- #1

Shaun_W

- 320

- 10

## Homework Statement

3. Generator G [STRIKE]in the above system[/STRIKE] is a steam turbine driven, 4-pole round rotor synchronous generator and has the following data:

Rated output 250 MVA

Rated Voltage 13.8 kV

Rated frequency 60 Hz

Rated power factor 0.85 lag

Maximum reactive power 140 MVAr

Minimum reactive power -140 MVAr

Impedance data

(to a base of rating)

Calculate

(i) the synchronous speed.

[2]

(ii) the complex power output (P + jQ) when operating at rated conditions.

[4]

(iii) the turbine output torque.

[6]

(iv) if the power output is reduced by 15% calculate the complex power output if the terminal voltage and excitation voltage remain constant.

[10]

(v) if the excitation current is now reduced resulting in a reduction of E by 20% calculate the complex power output if the terminal voltage and active power output remain constant.

[10]

(vi) the theoretical steady state stability limit power available with the parameters of part (v).

[4]

(vii) draw the operating chart for this generator assuming a maximum excitation voltage of 1.9 pu and a 10% stability margin.

[14]

## Homework Equations

Just the standard electrical equations, I hope. Although I could be missing something.

## The Attempt at a Solution

Part i) was easy enough, I got 1800rpm because N = (120f)/P = (120*60)/4 = 1800rpm.

Part ii) is where I'm stuck. It seems really easy but I think I am missing something. What I

*think*is that S = 250MVA and Q = 140MVAr; therefore P can be found with simple Pythagoras and is 207MW. That sort of makes sense as S x pf should equal the actual power, and 250 x 0.85 = 212, which is fairly close.

Part iii) also seems far too simple to be true. Torque is equal to power x speed, so 207MW x 188rad/s, which equals 39GNm...

I'm a mechanical student and really quite lost.

Thanks for any help.