Electrical power systems question

[Shaun_W]

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.

 

[SirAskalot]

ii) Q=140MVAr is incorrect as the rated power. Q=cos(phi) * S. Q=140MVAr is as stated the max/min reactive power, not the rated.

iii) To be strictly correct you need the efficiency of the generator to calculate the input power. If not given, your answer might be considered correct.

 

[Shaun_W]

Thanks for your help.

I've calculated the complex power output to be 212.5 + j131.7, i.e. 212.5MW output with 131.7MVArs.

An efficiency is not given; however, it is possible to calculate one from the data supplied? It's just that it seems to be worth a lot of marks [6] for something so easy.

 

[Shaun_W]

And also, if the terminal and excitation voltages remain constant whilst the power output decreases, does this also mean that the power factor remains constant? I'm assuming not.