Reduced load in a turbine generator

[Leannie]

Homework Statement

A turbine generator is delivering a 20MW load at 50Hz, to a local load.; it is not connected to the grid. The load suddenly drops to 15 MW, and the governor starts to open the steam valve after 0.5s. Calculate the frequency to which the generated voltage rises, before the steam flow decreases in response to the reduced load. The stored energy in the rotating parts is 80MJ at 3000rpm.

Homework Equations

I know it a 2 pole generator from p=120f/n (don't know if this matters)
I also know reducing the torque will give a reduced power output.

power(kW)=(2∏×torque(Nm)×rpm)/60000
torque=(60000×power)/(2∏×rpm)
P=E/t

The Attempt at a Solution

During the 0.5 seconds before the steam flow is reduced there is extra power generated.
20MW-15MW=5MW
E=Pt=5MWx0.5s
E=2.5MJ

Total energy from rotating parts=80MJ+2.5MJ=82.5MJ
(2.5/80)x100=3.125% increase in energy at shaft

Will the frequency simply then be an increase of 3.125% i.e. 50+(50x0.03125)=51.5625Hz

Or is it more complicated than this, would the torque be considered?

Thanks

 

[aralbrec]

Total energy from rotating parts=80MJ+2.5MJ=82.5MJ
(2.5/80)x100=3.125% increase in energy at shaft

Will the frequency simply then be an increase of 3.125% i.e. 50+(50x0.03125)=51.5625Hz

Or is it more complicated than this, would the torque be considered?

No, it won't be a linear relationship since the relationship between rotational kinetic energy and angular speed is quadratic.

I would try an energy conservation equation instead.

 

[Leannie]

ok thanks, i thought it wouldn't be as straight forward as that. i will try the an energy conservation equation instead.