4) A synchronous generator is connected to an infinite bus through a transmission line. The

infinite bus voltage is 23 kV, the inductive reactance of the transmission line is 192, and the

synchronous reactance of the machine is 2 2. When the excitation of the generator is adjusted

so that the line-to-line equivalent field voltage is 28 kV, the generator delivers 100 MW of

real power to the infinite bus. Compute the following:

a) Terminal voltage of the machine

b) Reactive power at the infinite bus

c) Reactive power consumed by the transmission line

d) Reactive power at the terminals of the generator

a) The terminal voltage of the generator can be computed if we know the current in the transmission line. The

current is a function of the angle between the infinite bus voltage and the equivalent field voltage. From the

power equation, we can compute the angle &: (8: 5 points; la: 5 points; V: 5 points)

3V,E₁

P=sin 8

23×28

sin 8

100=

8 = 27.76°

E, V. 5 27.16

Or

= 2.53/ -7.75" KA

V₁ = V₂+1₂X₁ = 20° +(2.53-7.75°)1/90° = 13.85/10.44 kV

The line-to-line terminal voltage is √3 x 13.85-24 kV.

b) (5 points)

Q. - (E, cos 8 - V.) - (cos(27.76¹)-) = 13.62 MV Ar

c) The reactive power consumed by the transmission line is (5 points)

Q₁ = 31²X₁ = 3 × 2.53² × 1 = 19.25 MV Ar

d) The reactive power at the terminals of the generator can be computed by two methods. The first is to sum the

reactive powers at the infinite bus and the reactive power consumed by the transmission line: 5 points

Q: Qo+Q-32.87 MV Ar

a = 8 - LV₁ = 27.76° -10.44* = 17.32

1x11.85

9₁-(E, cosa-V₁)-(cos 17.32-13.85) -32.87 MVAr