2011 International Conference on Alternative Energy in Developing Countries and Emerging Economies
- 257 -
PV Curves and QV Curves for Agra-
Unnao Transmission Line
Asfar A Khan, Mohd. Moaz Ansari, M.Areeb, S Al Fawaz.
Department of Electrical Engineering
Aligarh Muslim University, Aligarh
Abstract
–
Maximum power transfer through
transmission line using exact representation of
transmission line with ABCD parameters has been
used for plotting PV curve at different power
factors of the existing 275 km long Agra-Unnao
transmission line. For a fixed real power, QV
curve is plotted and the limiting value of reactive
power determined.
Key Words
:
Voltage Stability, Power Transfer,
PV Curve, QV Curve, Limiting Reactive Power
I. INTRODUCTION
Increasing loads and large inter-
utility power transfers are stressing transmission
systems to the limit. Due to economic and
environmental concerns, the efficient operation
of the power system is becoming increasingly
threatened due to problem of voltage instability
and collapse.
Voltage stability creates a serious
problem in the ability of a transmission line to
transfer maximum power, particularly with
higher VAR demand [1].QV and PV curves are
the most widely used voltage stability analysis
tools today. The PV curve is formed by varying
system load or transfer and plotting it against
voltage. The PV curve can provide real power
and voltage margins using the knee of the curve
as reference point. It is used in control centers
where the complexity of QV curve is impractical
[2]. PV Curves at constant power factor are used
to get maximum power transfer at critical
voltage .QV curves are plot of voltage at a bus to
the reactive power at the same bus. The value of
Q is obtained for a given power factor and real
power. The curve provides knowledge of
limiting values of reactive power and closeness
to point of instability [3] [4][5].
Analytical expression using
exact representation of transmission line
with ABCD parameters is suitably used for
finding complex power, real power, reactive
power [6]. The application of PV and QV curve
in voltage stability studies are enormous. Many
proximity indicators are identified using PV and
QV Curves [3][4],[5].
II. LOADABILITY OF A
RADIAL
TRANSMISSION
LINE
LIMITED BY VOLTAGE STABILITY
A radial transmission
line is shown in figure 1 in which a
generator with a constant voltage E
S
G
supplying complex power S
R
to a load with a
terminal voltage E
R
0 through a
transmission line represented by its ABCD
parameters.
Complex power at the
receiving end of a transmission line shown
in figure 1 is given as
)
1(
2
δ β
B
RESE
α β
B
RAE
RS
The above equation (1) represents a circle
for varying value of
G
with position of
centre indicated by
αβ
B
AE
R
2
and
radius by
B
EE
R S
Where
A
= A
D
and
B
= B
E
are the
line constants and
G
is power angle
In figure 2, using properties of similar
triangles, trigonometrical identities and
basic mathematics we get
D
G
G
'
(1)
I
D
E
I
q
180 '
(2)
I
is the power factor angle and is positive
for lagging power factor and negative for
leading power factor
The expressions for S
R
, S
R max
, E
R
, E
R cr
, P
R
and Q
R
are obtained [6], [7]
