Generator Reactance 2

[prc]

I find the following terms when referring to a turbogenerator(400MVA)data sheet.

1) Direct axis synchronous reactance

2) Direct axis transient reactance

3) Direct axis subtransient reactance

4) Quadrature axis synchronous reactance

5) Quadrature axis transient reactance

6) Quadrature axis subtransient reactance.

Hope the percentage reactances mentiond should be with respect to the rated full load rating, at rated lagging power factor and maximum hydrogen temperature.

Can the experts briefly say what it is,significance for operation,which ones come in to effect during short circuit, normal operation and load sharing (if loading to a common bus.

 

[7anoter4]

I'm not pretending to be an "expert" in Electrical Power System Analysis.
So, simplifying the basic equations I think we may say the following:
Ik=U/Xd Permanent short-circuit current[ss c]
I'k=U/X'd Transitory ssc
I"k=U/X"d Supertransitory ssc
Where:
U=Generator terminal voltage
delta=load angle [between Eo and U]
Eo=no-load emf
E'do=transitory emf
Pa=Eo*U/Xd*sin(delta)+U^2/2*(Xd-Xq)/(Xd*Xq) Stationary regime active power.
P"a=E'do*U/X'd*sin(delta)+U^2/2*(X'd-Xq)/(X'd*Xq) Transitory regime active power
A phasor diagram may be more explicating

 

[7anoter4]

I forgot the phase-to-ground short-circuit.
For phase-to-ground short-circuit we need Z2. X2=(X"d+X"q)/2

 

[Skogsgurra]

Would that mean that "Direct" means resistive and "Quadrature" neans reactive (90 degrees)?

Gunnar Englund

http://www.gke.org

--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

 

[Hoxton]

Would that mean that "Direct" means resistive and "Quadrature" means reactive (90 degrees)? - yes

I usually explain all this to my mechanical engineer colleagues by saying that reactances do not exist..... If you put a short circuit across the terminals of a generator, the current will rapidly increase and then gradually decrease.

To use this in calculations you have to imagine a generator with a voltage source and a variable reactance.

When operating normally, the reactance is large (synchronous)

When the fault is applied, it is very small (subtransient)

And the then rises (transient)

As regards the direct and quadrature components, if you look at a salient pole generator (like fitted to a 500kVA standby diesel). The magnetic path between the rotor pole face and the stator is easier (only interupeted by the air gaps) than if you took the path between the poles where the air gap is large. Basically that explains the difference.

The reactances are usually referred to the rated VA of the generator.

 

[7anoter4]

The Salient Poles Synchronous Generator Rotor [inductor] magnetic field is deformed by stator [induced] reaction field.
Mathematically we can decompose this field in 2 sinusoidal magnetic fields produced by stator one acting in the pole and another
between poles. The reactance produced by these fields will be xad [direct armature reactance in pole axis ]
and xaq [Quadrature axis armature reactance]
The stator magnetic field losses produces a loss reactance Xs. The direct axis synchronous reactance then will be Xd=Xs+Xad
and Quadrature axis synchronous reactance will be Xq=Xs+Xaq
As we know the pole is provided with excitation winding and [usually] oscillation damping [I don't know if my translation is correct name]
winding and in a short-circuit case these fields will produce an other change in synchronous reactance and we'll get X'd and X"d [respectively X'q and X"q]

 

[dpc]

http://en.wikipedia.org/wiki/Dqo_transformation

Some info on Park's (or Dq0) transformation.

 

[prc]

Thank you gentlemen.Then what is the significance of following:

1) Stator Leakage Reactance

2) Zero sequence reactance

3) Negative Sequence Reactance

 

[7anoter4]

First of all I'm sorry I didn't notice the first sentence of the o.p.:
"I find the following terms when referring to a turbogenerator(400MVA)data sheet."
So, as a turbogenerator has a cylindrical [not a salient pole] rotor and Xd=Xq.
Second, I translated wrong instead of "field leakage reactance " into "field losses reactance" so what I noted Xs it is actually Xla [armature-stator-leakage reactance].
I have to apologize for my bad English!
Stator leakage field is "a lost field" indeed, since it does not flow with the main flux but it remains in the air space as slot and open winding ends. This includes also the magnetic field harmonics[ as differential leakage].
The negative and zero sequence reactance are used in the connection with short-circuit case as in steady state balanced regime the generator only generate
positive sequence voltage and negative and zero sequence voltages are zero.
Nevertheless, negative sequence currents can arise whenever there is
any unbalance present in the system. Their effect is to
set up a field rotating in the opposite direction to the
main field generated by the rotor winding, so subjecting
the rotor to double frequency flux pulsations. This gives
rise to parasitic currents and heating.
If a machine is operating with an earthed neutral, a
system earth fault will give rise to zero sequence
currents in the machine. This reactance represents the
machine's contribution to the total impedance offered to
these currents. In practice it is generally low and often
outweighed by other impedances present in the circuit.
If Y point is grounded through impedance Zg , then 3*Zg
will have to be added to zero sequence impedance of generator.