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CHAPTER 7
ATC ENHANCEMENT BY SERIES AND
SHUNT COMPENSATION
7.1
INTRODUCTION
Deregulation of power system around the world is aimed at
providing non discriminatory and fair participation of all the market players.
The transmission system being the natural monopoly should have the
adequate capacity to meet all the transaction requirements. The economic
efficiency of the restructured power system can be realized by
accommodating all the transactions without violating system operating limits.
The power transaction between an interface is limited by factors such as
thermal limits of the branches and bus voltage limits. In spite of having
adequate power generation to meet the power demands the system bottlenecks
restricts the transactions. These bottlenecks can be resolved by providing
series compensation at few branches which in turn reroute the power to the
sink buses. Hence the ATC of an interface can be enhanced without
overloading the branches. The limitation due to the bus voltage limits can be
solved by reactive power injections at the weak buses. This chapter proposes
a SVM based model to estimate the degree of series and shunt compensation
needed to obtain the desired ATC value at a given operating condition.
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7.2
BASIC PRINCIPLE OF COMPENSATION IN TRANSMISSION
SYSTEM
Figure 7.1 shows the simplified model of a power transmission
system. Two power grids are connected by a transmission line which is
assumed lossless
Figure 7.1 Power transmission system simplified model
The expression for the current in the transmission line is given by
V1
I
1
V2
2
(7.1)
jX L
The active power and reactive power at bus 1 are given by:
V1V2 sin
,
XL
P1
where
=
1
-
Q1
V1 (V1 V2 cos )
XL
(7.2)
2
The active power and reactive power at bus 2 are given by:
P2
V1V2 sin
,
XL
Q2
V2 (V2 V1 cos )
XL
(7.3)
Equations (7.1) through (7.3) indicate that the active and reactive
power flow can be regulated by controlling the voltages, phase angles and line
impedance of the transmission system.
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7.2.1
Shunt Compensation
Shunt compensation, especially shunt reactive compensation has
been widely used in transmission system to regulate the voltage magnitude
and enhance the system stability.
A simplified model of a transmission system with shunt
compensation is shown in Figure 7.2. The voltage magnitudes of the two
buses are assumed equal as V and the phase angle between them is . The
transmission line is assumed lossless and represented by the reactance XL. At
the midpoint of the transmission line a controlled capacitor C is shunt
connected. The voltage magnitude at the connection point is maintained as V.
Figure 7.2 Transmission system with shunt compensation
As discussed previously, the active powers at bus 1 and bus 2 are
equal.
P1
P2
V2
2
sin
XL
2
(7.4)
The injected reactive power by the capacitor to regulate the voltage
at the mid-point of the transmission line is calculated as
Qc
V2
4
(1 cos )
XL
2
(7.5)
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7.2.2
Series Compensation
Series compensation aims to directly control the overall series line
impedance of the transmission line.
A simplified model of a transmission system with series
compensation is shown in Figure 7.3. The voltage magnitudes of the two
buses are assumed equal as V and the phase angle between them is . The
transmission line is assumed lossless and represented by the reactance XL. A
controlled capacitor is series-connected in the transmission line with voltage
addition Vinj.
Figure 7.3 Transmission system with series compensation
Defining the capacitance of C as a portion of the line reactance,
Xc = kXL
(7.6)
The overall series inductance of the transmission line is,
X
XL
Xc
(1 k)X L
(7.7)
The active power transmitted is ,
P
V2
sin
(1 k)X L
(7.8)
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The reactive power supplied by the capacitor is calculated as:
Qc
7.3
V2 k
(1 cos )
X L (1 k)
(7.9)
ATC ENHANCEMENT BY SHUNT COMPENSATION
The bus voltage is one of the important limiting factors for ATC.
The transmission system may not be utilized to its maximum capacity due to
the poor voltage profiles at few buses. Hence the ATC can be enhanced by
maintaining good voltage profile at all buses irrespective of the loading
conditions. Reactive power injections at the weak buses will help in
maintaining the voltage profile. The theory of shunt compensation is
explained in the section 7.2.1. Identification of weak bus and the estimation of
amount of reactive power to be injected to obtain the desired ATC value are
the major problem in shunt compensation. This chapter proposes a method to
estimate the shunt compensation required to get the desired ATC for an
interface.
7.4
ATC ENHANCEMENT BY SERIES COMPENSATION
The feasibility of a proposed transaction through an interface will
be decided based on the availability of adequate transmission capacity. In an
interconnected power system the power sharing between the branches is based
on their respective impedance values. Assume an interface between the source
and sink bus is connected by two paths. Let the path 1 is having lesser
impedance compared to path 2. The maximum share of power that is injected
at the source bus will tend to reach the sink bus through path 1. This in turn
may over load one or more branches in that path. Hence the ATC between the
given interface is restricted by the thermal limits of few branches of path 1.
But the ATC between the given interface can be enhanced by achieving
proper sharing of power between the paths. The sharing of power can be
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controlled by changing the value of reactance of the paths. The basic principle
of series compensation is explained in section 7.2.3. This chapter proposes a
method to estimate the degree of compensation required to obtain the desired
ATC for an interface.
7.5
SELECTION CRITERIA FOR COMPENSATION
Selection of type of compensation, identification of location for
reactive power compensation and degree of compensation required are the
major tasks in ATC enhancement. The ATC of the given operating condition
will be estimated using the RPF algorithm. The limiting factor is identified
from the RPF results. Shunt compensation is selected if the voltage
magnitudes are the limiting factor and the series compensation is chosen if the
line loading is the limiting factor. RPF is conducted with a particular degree
of compensation and the respective ATC is obtained. This value will be
treated as desired ATC. The loading condition and the desired ATC are
selected as inputs and the degree of compensation will be the output. Data
patterns are obtained in two ways. First method for a given operating
condition degree of compensation is varied and the respective ATCs are
obtained. In second method both operating conditions and degree of
compensation are changed. SVM model is developed using the data patterns
generated.
The proposed AI model will estimate the degree of compensation
required to obtain the desired ATC value for a given operating condition.
7.6
ALGORITHM FOR DATA GENERATION
Step 1.
Select an operating condition
Step 2.
Run Repeated Power Flow (RPF) and obtain the ATC value for a
given interface.
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Step 3.
Identify the limiting factor which limits ATC
Step 4.
If the bus voltage is the limiting factor inject reactive power at the
weak buses by some value.
Step 5.
Run RPF and obtain ATC with reactive power injection. This ATC
is considered as desired ATC
Step 6.
A data set is formed with the loads at buses, the desired ATC as
inputs and the degree of compensation as output.
Step 7.
Steps 1-6 are repeated to obtain more number of data sets with
different loading conditions and with different degree of
compensation.
Step 8.
If the line loading is the limiting factor, provide series
compensation at the alternate path and obtain ATC value by
conducting RPF. This value is considered as desired ATC
Step 9.
For some loading conditions both series and shunt compensation is
provided simultaneously and the respective ATC values are
obtained.
More number of data sets is generated by repeating the steps 1-9.
The loading condition, the source bus injections and the desired ATC are
inputs. The required degree of series and shunt compensation will be the
output. SVM model is developed using the data sets generated.
7.7
SYSTEM STUDIES AND RESULTS
IEEE 24 bus Reliability Test System is used to test the feasibility of
proposed method. The interface considered is connected between the source
bus 23 and sink bus 3. The weak buses are identified as 3 and 24. The reactive
power is injected at these weak buses and the ATC obtained with reactive
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injections are obtained by conducting RPF. V3 and V24 are the voltage
magnitudes at buses 3 and 24 respectively.
From the off-line power flow studies it is observed that 24-3 is the
limiting line which hits the MW limit. To enhance the ATC without
overloading the line 24-3 the series compensation is provided at the alternate
path connected by the lines 16-14, 14-11, 11-9 and 9-3. This in turn increases
the power sharing of the alternate path and reduces the power flow through
the limiting line and hence enhances the ATC.
Table 7.1 shows the degree of shunt compensation required to
obtain the desired ATC for a given operating condition. The results of SVM
model is compared with RPF results.
Table 7.1 Comparison of shunt compensation required to obtain desired
ATC estimated by RPF and SVM
Compensation
Compensation
Limiting
Actual Desired
obtained
using
RPF
obtained
using SVM
factor
Data
ATC ATC
obtained
set No
Shunt (MVAr)
Shunt (MVAr)
(MW) (MW)
using RPF Bus 3
Bus 24
Bus 3
Bus 24
1
70
210
V24
45
50
49
53
2
120
355
V3 .
80
65
85
61
3
140
275
V3
65
45
61
49
The voltage magnitude at 3rd bus without compensation was 0.9 p.u
for 120 MW increase in the demand at the sink bus. With the compensation
at 3rd and 24th buses as given in Table 7.1 the voltage magnitude at 3rd bus
is1.103 p.u for the same 70MW increase in the demand at the sink bus. As the
voltage magnitude is above 0.9 p.u demand is increased further. ATC with
compensation is found to be 355MW.
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From the off-line power flow studies it is observed that 24-3 is the
limiting line which hits the MW limit. To enhance the ATC without
overloading the line 24-3 the series compensation is provided at the alternate
path connected by the lines 16-14, 14-11, 11-9 and 9-3. This in turn increases
the power sharing of the alternate path and reduces the power flow through
the limiting line and hence enhances the ATC.The percentage of series
compensation required to get the desired ATC is estimated by RPF method
and SVM model. The results are presented in Table 7.2.
Table 7.2 Comparison of series compensation required to obtain desired
ATC estimated by RPF and SVM
Data set
No
4
5
6
Actual Desired Limiting factor
obtained using
ATC
ATC
RPF
(MW) (MW)
90
130
120
210
225
195
line loading 24-3
line loading 24-3
line loading 24-3
Compensation
obtained using
SVM
Series
%
% compensation
compensation
55
49
45
51
30
27
Compensation
obtained using
RPF
Series
From the Table 7.2 it is observed that the ATC between an interface
can be enhanced by providing series compensation at the branches of alternate
path. For data set 4, the possible increase in demand (ATC value) at the sink
bus load is limited to 90MW by the line loading limit of the branch 24-3.
For data set 4, the power flow through the branch 24-3 is 392 MVA
for the ATC of 90MW. The ATC can be enhanced by providing the series
compensation at the alternate path. The alternate path for the interface 23-3 is
connected by the lines 16-14, 14-11, 11-9 and 9-3. 55% of series
compensation is provided at these lines to increase the ATC to 210MW. The
power flow through the lines 16-14, 14-11, 11-9 and 9-3 without
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compensation is 246MW, 147MW, 125MW and 37MW for the ATC of
90MW. As the series compensation reduces the reactance the power flow
through these branches with compensation is found to be 365MW, 310MW,
115MW and 55MW and the ATC is increased to 210MW.
Table 7.3 Comparison of series and shunt compensation required to
obtain desired ATC estimated by RPF and SVM
Compensation
Compensation
obtained
using
RPF
obtained
using SVM
Limiting
Actual Desired
Shunt
Shunt
factor
Data set
ATC ATC
Series
Series
No
obtained
(MVAr)
(MVAr)
(MW) (MW)
using RPF
%
Bus Bus
Bus Bus
%
compensation 3 24 compensation 3 24
7
90
300
V3, V24.
45
110 95
43
115 46
and line
loading24-3
8
70
350
V3 , V24.
55
130 110
58
137 119
and line
loading24-3
9
260
510
V3 , V24.
30
80 65
24
83 68
and line
loading24-3
From the Table 7.3 it is inferred that some operating conditions
require both series and shunt compensation to get the desired ATC. From the
values of degree of compensation obtained by RPF method and SVM model it
is inferred that the SVM model can estimate the degree of compensation
accurately.
Table 7.4 Comparison of Computation time (in secs)
Test case
RPF
SVM
1
1.104
0.0045
2
0.986
0.0052
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From the Table 7.4 it is observed that the computation time of SVM
model is much lesser than the RPF method. The proposed SVM model
estimates the degree of compensation accurately in lesser computation time.
Therefore it is suitable for real time operation of large scale power systems.
7.8
CONCLUSIONS
The economic efficiency of restructured power system is greatly
depends on transaction management. The adequate transmission capacity to
meet all the proposed transactions is essential to realize this. The transmission
capacity or ATC of an interface will often be limited by the system bottle
necks. The series and shunt compensation enable the system operators to
utilize the transmission capacity to its maximum value. The effectiveness of
the proposed SVM model was tested and validated on IEEE 24 bus RTS. The
results obtained from SVM model were reasonably accurate and the
computation time of SVM model was much lesser than the RPF method.