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Functions
Maximum Power
Swing Frequency
144
The setting Z
is decisive for the width of the power swing polygon. This setting value
a
3504 Za is determined by the total impedance Z
equation in Figure 2-70. Z
power swing angle is valid between the machine e.m.f. and the network. Optionally,
Z
can be calculated from Z
tot
the machine e.m.f. and the unit transformer. The default setting of address 3504 Za
corresponds to the latter case. Usually, a power swing angle δ = 120° is chosen, since
the generator voltage U
ì
ì
í
Z
+Z
b
d
í
Z
+Z
b
c
î
î
Power Swing Polygon and Impedance Vectors with Power Swing Angle δ
Figure 2-70
The polygon width Z
determines also the maximum detectable power swing
a
frequency. The consideration that, at maximum power swing frequency, at least two
impedance measurements must have been carried out within the power swing
polygon, leads to the following approximative formula for the maximum detectable
power swing frequency f
Z
4
1
⋅
⋅
-- -
-- -
---------
f
=
π
P
T
Z
tot
For a rated frequency of 50 Hz (i.e. T = 20 ms), for example, the above formula
delivers:
as the maximum detectable power swing frequency.
can be calculated from the sum of Z
tot
+ Z
; in this case the power swing angle is valid between
b
c
and the system voltage U
G
Im(Z)
Z
d
Z = R + jX
Z
c
Z
a
U N
δ
-------- -
U G
Z
b
with Z
= Z
tot
b
with Z
= Z
tot
b
:
P
a
with T = a.c. period
≈
⋅
Z
0.289 Z
a
≈
f
18 Hz
P
and can be derived from the
tot
and Z
b
equal the voltage difference:
N
Z
----------------------- -
=
a
tan
with δ = 120°
---------------------------------
Z
=
a
tan
)
Re(Z
≈
Z
0.289 Z
a
1
=
+ Z
Power swing angle between
c
generator and unit transformer
(as illustrated) or
+ Z
Power swing angle between
c
generator and network
tot
C53000-G1176-C149-3
; then the
d
2 ⁄
Z
tot
(
δ 2 ⁄
)
2 ⁄
Z
tot
(
120° 2 ⁄
)
⋅
tot
7UM62 Manual
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