A 6mart 9oltage 6tability 0aneuver $lgorithm
IRU9oltage &ollapses 0itigation
Mohamed Usama 1, Hoda K.Mohamed 1, Islam A.M. El-Maddah 1, M.Amer Shedied 2
1
(Computer and Systems Engineering Department, Ain Shams University, Cairo-Egypt)
2
(Computer Science Department, Future Academy, Cairo-Egypt)
1
moh.usama88@yahoo.com , hoda.korashy@eng.asu.edu.eg , islam.elmadah@eng.asu.edu.eg
2
mo_amer2002@yahoo.com
decades [1]. In general, the stability of a system can be defined
as the ability of a system to return to its original condition after
being subjected to a disturbance and remain its condition over
time [2]. There are several types of instability that could face
the system operator such as voltage instability, frequency
instability, and inter-area oscillations. In V.S.A.M.A we only
concerned about handling the voltage instability issue using
machine learning techniques by developing an early warning
system and an automatic maneuver system that can mitigate the
power outage. We can define the voltage stability [3] as the
process of maintaining acceptable voltages level at all buses
after being subjected to a disturbance. We can achieve that
stability by balancing between the supplies from the generation
stations and the load demands of the consumers. This balance
could be lost when a heavy reactive loaded system happens. To
evaluate the voltage stability of the power grid, there are
several mathematical indices [8] that can indicate how close
the system to the failure or voltage collapses. In [4] voltage
stability indices are used to find out the weak buses and use
these results as an overall evaluation of the power grid .this
could be used as an early warning system for blackouts. After
obtaining an overall evaluation of the power grid, we can then
propose different control conditions and evaluate them to
choose the most suitable one to enhance the voltage stability.
In [5] a novel index had proposed to evaluate the power grid
and proposed voltage stability control strategy to improve the
system-level voltage stability. We can use artificial intelligence
techniques for voltage stability evaluation such as the artificial
neural network (A.N.N), Deep learning and machine learning
instead of mathematical indices. In [6] a neural network was
used instead of ordinary mathematical methods to evaluate the
voltage stability of the power grid.
Abstract— In the power system, the instantaneous and
permanent stability is a major requirement cannot be
overlooked. Because of the power grid large-scale systems, any
disturbance anywhere on the power grid could pose a reason of
overall dynamic imbalances. Major consequences could be
occurred to the electricity feeding across wide areas of country
which is called partial blackout, even entire country which is
called overall blackout. It is perhaps for this reason that the
existence voltage stability indices which indicate the power grid
system stability level is very essential .With knowing the voltage
stability level of the transmission lines that involves the power
grid in real time ( online operation) , the voltage stability of the
entire power grid could be obtained easily . There are several
mathematical base voltage indices. But in this proposal, another
voltage stability index will be build based on the machine
learning techniques to mitigate the voltage collapse phenomenon.
This novel predictor is proposed in transient stability analysis
based on machine learning techniques such as (Linear regression,
neural network, and Decision tree). This predictor is built after a
comparison was made between the impacts of various machine
learning algorithms using different datasets. Three different
mathematical voltage stability indices (FVSI, Lmn, and NLSI)
had been used to prepare datasets for the training purpose. An
early warning system had been built based on the proposed
predictor. This early warning system could be used to inform the
system operator with the hazards of voltage instability issues face
the electric power grid and visualize these hazards. The E.W.S
had then been used as a kernel to build V.S.A.M.A (Voltage
Stability Automatic Maneuver Algorithm) that can handle the
voltage instability issue.
Index Terms— Decision tree, Early warning, Line stability
index, Linear regression, Maneuver algorithm, Neural network,
Predictive analysis , Predictive modeling , Predictors ,
RapidMiner programming, Voltage stability.
I. INTRODUCTION
In V.S.A.M.A, A novel voltage instability predictor
will be proposed as a kernel of an early warning system
and automatic maneuver algorithm that target to mitigate
the power outage via suggesting suitable operating
conditions. The impacts of these operating conditions are
valuated using the predictor which is based on machine
learning algorithms. Section two will discuss the
background needed to complete this work including
voltage stability indices used to evaluate the voltage
stability, machine learning use in this proposal and some
In the modern power system, real-time monitoring and
operating of the electric power grid are the main tasks of the
system operator. These tasks had become more complex and
difficult because of the wide geographical regions covered by
the power grid, a massive calculations were done, the difficulty
of the decision taken and also the hardness of action rollback.
One of the major concern issues in the electric power system is
the grid stability. The power instability issue caused many
notable wide-scale power outages or Blackouts in recent
‹,(((
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.
other utilities such as load flow algorithms, early
warning and visualizer. Section three will discuss
methodology used to build the voltage instability
predictor, E.W.S, Visualizer, and the V.S.A.M.A. In
section four and five, the results had been achieved and
the conclusion will be demonstrated.
3) Novel line stability index (NLSI)
Yazdanpanah-Goharrizi derived a line stability index based
on the same concept as Lmn and FVSI [8], [10], [12]. The
NLSI equation is illustrated below in eq-3. As Lmn and FVSI,
NLSI must remain less than 1 to ensure the stability and avoid
the voltage collapses.
II. BACKGROUND
ܰ‫ ܫܵܮ‬ൌ
A. Voltage Stability Indices
To build the predictor in V.S.A.M.A which is the main
component, firstly we need to train the selected machine
learning algorithm using a bulk dataset. These dataset can be
obtained by evaluating the voltage stability of the power grid
transmission lines In several situations mathematically via
voltage stability indices such as fast voltage stability indices
(FVSI), line stability index (Lmn), line stability factor (LQP),
novel line stability index (NLSI),…etc. These indices will be
applied separately to each transmission line of an
interconnected network. The representation of a transmission
line between two buses is illustrated in figure 1. In V.S.A.M.A
we will use three different indices (FVSI, Lmn, and NLSI) and
compare the predictor result for each index.
1) Fast voltage stability indices (FVSI)
Musirin proposed a novel Fast Voltage Stability Index
(FVSI) [7], [8], [9], and [10] simplified from the voltage
quadratic equation at the sending end of a representation of a 2bus system. The FVSI equation is illustrated below in
equation-1. The value of the FVSI must remain less than 1 to
ensure the stability and avoid the voltage collapses.
Ͷܼ ଶ ܳ‫ݎ‬
ܸ‫ ݏ‬ଶ ܺ
C. Early warning and Visualization
The United Nations International Strategy for Disaster
Reduction (UNISDR) defined the early warning system in [13].
It is the set of capacities needed to generate and disseminate
timely and meaningful warning information to enable
individuals threatened by a hazard to prepare and to act
appropriately to reduce the possibility of harm or loss. In the
power system, the operator in the control center is the one who
concerned with this utility. The system operator needs to be
informed acknowledgment of hazards and risks connected with
the voltage instability issue. This will help the operator to take
suitable actions to avoid the power grid failure. These hazards
can be visualized to the system operator in percentage form or
gradually colored form to make the extraction of data easier
and taking the decision faster and more accurate.
ሺͳሻ
2) Line stability index (Lmn)
Moghavemmi proposed a novel method [8], [11] that
examined the line voltage stability by an index which is varied
from zero to one. This index formulated using power transfer
concept in the single line power transmission network. The
novel index equation is illustrated below in eq-2. Also, the
value of the Lmn index must remain less than 1 to ensure the
stability and avoid the voltage collapses.
‫ ݊݉ܮ‬ൌ
Ͷܳ‫ݎ‬
ሺܸ‫݊݅ܵݏ‬ሺˁ െ ߜሻሻଶ
ሺ͵ሻ
B. Machine Learning
One of the most important targets of V.S.A.M.A is to
replace the mathematical voltage stability index with predictor
based on machine learning algorithm and evaluate the stability
of the electric power grid with this predictor. Different
algorithms had been used to produce several predictors and
compare results to obtain most accurate predictor. The
algorithms of machine learning can be classified into three
main categories 1) Clustering algorithms 2) Classification
algorithms 3) Regression algorithms. The predictor needed to
be built has continues output from 0 to 1. That is mean we can
classify our problem as a regression problem. There are several
regression machine learning algorithms [12] such as 1) Linear
regression 2) Polynomial regression 3) Vector linear regression
4) Local polynomial regression 5) Neural network 6) Deep
learning.
Because of the narrow output range of our proposed
predictor, we can convert our problem from regression problem
to classification problem by discretizing the output with some
acceptable resolution. Now we can also use the classification
algorithms to build the predictor. There are several
classification machine learning algorithms [12] such as 1)
Decision tree 2) K-Nearest Neighborhood 3) Neural network.
In V.S.A.M.A, three different indices (FVSI, Lmn and NLSI)
will be used to prepare the training datasets. These datasets will
be used to train three different learning machine algorithms
(Linear regression, neural network, and Decision tree). A
competition will be held between these three datasets once for
each algorithm to produce three predictors. The most accurate
predictor will be chosen as a kernel of the V.S.A.M.A.
Figure 1: “The two bus representation of a power system”
‫ ܫܸܵܨ‬ൌ
ܲ‫ ܴݎ‬൅ ܳ‫ܺݎ‬
ͲǤʹͷܸ‫ ݏ‬ଶ
ሺʹሻ
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.
D. Load Flow
The power flow or load flow analysis could be defined as
[13] the study to predict the effect of some certain loading
condition on the power system grid parameters. In proposed
system we can look to the power flow analysis as block gets
the line data, bus data and loading conditions and this block
outputs the voltage magnitude and angle at each bus as
illustrated in figure 2.
that will solve the issue of massive computation resources
needed and the limited time available during online analysis.
The block diagram of the proposed system is illustrated in
figure 4.
Figure 4: “V.S.A.M.A block diagram”
The methodology section consists of four subsections (Select
case study, Prepare data, Build the predictor and V.S.A.M.A).
The first section discusses the structure of appropriate electric
power grid that will be used to test and evaluate our algorithm.
The second section discusses how to extract the datasets from
the testing environment for the algorithm training. The third
section discusses three algorithms used to build three predictors
and how to implement these algorithms on RapidMiner Studio
to build the predictors. The last section discusses the procedure
of building the V.S.A.M.A and developing it using Matlab
program.
Figure 2: “Load Flow Block Diagram”
The rest of system parameters such as the real power and
reactive power flows, current flow, voltage drop, power flow
losses, .etc. can be driven easily from the voltage magnitude
and angle. There are several methods to perform the load flow
study such as Gauss iterative method and Newton- Rapson
method. In V.S.A.M.A, we used Gauss-Seidel method [13]
[14]. The flowchart of this method is illustrated in figure 3.
A. Select case study
The IEEE 9-Bus system selected as a test case. It represents
a simple approximation of a portion of the Western System
Coordinating Council (WSCC). It consists of 3 generators, 3
transformers, 3 loads, 9 buses and 6 lines. The bus data and
line data are illustrated in table 1 and table 2. Also, the
structure of the network illustrated in figure 5.
Figure 5: “The IEEE 9-Bus system structure”
Figure 3: “Gauss iterative method flowchart”
Table 1: “Line data”
III. METHODOLOGY
The target of V.S.A.M.A is to design a predictor that can
evaluate the voltage stability of the power network and use this
predictor to build an early warning system for the outage and
over blackout. Starting from this, we can build an automatic
maneuver algorithm that will be a kernel for a fully automatic
maneuver system. The maneuver algorithm can handle the
voltage instability issue under the system operator supervision.
The proposed system will be based on predictive techniques
Line
From Bus
To Bus
R
X
B
1
4
1
0
0.0576
0
2
2
7
0
0.0625
0
3
9
3
0
0.0586
0
4
5
4
0.010
0.0680
0.176
5
6
4
0.017
0.0920
0.158
6
7
5
0.032
0.1610
0.306
7
9
6
0.039
0.1738
0.358
8
7
8
0.0085
0.0576
0.149
9
8
9
0.0119
0.1008
0.209
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.
Table 2: “Bus data”
Table 3: “A sample of the labeled dataset”
#
Nom
KV
PU
Volt
Angle
(Deg)
Gen
MW
Gen
Mvar
Load
MW
Load
Mvar
1
16.5
1.040
0
45.44
4.26
-
-
2
18.0
1.043
8.86
158
4.9
-
-
3
13.8
1.039
5.22
90
-11.45
-
-
4
230
1.037
-1.39
-
-
-
-
5
230
1.027
-1.77
-
-
75
35
6
230
1.026
-2.95
-
-
90
30
7
230
1.045
3.67
-
-
-
-
8
230
1.031
0.84
-
-
125
40
9
230
1.047
2.44
-
-
-
-
R
(p.u)
X
(p.u)
B
(p.u)
Nom
Vs
Mag
Vs
Angle
Vs
Nom
Vr
…
VSI
0
0
0
0.01
0.017
0.032
0.039
0.0085
0.0119
0
0
0
0.0576
0.0625
0.0586
0.068
0.092
0.161
0.1738
0.0576
0.1008
0.0576
0.0625
0.0586
0
0
0
0.176
0.158
0.306
0.358
0.149
0.209
0
0
0
230
18
230
230
230
230
230
230
230
230
18
230
1.02313
1.025
1.03201
0.99241
1.01089
1.02504
1.03201
1.02504
1.01594
1.02133
1.025
1.03149
-3.797
6.531
0.067
-7.009
-5.427
0.966
0.067
0.966
-1.333
-3.805
6.53
0.053
16.5
230
13.8
230
230
230
230
230
230
16.5
230
13.8
…
…
…
…
…
…
…
…
…
…
…
…
0.072146948
0.056632164
0.040984084
0.112662127
0.055924315
0.147371653
0.134235962
0.031732019
0.091555124
0.078840694
0.052572214
0.03894044
C. Build the predictor
The predictor is an iterative trained machine learning
algorithm. The concept of building predictor is to learn
machine learning algorithm from a large number of inputs and
its corresponding outputs and try to configure a relation
between these data to estimate the output for new inputs as
illustrated below in figure 7. Both input data gathered with the
corresponding output data is called labeled dataset.
B. Prepare data
In machine learning, it is very important to feed our
supervised algorithms with a huge amount of labeled data set to
achieve better results. Labeled data can be defined as input data
and its corresponding outputs. In V.S.A.M.A the output data is
the evaluation of voltage stability and the inputs is the system
parameters such as resistance, reactance, voltage magnitude
and its angle from and to bus, active and reactive power from
and to bus,…etc. For the predictor training, the input data can
be collected through two stages. The first stage is to simulate
the network in different loading conditions and get the
corresponding system parameters for each run as illustrated in
figure 6. The Power World Simulation tool is used to simulate
two hundred different loading conditions to produce around
one thousand three hundred different examples as a dataset. We
can obtain these loading conditions by changing the reactive
power and active power of loads and generators. The second
stage is to calculate the corresponding outputs by ordinary
mathematical methods and we use three different voltage
stability indices (FVSI, Lmn and NLSI). The labeled dataset
used for the predictor training are illustrated in table 3.
Figure 7: “Machine learning workflow”
A sophisticated platform is used for predictive analysis and
modeling called RapidMiner Studio. It is a graphically
programming language that analyses data using connected
blocks without code.
1) Linear regression
The first machine learning algorithm used is the linear
regression. It is a statistical method that allows us to discover
the relationship between one dependent variable called labeled
attribute and a series of other changing variables. In
V.S.A.M.A, the predicted variable is the voltage stability index
and it is continuous variable from 0 to 1. A competition
between three indices had been done to select the most
compatible index with the linear regression algorithm. The
process of building the predictor design using linear regression
algorithm is illustrated in figure-8 and the predictor equation
for the winning index is illustrated in figure 9.
Figure 6: “The 9-Bus system implementation in power-world”
Figure 8: “The process of building linear regression predictor in
RapidMiner”
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.
Figure 12: “The process of building the decision tree predictor in
RapidMiner”
Figure 9: “The Linear regression predictor equation”
2) Neural Network
The second machine learning algorithm used is the artificial
neural network. Our predictor had been learned by means of a
feed-forward neural network trained by a back propagation
algorithm (multi-layer perceptron). A competition between
three indices had been done to select the most compatible index
with the neural network algorithm. The process of building the
predictor based on neural network algorithm is illustrated in
figure 10 .A sample of the network weights of the predictor for
the winning index is illustrated in table 4.
Figure 13: “Graphical representation of the decision tree
predictor”
D. V.S.A.M.A
After we had built our predictor that can predict the level
of voltage stability for a transmission line using machine
learning technique instead of the ordinary mathematical
method, we can now use it as a kernel of the V.S.A.M.A. That
algorithm can handle the voltage instability issue by suggesting
suitable loading conditions. Also, the predictor can be applied
on all over the network and visualize the stability evaluation of
it to the system operator. By setting certain setpoint we can
build an early warning system that can notify the system
operator with abnormal behavior and trigger the maneuver
algorithm. The flow chart of the V.S.A.M.A is illustrated
bellow in figure 13.
Figure 10: “The process of building A.N.N predictor in
RapidMiner”
Figure 11: “The weighting arrays for the A.N.N model”
3) Decision tree
The third machine learning algorithm used is the decision
tree. As we mentioned before, the output of the predictor
bounded between small ranges from zero to one. That is why
we can consider our problem as a classification problem. The
decision tree algorithm is a supervised classification algorithm
in the form of a tree structure by starting at the root of the tree
and moving through it until a leaf node. The predictor is a set
of rules that can be graphically represented. A competition
between three indices had been done to select the most
compatible index with the decision tree algorithm. The process
of building the predictor designed using decision tree algorithm
is illustrated in figure 11 and the predictor graphical
representation of the winning index is illustrated in figure 12.
Figure 14: “The flow chart of the V.S.A.M.A”
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.
IV. RESULTS
A. Predictor results
Three different datasets used to train three different
machine learning algorithms. All datasets have the same data
except the voltage stability indices (FVSI, Lmn and NLSI)
used as labeled attribute. The table-5 illustrates the accuracy by
the RMS (Root Mean Square) value of each predictor using the
three datasets. The graphs below (14, 15, and 16) show the
actual value of voltage index on the x-axis and its predicted
value on the y-axis for each winning index in each Predictor.
As shown in the table 5, the more accurate predictor is the
A.N.N with the NLSI labeled attribute dataset.
Table 4: “Predictors accuracy Comparison”
FVSI
Lmn
NLSI
Linear Reg.
0.036
0.043
0.038
A.N.N
0.020
0.010
0.008
Decision tree
0.033
0.047
0.065
Figure 17: “Decision Tree Accuracy”
B. Case study
For V.S.A.M.A testing, we choose a snapshot of the
IEEE 9-Bus system operating conditions that have one line of
nine exceeded the preset instability warning boundary which is
equal 0.5. As shown in figure 15, the visualizer informs the
operator that line number four has voltage instability issue and
the V.S.A.M.A had to start solving this problem. After the
V.S.A.M.A had been triggered by the warning system, the
V.S.A.M.A suggested ten different loading conditions and used
the predictor to evaluate the stability of the overall network for
these different scenarios. The V.S.A.M.A suggests ten different
loading conditions each time until it achieves a loading
condition that guarantees the stability of the overall network
with fewer changes in the operation conditions. In our test case,
the voltage stability evaluation of the network for each scenario
is shown in Table 6. Scenario number five shows that all lines
will be stable and the stability issue for line four will be solved
by this suggestion and the operator should apply these loading
conditions to achieve the stability.
Figure 15: “Linear Regression Accuracy”
Table 5: “Evaluation of the V.S.A.M.A Suggestions”
1
2
3
4
5
6
7
8
9
10
Figure 16: “A.N.N Accuracy”
Line1
Line2
Line3
Line4
Line5
Line6
Line7
Line8
Line9
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.035
0.265
0.260
0.260
0.265
0.256
0.256
0.266
0.251
0.253
0.224
0.225
0.227
0.225
0.228
0.230
0.226
0.231
0.234
0.513
0.505
0.505
0.513
0.496
0.496
0.513
0.487
0.488
0.129
0.146
0.147
0.130
0.164
0.165
0.130
0.181
0.182
0.346
0.336
0.334
0.344
0.324
0.320
0.342
0.312
0.305
0.291
0.277
0.278
0.293
0.263
0.266
0.294
0.250
0.254
0.005
0.006
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.079
0.072
0.072
0.079
0.065
0.065
0.079
0.058
0.058
0.035
0.264
0.223
0.513
0.129
0.348
0.290
0.006
0.079
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.
[5] Houhe Chen, Tao Jiang, Haoyu Yuan, Hongjie Jia, Linquan
Bai, Fangxing Li. "Wide-area measurement-based voltage
stability sensitivity and its application in voltage control."
Elsevier, 2016.
[6] "Voltage stability monitoring of power systems using
reduced network and artificial neural network." Elsevier,
2016.
[7] I. Musirin; T. K. Abdul Rahman. "Novel fast voltage
stability index (FVSI) for voltage stability analysis in
power
transmission
system."
IEEE
Conference
Publications. IEEE, 2002.
[8] Danish, Mir Sayed Shah. Voltage Stability in Electric
Power System: A Practical Introduction. Logos Verlag
Berlin, 2015.
[9] Aziz Oukennou,Abdelhalim Sandali. "Assessment and
analysis of Voltage Stability Indices in electrical network
using PSAT Software." Power Systems Conference
(MEPCON), 2016 Eighteenth International Middle East.
IEEE, 2017.
[10] M. Cupelli, C. Doig Cardet, A. Monti. "Comparison of line
voltage stability indices using dynamic real time
simulation." Innovative Smart Grid Technologies (ISGT
Europe), 2012 3rd IEEE PES International Conference and
Exhibition on. IEEE, 2013.
[11] K. R. Hridya, V. Mini, R. Visakhan, Asha Anu Kurian.
"Analysis of voltage stability enhancement of a grid and
loss reduction using series FACTS controllers." Power,
Instrumentation, Control and Computing (PICC), 2015
International Conference on. IEEE, 2015.
[12] Isaac A. Samuel, James Katende, Claudius O. A. Awosope,
Ayokunle A. Awelewa. "Prediction of Voltage Collapse in
Electrical Power System Networks using a New Voltage
Stability Index." International Journal of Applied
Engineering Research, 2017.
[13] Das, J. C. Power System Analysis Short-Circuit Load Flow
and Harmonics. Taylor & Francis Group, LLC, 2012.
[14] C.P. Salomon, Germano Lambert-Torres. "Hybrid Particle
Swarm
Optimization
Approach
for
Load-Flow
Computation." International journal of innovative
computing, information & control: IJICIC, 2013.
[15] A.Yazdanpanah-Goharrizi, R.Asghari. "A Novel Line
Stability Index (NLSI) for Voltage Stability Assessment of
Power Systems." 7th WSEAS International Conference on
Power Systems. 2007.
[16] Mohssen Mohammed, Muhammad Badruddin Khan, Eihab
Bashier Mohammed Bashier. Machine Learning:
Algorithms and Applications. CRC Press, 2016.
[17] Ashbindu Singh, Zinta Zommers. Reducing Disaster: Early
Warning Systems for Climate Change. Springer, 2014.
[18] Glenn W. Stagg, Ahmed H.El-Abiad. Computer methods in
power system analysis. McGraw-Hill, 1987.
Figure 18: “Visualizer”
V. CONCLUSION
A voltage stability automatic maneuver algorithm based on
machine learning had been presented. The main contribution is
to propose a novel voltage stability predictor by introduce a
comparison between three different machine learning
algorithms (Linear regression, neural network, and Decision
tree) which are trained using three different datasets based on
different voltage indices (FVSI, Lmn and NLSI) for each
algorithm , that produces nine predictors. The best results
achieved by predictor based on A.N.N algorithm trained by
NLSI dataset. This predictor used to build an early warning
system and maneuver algorithm that can handle the voltage
stability issue under the system operator supervision.
VI. FUTURE WORK
The future work will focus on how to build an early warning
system based on learning machine algorithm that can choose a
trigger to V.S.A.M.A for each line based on the historical data
instead of the fixed triggers value used in this work which is
preset by the system operator. Next we will develop a fully
automated maneuver system that can dispense of the system
operator.
VII. REFERENCES
[1] Arulampalam Atputharajah, Tapan Kumar Saha. "Power
system blackouts - literature review." Industrial and
Information Systems (ICIIS), IEEE, 2009.
[2] Pansini, Anthony J. Power Systems Stability Handbook.
The Fairmont Press, 1992.
[3] P. Kundur ; J. Paserba ; V. Ajjarapu ; G. Andersson ; A.
Bose ; C. Canizares ; N. Hatziargyriou ; D. Hill ; A.
Stankovic ; C. Taylor ; T. Van Cutsem ; V. Vittal.
"Definition and classification of power system stability
IEEE/CIGRE joint task force on stability terms and
definitions." (IEEE Transactions on Power Systems) 2004.
[4] Pasllavi Choudekar, Divya Asija and Ruchira. "Prediction
of Voltage Collapase in Power System Using Voltage
Stability Indices." Proceeding of International Conference.
Springer, 2017.
Authorized licensed use limited to: Cape Peninsula University of Technology. Downloaded on September 05,2022 at 10:10:05 UTC from IEEE Xplore. Restrictions apply.