22-05-2012, 10:30 AM
Transient Stability Assessment using Artificial Neural Networks
[attachment=22650]
Ab3tract
Online transient stability assessment (TSA) of a
power system is not yet feasible due to the intensive computation
involved. Artificial neural networks(ANN) have been
proposed as one of the approaches to this problem because
of its ability to quickly map nonlinear relationships between
the input data and the output. In this paper a review of
the previously. published papers on TSA using ANN is presented.
The paper also reports the results of the application
of ANN to the problem of TSA of a 10 machine 39 bus system.
I. INTRODUCTION
The security assessment of a power system requires analysis
of the dynamic system behaviour under a prescribed
set of events known as contingencies. Conventionally this is
done by simulating the system nonlinear equations. Since
the stability limits cannot be determined from a single simulation.
more than one simulation is required. The large
size of the system adds to the complexity. Hence online
transient stability assessment(TSA) by simulation is not
yet feasible.
The difficulties mentioned above can be overcome to a
large extent by the method of energy function for direct stability
evaluation. This method involves comparison of the
value of the energy function at the instant of last switching
W(t,) to the critical value W,,.; the system is transiently
stable if W(t,) < Wcr. But this method is not yet suitable
for online computation.
Artificial neural networks(ANN) have been proposed as
an alternative method for the TSA problem by many aut,
hors since Sobajic et a1.[1] explored the capability of ANN
for TSA. Since trained ANN can quickly map nonlinear
relationship between input data and the ouput, they are
considered to be suitable for online use. There are a number
of publications on ANN application to TSA. In this
paper, a review of some of the previously published papers
on this topic is presented. The paper also reports the results
of ANN application to the determination of stability
and mode of instability for a 10 machine 39 bus system.
11. ANN APPLIED TO TSA
The main objectives of online TSA are fast evaluation
and 'accuracy of results. ANN is a possible alternative because
of its fast response. Application of ANN consists of
the following steps.
A. Data generation
It is important to obtain a set of training patterns that
adequately covers the space of possible operating conditions.
Different operating conditions are generated by different
combinations of load levels and network topology.
Since ANN are known to do interpolation very well but
hardly any extrapolation, the test patterns are required to
be within the range of training patterns.
B. Selection of input variables
The selection of inputs is an important factor in the successful
use of ANN. It is obvious that the candidates for
inputs are those independent variables which influence the
output. Different prefault variables, variables during fault
and postfault variables have been used as input variables
in the previous studies.
C. Selection af ANN architecture
Multilayered backpropagation network is the most commonly
used ANN in the previously published papers on
this subject. It has also been successfully applied in many
other practical applications. A few authors have applied
functional link network(FLN) [2,3] for TSA.
D. Training the ANN and testing
The advantage of ANN is that it can be used for online
applications, since most of the computations are done offline
and negligible online computation is required. Data
generation and ANN training constitute offline computation.
Usually training is the most time consuming part in
the design and use of ANN. For a given ANN architecture
many training algorithms exist and a choice has to be made
judiciously to obtain fast and efficient training of the ANN.
111. REVIEW
A large number of publications have appeared on ANN
application to TSA since the paper by Sobajic et al.[l].
Sobajic et al. used ANN for prediction of critical clearing
time(CCT) for a small test power system. A good agreement
between estimated and actual CCT was obtained considering
different operating conditions and topologies.
0-7803-5812-0/00/$10.0002000IEEE
627
Djukanovic et a1.121 used individual energy function normalized
by the critical value of global energy function, evaluated
at fault clearing time to predict energy margin and
stability. A function of generator rotor acceleration and
elements of admittance matrix were used to identify mode
of instability and predict CCT. In both cases a functional
link network(FLN) which assumes a flat computation platform(
no hidden layers) was implemented. The network was
trained for faults on generator buses by restoring the network
topology and for faults on non-generator buses by
tripping the faulted line, at different load levels.
In [3], Sobajic et al. proposed combined use of unsupervised
and supervised learning for TSA. An unsupervised
algorithm was proposed for clustering large amount of data
based on similarities. Covariance analysis was performed
on clustered data to determine the features of the input
pattern which are highly correlated. In addition to the
original input features, enhanced features obtained by taking
the products of highly correlated features were included
to train a FLN to synthesize the CCT. Learning rate for
FLN'is generally many times higher than that for backpropagation
networks with hidden layers of neurons.
Fast pattern recognition and classification of dynamic
security states were reported by Zhou et a1.[4]. A feedforward
network was tr?ined using energy margin and unstable
equilibrium point angles of advanced generators as inputs
with power system vulnerability as the output. Power
system vulnerability is an indicator of dynamic security obtained
by the combination of transient energy margin and
sensitivity of energy margin to a changing system parameter.
Accurate vulnerability classification was obtained for
the test cases using active power generation as the changing
parameter.
Hobson et al.[5] have reported that ANN have difficulty
in returning consistently accurate answers under varying
network conditions. ANN was trained to predict CCT for
three phase faults, for two systems(4 generator and 20 generator)
at 5 load levels and 3 different topologies. A fault
at a bus is considered to simulate a line fault close to that
bus and the fault is cleared by tripping the faulted line.
This was repeated for every line with fault at both ends.
Unacceptably large errors were reported for both training
and testing data.
Edwards et al.[6] made use of statistical information for
feature selection. 1916 composite indices were generated
for 838 training contingencies(three phase short circuit, loss
of line, loss of generation, loss of load). Performing correlations,
18 composite indices were selected as inputs to the
ANN which was trained to determine stability. The ANN
was conservative in its stability classification.
In [7], Aboytes et al. used ANN to predict stability of
a 53 generator system which is part of Mexican power system.
Training patterns were organised by dividing them
into different sets and using separate ANN for each set.
Best results were obtained by separating patterns by type
of contingencies and voltage level.
Mansour et a1.[8] used ANN to predict energy margin
and largest angular swing for two large systems viz.
B.C.Hydro(209 generators) and Hydro Quebec(87 generators).
The ANN was able to perform classification with
an error of 4% and determine the stability margin with an
average error of 5%.
The above papers were concerned with transient stability
assessment for preventive control. Chih-Wen Liu et al.[9]
utilised the ability to rapidly acquire synchronized phasor
measurements to evaluate transient stability for emergency
control. With the advent of phasor measurement units
aided with global positioning systems, it is possible to track
the dynamics of a power system. The authors of [9] applied
a novel fuzzy neural network to real time transient stability
prediction using synchronized phasor measurements.
Security assessment through boundary visualization provides
the operator with knowledge of system security in
terms of easily monitorable operating parameters. McCalley
et a1.[10] presented a methodology for online security
boundary visualization using neural networks. Feature selection
was done using genetic algorithms. The procedure
for this methodology is applied to thermal overload, voltage
instability and transient instability problems to obtain
deterministic boundaries.
Conventionally, TSA involves determination of CCT.
This has probably influenced many authors [1,2,3,5] to
train ANN to predict CCT. In [2,6,7,9], system stability
for large disturbaikes is obtained as the output. Energy
margin is obtaidd as output in [2,8]. In [2], mode of instability
is also obtained as an output of an ANN. System
vulnerability is obtained as the ANN output in [4].
/
In almost all the papers prefault variables and variables
during fault are used as inputs to the ANN. In [4], energy
margin and unstable equilibrium point angles of advanced
generators are used as inputs to obtain system vulnerability.
In [9], postfault values of generator rotor angles,
velocities and acceleration are used as inputs.
Supervised learning involves training an ANN to obtain
a desired output, whereas unsupervised learning involves
processing the input variables with no knowledge of the
output. All the authors have used supervised learning techniques
to train the ANN. In [3], an unsupervised learning
algorithm was proposed for clustering data based on similarities.
Covariance analysis was performed on clustered
data to obtain additional features which were used to train
the ANN. In [6], correlation analysis was performed to arrive
at the most suitable input variables.
Multilayered backpropagation network is the most com-
628
Stability and mode of instability are predicted by training
two separate ANN’S. Two sets of test patterns are generated
for each ANN. The first test set for first ANN which
is trained to predict stability, includes three phase faults at
different buses selected randomly with load levels between
100% and 130% of nominal load selected randomly. The
first test set for second ANN which is trained to predict
mode of instability, includes three phase faults at different
buses selected randomly with load levels between 100%
and 110% of nominal load selected randomly. The second
test set for both ANN’S considered load levels selected ran-
29
12 I 37 7 I
11 1 36
r
domly in the same ranges as those for the first set, but
three phase faults were simulated at random locations on
different lines.
[attachment=22650]
Ab3tract
Online transient stability assessment (TSA) of a
power system is not yet feasible due to the intensive computation
involved. Artificial neural networks(ANN) have been
proposed as one of the approaches to this problem because
of its ability to quickly map nonlinear relationships between
the input data and the output. In this paper a review of
the previously. published papers on TSA using ANN is presented.
The paper also reports the results of the application
of ANN to the problem of TSA of a 10 machine 39 bus system.
I. INTRODUCTION
The security assessment of a power system requires analysis
of the dynamic system behaviour under a prescribed
set of events known as contingencies. Conventionally this is
done by simulating the system nonlinear equations. Since
the stability limits cannot be determined from a single simulation.
more than one simulation is required. The large
size of the system adds to the complexity. Hence online
transient stability assessment(TSA) by simulation is not
yet feasible.
The difficulties mentioned above can be overcome to a
large extent by the method of energy function for direct stability
evaluation. This method involves comparison of the
value of the energy function at the instant of last switching
W(t,) to the critical value W,,.; the system is transiently
stable if W(t,) < Wcr. But this method is not yet suitable
for online computation.
Artificial neural networks(ANN) have been proposed as
an alternative method for the TSA problem by many aut,
hors since Sobajic et a1.[1] explored the capability of ANN
for TSA. Since trained ANN can quickly map nonlinear
relationship between input data and the ouput, they are
considered to be suitable for online use. There are a number
of publications on ANN application to TSA. In this
paper, a review of some of the previously published papers
on this topic is presented. The paper also reports the results
of ANN application to the determination of stability
and mode of instability for a 10 machine 39 bus system.
11. ANN APPLIED TO TSA
The main objectives of online TSA are fast evaluation
and 'accuracy of results. ANN is a possible alternative because
of its fast response. Application of ANN consists of
the following steps.
A. Data generation
It is important to obtain a set of training patterns that
adequately covers the space of possible operating conditions.
Different operating conditions are generated by different
combinations of load levels and network topology.
Since ANN are known to do interpolation very well but
hardly any extrapolation, the test patterns are required to
be within the range of training patterns.
B. Selection of input variables
The selection of inputs is an important factor in the successful
use of ANN. It is obvious that the candidates for
inputs are those independent variables which influence the
output. Different prefault variables, variables during fault
and postfault variables have been used as input variables
in the previous studies.
C. Selection af ANN architecture
Multilayered backpropagation network is the most commonly
used ANN in the previously published papers on
this subject. It has also been successfully applied in many
other practical applications. A few authors have applied
functional link network(FLN) [2,3] for TSA.
D. Training the ANN and testing
The advantage of ANN is that it can be used for online
applications, since most of the computations are done offline
and negligible online computation is required. Data
generation and ANN training constitute offline computation.
Usually training is the most time consuming part in
the design and use of ANN. For a given ANN architecture
many training algorithms exist and a choice has to be made
judiciously to obtain fast and efficient training of the ANN.
111. REVIEW
A large number of publications have appeared on ANN
application to TSA since the paper by Sobajic et al.[l].
Sobajic et al. used ANN for prediction of critical clearing
time(CCT) for a small test power system. A good agreement
between estimated and actual CCT was obtained considering
different operating conditions and topologies.
0-7803-5812-0/00/$10.0002000IEEE
627
Djukanovic et a1.121 used individual energy function normalized
by the critical value of global energy function, evaluated
at fault clearing time to predict energy margin and
stability. A function of generator rotor acceleration and
elements of admittance matrix were used to identify mode
of instability and predict CCT. In both cases a functional
link network(FLN) which assumes a flat computation platform(
no hidden layers) was implemented. The network was
trained for faults on generator buses by restoring the network
topology and for faults on non-generator buses by
tripping the faulted line, at different load levels.
In [3], Sobajic et al. proposed combined use of unsupervised
and supervised learning for TSA. An unsupervised
algorithm was proposed for clustering large amount of data
based on similarities. Covariance analysis was performed
on clustered data to determine the features of the input
pattern which are highly correlated. In addition to the
original input features, enhanced features obtained by taking
the products of highly correlated features were included
to train a FLN to synthesize the CCT. Learning rate for
FLN'is generally many times higher than that for backpropagation
networks with hidden layers of neurons.
Fast pattern recognition and classification of dynamic
security states were reported by Zhou et a1.[4]. A feedforward
network was tr?ined using energy margin and unstable
equilibrium point angles of advanced generators as inputs
with power system vulnerability as the output. Power
system vulnerability is an indicator of dynamic security obtained
by the combination of transient energy margin and
sensitivity of energy margin to a changing system parameter.
Accurate vulnerability classification was obtained for
the test cases using active power generation as the changing
parameter.
Hobson et al.[5] have reported that ANN have difficulty
in returning consistently accurate answers under varying
network conditions. ANN was trained to predict CCT for
three phase faults, for two systems(4 generator and 20 generator)
at 5 load levels and 3 different topologies. A fault
at a bus is considered to simulate a line fault close to that
bus and the fault is cleared by tripping the faulted line.
This was repeated for every line with fault at both ends.
Unacceptably large errors were reported for both training
and testing data.
Edwards et al.[6] made use of statistical information for
feature selection. 1916 composite indices were generated
for 838 training contingencies(three phase short circuit, loss
of line, loss of generation, loss of load). Performing correlations,
18 composite indices were selected as inputs to the
ANN which was trained to determine stability. The ANN
was conservative in its stability classification.
In [7], Aboytes et al. used ANN to predict stability of
a 53 generator system which is part of Mexican power system.
Training patterns were organised by dividing them
into different sets and using separate ANN for each set.
Best results were obtained by separating patterns by type
of contingencies and voltage level.
Mansour et a1.[8] used ANN to predict energy margin
and largest angular swing for two large systems viz.
B.C.Hydro(209 generators) and Hydro Quebec(87 generators).
The ANN was able to perform classification with
an error of 4% and determine the stability margin with an
average error of 5%.
The above papers were concerned with transient stability
assessment for preventive control. Chih-Wen Liu et al.[9]
utilised the ability to rapidly acquire synchronized phasor
measurements to evaluate transient stability for emergency
control. With the advent of phasor measurement units
aided with global positioning systems, it is possible to track
the dynamics of a power system. The authors of [9] applied
a novel fuzzy neural network to real time transient stability
prediction using synchronized phasor measurements.
Security assessment through boundary visualization provides
the operator with knowledge of system security in
terms of easily monitorable operating parameters. McCalley
et a1.[10] presented a methodology for online security
boundary visualization using neural networks. Feature selection
was done using genetic algorithms. The procedure
for this methodology is applied to thermal overload, voltage
instability and transient instability problems to obtain
deterministic boundaries.
Conventionally, TSA involves determination of CCT.
This has probably influenced many authors [1,2,3,5] to
train ANN to predict CCT. In [2,6,7,9], system stability
for large disturbaikes is obtained as the output. Energy
margin is obtaidd as output in [2,8]. In [2], mode of instability
is also obtained as an output of an ANN. System
vulnerability is obtained as the ANN output in [4].
/
In almost all the papers prefault variables and variables
during fault are used as inputs to the ANN. In [4], energy
margin and unstable equilibrium point angles of advanced
generators are used as inputs to obtain system vulnerability.
In [9], postfault values of generator rotor angles,
velocities and acceleration are used as inputs.
Supervised learning involves training an ANN to obtain
a desired output, whereas unsupervised learning involves
processing the input variables with no knowledge of the
output. All the authors have used supervised learning techniques
to train the ANN. In [3], an unsupervised learning
algorithm was proposed for clustering data based on similarities.
Covariance analysis was performed on clustered
data to obtain additional features which were used to train
the ANN. In [6], correlation analysis was performed to arrive
at the most suitable input variables.
Multilayered backpropagation network is the most com-
628
Stability and mode of instability are predicted by training
two separate ANN’S. Two sets of test patterns are generated
for each ANN. The first test set for first ANN which
is trained to predict stability, includes three phase faults at
different buses selected randomly with load levels between
100% and 130% of nominal load selected randomly. The
first test set for second ANN which is trained to predict
mode of instability, includes three phase faults at different
buses selected randomly with load levels between 100%
and 110% of nominal load selected randomly. The second
test set for both ANN’S considered load levels selected ran-
29
12 I 37 7 I
11 1 36
r
domly in the same ranges as those for the first set, but
three phase faults were simulated at random locations on
different lines.