Design and Analysis of a Low Voltage Simulink Model (LVSM) of IEEE
57 Bus
G. VEERA BHADRA CHARY, RAGHAVAIAH KATURI*, K. MERCY ROSALINA
Department of Electrical and Electronics Engineering,
Vignan’s Foundation for Science Technology and Research deemed to be a University,
Guntur, Andhra Pradesh,
INDIA
*Corresponding Author
Abstract: - The present power system is gaining momentum towards designing equivalent circuit models. The
Ward and REI methods involve the admittance reduction method as well as being merged with the EMS model
to derive boundary parameters, but these methods are limited and valid for a predefined condition. Therefore, it
is required to design an equivalent circuit that adopts the real power system for analysis. In this paper, a new
method is proposed to design a scaled-down power system model without changing the impedance of
components. In this regard, a Low Voltage Simulink Model (LVSM) of the IEEE 57 bus network was designed
in MATLAB/ Simulink so that it could be useful for laboratory model design purposes. The main objectives of
this paper are to propose a mathematical procedure to scale down the network parameters and design a 3-phase
LVSM of an IEEE 57 bus power system network within the Simulink platform. The performance of LVSM was
analyzed with no-load, balanced load, and unbalanced load models. These simulation studies were validated
and compared with the theoretical results to prove that the proposed LVSM modeling has good mathematical
accuracy, robustness, and validity for practical model implementation.
Key-Words: - Boundary parameters, equivalent circuit, IEEE 57 bus, LVSM, MATLAB / Simulink, real power
system, scale-down power system model.
Received: February 23, 2023. Revised: December 7, 2023. Accepted: December 19, 2023. Published: March 12, 2024.
Nomenclature
i ith Bus / Load / Generator component
Voltage and Current in test case system
Active and Reactive powers in test case system
Voltage and Current in LVSM
Active and Reactive Powers in LVSM
Resistance and Reactance in test case system
Resistance and Reactance in LVSM
Voltage and Current angle in test case system
Voltage and current angle in the LVSM
1 Introduction
The power system engineers always strive to design
practical models of big power system networks to
predict practical outcomes. In earlier days, there
were Analog equivalent models; in these
transmission lines, basic elements and generators
represented variable voltage sources. After that,
digital simulation was born. In this, the digital
computer is used for load flow and other problems.
Nowadays, the complexity of the power system has
increased drastically due to the addition of
renewable sources, power converters, and smart
technologies, [1]. At present, real-time simulation
(RTS) is used for modeling; this modeling is
categorized as long-term modeling for planning
purposes, short-term modeling, and -time modeling
for operational management. Table 1 shows various
software packages used for the type of modeling,
purpose, and study. Apart from those, there are
commercial software programs that model the
power system in economic and market aspects, [2].
Various types of digital real-time simulators
(DRTS) for modeling, hardware, software,
communication interfacing, I/O protocols, solution
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DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
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Volume 19, 2024
methods, and applications are explained in detail,
[3].
MATPOWER has facilitated an extensive suite
of tests to ensure quality code. Many researchers are
using MATLAB 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
and Simulink have been supported in designing the
power system, which includes power electronics,
FACTS, control systems, renewable sources, etc.
The state-space modeling and GUI-based PSB
components are discussed in, [4]. Simulink has been
developed as an educational package since 1997.
ULg 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, [5]. A Power Analysis Toolbox
(PAT) was developed by West Virginia University’s
Advanced Power Engineering Research Centre
(APERC). It includes facts and is flexible enough to
perform load flow, transient, and small signal
analysis of power systems, [6], [7]. 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, [8], [9]. The PSAT was the first open-
source software that ran 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, [10]. It has been used
by many universities for teaching both UG and PG
courses and has also formed an online virtual
laboratory to support students via the Internet, [11],
[12].
The “PowSim” simulator was designed by the
University of Bath for real-time simulations; the
operation of the algorithm was verified on IEEE 57
bus traditional methods and the reduced British
National grid system, [13], together with
knowledge-based systems, [14]. Dynamic modeling
and analysis with real-time simulators; Hydro-
QuObec (IREQ) in, [15], reduction of a power
system to a dynamic equivalent model in, [16], as
well as generator dynamics and transient
disturbances in, [17]. For information analysis of
future power systems, an architecture was proposed;
it has an alternate communication network that
adopts suitable computing, [18]. Interfacing the
simulator with the physical power system is an
improvement in hardware testing by using Kron’s
method of network tearing, components, and
procedure, discussed in, [19]. Several ways of
probabilistic-based modeling and diagnosis by using
Bayesian networks (BN) and arithmetic circuits
(ACs) are discussed in, [20]. The Energy
Management System (EMS) has a limited part of the
interconnected system; therefore, an equivalent
circuit is required to determine operating constraints
offline. Other than the Ward and REI methods,
based on boundary-measured parameters (voltage,
angle, and powers), an equivalent circuit is designed
in, [21].
Table 1. Simulation software’s for power system
analysis and modeling
S.no.
Modeling /
Analysis
Type of Study
Software Package
1
Dynamic
dynamic
voltage control,
Transient
stability,
critical clearing
time, faults
DINIS,
DIgSILENT,
ERACS, ETAP,
IPSA, PSS/E,
SKM Power Tools,
Power World,
2
Steady State
Load flow,
DG’s
contribution,
Fault level,
Voltage step
DIgSILENT,
DINIS, ERACS,
IPSA, Open DSS,
ETAP, Power
World, PSS/E,
SKM Power Tools,
3
Electro
Magnetic
Transient
(EMT)
FACTS /
HVDC design,
SSR, Insulation
coordination
ATP-EMTP,
EMTP-RV,
PSCAD/ EMTDC
4
Real-Time
Simulation
(RTS)
Protection and
Control testing;
Real-time
simulations
Opal-RT, RTDS
5
Multi-
Domain
Analysis
Electrical,
Power
Electronics,
Mechanical,
and Fluid
dynamic
systems.
MATLAB
(including
Simulink and
SPS/Simulink),
DYMOLA
6
Hybrid
Simulation
Dynamic
analysis
between two
systems
ETRAN (PSS/E
and PSCAD)
7
Harmonic
Analysis
Impedance
scan, Load flow
with VSC
DIgSILENT,
ERACS, ETAP,
IPSA, PSS Sincal,
SKM Power Tools
Without admittance reduction, with boundary-
measured parameters, a new methodology is
proposed in this paper, which mainly focuses on
scale-down bus-measured parameters by keeping
impedance constant for all components such as
transmission lines, synchronous generators,
transformers, loads, etc. Therefore, the size and
operating ranges (voltage, current, and power) of
every component are scaled, making it easy to
design a power system. This paper designs a 3-
phase low-voltage Simulink Model (LVSM) of the
IEEE 57 bus test case system in Simulink. The test
case data and power system one-line diagram
obtained from, [22], scale down according to the
methodology. The performance of LVSM was
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
33
Volume 19, 2024
obtained from the no-load, balanced load, and
unbalanced load simulations. Thus, simulation
results show power flows in lines and bus powers,
as well as voltage, angle, and currents. These
analyses prove the accuracy of the methodology and
LVSM validity while designing the model.
The other sections are organized as follows:
Section II discusses the proposed methodology and
LVSM design. Section III explains the simulation
results of three load tests. The key points of the
results and the scope of future work are discussed in
Section V.
2 Methodology and LVSM Design
The Scale-Down modeling concept in this paper
discusses two main steps, first, scale the ratings of
all components according to the proposed method,
and second, develop a 3-phase equivalent power
system model in MATLAB / Simulink.
2.1 Proposed Mathematical Procedure
In order to develop LVSM, consider standard power
system data of all components such as voltage,
current, powers and line parameters. The present
concept relies on the following assumptions.
Balanced power system network.
Magnitude of phase angle independent of
scaled voltage.
The magnitude of resistance, reactance, and
shunt component remain the same
irrespective of its current.
Therefore, p.f will be the same in both
cases.
All transmission lines are assumed to be as
per km distributed pi model lines (R=0).
Temperature assumed to be constant.
With the above assumptions, the following
conditions are also used to derive the
methodology.
The voltage of any component directly
proportional to the current (V .
Active and Reactive power of
load/generator / bus directly proportional to
the square of its voltage (P
.
Let us consider a power system network, to
Scale down each component rating consider the
standard data such as voltage, current, and powers
w.r.t its bus. Define the operating voltage of the
model according to the design requirement and find
the scaling factor of voltage, which is known as the
Voltage Scaling Factor (VSF). It can be defined as
“the ratio magnitude of test case voltage ( to
scale down voltage ( ith component of in
the network by assuming magnitude of phase angles
equal ( “.
(1)
Similarly, Current Scaling Factor (CSF) is also
used to scale down the current rating of the
component in the network. It can define as “the ratio
of the current ( of component in the test case to
scale down current ( of ith component in the
network by assuming magnitudes of phase angles
equal ( ”.
(2)
Consider active and reactive powers of load /
generator / transformer, either (1) or (2) equation is
using for calculation of new power rating of the
component.
Active power ( of actual network
defined as:
(3)
Similarly, for LVSM as,
(4)
(5)
From equations (3), (4) and (5),
(6)
However,
(7)
(8)
Reactive power ( of actual network defined
as:
(9)
Similarly, for LVSM as,
(10)
(11)
From equations (9), (10) and (11),
(12)
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G. Veera Bhadra Chary,
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Volume 19, 2024
However,
(13)
(14)
The equations (1), (2), (8) and (14) are used to
calculate the voltage and power ratings of LVSM
components. However, CSF can also use to
calculate power ratings as well as losses of the
equipment.
2.2 IEEE 57 Bus Test Case LVSM
The methodology proposed in the previous section
is used to design the IEEE 57 bus test case as
LVSM, it consists of 7 voltage sources, 57 buses, 9
distribution transformers, 6 voltage regulating
transformers, and 63 pi-model transmission lines.
The structure of 3- phase LVSM designed in
MATLAB / Simulink as per scaled bus voltage and
powers of load / generator / transformer as shown in
Figure 1. Whereas the total network identified as
two sub-networks SN1 and SN2; red highlighted
SN1 (1 - 17 buses) has 414 (l-l) volts as well as SN2
(18 - 57 buses) has 207 (l-l) volts.
The standard data of the test case system
corresponds to the balanced network; therefore, the
calculated parameters of all components also
correspond to the balanced LVSM. The
transmission lines are composed of per km
distributed pi sections, each section parameters are
Rs=0.12 Ω / km, Ls=1.5273 mH / km and Csh=0.02
MFD/km (typical line parameters of 138kv line)
without mutual coupling between lines, [23]. As per
the line parameters data, for each line no. of pi
section and length calculated. All generators are
voltage sources which supply balanced voltage, and
every load is termed as constant PQ balanced load.
Each bus is considered as a boundary point to
connected lines, which is used to measure voltage,
angle, and power injection to the connected lines.
Fig. 1: 3-phase equivalent one-line diagram of IEEE
57 bus test case network
3 Results Analysis
The steady-state simulation carried out with the
discretized 3-phase LVSM Simulink model, with a
time step of 50 and simulation performed for 1s.
Three simulation studies were considered to assess
the accuracy and robustness of LVSM while
designing a practical model. Those are the No-load
test which does not consider the load at buses, the
Balanced-load which consists of balanced
distribution of load at buses and the Unbalanced-
load which considers the unbalanced distribution of
load at buses. All these simulations verify the
boundary (bus) parameters such as voltage, angle,
and powers at buses as well as power flow through
the π-model lines and distribution / voltage
regulating transformers. In each test case, the
simulation results analyzed sub-network as shown in
Figure 1.
3.1 No-load LVSM
In this test, the voltage shown at the bus has an error
due to the small current through lines, Table 2 and
Table 3 show results corresponding to the ‘R’ phase
only. It can be observed that bus 14 draws more
reactive power so that it has a 2.86% voltage error,
as well as due to more active power at bus 9 cause
the largest current of 0.37amp in SN1.
Table 2. Phase R: No-load simulation results of
414(l-L) voltage buses
Bus
no.
VR
volts
(rms)
Angle
(deg.)
IR
amps
(rms)
Angle
(deg.)
PRYB
watts
QRYB
var
1
238.62
-0.21
0.17
-16.76
115.8
34.17
2
238.79
-0.14
0.11
-14.00
76.37
18.66
3
238.18
-0.29
0.26
-26.57
165.7
81.46
4
238.56
-0.32
0.05
89.80
0.124
-34.76
5
239.09
-0.24
0.02
-171.43
-12.16
1.87
6
238.99
-0.18
0.13
5.89
95.09
-9.996
7
237.62
-0.51
0.11
-38.33
59.53
46.25
8
238.57
-0.24
0.19
-16.71
129.2
38.01
9
237.76
-0.41
0.37
-28.32
234.1
123.4
10
237.96
-0.72
0.05
-1.32
35.65
0.537
11
235.34
-1.00
0.15
101.98
-24.06
-100.8
12
237.83
-0.40
0.36
-27.52
228.3
116.11
13
233.07
-0.98
0.12
137.63
64.64
-56.98
14
232.16
-1.12
0.32
-57.45
123
182.8
15
235.27
-0.84
0.36
-39.71
197.5
158.7
16
238.53
-0.38
0.03
-59.40
12.32
20.49
17
238.87
-0.32
0.02
1.05
12.5
-0.317
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G. Veera Bhadra Chary,
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E-ISSN: 2224-350X
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Volume 19, 2024
As shown in Table 3, in SN2 almost all the
buses show negative voltage error because of the
absence of loads, but bus 26 show 1.15% error. It
was observed bus 49 drew more active and reactive
powers as well as current; therefore, it has more
voltage than all other buses.
Table 3. Phase R: No-load simulation results of
207(L-L) voltage buses
Bus
no.
VR
volts
(rms)
Angle
(deg.)
IR
amps
(rms)
Angle
(deg.)
PRYB
watts
QRYB
var
18
122.84
-0.43
0.07
-23.70
23.97
10.29
19
120.99
-1.28
0.08
-40.27
23.75
19.23
20
119.39
-1.77
0.10
-47.92
23.58
24.59
21
124.53
-1.77
0.16
133.90
-41.62
-40.52
22
125.28
-1.55
0.15
135.12
-41.73
-39.22
23
125.17
-1.59
0.18
-44.09
51.05
46.64
24
123.19
-2.17
0.19
-46.29
50.69
49.04
25
123.17
-2.18
0.03
74.15
2.723
-10.84
26
118.13
-2.16
0.29
-42.53
79.66
67.57
27
121.07
-1.14
0.29
-41.10
80.47
67.27
28
122.16
-0.77
0.29
-40.55
80.77
67.09
29
122.82
-0.54
0.20
-21.81
69.39
27.12
30
123.40
-2.24
0.02
69.54
2.695
-7.996
31
123.64
-2.36
0.01
17.21
2.636
-0.925
32
123.15
-2.42
0.03
-77.41
2.546
9.798
33
123.15
-2.42
0.00
0.00
0
0
34
120.08
-2.42
0.21
-43.36
58.1
50.23
35
120.75
-2.19
0.21
-42.76
58.23
49.68
36
121.20
-2.04
0.21
137.65
-58.32
-49.29
37
122.23
-1.95
0.74
-59.82
144.6
227.8
38
125.69
-1.43
0.31
75.94
24.46
-112.9
39
122.00
-2.05
0.17
-34.13
53.43
33.6
40
120.26
-2.03
0.41
-79.88
32.08
143.5
41
123.24
-1.02
0.10
-
118.09
-16.89
33.36
42
124.46
-1.54
0.09
-
121.99
-16.73
28.77
43
122.90
-1.00
0.02
94.51
-0.8944
-8.995
44
124.89
-1.25
0.31
76.03
24.67
-113
45
123.19
-0.85
0.32
76.23
25.13
-113
46
128.92
-1.14
0.33
-66.01
55.39
116
47
127.83
-1.23
0.33
-66.21
55.1
116
48
127.45
-1.27
0.34
-66.28
55
116
49
130.07
-1.01
1.04
-67.86
162.2
372.8
50
129.31
-0.91
0.13
-93.30
-1.587
49.11
51
127.95
-0.73
0.14
-93.14
1.755
51.98
52
123.82
-0.52
0.11
106.42
-11.66
-37.49
53
124.33
-0.51
0.10
107.05
-11.71
-36.23
Bus
no.
VR
volts
(rms)
Angle
(deg.)
IR
amps
(rms)
Angle
(deg.)
PRYB
watts
QRYB
var
54
125.44
-0.47
0.09
108.71
-11.82
-33.16
55
126.43
-0.43
0.09
110.67
-11.91
-30.06
56
125.46
-2.03
0.07
107.61
-9.239
-25.31
57
124.49
-2.06
0.08
105.21
-9.154
-28.89
3.2 Balanced Loads LVSM
With the addition of constant PQ load at buses, the
LVSM equivalent to the scale-down model of the
IEEE 57 bus test case system. Since all loads
equally distributed among R Y B phases; therefore,
results have shown w.r.t ‘R’ phase, and the Table 4
and Table 5 results considered only load buses. Bus
14 is connected to the transformer, which is more
loaded than the 12th bus; therefore, it has 8.37%
more error in SN1. However, the current drawn by
this bus is 4.83amp, which is more than the
remaining buses because of a large connected load.
Table 4. Phase R.: Balanced loads simulation results
of 414(L-L) voltage buses
Bus
no.
VR volts
(rms)
Angle
(deg.)
IR amps
(rms)
Angle
(deg.)
PRYB
watts
QRYB
var
1
233.16
-2.24
1.90
-25.36
1219
519
2
233.22
-1.24
1.34
-41.18
718.1
600
3
232.83
-2.31
1.97
-26.05
1258
551
5
233.84
-2.87
0.04
114.07
-14.09
-27.4
6
235.36
-2.39
1.83
-13.37
1267
244.7
8
233.33
-3.28
2.54
-16.35
1729
400.3
9
230.70
-4.01
3.19
-20.73
2110
632.2
10
225.73
-6.84
0.15
-50.48
71.15
68.09
12
228.37
-6.32
4.83
-17.45
3242
635.7
13
220.31
-6.80
0.15
92.82
-16.59
-97.57
14
218.99
-6.77
0.81
-34.69
468.3
247.3
15
224.80
-5.12
1.33
-25.57
837.8
311.9
16
228.17
-6.58
0.45
-10.08
307
18.79
17
228.81
-5.32
0.62
-10.49
423.6
38.27
The 35th bus has more voltage error of 7.8%,
which is because of the large power drawn by the
nearest voltage regulating transformer. However,
bus 49 has more load; therefore, it draws more
current than all other buses in SN2.
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G. Veera Bhadra Chary,
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Volume 19, 2024
Table 5. Phase R: Balanced loads simulation results
of 207(L-L) voltage buses
Bus
no.
VR
volts
(rms)
Angle
(deg.)
IR
amps
(rms)
Angle
(deg.)
PRYB
watts
QRYB
var
18
118.36
-4.44
0.94
-24.93
313.4
116.8
19
113.58
-7.45
0.24
-32.77
72.41
34.23
20
110.97
-8.62
0.17
-44.77
44.94
32.83
23
116.14
-8.55
0.40
-39.35
118.3
70.4
25
113.63
-9.50
0.36
-32.63
113.2
48.05
27
114.38
-6.96
0.77
-33.09
237.4
116.2
28
116.74
-5.60
0.90
-32.79
278.5
142.7
29
118.45
-4.67
1.67
-25.09
555.6
206.3
30
112.54
-10.31
0.20
-31.37
61.57
23.56
31
111.10
-11.40
0.11
-34.91
33.08
14.34
32
111.83
-10.81
0.04
171.77
-11.74
0.5894
33
111.71
-10.88
0.10
-37.58
29.56
14.81
35
110.16
-10.27
0.54
-42.37
149.5
93.52
38
116.90
-8.21
0.51
6.30
170.3
-44.16
41
116.81
-6.40
0.28
164.10
-97.71
-16.33
42
114.83
-8.63
0.12
-161.24
-37.88
19.55
43
116.47
-6.40
0.05
-7.57
15.68
0.2914
44
116.90
-7.49
0.79
-1.78
273.9
-27.36
47
119.21
-7.84
0.96
-41.12
285.6
186.6
49
122.86
-6.91
2.35
-49.42
639.5
583
50
120.76
-7.76
0.44
-42.83
131.1
91.43
51
121.30
-6.92
0.17
171.00
-61.32
-2.165
52
116.79
-6.10
0.37
-21.27
124.5
33.58
53
116.30
-6.63
0.24
-17.18
82.44
15.25
54
119.18
-5.55
0.32
136.00
-88.28
-69.66
55
122.61
-4.08
0.41
141.98
-126.4
-84.62
56
115.24
-9.67
0.07
107.66
-11.04
-21.02
57
114.33
-9.76
0.13
0.11
43.71
-7.66
Table 6 shows the transformers power flow,
these results are useful for finding the rating of
transformers while designing the LVSM. More
power flew through the distribution transformer
connected between 13-49 buses. Grey colored cells
in the table show voltage regulating transformers,
among those, the transformer connected between
24-25 buses draws more power. However,
transformers have almost negligible power losses.
Table 6. Balanced loads- power flow through step-
down and voltage regulating transformers
S.
no
Fb
Tb
PRYB
watts
QRYB
var
S.
no
Fb
Tb
PRYB
watts
QRYB
var
1
4
18
308.61
128.39
9
9
55
248.67
163.78
2
7
29
567.67
226.41
10
21
20
20.70
5.28
3
11
41
301.47
79.44
11
24
25
151.89
82.48
4
15
45
302.99
45.24
12
24
26
-118.7
-73.81
5
14
46
346.49
271.99
13
34
32
92.99
52.35
6
10
51
293.4
79.46
14
40
56
-39.02
84.23
7
13
49
779.26
687.75
15
39
57
74.53
20.41
8
11
43
18.64
2.10
Table 7 and Table 8 show power flow in the pi-
model transmission lines, some of the lines
interconnected between generator buses drawn
zero/negligible power and losses shown in grey
colored rows. In SN1 among all lines, the line
between 12-13 buses has more power flow as well
losses.
Table 7. Power flow through π-lines in 414(l-l)
voltage section and line power losses
S.
no
Line
From bus Power
flow
Losses
Fb
Tb
PRYB
(watts)
QRYB
(var)
PRYB
(watts)
QRYB
(var)
1
1
2
0
-2.99
0
0
2
2
3
0
-9.07
0
0
3
3
4
243.85
69.73
0.65
-5.13
4
4
5
-7.2
-22.27
0.01
-17.08
5
4
6
-60.18
-33.22
0.16
-30.8
6
6
7
247.31
94.94
2.05
-13.49
7
6
8
0
-18.49
0
0
8
8
9
0
-5.39
0
0
9
9
10
159
28.42
1.27
-30.21
10
9
11
439.24
228.30
5.87
5.93
11
9
12
0
-31.56
0
0
12
9
13
273.60
168.65
4.79
-13.17
13
13
14
186.21
110.18
0.63
-5.89
14
13
15
-107.99
118.91
0.62
14.72
15
1
15
371.69
197.50
4.57
-0.58
16
1
16
110.32
-20.15
0.69
0.67
17
1
17
237.40
21.50
1.72
-15.95
18
3
15
637.93
349.94
7.85
20.4
19
5
6
-124.21
-30.34
0.28
-12.49
20
7
8
-351.29
-147.16
2.93
-3.19
21
10
12
-209.74
-67.89
1.69
-19.76
22
11
13
83.28
110.84
0.46
-12.67
23
12
13
744.88
498.71
13.04
40.3
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
37
Volume 19, 2024
S.
no
Line
From bus Power
flow
Losses
Fb
Tb
PRYB
(watts)
QRYB
(var)
PRYB
(watts)
QRYB
(var)
24
12
16
279.12
-4.05
1.76
2.12
25
12
17
143.35
0.85
1.04
-33.69
26
14
15
-318.84
-266.56
2.87
0.72
Line power flows in SN2 shown in Table 8,
more power flew in a line connected between 46-47
buses, but more losses in a line connected between
37-38 buses. Whereas, the effective active and
reactive power losses found in LVSM were
93.43watts, 64.75var respectively.
Table 8. Power flow through π-lines in 207(l-l)
voltage section and line power losses
S.
no
Line
From bus Power
flow
Losses
Fb
Tb
PRYB
(watts)
QRYB
var)
PRYB
(watts)
QRYB
(var)
1
18
19
61.44
29.22
0.9
-5.44
2
19
20
30.54
29.26
0.25
-4.45
3
21
22
-50.69
-35.28
0.12
-1.08
4
22
23
148.63
85.61
0.13
0.28
5
23
24
91.50
66.43
0.92
0.32
6
26
27
-147.50
-102.67
2.56
7.12
7
27
28
-234.06
-114.29
1.86
6.21
8
28
29
-276.92
-141.2
1.58
5.5
9
25
30
66.19
24.81
0.3
-1.37
10
30
31
33.89
9.98
0.19
-5.37
11
31
32
-18.29
-10.74
0.08
-8.97
12
32
33
34.01
16.71
0.01
-0.39
13
34
35
-119.60
-78.96
0.5
1.07
14
35
36
-174.10
-107.03
0.68
2.08
15
36
37
-163.32
-220.87
0.83
2.86
16
37
38
-267.00
-272.43
4.31
15.88
17
37
39
102.85
48.69
0.15
0.1
18
36
40
-11.46
111.76
0.17
0.14
19
22
38
-199.44
-119.81
0.44
1.35
20
41
42
112.05
29.09
1.24
9.24
21
41
43
1.23
3.18
0
-5.61
22
38
44
-126.94
43.27
0.28
0.35
23
46
47
283.64
208.65
2.12
7.47
24
47
48
14.52
96.78
0.06
-0.1
25
48
49
-227.87
-202.26
3.12
10.59
26
49
50
87.72
91.41
0.51
0.11
27
50
51
-101.78
-3.193
0.57
-
0.983
28
29
52
107.31
25.43
0.62
-0.06
S.
no
Line
From bus Power
flow
Losses
Fb
Tb
PRYB
(watts)
QRYB
var)
PRYB
(watts)
QRYB
(var)
29
52
53
62.69
5.69
0.11
-0.89
30
53
54
-117.41
-83.41
1.32
2.09
31
54
55
-155.73
-98.10
1.99
4.66
32
44
45
-235.22
26.72
1.9
5.87
33
56
41
-101.50
-1.61
1.58
-1.09
34
56
42
-46.56
16.04
0.25
-3.7
35
57
56
-13.63
-25.78
0.06
-3.19
36
38
49
-229.79
-223.41
4.9
17.08
37
38
48
-240.46
-292.33
1.87
6.81
3.3 Unbalanced loads LVSM
In this test, all constant PQ loads shared as 26%,
34% and 40%, uniformly on R, Y, B phases
respectively; therefore, more voltage regulation was
found on the B-phase. Table 9 shows, bus 14 has a
9.76% large voltage error and a load angle of 8.35
deg lag in SN1.
Table 9. Voltage magnitude and angle of buses in
414(l-l) VOLTAGE section
Bus
no.
VR
volts
(rms)
Angle
(deg.)
VY
volts
(rms)
Angle
(deg.)
VB
volts
(rms)
Angle
(deg.)
1
234.32
-1.83
233.16
-122.29
231.98
117.41
2
234.34
-1.08
233.42
-121.25
231.89
118.63
3
233.97
-1.92
232.87
-122.35
231.63
117.35
5
235.43
-2.26
233.37
-122.86
232.71
116.83
6
236.09
-1.93
235.40
-122.45
234.58
117.22
8
234.47
-2.64
233.39
-123.35
232.21
116.17
9
232.30
-3.27
230.67
-124.07
229.11
115.34
10
230.11
-5.40
224.20
-126.67
222.89
111.58
12
230.94
-4.98
227.71
-126.40
226.42
112.44
13
225.03
-5.46
218.76
-126.55
217.17
111.63
14
224
-5.47
217.34
-126.47
215.67
111.65
15
228.49
-4.16
223.71
-124.94
222.19
113.76
16
231.99
-4.99
226.31
-126.53
111.80
17
232.64
-4.02
227.04
-125.20
226.77
113.29
Table 10 represents that because of more power
drawn by the 34 bus, the preceding 35th has a large
voltage error of 10.22%, and the 31 bus has a more
voltage angle of 14.42 deg., in SN2.
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
38
Volume 19, 2024
Table 10. Voltage magnitude and angle of buses in
207(l-l) VOLTAGE section
Bus
no.
VR
volts
(rms)
Angle
(deg.)
VY
volts
(rms)
Angle
(deg.)
VB
volts
(rms)
Angle
(deg.)
18
119.61
-3.55
118.10
-124.43
117.37
114.69
19
116.47
-6.00
112.57
-127.09
111.74
110.78
20
114.35
-7.04
109.84
-128.14
108.78
109.34
23
119.81
-6.93
114.86
-128.05
113.81
109.33
25
117.53
-7.85
112.37
-128.91
111.07
108.27
27
117.12
-5.57
113.35
-126.61
112.72
111.32
28
118.83
-4.47
115.99
-125.38
115.41
113.06
29
120
-3.37
117.93
-124.55
117.42
114.28
30
117.09
-8.49
111.02
-129.57
109.59
107.11
31
116.46
-9.37
109.31
-130.48
107.68
105.58
32
116.50
-8.95
110.34
-130.05
108.74
106.54
33
116.44
-9
110.20
-130.11
108.60
106.44
35
114.52
-8.46
108.73
-129.57
107.30
107.19
37
116.43
-7.79
111.10
-128.90
109.82
108.17
38
120.45
-6.63
115.67
-127.73
114.65
109.75
41
119.07
-5.21
116.18
-126.18
115.18
112.22
42
118.69
-7.04
113.60
-128.07
112.26
109.22
43
118.73
-5.21
115.84
-126.18
114.85
112.22
44
120.10
-6.03
115.76
-127.09
114.87
110.65
47
122.69
-6.28
117.96
-127.40
117.04
110.17
49
125.51
-5.55
121.99
-126.66
121.09
111.51
50
124.15
-6.13
119.52
-127.37
118.65
110.24
51
123.67
-5.47
120.48
-126.76
119.76
111.48
52
119.70
-4.76
115.69
-125.72
115.02
112.18
53
119.69
-5.14
115.01
-126.15
114.27
111.42
54
121.51
-4.38
118.41
-125.31
117.63
113.05
55
123.47
-3.33
122.59
-124.14
121.74
115.26
56
119.40
-7.95
113.88
-129.05
112.50
107.98
57
118.48
-8.02
112.96
-129.14
111.62
107.86
The highest load at bus 12 on phase ‘B’; as
shown in Table 11, draws the highest current of 5.75
amps. However, the highest angle is 38.84 deg
which is at bus 2, in SN1.
Table 11. Current magnitude and angle of buses in
414(l-l) VOLTAGE section
Bus
no.
IR
amp
(rms)
Angle
(deg.)
IY
amp
(rms)
Angle
(deg.)
IB
amp
(rms)
Angle
(deg.)
1
1.54
-24.65
1.93
-144.82
2.21
93.35
2
1.12
-38.84
1.32
-159.88
1.58
75.78
3
1.63
-25.35
1.99
-145.45
2.28
92.64
5
0.04
117.87
0.05
-3.90
0.05
-131.5
6
1.48
-12.95
1.87
-132.76
2.13
105.58
8
2.05
-15.86
2.59
-136.13
2.97
102.86
9
2.61
-20.01
3.23
-140.52
3.72
98.29
10
0.12
-46
0.15
-173.39
0.17
68.74
12
3.80
-15.93
4.92
-138.51
5.75
102.07
13
0.13
97.59
0.16
-28.47
0.16
-150.3
14
0.72
-35.89
0.81
-153.28
0.90
84.59
15
1.16
-25.86
1.33
-144.13
1.49
92.96
16
0.38
-10.83
0.46
-127.69
0.52
107.87
17
0.51
-10.06
0.63
-128.76
0.72
107.25
In SN2, the transformer at bus 13 is heavily
loaded so as shown in Table 12 secondary side bus
49 draws the highest current of 2.62 amps on the ‘B’
phase.
Table 12. Current magnitude and angle of buses in
207(l-l) VOLTAGE section
Bus
no.
IR
amp
(rms)
Angle
(deg.)
IY
amp
(rms)
Angle
(deg.)
IB
amp
(rms)
Angle
(deg.)
18
0.76
-24.01
0.96
-144.81
1.11
93.97
19
0.21
-32.39
0.24
-152.23
0.26
85.91
20
0.16
-44.22
0.17
-164.06
0.18
73.97
23
0.36
-38.83
0.40
-158.98
0.43
79.43
25
0.29
-29.64
0.37
-151.85
0.42
84.11
27
0.68
-33.01
0.77
-152.21
0.85
85.58
28
0.78
-32.53
0.90
-151.98
1
85.89
29
1.39
-24.09
1.69
-144.39
1.93
93.19
30
0.16
-32.35
0.2
-150.32
0.23
84.91
31
0.09
-32.35
0.11
-153.62
0.13
81.63
32
0.03
-173.70
0.04
51.13
0.04
-77.46
33
0.08
-35.56
0.10
-156.67
0.12
79.87
35
0.48
-41.18
0.54
-161.53
0.59
75.67
38
0.45
13.11
0.52
-111.88
0.55
118.93
41
0.24
170.05
0.29
44.84
0.33
-81.27
42
0.12
-156.17
0.13
79.51
0.13
-46.94
43
0.04
1.86
0.05
-127.82
0.05
106.17
44
0.67
3.76
0.8
-120.42
0.9
112.55
47
0.83
-41.99
0.96
-160.45
1.08
78.52
49
2.07
-50.37
2.37
-169.29
2.62
70.81
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
39
Volume 19, 2024
Bus
no.
IR
amp
(rms)
Angle
(deg.)
IY
amp
(rms)
Angle
(deg.)
IB
amp
(rms)
Angle
(deg.)
50
0.37
-44.56
0.44
-162.04
0.51
77.22
51
0.14
-175.31
0.17
49.93
0.20
-77.69
52
0.29
-16.61
0.38
-140.35
0.44
94.41
53
0.19
-10.84
0.25
-136
0.29
97.18
54
0.27
135.39
0.32
15.83
0.36
-103.8
55
0.34
141.76
0.42
21.89
0.48
-98.27
56
0.07
107.36
0.07
-12.57
0.07
-131.9
57
0.11
10.22
0.13
-119.38
0.15
112.27
Out of all generator buses in SN1, 9 and 12 have
high loads; therefore, as shown in Table 13 these
two buses draw more power than all other buses.
Although, some of the buses are caused by low
reverse power flow.
Table 13. Active and reactive powers of buses in
414(l-l) VOLTAGE section
Bus
no.
PRYB
watts
QRYB
var
Bus
no.
PRYB
watts
QRYB
var
1
1356
507.4
10
74.81
60.91
2
811.3
561
11
-127.7
-104
3
1391
540.5
12
3583
667.2
4
264.4
7.297
13
-9.91
-90.32
5
-14.92
-23.78
14
501.5
246.6
6
1406
264.2
15
907
312.3
7
363.4
130
16
339.5
27.79
8
1917
421.2
17
469.8
47.6
9
2328
640.3
In SN2, Table 14 shows buses 29 and 49 found
to be heavily loaded; also, some buses have reverse
power flow.
Table 14. Active and reactive powers of buses in
207(l-l) VOLTAGE section
Bus no.
PRYB
watts
QRYB
var
Bus no.
PRYB
watts
QRYB
var
18
346.7
114.6
38
188.2
-47.36
19
76.97
33.3
39
99.95
43.7
20
46.58
31.79
40
-5.922
107.8
21
-26.91
-31.44
41
-107.1
-12.77
22
-27.01
-30.21
42
-41.02
19.7
23
123.6
68.09
43
17.68
-0.241
24
64.17
52.42
44
302.8
-29.82
25
123.5
42.6
45
306.6
-20.67
26
163.1
98.7
46
310
189.4
27
252.6
113.4
47
306.3
181.6
28
299.7
138.8
48
14.56
84.87
29
611.3
200.9
49
681.5
565
30
67.17
20.5
50
143.3
88.74
31
35.55
12.69
51
-68.74
2.257
32
-13.12
1.387
52
140
29.47
33
32.1
13.26
53
93.05
12.15
34
106.1
66.91
54
-96.07
-67.27
35
156.2
88.16
55
139.2
-81.87
36
-157.1
-89.72
56
-10.54
-21.11
37
252.5
244
57
49.71
-8.891
3.4 Results Comparison with Methodology
This section shows the reliability scale of the
proposed method; from Figure 2, Figure 3, Figure 4
and Figure 5 are boundary bus parameters of load
buses on the ‘R’ phase. As shown in Figure 2,
voltage curves were almost identical but the
magnitude variations due to the line voltage drop,
all the voltages compared against the nominal
voltage (pink) of the bus. As shown in Figure 3, the
current at the buses is more than calculated because
the methodology considers only connected load
current but not lines.
Fig. 2: The voltage at load buses, for all tests with
the methodology
Fig. 3: The current at-load buses, for all tests with
the methodology
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
40
Volume 19, 2024
As shown in Figure 4, between 1 to 10 buses
calculated powers show more difference with
simulation results.
Fig. 4: The power flow at the buses, for all tests and
methodology
Figure 5 shows, that bus 2 has very low p.f and
some buses show leading p.f because of reverse
power flow.
Fig. 5: The p.f at the buses, for all tests and
methodology
4 Conclusions
The present paper discussed the development of
methodology and procedure to design a 3-phase
LVSM of IEEE 57 bus power system in the
Simulink platform. Three simulation tests were
performed on LVSM to determine the maximum
voltage regulation, bus powers, and angles, as well
as power, flows in lines, and transformers. Table 15
shows the summary of simulations of SN1 and SN2.
Table 15. Subnetwork wise bus parameters
summary
The main advantage of this work is that the
methodology used in this paper is applicable to any
standard power system model. However, the LVSM
design procedure, and the boundary bus parameters
from the results useful for implementing the
practical model in the laboratory. While designing,
powers are useful to design the rating of equipment,
power flows are useful to design pi-lines, voltages
to design equipment, and the size of the component
by currents. Also, the model can be simulated with
real-time simulators either with the required sub-
network or the total network.
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
41
Volume 19, 2024
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
42
Volume 19, 2024
Matrix. IEEE Latin America Transactions,
19(02), 182-190.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed to 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.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.5
G. Veera Bhadra Chary,
Raghavaiah Katuri, K. Mercy Rosalina
E-ISSN: 2224-350X
43
Volume 19, 2024
