Sequence components in fault study

[honyeehong8692]

Hi all! I am currently learning fault study in power systems.

To my understanding-

In any network (symmetrical or unsymmetrical) , there would be 3 components- positive sequence component, negative sequence component and zero sequence component.

Question:

For generators and transformers , would synchronous reactance mean/signify its positive sequence reactance?

It would be very helpful if an explanation about the definition and differentiation among: subtransient, transient and synchronous reactance be provided.

A prompt reply from any user is much appreciated. :)

 

[honyeehong8692]

btw, please and thank you!

 

[FOIWATER]

Yes the synchronous reactance is the positive sequence reactance. It is only useful directly when modelling lines, because generators and transformers are not modeled (usually) by a lumped reactance. Good treatment is given in 'Power system analysis' by Grainger & Stevenson. I could be corrected but I think page 460 describes how 3 phase transformers are modeled for fault conditions based on transformer type. For synch. Generators without grounded neutral, the pos. and neg. sequence diagrams can be modeled by the synch reactances of the machine. If the neutral is ungrounded, the zero sequence diagram is opened at that point, too. If the neutral is grounded through a a reactance, the zero sequence diagram has to be analyzed with 3 x the grounding reactance in series with the machine reactance.

It's a lot to describe briefly, see Grainger.

 

[Babadag]

As per IEC 60909-0: usually the positive-sequence reactance and negative-sequence reactance are the same:
for synchronous machine X2=~X1=X”d [saturated is less then unsaturated].
If X”d<>X”q then X2[negative-sequence]=(X”d+X”q)/2
For 2 windings transformers X1=X2=XT [at the main position of the on-load tapchanger]
XT=sqrt(ZT^2-RT^2) ZT=uk%/100*Vrat^2/Strf uk% =short-circuit voltage of transformer Vrat=Rated voltage Strf=rated apparent power of the transformer.

 

[honyeehong8692]

Yes the synchronous reactance is the positive sequence reactance. It is only useful directly when modelling lines, because generators and transformers are not modeled (usually) by a lumped reactance. Good treatment is given in 'Power system analysis' by Grainger & Stevenson. I could be corrected but I think page 460 describes how 3 phase transformers are modeled for fault conditions based on transformer type. For synch. Generators without grounded neutral, the pos. and neg. sequence diagrams can be modeled by the synch reactances of the machine. If the neutral is ungrounded, the zero sequence diagram is opened at that point, too. If the neutral is grounded through a a reactance, the zero sequence diagram has to be analyzed with 3 x the grounding reactance in series with the machine reactance.

It's a lot to describe briefly, see Grainger.

thank you very much, foiwater!

 

[honyeehong8692]

As per IEC 60909-0: usually the positive-sequence reactance and negative-sequence reactance are the same:
for synchronous machine X2=~X1=X”d [saturated is less then unsaturated].
If X”d<>X”q then X2[negative-sequence]=(X”d+X”q)/2
For 2 windings transformers X1=X2=XT [at the main position of the on-load tapchanger]
XT=sqrt(ZT^2-RT^2) ZT=uk%/100*Vrat^2/Strf uk% =short-circuit voltage of transformer Vrat=Rated voltage Strf=rated apparent power of the transformer.

thanks, babadag!

 

[honyeehong8692]

saturation..?

As per IEC 60909-0: usually the positive-sequence reactance and negative-sequence reactance are the same:
for synchronous machine X2=~X1=X”d [saturated is less then unsaturated].
If X”d<>X”q then X2[negative-sequence]=(X”d+X”q)/2
For 2 windings transformers X1=X2=XT [at the main position of the on-load tapchanger]
XT=sqrt(ZT^2-RT^2) ZT=uk%/100*Vrat^2/Strf uk% =short-circuit voltage of transformer Vrat=Rated voltage Strf=rated apparent power of the transformer.

Badabag, what does saturation mean? and how is it related to synchronous reactance and sequencing?

 

[Babadag]

The open-circuit voltage does not increase linearly with field current.
If the field current is increased, the machine steel saturates and the open-circuit characteristic exhibits
stagnation-the field current goes up the voltage does not.
For low values of field current, the machine is unsaturated and the reactance value is referred to as the unsaturated reactance [Xsu]. The saturated reactance is defined as the reactance calculated at a field current which corresponds to rated armature voltage on the open circuit curve.

 

[honyeehong8692]

Yes the synchronous reactance is the positive sequence reactance. It is only useful directly when modelling lines, because generators and transformers are not modeled (usually) by a lumped reactance. Good treatment is given in 'Power system analysis' by Grainger & Stevenson. I could be corrected but I think page 460 describes how 3 phase transformers are modeled for fault conditions based on transformer type. For synch. Generators without grounded neutral, the pos. and neg. sequence diagrams can be modeled by the synch reactances of the machine. If the neutral is ungrounded, the zero sequence diagram is opened at that point, too. If the neutral is grounded through a a reactance, the zero sequence diagram has to be analyzed with 3 x the grounding reactance in series with the machine reactance.

It's a lot to describe briefly, see Grainger.

here's a link to download the Solutions Manual for Grainger and Stevenson-

https://docs.google.com/file/d/0B21HoBq6u9TsbmpNUFlfMEJ0T00/edit?pli=1