IEEE Power Engineering SocietyIEEE Power Engineering Society2001 Winter Meeting2001 Winter Meeting

Columbus, OHColumbus, OH

Panel SessionPanel SessionData for Modeling System TransientsData for Modeling System Transients

Parameters for Modeling Transmission LinesParameters for Modeling Transmission Linesand Transformers in Transient Studiesand Transformers in Transient Studies

Bruce MorkBruce MorkMichigan Technological UniversityMichigan Technological University

January 29, 2001January 29, 2001

Simulation of Transient BehaviorsSimulation of Transient Behaviors•• EMTP-like programs are used.EMTP-like programs are used.

•• Simulation results are as good as the modelSimulation results are as good as the modelthat is implemented. We must considerthat is implemented. We must consider

–– Frequency range of the behavior being simulatedFrequency range of the behavior being simulated

–– Available models for each component in theAvailable models for each component in thesimulation package being used.simulation package being used.

–– You must correctly choose and implement eachYou must correctly choose and implement eachmodel, within the capabilities of available models.model, within the capabilities of available models.

–– Not all component models are mature, so someNot all component models are mature, so someintelligence must be used.intelligence must be used.

•• Models representing components are atModels representing components are atvarious stages of maturity.various stages of maturity.

A Question of TimeA Question of Time

How much time is spent on eachHow much time is spent on eachof the following activities?of the following activities?

•• Constructing the overall system model.Constructing the overall system model.•• Obtaining parameters for components.Obtaining parameters for components.

•• Benchmarking the component models.Benchmarking the component models.

•• Benchmarking the overall systemBenchmarking the overall systemmodel.model.

•• Running the simulations and gettingRunning the simulations and gettingresults.results.

Transmission Line ModelsTransmission Line Models

•• The model chosen depends on line length andThe model chosen depends on line length andthe highest frequency to be simulated.the highest frequency to be simulated.

•• For “short” or “medium” lines, a simpleFor “short” or “medium” lines, a simplelumped coupled-lumped coupled-BBBB or several cascaded in or several cascaded inseries may be sufficient.series may be sufficient.

•• Distributed parameter lines are typically usedDistributed parameter lines are typically usedexcept for some of the shortest line sections.except for some of the shortest line sections.

•• Various distributed line models exist, eachVarious distributed line models exist, eachusing different representations ofusing different representations ofcharacteristic impedance and frequencycharacteristic impedance and frequencydependence.dependence.

Basic Features of DistributedBasic Features of DistributedParameter Line ModelsParameter Line Models

iZxv

=∂∂

− vYx

i=

∂∂

−

•• Based on “text book” traveling waveBased on “text book” traveling waveequations [2,3]:equations [2,3]:

•• v and i are the vectors of node voltage andv and i are the vectors of node voltage andline currents at distance x from receiving endline currents at distance x from receiving endof line.of line.

Model DerivationModel Derivation•• Details given in references [2,4,5,6,7]Details given in references [2,4,5,6,7]•• Basic approach:Basic approach:

–– Derive model in frequency domain.Derive model in frequency domain.

–– Use Modal Transformations to Use Modal Transformations to decouple decouple phases.phases.–– Use convolution/Use convolution/deconvolution deconvolution methods to convertmethods to convert

frequency domain solution to time-domainfrequency domain solution to time-domain“equivalent” that can be implemented via“equivalent” that can be implemented vianumerical integration methods. Problematicnumerical integration methods. Problematicrealizationsrealizations

•• Problems:Problems:–– Derived model is only valid for the frequency atDerived model is only valid for the frequency at

which the Modal Transformation was done.which the Modal Transformation was done.–– Frequency fitting techniques can be used toFrequency fitting techniques can be used to

improve results [7].improve results [7].

–– Newer models are based in the phase domain andNewer models are based in the phase domain andavoid the Modal Transformation [8].avoid the Modal Transformation [8].

Transmission Line Data - A DilemmaTransmission Line Data - A Dilemma

•• Existing transmission line data may exist onlyExisting transmission line data may exist onlyin a format useful for load flow, short circuit,in a format useful for load flow, short circuit,and stability studies.and stability studies.

•• Short-circuit data: positive and zero sequenceShort-circuit data: positive and zero sequenceper-phase seriesper-phase series impedances impedances. For double-. For double-circuit lines, you will also have the “mutualcircuit lines, you will also have the “mutualimpedance” -- the zero-sequence couplingimpedance” -- the zero-sequence couplingbetween circuits. Total positive sequencebetween circuits. Total positive sequenceline-charging MVA may be known.line-charging MVA may be known.

•• For load flow and stability studies, you willFor load flow and stability studies, you willhave short-circuit data as above, plus positivehave short-circuit data as above, plus positiveand negative sequence and negative sequence capacitive capacitive coupling.coupling.

A Data Base of Physical DesignA Data Base of Physical DesignParameters Must be DevelopedParameters Must be Developed

•• (x, y) coordinates of conductors and shield(x, y) coordinates of conductors and shieldwires.wires.

•• Bundle Bundle spacingsspacings, orientations., orientations.•• Phase (A,B,C) and circuit (1,2,3) designationPhase (A,B,C) and circuit (1,2,3) designation

of each conductorof each conductor•• Phase “rotation” or swapping at eachPhase “rotation” or swapping at each

transpositiontransposition•• Physical dimensions of each conductor (bothPhysical dimensions of each conductor (both

inner and outer radii for bus bar and strandedinner and outer radii for bus bar and strandedconductor).conductor).

•• Earth Earth resistivity resistivity of the ground return path.of the ground return path.•• Other information such as segmentedOther information such as segmented

grounds, transpositions.grounds, transpositions.

Transmission Lines - Two ExamplesTransmission Lines - Two Examples

345-kV Single-Circuit345-kV Single-Circuit 345-kV Double-Circuit345-kV Double-Circuit

345-kV Single-Circuit345-kV Single-CircuitPhysical Input ParametersPhysical Input Parameters

Acknowledgement: Sung Don Cho for putting together these examplesAcknowledgement: Sung Don Cho for putting together these examples

Typical set of input, representative of most so-calledTypical set of input, representative of most so-called“LINE CONSTANTS” programs or supporting routines.“LINE CONSTANTS” programs or supporting routines.

Comments on ParametersComments on Parameters•• Conductor Numbers 1,2,3 ==> phase A,B,CConductor Numbers 1,2,3 ==> phase A,B,C•• Conductors Numbered 0 ==> shield wireConductors Numbered 0 ==> shield wire•• Inner Radius: Radius of steel stranded core orInner Radius: Radius of steel stranded core or

radius of inner tube diameter of bus bar.radius of inner tube diameter of bus bar.•• DC Resistance: usually choose to be at 50°C orDC Resistance: usually choose to be at 50°C or

higher, not at 25 °Chigher, not at 25 °C•• Horizontal (x-axis) value: relative horizontalHorizontal (x-axis) value: relative horizontal

position of each conductor. Absolute value is notposition of each conductor. Absolute value is notimportant.important.

•• Typical height at tower and height at Typical height at tower and height at midspan midspan areareused to determine average height above terrainused to determine average height above terrainassuming a assuming a catenary catenary sag.sag.

•• Bundled conductors are usually handled as aBundled conductors are usually handled as agroup: number in bundle, separation, orientation ofgroup: number in bundle, separation, orientation ofbundle.bundle.

Choice of Model to ImplementChoice of Model to Implement

•• Accuracy of model for given range of frequenciesAccuracy of model for given range of frequenciesis key concern.is key concern.

•• Several “standard” choices, available in theSeveral “standard” choices, available in theoriginal EMTP program are discussed here. Otheroriginal EMTP program are discussed here. Othermodels may be available in various simulationmodels may be available in various simulationpackages.packages.

–– Lumped parameter coupled PI.Lumped parameter coupled PI.

–– Bergeron Bergeron (distributed parameter, constant Z(distributed parameter, constant ZCC. ), also. ), alsoreferred to as “Constant Parameter” which is built on thereferred to as “Constant Parameter” which is built on thepaper by paper by SnelsonSnelson [4] and developed by Meyer and [4] and developed by Meyer andDommelDommel [5]. [5].

–– J-Marti Model (distributed parameter, constant ZJ-Marti Model (distributed parameter, constant ZCC. ). )

•• With physical parameters entered, various modelsWith physical parameters entered, various modelsfor a given line section can be implemented andfor a given line section can be implemented andbenchmarked until satisfied.benchmarked until satisfied.

Steady-State BenchmarkingSteady-State BenchmarkingSingle Phase ModelSingle Phase Model

•• A utility’s existing transmission line data baseA utility’s existing transmission line data basecontains some information that should becontains some information that should beused to verify that you’ve developed a modelused to verify that you’ve developed a modelwhich is basically correct.which is basically correct.

Length(miles)

R0(ohms)

X0(ohms)

R1(ohms)

X1(ohms)

ChargingMVar

UtilitySC Data 20.30 12.05 36.25 1.12 12.33 16.67

ATP 20.30 12.68 35.33 1.10 12.15 17.38

%difference 0.0% 5.2% -2.5% -2.0% -1.4% 4.3%

Steady-State BenchmarkingSteady-State BenchmarkingDouble-Circuit LineDouble-Circuit Line

•• Zero-Sequence coupling between phases isZero-Sequence coupling between phases isalso a consideration in this case [2].also a consideration in this case [2].

Length(miles)

R0(ohms)

X0(ohms)

R1(ohms)

X1(ohms)

ChargingMVar

R00(ohms)

X00(ohms)

UtilityS.C. Data 9.64 5.22 18.54 0.53 5.51 8.40 4.69 10.64

ATP 9.64 5.45 18.17 0.52 5.51 8.55 4.87 10.31

%difference 0.0% 4.4% -2.0% -2.3% 0.0% 1.9% 3.8% -3.1%

Frequency Scan BenchmarkingFrequency Scan Benchmarking

•• A pair of frequency scans can be performedA pair of frequency scans can be performedon the developed line model, determiningon the developed line model, determininginput impedance with the receiving end open-input impedance with the receiving end open-circuited.circuited.

–– First perform frequency scan on the model you’veFirst perform frequency scan on the model you’vedeveloped, stepping the source through the desireddeveloped, stepping the source through the desiredfrequency range in discrete steps.frequency range in discrete steps.

–– Next, perform a series of open-circuit simulationsNext, perform a series of open-circuit simulationson the ideal coupled PI model (redevelop coupled-on the ideal coupled PI model (redevelop coupled-PI model for each frequency). This result isPI model for each frequency). This result isassumed to be the “true” frequency response.assumed to be the “true” frequency response.

–– OverplotOverplot the two frequency scan results. the two frequency scan results.

Frequency Scan VerificationFrequency Scan VerificationSingle-Circuit Line, 1 Hz - 5 kHzSingle-Circuit Line, 1 Hz - 5 kHz

Miscellaneous CommentsMiscellaneous Commentson Line Modelson Line Models

•• Frequency dependency of resistance typicallyFrequency dependency of resistance typicallyassumes a solid conductor (or hollow conductor)assumes a solid conductor (or hollow conductor)and applies skin effect corrections. Skin effectand applies skin effect corrections. Skin effectassumes that highest current density is atassumes that highest current density is atsurface. However, for stranded conductorssurface. However, for stranded conductorshaving 3 or more layers of aluminum, this is nothaving 3 or more layers of aluminum, this is nottrue.true.

•• Other more advanced line models are beingOther more advanced line models are beingdeveloped, but are not generally available in alldeveloped, but are not generally available in alltransients packages.transients packages.

–– Taku Taku Noda - phase-domain frequency dependent [8].Noda - phase-domain frequency dependent [8].

–– Other models and frequency fitting techniques byOther models and frequency fitting techniques byGustavsen Gustavsen and others.and others.

Miscellaneous CommentsMiscellaneous Commentson Line Modelson Line Models

•• Choose integration Choose integration timestep timestep to be smaller thanto be smaller thanthe smallest propagation time for all modes.the smallest propagation time for all modes.

•• Segmented ground?Segmented ground?•• Transpositions? Full Transpositions? Full vsvs. approximate.. approximate.•• Choosing real Choosing real vsvs. complex transformation matrix. complex transformation matrix

affects numerical stability. Usually choose realaffects numerical stability. Usually choose realfor transient studies.for transient studies.

Key ReferencesKey References[1] Modeling and Analysis of Power System Transients Using Digital Programs,IEEE Special Publication TP-133-0, IEEE Catalog No. 99TP133-0, 1999.[2] H.W. Dommel, EMTP Theory Book, Microtran Power System AnalysisCorporation, Vancouver, BC, May 1992.[3] A. Greenwood, Electrical Transients in Power Systems, 2nd Edition, JohnWiley & Sons, Inc., ©1991.[4] J.K. Snelson, “Propagation of Travelling Waves on Transmission Lines –Frequency Dependent Parameters,” IEEE Trans. PAS, Vol. 91, pp. 85-91, 1973.[5] W.S. Meyer and H.W. Dommel, “Numerical Modeling of Frequency-Dependent Transmission Line Parameters in an Electromagnetic TransientsProgram,” IEEE Trans. PAS, Vol. PAS-93, pp. 1401-1409, 1974.[6] A. Semlyen and A. Dabuleanu, “Fast and Accurate Switching TransientCalculations on Transmission Lines with Ground Return Using RecursiveConvolutions,” IEEE Trans. PAS, Vol. PAS-94, pp. 561-571, 1975.[7] J.R. Marti, “Accurate Modeling of Frequency-Dependent Transmission Linesin Electromagnetic Transient Simulations,” Power Industry ComputerApplications, pp. 326-334, 1981.[8] T. Noda, N. Nagaoka, A. Ametani, “Phase Domain Modeling of Frequency-Dependent Transmission Lines by Means of an ARMA Model,” IEEE Trans.Power Delivery, Vol. 11, No. 1, January 1996.[9] G.R. Slemon, “Equivalent Circuits for Transformers and Machines IncludingNon-Linear Effects,” Proc. IEE, Vol. 100, part IV, pp. 129-143, 1953.[10] V. Brandwajn, H.W. Dommel, I.I. Dommel, “Matrix Representation of Three-Phase N-Winding Transformers for Steady-State and Transient Studies,” IEEETrans. PAS, Vol. PAS-101, No. 6, pp. 1369-1378, June 1982.

Example of “Example of “BCTranBCTran” Modeling” ModelingAcknowledgement: Sung Don Cho for putting together this exampleAcknowledgement: Sung Don Cho for putting together this example

• 345000 Grd.Y/ 165000 Grd.Y/ 13800 Delta

• 161MVA@OA

Exciting Current No Load LossOpen-CircuitTest 0.34%@100%Voltage

0.73%@110%Voltage130.275kW@100%Voltage168.265kW@110%Voltage

Impedance LossShort-CircuitTest P-S: 6.85%

P-T: 9.40% @36.6MVAS-T: 8.22% @36.6MVA

P-S: 194.77kWP-T: 62.693kW @36.6MVAS-T: 71.682kW @36.6MVA

• Verify steady-state exciting currents and no-load loss.

• Verify the “Binary Short Circuit” currents and losses.

Short-Circuit RepresentationShort-Circuit Representation

•• For N-Winding TransformerFor N-Winding Transformer•• Represents short-circuit effects as equivalentRepresents short-circuit effects as equivalent

winding resistance and leakage reactance.winding resistance and leakage reactance.

v

v

v

R

R

R

i

i

i

L L L

L L L

L L L

ddt

i

i

iN NN N

N

N

N N NN N

1

2

11

22

1

2

11 12 1

12 22 2

1 2

1

2

0 0

0 0

0 0

M

L

L

M M O M

L

M

L

L

M M O M

L

M

=

+

Inclusion of Core Saturation & LossInclusion of Core Saturation & Loss

•• Standard factory test reports typically reportStandard factory test reports typically reporton the total open-circuit losses at 100% andon the total open-circuit losses at 100% andat 110% rated voltage.at 110% rated voltage.

•• Standard factory test reports typically reportStandard factory test reports typically reportthe average of the RMS exciting currents ofthe average of the RMS exciting currents ofthe three phases. This data is only useful ifthe three phases. This data is only useful ifyou have a bank of three single phaseyou have a bank of three single phasetransformers. Otherwise, the coretransformers. Otherwise, the coreconfiguration should be taken into account.configuration should be taken into account.

•• An approximate core representation can beAn approximate core representation can beattached (usually to the low-voltage terminalsattached (usually to the low-voltage terminalsof the BCTRAN model).of the BCTRAN model).

Core ConfigurationsCore Configurations

Development of an ApproximateDevelopment of an ApproximateEquivalent CoreEquivalent Core

•• Basic calculations are given in [2].Basic calculations are given in [2].

puAVI

puAVP

IVI

AAIV

AAIV

AkV

MVAIb

MVAMVA

MVA

EE

E

E

32

2

32

22

2

1

10240.716.2818.131.13

625.1684.28%110@

10296.382.128.133

265.1302.13

3%100@

4.28%73.03889%110@%73.0

2.13%34.03889%100@%34.0

889,38.133

161

7.533

161

−

−

⋅==

∗∗−=

⋅==

∗−=

−=

=∗=⇒=∗=⇒

=∗

=

==

φ

φ

φ

Using SATURATION RoutineUsing SATURATION Routine•• Input RMS V-I saturation curve, including (0,0)Input RMS V-I saturation curve, including (0,0)

point at origin.point at origin.•• Run EMTP supporting routine SATURATION toRun EMTP supporting routine SATURATION to

get corresponding peak (current, flux-linked)get corresponding peak (current, flux-linked)

C SATURATIONC $ERASEC 60. 13.8 53.7 1C 3.296e-3 1.C 7.240e-3 1.1C 9999 1.81383342E+01 5.17681882E+01 6.39542221E+01 5.69450070E+01 9999

Incorporating with BCTRANIncorporating with BCTRAN

•• The output of SATURATION can then beThe output of SATURATION can then bepasted into a nonlinear inductance element.pasted into a nonlinear inductance element.

•• Suggest either “type-98” or “type-93”Suggest either “type-98” or “type-93”inductance. The inductance. The hysteretic hysteretic “type-96” has“type-96” hasproblems reproducing loop area (losses) overproblems reproducing loop area (losses) overthe full range of excitation. This is bad,the full range of excitation. This is bad,especially for CT core models.especially for CT core models.

•• Core representation can be connected eitherCore representation can be connected eitherin in Wye Wye or Delta. Problems with convergenceor Delta. Problems with convergenceof nonlinear inductance operation points canof nonlinear inductance operation points canbe a problem when connected in Delta.be a problem when connected in Delta.

•• Include core loss resistance in parallel withInclude core loss resistance in parallel withcore inductance. Losses are quite dependentcore inductance. Losses are quite dependenton voltage.on voltage.

CLOSING COMMENTSCLOSING COMMENTS

•• Have an intuitive feel for what you’re doing.Have an intuitive feel for what you’re doing.•• Always at least verify the model’s steady-Always at least verify the model’s steady-

state performance.state performance.•• Confirm that model should be valid within theConfirm that model should be valid within the

range of frequencies you will be simulating.range of frequencies you will be simulating.Sometimes this requires that you first run theSometimes this requires that you first run thesimulation. In cases involving simulation. In cases involving nonlinearitiesnonlinearities,,it is impossible to predict all frequenciesit is impossible to predict all frequenciespresent. Run simulation, find out what thepresent. Run simulation, find out what thenatural response frequencies are. Adjustnatural response frequencies are. Adjustmodel if need be.model if need be.

COMMENTS?COMMENTS?

QUESTIONS?QUESTIONS?