Reliability Assessment of Power System based on Load Flow Analysis of
the IEEE 57 Bus used in Micro Grid Applications
G. VEERA BHADRA CHARY1, RAGHAVAIAH KATURI2*, K. MERCY ROSALINA3
Department of Electrical and Electronics Engineering,
VFSTR deemed to be University, Vadlamudi,
Guntur, Andhra Pradesh,
INDIA
*Corresponding Author
Abstract: - The complex power system consists of more interconnections; therefore, modelling such a type of
network is a very difficult task in the commercialization area cycle. MATPOWER has all steady-state power
system models, which are extensively used in academic research for power flow (PF) modeling. The PF
architecture designed in this is extensible; it is easy to add or modify variables and constraints in the standard
case structure. This paper presents the details of the mathematically scaled loads in IEEE 57 bus power system
network modelling by using the standard test case data. Internally, all the bus voltages are expressed in p.u.,
and phase angles are expressed in radians, but the generators and loads are expressed in terms of power ratings.
The scaling of these is defined based on the scaled voltage of the corresponding bus voltage. The scaling load
procedure used in this paper is very useful for designing a low-voltage power system network for practical
analysis purposes. Two simulations are performed in this paper for the analysis of the actual load flow (ALF)
and scaled load flow (SLF) power system models. The voltage, phase angle, and power flow through the lines
are compared to analyze the accuracy of both simulations. When compared with ALF, it has shown good
accuracy, computational efficiency, and convergence properties.
Key-Words: - ALF, Complex power system, IEEE 57 bus, MATPOWER, PF, Scaled Load, SLF, Steady-Stat.
Received: March 12, 2023. Revised: December 4, 2023. Accepted: December 24, 2023. Published: December 31, 2023.
1 Introduction
MATPOWER is an open-source MATLAB power
system tool that is mostly used in academic research
for AC and DC power flow (PF) and optimal power
flow (OPF). It consists of a predetermined set of m-
files, which are designed to give the best
performance of simulation, [1], for any problem
formulation. It has become a more popular tool
today for high-level computation languages.
Therefore, it is very suitable to study steady-state
power systems. When comparing the use of
MATPOWER with earlier days, it is growing day
by day, with about 50% for academia, 43% for
research, and 7% for industry and others, [2]. The
main motivation for the development of this tool is
to design a MATLAB-based PF and OPF to achieve
the computational requirements of the Power Web
platform, which is a web-based testing simulation
platform used in the electricity markets, [3], [4]. It
requires software that uses the OPF for the
computation of power allocation and the pricing of
electrical energy. Due to its clear potential and
usefulness to the researchers, MATPOWER was
released as open-source software through the
Internet. The extensive OPF architecture in this
problem has allowed the researchers to add new
variables, constraints, and costs to the standard
problem, [5]. For the operation and planning
purposes of a power system network, a stochastic
method was proposed that can maximize the total
expected benefits for planning, incorporation of
costs, and benefits of electricity consumption, power
generation, services, storage, and load shedding.
However, the uncertainty was modelling for
maintenance of the power system security and for
proper representation of stochastic cost, [6].
Deregulation markets in power systems always look
for robust OPF, whereas they should provide
deterministic convergence, accurate computation of
prices, smooth costing, etc. Instead of the
advancements that have been made, [7], [8], [9],
[10], [11], [12], the ACOPF was not adopted in the
real-time operation of complex power systems. In
the reference, [13], three new OPF methods were
proposed: the Trust Region-Based Augmented
Lagrangian Method (TRALM), the Step-Controlled
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.39
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
392
Volume 18, 2023
primal-dual Interior Point Method (SCIPM), and the
Constrained Cost Variable (CCV) formulations. The
MOST, [14] is used to compare and analyze the
stochastic day-ahead Security Constrained Unit
Commitment (SUCC) in the traditional approach. In
the reference, [15], it is shown that this tool is used
to compare multi-stage uncertainties and reduce the
effect of modelling assumptions on the power
system.
MATPOWER is facilitated by an extensive suite
of tests to ensure the quality of the code. Many
researchers are using this to find the testing
framework for designing their own MATLAB
programs. There are various software packages used
for power system simulation developed by the
researchers. MATLAB / Simulink has been
supported in designing the power system which
includes power electronics, FACTS, control
systems, renewable sources, etc. The state-space
modelling and GUI-based PSB components are
discussed in, [16]. Simulink has been developed as
an educational package since 1997. ULg was
collaborated with Bologna University and
developed various traditional components such as
synchronous generators, transmission lines,
transformers, etc. in the Electrical Energy Systems
Lab. of NTUA, [17]. A Power Analysis Toolbox
(PAT) was developed by the West Virginia
Universities Advanced Power Engineering Research
Centre (APERC), it includes FACTS, flexible to
perform load flow, transient, and small signal
analysis of power systems, [18]. Mat Dyn is open-
source software meant to focus on transient stability
analysis and time domain simulation. The design
criteria, advantages, and code structure are
discussed in, [19]. The PSAT was the first open-
source software that was runs on the GNU / Octave
and network editor to perform power system
analysis. Other than those features, it has
continuation power flow (CPF), GUI, and GNE,
[20]. It has been used by many universities for
teaching both UG and PG courses and also formed
an online virtual laboratory to support the students
via Internet, [21], [22].
Analysis of a bulk power system network is a
very tedious task due to the greater number of
interconnections between the transmission lines and
the many components connected to it. Each
component has its own characteristics and posture
and is meant for a particular goal. Therefore, it is
very difficult to understand the interactions in a
network and the representation of its behavior with
mathematical equations, [23], [24]. The dynamic
behavior of such a system is more important, so it is
very essential to increase stability when the
electrical loads in the system are increasing. In
addition to that, it is very essential to study the
changes in generation, load, and disturbances.
Therefore, it is required to monitor the operating
conditions by using a real-time power system model
that should be useful for power system operators to
analyze the power system model during abnormal
threats, [25], [26]. The design of such a high-voltage
power system network is practically impossible
because of the constraints involved in its huge
dimensions, high rating of equipment, and complex
system theory. Therefore, it is essential to design
such complex power system networks in the
laboratory for analysis, and that network should
possess characteristics that are similar to the original
network, [27]. Generally, the power system consists
of various components that would be deployed for
electrical supply, power transfer, and use of supply.
In the power system network, the synchronous
generators would supply electrical power, and
transmission lines would carry power to loads such
as homes, industries, etc. The analysis of a multi-
machine power system network consisted of the
study of power transfer in transmission lines, [28],
continuous monitoring of control, supervision, and
protection under steady-state operation and
contingency conditions. In addition to those, it is
very essential to capture the behavior of the network
within a time span of a few microseconds to several
hours, or even for years. This was found by using
static, dynamic, and transient analyses. However, it
is found that the type of study and its objectives are
changing from one power system to another, even
though they would have identical prospective and
the same analysis modules, [29].
The modelling of a practical power system
network is a critical task in terms of successful
operation and management. The MATPOWER tool
is very useful to test the power system in an off-line
environment so that it would verify the operation of
network to plan and optimize in a correct way to
model the power system. The main aim of this paper
is to design a scaled-load steady-state model of the
IEEE 57 bus power system network, [30]. The
proposed system consists of 57 buses, 42 PQ loads,
7 PV generators, 63 positive sequence pi model
transmission lines, and 17 transformers. The scale
load (SL) procedure is used to derive the ratings of
loads and generators by using the specific SL ratio
of each bus. According to the standard system data,
it has 138kv (from 1 to 17 buses) and 69kv (from 18
to57 buses, the SL derived for each bus by using the
voltages 414 volts and 207 volts respectively. The
standard Newton-Raphson (NR) AC power flow
method is used for finding the bus voltage, phase
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.39
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
393
Volume 18, 2023
angle, and power flow in lines. As per the standard
test case data modification of loads and generators
made in the MATPOWER extensible case 57
structures for ALF and SLF simulations, The
simulation results have shown the accuracy,
efficiency, and computation of the SL procedure
used in this paper. It also, helps to understand the
behavior of a power system network when it is
mathematically well-conditioned at low voltages.
The evaluation of results is useful to design a hands-
on equivalent circuit practically. It can be used for
various power system experimentations in academic
research.
The fore coming sections are explained as
follows, the Section 2 discussed about the Scaled
Power Flow procedure and modifications of loads in
case structure. The IEEE 57 bus power system
model summary is explained in Section 3. The
comparison of voltage, phase angle, and power flow
results is explained in Section 4. Accuracy of results
and conclusions are discussed in Section 5.
2 Scaled Load Flow Formulation
The traditional power flow problem is used to find
voltage, phase angle, and power flows in lines for
specified load and generation patterns. Normally, in
MATPOWER, the power flow is executed by
calling runpf with a case structure. Whether it is AC
or DC power flows, the solution to the set of
equations is in the form of:
󰇛󰇜 (1)
The above equation is defined to derive the
subset of the bus power balance equation in the
polar coordinate’s method as a function of unknown
voltages. The AC power balance equation is
obtained from the matched bus injections of the
loads and generators. It is expressed as a function of
the bus voltage and generator injections in complex
matrix form.
󰇛󰇜󰇛󰇜 (2)
2.1 A.C Power Flow
In AC power flow, by convention, one of the
generators is considered a slack bus; it serves as a
voltage reference and real power. Although the real
power at this bus is specified as unknown to avoid
overstating the problem, the remaining generator
buses are considered PV buses; these buses are
specified with voltage and real power injection.
Remaining all the buses are considered as load
buses (i.e., PQ) with specified active and reactive
power load demands. The power balance in power
flow is expressed in polar coordinates as a function
of voltage, phase angle, generator injections, and
constant load demands.
󰇛󰇜
(3)
󰇛󰇜󰇛󰇜
(4)
For 󰇛󰇜 function, let us consider the equations
(3) & (4) for all buses except slack bus. Where,
, , and  are the refernce bus, PV bus,
and PQ bus respectively. Therefore,
󰇛󰇜󰇧
󰇛󰇜  
󰇛󰇜  󰇨 (5)
Where the consists of voltages of PQ buses
and phase angles of non-reference buses. It is
derived as,
󰇛󰇜 (6)
The Eq. 6 derives   non-linear
equations and unknown values, where  and 
are number of  and  buses respectively. After
the solution of Eq. 5 the Eq. 3 compute the slack bus
real power injection. In addition to that the 
equations derive the PV buses reactive power
injections.
2.2 Scaled Power Flow
MATPOWER has pre-defined extensible structures;
it can allow modifications and additions to the
standard problem. In the research point of view, this
tool is very desirable for modifying the problem
without overwriting the standard power flow
problem, [2], [3], [4], [5], according to the
requirements. In this paper, Scaled-Load (SL)
function is used to scale active and reactive powers
in the network according to the base voltage
specified in, [30], for the design and verification of
the power flow of a low-voltage power system
network. In this paper, the authors designed a low-
voltage IEEE 57 bus model. Let us consider that the
physical properties of the load and generator are
constant. Therefore, the SL is the ratio of the actual
bus voltage to the scaled voltage of the ith bus.


(7)
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DOI: 10.37394/232016.2023.18.39
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
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The quantity of scaling of active power and
reactive power are based on the SL which are
derived by the Eq. 7. Whereas the active power is
directly proportional to the square of the voltage
󰇛󰇜, therefore the scaled active power of
the bus is as follows:


 (8)
Similarly, the reactive power also directly
proportional to the square of the voltage 󰇛󰇜,
therefore the scaled reactive power of the bus
also as,


(9)
The Eq. 8 and Eq. 9 are used to specify the
ratings of loads and generators in the scaled power
system. Therefore, based on the direct scaling factor
SL the scaled load and generator rating are specified
with in the IEEE 57 bus base case structure for
Scaled Load Flow (SLF) model for analysis with the
Actual Load Flow (ALF).
3 Power System Modeling
The present work aims to design a Scaled load flow
(SLF) model of an IEEE 57 bus power system
network. Referring to the single-line diagram of the
network shown in Figure 1, it consists of
information about the interconnection of
transmission lines to the buses, generators, loads,
and location of transformers, as well as all the
components' standard data, like voltage and power,
considered from standard system data. The power
system has 57 buses; among those, up to 17 buses
are specified with a voltage of 138 kV, and reaming
buses are specified with a voltage of 69 kV. For the
design of the scaled load model, these voltages are
scaled to 414 volts and 207 volts, respectively.
The load flow analysis for this work uses
standard steady-state models. The NR load flow
analysis uses the following AC simplified models,
which are referenced in, [1], [2].
Fig. 1: IEEE 57 Bus Power System network single-
line block diagram.
4 Result Analysis
This section has discussed the simulations of both
ALF and SLF case models, whereas the ALF is
modelled according to the standard IEEE 57 bus
case data. The SLF is modelled by editing the case
structure fields such as base MVA, bus load data,
and generator data as per the scaled values;
however, the bus voltages are already expressed in
the p.u. values. The polar coordinate load flow
solution is obtained by using power balance Eq. 2,
and the AC NR load flow simulation converged in 3
iterations for both models. The similarity between
the ALF and SLF models has been compared with
the MATPOWER function of compare_case. It has
verified the bus, branch, and generator matrixes of
two models of each column and printed any non-
zero differences.
4.1 Load Flow Analysis of Actual and Actual
and Scaled Power Systems
Table 1 (Appendix) shows the bus voltage results of
both load flows. The ALF has converged in 1.61
seconds. The total active power generation of the
system is 1975.9 Mw, and the reactive power is
limited to 699 Mvar. The minimum voltage is found
at 0.936 p.u. at bus 31, and the maximum voltage is
found at 1.06 p.u. at bus 46. The magnitude of the
maximum phase angle is 19.51 deg, which is at bus
31. Similarly, when the results of SLF are observed,
they converge in 0.19 seconds. The total active
power generation capacity of this system is 17.78
kw, and the maximum reactive power is limited to
4.5 kvar. The minimum voltage is found on the
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.39
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
395
Volume 18, 2023
same 31 bus as in ALf, but the magnitude is 0.904
p.u.; likewise, the maximum voltage is also on bus
46, but the magnitude is 1.057 p.u. The maximum
phase is like in ALF on the same bus. However, the
minimum phase angle is zero deg, which is found on
bus 1 in both simulations.
The power system consists of 42 fixed PQ
loads. As shown in Table 2 (Appendix), the line
flows are similar in both simulations of the system.
The actual system has 1250.8 Mw of active power
and 321.1 Mvar of reactive power. The simulation
results have shown that the total line active power
loss is 27.86 Mw and 121.67 Mvar of reactive
power losses. However, the maximum active power
loss is 3.9 Mw and the reactive power loss is 19.96
Mvar, as found in lines 1–15. Similarly, when a
scaled power system is considered, it has 11.26 kw
of active power and 3.02 kvar of reactive power
loads. The simulation result of the scaled system has
shown that the total active power loss is 255.5 watts
and the reactive power loss is 1.11 kvar. Although
the losses found in lines 1–15 are the same as in
ALF, the maximum active power loss is 35.31 watts
and the maximum reactive power is 180.5 var.
4.2 Comparative Analysis
This section has shown the comparative analysis of
voltage, phase angle, line power flows, and
percentage of losses of line powers from Figure 2 to
Figure 7. This analysis is very useful to compare the
results on any bus and in any line. Figure 2 shows
that the bus voltage has decreased at most of the
buses for the SLF solution.
Fig. 2: Magnitude of bus voltage in p.u.
When comparing phase angles in Figure 3, there
is no difference between phase angles. However,
negligible differences were found at buses 31, 32,
and 33.
Fig. 3: Magnitude of phase angle at bus in deg.
As shown in Figure 4, the active power flow in
the transmission lines from the bus is the same in
all. However, few lines have carried more active
power; those lines are 1-2, 2-3, 8-9, 1-15, 1-16, and
1-17, most of them connected to bus 1.
Similarly, Figure 5 shows the reactive power of
transmission lines in the view of the bus, which is
the same for all lines. However, lines 1-2 and 12–13
have carried more reactive power.
Fig. 4: From bus active power of transmission line.
Fig. 5: From bus reactive power of transmission
line.
Figure 6 and Figure 7 show the percentage of
active and reactive power losses, respectively.
Maximum power losses are found in lines 1-2, 2-3,
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DOI: 10.37394/232016.2023.18.39
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
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Volume 18, 2023
8-9, 1-15, 1-6, and 1-17. As shown in Figure 6, all
the transformers carry zero active power; the
maximum power loss is found at 3.9% in lines 1–15.
Even though there is no active power loss in the
transformer, the reactive power has flown in all; the
maximum reactive power is 19.96%, which is found
in the same line.
Fig. 6: Transmission line active power loss in
percentage.
Fig. 7: Transmission line reactive power loss in
percentage.
5 Conclusions
In this work, the scaling procedure was used to
design a low-voltage power flow model of an IEEE
57 bus power system network. The scaled model
was designed by using the actual SL factor, which is
derived from the actual system voltages and scaling
voltages. By using the power balance method, the
NR load flow solution is obtained for both the ALF
and SLF models. The simulation results have been
thoroughly compared for analysis of the accuracy of
the scaling method, and it was shown that the
suggested scaling procedure can be used to design
practical low-voltage power system models. The
analysis of the results has shown good
computational capacity, efficiency, accuracy, and
robust behaviour-scaling procedures. A better
understanding of this scaled modelling procedure is
very useful for designing the low-voltage real-time
power system model. It is very useful in academic
research to assess the real-time performance of
power systems. The results presented in this paper
are very useful for designing a low-voltage IEEE 57
bus-equivalent network model. This model can help
researchers assess the real-time behaviour of the
network for various power system research
applications.
Acknowledgment:
We would like to show our gratitude to Vignan's
Foundation for Science, Technology, and Research
for their encouragement during this work.
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APPENDIX
Table 1. Bus voltage results of both actual and scaled Load Flows
bus
RLF
ALF
Angle
V
Angle
(deg.)
(volts)
(deg.)
1
0.000
1.040
0.000
2
-1.189
1.010
-1.188
3
-5.992
0.985
-5.988
4
-7.297
0.981
-7.337
5
-8.543
0.976
-8.546
6
-8.687
0.980
-8.674
7
-7.589
0.984
-7.601
8
-4.496
1.005
-4.478
9
-9.613
0.980
-9.585
10
-11.484
0.986
-11.450
11
-10.213
0.974
-10.193
12
-10.497
1.015
-10.471
13
-9.818
0.979
-9.804
14
-9.358
0.970
-9.350
15
-7.194
0.988
-7.190
16
-8.877
1.013
-8.859
17
-5.406
1.017
-5.396
18
-11.748
1.001
-11.730
19
-13.345
0.970
-13.227
20
-13.591
0.964
-13.444
21
-12.887
1.008
-12.929
22
-12.837
1.010
-12.874
23
-12.888
1.008
-12.940
24
-12.988
0.999
-13.292
25
-18.022
0.983
-18.173
26
-12.678
0.959
-12.981
27
-11.399
0.982
-11.514
28
-10.431
0.997
-10.482
29
-9.764
1.010
-9.772
30
-18.667
0.963
-18.720
31
-19.512
0.936
-19.384
32
-18.792
0.950
-18.512
33
-18.833
0.948
-18.552
34
-14.089
0.959
-14.149
35
-13.867
0.966
-13.906
36
-13.614
0.976
-13.635
37
-13.432
0.985
-13.446
38
-12.726
1.013
-12.735
39
-13.480
0.983
-13.491
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bus
RLF
ALF
Angle
V
Angle
(deg.)
(volts)
(deg.)
40
-13.643
0.973
-13.658
41
-14.118
0.996
-14.077
42
-15.556
0.967
-15.533
43
-11.379
1.010
-11.354
44
-11.857
1.017
-11.856
45
-9.291
1.036
-9.270
46
-11.141
1.060
-11.116
47
-12.537
1.033
-12.512
48
-12.626
1.027
-12.611
49
-12.971
1.036
-12.936
50
-13.454
1.023
-13.413
51
-12.578
1.052
-12.533
52
-11.249
0.980
-11.498
53
-11.874
0.971
-12.253
54
-11.560
0.996
-11.710
55
-10.847
1.031
-10.801
56
-16.064
0.968
-16.065
57
-16.576
0.965
-16.584
Table 2. From bus active and reactive powers of both Actual and scaled load flows
FB
TB
Scaled load flow
Actual load flow
Pf
Qf
Pf
Qf
(watts)
(var)
(Mwatts)
(Mvar)
1
2
919.32
674.83
102.09
75.00
2
3
880.47
-41.89
97.77
-4.64
3
4
538.90
-19.88
60.21
-8.18
4
5
123.50
-49.31
13.80
-4.43
4
6
128.65
-59.10
14.16
-5.09
6
7
-159.97
2.70
-17.78
-1.71
6
8
-382.14
-59.18
-42.50
-6.56
8
9
1605.48
178.10
178.03
19.83
9
10
155.43
-80.85
17.17
-9.23
9
11
116.47
25.31
12.90
2.07
9
12
22.81
-142.66
2.55
-15.85
9
13
20.89
-12.95
2.32
-1.96
13
14
-92.45
209.12
-10.35
22.34
13
15
-441.01
44.09
-48.89
4.89
1
15
1342.11
312.16
148.99
33.79
1
16
714.68
-7.84
79.25
-0.87
1
17
841.54
35.41
93.34
3.94
3
15
307.41
-151.30
33.77
-18.19
4
18
124.13
55.53
13.96
2.44
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FB
TB
Scaled load flow
Actual load flow
Pf
Qf
Pf
Qf
(watts)
(var)
(Mwatts)
(Mvar)
4
18
158.90
53.80
17.87
1.19
5
6
5.28
-65.69
0.67
-6.24
7
8
-698.51
-137.96
-77.94
-12.41
10
12
-159.97
-183.50
-17.60
-20.09
11
13
-89.54
-37.14
-9.93
-4.39
12
13
-3.39
556.18
-0.49
60.35
12
16
-301.92
79.91
-33.40
8.82
12
17
-437.50
83.03
-48.46
9.17
14
15
-621.36
-92.64
-68.84
-9.60
18
19
38.23
6.05
4.63
1.39
19
20
7.72
-0.54
1.23
0.63
21
20
13.00
9.82
1.08
0.39
21
22
-13.00
-9.82
-1.08
-0.39
22
23
86.81
52.13
9.65
3.11
23
24
30.00
33.06
3.34
1.00
24
25
62.08
35.16
7.07
1.71
24
25
59.65
33.79
6.79
1.65
24
26
-92.14
-29.07
-10.54
-1.55
26
27
-92.14
-29.62
-10.54
-1.61
27
28
-177.76
-37.06
-20.04
-2.43
28
29
-221.55
-61.45
-24.90
-5.13
7
29
537.94
161.52
60.09
13.03
25
30
65.03
31.91
7.56
4.63
30
31
31.75
14.38
3.85
2.66
31
32
-20.97
-12.50
-2.03
-0.35
32
33
34.27
17.17
3.81
1.91
34
32
70.05
45.24
7.46
3.79
34
35
-70.05
-45.24
-7.46
-3.79
35
36
-124.49
-70.27
-13.50
-6.55
36
37
-156.58
-104.36
-17.07
-10.61
37
38
-192.18
-130.73
-21.05
-13.70
37
39
34.39
24.83
3.86
2.93
36
40
31.03
34.11
3.46
4.09
22
38
-99.83
-61.99
-10.73
-3.51
11
41
82.91
33.60
9.19
3.53
41
42
79.91
31.41
8.88
3.27
41
43
-104.66
-28.83
-11.59
-2.95
38
44
-220.68
34.44
-24.35
5.23
15
45
337.66
6.43
37.33
-0.73
14
46
433.57
260.70
47.89
27.40
46
47
433.57
242.67
47.89
25.47
47
48
160.61
124.67
17.59
12.43
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FB
TB
Scaled load flow
Actual load flow
Pf
Qf
Pf
Qf
(watts)
(var)
(Mwatts)
(Mvar)
48
49
-0.40
-71.56
0.08
-7.38
49
50
84.66
35.37
9.66
4.43
50
51
-105.04
-60.25
-11.42
-6.20
10
51
269.21
117.47
29.64
12.51
13
49
292.61
315.12
32.43
33.80
29
52
160.89
51.14
17.92
2.55
52
53
112.27
25.47
12.55
-0.25
53
54
-68.93
-60.31
-7.57
-4.47
54
55
-107.74
-75.27
-11.82
-6.06
11
43
122.66
46.11
13.59
4.85
44
45
-330.26
16.88
-36.52
3.28
40
56
30.95
33.99
3.46
4.07
56
41
-49.34
4.00
-5.43
0.66
56
42
-14.21
11.25
-1.58
1.46
39
57
34.34
24.75
3.85
2.92
57
56
-25.96
4.04
-2.85
0.61
38
49
-43.58
-103.17
-4.66
-10.53
38
48
-158.11
-191.96
-17.22
-19.39
9
55
172.35
115.63
18.93
10.38
Contribution of Individual Authors to the
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The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
We would like to show our gratitude to Vignan's
Foundation for Science, Technology, and Research
for their encouragement during this work.
Conflict of Interest
The authors have no conflicts of interest to declare.
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.39
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
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Volume 18, 2023