Open Stator Circuit Voltage Build-up
I. Define the Situation
A synchronous generator is rotating at aconstant angular velocity,
The rotor angle,
The three stator windings are open-circuited; i.e.,
A DC voltage is applied to the field voltage at time equal to zero; i.e.,
for time greater or equal to zero
Initial field current is zero.
II. Determine if(t).
Substitute Eq. 2 in to Eq. 1.
Lff is a constant w.r.t. time.
The solution of Eq. 4 is given below.
III. Determine va(t).
Substitute Eq. 8 in to Eq. 7.
Substitute Eq. 9 in to Eq. 6.
Using the product rule of differentiating yields:
or
IV. Graph to Visualize
A 24 kV machine.
The transformer voltage term is negligible compared to the speed voltage term.