Generator torque, internal angle and E0

[davrom]

The question is refered to a 1P synchronous generator. It is known the output voltage U2, nominal power, revolution rpm, synchronous reactance Xs and pf of load (e.g 0.9 inductive). The rest of parameters are neglected/neglegible.

1. How can be determined the nominal internal angle teta, the nominal electro-induced voltage E0 (excitation voltage) and the nominal torque M opossed to driving motor? I have the formula of torque M=[E0*U2*sin(t)]/(Xs*omega).

2. Considering U2 and pf constant regardless of how big is the load, can be kept torque M constant adjusting the internal angle and E0 or the torque changes with load size? If can be kept constant, why the voltages triangle U2-E0-I*Xs does not get closed? What is the correct triangle? The internal angle teta should decrease when E0 increases.

 

[jbartos]

Suggestion: The theta is linked to the generator stability. If it is too large, the generator will become out of its synchronism.
Reference:
1. William D. Stevenson, Jr. "Elements of Power System Analysis," Third Edition, McGraw-Hill Book Company, 1975, Chapter 14 Power - System Stability. Concentrate on the stability, steady state stability, transient stability, equal area criterion, etc.
Also, concentrate on Chapter 9 "Some Principles of Load-Flow Control."
Please, notice that:
1. Generator has:
U2-E0+I*Xs=0
2. Motor has:
U2-E0-I*Xs=0

 

[davrom]

Thank you, jbartos. I am not an American teritorial and I cannot get the book you referenced, but thank you anyway.

I have been thinking to the problem and the result is that I realized I made a mistake, resp. it is obviously that the torque is direct proportional with the load (I2 current); I started from he assumption of that the torque is constant any time but is not.

With U2 and pf kept constant, E0 phasor moves its head (arrow head) along the phasor I2*Xs, internal angle theta changing accordingly (E0 increases - theta increases). E0 and theta increase (with U2 and pf constant) untill the current reaches the rated current I2 of generator when I can obtain the rated torque, rated E0 and rated theta.

At last, I have to understand the realtionship between the a.m. scheme and the critical torque Mcr (where the generator gets out of synchronism and stops). I know Mcr is obtained when theta=90 degrees.

But the question is: can I reach 90 degrees with theta if I always keep constant U2 and pf? I may say no, but I am not for sure.

Anyone?

 

[jbartos]

Suggestion: Visit

http://www.ee.und.ac.za/coursemain/DNE4SS2/notes/4SS2SLIDES_5.pdf

http://www.ee.und.ac.za/coursemain/DNE4SS2/notes/4SS2SLIDES_3.pdf

http://www.pdhonline.org/courses/e105/Module6.pdf

etc. for more info