Power swing prediction for out-of-step mitigation

Abstract

This paper explored the possibility of accurately predicting the classification of developing power swings. The notion of machine learning was employed, and tested the application of Decision Tree (DT) algorithms to wide area power system protection schemes. The novelty of the designed Wide Area Protection (WAP) scheme was portrayed by the WAP's ability to adaptively and accurately predict the classification of developing successive power swings. DTs being a Data Mining (DM) technique, a transient stability analysis was performed on an IEEE 39 bus test system in Dig SILENT®. The learning sample from the Phasor Measurement Unit (PMU) data was organized and stored in a data base in Microsoft Excel® 2010. The CART analysis and DT model design was done using Salford Predictive Modeller-CART® v6, trial licence. The results of this investigation were quite accurate and gave DT algorithms 'thumbs-up' in terms of classification prediction.

Full text

International Journal of Energy and Power Engineering
2015; 4(2-1): 63-72
Published online December 26, 2014 (http://www.sciencepublishinggroup.com/j/ijepe)
doi: 10.11648/j.ijepe.s.2015040201.16
ISSN: 2326-957X (Print); ISSN: 2326-960X (Online)
Power swing prediction for out-of-step mitigation
V. Siyoi
1
, S. Kariuki
2
, M. J. Saulo
2
1
Department of Electrical Engineering, Pan African University of Basic Science and Technology, Nairobi, Kenya
2
Department of Electrical Engineering, Technical University of Mombasa, Mombasa, Kenya
Email address:
v.siyoi@gmail.com (V. Siyoi), kariukisamuel2004@yahoo.com (S. Kariuki), michaelsaulo@yahoo.com (M. J. Saulo)
To cite this article:
V. Siyoi, S. Kariuki, M. J. Saulo. Power Swing Prediction for Out-of-Step Mitigation. International Journal of Energy and Power
Engineering. Special Issue: Electrical Power Systems Operation and Planning. Vol. 4, No. 2-1, 2015, pp. 63-72.
doi: 10.11648/j.ijepe.s.2015040201.16
Abstract:
This paper explored the possibility of accurately predicting the classification of developing power swings. The
notion of machine learning was employed, and tested the application of Decision Tree (DT) algorithms to wide area power
system protection schemes. The novelty of the designed Wide Area Protection (WAP) scheme was portrayed by the WAP’s
ability to adaptively and accurately predict the classification of developing successive power swings. DTs being a Data Mining
(DM) technique, a transient stability analysis was performed on an IEEE 39 bus test system in Dig SILENT®. The learning
sample from the Phasor Measurement Unit (PMU) data was organized and stored in a data base in Microsoft Excel® 2010. The
CART analysis and DT model design was done using Salford Predictive Modeller-CART® v6, trial licence. The results of this
investigation were quite accurate and gave DT algorithms ‘thumbs-up’ in terms of classification prediction.
Keywords:
Decision Trees, Power Swing, Out-of-Step, Wide Area Protection
1. Introduction
Despite the profound success of various automated industrial
processes, automation capabilities were not superior enough to
match up to power system dynamism and the rate at which
power system changes occur. This was because power system
transients, faults, power swings and other power system
abnormalities develop within milliseconds, a time too fast for
autonomous systems to detect and to respond to. The immediate
discussion presents a non-conventional method of designing a
WAP scheme that enhances the stability of a power system.
2. Decision Trees
The DT technique using the Classification and Regression
Trees (CART) is employed to perform the prediction of a
power swing classification. As developed in this work, DT
algorithms have been used to predict power swings which are
also discussed in references [4], [5], [14], [21], [22], [23],
[24], [25], [26], [27], [28], [29], [30], [31].
The CART algorithm is recommended for developing DT
models, the most significant traits being simplicity and
speedy execution of the models. Complex hidden information
is classified and simplified into binary ‘yes/no’ recursive
statements.
The major limitation to employing DTs is that there is only
a single pair of a binary output which infers the classification
problems as a binary output; as either ‘yes/no’ answers. DTs
are also unstable; a small change in the input learning sample
may give a completely different decision model. The DT
using the CART technique was developed as follows:
(i) The learning sample L was arranged as an
n
m
×
matrix..
(ii) Attributes were sorted in order to initialize the
splitting points that maximized the splitting criterion.
(a) From the set of attributes
{
}
n
aaaA ,...,,
21
=
in the
learning sample L, an attribute
Aa
∈
was selected. If
a
was numeric, the splitting was as equation (1)
( )
(
)
(
)
2
1kxkx
kS
aa
a
−+
= (1)
(b)
If
a
was defined as a categorical variable of sets
{
}
na
sssS ,...,,
21
=
, then the possible splitting point
was within the range of available sets of that
particular attribute.
(iii)
The impurity reduction level was computed from the
Gini improvement function as represented in equation
(2).

64 V. Siyoi et al.: Power Swing Prediction for Out-of-Step Mitigation
)]t(iP)t(iP[)t(i)t,s(i
)t(i
)t(n )t(n
)t(i
)t(n )t(n
)t(i)t,s(i
)t|C(P1)t(i
)t|C(P)C()t(i
RRLL
R
R
L
L
J
jj
2
j
2
j
+−=∆
+−=∆
−=
=
∑
π
(2)
(iv) A variable ranking of all attributes was performed.
The measure of importance of a variable in
relation to the final tree T is the weighted sum across
all splits in the tree of improvements that has
when it is used as a surrogate as shown in equation
(3).
∑
∈
∆=
∆
Tt x
xi
tSIxM
tSIC
),
~
()(
),
~
(max
(3)
The variable importance
)(xVI
was expressed in terms of
a normalised quantity relative to the variable having the
largest measure of importance, shown in equation (4).
100
)( )(
)(
max
×= xM xM
xVI
(4)
(v) Using the Gini purity index, the root node was
identified.
(vi) On the root node of the DT, the splitting points for
the resulting child nodes were located. The splitting
point of the root node was determined from amongst
the set of all possible splitting points of all the
attribute/variables. For each splitting value
a
Ss
∈
at
a particular node
t
, the learning sample was
partitioned into separate subsets
L
t
and
R
t
forming
the left and right child nodes respectively.
(a) For numerical variables, then the partitioning is as
shown in equation (5).
(
)
(
)
{
}
( ) ( )
{ }
k
aa
k
aa
skxifkxtR
skxifkxtL >= ≤=
(5)
(b)
For categorical variables, (have finite sets) then the
partitioning is as shown in equation (6).
(
)
(
)
{
}
( ) ( )
{ }
k
aa
k
aa
skxifkxtR
skxifkxtL ≠= ==
(6)
(vii)
Optimal split over all possible splitting
values
a
Ss
∈
amongst all attributes
Aa
∈
was
found. Gini splitting points were computed as shown
in equation (7).
∑
∈
=
)(
)(
|| ||
)(
svaluesi
t
Split
ti
n
n
SGINI
(7)
)()()(
R
j
L
i
Split
ti
n
n
ti
n
n
SGINI += (8)
(viii)
A classification decision was made from terminal
nodes. A node was classified in class
i
if equation (9)
was satisfied.
(
)
(
)
(
)
( )
( ) ( )
j
i
j
i
N
N
tNjjiC
tNiijC >
π
π
for all values of j (9)
(ix)
Each of the remaining predictor’s best split points
were defined using the Gini split criterion. The next
splitting point of the subsequent node that maximizes
the splitting criterion was selected and steps (viii)
through (ix) were repeated.
(x)
If the stopping rules had not been satisfied, steps (viii)
through (x) were repeated, otherwise process stopped
.
To avoid unnecessary redundancy, optimization through
pruning the decision model is performed. This is by
removing tree branches whose cost complexities (penalty
associated with misclassification of cases) reduce the
reliability of the tree. For a maximal sized tree, the cost
complexity
0
=
α
. Pruning therefore evaluates tree branches
as shown in equation (10) where each subsequent branch
removal
t
TTTR >>> ,...,
2
1
,
α
increases the cost complexity
thus optimizing the DT.
(
)
LTRR
⋅
+
=
α
α
(10)
Where
α
is the complexity function,
(
)
TR
is the re-
substitution error and
L
is the number of branch nodes.
Validation of the DT model was done through a v-fold
cross-validation. Specifically, a 10-fold cross-validation was
performed as follows: Let
T
be a tree grown using all data
from the whole data set
0
ℏ
and let 2
≥
v be a positive
integer.
(i)
Divide
0
ℏ
into
v
mutually exclusive subsets
v
ℏ
′
where
vv ,...,2,1
=
. Let
vv
ℏ
ℏ
ℏ
′
−=
0
.
(ii)
For each
v
, consider
v
ℏ
as a learning sample and
grow a tree
v
T
on
v
ℏ
.
(iii)
Assign
(
)
(
)
tytj
vv
or
*
for a node
t
of
v
T
.
(iv)
Consider
v
ℏ
′
as a test sample and calculate its test
sample risk estimate
(
)
v
ts
TR
.
(v)
Repeat step (iv) for each value of
v
. The average of
the test samples is used as the v-fold cross validation
risk estimate of T.
The v-fold cross-validation estimate,
(
)
TR
cv
of the risk of
the tree
T
and its variance are estimated by equation (13) as
developed by references [32], [33], [34] and [35].
x
x
optimal
s

International Journal of Energy and Power Engineering 2015; 4(2-1): 63-72 65
( ) ( )
(
)
( )









∑′
∑ ∑ ′
=M1 andcat Yor cont, Y
M2 cat, Y
,
0
1
,,
0,
1
v
T
ts
R
fv
N
f
N
jvj
v
T
ts
R
jfv
N
jf
N
j
T
cv
R
π
(11)
( )
( ) ( ) ( )
( )














∑ ∑ ′
∈∑′
∈−
′
=




































M1 cat, Y
2
0
2
*
,,
2
0
1
var vv
Tt t
v
nT
cv
R
f
Njt
v
jCt
jfv
N
f
N
T
cv
R
ℏ
(12)
( )
( )
( )
( )
( )
( )
( )
( )
( )





















∑ ∑ ′
∈∑
′
∈−−






∑ ∑ ′





















∑=
′
−






∑ ∑ ′
∈′










=












cont Y
M1 cont, Y
vv
Tt t
v
n
2
T
cv
R
0
f
N
4
t
v
y
n
y
n
f
2
0
f
N
1
j v j
v
T
ts
R
j,f,v
N
2
j,f
0
N
jY
v
T
ts
R
j,f,v
N
2
jt
*
v
jC
vv
Tt t
j,f,v
N
2
0j,f
N
j
T
cv
Rvar
ℏ
π
(13)
The ROC curve represents the ability of the DT model to
accurately discriminate between the stable power swings and
the unstable power swings. Let
x
be the scale of test result
variable; low values suggest a negative
−
x
result while a
high value suggests a positive
+
x
result. Area under the
ROC curve is calculated as equation (14).
(
)
−
>
+
=
xx
r
P
θ
(14)
Successive points in the ROC curve are connected by the
trapezoidal rule as expressed in equation (15).
( )
∑
∈













>+
×
=−
+
>+
×
=−
−+
= valuesallx 2
1j
n
j
n
j
n
j
n
nn
W
(15)
3. Results & Analysis
The aim of the transient stability simulation was to induce
power disturbances/swings at the critical load centres and at
the extra-high voltage lines to create generator-load
imbalance. The simulation was done considering all possible
power system states, until the power system was observed to
be transiently unstable in each of the various states.
Graphical representations of the response of the coherent
generators due various contingencies induced during the
simulation are shown in figure 1, figure 2 and figure 3. The
figure 1 shows a successive OOS response of each of the
generators after a single contingency simulation. The normal
operating conditions for the transient stability study was set
such that:-
(i) The voltage should be within 0.95-1.05 p.u.
(ii) The load phasor voltage angle should not advance the
generator phasor voltage angle by exactly 4 pole slips.
(iii) The frequency deviation from the nominal frequency
of the reference machine should not be greater than ±
4%.
Figure 1. Simulation Responses of Successive Swings
-10 0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Time (Seconds)
Out-of-S tep Status
Successive Power Swings
Gen1
Gen2
Gen3
Gen4
Gen
Gen6
Gen7
Gen8
Gen9
Gen10

66 V. Siyoi et al.: Power Swing Prediction for Out-of-Step Mitigation
Figure 2. Rotor Angle Slip from Reference Machine
Figure 3. Generator Speed Deviations
Figure 4. Expert System DT Models
The figure 2 shows the response of each of the generator’s
rotor position. A pole slip at the onset of the fourth pole slip
reflects an oscillating response on the graph figure 2. The
figure 3 shows the speed response due contingencies
simulated. The response curve shows the speed deviation of
the generators due loss of synchronism and therefore deviate
-10 0 10 20 30 40 50 60
-200
-150
-100
-50
0
50
100
150
200
Time (Seconds)
Rotor Angle (Degrees)
Rotor Angle Slip (Degrees) w.r.t Reference Machine
Gen1
Gen2
Gen3
Gen4
Gen5
Gen6
Gen7
Gen8
Gen9
Gen10
-10 0 10 20 30 40 50 60
-60
-40
-20
0
20
40
60
80
100
Time (Seconds)
Speed D eviation ( HZ)
Generator Speed Deviation (HZ)
Gen1
Gen2
Gen3
Gen4
Gen5
Gen6
Gen7
Gen8
Gen9
Gen10

International Journal of Energy and Power Engineering 2015; 4(2-1): 63-72 67
from their normal synchronism speed.
Figure 5. DT Model Execution Process Flow

68 V. Siyoi et al.: Power Swing Prediction for Out-of-Step Mitigation
The process of executing the designed DT model involved
a procedure proposed by this paper illustrated in
figure 5. An Expert System (ES) was chosen as the
secondary engine for executing the DT model for the
following reasons:
(i) The proposed ES as shown in figure 4 has the ability
to learn from a wider base of experience than
conventional decision support systems.
(ii) Ability to respond quickly and successfully to new
situations.
(iii) Utilizes reasoning to solve problems at perplexing
situations.
(iv) Recognizes the relative importance of different
elements in a situation.
(v) Ease of duplication of decisions and dissemination of
the same [1], [36].
The ES manipulates DT models from three different
sources, all of which are stored within the memory of the ES.
The sources of these DT models are:
(i) Developed by the ES independently from the main
population database of measurements.
(ii) Knowledge induced to the ES by the control centre
operator and protection engineer.
(iii) A replica copy of the final DT model developed by the
main Intelligent Decision Support System IDSS
(adaptive OOS digital-relay).
The management and timing functions are important when
successive swings develop. If an instantaneous swing or
successive swings develop within a duration of >0.1 seconds,
then the DT model in the IDSS is given first priority to
execute. If the swings develop within a duration of <0.1
seconds or when the DT model from the main IDSS fails,
then the DT model from the ES is executed. The main
IDSSmay fail if its window cycles are not complete amongst
other time factors. Both the IDSS and ES models are updated
to learn of new cases. The chosen DT model to execute
compares its decision rules with that of an online PMU to
initiate Out-of-Step Trip (OST) or Out-of-Step Block (OSB)
functions.
The DT model therefore gives an insight on relay
algorithms in mitigating various power system faults without
over depending on impedance transfer methods. The
hypothesis thus tested was that unlike conventional distance
relays which use impedance tracking, WAP schemes can use
selected important variables for OOS detection. For real time
applications, these important variables are the only
parameters updated to keep the model attuned to prevailing
power system conditions. Updating only these selected
variables reduces the digital relay execution time and is thus
able to perform with speed.
The implementation of these DT models is achieved
through a top-down induction of the DT rules. The DT rules
from the optimum DT (figure 8) for predicting power swings
are shown in figure 6.
Figure 6. DT model representing rules for Predicting Power Swings
The variable ranking of individual attributes in predicting a power swing is shown in
TABLE 1. The reliability index of the performance of the
DT model in making an accurate decision to a predicted
power swing was given in terms of the relative cost. Figure 7
shows the quantitative graph representing the relative cost.
The relative cost is the penalty assigned (as a numeric
quantity) due to wrong classification made by the DT model.
The relative cost as observed is quite low implying that the
DT model generally made the right decisions.
Figure 7. Optimal Tree’s Relative Cost Performance
0.00
0.10
0.20
0.30
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Re lative Co st
Number of Nodes
0.0000.003

International Journal of Energy and Power Engineering 2015; 4(2-1): 63-72 69
Figure 8.Optimal Decision Tree Model
The area under ROC curve strengthens the validity of the
designed DT model. The area under the ROC curve evaluates
the accuracy of discrimination between two decisions. As the
area value tends towards 1, then the more accurate the choice
of decision made by the DT model. Performance of the DT
model as valued by the area under ROC curve is represented
in TABLE 4.
The response statistics of each of the terminal node of the
optimum DT model are shown in TABLE 2. The overall test
performance of 99.82% as shown in TABLE 3 was quite
accurate and therefore suggested a reliable DT model.
Table 1. Variable Ranking
Variable Percentage score
GEN_ROTOR_ANGLE_WRT_MACHINE_ANG__DEG 100.00
GEN_I1P_KA 79.95
GEN_SPEED_DEVIATION_HZ 75.66
GEN_ACTIVE_PWR_MW 73.51
GEN_CURRENT_MAG_KA 73.44
GEN_ELECTRICAL_TORQUE_IN_P_U 72.35
L23_24_VOLT_ANG_IN_DEG 31.41
L38_39_VOLT_ANG_IN_DEG 24.57
Table 2. Response Statistics Of Optimal Tree’s Terminal Nodes
Node Cases
Percent
Score Data Percent
Train Data
Node Class Percent
Correct Train Pct.Stable
Power Swing Train Pct.Unstable
Power Swing Score Pct.Stable
Power Swing Score Pct.Unstable
Power Swing
1 14586
24.18 27.08 Stable Swing 99.99 99.99 0.01 99.99 0.01
2 25 0.04 0.05 Unstable Swing
100.00 0.00 100.00 0.00 100.00
3 73 0.12 0.14 Unstable Swing
100.00 0.00 100.00 0.00 100.00
4 169 0.28 0.31 Unstable Swing
91.12 8.88 91.12 8.88 91.12
5 4309 7.14 8.00 Unstable Swing
99.81 0.19 99.81 0.19 99.81
6 441 0.73 0.82 Unstable Swing
100.00 0.00 100.00 0.00 100.00
7 3637 6.03 2.31 Stable Swing 98.68 96.14 3.86 98.68 1.32
8 996 1.65 0.06 Unstable Swing
3.01 0.00 100.00 96.99 3.01
9 2286 3.79 0.16 Stable Swing 100.00 100.00 0.00 100.00 0.00
10 33492
55.51 60.61 Unstable Swing
98.78 0.00 100.00 1.22 98.78
11 87 0.14 0.04 Stable Swing 100.00 100.00 0.00 100.00 0.00
12 229 0.38 0.43 Unstable Swing
100.00 0.00 100.00 0.00 100.00
L11_35_I1P_IN_KA <= 0.25
Terminal
Node 1
Class = Stable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 14585100.0
Unstable_Power_Sw ing 1 0.0
W = 14586.00
N = 14586
L1 1_35_I1P_IN_KA > 0.25
Terminal
Node 2
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 0 0.0
Unstable_Power_Swing 25 100.0
W = 25.00
N = 25
L2 3_24_I1P_IN_KA <= 0.53
Node 5
Class = Stable_Pow er_Swing
L11_35_I1P_IN_KA <= 0.25
Class Cases %
Stable_Power_Swing 14585 99.8
Unstable_Power_Swing 26 0.2
W = 14611.00
N = 14611
L23_24_I1P_IN_KA > 0.53
Terminal
Node 3
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 0 0.0
Unstable_Power_Swing 73 100.0
W = 73.00
N = 73
L22_23_I1P_IN_KA <= 0.89
Node 4
Class = Stable_Power_Sw ing
L23_24_I1P_IN_KA <= 0.53
Class Cases %
Stable_Power_Swing 1458599.3
Unstable_Power_Swing 99 0.7
W = 14684.00
N = 14684
L22_23_I1P_IN_KA > 0.89
Terminal
Node 4
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 15 8.9
Unstable_Power_Swing 154 91.1
W = 169.00
N = 169
L2 3_24_VOLT_ANG_IN_DEG <= 126.12
Node 3
Class = Stable_Pow er_Sw ing
L22_23_I1P_IN_KA <= 0.89
Class Cases %
Stable_Power_Swing 14600 98.3
Unstable_Power_Swing 2 53 1. 7
W = 14853.00
N = 14853
L2 3_24_VOLT_ANG_IN_DEG > 126.12
Terminal
Node 5
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 8 0.2
Unstable_Power_Swing 4301 99.8
W = 4309.00
N = 4309
GEN_ROTOR_ANGLE_WRT_MACHINE_A NG__DEG_ <= -43.98
Node 2
Class = Stable_Pow er_Sw ing
L23_24_VOLT_ANG_IN_DEG <= 126.12
Class Cases %
Stable_Power_Swing 14608 76.2
Unstable_Power_Swing 4554 23.8
W = 19162.00
N = 19162
L1 5_16_CURRENT_MAG_IN_KA <= 0.05
Terminal
Node 6
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 0 0.0
Unstable_Power_Sw ing 441 100.0
W = 441.00
N = 441
L15_16_CURRENT_MAG_IN_KA > 0.05
Terminal
Node 7
Class = Stable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 1196 96.1
Unstable_Power_Sw ing 48 3.9
W = 1244.00
N = 1244
L1 6_24_I1QIN_KA <= -0.06
Node 7
Class = Stable_Power_Sw ing
L15_16_CURRENT_MAG_IN_KA <= 0.05
Class Cases %
Stable_Power_Swing 1196 71.0
Unstable_Power_Sw ing 489 29.0
W = 1685.00
N = 1685
L31_32_CURRENT_MAG_IN_KA <= 0.58
Terminal
Node 8
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 0 0.0
Unstable_Power_Sw ing 30 100.0
W = 30.00
N = 30
L31_32_CURRENT_MAG_IN_KA > 0.58
Terminal
Node 9
Class = Stable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 85 100.0
Unstable_Power_Swing 0 0.0
W = 85.00
N = 85
GEN_SPEED_DEVIATION_HZ_ <= -29.92
Node 9
Class = Stable_Power_Sw ing
L31_32_CURRENT_MAG_IN_KA <= 0.58
Class Cases %
Stable_Power_Swing 85 73.9
Unstable_Power_Swing 30 2 6.1
W = 115.00
N = 115
L1 1_35_I1Q_IN_KA <= 0.17
Terminal
Node 10
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 0 0.0
Unstable_Power_Sw ing 32650 100.0
W = 32650.00
N = 32650
L2 3_24_VOLT_ANG_IN_DEG <= 118.75
Terminal
Node 11
Class = Stable_Power_Sw ing
Class Cases %
Stable_Power_Swing 2 4 100.0
Unstable_Power_Swing 0 0.0
W = 24.00
N = 24
L23_24_VOLT_ANG_IN_DEG > 118.75
Terminal
Node 12
Class = Unstable_Pow er_Sw ing
Class Cases %
Stable_Power_Swing 0 0.0
Unstable_Power_Swing 229 100.0
W = 229.00
N = 229
L11_35_I1Q_IN_KA > 0.17
Node 11
Class = Unstable_Pow er_Sw ing
L23_24_VOLT_ANG_IN_DEG <= 118.75
Class Cases %
Stable_Power_Swing 24 9.5
Unstable_Power_Sw ing 229 90.5
W = 253.00
N = 253
GEN_SPEED_DEVIATION_HZ_ > -29.92
Node 10
Class = Unstable_Pow er_Sw ing
L11_35_I1Q_IN_KA <= 0.17
Class Cases %
Stable_Power_Swing 24 0.1
Unstable_Power_Swing 32879 99.9
W = 32903.00
N = 32903
L1 6_24_I1QIN_KA > -0.06
Node 8
Class = Unstable_Pow er_Sw ing
GEN_SPEED_DEV IATION_HZ _ <= -29.92
Class Cases %
Stable_Power_Swing 109 0.3
Unstable_Power_Swing 32909 99.7
W = 33018.00
N = 33018
GEN_ROTOR_ANG LE_WRT_MACHINE_ANG__DEG_ > -43.98
Node 6
Class = Unstable_Pow er_Sw ing
L16_24_I1QIN_KA <= -0.06
Class Cases %
Stable_Power_Swing 1305 3.8
Unstable_Power_Swing 33398 96.2
W = 34703.00
N = 34703
Node 1
Class = Stable_Pow er_Sw ing
GEN_ROTOR_ANGLE_WRT_MACHINE_A NG__DEG_ <= -43.98
Class Cases %
Stable_Power_Swing 15913 2 9.5
Unstable_Power_Swing 37952 70.5
W = 53865.00
N = 53865

70 V. Siyoi et al.: Power Swing Prediction for Out-of-Step Mitigation
Table 3. Test Prediction Success
Actual Class Total Class Percent Correct Unstable Swing N=37899 Stable Swing N=15966
Unstable_Power_Swing 37952 99.80 37877 75
Stable_Power_Swing 15913 99.86 22 15891
Total: 53865.00
Average: 99.83
Overall % Correct: 99.82
Table 4. ROC &Error Profiles
No. of
Nodes 5-foldRel.
Error 10-fold
Rel. Error
20-fold
Rel. Error
Average
Rel. Error
Min Rel.
Error Max Rel.
Error 5-fold
ROC 10-fold
ROC 20-fold
ROC Average
ROC Min ROC
Max ROC
2 0.2023 0.2024 0.2026 0.2025 0.2023 0.2026 0.8988 0.8988 0.8987 0.8988 0.8987 0.8988
3 0.0895 0.0893 0.0896 0.0894 0.0893 0.0896 0.9597 0.9598 0.9597 0.9597 0.9597 0.9598
4 0.0269 0.0269 0.0269 0.0269 0.0269 0.0269 0.9924 0.9924 0.9924 0.9924 0.9924 0.9924
5 0.0153 0.0153 0.0153 0.0153 0.0153 0.0153 0.9929 0.9929 0.9929 0.9929 0.9929 0.9929
6 0.0108 0.0108 0.0108 0.0108 0.0108 0.0108 0.9955 0.9954 0.9954 0.9954 0.9954 0.9955
7 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.9976 0.9976 0.9976 0.9976 0.9976 0.9976
8 0.0058 0.0058 0.0058 0.0058 0.0058 0.0058 0.9987 0.9987 0.9987 0.9987 0.9987 0.9987
9 0.0054 0.0055 0.0055 0.0055 0.0054 0.0055 0.9990 0.9987 0.9987 0.9988 0.9987 0.9990
11 0.0044 0.0040 0.0040 0.0041 0.0040 0.0044 0.9990 0.9992 0.9992 0.9992 0.9990 0.9992
12 0.0037 0.0034 0.0034 0.0035 0.0034 0.0037 0.9994 0.9997 0.9997 0.9996 0.9994 0.9997
13 0.0030 0.0027 0.0030 0.0029 0.0027 0.0030 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
14 0.0023 0.0018 0.0018 0.0020 0.0018 0.0023 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
15 0.0019 0.0017 0.0018 0.0018 0.0017 0.0019 0.9997 0.9998 0.9998 0.9998 0.9997 0.9998
16 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.9996 0.9998 0.9997 0.9997 0.9996 0.9998
18 0.0012 0.0010 0.0011 0.0011 0.0010 0.0012 0.9997 0.9998 0.9997 0.9997 0.9997 0.9998
20 0.0007 0.0005 0.0006 0.0006 0.0005 0.0007 0.9997 0.9998 0.9997 0.9997 0.9997 0.9998
21 0.0007 0.0005 0.0006 0.0006 0.0005 0.0007 0.9997 0.9998 0.9997 0.9997 0.9997 0.9998
23 0.0006 0.0005 0.0006 0.0006 0.0005 0.0006 0.9997 0.9998 0.9997 0.9997 0.9997 0.9998
25 0.0006 0.0004 0.0005 0.0005 0.0004 0.0006 0.9997 0.9998 0.9997 0.9997 0.9997 0.9998
4. Conclusion
This paper investigated the suitability of DTs in enhancing
WAP schemes. DT models enable fast execution and present a
simplified interpretation of rules to the task involved. Upon
testing of the optimal DT model, it was found to be 99.82%
accurate in predicting power swings as presented in TABLE 3.
The application of DT models shows significance in digital
relay configuration settings. The splitting point values of the
optimal DT model mark the boundary between the stable and
unstable cases, therefore the threshold digital relay settings.
The violation of these threshold limits would actuate the
digital distance relay to perform the RAS, specifically the
OST and OSB. The RAS is to mitigate the impact of OOS of
generators, pole slip/frequency deviation of the power system
and the loss of stability of the power system network due to
power swings/transients.
In performing the RAS it is recommended that circuit
breaker locations for OST should be at the electrical centre
where the voltage is zero. The electrical centre is found
at . Further work could be investigated on methods
of islanding location. The identified islands should reduce
areas cut out of power supply by employing smart dispatch
programs.
On studying DT suitability to enhancing WAP schemes,
the author’s specific contributions presented in this paper are
thus:
(i) Designed an adaptive OOS relay using a DT model,
which illustrated how a reliable WAP scheme could be
developed. The designed model exhibited novelty in its
ability to predict successive power swings in a timely
fashion. The DT model had a high accuracy in
discriminating between the various power swing types.
(ii) Proposed a novel execution procedure for the designed
DT model. The procedure was to ensure timely
execution of the right RAS.
The beneficiaries of the findings of this paper include
power system protection engineers and system operators.
Acronyms and Notation
0
ℏ
Whole data set.
(
)
ti
Gini index.
T Final tree.
(
)
tn
The total number of vector measurements
at node
t
.
(
)
(
)
RL
tn and tn
Total number of vectors falling into the
left and right subsets respectively.
(
)
jt
Cn
The actual number of cases of class
j
C
at
node
t
.
(
)
ijC
Cost of classifying
i
as
j
.
RL
P and P
Impurity levels at both subsets
L
t
and
R
t
respectively.
0
180=
δ

International Journal of Energy and Power Engineering 2015; 4(2-1): 63-72 71
(
)
t,Cp
j
Re-substitution estimator of the
probability that a case falls in node
t
and
belongs to class
j
C
.
−
+
n,n
Number of cases with positive and
negative actual states respectively.
j
n=−
Number of true negative cases with test
results equal to
j
.
j
n=+
Number of true positive cases with test
results equal to
j
.
j
n>+
Number of true positive cases with test
results less than
j
.
j
n
<+
Number of true positive cases with test
results greater than
j
.
1
M
For categorical
Y
denotes the empirical
prior situation.
2
M
For categorical
Y
denotes the non-
empirical prior situation.
f
N
∑
∈
ℏ
nn
f
; number of cases in data set in
test sample.
jf
N
,
(
)
( )
∑′
∈=
t
v
nj
n
yI
n
f
ℏ
; number of class
j
in
ℏ
.
M
)t(y
( )
( )
∑
∈tn n
y
n
f
t
f
N1
ℏ
Mean dependent
variable in
(
)
t
ℏ
)t,S
~
(I
x
∆
Maximal decrease in node impurity for
division of a parent node into child
nodes
1
`C
and
2
`C
guided by surrogate
splits.
(
)
tp
∑





J
jj
Cp
; estimator of the probability that
a case falls in node
t
.
(
)
j
C
π
(
)
n
Cn
j
; prior probability provided by the
trainer of the data.
(
)
tCp
j
(
)
( )
tp
tCp
j
,
; estimated probability that a case
falls in node
t
and belongs to class
j
C
.
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