2011 International Conference on Alternative Energy in Developing Countries and Emerging Economies
- 258 -
'
'
2
2
I
G
T
ABSin
Sin Sin E S
S
R
(3)
2
'
90 '
I
G
q
(4)
2
'
90 '
I
G
q
cr
and
D
I
G
q
2
90
cr
(5)
2/' 2
4
2
max
I
ABSin
SE
RS
(6)
For
cr
G
G
'
we obtain critical value of
receiving end voltage
2/'
2
I
ASin
E
crE
S
R
(7)
we relate complex power with maximum
complex power
>
@
2/' 2
'
)'
' (
max
I
G
G
I
Cos
Sin
Sin
RS
RS
(8)
Real power
R
P
and reactive power
R
Q
can
be obtained as
I
Cos S P
R R
,
I
Sin S Q
R R
(9)
Receiving end voltage is obtained as
'
)'
' (
I
G
I
ASin
Sin E
E
S
R
(10)
IV ALGORITHM
The expressions derived above are used to
plot PV and QV curve.
The algorithm used is as given below:
(i)
Compute
G
' =
G
cr
r 'G
G
cr is obtained from equation 4
'G
is change in value of
G
from 5
q
to
20
q
(ii) Compute S
R
(iii) Compute P
R
(iv) Compute E
R
(v) Plot P
R
vs E
R
(vi) For a fixed P
R
find Q
R
using power
factor angle and plot Q
R
vs E
R
III. ILLUSTRATIVE EXAMPLE
System 1
To study the loadability of a radial
transmission line we consider a 400 KV
three phase line with following parameters
[8].
A = 1
1
q
B = 100
85
q
The PV Curve is given in figure 3 [6][7].
System 2
Existing Agra-Unnao transmission line in
the state of Uttar Pradesh is taken. The line
parameters are given in table 1 [9][10].
Table 1
Parameters
Values/ Type
Sending End Voltage 400 kV
A
0.956
0.23
q
B
85.59
85.14
q
Conductor Type
Twin Moose
Line Length
275 km
.
The PV and QV curves for sample system
are plotted using the algorithm given in
section IV
V. RESULTS
PV curve for sample system has been
drawn in figure 3 for 20
q
lagging, 0
q
and 20
q
leading power factor angle. From the curve
we obtain that value of P
R
increases from
lagging to leading power factor. We also
obtain that there are two values of E
R
for a
given P
R
except at P
R
max.
PV curve for existing agra
–
Unnao
transmission line is drawn for 20
q
lagging,
0
q
and 20
q
leading power factor angle
(figure 4). From the PV curve given in
figure 4, result from derived expression the
P
R max
is 646 MW at 244 kV (20
q
lagging
power factor) and result from MATLAB
simulated version for 20
q
lagging, P
R max
is
631 MW at 240 kV.
For fixed values of P
R
, by variation
of E
R
, QV curves are plotted (figure 5). The
limiting value of reactive power (derived
expression) is obtained as -264MVr for P
R
value of 511.644 MW. The limiting value of
reactive power (MATLAB simulated
version) is obtained as -289.93MVr for P
R
value of 511.644 MW.
V. CONCLUSION
Simple analytical expression for real power
(P
R
) critical voltage (E
R
cr ) has been used
to draw PV curve and QV curve of a
