Congestion Management in Power Transmission Lines with Advanced
Control Using Innovative Algorithm
BALA SAIBABU BOMMIDI1, BADDU NAIK BHUKYA2
SWARUPA RANI BONDALAPATI3, HEMANTH SAI MADUPU4
1,2&4Department of Electrical and Electronics Engineering,
Prasad V. Potluri Siddhartha Institute of Technology, Vijayawada, Andhra Pradesh, INDIA
3Department of Electrical and Electronics Engineering,
Velagapudi Ramakrishna Siddhartha Engineering College, Vijayawada, Andhra Pradesh, INDIA
Abstract: It can be challenging to allocate all the necessary power to a supply in a modern power system if
the power lines are overloaded. The conventional power system, monitored by flexible AC transmission
system (FACTS) controllers, is one answer to this issue because it can increase the electrical power system's
ability to deal with rapid variations in working circumstances. The advanced interline power flow controller
using a constriction factor-based particle swarm optimization (CFBPSO) algorithm (AIPFC) was proposed in
this paper as an optimal power flow control for controlling congestion in transmission lines. When
comparing the performance of single-line and multi-line FACTS controllers, the latter is shown to be more
effective overall. This paper presents a comprehensive model of an advanced interline power flow controller
(AIPFC) and explores the effect of situating the controller in the most advantageous physical location. To
address OPF concerns when using state-of-the-art IPFC, a novel algorithm, CFBPSO, is proposed. A
traditional IEEE 30 bus test system is used to verify the proposed method. A standard IEEE 30 bus test
system is used to verify the accuracy of the proposed method. In their paper, the researchers show that their
proposed algorithm works by showing that the value of the objective function goes down.
Keywords: Congestion management, Optimal Power Flow (OPF), Flexible AC Transmission System
(FACTS), Constriction Factor Based Particle Swarm Optimization (CFBPSO) and Advanced Interline Power
Flow Controller (AIPFC).
Received: September 9, 2021. Revised: September 11, 2022. Accepted: October 16, 2022. Published: November 8, 2022.
1. Introduction
Power companies have to increase their
production in response to rising global demand for
electricity. The amount of electrical power that
can be transmitted between any two nodes in a
transmission network is, however, constrained by
a number of transfer limits, including thermal
limits, voltage limits, and stability limits. Once
that threshold is hit, we say that the system is
congested. Maintaining power system security
requires constant vigilance to prevent outages that
could have far-reaching social and economic
effects if not kept within acceptable parameters.
Perhaps the most basic challenge of transmission
management is congestion management or
regulating the system so that transfer limits are
respected [1]–[3]. Normal methods for dealing
with congestion include rescheduling generator
outputs, providing reactive power support, and
imposing physical limits on transactions. System
operators typically prefer the former and only
resort to the latter.
Several methods for dealing with traffic jams
have been detailed in published works [4].
Multiple models are discussed in [5] for dealing
with the economic viability of the energy market
and the transmission system's myriad dealings,
interactions, and constraints. Methods for
reducing traffic congestion in a range of
electricity markets are detailed in [6]. The issue of
voltage stability is addressed by congestion
management in [7]. In [8], the authors show the
best way to set up a power system's topology so
that it can be used to manage congestion.
There is existing research on multiple
transaction systems that explores congestion
management schemes based on optimal power
flow (OPF). Congestion and service costs can be
reduced using the method proposed in [9], which
is based on optimal path finding (OPF). In [10],
the possibility of power generators and system
operators coordinating via load flow analysis via
Benders cuts is discussed. Congestion caused by
voltage instability and thermal loads is reduced by
the method proposed in [11]. Standard solvers can
also solve this because it employs OPF. In [12]-
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DOI: 10.37394/232016.2022.17.35
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[13], a zonal model is proposed that is based on
the circulation of air conditioning loads. In [14],
the authors use the sensitivity of line flow to
modifications in generation to alleviate
congestion, but they make no attempt to decrease
the number of generators implicated. In [15], a
method is proposed for selecting the participating
generators that takes into account both their bids
and their sensitivity to the current flow on a
crowded line. The concept of relative electrical
distance (RED) is introduced as a means of
rescheduling actual power generation to reduce
overload. This method is supposed to increase
stability margin by reducing system losses and
keeping a more constant voltage across the board.
While rescheduling costs and individual
generation unit bids are considered elsewhere,
they are not included here The output values of
generators that have the same RED but separate
price bids must be rescheduled to reduce the
overall rescheduling cost. [16] Does not attempt to
solve this issue.
Because of their superior performance and
reliability, FACTS devices [17] are favored in
modern power systems. The unified power flow
controller (UPFC) and the intelligent power factor
corrector (IPFC) are two examples of combined
compensators that are among the most powerful
and flexible FACTS devices. The two voltage-
sourced switching converters (VSCs) in a UPFC
share a common DC voltage link, allowing for
separate active and reactive power flow
regulation. IPFC, on the other hand, can
compensate for multiple transmission lines at a
given substation because its VSCs are connected
in series with different lines, whereas UPFC is
limited to controlling the power flow of a single
line. Optimal power flow control and power flow
control utilizing IPFC necessitate accurate
mathematical modeling of this FACTS device.
IPFC injection models and transmission lines with
IPFC built in are created using the mathematical
model shown in [22], just as UPFC injection
models are frequently used [18]-[20] and the exact
pi-model of UPFC-inserted transmission lines can
be found [21].
This paper's goal is to investigate whether or
not the particle swarm optimization method,
which is based on the concept of a "congestion
factor," can be used to effectively address the
issue of congestion management. A mathematical
optimization problem is used to represent the
clogged system. Methods for solving OPFS that
have been around for a while typically use search
directions calculated from the derivative of the
function. As a result, it is crucial to formulate the
problem as a continuously differentiable function;
otherwise, the effectiveness of these techniques
will be diminished. In this paper, we use a particle
swarm optimization strategy based on the
constriction factor to solve this problem.
Optimization algorithms typically refer to the
value of the objective function as the fitness
function and the binding constraints as the penalty
functions. In particular, it has many drawbacks
because the penalty variables are assigned
empirically and are heavily dependent on the test,
as is typical. In this paper, however, we take a
fresh approach to addressing these constraints by
employing restriction factor-based particle swarm
optimization. This paper uses the IEEE 30 bus
system to prove that the envisaged technique for
congestion management works.
2. Advanced Interline Power Flow
Controller (AIPFC)
The IPFC is a flexible replacement for the UPFC
and the SSSC because it employs at least two
converters and controls power flows over several
lines. Transmission network congestion
management is a challenging problem that may be
tackled with the help of the IPFC. So, the author is
inspired to come up with a new model for IPFC
that can be used in power flow analysis.
In general, the current steady-state models can
be split up into two categories: decoupled and
coupled. As part of a decoupled model, the
FACTS devices are replaced by a made-up PQ or
PV bus, resulting in a different Jacobian matrix
structure. Power injection models (PIM) [24]–[26]
and voltage source models (VSM) [23] and [27]–
[29] are the two main components of a coupled
model. Furthermore, dealing with the practical
limitations imposed by FACTS devices is
significant issue [30] .The power flow software in
the papers didn't say anything about how IPFC's
limitations are dealt with.
This paper introduces a new IPFC Power
Injection Model to analyze power flow. This
model takes into account both the line charging
susceptance and the impedance of the series
converter transformer. It is demonstrated that the
admittance matrix's original structure and
symmetry can be maintained, thus allowing the
Jacobian matrix to keep its block-diagonal
properties and facilitating the application of a
sparsity technique. When making changes to the
network state variables, it's also necessary to make
corresponding changes to the IPFC's state
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2022.17.35
Bala Saibabu Bommidi, Baddu Naik Bhukya,
Swarupa Rani Bondalapati, Hemanth Sai Madupu
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variables. In addition, the model can account for
IPFC's real-world limitations, and we show how
to do so in detail using Newton power flow. [31]-
[32].
2.1 Intuitive Model of the AIPFC
An AIPFC with many series converters can use
the numerical induction method.
Fig. 1: The AIPFC equivalent circuit
and :The complex
bus voltages at buses in and jn
and :The complex currents
injection at buses in and jn
: The complex
controllable series injected voltage
: The series transformer
impedance
: The line series
impedance
: The line charging susceptance
From Figure 1:
nnnnn tseiseiVZIVV
(1)
2
10
101
B
jV
Z
VV
III n
n
nn
nt
l
rt
i
(2)
nnn jlt VZIV 1
(3)
(4)
Where
2
2
10
10
B
jV
jB
V
Z
V
In
nj
j
ab
ab
ab
(5)
2
10
1
B
jVII nn jj
(6)
nnnnn ljljt ZIZ
B
jVV
2
110
(7)
2
2
10
10
10
jB
V
jB
V
Z
V
II n
nt
t
cd
cd
cd
(8)
242
10
2
1010
10
B
jZI
B
ZV
jB
VI nnnn ljnljj
(9)
2
1
4
10
2
10
10
B
jZI
B
ZjBVI nnnn ljnlji
(10)
4
2
10
10
B
ZjBDn
l
and
2
110
B
jZE n
l
nnnn ljjt ZIEVV
(11)
EIDVI jnji nn
(12)
nn
nn
nn
n
nn
n
lse
sej
lse
i
lse
se
jn
ZEZ
EDZV
ZEZ
V
ZEZ
V
I
(13)
nn lse ZEZN
and
EDZM n
se
N
V
N
V
N
M
VI nn
n
sei
jjn
(14)
N
E
V
N
E
V
N
EM
DVI nnnn seiji
(15)
Equation (14) and (15) can also be written in
matrix form as
n
n
n
n
n
nn
nn
n
nse
ji
ii
j
i
jjji
ijii
j
iV
W
W
V
V
AA
AA
I
I
(16)
Where
N
E
An
ii
,
N
M
An
jj
,
N
ME
DA n
ij
,
N
An
ji
1
N
E
Wn
ii
,
N
Wn
ji
1
nn jiij AA
(17)
nnn iii VV
nnn jjj VV
n
i
I
n
j
I
nnn sesese VV
nnn sesese jXRZ
nnn lll jXXZ
10
B
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DOI: 10.37394/232016.2022.17.35
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Volume 17, 2022
0
nnn iijii AAA
,
N
ME
DAn
i
1
0
0
nnn jjijj AAA
,
N
NM
DA n
j
0
(18)
nnnn
n
nseisei
l
se
iVV
H
X
B
P
sin
2
110
(19)
nnnn
n
nseisei
l
se
iVV
H
X
B
Q
cos
2
110
(20)
nn
nn
nsej
sej
se
jH
VV
P
sin
(21)
nn
nn
nsej
sej
se
jH
VV
P
cos
(22)
Where
nnn llse XX
B
XH
2
110
0
nnnnnn iiijriij AVAVVI
(23)
0
nnnnnn jjijijji AVAVVI
(24)
nnnnnn ijjiijiij VV
H
IVP
sin
1
Re *
(25)
H
VVVX
B
IVQ
nnnnn
nnn
ijjiil
ijiij
cos
2
1
Im
2
10
*
(26)
nnnnnn jijijijji VV
H
IVP
sin
1
Re *
(27)
*
Im nnn jijji IVQ
24
cos
10
2
10
10
nn
nn
nnn
n
n
ll
sej
jiij
j
ji
XBXB
BXV
VV
H
V
Q
(28)
nexdc n
PP 0
(29)
0
sin
2
1
sin
4
10
2
10
10
H
VV
XB
VV
H
G
XB
BP
nnnn
n
nnnn
n
n
isesei
l
jsejse
l
ex
(30)
2
1
2
1
410
10
2
10
10 B
X
B
X
B
XBX
Gn
n
nn
l
l
lse
3. Particle Swarm Optimization
In 1995, Kennedy and Eberhart [33] introduced
the evolutionary algorithm known as particle
swarm optimization. Fish schooling and bird
flocking are two examples of social behaviour in
nature that serve as inspiration. A flock of birds
has been seen to discover food sources in an area
through a random process. In a flock, some
members may know the general area around the
food source, but everyone knows the general area
around the food source (the food). In order to find
food quickly and easily, it is best to start your
search near your current best position.
PSO is an alternative to more common
optimization algorithms because it does not
require knowing the derivative of functions used
in the model. If fitness values for the optimization
model can be calculated, then the algorithm will
work. Also, the PSO algorithm is based on a lot of
deep thinking, but it is still easy enough for non-
experts to understand.
Several power system optimization issues have
already benefited from PSO's application. The
economic dispatch of power plant generators is a
problem addressed by PSO in [34]. In [35], a
method for regulating voltage and reactive power
was proposed for ensuring the reliability of power
grids. It has been discussed in [36] how PSO can
be used for congestion management with a focus
on sensitivity. But it does not explain how
constraints are dealt with in any detail.
3.1 Constriction Factor Based PSO
(CFBPSO)
The following equation can be used to adjust the
speed of each actor:
)(*
)(*
22
11
1
k
i
k
ii
k
i
k
i
sgbestrandc
spbestrandcwvv
(31)
iteriterwwww *))/()(( maxminmaxmax
(32)
11 k
i
k
i
k
ivss
(33)
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The equations [(31), [(32), and [(33)] that
make up the PSO system can be interpreted as a
difference equation. It is possible to investigate
the dynamics of the system or the search
procedure by examining the eigen values of the
difference equation.
)](*
)(**[
22
11
1
k
i
k
ii
k
i
k
i
sgbestrandc
spbestrandcvKv
(34)
,
42
2
2
K
4,
21
cc
(35)
where
and K are coefficients.
For example, if
=4.1, then K = 0.73. As w
increases above 4.0, K gets smaller.For example,
if
=5.0, then K =0.38, and the damping effect is
even more pronounced.
Users of the restriction factor method tend to
converge in the long run. Contrary to other
evolutionary computation approaches, the
constriction factor approach theoretically
guarantees the search procedure's convergence.
Since this is the case, the restriction factor
approach can yield superior results compared to
the standard PSO method. Contrarily, the dynamic
behaviour of a single individual and the impact of
inter-individual interactions are not taken into
account by the restriction factor approach. That's
why CFBPSO is able to produce higher-quality
results than the standard PSO method.
4. Formulation of the Congestion
Management Problem
Optimal control settings in a power network
are found by solving the optimal power flow
(OPF) problem, a static non-linear constrained
optimization problem. To do this, it
simultaneously optimises for a set of objective
functions while trying to minimise the network's
equality and inequality constraints.
The optimal power flow problem is an
example of a nonlinear optimization issue that can
be written as:
Minimize f(x)
Subject to h(x)=0
g(x)≤0 (36)
The corresponding mathematical expression is as
follows.
Ng
iGiiGiii PaPbcxc
1
2
minmin
(37)
0cos
1
ijijijj
nb
jiDiGi YVVPP
(38)
0sin
1
ijijijj
nb
jiDiGi YVVQQ
(39)
maxmin GiGiGi PPP
i=1,…,NG (40)
maxmin GiGiGi QQQ
i=1,…,NG (41)
maxmin DiDiDi PPP
i=1,…,NG (42)
maxmin DiDiDi QQQ
i=1,…,NG (43)
maxmin iii VVV
i=1,…,NL (44)
maxmin iii TTT
i=1,…,NT (45)
max
ii SS
i=1,…,nl (46)
5. Results and Discussion
Power systems face serious challenges due to
network congestion. This problem is due to
system overload. This section describes the end
result of applying CFBPSO to locate a state-of-
the-art IPFC model in an optimal spot to
simultaneously reduce expected costs. The
proposed technique was successfully implemented
on the IEEE 30 bus test system. A slack bus (Bus
2), PV buses (Bus 5, 8, 11, and 13), and load
buses (Bus 3-6) make up an IEEE 30 bus test
system with six generators. A total of 41 lines and
283.40 MW are needed to power the system. The
generator can be adjusted in a number of ways,
including its active power outputs, terminal
voltages, tap settings on the transformer, and
shunt compensations. The results of a MATLAB
calculation of the load flow for the IEEE 30 bus
test system are presented. The only thing you need
to worry about with a sophisticated IPFC model is
where to put the load buses. We present the results
of an analysis of peak demand that reveals the
presence of transmission bottlenecks. Where
traffic jams have formed due to an increase in the
use of load buses. Simulation studies are
conducted in three distinct scenarios (base case,
overload, and contingency) to demonstrate the
efficacy of the proposed CFBPSO algorithm with
AIPFC.
The OPF results obtained using the proposed
strategies are presented in comparison to some of
the most popular current writing methods in
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Figure 2. When compared to other strategies, it is
clear that the proposed CFBPSO strategy provides
superior results.
Fig. 2: Comparison of Fuel Costs
Case a: Base case condition
For the baseline scenario, the optimal power
system scheduling is determined by employing the
proposed CFBPSO with AIPFC. Reduced fuel
costs for the generator are the objective function
under consideration. Table 1 shows the optimum
values for the control variables in the base case
scenario when using CFBPSO with AIPFC.
Through CFBPSO, the AIPFC method yields a
lower generator fuel cost than the Newton
Raphson (NR) method, at 799.904$/hr. All of the
solutions found also meet the limits for the control
variables and the flow through the transmission
lines.
Table 1. Using the CFBPSO with the AIPFC with
the optimal settings for the base case scenario.
Variables
NR
CFBPSO
with AIPFC
Real
Power
Generation
PG1
159.29
177.66
PG2
58.12
48.82
PG3
12.87
21.34
PG4
18.71
12
PG5
22.42
21.33
PG6
21.1
11.15
Generator
Voltages
VG1
105
105
VG2
104.5
95.05
VG3
101
95
VG4
105
110
VG5
101
95
VG6
105
110
Loss (MW)
9.11
8.9
Cost ($/hr)
809.211
799.904
Case b: Congestion due Overloading
Overloading the system causes congestion, and
that's what this section is about. The proposed
approach has been tried and true under 10% load,
15% load, and 20% load.
A breakdown of the overloaded lines and the
associated power violations can be seen in Table
2. Assuming a 10% increase in the base load, the
first case displays 311.74 MW. Load readings in
the second scenario show 325.91 MW, which is
equivalent to an increase in base load of 15%. A
load of 340.08 MW was achieved in the latter
case; this represents an increase in base load of
20%. The line flow limit of 130 MW is not
exceeded by Lines 1-2 under the base case
conditions, i.e. with a load of 283.4 MW. The
simulation results demonstrate that conditions 1-2
are always not met.
Two of the 30 bus lines are linked to the other
two lines, 3 and 4. For this reason, we use two
scenarios to evaluate AIPFC placement.
Congestion between buses is measured and found
to be worst between lines serving buses 3-4 and 4-
12 across all test cases. Thus, AIPFC is best
installed along routes 3–4 and 4–12, which
correspond to certain bus lines. Congestion can be
reduced if AIPFC is located strategically.
Table 2. Power flows under various over-
burdening states of IEEE-30 bus system
Over loaded
line
Load
increment
in (%)
Power
flow
Limit
(MVA)
Power
flow
(MVA)
From
bus
To
bus
1
2
10
130
141.052
1
2
15
130
142.206
1
2
20
130
148.421
Fig. 3: Power flows in 10% loading situation
798
799
800
801
802
803
804
805
Fuel Cost ($/hr)
Methods
Comparison of Fuel Costs
Fuel Cost
($/hr)
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Volume 17, 2022
Fig. 4: Power flows in 15% loading situation
Fig. 5: Power flows in 20% loading situation
Table 3. Rundown of power flows of over-burden
lines under over-burdening utilizing CFBPSO
with AIPFC
Fig. 6: Rundown of power flows of over-burden
lines under over-burdening utilizing CFBPSO
with AIPFC
This proves that the OPF problem can be
solved by the CFBPSO using the AIPFC method
while fulfil constraints on dependent variables and
the flow limit in the transmission line. As can be
seen in Table 3 and Figure 6, the CFBPSO with
AIPFC method effectively reduces congestion
under overloading conditions.
Case c: Contingency Analysis
Congestion in transmission due to line failures is
discussed here. A potential risk assessment for the
IEEE 30 bus system is presented in Table 4. It is
assumed in the simulated world of congestion
scenarios that lines 1-2, 1-3, 3-4, and 2-5 are all
clogged at the same time. The contingency
analysis shows that lines 2-5 are severely
overloaded due to the outages of lines 1-2, 1-3, 3-
4, and 2-5.
Table 4. Analysis of Power flows under
contingency for IEEE 30-Bus System
Outage
of lines
Effected
lines
Power flow
limit
(MVA)
Power
flow
(MVA)
1-2
1-3
130
195.872
3-4
130
183.793
4-6
90
112.914
1-3
1-2
130
188.395
3-4
1-2
130
185.580
2-5
2-6
65
76.123
5-7
70
85.611
Table 5. Power flow under the particular four
network contingencies
S.
No.
Line
Limit
(MVA)
Power flow (MVA)
1-2
Line
outage
1-3
Line
outage
3-4
Line
outage
2-5
Line
outage
1
130
0
188.395
185.580
95.4973
2
130
195.872
0
2.6188
74.2383
3
65
34.762
59.926
58.726
54.799
4
130
183.793
2.525
0
69.3582
5
130
47.139
71.969
71.5525
0
6
65
22.536
64.103
63.1952
76.123
7
90
112.914
25.806
26.6306
86.3644
8
70
33.243
10.921
11.0494
85.611
9
130
51.183
25.353
25.7554
102.185
10
32
24.931
26.254
25.8779
24.0598
11
65
23.636
23.575
23.5338
23.4111
12
65
32.853
35.070
35.0258
33.1501
13
65
23.990
24.316
24.2401
23.4113
14
32
9.261
8.820
8.82701
9.19174
Lines
Load
increment
in (%)
Power flow
Limit
(MVA)
Power flow
with AIPFC
using CFBPSO
1-2
110
130
114.021
1-2
115
130
121.742
1-2
120
130
129.318
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2022.17.35
Bala Saibabu Bommidi, Baddu Naik Bhukya,
Swarupa Rani Bondalapati, Hemanth Sai Madupu
E-ISSN: 2224-350X
360
Volume 17, 2022
15
32
23.120
21.282
21.309
22.8107
16
32
12.141
10.287
10.3139
11.8284
17
16
2.721
2.362
2.36739
2.66655
18
16
7.961
6.289
6.31224
7.66939
19
16
8.376
7.308
7.32373
8.19141
20
16
4.941
3.976
3.98968
4.77237
21
32
5.191
6.349
6.33135
5.38504
22
32
7.588
8.752
8.73404
7.78277
23
32
2.892
4.876
4.84277
3.13201
24
32
18.297
18.538
18.5331
18.3273
25
32
8.641
8.802
8.7982
8.66193
26
32
2.752
2.581
2.5849
2.73815
27
16
8.427
7.510
7.52332
8.28954
28
16
5.882
6.327
6.31837
5.94816
29
16
4.725
3.952
3.96174
4.6038
30
16
2.160
1.659
1.66323
1.97658
31
16
4.267
4.267
4.26652
4.26649
32
16
5.353
5.573
5.56894
5.33215
33
16
6.420
6.419
6.41931
6.41932
34
16
7.295
7.295
7.29446
7.29448
35
16
3.755
3.755
3.75523
3.75523
36
32
4.318
4.553
4.46981
4.0831
37
32
15.487
16.128
16.1301
15.6469
38
65
12.723
15.143
15.0882
13.2111
39
32
9.173
10.729
10.7071
9.49283
40
65
31.102
26.524
26.5303
29.6023
41
65
15.690
16.544
16.5332
15.8535
Table 6. Line flow with AIPFC & CFBPSO
S.No
Line
Limit
(MVA)
Power flow (MVA)
1-2
Line
outage
1-8
Line
outage
8-11
Line
outage
2-5
Line
outage
1
130
0
99.78
93.59
34.19
2
130
102.56
0
2.84
45.29
3
65
20.92
47.88
45.80
40.62
4
130
83.40
2.78
0
41.70
5
130
42.46
56.76
55.36
0
6
65
22.57
50.01
48.17
52.03
7
90
62.98
16.65
17.16
52.14
8
70
20.68
9.76
9.60
55.68
9
130
41.36
25.26
25.47
75.57
P10
32
6.24
12.58
11.61
3.73
11
65
30.71
31.05
30.98
30.52
12
65
38.23
39.48
39.15
36.16
13
65
33.77
34.44
34.36
33.56
14
32
10.13
9.77
9.71
9.50
15
32
24.99
23.67
23.54
23.55
16
32
12.61
11.36
11.34
12.03
17
16
2.84
2.59
2.59
2.73
18
16
8.05
6.93
6.94
7.74
19
16
8.85
8.12
8.09
8.36
20
16
5.04
4.40
4.40
4.82
21
32
6.19
6.84
6.74
5.71
22
32
8.87
9.50
9.38
8.20
23
32
3.68
4.91
4.81
3.37
24
32
20.17
20.20
20.05
19.05
25
32
9.58
9.62
9.55
9.04
26
32
2.76
2.63
2.63
2.68
27
16
8.94
8.29
8.27
8.56
28
16
6.89
7.13
7.07
6.48
29
16
4.89
4.34
4.34
4.75
30
16
2.32
1.95
1.97
2.36
31
16
4.64
4.60
4.57
4.39
32
16
5.57
5.65
5.62
5.34
33
16
7.17
7.11
7.05
6.67
34
16
8.16
8.09
8.02
7.58
35
16
4.20
4.17
4.13
3.90
36
32
4.53
5.25
5.14
4.35
37
32
15.00
14.87
14.69
13.58
38
65
10.47
99.78
11.63
9.30
39
32
9.49
11.89
10.07
8.35
40
65
24.84
10.26
22.22
21.48
41
65
17.50
22.55
17.60
16.05
Table 7. An overview of CFBPSO with AIPFC-
calculated power flow for four network-loading
scenarios
Outage
Lines
Over Loaded
lines
Line flow
limit (MVA)
CFBPSO with
AIPFC
1-2
1-3
130
102.563
3-4
130
83.401
4-6
90
62.983
1-3
1-2
130
99.776
3-4
1-2
130
93.594
2-5
2-6
65
52.030
5-7
70
55.677
This proves that congestion problems can be
solved and the goal can be reached using the
CFBPSO and the AIPFC technique by satisfying
constraints on control variables and transmission
line flow limits. According to the data, the
CFBPSO with AIPFC technique reduces critical
congestion.
6. Conclusion
In the face of network overloading and the worst-
case scenarios, it has been shown that the
CFBPSO method, in conjunction with FACTS
devices like AIPFC, can solve congestion-
constrained optimal power flow issues. The
CFBPSO technique, in conjunction with AIPFC,
is applied to the analysis of congestion as an
optimization problem. The method has been
successfully tested on IEEE 30-bus systems, and
the cost results obtained on the systems have been
compared with the results reported using other
techniques. The proposed method with the AIPFC
device reliably converged to the optimal solution
in reaching the specified goal, provided that
constraints on control variables and the
transmission line flow limit were met. Along with
its many advantages, the CFBPSO algorithm is
also conceptually simple and straightforward. We
demonstrate the algorithm's robustness by solving
some overloaded and emergency situations. Poor
results can be achieved with the CFBPSO
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2022.17.35
Bala Saibabu Bommidi, Baddu Naik Bhukya,
Swarupa Rani Bondalapati, Hemanth Sai Madupu
E-ISSN: 2224-350X
361
Volume 17, 2022
algorithm if the particle size, inertia weight, and
maximum velocity are all chosen incorrectly.
However, results from the tests show that the
proposed implementation performs better under
heavily loaded and emergency conditions, and
that congestion is better managed.
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Bala Saibabu Bommidi, Baddu Naik Bhukya,
Swarupa Rani Bondalapati, Hemanth Sai Madupu
E-ISSN: 2224-350X
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Volume 17, 2022
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2022.17.35
Bala Saibabu Bommidi, Baddu Naik Bhukya,
Swarupa Rani Bondalapati, Hemanth Sai Madupu
E-ISSN: 2224-350X
363
Volume 17, 2022