Research Article Fuzzy Logic Controller Based Distributed...

Research ArticleFuzzy Logic Controller Based Distributed GenerationIntegration Strategy for Stochastic Performance Improvement

Jagdish Prasad Sharma1 and H Ravishankar Kamath2

1Mewar University Chittorgarh Rajasthan India2Malwa Institute of Technology Indore India

Correspondence should be addressed to Jagdish Prasad Sharma jpsharmacsebgmailcom

Received 15 July 2016 Accepted 12 October 2016

Academic Editor Mamun B Ibne Reaz

Copyright copy 2016 J P Sharma and H R Kamath This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In the restructured environment distributed generation (DG) is considered as a very promising option due to a high initial capitalcost of conventional plants environmental concerns and power shortage Apart from the above distributed generation (DG) hasalso abilities to improve performance of feeder Most of the distribution feeders have radial structure which compel to observethe impact of distributed generations on feeder performance having different characteristics and composition of time varyingstatic ZIP load models Two fuzzy-based expert system is proposed for selecting and ranking the most appropriated periods toan integration of distributed generations with a feeder Madami type fuzzy logic controller was developed for sizing of distributedgeneration whereas Sugeno type fuzzy logic controller was developed for the DG location Input parameters for Madami fuzzylogic controller are substation reserve capacity feeder power loss to load ratio voltage unbalance and apparent power imbalancesDG output survivability index and node distance from substation are chosen as input to Sugeno type fuzzy logic controller Thestochastic performance of proposed fuzzy expert systems was evaluated on a modified IEEE 37 node test feeder with 15 minutescharacteristics time interval varying static ZIP load models

1 Introduction

In the restructured environment feasibility study of dis-tributed generation (DG) integration to existing grid is akey interesting area of research Deployment of distributedgeneration (DG) in distribution system brings technical aswell as financial benefits to utilities The positive benefits areloss reduction reliability enhancement and power qualityimprovement and negative effects are increased fault leveland false operation of the feeder Most of the distributionfeeders have radial structure and are designed to operate witha single source along the feeder To compensate rapid growthof load demand and proliferation of electronic device avail-able options for utilities are network extension substationcapacity augmentation and DG integration Apart from theabove the majority of the existing radial distribution feedersare lengthy over and nonuniform loading which resulted inan excessive voltage drop poor voltage profile male trippingof protection devices and power loss DG integration to

existing grid is well suited option to utilities due to lack offinancial resources and long-term implementation of gridextension work As DG installation greatly influences theperformance of distribution feeder the optimal location andsizing of distributed generation (DG) are an active researchinterest which is needed to harness maximum benefits fromthe DG

Several researchers have used different optimizationmethods such as analytical numerical and heuristic forthe sake of power loss minimization cost reduction profitmaximization and environmental emission reduction Barinet al have used a fuzzy-based expert system for choosingand ranking of the most appropriated periods to integratedistribution generation with an existing distribution network[1] A fuzzy-based powermanagement technique is employedto schedule power dispatching for microgridutility gridTheproposed power management technique is subjected to a setof constraints including weather conditions load-sheddinghours and peak pricing hours [2] In order to mitigate

Hindawi Publishing CorporationAdvances in Electrical EngineeringVolume 2016 Article ID 9760538 13 pageshttpdxdoiorg10115520169760538

2 Advances in Electrical Engineering

demand and avoid power outage in peak hour two fuzzy logiccontroller are simulated for optimal location and sizing ofdistributed generation on IEEE 13 test feeder [3]

A fuzzy logic method is deployed for optimal DGplacement subjected to minimize total power loss constraintwhereas a new analytical method is used for DG sizing Theeffectiveness of DG on system voltage profile and branchpower losses is carried out on IEEE 69 and IEEE 33 radialfeeder [4] Manjili and Rajaee proposed fuzzy controllerfor energy management and cost reduction microgrid Theamount of power exchange from storage unit is based on theload demand renewable generation rate and electricity price[5]

Metia and Ghosh presented optimal location of DGunits with a 33-bus system based on the available amountof DG using fuzzy logic [6] A firefly based algorithm foroptimal location and capacity of CHP technology DG or aphotovoltaic DG is implemented on IEEE 37-node feederwith the objectives of profit maximization [7] Harmonysearch algorithm is utilized to determine appropriate size ofshunt capacitors with real power losses and installation costof shunt capacitors whereas the location of shunt capacitorsis identified using voltage stability index [8] Padma Lalithaet al presented a fuzzy approach for finding optimal DGlocations and a PSO algorithm for optimal DG sizes on IEEE33 node feeder [9] A probabilistic fuzzy solution is proposedto identify vulnerable nodes for the optimal reconfigurationproblem [10] Fuzzy expert system employed for optimalcapacitor placement and sizing for 35 buses with multilevelof loads [11]

Arabali et al carried out a stochastic framework tooptimal sizing and reliability analysis for a hybrid powersystem having wind power photovoltaic (PV) and energystorage system The stochastic nature of wind solar irradia-tion and photovoltaic (PV) power and load are stochasticallymodelled using ARMA [12] Soroudi and Ehsan investigatedthe impact of an uncertain power production of distributedgenerations (DGs) on active losses of distribution feederUncertainty in wind speed and gas turbines is modelled bya Weibull probability distribution function (PDF) and fuzzyrespectively [13]

Sharma and Ravishankar Kamath have presented voltageassessment indices for modified IEEE 37 node test feederhaving time varying composite voltage sensitive load [14]Performance indices to assess feeder performance of modi-fied IEEE 37 node test feeder were developed with the help offorward-backward sweep method and two port parametersrepresentation of feeder components [15]

The objective of this paper is to integrate DG usingtwo fuzzy logic controllers One fuzzy logic controller isused to determine the sizing of DG on the basis of feederperformance parameter such as substation reserve capacityfeeder power loss to load ratio voltage unbalance andapparent power imbalance Another fuzzy logic controller isused to choose the DG location node on the basis of DGoutput survivability index andnode distance from substationare chosen as input

2 Feeder Performance Indices

The quality of power supply for modified IEEE 37 nodetest feeder is evaluated to develop performance indices andthese performance indices are substation reserve capacityvoltage unbalance factor and feeder power loss to load ratiobranch loading voltage deviation and power factor [15] Itis observed that the said substation transformer of feederis highly overloaded between 35 and 71 characteristics timeinterval which could be relived with solar PV penetration atthe feeder Modified feeder has also accounted for stochasticcharacteristics and composition of voltage sensitive loadmodels These load models are categorized into residen-tial commercial and industrial consumers Each categoryconsumers are appliances with constant power constantcurrent and constant impedance in random propositionsThe participation of real and reactive power load exponentsfor the different type categories of consumers is characterizedby the following equations [15]

119875119896119886119887119888(ℎ) = 1198621119896

119886119887119888(ℎ) + 1198622119896

119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

2

+ 1198623119896119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

119876119896119886119887119888(ℎ) = 1198631119896

119886119887119888(ℎ) + 1198632119896

119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

2

+ 1198633119896119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

(1)

Calculation of ZIP loads compositions is shown inAppendix Tomeet smart grid implementation criterion per-formance indices are evaluated for 15 minutes characteristicstime interval for the whole day In these days distributiongeneration integration is a common practice to meet outcontinuously increased demandThe load and renewable DGgeneration probabilistic nature are considered in this study Itis observed from load flow solution that feeder is subjected tooverloading during 8AM to 6PMTherefore the fuzzy expertsystem is developed in a way that DG operated between theabove periods The photovoltaic DG system under differentpower factor scenario is considered for investigation

3 Proposed Fuzzy Expert System

The proposed fuzzy logic controller for DG integrationimplies Mamdani and Sugeno fuzzy inference system TheDG sizing is determined using Mamdani type fuzzy logiccontroller on the basis of feeder performance parametersuch as substation reserve capacity feeder power loss toload ratio voltage unbalance and apparent power imbalancewhereas Sugeno type fuzzy logic controller is used to choosethe DG location on the basis of DG output survivabilityindex and node distance from the substation The fuzzy-based expert system is tested using the MATLAB fuzzylogic tool box undermulti-rules-based decision andmultisetsconsiderations as in Figure 1

Advances in Electrical Engineering 3

TOD

SCRI

FLLR

UPQ

VUF

Input for Mamdani typefuzzy logic controller

Mamdani type

Distance

Input for Sugeno typefuzzy logic controller

Sugeno typefuzzy logiccontroller

fuzzy logic controller

round

Rounding

DG sizing

DG locationfunction

Survivability Index

Figure 1 Fuzzy logic controller for DG integration

TOD

PowerGAP

FLLR

UPQ

VUF

FCLperformancenew(mamdani)

PDGOUTPUT

Figure 2 Mamdani type fuzzy logic controller for DG sizing

Inference process forMamdani type fuzzy logic controllerhas MIN-MAX method of aggregation and SOM of thedefuzzification process as standard settings The other settingfor Sugeno type fuzzy logic controller remains the sameexcept for defuzzification method named as whatever [16]

31 Mamdani Type Fuzzy Logic Controller for DG SizingUnbalance in voltage and current increased apparent powerimbalance feeder loss voltage deviation and neutral currentIncreased neutral current in substation transformer leadsto communication interference equipment overloading andfalse operation of the protective system Apart from theabove apparent power imbalance is a more appropriateapproach to reactive power compensation The 15-minutecharacteristics time interval substation reserve capacity(SRCI) feeder power loss to load ratio (FLLR) voltage unbal-ance factor (VUF) and apparent power imbalance (APBI)indices are the five inputs to the Mamdani type inference sys-tem which are computed from the load flow solution over aneach 15-minute time interval for the whole day [15] ProposedMamdani type inference as shown in Figure 2 has a set of 15rules which involve heuristic rules for determining the size ofDG in the fuzzification process In the fuzzification processthese inputs are converted into logic form in accordance withthe associated membership functions

Membership function plots

TOD1 TOD2 TOD3 TOD4

Plot points 181

1

05

0

Input variable ldquoTODrdquo9080706050403020100

181

Figure 3 Membership function of TOD

Four different times of day (TOD) in terms of 15-minutemetering time interval is taken for the whole day andrepresented by four triangles membership function curvesas shown in Figure 3 In Figure 4 the power demand gap isdescribed by Z Gauss and S shape membership functionsTheZ shapemembership function represents the demand gapless than 05MW and demand gap greater than 05MW isrepresented by an S shape membership curve

Triangle membership function is used for medium valueFLLR UPQ and VUF whereas trapezoidal membershipfunctions are considered for the low and high of the abovethree variables Their graphical representations of member-ship function are depicted in Figures 5 6 and 7 respectively


Low Medium HighMembership function plots Plot points

1

05

0

181

0604020 08 1minus04minus06minus08 minus02minus1

Input variable ldquoPowerGAPrdquo

Figure 4 Membership function of power demand gap


1

05

0

181

005 006 007 008 009 01004

Input variable ldquoFLLRrdquo

Figure 5 Membership function of FLLR

DG sizing is shown with three trapezoidal membershipfunctions in Figure 8 Low DG output is assumed to bebetween 0 and 01MW whereas medium DG output hasranged between 012 and 04 The DG output is consideredbetween 04 and 1MW Surface view of fuzzy logic controllerrules for DG sizing is shown in Figure 9

32 Sugeno Type Fuzzy Logic Controller for DGLocation Thispaper proposes a fuzzy approach to predict vulnerability ofthe node using survivability index The proposed survivabil-ity index (SI) is computed by equation (2) below for eachnodeusing voltage stability margin (VSI) and voltage deviationindex (VDI) corresponds to 90 percentile over each 15-minute time interval for the whole day [14 15]

SI = min (VSIℎ119886119887119888) lowast 075 +max (VDIℎ

119886119887119888) lowast 025 (2)

Table 1 shows the survivability index of top 15 nodes fromthe list of nodes in or near vulnerability andTable 1 is depictedin the Appendix The membership function for vulnerablenodes is represented in Figure 12

Sugeno type fuzzy logic controller as shown in Figure 10has crisp input parameters such as node distance from thesubstation DG output and vulnerable node Node distance isdepicted by three intersecting trapezoidal curves in Figure 11The low distance corresponds to the range of 0 to 3300feet and medium distance is between 3400 and 6000 feetHigh distance is considered between 6000 and 8000 feetThe output of Sugeno type fuzzy logic controller has con-stant functions as shown in Figure 13 where the distributedgeneration can be added according to the demand from thecustomer premises The proposed Sugeno type inference hasa set of 09 rules to determine the location of DG as shownFigure 14


1

05

0

181

01 015 02 025 03005

Input variable ldquoUPQrdquo

Figure 6 Membership function of UPQ

Table 1 Survivability index of top 15 nodes

S number Node Distance (Feet) Survivability index

1 775 4930 08816722 709 4930 0880713 708 5250 08899384 733 5570 0905285 734 6130 09183966 737 6770 09292167 738 7170 0933718 711 7570 09361159 741 7970 093687210 732 5570 089094811 731 5530 088071212 710 6650 092179613 735 6850 092308314 736 7930 092193415 740 7770 0937371

Figures 15 and 16 show the inputs of Madami andSugeno fuzzy logic controller respectively whereas outputsof Madami and Sugeno fuzzy logic controller are depicted inFigure 17 Node 734 is found at the optimum DG locationwith 440KW per Phase capacity to be operational between37 and 73 characteristics time interval

4 Results and Analysis

The proposed algorithm has been implemented in MATLABand evaluated on modified unbalance IEEE 37 node testfeeder In this study total optimum DG capacity of 440KWper phase is considered at node 734 and the DG operatingtime interval very much resembles solar photovoltaic DG Inthis paper constant power factorDGmodel is considered andhas constant 119875dg active power at a pfdg constant power factorTo keep constant power factor required 119876dg reactive powerof the DG is computed by following equation [17]

119876dg = 119875dg tan (cosminus1 (119875dg)) (3)

In the base case the performance indices are computedwithout any DG integration for the whole day The base loss


LowMedium

HighMembership function plots Plot points

1

05

0

181

01 02 03 04 05 06 07 08 09 10

Input variable ldquoVUFrdquo

Figure 7 Membership function of VUF

Low Medium High

Output variable ldquoPDGOUTPUTrdquo1000900800700600500400300200100

Membership function plots Plot points

1

05

00

181

Figure 8 Membership function of DG output

PDG

OU

TPU

T

105

0minus05

minus1 TODPowerGAP

9080706050403020100

0

100

200

300

400

Figure 9 Surface view of fuzzy logic controller rules for DG sizing

PGOUTPUT

Distance

Surviablityindex

FCL2rule(sugeno)

DGNodeSelection

f(u)

Figure 10 Sugeno type fuzzy logic controller for DG location

of feeder is depicted in Figure 18 For the base case the dailyphase voltage profile for all buses is shown in Figures 19ndash21The least voltage in Phase A Phase-B and Phase C is foundon nodes 34 33 and 31 respectively These nodes can be usedfor shunt compensation

The impacts of distributed generation on various indicesare detailed as follows

Figure 22 reveals that DG operation at 095 power factorleading has the highest substation reserve capacity whereas

1

05

0

Low Medium HighMembership function plots Plot points 181

Input variable ldquoDistancerdquo800070006000500040003000200010000

Figure 11 Membership function of distance

1

05

0

Membership function plots Plot points 181

01 02 03 04 05 06 07 08 09 10

Input variable ldquoSurviablityindexrdquo

Low Medium High

Figure 12 Membership function of survivability index

Membership function plots plot Points 181

Output variable ldquoDGNodeSelectionrdquo

775709708733734737738711

741732731710735736740

Figure 13 Membership function of DG location


Distance PGOUTPUT

10009008007006005004003002001000 010002000

3000400050006000

70008000720722724726728730732

DG

Nod

eSele

ctio

n

Figure 14 Surface view of Sugeno type fuzzy logic controller rules

2000

minus200minus400minus600minus800

008

007

006

005

03

025

02

015

0908070605

Input to Mamdani Controller

FLLR

UPQ

VUF

80 90706050403020100

80 90706050403020100

80 90706050403020100

80 90706050403020100

Figure 15 Inputs to Mamdani fuzzy logic controller

the base case has the lowest substation reserve capacitybetween 35 and 71 characteristics time interval DG operationat 095 lagging power factor has the reverse effect on loadrelief

It is observed from Figures 23 24 and 25 that the highestFLLR for all phases is found in DG operation at 095 powerfactor lag Lowest reduction in FLLR in Phase-A Phase-Band Phase-C is found inDG 095 power factor (lag) base andDG 099 power factor (lead) case respectively

In Figures 26 27 and 28 it is observed that DG operationat 095 power factor leading showed highest BCLI reductionfor all phases the DG operation at 099 power factor leadinggot the second reduction in BCLI and then the DG operationat unity power factor and DG operation at 095 power factorlagging the next Base case showed a branch overloading

1173 and 115 at 53 and 55 characteristics time interval forPhase-A and C respectively

As shown in Figure 29 there is no significant impact ofDG placement over apparent power imbalance Figures 3031 and 32 reveal the same impact of DG placement on voltagedeviation for all phases which was observed in the case ofBCLI

As shown in Figures 33 34 and 35 DG operation at 095power factor lagging showed minimum power factor (MPF)for all phasesMaximumpower factor for Phase-A andPhase-C occurred in the DG operation at 095 power factor leadingwhile maximum power factor for Phase-B occurred in DGoperation at unity power factor

In Figure 36 base case showed a highest voltage unbal-ance factor (VUF) the DG operation at 095 power factor


80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088

Inputs of Sugeno logic controller

Survivability index

Survivability index

Per Phase DG Capacity

50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0

Figure 16 Inputs to Sugeno fuzzy controller

732734

730728726724722720

450400350300250200150100500

DG Node

DG Node

Simulink output of Madami and Sugeno logic controller


50403020100 90807060

50403020100 90807060

Figure 17 Simulink outputs of fuzzy logic controller

lagging got the second maximum VUF and then the DGoperation at unity power factor and DG operation at 099power factor leading the next DG operation at 095 powerfactor lagging showed a maximum VUF of 05177at 6 charac-teristics time interval

5 Conclusion

The stochastic behavior of DG integrated distribution feederis a challenging problem for operations and planning aspectsA fuzzy expert system is proposed to determine optimal


Tota

l fee

der l

oss (

KW)

253035404550556065

20 9010 50 60 70 8030 40Time in 15-minute interval

X 6Y 2522

X 52Y 5946

Figure 18 Feeder loss for base case

1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)

Time in 15-minute interval

Figure 19 Phase voltage profile of Phase-A

1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200


Figure 20 Phase voltage profile of Phase-B

0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number010203040

100806040200

0965

(48310962)


Figure 21 Phase voltage profile of Phase-C


Base casePQ at 099 lead pfPQ at 095 lead pf

PQ at unity pfPQ at 095 lag pf

20 30 40 50 60 70 9010 80Time in 15-minute interval

minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824

Figure 22 DG impact of substation reserve capacity index

FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)

Figure 23 DG impact of feeder loss to load ratio for Phase-A

X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568



80 9040 50 60 7020 3010Time in 15-minute interval

minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)

Figure 24 DG impact of feeder loss to load ratio for Phase-B

location and size of fixed PQ DG integration to a modifiedunbalance IEEE 37 feeder In this paper impact of DGintegration on performance indices has been demonstratedunder at different power factor under stochastic environ-ment To investigate clear effect of DG operation for making

FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425

Figure 25 DG impact of feeder loss to load ratio for Phase-C

BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112

Figure 26 DG impact on branch loading index of Phase-A

BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628

Figure 27 DG impact on branch loading index of Phase-B

useful decision support voltage regulator of the above feederis removed Comparative results obtained with different fixedPQ DG operating scenario are discussed and it is found thatthe results obtained by DG operation at 095 power factorleading are more suitable to improve performance of feeder





X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)

Figure 28 DG impact on branch loading index of Phase-C



160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)

Figure 29 DG impact on apparent powers unbalance index of feeder




VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)

Figure 30 DG impact on maximum voltage deviation Phase-A




02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)

Figure 31 DG impact on maximum voltage deviation Phase-B





X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)

Figure 32 DG impact on maximum voltage deviation Phase-C




MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1

Figure 33 DG impact on minimum power factor of Phase-A

X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)

Figure 34 DG impact on minimum power factor of Phase-B




X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)

Figure 35 DG impact of minimum power factor of Phase-C





Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09

Figure 36 DG impact of voltage unbalance factor of feeder

Appendix

A Survivability Index of Top 15 Nodes

(see Table 1)

B ZIP Load Compositions Calculation

To find ZIP load composition at each bus 119896 the followingequations were utilized to compute ZIP load composition ateach bus 119896 for each ℎ characteristics time interval

1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896

119886119887119888(ℎ) Total real and reactive power

load at bus 119896 during ℎ119881119873119886119887119888 119881

119896

119886119887119888(ℎ) Nominal and three-phase

voltage at 119896 node

1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896

119886119887119888(ℎ) ZIP active load composition

at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896

119886119887119888(ℎ) ZIP reactive load

composition at bus 119896 duringℎ

119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896

119886119887119888(ℎ) Active power for industrial

residential and commercialload connected at bus 119896during ℎ

119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896

119886119887119888(ℎ) Reactive power for

industrial residential andcommercial load connectedat bus 119896 during ℎ

ℎ 15-minute characteristicstime interval

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Barin C U Brazil L Martins and E S A Brazil ldquoFuzzybased expert system for renewable energy managementrdquo inProceedings of the CIREDWorkshop no 0020 Rome Italy 2014

[2] N Hashmi and S A Khan ldquoPower energy management fora grid-connected PV system using rule-base fuzzy logicrdquo inProceedings of the 3rd International Conference on ArtificialIntelligence Modelling amp Simulation (AIMS rsquo15) pp 31ndash36 KotaKinabalu Malaysia December 2015

[3] A R Kashfi and M E El-Hawary ldquoIntegration of distributedgeneration inmedium voltage distribution network using fuzzylogic controller for demand side managementrdquo in Proceedingsof the Electrical Power and Energy Conference (EPEC rsquo14) pp254ndash259 Calgary Canada November 2014

[4] S K Injeti and N P Kumar ldquoPlanning and operation of activeradial distribution networks for improved voltage stability andloss reductionrdquoWorld Journal of Modelling and Simulation vol8 no 3 pp 211ndash222 2012


[5] Y Manjili and A Rajaee ldquoFuzzy Control of Electricity StorageUnit for EnergyManagement of Micro-Gridsrdquo httpacewaco-ngorgAssetsdocFuzzy20Control20of20Electricity20Storage20Unit20for20Energy20Management20of20Micro-Grids Mexico20WAC202012pdf

[6] A Metia and S Ghosh ldquoFuzzy based DG allocation for LossMinimization in a Radial Distribution Systemrdquo Balkan Journalof Electrical amp Computer Engineering vol 3 no 3 pp 115ndash1232015

[7] E A Mohamed M M Othman and Y G Hegazy ldquoOpti-mal sizing and placement of distributed generators for profitmaximization using firefly algorithmrdquo in Proceedings of theInternational Conference on Artificial Intelligence Energy andManufacturing Engineering (ICAEME rsquo14) pp 6ndash10 2014

[8] K Muthukumar and S Jayalalitha ldquoOptimal reactive powercompensation by shunt capacitor sizing using harmony searchalgorithm in unbalanced radial distribution system for powerloss minimizationrdquo International Journal on Electrical Engineer-ing and Informatics vol 5 no 4 pp 474ndash491 2013

[9] M Padma Lalitha V C Veera Reddy and N Sivarami ReddyldquoApplication of fuzzy and ABC algorithm for DG placement forminimum loss in radial distribution systemrdquo Iranian Journal ofElectrical and Electronic Engineering vol 6 no 4 pp 248ndash2572010

[10] M S Thomas R Ranjan and R Roma ldquoProbabilistic fuzzyapproach to assess RDS vulnerability and plan corrective actionusing feeder reconfigurationrdquo Energy and Power Engineeringvol 4 no 5 pp 330ndash338 2012

[11] P N Si and S S Win ldquoFuzzy algorithm for capacitor allocationand sizing in radial distribution system to reduce lossesrdquoInternational Journal of Science Engineering and TechnologyResearch vol 3 no 12 2014

[12] A Arabali M Ghofrani M Etezadi-Amoli and M S FadalildquoStochastic performance assessment and sizing for a hybridpower system of SolarWindEnergy Storagerdquo IEEE Transac-tions on Sustainable Energy vol 5 no 2 pp 363ndash371 2014

[13] A Soroudi and M Ehsan ldquoA possibilistic-probabilistic tool forevaluating the impact of stochastic renewable and controllablepower generation on energy losses in distribution networksmdashacase studyrdquo Renewable and Sustainable Energy Reviews vol 15no 1 pp 794ndash800 2011

[14] J P Sharma and H Ravishankar Kamath ldquoStochastic voltageassessment of unbalance radial feederrdquo Journal of ElectricalSystems vol 11 no 3 pp 258ndash270 2015

[15] J P Sharma and H R Kamath ldquoPerformance analysis ofunbalance radial feeder with time varying composite loadrdquoJournal of Power and Energy Engineering vol 3 no 5 pp 56ndash702015

[16] The MathWorks Inc Types of Fuzzy Interefernece Systems TheMathWorks Inc 1994 1994ndash2014 httpwwwmathworkscomhelpfuzzytypes-of-fuzzyinference-systemshtml

[17] J-H Teng ldquoModelling distributed generations in three-phasedistribution load flowrdquo IET Generation Transmission and Dis-tribution vol 2 no 3 pp 330ndash340 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



demand and avoid power outage in peak hour two fuzzy logiccontroller are simulated for optimal location and sizing ofdistributed generation on IEEE 13 test feeder [3]

A fuzzy logic method is deployed for optimal DGplacement subjected to minimize total power loss constraintwhereas a new analytical method is used for DG sizing Theeffectiveness of DG on system voltage profile and branchpower losses is carried out on IEEE 69 and IEEE 33 radialfeeder [4] Manjili and Rajaee proposed fuzzy controllerfor energy management and cost reduction microgrid Theamount of power exchange from storage unit is based on theload demand renewable generation rate and electricity price[5]

Metia and Ghosh presented optimal location of DGunits with a 33-bus system based on the available amountof DG using fuzzy logic [6] A firefly based algorithm foroptimal location and capacity of CHP technology DG or aphotovoltaic DG is implemented on IEEE 37-node feederwith the objectives of profit maximization [7] Harmonysearch algorithm is utilized to determine appropriate size ofshunt capacitors with real power losses and installation costof shunt capacitors whereas the location of shunt capacitorsis identified using voltage stability index [8] Padma Lalithaet al presented a fuzzy approach for finding optimal DGlocations and a PSO algorithm for optimal DG sizes on IEEE33 node feeder [9] A probabilistic fuzzy solution is proposedto identify vulnerable nodes for the optimal reconfigurationproblem [10] Fuzzy expert system employed for optimalcapacitor placement and sizing for 35 buses with multilevelof loads [11]

Arabali et al carried out a stochastic framework tooptimal sizing and reliability analysis for a hybrid powersystem having wind power photovoltaic (PV) and energystorage system The stochastic nature of wind solar irradia-tion and photovoltaic (PV) power and load are stochasticallymodelled using ARMA [12] Soroudi and Ehsan investigatedthe impact of an uncertain power production of distributedgenerations (DGs) on active losses of distribution feederUncertainty in wind speed and gas turbines is modelled bya Weibull probability distribution function (PDF) and fuzzyrespectively [13]

Sharma and Ravishankar Kamath have presented voltageassessment indices for modified IEEE 37 node test feederhaving time varying composite voltage sensitive load [14]Performance indices to assess feeder performance of modi-fied IEEE 37 node test feeder were developed with the help offorward-backward sweep method and two port parametersrepresentation of feeder components [15]

The objective of this paper is to integrate DG usingtwo fuzzy logic controllers One fuzzy logic controller isused to determine the sizing of DG on the basis of feederperformance parameter such as substation reserve capacityfeeder power loss to load ratio voltage unbalance andapparent power imbalance Another fuzzy logic controller isused to choose the DG location node on the basis of DGoutput survivability index andnode distance from substationare chosen as input

2 Feeder Performance Indices

The quality of power supply for modified IEEE 37 nodetest feeder is evaluated to develop performance indices andthese performance indices are substation reserve capacityvoltage unbalance factor and feeder power loss to load ratiobranch loading voltage deviation and power factor [15] Itis observed that the said substation transformer of feederis highly overloaded between 35 and 71 characteristics timeinterval which could be relived with solar PV penetration atthe feeder Modified feeder has also accounted for stochasticcharacteristics and composition of voltage sensitive loadmodels These load models are categorized into residen-tial commercial and industrial consumers Each categoryconsumers are appliances with constant power constantcurrent and constant impedance in random propositionsThe participation of real and reactive power load exponentsfor the different type categories of consumers is characterizedby the following equations [15]

119875119896119886119887119888(ℎ) = 1198621119896

119886119887119888(ℎ) + 1198622119896

119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

2

+ 1198623119896119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

119876119896119886119887119888(ℎ) = 1198631119896

119886119887119888(ℎ) + 1198632119896

119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

2

+ 1198633119896119886119887119888(ℎ) lowast1003816100381610038161003816100381610038161003816100381610038161003816

119881119896119886119887119888(ℎ)119881119873119886119887119888

1003816100381610038161003816100381610038161003816100381610038161003816

(1)

Calculation of ZIP loads compositions is shown inAppendix Tomeet smart grid implementation criterion per-formance indices are evaluated for 15 minutes characteristicstime interval for the whole day In these days distributiongeneration integration is a common practice to meet outcontinuously increased demandThe load and renewable DGgeneration probabilistic nature are considered in this study Itis observed from load flow solution that feeder is subjected tooverloading during 8AM to 6PMTherefore the fuzzy expertsystem is developed in a way that DG operated between theabove periods The photovoltaic DG system under differentpower factor scenario is considered for investigation

3 Proposed Fuzzy Expert System

The proposed fuzzy logic controller for DG integrationimplies Mamdani and Sugeno fuzzy inference system TheDG sizing is determined using Mamdani type fuzzy logiccontroller on the basis of feeder performance parametersuch as substation reserve capacity feeder power loss toload ratio voltage unbalance and apparent power imbalancewhereas Sugeno type fuzzy logic controller is used to choosethe DG location on the basis of DG output survivabilityindex and node distance from the substation The fuzzy-based expert system is tested using the MATLAB fuzzylogic tool box undermulti-rules-based decision andmultisetsconsiderations as in Figure 1


TOD

SCRI

FLLR

UPQ

VUF


Mamdani type

Distance




round

Rounding

DG sizing

DG locationfunction

Survivability Index


TOD

PowerGAP

FLLR

UPQ

VUF


PDGOUTPUT





TOD1 TOD2 TOD3 TOD4

Plot points 181

1

05

0


181






1

05

0

181





1

05

0

181

005 006 007 008 009 01004






119886119887119888) lowast 025 (2)




1

05

0

181

01 015 02 025 03005





1 775 4930 08816722 709 4930 0880713 708 5250 08899384 733 5570 0905285 734 6130 09183966 737 6770 09292167 738 7170 0933718 711 7570 09361159 741 7970 093687210 732 5570 089094811 731 5530 088071212 710 6650 092179613 735 6850 092308314 736 7930 092193415 740 7770 0937371







LowMedium


1

05

0

181

01 02 03 04 05 06 07 08 09 10



Low Medium High



1

05

00

181


PDG

OU

TPU

T

105

0minus05

minus1 TODPowerGAP

9080706050403020100

0

100

200

300

400


PGOUTPUT

Distance

Surviablityindex

FCL2rule(sugeno)

DGNodeSelection

f(u)





1

05

0




1

05

0


01 02 03 04 05 06 07 08 09 10


Low Medium High




775709708733734737738711

741732731710735736740



Distance PGOUTPUT

10009008007006005004003002001000 010002000

3000400050006000

70008000720722724726728730732

DG

Nod

eSele

ctio

n


2000


008

007

006

005

03

025

02

015

0908070605


FLLR

UPQ

VUF

80 90706050403020100

80 90706050403020100

80 90706050403020100

80 90706050403020100










80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088


Survivability index

Survivability index


50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0


732734

730728726724722720

450400350300250200150100500

DG Node

DG Node



50403020100 90807060

50403020100 90807060



5 Conclusion



Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










TOD

SCRI

FLLR

UPQ

VUF


Mamdani type

Distance




round

Rounding

DG sizing

DG locationfunction

Survivability Index


TOD

PowerGAP

FLLR

UPQ

VUF


PDGOUTPUT





TOD1 TOD2 TOD3 TOD4

Plot points 181

1

05

0


181






1

05

0

181





1

05

0

181

005 006 007 008 009 01004






119886119887119888) lowast 025 (2)




1

05

0

181

01 015 02 025 03005





1 775 4930 08816722 709 4930 0880713 708 5250 08899384 733 5570 0905285 734 6130 09183966 737 6770 09292167 738 7170 0933718 711 7570 09361159 741 7970 093687210 732 5570 089094811 731 5530 088071212 710 6650 092179613 735 6850 092308314 736 7930 092193415 740 7770 0937371







LowMedium


1

05

0

181

01 02 03 04 05 06 07 08 09 10



Low Medium High



1

05

00

181


PDG

OU

TPU

T

105

0minus05

minus1 TODPowerGAP

9080706050403020100

0

100

200

300

400


PGOUTPUT

Distance

Surviablityindex

FCL2rule(sugeno)

DGNodeSelection

f(u)





1

05

0




1

05

0


01 02 03 04 05 06 07 08 09 10


Low Medium High




775709708733734737738711

741732731710735736740



Distance PGOUTPUT

10009008007006005004003002001000 010002000

3000400050006000

70008000720722724726728730732

DG

Nod

eSele

ctio

n


2000


008

007

006

005

03

025

02

015

0908070605


FLLR

UPQ

VUF

80 90706050403020100

80 90706050403020100

80 90706050403020100

80 90706050403020100










80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088


Survivability index

Survivability index


50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0


732734

730728726724722720

450400350300250200150100500

DG Node

DG Node



50403020100 90807060

50403020100 90807060



5 Conclusion



Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1

05

0

181





1

05

0

181

005 006 007 008 009 01004






119886119887119888) lowast 025 (2)




1

05

0

181

01 015 02 025 03005





1 775 4930 08816722 709 4930 0880713 708 5250 08899384 733 5570 0905285 734 6130 09183966 737 6770 09292167 738 7170 0933718 711 7570 09361159 741 7970 093687210 732 5570 089094811 731 5530 088071212 710 6650 092179613 735 6850 092308314 736 7930 092193415 740 7770 0937371







LowMedium


1

05

0

181

01 02 03 04 05 06 07 08 09 10



Low Medium High



1

05

00

181


PDG

OU

TPU

T

105

0minus05

minus1 TODPowerGAP

9080706050403020100

0

100

200

300

400


PGOUTPUT

Distance

Surviablityindex

FCL2rule(sugeno)

DGNodeSelection

f(u)





1

05

0




1

05

0


01 02 03 04 05 06 07 08 09 10


Low Medium High




775709708733734737738711

741732731710735736740



Distance PGOUTPUT

10009008007006005004003002001000 010002000

3000400050006000

70008000720722724726728730732

DG

Nod

eSele

ctio

n


2000


008

007

006

005

03

025

02

015

0908070605


FLLR

UPQ

VUF

80 90706050403020100

80 90706050403020100

80 90706050403020100

80 90706050403020100










80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088


Survivability index

Survivability index


50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0


732734

730728726724722720

450400350300250200150100500

DG Node

DG Node



50403020100 90807060

50403020100 90807060



5 Conclusion



Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










LowMedium


1

05

0

181

01 02 03 04 05 06 07 08 09 10



Low Medium High



1

05

00

181


PDG

OU

TPU

T

105

0minus05

minus1 TODPowerGAP

9080706050403020100

0

100

200

300

400


PGOUTPUT

Distance

Surviablityindex

FCL2rule(sugeno)

DGNodeSelection

f(u)





1

05

0




1

05

0


01 02 03 04 05 06 07 08 09 10


Low Medium High




775709708733734737738711

741732731710735736740



Distance PGOUTPUT

10009008007006005004003002001000 010002000

3000400050006000

70008000720722724726728730732

DG

Nod

eSele

ctio

n


2000


008

007

006

005

03

025

02

015

0908070605


FLLR

UPQ

VUF

80 90706050403020100

80 90706050403020100

80 90706050403020100

80 90706050403020100










80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088


Survivability index

Survivability index


50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0


732734

730728726724722720

450400350300250200150100500

DG Node

DG Node



50403020100 90807060

50403020100 90807060



5 Conclusion



Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Distance PGOUTPUT

10009008007006005004003002001000 010002000

3000400050006000

70008000720722724726728730732

DG

Nod

eSele

ctio

n


2000


008

007

006

005

03

025

02

015

0908070605


FLLR

UPQ

VUF

80 90706050403020100

80 90706050403020100

80 90706050403020100

80 90706050403020100










80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088


Survivability index

Survivability index


50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0


732734

730728726724722720

450400350300250200150100500

DG Node

DG Node



50403020100 90807060

50403020100 90807060



5 Conclusion



Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










80007000600050004000300020001000

500

Distance

Distance

09409309209109

089088


Survivability index

Survivability index


50403020100 90807060

50403020100 90807060

50403020100 90807060

400300200100

0


732734

730728726724722720

450400350300250200150100500

DG Node

DG Node



50403020100 90807060

50403020100 90807060



5 Conclusion



Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tota

l fee

der l

oss (

KW)

253035404550556065


X 6Y 2522

X 52Y 5946


1

098

096

094

1

099

098

097

096

095

Phas

e vol

tage

pro

file

Node number0

102030

40100806040200

(483409452)



1

099

098

097

096

095

0995

099

0985

098

0975

097

(56330966)

Phas

e vol

tage

pro

file

Node number010203040 100806040200



0995

099

0985

098

0975

097

1

099

098

097

096

095

Phas

e vol

tage

pro

file


100806040200

0965

(48310962)







minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













minus02

0

02

04

06

08

SRCI

(PU

)

X 35X 35

X 35X 35

Y 0546Y 04836

Y 04282Y 02816

X 73X 73

X 73

X 73

Y 05441Y 04819Y 04268Y 02824


FLLR

-Pha

se-A

(PU

)

minus002minus001

0001002003004005006007008




X 35

X 35

X 46

Y 007636

Y 004391

Y 002575

(720077)


X 35

X 35

Y 01209 Y 0124

Y 00771

Y 004061

X 73

X 71

X 56

Y 007568




minus0020

002004006008

01012014

FLLR

-Pha

se-B

(PU

)



FLLR

-Pha

se-C

(PU

)

001

0015

002

0025




X 35Y 002184

X 34Y 001736 X 56

Y 001862

X 73Y 002224

X 74Y 001754

X 70Y 001425


BCLI

-Pha

se-A

(PU

)



(3507117)

(3508666)(531173)

X 35Y 05765

X 75Y 1105

X 73Y 05746


040506070809

11112


BCLI

-Pha

se-B

(PU

)




040506070809

111

X 34Y 08137

X 35Y 06739X 35Y 05325X 35

Y 04917X 35Y 04641

X 75Y 08246

X 73Y 0678

X 73Y 05316 X 73

Y 04906X 73Y 04628







X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













X 34Y 1045

X 35Y 04945

X 74Y 1057

X 70Y 06878

X 71Y 04907

(55115)

040506070809

11112

BCLI

minusPha

seminusC

(PU

)




160180200220240260280300

Unb

alan

ce fe

eder

pow

er(K

VA)


X 6Y 1768

X 82Y 2656

X 82Y 2391

(422813)





VD

I-Ph

ase-

A (P

U)

03040506070809

111

X 34Y 09884

X 35Y 04341

X 35Y 02874

X 73Y 04457X 73Y 02871

(551084)





02

03

04

05

06

07

VD

I-Ph

ase-

B (P

U)

X 34Y 06145

X 35Y 03889X 35Y 03379

X 35Y 03156 X 35

Y 0287

X 75Y 06252

X 73Y 03959X 73Y 03411

X 73Y 03189X 73

Y 02904

(5206797)






X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













X 34Y 06916

X 35Y 03766

X 55Y 07598 X 74

Y 0695

X 71Y 03784

02030405060708

VD

I-Ph

ase-

C (P

U)





MPF

-Pha

se-A

(PU

)

X 73Y 05634

(3509594)(340917)

(72minus09757)0

02

04

06

08

1


X 73X 73X 73




X 35Y 0779X 35

Y 0779X 35Y 06893

X 35Y 03432

X 73Y 07722X 73Y 07344X 73

Y 06813

X 73Y 0327302

03040506070809

1

MPF

-Pha

se-B

(PU

)





X 34Y 08142

X 35Y 06906

X 35Y 04764

X 35Y minus01302

X 74Y 08142

X 73Y 0692

X 73Y 04777

X 73Y minus01228

(5507574)

minus02

002040608

1

MPF

-Pha

se-C

(PU

)






Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Volta

ge U

nbal

ance

fact

or (

)

X 55Y 08497

X 48Y 06419

X 35Y 05578

X 55Y 06498

X 73Y 05576(605177)

05055

06065

07075

08085

09


Appendix


(see Table 1)



1198621119896119886119887119888(ℎ) = 08 lowast 119875119868119896

119886119887119888(ℎ) + 06 lowast 119875119862119896

119886119887119888(ℎ) + 08

lowast 119875119877119896119886119887119888(ℎ)

1198622119896119886119887119888(ℎ) = 02 lowast 119875119868119896

119886119887119888(ℎ) + 04 lowast 119875119862119896

119886119887119888(ℎ) + 019

lowast 119875119877119896119886119887119888(ℎ)

1198623119896119886119887119888(ℎ) = 0 lowast 119875119868119896

119886119887119888(ℎ) + 0 lowast 119875119862119896

119886119887119888(ℎ) + 001

lowast 119875119877119896119886119887119888(ℎ)

1198631119896119886119887119888(ℎ) = 08 lowast 119876119868119896

119886119887119888(ℎ) + 06 lowast 119876119862119896

119886119887119888(ℎ) + 08

lowast 119876119877119896119886119887119888(ℎ)

1198632119896119886119887119888(ℎ) = 02 lowast 119876119868119896

119886119887119888(ℎ) + 04 lowast 119876119862119896

119886119887119888(ℎ) + 019

lowast 119876119877119896119886119887119888(ℎ)

1198633119896119886119887119888(ℎ) = 0 lowast 119876119868119896

119886119887119888(ℎ) + 0 lowast 119876119862119896

119886119887119888(ℎ) + 001

lowast 119876119877119896119886119887119888(ℎ)

(B1)

Nomenclature

119875119896119886119887119888(ℎ) 119876119896



119896



1198621119896119886119887119888(ℎ) 1198622119896

119886119887119888(ℎ) 1198623119896


at bus 119896 during ℎ1198631119896119886119887119888(ℎ)1198632119896

119886119887119888(ℎ)1198633119896



119875119868119896119886119887119888(ℎ) 119875119877119896

119886119887119888(ℎ) 119875119862119896



119876119868119896119886119887119888(ℎ) 119876119877119896

119886119887119888(ℎ) 119876119862119896




Competing Interests


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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