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Secondary Low-Voltage Circuit Models – How Good is Good Enough? Jouni Peppanen, Jason A. Taylor, Roger C. Dugan Power System Studies, Electric Power Research Institute, TN, USA [email protected] / [email protected] / [email protected] Celso Rocha Polytechnic School of the University of Sao Paulo, Brazil

Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

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Page 1: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Secondary Low-Voltage Circuit Models – HowGood is Good Enough?

Jouni Peppanen, Jason A. Taylor, Roger C. DuganPower System Studies, Electric Power Research Institute, TN, USA

[email protected] / [email protected] / [email protected]

Celso RochaPolytechnic School of the University of Sao Paulo, Brazil

Page 2: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Why Care About Secondary Circuits?• Distribution analysis

typically focuses on primarycircuits

• Many DER & sensors insecondary circuits

• Lack of accurate secondarymodels and data

• Many simplifications usedwithout considering theimpacts 115

120

125

Voltageon a 120-V Base

ANSI C84.1 Service Voltage Upper Limit

ANSI C84.1 Service Voltage Lower Limit

Secondary Voltage Drop

Primary Circuit Voltage Drop

Service Transformer Voltage Drop

?

Page 3: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Typical SimplificationsSimplification MotivationLoad allocation Lack of AMI measurements

Difficulty handling large AMI data setsSingle-phase models No split-phase measurements

Insufficient component informationConstant power factor Lack of AMI var measurementsLow measurement time-granularity (15-min or 1-hour)

Lack of/difficulty handling high-granularity data

SHOULD NOT BE USED TO ANALYZE SECONDARY SYSTEMS

Page 4: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Split-Phase Secondary Modeling

Fully detailed modeling requires:• Transformer & line/cable information• Information on topology & phasing• Load P & Q measurements from both 120-volt legs

PrimaryCircuit

Split-PhaseService Transformer

Customers with aSplit-phase Service

Triplex-CableService Lines

Page 5: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Split-Phase Secondary Modeling

VH

V1

V2

H1 X1

X2

X3

ZH Z1

Z2

+

-

+

-+

-

+

-

EH

-

-

+

+

Vt1

Vt2

IH I1

I2

:1

= 1 −

rp

rn

rp

dDpn

Dpp rnrp

Dpp

rp

d ddDpn

ZSL1

ZSL2

ZSLn

ZSL1n

ZSL2n

ZSL12

IS1 IR1

IRn

IR2IS2

ISn

VS1

VSn

VS2

VR1

VRn

VR2

ISL1

ISLn

ISL2

= +

+

--

+

VL1

VL2

VL3

+

-

IL1

ISL2

ISLn

IL2

IL3

ISL1

Split-Phase TransformerTriplex Line/Cable Split-Phase Customer

Page 6: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Single-Phase Equivalent Modeling

• What to do when split-phase data/models notavailable?

• Detailed split-phase modelhas an exact single-phaseequivalent

• Small Print: Currents in thetwo 120-volt currentcarrying legs must be equal( = − )

VH

V1

V2

H1 X1

X2

X3

ZH Z1

Z2

+

-

+

-+

-

+

-

EH

-

-

+

+

Vt1

Vt2

IH I1

I2

+

-+

-

VL1

VL2

VL3

+

-

IL1

IL2

IL3

ZSL1

ZSL2

ZSLn

ZSL1n

ZL2n

ZSL12

:1

In

VH V12

ZH Z1

Z2

+

-

+

-

+

-

EH

-

+Vt1

IH I1

I2=-I1

VL

+

-

IL=I1

ZSL1’

ZSL12’

ZSL2’

:1

Vt2

+-

Page 7: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Single-Phase Equivalent Model Parameters• Single-phase transformer:

– 240-volt L-N connectedsecondary winding

– Use full-winding impedance• Single-phase service lines

– Use 2 , − ,• Single-phase load

– 240-volt line-neutral connection– Total P, Q

VH V12

ZH Z1

Z2

+

-

+

-

+

-

EH

-

+Vt1

IH I1

I2=-I1

VL

+

-

IL=I1

ZSL1’

ZSL12’

ZSL2’

:1

Vt2

+-

Page 8: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Case Study Secondary Circuits

• Two real utility secondary circuits• Split-phase & single-phase

models derived

“Small Secondary Circuit”PrimaryCircuit

ServiceXmfr7.2D/0.24Y kV

25 kVAr+jx=1.18+j1.44Non-interlaced

48’ 4

167’ 3/0

Load110+j2

Load212+j4

PrimaryCircuit

ServiceXmfr7.2Y/0.24Y

25 kVAr+jx=1.18+1.44Non-interlaced

106’ 1/013’ 1/0 Load3

5.2+j3.2

206’ 1/010’ 1/0

11’ 1/0

Load11.6+j1.0

Load21.2+j0.7

61’ 1/0 Load48.3+j5.1

187’ 1/0

103’ 1/042’ 1/0

23’ 1/0

Load71.8+j1.1

Load85.7+j3.5

161’ 1/0286’ 1/0

116’ 1/0

Load52.6+j1.6

Load68.4+j5.1

All Lines Assumed toHave Full Neutrals

“Large Secondary Circuit”

Page 9: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Split-phase vs. Single-Phase Model Comparison• Under perfectly balanced

loads– Identical results from split-

phase and single-phase modelsfor both circuits

• What happens in unbalancedconditions?

Small Secondary CircuitPrimaryCircuit

ServiceXmfr7.2D/0.24Y kV

25 kVAr+jx=1.18+j1.44Non-interlaced

48’ 4

167’ 3/0

Load110+j2

Load212+j4

Quantity Split-PhaseModel Single-Phase Model

Load1 240 V Voltage 236.36∠ − 0.5 236.36∠ − 0.5Load2 240 V Voltage 236.36∠ − 0.5 236.36∠ − 0.5

Transformer 240 V Voltage 236.77∠ − 0.4 236.55∠ − 0.6Total Load Power 36.3+j20.1 36.3+j20.1

Total Losses 0.8+j0.4 0.8+j0.4

Page 10: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Single-Phase Model with Unbalanced Loads

When the small secondarycircuit phase A load shareis varied 0-100%:• 240-volt voltages still

very accurate• 120-voltages inaccurate• Losses underestimated

by up to 50%

[V]

Page 11: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Case Study Measurement Data• High-granularity residential house split-

phase measurements– Recorded with WattNode sensors– Two 120-volt voltages, active powers,

reactive power, currents, etc.– 417660 1-min samples over a 9-month time

period

• Each circuit load was assigned randomlyone of the measurement profiles

Page 12: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Measurement Time-Granularity

• Typical AMI @ 15-min orhigher

• Residential load shapeconsists of “needle peaks”

• Accurate analysis requires5-min or faster time-granularity

0

0.2

0.4

0.65-min vs. 1-min

Prob

abilit

y[0

,1]

Error [%] Against 1-min Measurements

Page 13: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Constant Power Factor• AMI reactive power measurements

often not available• Typical to assume constant power

factor• Residential load power factor driven

by large equipment duty cycles• Power factor varies over time and

between the two customer phases• Power factor distributions vary

largely from customer to customer

Example of Power Factors

Customer Power Factor Distributions

Page 14: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

How Balanced Are the 120-volt Loads?

• P, Q, and power factorare not balancedbetween customerphases

• Error of balanced loadassumption varies largelyfrom customer tocustomer

Page 15: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Studied Simplified CasesCase Model Measurements Description/Motivation

1 Split-phase

1-min, , , Base case for comparison

2 Single-phase

1-min, Impact of single-phase models and data

3 Split-phase

1-min,Assume PF=0.9

Impact of constant conservative (0.9) power factorassumption

4 Split-phase

15-min, , , Impact of low (15-min) measurement timegranularity

5 Single-phase

15-min, Today’s best case: Accurate single-phase modes anddata with typical 15-min AMI resolution

Page 16: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Single-phase vs. Split-phase (Case 2 vs. Case 1)• Losses underestimated on average by 15% (6%) for small

(large) circuit• 240-volt drops accurate• 120-volt drop have mean absolute percentage error (MAPE)

of 10-25% & mean absolute error (MAE) of 0.19-0.40 volt• 120-volt drop error driven by load unbalance and

connection (electrical) strength

Page 17: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Constant Power Factor Error (Case 3 vs. Case 1)

• Losses underestimated on average by ~20%– Results likely from selected (low) power factor of 0.90– Different power factor selection will yield better/worse results– Error depends on how well the assumed power factor

represents the loads

• 120-volt drop MAPE 10-16% (MAE 0.12-0.36 volt)• 240-volt drop MAPE 1.9-3.3% (MAE 0.27-0.46 volt)

Page 18: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

15-min vs. 1-min Error (Case 4 vs. Case 1)

• Losses underestimated on average by 6-7%– Losses proportional to the square of the currents– 15-min data does not capture “needle peaks”

• 120-volt drop MAPE 12-16% (MAE 0.08-0.27 volt)• 240-volt drop MAPE 11-12% (MAE 0.17-0.46 volt)

Page 19: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Practical Best Case Error (Case 5 vs. Case 1)

• Losses underestimated by 20% (12%) for small(large) circuit

• 120-volt drops MAPE 16-26% (MAE 0.21-0.47 Volts)• 240-volt drops MAPE 11-12% (MAE 0.17-0.46 Volts)

Page 20: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Practical Best Case Error (Case 5 vs. Case 1)

• Average errors fail togive the entire picture

• Voltage drop simulationerrors– Can be >2 Volts– Are frequently >1 Volt

Case 5 Volt Drop MAE Histograms

Case 5 Share of MAEs >1 Volt

Page 21: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Key Take Aways• Single-phase models accurately represent the 240-volt

voltages but not the 120-volt voltages• Constant power factor can lead to considerable errors

in estimating losses and some error in simulatedvoltages

• Typical best case (15-min AMI P & Q with single-phasemodel) can result in considerable errors in simulatedvoltages and losses

Page 22: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Going Forward• How good is good enough? Acceptable errors depend on

applications• The error from the simplifications may influence

– Analysis of advanced PV / DER inverter functionalities– Operational algorithms, such as distribution state estimation, that

use AMI and other sensors located in secondary circuits• More accurate models and more granular measurement

data will likely be needed• EPRI has on-going work on

– The impact of voltage excursions– Advanced load modeling techniques

Page 23: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Thank You!

Paper Title: Secondary Low-Voltage Circuit Models – How Good is Good Enough?

Jouni Peppanen, Jason A. Taylor, Roger C. DuganPower System Studies, Electric Power Research Institute, TN, USA

[email protected] / [email protected] / [email protected]

Celso RochaPolytechnic School of the University of Sao Paulo, Brazil

Page 24: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Extra Slides to Follow

Page 25: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Split-Phase Service Transformer Modeling

• 3-winding transformers with asingle L-L or L-N connected MVprimary winding and two 120-Vsecondary windings

• Winding impedances are typicallyestimated from full-windingshort-circuit impedance (shortingX1 to X3)

VH

V1

V2

H1 X1

X2

X3

ZH Z1

Z2

+

-

+

-+

-

+

-

EH

-

-

+

+

Vt1

Vt2

IH I1

I2

:1

= 1 −

Page 26: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Triplex Service Line Modeling

• Typically two identical insulatedconductors wrapped around a non-insulated neutral conductor

• Can be modeled with π-equivalentusing Carson’s equations

• Capacitance typically neglected• Impedances not very sensitive to

insulation thickness and conductorspacing

rp

rn

rp

dDpn

Dpp rnrp

Dpp

rp

d ddDpn

ZSL1

ZSL2

ZSLn

ZSL1n

ZSL2n

ZSL12

IS1 IR1

IRn

IR2IS2

ISn

VS1

VSn

VS2

VR1

VRn

VR2

ISL1

ISLn

ISL2

= +

Page 27: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Split-Phase Customer Modeling• Consists of

– A single 240-volt connected load– Two 120-volt connected loads

• Detailed split-phase modeling requiresP & Q measurements from both 120-volt lines (or from both 120-volt and240-volt load)

• What to do when no split-phasemeasurements are available?

+

--

+

VL1

VL2

VL3

+

-

IL1

ISL2

ISLn

IL2

IL3

ISL1

Page 28: Secondary Low-Voltage Circuit Models – How Good is Good ... · ANSI C84.1 Service Voltage Upper Limit ANSI C84.1 Service Voltage Lower Limit Secondary Voltage Drop Primary Circuit

Single-Phase Equivalent Model Parameters• Single-phase transformer:

– 240-volt L-N connectedsecondary winding

– Use full-winding impedance• Single-phase service lines

– Use 2 , − ,• Single-phase load

– 240-volt line-neutral connection– Total P, Q

VH V12

ZH Z1

Z2

+

-

+

-

+

-

EH

-

+Vt1

IH I1

I2=-I1

VL

+

-

IL=I1

ZSL1’

ZSL12’

ZSL2’

:1

Vt2

+-