OnlineIdentificationofDistributionLineParametersby …downloads.hindawi.com/journals/jece/2018/8719670.pdf · 2019-07-30 · for developing any asymmetrical analysis. e positive se-quenceequivalentπ-modelisshowninFigure1(b)

Research ArticleOnline Identification of Distribution Line Parameters byPMUs under Accuracy Positive Sequence andNoise Considerations

Mustafa M Al Khabbaz 1 and Mohamed A Abido 2

1Facilities Planning Department Saudi Arabian Oil Company (Saudi Aramco) Dhahran 31311 Saudi Arabia2Electrical Engineering Department King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia

Correspondence should be addressed to Mustafa M Al Khabbaz am1hotmailcom

Received 19 August 2018 Revised 27 October 2018 Accepted 15 November 2018 Published 20 December 2018

Academic Editor Salvatore Favuzza

Copyright copy 2018 Mustafa M Al Khabbaz and Mohamed A Abido is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

is paper proposes an inaccuracy mitigation measure to reduce the error associated with distribution line parameters identificationAdditionally it introduces the concept of positive sequence quantities for determining the line resistance reactive inductance andshunt admittancee positive sequence-based analysis is required for asymmetrical related studies such as unbalanced fault analysise paper also includes the consideration of noisy distribution networks It compares the performance of three line parametersidentification techniques by using different statistical measures A total of 12960 different case studies are simulated and analyzedunder six main loading scenarios and four categories with changing line parameters e line parameters are calculated online usingvoltage and current signals obtained from phasor measurement units (PMUs) placed at the line two terminals Finally the studyoutcomes and the associated recommendations have been summarized for future works considerations

1 Introduction

Distribution line (DL) parameters identification forms thebasis for distribution power system studies including dy-namic and transient stabilities state estimate protectionsetting etc e common practice in the industry till todayis to determine the parameters using values from designdatasheets manufacture specification sheets and engineerestimation e latter could base the calculation on con-ductor dimensions sag temperature tower geometries andother elements ese elements are used to identify the DLdata through different mechanisms such as calculating thegeometric mean radius and the geometric mean distancedenoted by GMR and GMD respectively Additionally theofficial electrical transient analysis program (known asETAP) model could be utilized to find the DL data which isan off-line tool Assumptions and approximations are in-cluded in the calculation process steps which reduce theaccuracy of results Basing DL parameter estimation on off-line techniques or preidentified information significantly

impacts the accuracy level of the power system studies thatdepend on these values due to the following

(1) Conductor resistance and reactance vary with ambientconditions conductor situation and power flow

(2) A number of installed circuits are spliced with otherconductors that are different in types and specifi-cations is represents an inhomogeneity of the linesections

(3) e overhead conductor arrangement changes dueto using different tower configurations and applyingthe concept of transposition

(4) Cable installation conditions such as groupingunderground overhead cable trays conduits andsubmarine etc play a major role in line parameterestimation

(5) Cable aging could impact the line parameters due toseveral factors such as degradation tension and lifecycle

HindawiJournal of Electrical and Computer EngineeringVolume 2018 Article ID 8719670 12 pageshttpsdoiorg10115520188719670

e above five factors are sources of conductor im-pedance and admittance identification errors With theemergence of PMU technology it is possible to obtain moreaccurate data about the system conditions with high-frequency samples along with the corresponding timestamp Accordingly it is possible to develop more accurateDL impedance parameters estimation by online measure-ment techniques using the synchronized PMUs is onlineanalysis can be used to improve power system operationsreliability as detailed below

(a) Power system restoration and reclosing phasor datais used to bring equipment back into service avoidingthe risk of instability or unsuccessful reclosing trials

(b) Automated management of voltage and frequencyresponse the data is used for better system man-agement to frequency and voltage changes

(c) Wide-area protection real-time phasor data allowsfor improved grid events identification and execu-tion of appropriate system protection measures

(d) Planned power system islanding this is to improveislanding of power system during instability situations

(e) Power plant monitoring and integration real-timedata is used for better integration of different powerplants that includes intermittent renewables ordistributed power sources

e majority of research works to estimate the powersystem line parameters are focused on transmission systemsNumerous techniques have been introduced to calculate thetransmission parameters using the synchronized measure-ment devices A two-port ABCD parameter identificationbased technique was introduced in [1] is method utilizedtwo sets of three samples of sending and receiving terminalsrsquovoltage and current signals is was to find three estimates ofABCD parameters e ABCD method is referred to in thisresearch work as a ldquotwo-port circuit measurement techniquerdquoIn Reference [2] fourmethods were discussed to identify shorttransmission line parameters by synchronized measurementsReference [3] proposed a novel method to identify trans-mission line parameters for different cases including short andlong transposed and untransposed lines with balanced andunbalanced load conditions e positive sequence line pa-rameters considering the effects of the line shunt capacitancewere estimated in [4] employing a two-terminal transmissionline model Likewise Reference [5] aimed to achieve the sameobjectives where a new estimation method was presentedusing synchronized phasor measurements at both line endse approach in [6] proposes the use of recursive parameterestimation to find the network branch parameters online andoff-line e least-square technique was leveraged in [7] withthe objective of obtaining the line parameters iteratively

Unlike the abundance of publications on transmissionline parameters estimation the work in distribution islimitede probability theory which builds on voltage droplinear equivalent model was used in [8] e approachobjective was to estimate the DL impedance and get preciseparameters Numerous works discussed the uncertaintiesof network parameters and inaccuracy of measurements

In particular the DL parameters and measurement uncer-tainties were analyzed in [9] A novel power system un-certainty analysis technique was proposed in [10] where atwo-step approach based on static weighted least-squaresanalysis was used Reference [11] presents a method toestimate distribution line parameters using only conven-tional SCADA measurements (voltage magnitude andpower measurements) It resulted in a negligible deviationbetween simulation experiment and the actual manufac-turer specifications e key outcomes of the DL parametersestimation studies were that the accuracy of line parametersis crucial for a number of applications including the gridcontrol stability analysis and fault location studies

To the best of the authorsrsquo knowledge the applicability ofdifferent methods to identify the sequence DL parameters hasnot been considered before is paper proposes the use ofPMU to identify the DL parameters under the consideration ofaccuracy positive sequence and noise e concept of sym-metrical components is leveraged to extract the positive se-quence of the synchronized phasor voltage and currentmeasurement signalse online synchronized signals obtainedfrom the PMUs will be used in calculating both the phase andpositive sequenceDL parameters In Section 2 three techniqueshave been developed to measure DL resistance reactive in-ductance and shunt admittance Section 3 describes the usedaccuracy statistical measures to evaluate and compare theperformance of the three techniques e developed casestudies along with their results and discussion are presented inSections 4 and 5 respectively Finally the study recommen-dations and outcomes are stipulated in Section 6emain dataused to support the findings of this study are included withinthis article If additional data is required it could be requestedfrom the corresponding author with proper justification

2 Techniques of Distribution LineParameters Estimation

ree different techniques are discussed in this section withthe objectives of identifying the DL parameters e tech-niques leverage the PMU voltage and current signals ob-tained at the two terminals of the line In order to performDL parameters estimation the line is represented in aπ-model equivalent circuit as illustrated in Figure 1(a)

e study considers the positive sequence of the voltageand current phasors in addition to the phase valuesis aimsto explore accuracy enhancement opportunities and comparethe results Additionally the sequence quantities are requiredfor developing any asymmetrical analysis e positive se-quence equivalent π-model is shown in Figure 1(b)

21Ohmrsquos FormulaTechnique e proposed ohmrsquos formulatechnique (OFT) depends on the ohmrsquos law [12] Under thismethod both phase and positive sequence voltage andcurrent phasors are used is method requires only singleset of voltage and current samples of the phasor voltage andcurrent signals produced by PMUs

e developed OFT equations to calculate the DL pa-rameters are described below

2 Journal of Electrical and Computer Engineering

ZDL1 2 VS1 minusVR1( 1113857

IR1 + IS1

YDL1 IS1 minus IR1

VS1

(1)

22 Single Measurement Technique e proposed singlemeasurement technique (SMT) aims to find DL resistancereactive inductance and shunt admittance [12] It uses boththe phase and positive sequence of the voltage and currentsignals that are obtained from PMUs at the steady state eSMT equations are formulated as follows

ZDL1 V2

S1 minusV2R1

VR1IS1 + VS1IR1

YDL1 2 VS1 minusVR1( 1113857

IR1 + IS1

(2)

23 Two-Port CircuitMeasurement Technique e two-portcircuit measurement technique (TPCMT) requires two setsof synchronized measurement samples at different loadingconditions [12] e samples are taken from the DL ter-minals to calculate the two-port circuit parameter known asA B C and D e DL impedance and admittance areidentified from the ABCD matrix

e TPCMT is conventionally used to represent trans-mission lines Additionally it provides adequate accuracyfor DLs at some cases Representation of positive sequenceTPCMT for DL is shown in Figure 2 where VS1 VR1 IR1and IS1 are the positive sequence of the sending and re-ceiving ends voltage and current signals respectively

e following equations form the relation between thesending end and the receiving end quantities

VS1 A VR1 + B IR1

IS1 C VR1 + D IR1(3)

where the parameters A B C and D are influenced by theDL resistance inductance capacitance and conductance eABDCparameters are complex numbers in whichA andD areunit less B is measured in ohms and C has a unit of Siemens

e ABCD parameters of the DL equivalent π-modelshown in Figure 1 are obtained by the following equations

VS1 VR1 + ZDL1 IR1 +VR1YDL1

21113874 1113875

1 +ZDL1YDL1

21113874 1113875VR1 + ZDL1IR1

(4)

By applying the Kirchhoff current law (known as KCL) atthe sending end the following equation is obtained

IS1 IR1 +YDL1 VR1 + VS1( 1113857

2 (5)

Combining the previous two equations yields

IS1 IR1 +YDL1VR1

2+ 1 +

ZDL1YDL1

21113874 1113875VR1 + ZDL1IR11113890 1113891

YDL1

2

YDL1 1 +ZDL1YDL1

41113874 1113875VR1 + 1 +

ZDL1YDL1

21113874 1113875IR1

(6)

ZS

YDL2

ZDL ZR

VS VR

Sending (S) Receiving (R)

YDL2

Utility

IS IR

(a)

ZS1

YDL12

ZDL1 ZR1

VS1 VR1


YDL12

Utility

IS1 IR1

(b)

Figure 1 Distribution line equivalent model (π-Type) (a) One-line diagram using the phasor quantities (b) One-line diagram using thepositive sequence quantities e parameters of the above circuits are described as follows ZS equivalent impedance at the source side ZS1positive sequence equivalent impedance at the source side ZR equivalent impedance at the receiving end ZR1 ppositive sequenceequivalent impedance at the receiving end ZDL distribution line impedance ZDL1 positive sequence distribution line impedance YDLdistribution line admittance YDL1 positive sequence distribution line admittance VS phase voltages at sending end VS1 positive sequencephase voltages at sending end VR phase voltages at receiving end VR1 positive sequence phase voltages at receiving end IS Phase current atsending end IS1 positive sequence phase current at sending end IR phase current at receiving end IR1 positive sequence phase current atreceiving end

Two-portcircuit

IS1 IR1

+VS1ndash

+VR1ndash

Figure 2 Representation of positive sequence two-port circuit fordistribution line

Journal of Electrical and Computer Engineering 3

Comparing the last above formula with the ABCDequations yields

A D

1 +ZDL1YDL1

21113874 1113875 per unit

C YDL1 1 +ZDL1YDL1

41113874 1113875 ohm

(7)

From the simple DL (only series impedance represen-tation) analysis and derivation B is obtained to be

B ZDL1 ohm (8)

e above A B C and D equations are solved to findZDL1 and YDL1 which will be as follows

ZDL1 B ohm

YDL1 2(Aminus 1)

BSiemens

(9)

ismethod could be extended to accommodate two setsof PMUmeasurements e two sets could be obtained fromtwo different redundant PMUs or from two readingsrecorded at different timing or loading conditions eABCD equations for the two sets are as follows

VS1prime A VR1prime + B IR1prime

IS1prime C VR1prime + D IR1prime

VPrimeS1 A VPrimeR1 + B IPrimeR1

IPrimeS1 C VPrimeR1 + D IPrimeR1

(10)

e samples of the voltages and currents for the receivingand sending ends are as the following

(i) VS1prime VR1prime IS1prime and IR1prime are for the first set(ii) VPrimeS1 VPrimeR1 IPrimeS1 and IPrimeR1 are for the second set

e ABCD parameters are calculated to account for thetwo sets to be as follows

A IR1prime VPrimeS1 minus IPrimeR1 VS1prime

IR1prime VPrimeR1 minus IPrimeR1VR1prime

B VPrimeR1 VS1prime minus VR1prime VPrimeS1


C IR1prime IPrimeS1 minus IPrimeR1IS1prime


D IS1prime VPrimeR1 minus IPrimeS1 VR1prime


(11)

3 Accuracy Statistical Measures

e accuracy of the proposed methods is evaluated usingdifferent statistical measures is is to ensure that the mea-sures will converge for all case studies analyzed in this paper

at is in case one statistical measure fails to perform in one ofthe cases the evaluation will be achieved by the othermeasures

31 Percentage Error e first step toward accepting orrejecting the proposed methods is assessing its accuracyusing the percentage error given by the following equation

error() |actual valuesminus calculated value|

actual valuetimes 100 (12)

32 Coefficient of Determination e coefficient of de-termination (CoD) denoted by R2 is used to indicate thedifference of the obtained values by a proposed formulacompared to the actual ones It measures the strength of theproposed formula and benchmarks it with the ideal situationwhich will result in a coefficient of determination of 100 Itis also called the squared error which is the error between thecurve obtained by the proposed formula and the actual curvee range of coefficient of determination varies between 0 and1 e higher the number means the proposed formula ismore descriptive and reflective to the actual values Figure 3 isan explanatory sketch for calculating the CoD

e coefficient of determination equation is formulatedas follows

CoD 1minus1113936

k1 ycalc minusyact( 1113857

2

1113936k1 ycalc minusyact( 1113857

2

1minusSETV

SE 1113944k

1ycalc minusyact( 1113857

2

TV 1113944k


2

(13)

e parameters are described as follows CoD coefficientof determination SE total square error between the calcu-lated points and the actual values TV total variation betweenthe calculated points and the actual values yact mean of theactual values ycalc calculated value and yact actual value

33 Other Accuracy Statistical Measures Other accuracystatistical measures are required to be integrated with thepercentage error and CoD is is due to the fact that thepercentage error does not represent the correlation and the CoDhas certain shortfalls especially for small scientific numbers

e following additional statistical measures are used toevaluate the proposals presented in this paper

(1) Mean absolute deviation (MAD) which is thesummation of the absolute deviation between theactual and calculated values over the number ofrecords (or the length of the range)

(2) Mean square error (MSE) which is considered asthe most common error metric It is mainly thesummation of the squared errors over the number ofrecords


(3) Root mean square error (RMSE) is obtained byapplying the square root to the MSE

(4) Mean absolute percentage error (MAPE) is the av-erage of absolute errors over the actual records

4 Case Studies

A 25-kV distribution system (refer to Figure 4) is modeled inMATLABSimulink to verify the effectiveness of the threeline parameters identification techniques A total of 12960different case studies have been performed under six mainloading scenarios (stated in Table 1) and four categories(presented in Table 2) with changing of the line parameterse line parameters have been varied in 60 stepse loadingscenarios and categories considered under this study aretabulated in below tables

e large number of case studies has been developed totest the robustness and accuracy of this paper proposals e12960 simulations differ in the loading conditions linelengths noise and inaccuracy mitigations

e selected DL is modeled as three-phase DL with aπ-type e model consists of one set of resistance andinductance elements in series connected between sendingand receiving terminals Two sets of shunt capacitanceslumped are also included at both ends as illustrated inFigure 1 e initial DL parameters are stated in Table 3

e total series resistance reactive inductance and shuntadmittance are given by the following formulas respectively

R rℓ

XDL1 ωLℓ

YDL ωCℓ

(14)

where R L and C are the total DL resistance inductanceand capacitance and ℓ is the total length of the line

In MATLAB two sets of simulated PMUs are placed atboth terminals of the selected DL to measure the voltagesand currents waveforms simultaneously e recordedwaveforms are in the shape of sinusoidal signals and thenconverted into phasor equivalents

5 Results and Discussions

e simulation results of the 12960 cases are summarized inthis section and organized into four categories Under eachcategory the resistance reactive inductance and shuntadmittance are calculated using the three methods for

different loading conditions and parameter values ecalculation is based on the voltage and current signals ob-tained from PMUs that are installed at both ends of the lineFigure 5 shows the voltage and current signals obtained fromPMU devices considering noise-free system

51 Phase Quantities In this category the phase quantitiesof voltage and current are used to perform the analysis istype of analysis is required for asymmetrical related studiessuch as unbalanced fault analysis

DL under studyBus 1 Bus 2 Bus 3 Bus 4 Bus 5

Bus 6 Bus 7 Bus 8

Bus 9 Bus 10

Bus 11 Bus 12 Bus 13 Bus 14

Load 6

Load 10

Load 11 Load 12 Load 13

120 kVUtility

Main powertransformer

120 kV25 kV

Load 14

Load 8

Figure 4 e 25 kV 14-bus test distribution network underconsideration

(x1 y1_calc)

(x1 y1_act)Y-

axis

X-axis

Figure 3 Coefficient of determination explanatory sketch

Table 1 e six loading scenarios for simulations

ScenarioLoad

Active (MW) Reactive (MVar)1 1 0252 2 053 3 0754 4 15 5 1256 6 15

Table 2 e four categories for this study

Category Description1 Phase quantities2 Positive sequence quantities3 Phase quantities with noise

4 Phase quantities with the proposed inaccuracymitigation for noisy systems in category 3

Table 3 Initial parameters of the distribution line test circuits

Parameter Actual value Dimensionr 01153 (Ohmskm)l 105e-3 (Hkm)c 1133e-009 (Fkm)where r l and c are the resistance inductance and capacitance per unitlength respectively


e values of resistance reactive inductance and shuntadmittance are changing in 60 steps e parametersidentification errors of the six loading scenarios are averagedfor the three methods e voltage and current waveformsare assumed to be noise-free Results of the average errors forthe resistance reactive inductance and shunt admittance areshown in Figure 6emaximum errors for eachmethod arestated in Table 4 e results reveal that SMT is more ef-fective in calculating the DL parameters

e TPCMT shows weakness in calculating the shuntadmittance for short lines is is expected as the methodwas developed specifically for medium transmission linesHowever it performs very well when the DL length isranging between 10 and 30 km which is a common sort ofDLs

52 Positive Sequence Quantities Both OFT and SMT haveexcellent performance in identifying the DL parametersusing positive sequence quantities e average and maxi-mum errors recorded in the simulated studies are presented

in Figure 7 and Table 4 separately It is observed form theresults that TPCMT fails to calculate the line parametersusing positive sequence voltage and current quantitieserefore the results were excluded from Figure 7 eresults demonstrate that SMT is superior to OFT in calcu-lating the line parameters using positive sequence quantities

53 PhaseQuantities withNoise Actual voltage and currentsignals of any distribution system are not pure sinusoidalNoise is always impeded in the signals due to severalfactors eg harmonics produced from electronic baseddevices e electronic devices could be at residential areassuch as televisions computers laptops electronic gamesand so on ere are a number of applications that produceharmonics at the industrial sector for example capacitorbank variable frequency drives and other electronic basedequipment

Accordingly all input signals to PMUs will be associ-ated with additional harmonics beside the fundamentalfrequency (60Hz) as in the Kingdome power system

Time

Am

p

0005 0015 0025 0035 0045001 002 003 0040

40

20

0

ndash20

ndash40

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

Vs 1

Vs

Vs 2Vs 3

times104

3

2

1

0

0 0005 0015 0025 0035 0045001 002 003 004

ndash1

ndash2

ndash3

(b)

Figure 5 PMU current and voltage signals with noise-free


Although PMU measurements showed an improved accu-racy compared to other devices this performance is not fullymaterialized in the actual field due to errors from otherchannels such as instrumentation CT and potentialtransformer (shortly PT) and etc

Figure 8 shows the voltage and current signals obtainedfrom PMU devices considering noisy system

e OFTand SMT have extraordinary performance whenapplying the phase values to noisy system (Figure 9) TPCMT

still shows weakness in estimating the line parameters es-pecially for short lines capacitance As the line length in-creases as TPCMT converges for identifying the XC

e maximum error recorded in the simulated studiesis shown in Table 4 From the calculated average andmaximum errors of the six loading scenarios for the threemethods considering phasor quantities it is concludedthat SMT is superior to the other techniques for noisysystem

54 Phase Quantities with Inaccuracy Mitigation for NoisySystems It is observed form the simulated case studies thatthe error follows specific trend under different line pa-rameters irrespective of the loading conditions Knowingthe error trend will ease predicting the error magnitude andhence mitigating it is category proposes to apply inac-curacy mitigation measures to improve the line parametercalculation errors e measures are developed based on linecharacteristics and possible loadings e proposed inac-curacy mitigation measure concept is illustrated in Figure 10and given by the following formula

euroy _y(1 + ε( _y)) (15)

where _y is the originally calculated value and euroy is the en-hanced measurement e symbol ε is taken from the

ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r

Actual line resistance (ohms)

OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r

Actual line reactive inductance (ohms)

OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r

Actual shunt admittance (S)

OFTSMTTPCMT

(c)

Figure 6 Calculation average errors of the six loading scenarios for the three methods under Category 1 (a) Resistance (b) Reactiveinductance (c) Shunt admittance

Table 4 Maximum errors of the six loading scenarios consideringthe variation of the line parameters

Category Method R XL XC

11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High


predeveloped inaccuracy mitigation measures demonstratedin Figure 10 e inaccuracy mitigation curve could takedifferent shapes based on line loading and characteristics

e proposed concept has been applied to Category 3and the simulation results are illustrated in Figure 11 eresults reveal significant improvements of Category 4compared to Category 3 in Figure 9

e inaccuracy mitigation measures will result in ac-curacy improvement up to 98 of the maximum error ofCategory 3 e maximum errors for the four categories andsix loading scenarios considering the variation of the lineparameters are tabulated in Table 4

e MAD MSE RMSE MAPE and CoD have beenapplied to the four categories and six loading scenarios eresults for the latter are averaged into one value for eachcategory and parametere results are tabulated in Table 5 toevaluate the robustness of this paper proposals It is noticedfrom the table that generally the values under the proposedinaccuracy mitigation measures category (Category 4) areimproved compared to those in Category 3 is shows thestrength of the proposed inaccuracymitigation concept whichcould be applied for ideal and noisy systems e use ofpositive sequence quantities will perform very well whenusing OFTand SMT However the phase quantities will resultin more accurate line parameters estimation Unlike OFTandSMT TPCMT does not function when using the positivesequence valueserefore ABCD should not be used for anyasymmetrical related studies in DLs

MAPE is found to be the only method applicable forcalculating the line shunt admittance since the values of thecapacitances are very small scientific numbers

6 Conclusions

To carry out any asymmetrical related analysis at DLs suchas asymmetrical fault studies the symmetrical compo-nents should be leveraged to identify the positive nega-tive and zero sequences erefore robust and accurateline parameters calculation techniques are required Basedon that three line parameters identification techniqueshave been applied to different case studies and evaluatedusing different statistical measures e outcomes of thisanalysis along with the associated recommendations are asfollows

(1) e proposed inaccuracy mitigation concept willresult in accuracy improvement up to 98 of themaximum error erefore it is recommended touse this concept for any online impedance andadmittance calculations using PMUs

(2) e inaccuracy of the line parameters estima-tion follows a specific trend over different scenariosis will allow proper inaccuracy prediction andhence mitigation

(3) e proposed inaccuracy prediction and mitigationhave resulted in a negligible deviation between

ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)

Figure 7 Calculation average errors of the six loading scenarios for the OFT and SMT techniques under Category 2 (a) Resistance (b)Reactive inductance (c) Shunt admittance


Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)

Figure 8 PMU current and voltage signals with noise

ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000

ndash800ndash600ndash400ndash200

000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)


Actual line parameter (X)

Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)

Calculated line parameter (y)

(b)

Figure 10 Indicative graphs of the proposed inaccuracy mitigationmeasure concept (a) Actual vs calculated line parameters (b) Proposedinaccuracy mitigation measure

000002004006008010012014

006

029

052

075

098

121

144

167

190

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236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



calculated and actual DL parameters is provesthe robustness of the proposals of this paper

(4) Both OFT and SMT have extraordinary perfor-mance in calculating the DL parameters usingpositive sequence quantities erefore it is rec-ommended to use them for any asymmetrical basedanalysis such as unbalanced fault studies

(5) SMT is superior to OFT in calculating the lineparameters using positive sequence quantities

(6) TPCMT does not perform when the line resistanceis small (short line) and using phase quantities isis expected as the method was developed for me-dium transmission lines As the line impedance orlength increase TPCMTwill boost up its resistancecalculation accuracy

(7) It is expected the TPCMTwill not perform very wellfor capacitance identification of short DLs ere-fore it is unrecommended to use this method forshort DLs

(8) TPCMT fails to produce result using positive se-quence voltage and current signals erefore itshould not be applied for any asymmetrical studiesat the distribution level

(9) Some statistical measures do not function undercertain conditions such as in case of small scientificfigures erefore there is a need for a wide range ofstatistical measures to ensure covering all study cases

(10) SMT is ranked to be the most robust technique foridentifying all DL parameters under differentconditions and OFTcomes the second erefore itis recommended to use SMT for any distributionrelated case studies

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] R EWilson G A Zevenbergen D L Mah and A J MurphyldquoCalculation of transmission line parameters from synchro-nized measurementsrdquo Electric Machines and Power Systemsvol 27 no 12 pp 1269ndash1278 1999

[2] D Shi D J Tylavsky N Logic and K M Koellner ldquoIden-tification of short transmission-line parameters from syn-chrophasor measurementsrdquo in Proceedings of 2008 40th NorthAmerican Power Symposium pp 1ndash8 Calgary AlbertaCanada September 2008

[3] D Shi D Tylavsky K Koellner D Wheeler and N LogicldquoTransmission line parameter identification using PMUmeasurementsrdquo European Transactions on Electrical Powervol 21 no 4 pp 1574ndash1588 2010

[4] Y Liao and M Kezunovic ldquoOnline optimal transmission lineparameter estimation for relaying applicationsrdquo IEEETransactions on Power Delivery vol 24 no 1 pp 96ndash1022009

[5] A M Dan and D Raisz ldquoEstimation of transmission lineparameters using wide-area measurement methodrdquo in Pro-ceedings of 2011 IEEE Trondheim PowerTech pp 1ndash6Trondheim Norway June 2011

[6] I W Slutsker S Mokhtari and K A Clements ldquoReal timerecursive parameter estimation in energy management sys-temsrdquo IEEE Transactions on Power Systems vol 11 no 3pp 1393ndash1399 1996

[7] Y Liao ldquoAlgorithms for fault location and line parameterestimation utilizing voltage and current data during the faultrdquoin Proceedings of 2008 40th Southeastern Symposium onSystem eory (SSST) pp 183ndash187 New Orleans LA USAMarch 2008

[8] D Jia W Sheng X Song and X Meng ldquoA systemidentification method for smart distribution gridrdquo inProceedings of 2014 International Conference on PowerSystem Technology (POWERCON) pp 14ndash19 ChengduChina October 2014

Table 5 Statistical measures results for all cases ()

Parameter Statistical measureMethod 1 Method 2 Method 3

Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance

MAD 000 000 000 000 000 000 000 000 000 000 001 004MSE 000 000 000 000 000 000 000 000 000 000 000 000RMSE 000 000 000 000 000 000 000 000 000 000 001 009MAPE 183 215 142 088 012 021 236 003 1668 000 High High

R2 Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero


[9] G DrsquoAntona and M Davoudi ldquoEffect of phasor measurementunit on power state estimation considering parameters un-certaintyrdquo in Proceedings of 2012 IEEE International Work-shop on Applied Measurements for Power Systems (AMPS)pp 1ndash5 Aachen Germany September 2012

[10] R N Mahanty and P B Dutta Gupta ldquoApplication of RBFneural network to fault classification and location in trans-mission linesrdquo IEE Proceedings-Generation Transmission andDistribution vol 151 no 2 p 201 2004

[11] A M Prostejovsky O Gehrke A M Kosek T Strasser andHW Bindner ldquoDistribution line parameter estimation underconsideration of measurement tolerancesrdquo IEEE Transactionson Industrial Informatics vol 12 no 2 pp 726ndash735 2016

[12] M M J Al-Khabbaz Fault Location in Power DistributionGrids using Phasor Measurement Units King Fahd Universityof Petroleum and Minerals Dhahran Eastern Province SaudiArabia 2018


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Electrical and Computer Engineering

Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

e above five factors are sources of conductor im-pedance and admittance identification errors With theemergence of PMU technology it is possible to obtain moreaccurate data about the system conditions with high-frequency samples along with the corresponding timestamp Accordingly it is possible to develop more accurateDL impedance parameters estimation by online measure-ment techniques using the synchronized PMUs is onlineanalysis can be used to improve power system operationsreliability as detailed below

(a) Power system restoration and reclosing phasor datais used to bring equipment back into service avoidingthe risk of instability or unsuccessful reclosing trials

(b) Automated management of voltage and frequencyresponse the data is used for better system man-agement to frequency and voltage changes

(c) Wide-area protection real-time phasor data allowsfor improved grid events identification and execu-tion of appropriate system protection measures

(d) Planned power system islanding this is to improveislanding of power system during instability situations

(e) Power plant monitoring and integration real-timedata is used for better integration of different powerplants that includes intermittent renewables ordistributed power sources

e majority of research works to estimate the powersystem line parameters are focused on transmission systemsNumerous techniques have been introduced to calculate thetransmission parameters using the synchronized measure-ment devices A two-port ABCD parameter identificationbased technique was introduced in [1] is method utilizedtwo sets of three samples of sending and receiving terminalsrsquovoltage and current signals is was to find three estimates ofABCD parameters e ABCD method is referred to in thisresearch work as a ldquotwo-port circuit measurement techniquerdquoIn Reference [2] fourmethods were discussed to identify shorttransmission line parameters by synchronized measurementsReference [3] proposed a novel method to identify trans-mission line parameters for different cases including short andlong transposed and untransposed lines with balanced andunbalanced load conditions e positive sequence line pa-rameters considering the effects of the line shunt capacitancewere estimated in [4] employing a two-terminal transmissionline model Likewise Reference [5] aimed to achieve the sameobjectives where a new estimation method was presentedusing synchronized phasor measurements at both line endse approach in [6] proposes the use of recursive parameterestimation to find the network branch parameters online andoff-line e least-square technique was leveraged in [7] withthe objective of obtaining the line parameters iteratively

Unlike the abundance of publications on transmissionline parameters estimation the work in distribution islimitede probability theory which builds on voltage droplinear equivalent model was used in [8] e approachobjective was to estimate the DL impedance and get preciseparameters Numerous works discussed the uncertaintiesof network parameters and inaccuracy of measurements

In particular the DL parameters and measurement uncer-tainties were analyzed in [9] A novel power system un-certainty analysis technique was proposed in [10] where atwo-step approach based on static weighted least-squaresanalysis was used Reference [11] presents a method toestimate distribution line parameters using only conven-tional SCADA measurements (voltage magnitude andpower measurements) It resulted in a negligible deviationbetween simulation experiment and the actual manufac-turer specifications e key outcomes of the DL parametersestimation studies were that the accuracy of line parametersis crucial for a number of applications including the gridcontrol stability analysis and fault location studies

To the best of the authorsrsquo knowledge the applicability ofdifferent methods to identify the sequence DL parameters hasnot been considered before is paper proposes the use ofPMU to identify the DL parameters under the consideration ofaccuracy positive sequence and noise e concept of sym-metrical components is leveraged to extract the positive se-quence of the synchronized phasor voltage and currentmeasurement signalse online synchronized signals obtainedfrom the PMUs will be used in calculating both the phase andpositive sequenceDL parameters In Section 2 three techniqueshave been developed to measure DL resistance reactive in-ductance and shunt admittance Section 3 describes the usedaccuracy statistical measures to evaluate and compare theperformance of the three techniques e developed casestudies along with their results and discussion are presented inSections 4 and 5 respectively Finally the study recommen-dations and outcomes are stipulated in Section 6emain dataused to support the findings of this study are included withinthis article If additional data is required it could be requestedfrom the corresponding author with proper justification

2 Techniques of Distribution LineParameters Estimation

ree different techniques are discussed in this section withthe objectives of identifying the DL parameters e tech-niques leverage the PMU voltage and current signals ob-tained at the two terminals of the line In order to performDL parameters estimation the line is represented in aπ-model equivalent circuit as illustrated in Figure 1(a)

e study considers the positive sequence of the voltageand current phasors in addition to the phase valuesis aimsto explore accuracy enhancement opportunities and comparethe results Additionally the sequence quantities are requiredfor developing any asymmetrical analysis e positive se-quence equivalent π-model is shown in Figure 1(b)

21Ohmrsquos FormulaTechnique e proposed ohmrsquos formulatechnique (OFT) depends on the ohmrsquos law [12] Under thismethod both phase and positive sequence voltage andcurrent phasors are used is method requires only singleset of voltage and current samples of the phasor voltage andcurrent signals produced by PMUs

e developed OFT equations to calculate the DL pa-rameters are described below



IR1 + IS1

YDL1 IS1 minus IR1

VS1

(1)


ZDL1 V2

S1 minusV2R1

VR1IS1 + VS1IR1


IR1 + IS1

(2)




VS1 A VR1 + B IR1





21113874 1113875

1 +ZDL1YDL1

21113874 1113875VR1 + ZDL1IR1

(4)


IS1 IR1 +YDL1 VR1 + VS1( 1113857

2 (5)


IS1 IR1 +YDL1VR1

2+ 1 +

ZDL1YDL1

21113874 1113875VR1 + ZDL1IR11113890 1113891

YDL1

2

YDL1 1 +ZDL1YDL1

41113874 1113875VR1 + 1 +

ZDL1YDL1

21113874 1113875IR1

(6)

ZS

YDL2

ZDL ZR

VS VR


YDL2

Utility

IS IR

(a)

ZS1

YDL12

ZDL1 ZR1

VS1 VR1


YDL12

Utility

IS1 IR1

(b)


Two-portcircuit

IS1 IR1

+VS1ndash

+VR1ndash




A D

1 +ZDL1YDL1

21113874 1113875 per unit

C YDL1 1 +ZDL1YDL1

41113874 1113875 ohm

(7)


B ZDL1 ohm (8)


ZDL1 B ohm

YDL1 2(Aminus 1)

BSiemens

(9)






(10)












(11)









CoD 1minus1113936


2


2

1minusSETV

SE 1113944k


2

TV 1113944k


2

(13)









4 Case Studies





R rℓ

XDL1 ωLℓ

YDL ωCℓ

(14)








Bus 6 Bus 7 Bus 8

Bus 9 Bus 10


Load 6

Load 10


120 kVUtility


120 kV25 kV

Load 14

Load 8


(x1 y1_calc)

(x1 y1_act)Y-

axis

X-axis



ScenarioLoad














Time

Am

p

0005 0015 0025 0035 0045001 002 003 0040

40

20

0

ndash20

ndash40

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

Vs 1

Vs

Vs 2Vs 3

times104

3

2

1

0

0 0005 0015 0025 0035 0045001 002 003 004

ndash1

ndash2

ndash3

(b)









euroy _y(1 + ε( _y)) (15)


ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)




11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



IR1 + IS1

YDL1 IS1 minus IR1

VS1

(1)


ZDL1 V2

S1 minusV2R1

VR1IS1 + VS1IR1


IR1 + IS1

(2)




VS1 A VR1 + B IR1





21113874 1113875

1 +ZDL1YDL1

21113874 1113875VR1 + ZDL1IR1

(4)


IS1 IR1 +YDL1 VR1 + VS1( 1113857

2 (5)


IS1 IR1 +YDL1VR1

2+ 1 +

ZDL1YDL1

21113874 1113875VR1 + ZDL1IR11113890 1113891

YDL1

2

YDL1 1 +ZDL1YDL1

41113874 1113875VR1 + 1 +

ZDL1YDL1

21113874 1113875IR1

(6)

ZS

YDL2

ZDL ZR

VS VR


YDL2

Utility

IS IR

(a)

ZS1

YDL12

ZDL1 ZR1

VS1 VR1


YDL12

Utility

IS1 IR1

(b)


Two-portcircuit

IS1 IR1

+VS1ndash

+VR1ndash




A D

1 +ZDL1YDL1

21113874 1113875 per unit

C YDL1 1 +ZDL1YDL1

41113874 1113875 ohm

(7)


B ZDL1 ohm (8)


ZDL1 B ohm

YDL1 2(Aminus 1)

BSiemens

(9)






(10)












(11)









CoD 1minus1113936


2


2

1minusSETV

SE 1113944k


2

TV 1113944k


2

(13)









4 Case Studies





R rℓ

XDL1 ωLℓ

YDL ωCℓ

(14)








Bus 6 Bus 7 Bus 8

Bus 9 Bus 10


Load 6

Load 10


120 kVUtility


120 kV25 kV

Load 14

Load 8


(x1 y1_calc)

(x1 y1_act)Y-

axis

X-axis



ScenarioLoad














Time

Am

p

0005 0015 0025 0035 0045001 002 003 0040

40

20

0

ndash20

ndash40

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

Vs 1

Vs

Vs 2Vs 3

times104

3

2

1

0

0 0005 0015 0025 0035 0045001 002 003 004

ndash1

ndash2

ndash3

(b)









euroy _y(1 + ε( _y)) (15)


ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)




11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



A D

1 +ZDL1YDL1

21113874 1113875 per unit

C YDL1 1 +ZDL1YDL1

41113874 1113875 ohm

(7)


B ZDL1 ohm (8)


ZDL1 B ohm

YDL1 2(Aminus 1)

BSiemens

(9)






(10)












(11)









CoD 1minus1113936


2


2

1minusSETV

SE 1113944k


2

TV 1113944k


2

(13)









4 Case Studies





R rℓ

XDL1 ωLℓ

YDL ωCℓ

(14)








Bus 6 Bus 7 Bus 8

Bus 9 Bus 10


Load 6

Load 10


120 kVUtility


120 kV25 kV

Load 14

Load 8


(x1 y1_calc)

(x1 y1_act)Y-

axis

X-axis



ScenarioLoad














Time

Am

p

0005 0015 0025 0035 0045001 002 003 0040

40

20

0

ndash20

ndash40

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

Vs 1

Vs

Vs 2Vs 3

times104

3

2

1

0

0 0005 0015 0025 0035 0045001 002 003 004

ndash1

ndash2

ndash3

(b)









euroy _y(1 + ε( _y)) (15)


ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)




11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




4 Case Studies





R rℓ

XDL1 ωLℓ

YDL ωCℓ

(14)








Bus 6 Bus 7 Bus 8

Bus 9 Bus 10


Load 6

Load 10


120 kVUtility


120 kV25 kV

Load 14

Load 8


(x1 y1_calc)

(x1 y1_act)Y-

axis

X-axis



ScenarioLoad














Time

Am

p

0005 0015 0025 0035 0045001 002 003 0040

40

20

0

ndash20

ndash40

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

Vs 1

Vs

Vs 2Vs 3

times104

3

2

1

0

0 0005 0015 0025 0035 0045001 002 003 004

ndash1

ndash2

ndash3

(b)









euroy _y(1 + ε( _y)) (15)


ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)




11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Time

Am

p

0005 0015 0025 0035 0045001 002 003 0040

40

20

0

ndash20

ndash40

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

Vs 1

Vs

Vs 2Vs 3

times104

3

2

1

0

0 0005 0015 0025 0035 0045001 002 003 004

ndash1

ndash2

ndash3

(b)









euroy _y(1 + ε( _y)) (15)


ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)




11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








euroy _y(1 + ε( _y)) (15)


ndash010

ndash005

000

005

010

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash008

ndash006

ndash004

ndash002

000

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

ndash20000

ndash15000

ndash10000

ndash5000

000

5000

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)




11 004 007 3352 009 015 0073 012 004 High

21 011 013 3452 008 015 0113 High High High

31 045 110 2222 038 108 1223 187 052 High

41 034 059 1492 034 059 0033 010 004816 High







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







6 Conclusions





ndash008

ndash006

ndash004

ndash002

000

002

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMT

(a)

000

005

010

015

020

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMT

(b)

000050100150200250

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMT

(c)



Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Time

Am

p

0 0005 0015 0025 0035 004001 002 003

60

40

20

0

ndash20

ndash40

ndash60

Is

Is 1Is 2Is 3

(a)

Time

Vol

ts

3

2

1

0

ndash1

ndash2

ndash30 0005 0015 0025 0035 004001 002 003

Vstimes104

Vs 1Vs 2Vs 3

(b)


ndash050

000

050

100

150

200

006

035

063

092

121

150

179

208

236

265

294

323

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

ndash060

ndash040

ndash020

000

020

040

060

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

Figure 9 Continued


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ndash1200ndash1000


000200

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)



Calc

ulat

ed li

ne p

aram

eter

(y)

(x1y1_calc)

(x1y1_act)

(a)

Inac

cura

cy m

itiga

tion

mea

sure

(ε)


(b)


000002004006008010012014

006

029

052

075

098

121

144

167

190

213

236

259

306

329

282

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(a)

000005010015020025

020

119

218

317

416

515

614

713

811

910

100

911

08

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(b)

000200400600800

100012001400

214E

ndash06

128E

ndash05

235E

ndash05

342E

ndash05

448E

ndash05

555E

ndash05

662E

ndash05

769E

ndash05

876E

ndash05

982E

ndash05

109E

ndash04

120E

ndash04

Calc

ulat

ion

erro

r


OFTSMTTPCMT

(c)











Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Data Availability




References











Category1 2 3 4 1 2 3 4 1 2 3 4

Resistance

MAD 005 014 041 041 013 009 038 041 014 000 620 014MSE 000 000 000 000 000 000 000 000 000 000 026 000RMSE 004 014 034 034 014 008 033 034 015 000 507 012MAPE 002 006 024 022 005 004 022 022 008 000 349 007

R2 9999 9998 9988 9990 9998 9998 9989 9990 9996 000 9840 9997

Inductance

MAD 083 144 597 278 061 165 576 278 034 000 508 025MSE 000 001 032 008 000 002 030 008 000 000 018 000RMSE 069 116 488 227 048 137 467 226 026 000 428 023MAPE 013 024 098 046 011 027 096 046 006 000 079 003

R2 9999 9999 9996 9998 1000 9999 9996 9998 1000 000 9997 1000

Capacitance











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

OnlineIdentificationofDistributionLineParametersby …downloads.hindawi.com/journals/jece/2018/8719670.pdf · 2019-07-30 · for developing any asymmetrical analysis. e positive se-quenceequivalentπ-modelisshowninFigure1(b)