Civil Engineering Reference
In-Depth Information
If the voltages at both ends of the lines are held constant in magnitude,
the receiving end real power and reactive power points plotted for several
loads would lie on a circle known as the power circle diagram. The reader
is referred to Stevenson
for further reading on the transmission line circle
1
diagrams.
13.3.2
Stability Limit
The direction of the power flow depends on the sending and receiving end
voltages, and the electrical phase angle between the two. However, the
maximum power the line can transfer while maintaining stable operation
has a limit. We derive below the stability limit assuming that the power
flows from the renewable power site to the grid, although the same limit
applies in the reverse direction as well. The series resistance in most lines is
negligible, hence, is ignored here.
The power transferred to the grid by the transmission line is as follows:
PVI
r
=
cos
φ
(13-4)
Using the phasor diagram of
Figure 13-9
,
the current I can be expressed
as follows:
PkPPL
+
2
)
−++
(
1
(
kP
2
)
d
dP
η
=
o
=
0
(13-5)
(
)
2
2
PL kP
++
o
The real part of this current is as follows:
V
⋅
sin
δ
I
=
s
(13-6)
real
X
This, when multiplied with the receiving end voltage Vr, gives the follow-
ing power:
VV
X
⋅
P
=
s
r
sin
δ
(13-7)
Thus, the magnitude of the real power transferred by the line depends on
the power angle
δ
. If
δ
> 0, the power flows from the site to the grid. On the
other hand, if
< 0, the site draws power from the grid.
The reactive power depends on (Vs-Vr). If Vs > Vr, the reactive power
flows from the site to the grid. If Vs < Vr, the reactive power flows from the
grid to the site.
δ
