how to calculate the short circuits currents 3

[mottt]

I got a question about the calculation of shrt circuit current, I got a salient poles generator with X`d and X`q, how i could use it.. in example: the reactance base is 18 ohms, and X`d is 20% and X`q is 25 %, the voltage is 6000 V, how do you take into account the reactances. Do you sum?

 

[alehman]

No, don't add them. Normally you would use X"d (direct axis sub-transient reactance).

 

[mottt]

X`d is the transient reactance, but it´s the syncronous reactance in direct axis, and X`q is the transient reactance on the quadrature axis....
if i write it i think its
Xtotal transient= X`d+ jX`q is this true?

 

[alehman]

No. There would normally be no reason to add them.

The Xd is the reactance for current 90deg out of phase with the no-load generated voltage. Xq is the reactance for current that is in phase with the no-load generated voltage. Short circuit current is usually close to 90deg out of phase with the voltage, hence the reason direct axis components are normally used for fault calculations.

You might want to take a look at a couple of references listed in the faq238-1287 for this forum -

Elements of Power System Analysis by William Stevenson
or
IEEE Red Book - Industrial Power Systems

 

[flexoprinting]

alehman

Thank you for your post and link really nice info.

 

[davidbeach]

Fault calculations also generally start with Xd'', the subtransient direct axis reactance (actually Zd'', but it is very close to being Xd'' and often simplified to be Xd''), since that more accurately represents the currents that will stress withstand ratings even if nothing is fast enough to be breaking the subtransient currents.

 

[mottt]

if you didn´t use for calculations of the short circuit currents the Xq reactance, why the manufacturers send it? what is the use of this Xq reactance??

thanks a lot for your answers

 

[slavag]

Hi.
You need calculate not only short circuit current.
In your case for example, you need use Xq for calculate underexcitaton ( or min. reactance) setting.
Regards.
Slava

 

[7anoter4]

Hi motorxplosion
I agree with Slava:
The transversal reactance[xq,xq',xq"] is used to calculate other important parameters as for instance:.
Synchronizing power Ps is defined as the power per electrical radian of rotor displacement; in other words = ?P/??
For steady-state[ very small changes] :
Ps=Eo*U1/xd*cos??U1^2*(xd-xq)/xd/xq*cos2?
Were ? is the internal angle from Eo to U1
The synchronizing torque Ts is given by
Ts=Ps/?s
where ?s is the synchronous angular speed of the machine.
From Eq. (8), it is clear that the synchronizing power is a maximum for no load (? = 0) and decreases as the load on the machine increases.
For a load angle of 90 electrical degrees, the synchronizing power is zero, meaning that the machine is on the verge of instability.
The larger the load angle, the less stable the synchronous machine becomes.
The output power per phase is also[for steady state]:
Pa=Eo*U1/xd*sin?+U1^2/2*(xd-xq)/xd/xq*sin2?

The are a lot of other application also.
Best regards

 

[7anoter4]

Sorry! The Greek alphabet is still a problem.
Find pls. a jpeg attached, better.

 

[7anoter4]

Two sentences still are missing.
Attached is the correction.

 

[mottt]

ok, last question about this... normally i take minimum excitation current, as 10 % of full load excitation current, i have asked to the manufacturers sometimes and they said always the same... but i wonder from the beginning that must be a way to calculate it exactly, and you said you use the Xq to calculate it.. could you explain it... or i could use the 10 % full load excitation to limit the minimum excitation...
thanks to all of you for your time and hope all of you got a happy entering on the new year.....

 

[slavag]

Hi Motorxplosion.
Again mix of terms.
I wrote about underexcitaion/min. reactance/loss of excitation setting for the electrical protection 40, where for the silent gen. possible used Xq instead Xd.
You ask about excitaion current limit. This Q for the genrator mnf. only.
Regards.
Slava