Download S13 Review (s14review13)

Review of lecture #13 (Determine parameters for generator transient model)
For a synchronous generator without damper winding model, determine Xd, X’d, and T’do.
Note: Although the “u” has been dropped from the subscript, it should be noted that these
parameters are unsaturated values. Unless otherwise noted, I will use per unit values in this
class. Only the saturation needs to be accounted for to complete the model
The test to determine these parameters consists of synchronizing a generator to the system and
adjusting the generator to produce no real load and absorb reactive power in the amount of 1020% rated MVA. Trip the unit while measuring field voltage, field current, stator voltage,
reactive generation, and speed (have controls/protection set to maintain a constant field voltage
and remain at synchronous speed). If the unit speeds up or slows down significantly on the trip,
question the assumption of no real power initially. If the field voltage changes, find out why; fix
the problem; and rerun the test. Graph the stator voltage and field current versus time. The
results should look like:
Direct axis parameter test
1.1
I_fd
1.05
Va(0-)
1
0.95
Field current (p.u.)
Stator Voltage (pu)
|V_ds|
Va(0+)
0.9
0.85
Va(inf)
Tdo’
0.8
-1
0
1
2
3
4
5
Time (s)
Review of Lecture #13
Page 1 of 2
6
7
8
9
10
Use the measured reactive power to determine id (iq should be zero with no real power).
Determine the (unsaturated) direct axis transient reactance, Xd’ from the initial change in voltage
Xd’ = {|Va(0-)| -|Va(0+)}/| id |
Determine the (unsaturated) direct axis reactance, Xd from the change from the initial to the final
voltage.
Xd = {|Va(0-)| -|Va(inf)}/| id |
Mark the time of the unit was tripped as 0 seconds. The transient open circuit time constant,
Tdo’, is determined by drawing a straight line (with a slope equal to the initial slope of Va – that
is tangent to Va). The value of Tdo’ is where this line crosses the horizontal final voltage line,
Va(inf).
Initial the machine is under-excited, so armature reaction is helping to support the flux linkages
in the stator winding. With no real power, all the flux is in the q-axis (and the induced voltage
leads by 90º – Kundar notation). Most of the flux in the “stator” field is links the rotor field.
The stator current drops to zero when the unit trips; so, the rotor field current must increase to
maintain the flux linking the rotor field winding. The initial voltage drop in the stator is from
flux in the stator winding that did not link the rotor. If the field voltage is not changed, then the
field current will decay back to its initial value; as it does the stator voltage will also decrease.
Note1: When this test is conducted on a real machine, most of the flux in the stator field links
not only the rotor field winding, but also the amortisseur winding. When the unit trips and the
stator current drops to zero, a current will develop in the amortisseur along with the increase in
field current to maintain flux through these two windings. The current in the amortisseur will
relatively quickly decay back to zero and the current in the field winding will decay back to its
original value (at a slower rate than the amortisseur). The sub-transient direct axis and reactance
and time constant may be obtained from this test.
Note2: A similar test can be conducted to determine the q-axis parameters; however, it is more
difficult to align the rotor only with the d-axis. Note that while the rotor will be aligned with the
q-axis with zero real power out, the rotor will not be aligned with the d-axis with only real power
and no reactive power. Prior to tripping the unit for this test, adjust the output to generating
small real power and absorbing a small reactive power. Trip the unit and watch the field current.
If the field current changes on the trip then the rotor wasn’t aligned solely with the d-axis. If the
field current increased repeat the test with the same real power and absorbing less reactive
power. If the field current decreased, repeat the test with the same real power and absorbing
more reactive power.
Review of Lecture #13
Page 2 of 2