Energy and Power Engineering, 2013, 5, 999-1004
doi:10.4236/epe.2013.54B191 Published Online July 2013 (http://www.scirp.org/journal/epe)
Accuracy Improvement in CCT Estimation of Power
Systems by iRprop-RAN Hybrid Neural Network
Teruhisa Kumano, Shinjiro Netsu
Department of Electronics and Bioinformatics, Meiji University, Kawasaki, Japan
Received March, 2013
ABSTRACT
This paper proposes a new Initial CCT (Critical Clearing Time) estimation method using a hybrid neural network com-
posed of iRprop (Improving the Resilient back PROPation Algorithm) and RAN (Resource Allocation Network). In
transient stability study, CCT evaluation is very important bu t time consuming due to the fact it needs many iteration of
time domain simulations gradu ally increasing the fault clearing time. The key to reduce th e required computing time in
this process is to find accurate initial estimation of CCT by a certain handy method before going to the iterative stage.
As one of the strongest candidates of this handy method is the utilization of the pattern recognition ability of neural
networks, which enable us to jump to a close estimation of the real CCT without any heavy computing burden. This
paper proposes a new hybrid neural network which is a combination of the well-known iRprop and RAN. In the pro-
posed method, the outputs of the hidden units of RAN are modified by multiplying the contribution factors calculated
by an additional iRprop network. Numerical studies are done using two different test systems for the purpose of con-
firming the validity of the proposal. The result of the proposed method is the best. Properly evaluating the contribution
of each input to the hidden units, the estimation error obtained by the proposed method is improved further than the
original RAN based estimation.
Keywords: Critical Clearing Time; Estimation; Power System; iRprop; Resource Allocation Network
1. Introduction
In large power systems operation, stability check in the
contingency analysis is always important. In particular,
in these two years, we, Japanese electric power engineers,
cannot depend upon the strong power supply from the
nuclear power plants and the basic power flow pattern is
different from the original schedule. It implies that every
daily grid operation needs more careful study, in which
stability check should be done. The long and narrow
power corridor is, in a sense, inevitable due to the geo-
graphical restriction of our country, which makes the
stability the main restricting factor for the long and heavy
power transmission.
One of the biggest problems in the transient stability
constrained contingency analysis is the long computing
time required. Transient stability study itself is a typical
time consuming calculation. Here, we need to iterate
dynamic simulation many times gradually increasing
power flow or fault clearing time to reach their critical
value. Comparing these two, the critical clearing time
(CCT) is easy to calculate and is often used. For the fast
evaluation of CCT, we need accurate initial guess of the
clearing time. If we can start from close guess, the re-
quired time to get the true CCT can be shorter. Since the
power flow pattern in the whole system gives a substan-
tial effects on the resultant CCT, it can be expected that
we can accurately estimate CCT if the important vari-
ables such as the specified values of the active and reac-
tive power at each node is given.
Many methods based on so called artificial neural
network (ANN) techniques have been studied for this
initial guess. Ikenono et al proposed to use BP (back
propagation) based ANN [1]. Bettiol et al proposed to
use RBF (Radial Basis Function) network for this pur-
pose [2]. The authors ourselves studied this problem and
proposed to use support vector machine [3] and rele-
vance vector machine [4]. Once properly trained, ANN
can recognize the given input pattern and make classifi-
cation or give a regression in a short computing time.
Because of its nonlinear knowledge representation ability,
it has been a strong candidate for this initial estimator.
However, even after the above mentioned research ef-
forts, it still remains as a research theme and not a real
field application.
In this paper, a new ANN method is proposed for the
above stated purpose. In this proposal so called RAN
(Resource Allocation Network) is coupled with iRprop
(Improving the Rprop Learning Algorithm, in which

T. KUMANO, S. NETSU
1000
Rprop stands for Resilient backPROPagation). RAN is
one type of RBF network, but it has a strong adap tability
given by the hidden layer adjustment. RAN and its modi-
fications are applied to various fields and makes a con-
siderable contribution. [5-7] The details of iRprop and
RAN will be described in the next chapter.
This paper is constructed as follows. Chapter 2 ex-
plains the proposal in this paper together with the basics
related to iRprop and RAN. Chapter 3 describes our tran-
sient stability problem, followed by numerical examples
written in Chapter 4. In Chapter 5 concluding remarks
are stated.
2. Related Networks and the Proposal
2.1. iRprop
The proposed method in this paper is a hybrid of iRprop
and RAN. The former (more strictly, iRprop+) is an im-
proved version of BP (Back Propagation) ANN. While
BP shifts the weight of each connection by the gradient
and needs the partial derivative calculated, iRprop only
watches the sign of the partial derivative. Its light com-
puting cost enables us to apply this method to many
fields.
The mathematical description of its learning algorithm
is as follows [8]. The weight of each connection is wij and
it is shifted by the following algorithm depending upon
the sign of(t-1)( )
ij
E
w
t
ij
E
w



, where E stands for the sum of
the output error. In the following equations, coefficient

+ and

- should satisfy 0<

-<1<

+. max and min imply
the upper and lower limits of ij(t)
i) In case (t-1)( )
ij
E0
w
t
ij
E
w




()( 1)max
()
() ()
,
(1) ()()
min ,
tt
ij ij
t
tt
ij ij
ij
ttt
ijij ij
E
wsign
w
www



  


 





ii) in case (t-1)( )
ij
E0
w
t
ij
E
w




()( 1)min
()(1)(1) ()(1)
(1) ()
()
max ,
if then
otherwise
0
tt
ij ij
tttt t
ijijij
tt
ij ij
t
ij
EEwww
ww
E
w




  






iii) in case (t-1)( )
ij
E0
w
t
ij
E
w



()
() ()
,
(1) ()()
t
tt
ij ij
ij
ttt
ijij ij
E
wsign
w
www




 





2.2. RAN
On the other hand, RAN is composed of 1) a network, 2)
strategy for allocating new units, and 3) a learning rule
for refining the n etwork. [9] It is based on the concept of
RBF (Radial Basis Function) machine. [2] Let I be the
input. Using c and

2, the center and the variance of the
RBF, y, the output of the hidden unit, is computed by
22
exp(/).
ipj
yIc
j

 (1)
where j, i, and p stand for the suffix fo r th e number of th e
hidden units, those of the input units, and sample id re-
spectively. The network output z is calculated, using the
weight h and the output bias
 , as follows.
kki
i
zhy
k




(2)
RAN also learns so as to minimize the sum of the
squared output error E. When the newly obtained input is
not found in the experience so far (far from the used data
sample obtained in the history), another hidden unit is
added. This algorithm is formulated as follows.
if E>
 and ||x-cnearest||>  then
j=j+1
cji=xpi

j2=k || x-cnearest||
hji=Tpk-zk
where Tpk is the teacher signal.
2.3. The Proposed Method
RAN modifies its structure by adding a new hidden unit
only in the case where the output error and the difference
between the input data and the nearest center of the ex-
isting radial basis functions are big enough simultane-
ously. However, in our specific problem, the input data
contain various quantity such as vo ltag e, power, and fault
location etc.. Some input might have strong effects on the
inputs to the hidden layer, but others not. In the proposed
method, this difference in the degree of the effects on the
hidden layer is assessed by an additional iRprop network
which connects every input variable with every hidden
unit.
Learning is done simultaneously in this additional iR-
prop network and the obtained weight of each connection
is multiplied to the difference between each input and the
nearest center, the sum of which is used to calculate the
output of the hidden units. Using y, I, c, and
 of the
same meaning as in the previous section, the output of

T. KUMANO, S. NETSU 1001
the hidden unit y is written as
22
2
exp( )
pj i
i
j
I
cef
y


 (3)
where th e new coeff icien t ef implies the degree of effects
and is calculated by the f ol l owing for mula;
,
ii
j
ef wj
which is the sum of the weights in th e above stated addi-
tional iRprop network. The proposed network takes the
form shown in Figure 1. The additional part on the top
(boxed in the broken rectangle) is iRprop, the sum of the
connection weight of which is ef and is multiplied to the
distance between input Ik and the nearest center as shown
in Equation (3). Figure 2 shows the type of input/output
data used in the proposed method.
3. Studied Problem
3.1. Data Preparation Procedure
In our particular problem, so called CCT (Critical Clear-
ing Time) is the target of the estimation. CCT is the
Figure 1. The structure of the proposed network.
gen output load power LFdata & transmission loss gen volt. fault location
CCT (Critic al C learing Time)
Figure 2. Inputs and output of the pr oposed network.
maximum fault duration which do es not cause instab ility.
In order to obtain the teacher signal fed to the proposed
method, the true CCT, dynamic simulation is run many
times. It is true that this is only a result of simulation
analysis, but is treated as the correct CCT.
Using CPAT (CRIEPI’s Power system Analysis Tool)
[10], a de facto standard stability analysis program in
many Japanese power utilities, the power system tran-
sient behavior is computed under various conditio ns such
as initial load flow, fault location etc., where the fault
clearing time is gradually increased. The assumed long-
est clearing time which causes no transient stability
problem such as out of step within the predetermined
time range (described later in Tables 1 and 2) is consid-
ered as CCT.
Table 1. Simulation Condition in 9 Node System.
item setting
gen. output increased at the constant rate to keep up with
the total demand
load demand 80, 90, 100, 110, 120%
input data gen and load power, branch power flow, nodal
voltage, branch loss, fault location
output CCT
fault locations sending end of all branches
fault type 3LG (three lines g r o u n d ed)
criterion of SOinternal bus angle > 180 deg
etc simulation quits after t=0.5sec
Table 2. Simulation Condition in 47 Node System.
item setting
gen. output
output from a gen in Area A is increased by
0.1pu step while the output from all gens in
Area B are reduced at the same rate to keep the
total demand unchan g ed
load demand 100% unchanged
input data gen power, branch power flow, nodal voltage,
fault location
output CCT
fault locations at HV bus of the step-up transformer of gen-
erators 8,9,10
fault type 3LG (three lines gr o un d ed)
criterion of SOinternal bus angle > 180 deg
etc simulation quits after t=4.0sec
3.2. Study Power Systems
Two model systems shown in Figures 3 and 4 are stud-
ied. The details such as machine constants used in the 9
bus model can be found in [11]. In the study of the 47

T. KUMANO, S. NETSU
1002
4. Numerical Study node system, base loading is set as its standard, or 100%
loading condition. The analysis condition is summarized
in Tables 1-3. For the purpose of confirmation of the validity of the
proposed method, it is compared with the two existing
networks, BP (the classical Back Propagation based net-
work) and iRprop. The parameters are determined by try
and error. They are summarized in Tables 5-6.
3.3. Transient Stability Analysis
The transient stability an alysis is done, which is required
to get the input and the teacher signal fed to our ANN, as
explained below. The simulation condition used for the
nine bus model is shown in Table 1. On the other hand,
Table 2 shows that used in 47 node model. In Table 2,
two area s are refereed in th e description of th e procedure
how the generator outputs are changed. Area A means
the northern part of the 47 node system, which includes
the three generators G8 - G10. The remaining region is
Area B. Tables 3 and 4 show the generation/demand
settings for each case.
Table 3. Generator Condition in 47 Node System.
gen No gen type voltage capacity
1 LNG 1.01pu 8240MVA
2 nuclear 1.00pu 12940MVA
3 pumped storage1.02pu 7060MVA
4 coal 1.01pu 12940MVA
5 pumped storage1.02pu 7060MVA
6 coal 1.02pu 12940MVA
7 nuclear 1.00pu 12940MVA
8 oil 1.00pu 8240MVA
9 oil 1.00pu 8240MVA
10 oil 1.02pu 5880MVA
G1
G3G2
4
1
65
9
8
7 23
Figure 3. Anderson and Fouad 9 bus system.
G1 0
G1
G3
G2 G4
G5
G7 G6
G9 G8
(10) (20)(37)(36)
(47) (19)
(9) (8)
(18)
(1)
(11) (12)
(2) (4)
(14)
(3)
(13)
(25)
(44)
(26)
(21)
(22)
(38) (39)
(24)
(23)
(27)
(40) (41)
(45)
(30)
(29)
(28)
(15)
(5)
(7)
(17)
(46)
(31) (32)
(33)
(42) (43)
(34)
(35)
(16)
(6)
<10> <52>
<40> <39>
<9>
<51 >
<37><38>
<50 >
<8>
<36>
<7> <6>
<153><53>
<32><30 ><28><25 ><22> <124><24>
<123><23>
<4><2>
<1>
<11>
<13>
<12>
<14>
<41> <42>
<15><20> <120>
<19><16>
<18> <118>
<117><17>
<43>
<27>
<26> <126>
<48> <49>
<35> <135>
<31> <33>
<34>
<45> <46><44>
<29>
<5>
<47>
<21>
<3>
Figure 4. IEEJ standard 47 bus model system EAST-10.

T. KUMANO, S. NETSU 1003
Table 4. Load Condition in 47 Node System.
Node No active power reactive power
38 3.5pu 0.986pu
39 7.0pu 1.972pu
40 7.0pu 1.972pu
41 7.0pu 1.972pu
42 7.0pu 1.972pu
43 3.5pu 0.986pu
44 3.5pu 0.1pu
45 3.5pu 0.1pu
46 3.5pu 0.1pu
18 3.85pu 1.205pu
19 3.85pu 1.205pu
47 2.8pu 0.806pu
Table 5. Settings in BP.
Hidden
units Learning rate treshold Initial setting max learning iteration
132 0.2 0.0 ra ndomly set
between -1.0 - 1.0 6000
Table 6. Settings in iRprop.
hidden
units initial update max/min update initial setting max lear n ing iteration
30 0.5 50, 10-6 randomly set
between -1.0 - 1.0 10000
The obtained results are summarized in Table 7 for the
9 node system, and in Table 8 for the 47 node system
respectively. Both in these two systems, the proposed
method, and the hybrid iRprop/RAN network gives the
best results. In our preliminary study, the existing RAN
network has also been applied to these two networks.
The results are shown in Table 9. This table shows the
fact that RAN itself has certain relative advantage over
the other existing networks, BP and iRprop. As far as the
authors know, the application of RAN to this problem is
the first attempt, but in this paper, RAN is further im-
proved to the hybrid network, and this proposed method
gives the be s t result .
The main reason why the proposed method gives the
better results compared to RAN is, as the authors esti-
mate, the contribution of the additional iRprop network.
Because iRprop itself has a certain strength in this CCT
estimation problem, it appropriately extracts the input
feature and enables us to judge the necessity of adding a
new hidden unit. The maximum error in the 9 node sys-
tem becomes worse than in case of the conventional
RAN but compared to the improvement from BP and
iRprop, this deterioration is very small.
Table 7. Resultant Error in the 9 node system.
BP iRprop proposed net
average0.0674sec 0.0396sec 0.0191sec
max 0.2488sec 0.2646sec 0.1131sec
Table 8. Resultant Error in the 47 node system.
BP iRprop proposed net
average0.00249sec 0.00263sec 0.00208sec
max 0.00884sec 0.01041sec 0.00691sec
Table 9. Error in Case of Conventional RAN.
9 node system 47 node system
average 0.03003sec 0.00229sec
max 0.09311sec 0.00855sec
Since the maximum error is reduced to be around 70%
of that by the existing method, the required computation
time is also expected to be around 70%.
Summarizing all these points, it can be said that the
proposed method gives significant improvement on the
initial CCT guess, and it implies that th e total computing
time required to get the true CCT can be shorten consid-
erably.
5. Conclusions
In this paper, a new ANN based CCT estimation method
is proposed to realize a faster power system transient
study. The proposed ANN is a hybrid of iRprop and
RAN, in which additional iRprop network gives helpful
information concerning the new hidden unit generation in
the conventional RAN.
Numerical study is done to confirm the validity of the
proposed method in the CCT estimation problem in the
power system stability analysis, where several existing
methods are also tested and compared. The existing RAN
is used for this purpose, which is, as far as the authors
know, also the first attempt so far, and gives a better re-
sult compared to other existing methods such as BP and
iRprop. Furthermore, the proposed method gives an even
better result in the sense of the maximum and averaged
estimation error.
In the present paper, initial load flow pattern and,
needless to say, the fault location are varied and the pro-
posed method is shown to be able to give a fairly good
result in a wide range of the condition. However, no to-
pological change is considered in the model system.
Since the addition of the iRprop network might have
given a strong ability of adapt and adjust to new operat-
ing condition in the proposed method, it can be expected

T. KUMANO, S. NETSU
1004
that our method might be well applied in a bigg er condi-
tion change such as topological. Due to the new grid par-
ticipants such as distributed generators, the grid configu-
ration might be more frequently changed from now,
which might affects the power transmission capability of
the trunk system. It implies that the importance of the
proposed method will become bigger and bigger in near
future.
REFERENCES
[1] K. Ikenono and S. Iwamoto, “Generalization of Transient
Stability Solution using Neural Network Theory,” Trans
IEEJ, Vol. 111, No. 7, 1991, pp. 723-728.
[2] A. L. Bettiol, A. Souza, J. L. Todesco and J. R. Tesch, Jr,
“Estimation of Critical Clearing Times Using Neural
Networks,” 2003 IEEE Bologna Power Tech Conference
Proceedings. doi:10.1109/PTC.2003.1304446
[3] H. Takahashi and T. Kumano, “Available Transfer Capa-
bility Screening Considering Transient Stability by Sup-
port Vector Machine,” 2008 IEEE PES General Meeting,
Pittsburgh. doi:10.1109/PES.2008.4596499v
[4] A. Wada and T. Kumano, “Fast Estimation of Transient
Stability Cconstrained ATC by Relevance Vector Ma-
chine,” IEEE 2nd International Power and Energy Con-
ference, 2008, doi:10.1109/PECON.2008.4762451v
[5] B. S. Mahanand, S. Suresh, N. Sundararajan, M. A. Ku-
mar, “Alzheimer's Disease Detection Using a
Self-adaptive Resource Allocation Network classifier,”
The 2011 International Conference on Neural Networks,
pp. 1930-1934.doi:10.1109/IJCNN.2011.6033460
[6] S. Shanthi and V. M. A. Bhaskaran, “Computer Aided
Detection and Classification of Mammogram Using
Self-adaptive Resource Allocation Network Classifier,”
2012 International Conference on Pattern Recognition,
Informatics and Medical Engineering (PRIME), pp.
284-289. doi:10.1109/ICPRIME.2012.6208359
[7] H. C. Lou and W. Z. Dai, “A Novel Non-linear Model
Predictive Controller Based on Minimal Resource Allo-
cation Network and Its Application in CSTR PH Proc-
ess,” 7th World Congress on Intelligent Control and
Automation, 2008. WCICA 2008, pp. 5672-5676.
doi:10.1109/WCICA.2008.4593855v
[8] C. Igel and M. Husken, “Empirical Evaluation of the
Improved Rprop Learning Algorithms,” Neurocomput-
ing, Vol. 50, 2003, pp. 105-123.
doi:10.1016/S0925-2312(01)00700-7
[9] J. Platt, “A Resource-Allocating Network for Function
Interpolation,” Neural Computation, Vol. 3, No. 2, 1991,
pp. 213-225.doi:10.1162/neco.1991.3.2.213v
[10] Y. Kitauchi, “Scheme of Power System Stability En-
hancement using Margin to Apparatus Limitation (Part II)
－Verification of Power System Stability Improvement
using Highly Voltage Control on IEEJ WEST 30-machine
System Model－”, CRIEPI REPORT R04010, 2005.
[11] P. M. Anderson and A. A. Fouad, Power System Control
and Stability, Iowa State University Press, 1977.