Transient Stability & Rotor Acceleration

[ccdubs]

Hi all,

I have just read something that has really confused me. I am researching transient stability of synchronous machines by reading "Power System Analysis" by Grainger and Stevenson.

Pg 718, describes a system where a generator supplies a bus with 3 transmission lines, two long and on short. All lines have CB's at each end. The short line has the CB at the remote end open and has a 3 phase fault close to the bus which is cleared by the CB at the near end.

The text then goes on to say: (I will summarise and not quote)

- There is a difference between mechanical and electrical power (Pm=unchanged (OK), Pe=0 (huh?)).
- This difference in power must be accounted for and is done so by acceleration of the rotor(if I accept the above I understand this).

Wouldn't an increase in load (like a short) act to slow down the rotor?

 

[electricpete]

In the model that you have, the only thing between the ideal voltage source and the short circuit is inductance.

Inductance is not capable of dissipating any real power. Generator power must go to zero.

Current will likely increase, but it is all reactive.

 

[avigodner]

You can rouhgly view it like this. At steady state, mechanical torque developed by prime mover is equalized by generator electromagnetic torque created by active current component. As sudden 3-phase short circuit fault happens, active current dramatically reduces and so electromagnetic torque. As a result, prime mover's constant torque starts accelerating rotor.

There are also second order effects - control, braking torque due to currents induced in rotor damping circuits etc.

 

[jbartos]

Suggestion: Reference:
L.L. Grigsby "The Electric Power Engineerng Handbook," CRC Press, IEEE Press, 2001, page 11-57, Figure 11.23.
Notice that Pe is a part of negative feedback and Pm is reference (constant)
Pe=E'V sin(delta)/X
Feedback, Pe, may be equal to zero while the error is equal to Pm.

 

[electricpete]

Using jb's formula:
Pe=E'V sin(delta)/X

V goes to zero for bolted short at terminal.
Therefore Pe goes to zero.

As avg mentioned. the turbine is slow to respond and Pmech originally stays constant, producing accelration.

 

[ccdubs]

Thank you all.

This now makes good sense. Sometimes the old brain needs a prod in the right direction!

 

[jbartos]

Suggestion: It depends under which angle one is approaching to the machinery. For example, the system approach is different from the machinery design approach or from machinery operation/maintenance approach.