Is landing detection

1. 3070 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010
A Pattern Recognition Approach for Detecting
Power Islands Using Transient Signals—Part I:
Design and Implementation
N. W. A. Lidula, Student Member, IEEE, and A. D. Rajapakse, Senior Member, IEEE
Abstract—A novel, pattern-recognition-based approach for fast
detection of power islands in a distribution network is investigated.
The proposed method utilizes transient signals generated during
an islanding event to detect the formation of the island. A deci-
sion-tree classifier is trained to categorize the transient generating
events as “islanding” or “non-islanding.” The feature vectors re-
quired for classification were extracted from the transient current
and voltage signals through discrete wavelet transform. The pro-
posed technique is tested on a medium-voltage distribution system
with multiple distributed generators. The results indicate that this
technique can accurately detect islanding events very fast.
Index Terms—Decision-tree classification, discrete wavelet
transform, distributed generation, islanding, transients.
I. INTRODUCTION
DISTRIBUTED generation (DG) changes the nature of the
distribution system from passive to active. This has given
rise to certain technical issues [1]–[10]. One of these issues is
power islanding, which is defined as “a condition in which a por-
tion of the utility system that contains both loads and distributed
energy resources (DER) remains energized while isolated from
the remainder of the utility system” [8]. Fig. 1 is a simple rep-
resentation of a distribution system with a DG. A power island
is formed if breaker B1 opens while DG is still energized and
connected to the grid (B2, B3 closed).
Islanding results in several safety and power-quality (PQ) is-
sues, including abnormal variations in frequency and voltage in
the power island, possibility of creating an ungrounded system
depending on the transformer connections, and potential safety
hazards for repair crews from unidentified islands. Most inter-
connection regulations, which are usually guided by the IEEE
standards 1547–2003 [8], recommend immediate disconnection
of the DG, upon the formation of an island. This is achieved
through anti-islanding protection, which is a subject that has
been extensively studied [10]–[18].
Manuscript received October 15, 2009; revised April 27, 2010, June 01, 2010;
accepted June 10, 2010. Date of publication August 12, 2010; date of current
version September 22, 2010. This work was supported in part by a research
grant from the Natural Sciences and Engineering Research Council (NSERC)
of Canada and in part by a research grant from Manitoba Hydro, Canada. Paper
no. TPWRD-00781-2009.
The authors are with the Department of Electrical and Computer Engineering,
University of Manitoba, Manitoba, Canada (e-mail: lidula@ee.umanitoba.ca,
athula@ee.umanitoba.ca).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRD.2010.2053724
Fig. 1. Illustration of a power island.
Although the islanded operation of DER has been recognized
as a hazardous situation, a generator or cluster of generators
operating in the islanded mode may be able to supply part of
the local loads when the grid supply is not available. This type
of operation is commonly known as intentional islanding and
the networks with this ability are commonly known as micro-
grids. In realizing microgrids, the local power balance between
the production and consumption needs to be maintained while
having the right level of local protection coordination [14]. Fast
and accurate detection of islands in distribution systems is the
first step toward the intentional islanded operation. In a situation
where the intentional islanded operation is considered, there is
a greater chance for the load and the generation of the island
to be approximately balanced. Some passive islanding detec-
tion methods may fail to detect or take a longer time to detect
the islands when this power balance exists. On the other hand,
anti-islanding protection cannot be made overly sensitive since
that could lead to some unexpected control actions in a micro-
grid type of setup. Thus, faster and more reliable islanding de-
tection methods can bring benefits to the development of micro-
grids. This paper proposes a new, fast, and reliable method to de-
tect power islands using the transient signals generated during
the disconnection of the grid. The method involves the extrac-
tion of current and voltage signal energies in different frequency
bands through wavelet transform and the use of classification
techniques.
Wavelet-transform-based techniques have been previously
used for islanding detection in [15]–[17]. In [15] and [16],
the absolute value of certain wavelet coefficient (of voltage or
frequency signal) is compared against a threshold value; and
if the relevant wavelet coefficient remains above this preset
threshold for a period longer than a certain time threshold, an
islanding condition is declared. These system specific threshold
values are determined through trials and/or based on the expe-
rience of utility engineers [16]. A hybrid islanding detection
algorithm based on wavelet transform, which is specifically
for single-phase photovoltaic (PV) DG systems is discussed
in [17]. An intelligence-based method is investigated in [18],
which uses the decision-tree (DT) classifier, but with some
0885-8977/$26.00 © 2010 IEEE

2. LIDULA AND RAJAPAKSE: PATTERN RECOGNITION APPROACH FOR DETECTING POWER ISLANDS—PART I 3071
Fig. 2. Basic model of the transient-based islanding detection technique.
complex set of features, including, total harmonic distortion of
current/voltage, gradient of the product of voltage and power
factor, etc. for classification. It has a misclassification rate
of 16.67% in islanding detection, which gives only 83.33%
islanding detection accuracy.
The method proposed in this paper differs from the previous
methods: this paper examines the use of a DT classifier in
identifying the islanding condition, instead of depending on
the threshold values determined by trial and error; furthermore,
it uses several wavelet coefficients corresponding to different
frequency bands of the current and voltage signal transients,
instead of using a complex set of indices.
II. PROPOSING ISLANDING DETECTION METHOD
The basic model of the passive islanding detection method
proposed in this paper is illustrated in Fig. 2. Transient wave-
forms of the currents and voltages in a power network contain
unique signatures that reveal the cause of the corresponding
transient event. The proposing islanding detection method is
based on the hypothesis that the transients generated during the
islanding event contain such a signature, and a classifier can be
developed to distinguish islanding events from the other distur-
bances. However, the event-specific characteristics embedded in
the transient waveforms are not directly distinguishable. There-
fore, they need to be preprocessed to extract features that assist
fast classification response. Wavelet transformation is thus used
for this purpose. Reference [19] by the authors of this paper ex-
amines the use of different pattern-recognition techniques for
classifying islanding and nonislanding events using transient
signals. This paper concludes that DT performs better than prob-
abilistic neural networks or support vector machines. Based on
the conclusions arrived in [19], DT was used as the classifica-
tion technique in this paper.
III. DT CLASSIFIER AND CART ALGORITHM
Pattern recognition involves different mathematical ap-
proaches to classify data (patterns) based either on a priori
knowledge or on statistical information extracted from the
patterns. There are five main components associated with a
classification problem:
1) Class (dependent variable): categorical outcome;
2) Features (independent variables): predictors/input vari-
ables;
3) Learning dataset: includes values of the Class and the cor-
responding Features;
4) Test dataset: used to test trained classifier’s accuracy;
5) Misclassification cost: inherent cost associated with mis-
classifying future data.
Fig. 3. Example DT structure.
DT is a logical model constructed based on the training data,
and represented as a binary tree. The DT starts with the “Root,”
which contains whole training dataset. Each “Internal Node”
tests an attribute and each “Arc” corresponds to an attribute
value. “Terminal Node” represents the predicted class [20]–[22].
Fig. 3 shows a sample structure of a DT of a two-class problem.
Classification and regression trees (CART) [21]–[24] is a
nonparametric technique that produces either classification or
regression trees, depending on whether the dependent variable
is categorical or numeric, respectively. The CART algorithm
generates DTs based on a splitting rule. The basic idea of the
splitting rule is to choose a split among all possible splits at
each node so that the resulting child nodes are the “purest.” The
splitting rule is processed in three steps as follows.
1) Find the best split of each predictor variable.
2) Find the best split of node.
3) Assign the class.
A brief explanation of the aforementioned steps is given in
the Appendix. A detailed explanation of the CART algorithm
can be found in [21]–[24]. The CART® Pro V6 commercial soft-
ware [22] was used to develop the DT classifier. The “Gini rule,”
which works well with noisy data was selected as the splitting
rule. The concept behind the Gini rule is to search the learning
dataset for the largest class and to isolate it from the rest of the
data. The mathematical representation of the Gini rule is also
given in Appendix A. Besides the classification tree with sur-
rogates, CART provides a ranking of input features based on
each variable’s contribution to the overall tree. It is determined
by looking at every node in which a variable appears as a pri-
mary splitter or as a surrogate splitter and totaling the accuracies
throughout the tree. Variable importance is presented by scaling
the values relative to the best performing variable, which is the
variable that minimizes the Gini impurity the most at every node
it considers to be a splitter.
IV. FEATURES USED FOR CLASSIFICATION
Wavelet transform is considered as an effective tool for
processing transient signals, which are nonstationary in nature.
Using the discrete wavelet transform (DWT), it is possible to
decompose a signal into several signals in different frequency
bands, which are known as wavelet coefficients. Due to the
wavelet transform’s nature of adapting the time width of the

3. 3072 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010
Fig. 4. Test system.
mother wavelet to its frequency, it is better suited to analyze
transients compared to other frequency-domain techniques,
such as windowed Fourier transform (WFT) [25]–[31]. More-
over, DWT allows extracting a range of frequencies through a
single coefficient; the computational cost of obtaining the same
set of information through WFT would be much higher. A good
comparison of WFT and DWT can be found in [28].
The DWT of a sampled signal is mathematically defined
as
(1)
where is the discretized mother wavelet given by
(2)
and are fixed real values, and and are
positive integers. The DWT analyzes a signal by decomposing
the signal into a coarse approximation and detail information.
The coarse approximation is decomposed again to obtain the
details of the next level, and so on. At each level of this suc-
cessive decomposition, the parameter in (2) is incremented
to increase the frequency resolution. Good reviews of wavelets
can be found in [27]–[29].
V. SIMULATION RESULTS AND ANALYSIS
Simulation studies were carried out using PSCAD/EMTDC
power system simulation software. The distribution network de-
rived from the CIGRE MV benchmark system [32] shown in
Fig. 4 was simulated. It is a system with two DGs: a 1.5-MVA
induction generator (DG1) connected to bus-7 with 0.48 MVars
of capacitive compensation and a 1-MW, 100-kVar synchronous
generator (DG2) connected to bus-9. All loads in the network
were simulated as constant impedances. The system has two
switches S1, S2 (which are kept normally open), making it pos-
sible to change the network configuration from radial to ring
operation.
Two classes of events, namely “non-islanding” and “is-
landing” were considered. The non-islanding cases simulated
include: 1) normal operation; 2) temporary faults, including
three phase to ground, three phase, line to line, and line to
ground; 3) switching of loads; and 4) switching of DGs. The
islanding cases simulated include: 1) opening of the breaker
B1; 2) opening of the feeder breakers B2 and B3, after fault
on Bus-2; and 3) opening of breakers B3, B4, and B5 after the
fault on Bus-3. The data were collected at different loading
conditions and under different system configurations obtained
by opening and closing switch S1.
A total of 348 islanding and 539 non-islanding cases were
simulated and the three-phase currents and voltages measured
at the terminals of both DGs were recorded. Nearly 85% of the
data, which includes 279 islanding cases and 479 non-islanding
cases, were used for training. The remaining cases were used as
testing data. Testing data were extracted randomly from each
category of events described before to ensure testing against
all types of transient events. In testing the performance of the
proposed relay, the cross-validation procedure discussed in [19]
was applied to avoid the errors that could occur due to relying
on a particular data set.
A. Feature Extraction
As discussed in Section IV, the DWT was used to extract
the features for the classifiers. The DWT was performed on-
line in the PSCAD simulation program using the DWT compo-
nent developed in [33]. Phase current and voltage signals were
sampled at 10 kHz. The DWT was performed on the sampled
waveforms with the Daubechie’s 4 (Db4) mother wavelet. The
approach for selecting the mother wavelet and sampling fre-
quency was a trial-and-error procedure combined with prior ex-
perience. The successful application of Db4 for characterizing
power system transients is reported in many studies [29]–[31],
[33]. A comparison of the islanding detection performance with
several mother wavelets types during the preliminary investiga-
tions confirmed the suitability of Db4 mother wavelet. Further-
more, during the initial investigations, three sampling frequen-
cies: 20 kHz, 10 kHz, and 5 kHz, were considered [19], [34]. The
choice of 10-kHz sampling frequency for detailed studies was
based on the accuracy of classification, speed of detection, and
hardware cost/capability required for real-time implementation.
The frequency bands filtered out by DWT at each level are in
accordance with the Mallat algorithm and Nyquist’s rule. Table I
presents the frequency bands filtered out along with the size
of mother wavelet at each level of DWT output. According to
[35], and of (2) are set to 2 and 1, respectively, in ap-
plying Mallat’s algorithm. This results in a geometric scaling of
and translation by , which decom-
pose the input signal into subbands with a bandwidth that in-
creases exponentially with frequency. This scaling gives the
DWT logarithmic frequency coverage in contrast to the uniform
frequency coverage of Fourier transformation.
The original signals and the detail wavelet coefficients of the
current and voltage measured in phase- at DG1 (induction gen-
erator) terminals for 1) an islanding event, 2) a line-to-ground
high impedance fault, and 3) a load trip situation are shown in
Fig. 5(a) and (b). The disturbance is applied at 11.5 s, and DWT
coefficients are shown on an expanded scale that covers a time
window of 0.03 s, extending from 11.5 s to 11.53 s. In addi-
tion to the obvious variations in the range of amplitudes, there

4. LIDULA AND RAJAPAKSE: PATTERN RECOGNITION APPROACH FOR DETECTING POWER ISLANDS—PART I 3073
TABLE I
DB4 MOTHER WAVELET AT 10-kHz SAMPLING FREQUENCY
Fig. 5. (a). Original and DWT detail wavelet components of current signals.
(b). Original and DWT detail wavelet components of voltage signals.
are other noticeable differences between the islanding and non-
islanding events. Furthermore, it is clear that different nonis-
landing events themselves hold identities. Thus, an approach,
Fig. 6. Feature extraction methodology.
such as a simple threshold, cannot be used to distinguish be-
tween islanding and nonislanding events. Consequently, a more
sophisticated method, involving pattern recognition, is required.
Direct use of wavelet coefficients, which are essentially wave-
forms, as inputs to a classifier (in this case, to a DT) is imprac-
tical. Thus, energies associated with the wavelet coefficients in a
time window that encompass the transient were used as features
for the classifier. Wavelet energy is obtained by integrating the
square of the wavelet coefficient over a time window of 0.01 s.
The analysis uses a moving window, thus preserving the tem-
poral information. This time window length was selected after
preliminary investigations as a compromise between the accu-
racy and response time.
At each decomposition level, the energies of the three phases
were added to form a combined “three-phase energy” value in
the particular frequency band. This feature extraction method is
illustrated in Fig. 6. Only the decomposition of Phase-a current
is shown in detail to reduce the complexity of the figure. The
so-calculated “three-phase energy” values of the currents and
voltages create a 12-D feature space (6 levels of currents 6
levels of voltages) for each generator, if the output of six levels
from the DWT is used.
B. Initial Classifier and Feature Selection
Initially, a DT was trained for DG1 using all 12 features.
When a DT is trained, the CART software produces an output
such as Table II, which indicates the importance of each input
feature to the classification process as a percentage of the values
relative to the best performing variable. In Table II, EVD and
EID denote the energy values of the level wavelet coeffi-
cient of the voltages and the currents, respectively. An analysis
of Table II shows that the relevancy of some of the features is
very low and they can be omitted without significantly reducing
the accuracy. After analyzing the tables for DG1 and DG2, it
was found that using only up to four decomposition levels is
sufficient.
C. DT-Based Classifier
Two different approaches were tested: 1) the development
of two separate classifiers for DG1 (induction generator) and
DG2 (synchronous generator) by training the classifiers sepa-
rately with the data measured at the respective generators and
2) the development of a single classifier using the waveforms
measured at both generators (DG1 and DG2).
1) Training a Separate Classifier for Each Generator:
Table III summarizes the results of the classifier trained for
induction generator (DG1) to identify islanding. The overall

5. 3074 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010
TABLE II
IMPORTANCE OF FEATURES IN TRAINING A CLASSIFIER FOR DG1 TO IDENTIFY
ISLANDING USING A 12-D FEATURE SPACE
TABLE III
DT CLASSIFIER TRAINED FOR DG1
TABLE IV
DT CLASSIFIER TRAINED FOR DG2
TABLE V
DT CLASSIFIER—TRAINED FOR DG1 AND DG2
classification accuracy (accurate classification of islanding and
nonislanding as a percentage of the total data set) achieved in
testing the classifier was 99.22%. The depth of the DT (number
of nodes from the root to the farthest terminal node) was eight
nodes.
The results obtained with the classifier trained for the syn-
chronous generator (DG2) are summarized in Table IV. An
overall classification accuracy of 100% was achieved in testing
the classifier and the depth of the tree in this case was only five
nodes.
2) Training a Common Classifier for Both Generators: The
idea behind training a common classifier is that if this is suc-
cessful, identical classifiers can be used at all generators. The
results of this experiment are given in Table V.
The classifier trained for both generators gave 98.28% overall
accuracy on the training dataset. With the testing data for the
induction generator (DG1), it achieved an overall accuracy
of 99.22%, while achieving 100% accuracy in identifying is-
landing events. With testing data for the synchronous generator
(DG2), the classifier achieved 100% overall accuracy.
Fig. 7. DT classifier for detecting power system islands.
Thus, the classifier gives an overall accuracy of 99.61% when
both generators are considered. Based on the simulation exper-
iment that included 258 observations (considering both genera-
tors), it could be stated with 95% confidence [36] that:
1) relay dependability is greater than 95%;
2) relay security is greater than 96%;
3) relay overall accuracy is greater than 98%.
It should be noted that the data corresponding to normal oper-
ation (no transients) were excluded when calculating the accu-
racy values reported in Tables III–V. The trained classifiers were
found to be always accurate under normal operation. Thus, the
removal of normal operation cases results in more conservative
(lower) estimates for the accuracy.
Fig. 7 shows the DT structure of the classifier trained for both
generators. The depth of the tree is five nodes. This tree was
built in accordance to the CART algorithm (explained in the Ap-
pendix) by using the CART® Pro V6 commercial software [22].
The root (Node 1) has the total training data set. The percentage
values in each other node indicate how well the each splitter per-
forms in classifying the assigned class. For example, based on
the first splitter, that is, when 8483.74, a total of 535
cases were classified as Class-1 (non-islanding). Out of these,
only 533 actually belonged to Class-1; the other two belonged
to Class-2. With two misclassified cases, it gives 99.6% classi-
fication accuracy at the particular splitter.
Features EVD1, EID1, EID2, and EID3 are not used in the
final DT, but they can be used as surrogate variables, that is, to
replace a particular variable from the final classifier if needed
(for example, to improve the noise immunity). Since the calcu-
lation of EID4 using the Mallet tree algorithm requires the cal-
culation of EID1, EID2, and EID3 as intermediate signals, the
feature extraction structure presented in Fig. 6 was retained.
The results presented before indicate that the common clas-
sifier is able to give the same accuracy as separate classifiers in
identifying islanding, while keeping the depth of the tree smaller
than the separate classifier trained for DG1. Thus, the common
classifier was selected for further evaluation.

6. LIDULA AND RAJAPAKSE: PATTERN RECOGNITION APPROACH FOR DETECTING POWER ISLANDS—PART I 3075
Fig. 8. Process in the DT relay: (a) input signals, (b) DWT output, (c) Log
(“3-phase wavelet energy contents”), (d) transient signal detection (trigger), (e)
DT classification process, and (f) DT relay output.
D. Process of Islanding Detection
Fig. 8(a)–(e) illustrates how the signals are processed through
the proposed method in the DT relay at DG1 for a sample is-
landing event (opening of breaker B3) that occurs at 11.5 s.
The feature extraction and classification process, which in-
volves the extraction of DWT coefficients, calculation of energy
content of wavelets, transient detection, and the processing in
the DT classifier is associated with a certain time delay.
Fig. 8(a) reveals that the transient appears in the input voltage
and current signals at the moment the disturbance occurred
( 11.5 s). However, as can be seen from Fig. 8(b)–(d), the
DWT and energy content calculation introduces a delay of
about 0.0139 s for this particular islanding event.
The classifier is triggered by using a transient detector. Fig.
8(d) illustrates how the transient is detected by using the energy
content of the level four detail coefficient of the DG terminal
voltage (EVD4) in a sliding window of 0.0005 s. EVD4 was se-
lected as the trigger initiator considering its quality of showing
comparatively large variation in the event of a transient. If the
value of EDV4 exceeds a preset threshold value (2000), the clas-
sification is carried out after a delay of 0.01 s. This delay is equal
to the window length for calculating wavelet energy values that
are fed to the classifier. The trigger threshold was set by studying
the data set. According to Fig. 8(d), the transient is detected at
11.5139 s and a trigger is generated after 0.01 s to acti-
vate the classifier. With already prepared inputs, the classifier
operation is almost instantaneous and, thus, the relay output is
generated at 11.5239 s. The response time of the proposed
relay for this particular islanding event is 0.0239 s (23.9 ms).
The relay shows a similar response, which was observed to be
always less than 24 ms at every islanding event tested.
VI. CONCLUSION
A fast and reliable islanding detection method based on
wavelet coefficients of transient signals was proposed. A
trained DT classifier was able to successfully categorize the
transient generating events as “islanding” or “non-islanding”
using the energy associated with the wavelet coefficients. When
tested with a large number of test cases, the proposed technique
showed more than 95% dependability and over 96% security
at a 95% confidence level. This gave an overall classification
accuracy of more than 98%. The response time of the relay
remained below two cycles for all test cases.
Part II of this paper presents a performance evaluation of this
islanding detection method. It covers a comparison of the pro-
posed method with established passive methods of detecting
power islands under different scenarios, as well as the effects
of factors, such as measurement noise on the proposed power
islands detection method.
APPENDIX
The steps involved in learning a DT using the CART algo-
rithm are presented in the following sections.
A. Finding the Best Split of Each Predictor
In the CART algorithm, each split depends on the value of
only one predictor variable (input feature). It carries out a brute
force search through all possible splits to find the particular split.
Let
class
predictor variable
value of variable
learning data set
1) Tree Building Starts at the “Root” With the Variable
: If the predictor variable is an ordinal variable with
“ ” different values , there are different splits
on . The splits are found by sorting the values
from the smallest to the largest. For the purpose of illustra-
tion, let us take a sample case corresponding to Fig. 3. The
learning dataset , where is
given in Table VI. The size of the dataset is 10. Table VI
also shows the sample dataset when sorted by predictor

7. 3076 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010
TABLE VI
SAMPLE DATASET TO EXPLAIN THE SELECTION OF SPLIT POINTS
Fig. 9. Example on goodness of split calculation.
TABLE VII
GOODNESS OF SPLIT VALUES AT EACH POSSIBLE SPLIT OF X
are possible “split
points” of . At each possible “split point” of the variable,
the sample is split into two child nodes. Cases with a “yes”
response to the question posed are sent to the left node and
those with “no” responses are sent to the right node.
2) Application of the Splitting Rule: There are different split-
ting rules: “Gini rule,” “Twoing rule,” “Ordered rule” etc.
Gini rule works well for noisy data and it is used in this study
to find the best split [21]. The basic idea behind the Gini rule is
to search the learning dataset for the largest class and to isolate
it from the rest of the data. The mathematical representation is
as follows. Let
node number;
class probability distribution of the dependent
variable at node t;
impurity measure at node ;
particular split;
proportion of cases at node that go into the left
child node ;
proportion of cases at node that go into the right
child node ;
impurity of the left child node;
TABLE VIII
MAXIMUM GOODNESS OF SPLIT VALUES OF EACH PREDICTOR X
impurity of the right child node;
goodness of split at node .
For a particular split at node , the Gini impurity measure
is defined as
(A1)
If priors are proportional to data, then these probabilities are
the observed relative frequencies of each class at the node .
Therefore
(A2)
Once the impurity measure is calculated, then the goodness
of split is calculated
(A3)
The best split point is the one that maximizes the
when the node is split according to it.
As an example, the calculation for split point
7.9 at the Root node is presented in Fig. 9, and
of all possible split points of is given in Table VII. From the
table, 7.9 has the largest and, thus, the best
split of .
B. Find the Best Split of the Node
To find the best split of the node, the aforementioned two
steps are repeated for each of the remaining variables at the
Root, and the best splits on each variable are ranked according
to the . The algorithm then selects the variable and its
split point that minimized the impurity of the Root.
As an illustration, Table VIII presents the best splits of each
predictor with their values. It shows that it is possible
to select either 7.9 or 78 as the best split
of the Root. If 7.9 is selected, 78 would
be a surrogate splitter (a splitting rule that closely mimics the
primary split).
C. Class Assignment
There are two rules for assigning classes to nodes that can be
described as follows.
1) Assign terminal node to a class for which is the
highest. The rule assumes equal misclassification costs for
each class (refer to Fig. 3).
2) Assign terminal node to a class for which the expected
misclassification cost is at a minimum. The application of
this rule takes the severity of the costs of misclassifying
cases or observations in a certain class into account, and in-
corporates cost variability into a Gini splitting rule, which
needs to be modified accordingly.
The CART algorithm does not use a stopping rule. It con-
tinues growing the classification tree repeatedly applying the

8. LIDULA AND RAJAPAKSE: PATTERN RECOGNITION APPROACH FOR DETECTING POWER ISLANDS—PART I 3077
aforementioned three steps at each child node until further split-
ting is impossible. When the maximal tree is found, CART ex-
amines smaller trees by pruning away the possible branches.
The best tree is determined by testing for error rates or costs
[21], [22].
REFERENCES
[1] N. Jenkins, R. Allan, P. Crossley, D. Kirschen, and G. Strbac, Em-
bedded Generation. London, U.K.: Inst. Elect. Eng., 2000.
[2] H. B. Püttgen, P. R. Macgregor, and F. C. Lambert, “Distributed gener-
ation: Semantic hype or the dawn of a new era?,” IEEE Power Energy
Mag., vol. 1, no. 1, pp. 22–29, Jan./Feb. 2003.
[3] A. M. Borbely and J. F. Kreider, Distributed Generation—The Power
Paradigm for the New Millennium. Boca Raton, FL: CRC, 2001.
[4] G. Hodgkinson, “System implications of embedded generation and
its protection and control-PES perspective,” Inst. Elect. Eng. Colloq.
System Implications of Embedded Generation Protection Control,
1998, (Digest No. 1998/277).
[5] T. Y. Ismall, “The implications of embedded generation on the ngc
transmission system,” Inst. Elect. Eng. Colloq. System Implications of
Embedded Generation Protection Control, 1998, (Digest No. 1998/
277).
[6] G. Carpinelli, G. Celli, F. Pilo, and A. Russo, “Distributed generation
siting and sizing under uncertainty,” in Proc. IEEE Power Tech., Porto,
Portugal, 2001, vol. 4, p. 7.
[7] M. E. H. Golshan and S. A. Arefifar, “Distributed generation, reactive
sources & network-configuration planning for power & energy-loss re-
duction,” Proc. Inst. Eng., Gen., Transm. Distrib., vol. 153, no. 2, pp.
127–136, Mar. 2006.
[8] Interconnecting Distributed Resources With Electric Power Systems,
IEEE Std. 1547-2003, 2003.
[9] R. A. Walling and N. W. Miller, “Distributed generation is-
landing—Implications on power system dynamic performance,”
in Proc. IEEE Power Eng. Soc. Summer Meeting, 2002, vol. 1, pp.
92–96.
[10] W. Freitas, W. Xu, C. M. Affonso, and Z. Haung, “Comparative anal-
ysis between ROCOF and vector surge relays for distributed genera-
tion applications,” IEEE Trans. Power Del,, vol. 20, no. 2, pt. 2, pp.
1315–1324, Apr. 2005.
[11] J. E. Kim and J. S. Hwang, “Islanding detection method of distributed
generation units connected to power distribution system,” in Proc. Pow-
erCon, Perth, Western Australia, 2000, vol. 2, pp. 643–647.
[12] W. Freitas, Z. Huang, and W. Xu, “A practical method for assessing the
effectiveness of vector surge relays for distributed generation applica-
tions,” IEEE Trans. Power Del., vol. 20, no. 1, pp. 57–63, Jan. 2005.
[13] T. Funabashi, K. Koyanagi, and R. Yokoyama, “A review of islanding
detection methods for distributed resources,” in Proc. IEEE Bologna
Power Tech Conf. , 2003, vol. 2, pp. 6–11.
[14] H. H. Zeineldin, E. F. El-Saadany, and M. M. A. Salama, “Distributed
generation micro-grid operation: Control & protection,” in Proc. Power
Systems Conf.: Advanced Metering, Protection, Control, Communica-
tion, and Distributed Resources, 2006, pp. 105–111.
[15] Y.-H. Liy, T.-S. Luor, S.-J. Huang, and J.-M. Lin, “Method and
System for Detecting Stand-Alone Operation of a Distributed Gener-
ating System,” U.S. Patent 7 342 758, Mar. 2008.
[16] C.-T. Hsieh, J.-M. Lin, and S.-J. Huang, “Enhancement of is-
landing-detection of distributed generation systems via wavelet
transform-based approaches,” Int. J. Elect. Power Energy Syst., vol.
30, no. 10, pp. 575–580, Dec. 2008.
[17] A. Pigazo, V. M. Moreno, M. Liserre, and A. Dell’Aquila, “Wavelet-
based islanding detection algorithm for single-phase PV distributed
generation systems,” in Proc. IEEE Int. Symp. Industrial Electronics,
Vigo, Spain, pp. 2409–2413.
[18] K. El-Arroudi, G. Joós, I. Kamwa, and D. T. McGillis, “Intelligent-
based approach to islanding detection in distributed generation,” IEEE
Trans. Power Del., vol. 22, no. 2, pp. 828–835, Apr. 2007.
[19] N. W. A. Lidula, N. Perera, and A. D. Rajapakse, “Investigation of a
fast islanding detection methodology using transient signals,” in Proc.
IEEE Power Energy Soc. General Meet., 2009, pp. 1–6.
[20] Y. Sheng and S. M. Rovnyak, “Decision tree-based methodology for
high impedance fault detection,” IEEE Trans. Power Del., vol. 19, no.
2, pp. 533–536, Apr. 2004.
[21] B. Leo, J. Friedman, R. Olshen, and C. Stone, Classification and Re-
gression Trees. Belmont, CA: Wadsworth, 1984.
[22] D. Steinberg and P. Colla, CART: Tree-Structured Non-Parametric
Data Analysis. San Diego, CA: Salford Systems, 1995.
[23] Y. Yohannes and P. Webb, “Classification and regression trees,
cart TM—A user manual for identifying indicators of vulnerability
to famine and chronic food insecurity,” Microcomputers in Policy
Research 3, Int. Food Policy Res. Inst., 1999.
[24] L. Bel, D. Allard, J. M. Laurent, R. Cheddadi, and A. Bar-Hend,
“CART algorithm for spatial data: Application to environmental
and ecological data,” Comput. Stat. Data Anal., vol. 53, no. 8, pp.
3082–3093, Jun. 2009.
[25] S. Chen, “Feature selection for identification and classification of
power quality disturbances,” in Proc. IEEE Power Eng. Soc. General
Meet., 2005, vol. 3, pp. 2301–2306.
[26] D. C. Robertson, O. I. Camps, J. S. Mayer, and W. B. Gish, “Wavelets
and electromagnetic power system transients,” IEEE Trans. Power
Del., vol. 11, no. 2, pp. 1050–1058, Apr. 1996.
[27] I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM,
1992.
[28] A. Graps, “An introduction to wavelets,” Comput. Sci. Eng., vol. 2, no.
2, pp. 50–61, Jun. 1995.
[29] C. H. Kim and R. Agganrval, “Wavelet transforms in power sys-
tems—Part 1: General introduction to the wavelet transforms,” IEEE
Power Eng. J., vol. 14, no. 2, pp. 81–87, Apr. 2000.
[30] C. H. Kim and R. Agganrval, “Wavelet transforms in power sys-
tems—Part 2: Examples of application to actual power system
transients,” IEEE Power Eng. J., vol. 15, no. 4, pp. 193–202, Apr.
2000.
[31] H. A. Darwish, M. H. Farouk, A.-M. I. Taalab, and N. M. Mansour, “In-
vestigation of real-time implementation of DSP-based dwt for power
system protection,” in Proc. IEEE Power Eng. Soc. Transmission and
Distribution Conf. Exhibit., 2005/2006, pp. 1258–1263.
[32] CIGRE C6.04.02 Task Force, Benchmark modeling and simulation for
analysis, design, and validation of distributed energy systems. Sep.
2006.
[33] N. Perera and A. D. Rajapakse, “Rapid isolation of faults in power net-
works with distributed generators,” M.Sc. dissertation, Univ. Manitoba,
Winnipeg, MB, Canada, May 2007.
[34] N. W. A. Lidula and A. D. Rajapakse, “Fast and reliable detection of
power islands using transient signals,” presented at the IEEE Int. Conf.
Industrial and Information Systems, Dec. 28–31, 2009, paper 1050395.
[35] T. Frederick and N. Erdol, “Arbitrary tilings of phase space,” in Proc.
IEEE Int. Conf. Accoustics, Speech, and Signal Processing, 1994, vol.
3, pp. III/25–III/28.
[36] D. C. Montgomery, G. C. Runger, and N. F. Hubel, Engineering Sta-
tistics. New York: Wiley, 1998.
N. W. A. Lidula (S’09) received the B.Sc. (Eng.)
degree from the University of Moratuwa, Sri Lanka,
in 2002, the M.Eng. degree from the Asian Institute
of Technology, Bangkok, Thailand, in 2006, and the
Ph.D. degree in electrical and computer engineering
from the University of Manitoba, Winnipeg, MB,
Canada.
Her research interests are in distributed and renew-
able energy systems.
A. D. Rajapakse (M’99–SM’08) received the B.Sc.
(Eng.) degree from the University of Moratuwa,
Katubedda, Sri Lanka, in 1990, the M.Eng. degree
from the Asian Institute of Technology, Bangkok,
Thailand, in 1993, and the Ph.D. degree from the
University of Tokyo, Tokyo, Japan, in 1998.
Currently, he is an Assistant Professor at the
University of Manitoba, Winnipeg, MB, Canada. His
research interests include power system protection,
transient simulation of power and power-electronic
systems, as well as distributed and renewable energy
systems.
Dr. Rajapakse is a Registered Professional Engineer in the Province of Man-
itoba, Canada.