX_s\hat{I}_a \\&= 265.6 – j 1.68 × 114 = 328 e^{- j35.8°} V,\text{ line-to-neutral}\end{aligned}
Thus, E_{af} = 328 V line-to-neutral and δ = -35.8° .
b. Having found L_{af} in Example 5.1, we can find the required field current from Eq. 5.21.
E_{af}=\frac{ω_e L_{af}I_f}{\sqrt{2}} (5.21)
I_f = \frac{\sqrt{2}E_{af}}{ω_e L_{af}} =\frac{\sqrt{2} × 328}{377× 0.0223}= 55.2 A