1

1

Elevated Neutral to Earth Voltages Due to Harmonics

– A T&D Update

E. R. (Randy) Collins, PhD, PE

Dept. of Electrical and Computer EngineeringClemson University

Clemson, South Carolina

Stray Voltage Panel Session2008 IEEE T&D Meeting - Chicago

April 24, 2008

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Two Publications of Interest“Analysis of Elevated Neutral-to-Earth Voltage in Distribution Systems with Harmonic Distortion” to appear in 2008, IEEE Trans. on Power Delivery, Paper TPWRD-00652-2006 by Randy Collins and Jian Jiang.“Elevated Neutral-To-Earth Voltage In

Distribution Systems With Harmonic Distortion,” PhD Dissertation, Clemson University, by Jian Jiang, 2007.

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3Three Phase Distribution Feeder with Single Phase Lateral

Earth

4

Equipotentials surround ground rods

3

5What do we mean by NEV and how does this relate to stray voltage?

Neutral-to-earth voltage is the neutral conductor voltage referred to remote earth.The NEV can be much higher than the “stray voltage” that can be contacted by humans or animals, so the results must be tempered with this understanding. Knowledge of NEV under different system conditions is extremely important in analyzing and mitigating stray voltage problems arising from NEV.

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Common Sources and Conventional Resolutions for Elevated NEV and Stray Voltage

SourcesPower system groundingLoad unbalanceTransformer connectionsNeutral conductor impedance

Alleviation methodsBalance the loads Three-phase single phase lateralsIncrease the neutral conductor sizeImprove grounding connection Repair bad neutral connections and splices

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7Trends of Consumer Electronics and Their Impact on NEV

Proliferation of single phase nonlinear power supplies in electronic appliancesNon-linear response of single-phase motors to voltage distortion

Increased triplen harmonic distortionElevated neutral conductor current

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Our Research ObjectivesDevelop means for systematic analysis of NEV in distribution power systems including harmonic distortionDevelop procedures to predict NEV for planning and assessment, and to troubleshoot existing problemsAssess the effects of NEV mitigation techniques in an environment with harmonic distortion

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Steps of This ProjectDevelop detailed power system models, including the nonlinear loads, for NEV analysis.Construct a multiphase harmonic load flow algorithm to calculate NEV.Test the algorithm accuracy by comparing with the actual field measurement.Examine the algorithm capabilities using a standard IEEE example system.Develop procedures for locating sources of elevated NEV and assess common methods in reducing NEV with nonlinear loads.

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Single-Phase Distribution Feeder Modeling

Phase Conductor

Neutral

Parallel Ground Current

6

11Conventional Transmission Line Model (Carson’s Line)

( )41060935.1

/1065.8

..._2ln210386.0

...cos23

18

,,

4ln24

4ln24

−×=×=

++−=

+−=

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛++=

GfSk

ijkijQ

ijijkijPnaji

GijQijDijS

jGijPijZ

GiiQDii

iiSjGiiPiriiZ

ijij ρ

θπ

ωωω

ωωω

S Distance between conductors and the imagesD Distance between conductors⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

−−

−−

n

a

gnngna

gangaa

nn

aa

II

ZZZZ

VV

'

'

12Practical Distribution Feeder with Non-zero Grounding Resistance

7

13

Equivalent PI ModelThe series impedance is the same as in Carson’s line

The shunt admittance matrix is obtained from the grounding resistance

[ ] ⎥⎦

⎤⎢⎣

⎡=

nnan

anaase ZZ

ZZZ

[ ]⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=−

gRR 10

001

Zse

[R]-1 [R]-1 NEV2NEV1

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Multiple Segments Assemblinga1

n1

g1

Za1

Zn1

Ia

In

Ig

Rg

a2

n2

g2

Za2

Zn2

a3

n3

g3

Ia

In

Ig

[ Y1 ] [ Y2 ]

Zan2 Zna2

Zng2

Zag2

Zan1 Zna1

Zng1

Zag1

Rg Rg

8

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Equivalent PI ModelApply Kron reduction to Ybus to eliminate the nodes in the middle of the feederDerive the equivalent pi model from the resultant matrix

[ ] [ ][ ] [ ]⎥⎦

⎤⎢⎣

⎡=⎥⎦

⎤⎢⎣⎡

ABBAnew

busY

[ ] 1−−= BseZ

[ ]BAshY += [ ]BAshY +=

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Step of This ProjectLinear modelingNonlinear modelingMultiphase harmonic load flowExamine algorithm capability using IEEE example systemTest algorithm accuracy by comparing with actual field measurementsAssess three-phasing method with harmonic distortion present

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17Typical Non-Linear Loads in Distribution Systems

Three phase AC/DC converterSingle phase load with uncontrolled rectifier front endSingle phase induction motorFluorescent lighting

Amps4.2 8.3 12.5 16.6

-28.09

-14.04

0

14.04

28.09

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Single Phase Rectifier

os

TsTth VddiLiRV ++=θ

ω

eq

oos R

VddVCi +=θ

ω

( ) ( ) thooo VV

ddV

dVd

323241412

2

ααααααθ

ααθ

=++++

( ) ( )θ

αααααααθ

ααθ d

dVViddi

did th

thsss

2423241412

2

+=++++

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19Typical Waveforms of a Single Phase Rectifier

0 50 100 150 200 250 300 350 400- 600

- 400

- 200

0

200

400

600

Degr ee

Volt

s/Am

ps

Vo

V th

-Vth

Is

1θ 2θ

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Step of This ProjectLinear modelingNonlinear modelingMultiphase harmonic load flowTest algorithm accuracy by comparing with actual field measurementExamine algorithm capability using IEEE example systemAssess three phasing method with harmonic distortion

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21Multiphase Harmonic Load Flow for NEV Analysis

The nature of NEV problems demands a multiphase load flow solutionNEV problems are often more prevalent in radial distribution systemsSimple load flow program with robust convergence is desired

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A Typical Radial Distribution TopologyRoot Node

Layer 11 2 3 4 5

6 7 8 9 10 11

12 13 14 15 16 17 18 19

20 21 22 23 24 25 2627 28

29 30 31 32 33 34 35

Layer 2

Layer 5

Layer 4

Layer 3

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23Multiphase Load Flow Algorithm -Iterative Solution

Calculate the series impedance matrix for each branch and sum up the shunt admittance at every node except for the root nodeAssume the node voltages for initializationFind the nodal injection current using the node voltage in the previous iteration and determine the division between the neutral conductor and earth currentsBack sweep the system to find the branch current from the last layer by applying KCLForward sweep the system to find the voltage drop for each branch from the first layer and update the nodal voltageCheck convergence and start a new iteration if necessary

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Steps of This ProjectLinear modelingNonlinear modelingMultiphase harmonic load flowTest algorithm accuracy by comparing with actual field measurementExamine algorithm capability using IEEE example systemAssess three phasing method with harmonic distortion

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25Algorithm Verification Using Actual System Measurement

Three phase feeder with a single phase lateral (all conductor sizes are 336 kcmil)Transformer impedance: 7%Assume uniformly distributed loads after the measuring point and ignore any load before it

YG/Δ

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Actual Measurement

Neutral

Phase

Meter ratios: Voltage (5000 V/div), Current (10 A/div)

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Synchronized Measurement Waveforms

Phase voltage

Phase current

Neutral plus messenger current

0 50 100 150 200 250 300 350 400-15

-10

-5

0

5

10

15

Degree

Volta

ge (k

V) a

nd C

urre

nt (A

)

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Synchronized Measurement Waveform

Phase voltage

Phase current

Neutral plus messenger current

0 50 100 150 200 250 300 350 400-15

-10

-5

0

5

10

15

Degree

Volta

ge (k

V) a

nd C

urre

nt (A

)

15

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NEV Simulation

The measured current is injected half way from the measuring point due to the uniform load distributionThe calculated neutral current in the single phase lateral is compared with the measurement to check the modeling and algorithm accuracy

YG/Δ

30Waveform Comparison Using Simulation Results

Phase voltage

Phase current

Calculated neutral current

Measured neutral current

0 50 100 150 200 250 300 350 400-15

-10

-5

0

5

10

15

Degree

Volta

ge (k

V) a

nd C

urre

nt (A

)

Close match-up between measurement and calculation

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31Comparison of Measurement and Simulation Results

Phase voltage

Phase current

Calculated neutral current

Measured neutral current

0 50 100 150 200 250 300 350 400-15

-10

-5

0

5

10

15

Degree

Volta

ge (k

V) a

nd C

urre

nt (A

)

Close match between measurement and calculation

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Step of This ProjectLinear modelingNonlinear modelingMultiphase harmonic load flowTest algorithm accuracy by comparing with actual field measurementExamine algorithm capability using IEEE example systemAssess three phasing method with harmonic distortion

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33Test on IEEE Example Distribution System

Black – Three phaseGreen – Two phaseRed – One phase

Load flow algorithms test system

Relative short feeder

High loading level

Various line configurations

Different load connections

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Linear Loads on The System

8017000009Y

15117000003Δ

2203852203852203853Δ

00132230005Δ

00125170002Y

90120901201101608Y

kvarkWkvarkWkvarkW

Phase 3Phase 2Phase 1BusNo.

LoadType

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35NEV Test with Linear Loads at Different Earth Resistivities

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9

Bus Number

Neu

tral t

o Ea

rth V

olta

ge (r

ms

Volts

)

1000 Ω-m100 Ω-m10 Ω-m

36The Effect of Non-Linear Loads on NEV

Single-phase rectifier: 240V, 30kW with a 4200μF smoothing capacitor

Case 1: A single rectifier on a single-phase line at bus 3Case 2: Three balanced rectifiers on a three-phase line at bus 3 Case 3: Two identical rectifiers on two phases of a three-phase line at bus 3 to form an unbalanced load

Layer 1

Layer 2

Layer 3

Layer 4

Root

1

2 3 4

5 6 7 8

9

Nonlinear load bus

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37NEV RMS Values with Different Nonlinear Load Combinations

0

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9

Bus Number

Neu

tral t

o Ea

rth V

olta

ge (r

ms

volts

)

Linear load onlyCase 1Case 2Case 3

Case 2: Three identical single-phase rectifiers at bus 3

100 Ω-m ground resistance

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Step of This ProjectLinear modelingNonlinear modelingMultiphase harmonic load flowTest algorithm accuracy by comparing with actual field measurementExamine algorithm capability using IEEE example systemAssess three phasing method with harmonic distortion

20

39

Three Phasing Single Phase Lateral

A common practice for distribution system upgradeSimulation setup

Three phasing the single phase lateralEvenly distribute the measured current among the three phasesInject the currents half way from the measuring point

YG/Δ

40Detailed Results of Harmonic Components

0.020.020.010.170.020.020.040.1715

1.0512.8TOT RMS

0.000.000.010.000.020.020.040.1913

0.000.000.010.000.020.020.030.1411

0.040.030.030.280.040.030.080.289

0.000.000.050.010.070.070.140.467

0.000.000.010.000.010.010.030.075

0.180.250.140.930.180.250.420.933

0.040.043.050.182.706.669.1512.741

IEInIphIEInIph

Current (A)NEV (V)

Current (A)NEV (V)

Three PhaseSingle PhaseHarmonic

Order

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41Assessing The Effect of Three Phasing with Nonlinear Loads

Same system configurationThe linear loads are modeled in constant power mode with its value doubled: 120kW @ 0.9 pf laggingNonlinear load: single phase rectifier at 240V, 60kW with 6000 μF smoothing capacitors

YG/Δ

42Single Phase Lateral NEV Spectrum with nonlinear load

At each bus, the NEV spectrum include the following components:

Total RMSFund.3rd

5th

7th

9th

1 2 30

10

20

30

40

50

60

Bus number

Vol

tage

(V)

22

43NEV Spectrum with Nonlinear load After Three Phasing

At each bus, the NEV spectrum include the following component:

Total RMSFund.3rd

5th

7th

9th

1 2 30

5

10

15

20

25

30

35

40

Bus number

Vol

tage

(V)

44Detailed Results for Harmonic Components with Nonlinear Load

0.260.220.162.240.210.180.391.8315

3757.2RMSTOT

0.010.010.250.070.400.320.723.1813

0.010.010.310.050.390.320.712.9311

0.930.780.566.350.870.721.585.949

0.020.030.620.130.910.801.675.587

0.040.062.400.253.003.075.8416.685

7.199.865.4236.346.448.8614.5432.563

0.120.129.690.558.0920.0027.4438.211

IEInIphIEInIph

Current (A)NEV (V)

Current (A)NEV (V)

Three PhaseSingle PhaseHar-

monicOrder

23

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ConclusionsCarson’s line model is adapted for NEV analysisA multiphase harmonic load flow algorithm is developed for NEV analysis in distribution systemsThe simple current injection method used in harmonic analysis achieves similar accuracy as the detailed nonlinear device modelIt is possible to approximately predict the NEV profile and help locate potential stray voltage problems Triplen harmonics elevates the NEV due to their additive nature in the neutralCommon methods for stray voltage mitigation, e.g. three phasing, may not be adequate when there is high harmonic distortion in the system

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Future Research OpportunitiesMore field measurements to validate model.Improve models to incorporate more complex situationsImprove load flow program to handle large scale systemsBetter understand the human sensitivity to harmonic frequency voltages