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Decision Tree-Based Fault Detection and Classification

in Solar Photovoltaic Arrays

Ye Zhao, Ling Yang, Brad Lehman*

Department of Electrical and Computer Engineering

Northeastern University

Boston, MA, US

[email protected]

Jean-Franois de Palma, Jerry Mosesian, Robert Lyons

MERSEN USA Newburyport-MA, LLC

Newburyport, MA, US

AbstractBecause of the non-linear output characteristics of

PV arrays, a variety of faults may be difficult to detect by

conventional protection devices. To detect and classify these

unnoticed faults, a fault detection and classification method has

been proposed based on decision trees (DT). Readily available

measurements in existing PV systems, such as PV array voltage,

current, operating temperature and irradiance, are used as

"attributes" in the training and test set. In experimental results,

the trained DT models have shown high accuracy of fault

detection and fault classification on the test set.

I. INTRODUCTIONFault detection in solar photovoltaic (PV) arrays is a

fundamental task to increase reliability, efficiency and safetyin PV systems. Without proper fault detection, unclearedfaults in PV arrays not only causes power losses, but alsomight lead to safety issues and fire hazards [1]. Conventionalfault detection and protection methods usually addovercurrent protection devices (OCPDs, such as fuses) inseries with PV components [2-3]. However, it has beenshown that certain faults in PV arrays may not be cleared byOCPDs, such as line-line faults, open-circuit faults, andpartial shadings, due to the current-limiting nature, non-linear

output characteristics of PV arrays, and even maximumpower point tracker (MPPT) [4-9]. Furthermore, this papershows that under different environmental conditions(irradiance and temperature), the faulted PV array could havethe same operating voltage and current as the normal PVarray. This would bring more difficulties to fault detectionand classification in solar PV installations.

Several fault detection and classification models for PVmodules/arrays have been studied in the literature [8-17]. PVfault detection models based on long-term energy yield andpower losses have been proposed in [8-12]. An extensiondiagnosis method based on the extended correlation functionand the matter-element model is proposed to identify specificfault types of a PV system [13]. The study in [14] uses thediscrepancy between simulated and real I-V curve of PVsystems to detect and identify the faults. To prevent PVcomponents from fire hazards, DC arc detection andprotection methods for PV arrays has been studied in [15].

Time domain reflectometry (TDR) is proposed for detectionand location of open-circuit faults and increased seriesresistance faults in PV strings [16]. At PV-string level, PVstring monitoring has been proposed for real-time faultdetection in [17]. However, none of the literature has used thedecision-tree based model or similar data mining techniquesin fault detection and classification.

A decision-tree (DT) based model is an effective

supervised technique to implement the classification methodsin high-dimensional data [18]. It has been developed in powersystems for fault detection, security assessment, and systemcontrol [19-21]. As for renewable system, such as solarphotovoltaic (PV) systems, this paper proposes a DT basedfault detection and classification method. Depending on thesize of the model, the proposed DT model shows highaccuracy on fault detection (up to 99.98%) and faultclassification (up to 99.8%) on the test data.

This paper develops a DT model at PV-array level anddemonstrates its feasibility on PV experiments in realworking conditions. Specifically, taking measurements, suchas voltage and current of the PV array, along with weatherconditions, the model can detect the fault and classify thespecific fault type.

In the proposed system, necessary data for thedevelopment of a DT model is created and recorded for theexperimental PV system in both normal and fault conditions.The collected data consists of commonly availablemeasurements in many PV systems, such as PV array voltage,current, operating temperature, and solar irradiance. UsingWEKA software [22], the collected and pre-processedtraining set are randomly chosen from experimental data, andare used to build the DT model. After that, the trained DTmodel is tested on unseen real data for model evaluation.

In summary, this paper presents the following researchcontributions:

For the first time, a DT model is developed for faultdetection and classification in solar PV arrays. TheDT model has several advantages, such as fast steps

*The author gratefully acknowledges the support through grants byMersen USA and the National Science Foundation (under grant 0901439).

978-1-4577-1216-6/12/$26.00 2012 IEEE 93


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of training and classification, explicit interpretation,and easy implementation as a software/algorithm.

The proposed DT model is able to identify faults inPV systems in real-time, with high predictionaccuracy. Depending on the size of the DT model, thefault detection accuracy varies from 93.56% to99.98%; the fault classification accuracy ranges from85.43% to 99.8%.

II. DECISION TREE-BASED MODEL IN SOLARPVARRAYSA. Typical Grid-Connedted PV Systems

A typical grid-connected PV system shown in Fig. 1 is theresearch target of this paper. It consists of several majorcomponents, including solar PV arrays, centralized inverterwith MPPT algorithm, electrical connection wirings, andprotection devices, such as overcurrent protection devices(OCPDs) and ground fault protection devices (GFPDs). Notethat the PV system in the research is a grounded system,which has a system grounding point Gsys according toNational Electric Code (NEC) in the US [23].

The PV array typically contains mn PV modules

connected electrically in series and parallel configuration.This array configuration is, nowadays, most common in PVtechnologies [24]. There are n number of PV strings inparallel. Each PV string consists ofm number of modules inseries.

B.Faults in Solar PV ArraysTypical faults in PV arrays consist of ground faults, line-

line faults, and mismatch faults among PV modules [25-26].Among these faults, line-line faults and mismatch faults arestudied in this paper, since they are more difficult to detect byconventional protection devices than ground faults [27].

A ground fault is an accidental electrical short circuitinvolving ground and one or more normally

designated current-carrying conductors.

Utility

grid

Centralized inverter

Ipv

Vpv

PV module

GFPD

+

_

Ig

Series fuse forovercurrent protection

String 1 String 2 String n-1 String n

Gsys

Ground

faults

Line-line

fault

Mismatch

faults

Rf

(Partial

shading)

(Open

circuit)

Figure 1. Typical faults in solar PV arrays

A line-line fault is an accidental short-circuitconnection between two points of different potentialin PV arrays.

Mismatch faults occur when the electrical parametersof module(s) is significantly changed from those ofthe remaining modules. Mismatch fault could betemporary, such as partial shading on PV modules.Also, it could be permanent, such as open circuit in

PV modules/strings, degradation, or defectivemodules.

It is necessary to mention that the PV array will work at anew system maximum power point (MPP) after the fault, aslong as the array voltage can sustain the inverters operating[4-7]. For this reason, the data used for DT model is recordedonly at the maximum power point (MPP) of the PV array.

Furthermore, it is considered that the PV array is the onlysource of fault current, since most PV inverters containtransformers that could provide good galvanic isolationbetween PV arrays and utility grids [28].

C. The Process to Build a DT ModelThe DT model will be built according to four key steps in

the process shown in Fig. 2. The first step is data acquisition,which obtains the training and test set from experiments. Thesecond step is to pre-process the experimental data, includingdata cleaning, sampling, creating new attributes and attributeselection. The third step is to train the DT model by using 66%of randomly chosen pre-processed data. The last step is usingremainder of pre-processed data to test the model.

Data acquisition

Data pre-processing

Training the model

Testing the model

Figure 2. The process to develop a DT model

Ipv

Vpv

Isc-array

*

Normal PV array at STCFaulted PV array at STC

MPPs of normal PV array

MPPs of faulted PV array

Voc-N

*

***

**

*

** *

*** *

*

*

* *

***

*

*

**

*

**

** **

**

***

*

*

**

***

*

*

*

V1

I1

V2 Voc-F

Area1

Area2

Area3

Area4

Figure 3. I-Vcurves of normal and faulted PV arrays

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Vpv< V1?

Y N

Ipv< I1?

Y N

Normal(Area1)

Vpv< V2? Fault(Area2)

Fault(Area3)

Normal

(Area4)

Y N

Root

node

Internal

node

Leaf

node

Figure 4. The DT model for fault detection

For example, in Fig. 3, faults (e.g. line-line faults) in PVarrays usually cause changed current vs. voltage (I-V) curvesand reduced maximum power points (MPPs). Fault MPPsmay vary from normal MPPs in the I-V curves. A DT is aflow-chart-like tree structure used to detect the faulted MPPsfrom normal ones (in Fig. 4). A DT consists of a root and

internal nodes that are labeled with attribute test conditions.Starting from the root node, every instance (consisting ofVpvandIpv at each MPP) will be split by the test at internal nodesand proceed down to the terminal nodes NormalorFault(called class-label attributes, or leaf node in the DT model).For illustration purposes only, the simple model in Fig. 4 onlyuses two attributes (Vpv andIpv) to detect the fault. However inthe real world, normal and fault MPPs may overlap in I-Vcurves. Therefore, high-dimensional attributes (e.g. irradiance,temperature, and output power) should be considered.

Once the DT model is built and tested, it can operate on-line for fault monitoring, as shown in Fig. 5. The DT modelcould be either programmed as if-then statements in aseparate microcontroller or integrated with the PV inverter for

real-time fault detection and classification.

Start

Alarm

Y

N

Fault detection by DT

model

Fault occurs?

Fault classification by DTmodel

Data acquisition and

pre-processing

Figure 5. The flowchart of proposed fault detection and classificationmodel

III. DATA ACQUISITION AND PRE-PROCESSING OFEXPERIMENTAL RESULTS

A.Data Acquisition1) Experimental setup: A small-scale grid-connected PV

system has been set up to create and record faults under real

working conditions. The schematic diagram and the photo are

shown in Fig. 6 and Fig. 7, respectively. The parameters of

PV components are summerized in Table I.Four types of faults mentioned previously have been

created: 1) solid line-line fault (LL) between the middle ofString 1 and negative bus bar; 2) the same solid line-line faultwith fault impedance Rf=20 ohms (LL-20); 3) Open-circuitfaults on String 2 (OPEN); 4) Partial shading faults on the PVmodules (SHADE).

When fault occurs in experiments, the PV array may havesome transients and it could operate off its nominal MPP. Butafter a few seconds, the MPPT algorithm will make the PVarray operate at a new MPP, which is called post-fault steadystate. In other words, the faulted PV system may still work atits MPPs, under changing and various faults.

2) Data acquisition in experiments: Seven parameters (orcalled attributes in the DT model) in the PV array arerecorded under both normal and fault conditions. They are

time, ambient and PV modules operating temperature, array

current (Ipv), reference current (Isc-ref), array voltage (Vpv) and

reference voltage (Voc-ref). The experiments are carried on

two clear days in Boston, MA. Under changing irradiance, 28

fault cases of aforementioned faults are recorded repetitively

at 20~40HZ sampling frequency. Each fault case lasts for

5~15 minutes.

Ig=0

Grid-connected

inverter

Utility

grid

Vpv

IpvGFPD

+

_

A

V

A

V

Isc-ref

Voc-ref

Short-circuit current reference

Open-circuit voltage reference

F

3)

4)

Rf

1) and 2)

+

Figure 6. Schematic diagram of the experimental PV system

Figure 7. Photo of the experimental PV system

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TABLE I. EXPERIMENTAL PVCOMPONENTS

EquipmentParameters

Type Detailed parameters

PV modulePower Film(amorphous

silicon)

At STC: Voc=18V,Isc=0.9A,Vmpp=14V,Impp=0.75A,

Pmpp=10.5W

Entire PV array2 8 modules

configuration

At STC: Psys=168 W, Vsys

mpp=31 V, Isys mpp=6 A

Grid-connectedinverter

Enphase

microinverterM190

Max. output power 190W,

min. start voltage: 28V; MPPTvoltage range: 22 ~ 40V

Note thatIsc-ref and Voc-ref are measured to incorporate theinformation of incident irradiance and temperature on thewhole PV array, since the reference modules have the samelocation and identical electrical parameters as other modules.Furthermore, the transients during the fault are not included inthe dataset. In other words, the data for the DT models areonly collected at pre-fault MPPs and post-fault MPPs.

B.Data Pre-processing1) Data cleaning and sampling: To improve the accuracy

and decrease the training cost of the DT model, outlier and

missing values in the data are removed. Also, originalexperimental data are randomly sampled down to 764,529

instances, which is approximately 80% of its original size.TheIpv-Vpv plot of experimental results is given in Fig. 8.

Notice that it is difficult to identifyNORMAL, LL,LL-20 andSHADEmerely by the two-dimension (I-V) dataset. Therefore,more attributes will be used to detect and classify the faults.

2) New attributes construction: Five new attributes areconstructed to help the development of the DT model. The

original and new attributes are summarized in Table II.The last two classes are called class-label attributes:

Detection and Classification. They are created off-line fortraining and testing the DT model. The class Detectionincludes NORMAL and FAULT. The class Classificationconsists ofNORMAL,LL,LL-20, OPEN, and SHADE.

Figure 8. Vpv vs.Ipv under various conditions

TABLE II. ORIGINAL ANDNEW ATTRIBUTES

Attribute name Unit Description

1 time seconds Time

2 Temp_amb C Ambient temperature

3 Temp_op C Operating temperature

4 Ipv A Array current

5 Isc-ref A Short-circuit current reference

6 Voc-ref V Open-circuit voltage reference

7 Vpv V Array voltage

8 Ppv W Array power = Ipv* Vpv

9 Inorm 0~1 Ipv/(8* Isc-ref)

10 Vnorm 0~1 Vpv/(2* Voc-ref)

11 FillFactor 0~1 Vnorm* Inorm

12 Irradiance W/m2 Isc-ref / Isc * 1000

13 Detection Nominal NORMAL, FAULT

14 Classification NominalNORMAL, LL, LL-20, OPEN,

SHADE

3) Attribute selection: To expedite the training process, itis necessary to remove the relatively less correlated and

redundant attributes. Then, the attributes are selected only if

they have low inter-correction but high correlation with the

class-label attributesDetection and Classification. In WEKA

software, information gain is used to evaluate the attributes.Information (entropy) needed to classify dataDj into class

Ci, i=1,,m:

InfoDj = pi log2mi=1 (pi ) (1)

wherepi is the probability of class Ci inDj.

At a non-leaf node, the information (entropy) needed afterusing attributeA to splitD into v number of partitionsD1,,Dv is defined as:

InfoA (D) = Dj

DInfovj=1 (Dj) (2)

Information gain by splitting at attributeA:

GainA (D) = Info(D) InfoA (D) (3)

Five attributes with high information gain ranking arechosen to develop the DT model: Inorm, FillFactor, Vpv,Voc-ref, and Ppv. It is interesting to see that irradiance and

temperature attributes are ruled out, since they have beenimplicitly included in the selected attributes already.

Notice that the new-attribute 3D plot ofInorm, Vpv andFillFactor (in Fig. 9) gives better fault classification thanoriginal attributes in Fig. 8. However, to further classify thefaults, high-dimensional attributes are necessary.

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Figure 9. 3D plot ofInorm, Vpv and FillFactor under various conditions

IV. TRAINING AND TESTING THE DECISION-TREE MODELA. Training the Model

WEKA is used to train the DT model according to the

training set that we have collected and selected previously[22]. The algorithm for DT induction is shown in Fig. 10, inwhich the Create_node() function grows the DT by adding anew node; the Classify() function determines the class labelto a leaf node; the Attribute_selection_method() functionfinds the best splitting criterion based on information gain;the Stop_condition() function terminates the growth of DT ifstopping conditions are met.

Applying the training set in the DT algorithm, the DTmodels of fault detection and classification are developed.Among 764,529 instances in all dataset, 66% of them arerandomly chosen as the training set. The remainder is used fortest set. Note that the performance baseline of model accuracy(majority vote is NORMAL) for fault detection and fault

classification is approximately 61.15% (see Table III).

B. Testing the ModelAt first, a simple and small-size DT model has been

trained and tested. The DT model for fault detection and faultclassification are shown in Fig. 11 and Fig. 12. The detectionaccuracy on test data is 93.56% and classification accuracy is85.43%.

Generate_decision_tree(D, A)

ifStop_condition(D, A) = truethen

leaf= Create_node();

leaf.label= Classify(D)

return leaf;

else

root= Create_node()root.split= Attribute_selection_method(D, A)

letDj (j=1,,v) be the possible outcome ofroot.split

for eachDj, do

child= Generate_decision_tree(Dj, A)

attach childto root;

end for

end if

return root

Figure 10. The DT induction algorithm

TABLE III. ENTIRE DATASET FOR THE DTMODEL

Class-label attribute

NORMAL LL LL-20 OPEN SHADE

# of

instances467,494 65,647 28,719 115,791 86,878

Percent 61.15% 8.59% 3.76% 15.15% 11.36%

The developed DT models can be easily programmed in amicrocontroller for real-time fault monitoring. For example, ifa new set of measurements are: Voc_ref=17V, Inorm=0.6,FillFactor=0.32, Ppv=60W and Vpv=25V, then according tothe DT model, the PV array will be classified as a SHADEfault.

By increasing the size, the DT model will become morecomplex and more accurate (up to 99.8%). The test accuracyof different sizes of DTs have been summarized in Table IVand Table V, where the number of leaf nodes for the DTmodel is defined as the external nodes that will denote a classprediction; and the size of the tree is defined as all nodesincluded in the tree structure. At leaf-nodes, the first and thesecond number in the parentheses represent the correct and

error predictions.

C.DiscussionTo train and test the DT model, 764,529 instances are

collected and pre-processed from 28 various fault cases underchanging irradiance. Both high accuracy at detection andclassification of specific pre-defined faults are achieved.Depending on the size of the model, the proposed DT modelshows high accuracy on fault detection (up to 99.98%) andfault classification (up to 99.8%) on the test data.

Voc-ref 17.645

| Inorm 0.57744

| | Vpv 25.07: NORMAL (415489.0/2208.0)

Figure 11. A simple fault detection model

Inorm 0.57629

| Vpv 25.314: NORMAL (427460.0/8627.0)

Figure 12. A simple fault classification model

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Even for the simple DT models, the fault detection andclassification accuracy can reach 93.56% and 85.43%,respectively. The classification accuracy for each class-labelattribute is:NORMAL 99.48%,LL 99.99%,LL-20 0%, OPEN89.78% and SHADE 21.3%. Notice that LL-20 is the mostdifficult fault to classify.

At the most complex model, the fault classificationaccuracy can achieve 99.8%. In this case, the classification

accuracy forLL-20 can reach 99.7%. However, the size of theDT model will be 1637 nodes with 819 leaf nodes, whichmight be too large for practical application. Therefore, aproper size DT model should be chosen by considering thetradeoff between accuracy and model complexity.

Limitations may exist in the DT model for solar PV arrays:1) Training cost may be high. The experimental data aregenerated in the real world. This could draw peoples concernof cost and safety; 2) The DT model may not performcorrectly at unknown data remarkably different from thetraining set. Since the operation of PV arrays greatly dependson environmental conditions, and a huge number of variousfaults conditions may occur in the PV array, it seems difficultto obtain the sufficient training and test dataset that can coverall possible fault scenarios.

TABLE IV. RESULTS OF FAULT DETECTION

Size of

the tree

# of

leaves

Trainingtime

(seconds)

Detection

Accuracy (%)

11 6 35.46 93.5639

17 9 48.03 95.8202

21 11 50.62 98.8476

47 24 54.82 99.6838

55 28 54.64 99.8369

69 35 56.3 99.9111

81 41 65.43 99.9161

85 43 62.2 99.9515

105 53 65.83 99.9608

115 58 66.24 99.9731139 70 66.32 99.9835

159 80 75.83 99.9892

TABLE V. RESULTS OF FAULT CLASSIFICATION

Size of

the tree

# of

leaves

Training

time

(seconds)

Classification

Accuracy (%)

19 10 34.94 85.4343

31 16 48.61 91.0749

59 30 54.48 93.1827

113 57 64.14 97.8033

133 67 69.91 98.5643

235 118 81.33 98.9909

311 156 87.6 99.3083

431 216 93.74 99.4991

667 334 116.37 99.6218

919 460 128.9 99.7207

1247 624 142.79 99.7761

1637 819 161.68 99.8

V. CONCLUSION AND FUTURE WORKFor the first time, a new fault detection and classification

in solar photovoltaic (PV) systems based on decision-tree (DT)models has been proposed. The process of training the modelis straightforward and easy to implement. The trained modelshows good detection accuracy (up to 99.98%) andclassification accuracy (up to 99.8%) that may havepromising application in the real world.

The future research plans to address some of thepreviously discussed limitations, which include modeloptimization, cost reduction of fault data acquisition, andintegration with PV inverters.

REFERENCES

[1] B. Brooks. (2011) The Bakersfield Fire - A Lesson in Ground-Fault Protection. SolarPro. Page 62 - 70.

[2] W. Bower and J. Wiles, "Investigation of ground-fault protectiondevices for photovoltaic power system applications," in

Photovoltaic Specialists Conference, 2000. Conference Record of

the Twenty-Eighth IEEE, 2000, pp. 1378-1383.

[3] J. Wiles. (2008) To Fuse or Not to Fuse?Home Power #125,code corner. 106-108.

[4] Y. Zhao, B. Lehman, J.-F. de Palma, J. Mosesian, and R. Lyons,"Fault evolution in photovoltaic array during night-to-daytransition," in Control and Modeling for Power Electronics

(COMPEL), 2010 IEEE 12th Workshop on, 2010, pp. 1-6.[5] Y. Zhao, B. Lehman, J.-F. d. Palma, J. Mosesian, and R. Lyons,

"Fault Analysis in Solar PV Arrays under: Low Irradiance

Conditions and Reverse Connections," in the 37th IEEE

Photovoltaic Specialist Conference, Seattle, WA, 2011.[6] Y. Zhao, B. Lehman, J.-F. d. Palma, J. Mosesian, and R. Lyons,

"Challenges of Overcurrent Protection Devices in Photovoltaic

Arrays Brought by Maximum Power Point Tracker," in the 37thIEEE Photovoltaic Specialist Conference, Seattle, WA, 2011.

[7] Y. Zhao, B. Lehman, J.-F. d. Palma, J. Mosesian, and R. Lyons,

"Challenges to Overcurrent Protection Devices under Line-lineFaults in Solar Photovoltaic Arrays," in the third IEEE Energy

Conversion Congress & Exposition (ECCE), Phoenix, AZ, USA,

2011.

[8] A. Chouder and S. Silvestre, "Automatic supervision and faultdetection of PV systems based on power losses analysis,"Energy

Conversion and Management, vol. 51, pp. 1929 - 1937, 2010.[9] A. Drews, A. C. d. Keizer, H. G. Beyer, E. Lorenz, J. Betcke, W.

G. J. H. M. v. Sark, W. Heydenreich, E. Wiemken, S. Stettler, P.

Toggweiler, S. Bofinger, M. Schneider, G. Heilscher, and D.Heinemann, "Monitoring and remote failure detection of grid-

connected PV systems based on satellite observations," SolarEnergy - Elsevier,pp. 548 - 564, 2007.

[10] H. Haeberlin and C. Beutler, "Normalized Representation of

Energy and Power for Analysis of Performance and on-line Error

Detection in PV-Systems," presented at the 13th EU PVConference on Photovoltaic Solar Energy Conversion, Nice,France, 1995.

[11] S. K. Firth, K. J. Lomas, and S. J. Rees, "A simple model of PVsystem performance and its use in fault detection,"ELSEVIER -

SOLAR ENERGY, 2009.

[12] S. Vergura, G. Acciani, V. Amoruso, G. E. Patrono, and F. Vacca,"Descriptive and Inferential Statistics for Supervising and

Monitoring the Operation of PV Plants,"Industrial Electronics,IEEE Transactions on, vol. 56, pp. 4456-4464, 2009.

[13] K.-H. Chao, S.-H. Ho, and M.-H. Wang, "Modeling and fault

diagnosis of a photovoltaic system,"Electric Power SystemsResearch, 2008.

[14] D. Stellbogen, "Use of PV circuit simulation for fault detection inPV array fields," inPhotovoltaic Specialists Conference, 1993.,Conference Record of the Twenty Third IEEE, 1993, pp. 1302-

1307.

98


7/7

[15] H. Haeberlin, "Arc Detector for Remote Detection of DangerousArcs on the DC Side of PV Plants," presented at the 22nd

European Photovoltaic Solar Energy Conference, Milano, Italy,

2007.[16] T. Takashima, J. Yamaguchi, and M. Ishida, "Fault detection by

signal response in PV module strings," inPhotovoltaic

Specialists Conference, 2008. PVSC '08. 33rd IEEE, 2008, pp. 1-5.

[17] N. Takehara and K. Fukae, "Abnormality detection method,

abnormality detection apparatus, and solar cell power generating

system using the same," 5669987, 1997.[18] J. Han and M. Kamber,Data Mining Concepts and Techniques,

Second ed., 2006.[19] S. Yong and S. M. Rovnyak, "Decision tree-based methodology

for high impedance fault detection,"Power Delivery, IEEETransactions on, vol. 19, pp. 533-536, 2004.

[20] S. Rovnyak, S. Kretsinger, J. Thorp, and D. Brown, "Decisiontrees for real-time transient stability prediction,"Power Systems,

IEEE Transactions on, vol. 9, pp. 1417-1426, 1994.

[21] H. Mori, "State-of-the-Art Overview on Data Mining in Power

Systems," inPower Systems Conference and Exposition, 2006.PSCE '06. 2006 IEEE PES, 2006, pp. 33-34.

[22] I. H. Witten and E. Frank,Data Mining: Practical MachineLearning Tools and Techniques: Morgan Kaufmann, 2000.

[23] NFPA70, "Article 690 - Solar Photovoltaic Systems of NationalElectrical Code," ed, 2011.

[24] J. Wiles, "Photovoltaic Power Systems And the 2005 National

Electrical Code: Suggested Practices," Southwest Technology

Development Institute, New Mexico State University November26, 2008.

[25] S. E. Forman, "Performance of Experimental Terrestrial

Photovoltaic Modules,"Reliability, IEEE Transactions on, vol.

R-31, pp. 235-245, 1982.[26] E. L. Meyer and E. E. van Dyk, "Assessing the reliability and

degradation of photovoltaic module performance parameters,"Reliability, IEEE Transactions on, vol. 53, pp. 83-92, 2004.

[27] Y. Zhao, "Master of Science Thesis: Fault Analysis in SolarPhotovoltaic Arrays," Electrical and Computer Engineering,

Northeastern University, Boston, 2010.

[28] L. Quan and P. Wolfs, "A Review of the Single PhasePhotovoltaic Module Integrated Converter Topologies With

Three Different DC Link Configurations,"Power Electronics,IEEE Transactions on, vol. 23, pp. 1320-1333, 2008.

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