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Project memo AN 02.12.22

Mathcad spreadsheet dedicated for induction motor model parameter

estimation

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Objective

The objective is to derive parameters for a motor model such that the model behaves as close as possible to the real motor

Develop a Mathcad spreadsheet which estimates input parameters for the induction motor model used in PSCAD/EMTDC (two-axis model with two rotor circuits)

Input data is to be data easily available for induction motors

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Illustartion of model

The equivalent circuit of the PSCAD/EMTDC induction motor model

R1 X1

Xm

X23

R2/s X3

R3/s

V2VmVs

Is

Im

Ir

I2

I3

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Input data to spreadsheet

Rms rated phase voltage Rated output mechanical power Rated electrical frequency Efficiency at rated operation Rated power factor Number of poles Rated speed Start current (relative to rated current) Start torque (relative to rated torque) Inertia

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Output data

Stator resistance (R1) First cage resistance (R2) Second cage resistance (R3) Stator unsaturated leakage reactance (X1) Mutual unsaturated reactance (Xm) Rotor unsaturated mutual reactance (X23) Second cage unsaturated reactance (X3) Polar moment of inertia (MW/MVA) Mechanical damping (p.u)

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Additional input data

User must also specify:

Approximate amount of stator losses relative to total losses (minor influence on final model)

Stator reactance relative to the motor reactance when rotor is blocked (minor influence on final model)

Artificial factor K not reflecting any physical motor parameter (see next slide)

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Effect of the artifical factor K Influences the shape of the torque curve and the current

amplitude (Is) during the start-up

Figureshowstorque andcurrent fortwo differentK values

00.10.20.30.40.50.60.70.80.910

0.6

1.2

1.8

2.4

3

3.6

4.2

4.8

5.4

6

Torque (1)Is (1)Torque (2)Is (2)

p.u. slip

p.u.

.

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Verification The verification part of the spreadsheet presents curves

and percent error between desired quantities and model quantities:

Rated speed Start torqueNv Nrated

Nrated0.0028%= Tstart_Nm_v Tstart_relTrated_Nm

Tstart_relTrated_Nm1.3268%=

Pow er factorOutput power Ef f iciency

cosv coscos 0.1868%=

Pmech_kW_v PoutPout

0.2052%= v 0.0183%=

Start current Rated torque

Trated_Nm_v Trated_NmTrated_Nm

0.2079%=Istart_v IstartIstart

0.0096%=

12X127 AN 02.12.22

PROJECT MEMO MEMO CONCERNS

Mathcad spreadsheet dedicated for induction motor model parameter estimation

DISTRIBUTION

SINTEF Energy Research Address: NO-7465 Trondheim, NORWAY Reception: Sem Slands vei 11 Telephone: +47 73 59 72 00 Telefax: +47 73 59 72 50 www.energy.sintef.no Enterprise No.: NO 939 350 675 MVA

Magnar Hernes Olve Mo Kjell Ljkelsy

AN NO. CLASSIFICATION REVIEWED BY

AN 02.12.22 Unrestricted Magnar Hernes ELECTRONIC FILE CODE AUTHOR(S) DATE

020205Mo10331 2002-04-18 PROJECT NO.

Olve Mo NO. OF PAGES

12X127 Olve.Mo@energy.sintef.no 31 DIVISION LOCATION LOCAL FAX

Energy Systems Sem Slands Vei 11 +47 735972 50 This memo presents a method for estimation of parameters for the induction motor-model in the PSCAD/EMTDC simulation software. The parameter estimation is based on the following motor data:

Rms rated phase voltage Rated output mechanical power Rated electrical frequency Efficiency at rated operation Rated power factor Number of poles Rated speed Start current (relative to rated current) Start torque (relative to rated torque) Inertia

In addition it is possible to tune one free input variable to get a desired break down torque (peak torque) The method is implemented in a Mathcad spreadsheet. The spreadsheet also includes a verification part. It is therefore possible to directly see the resulting performance data of the model including a torque-speed curve The estimated parameters are those needed for Explicit parameter specification in the induction motor model in the PSCAD/EMTDC simulation software. This method of specification gives behaviour much closer to the input data than the alternative EMTP Type 40 parameter input that are found in the PSCAD/EMTDC simulation software.

2

12X127 AN 02.12.22

TABLE OF CONTENTS

Page

1 THE PSCAD/EMTDC INDUCTION MOTOR MODEL................................................ 3 1.1 The equivalent circuit of the PSCAD/EMTDC model ......................................... 3 1.2 The Mathcad spreadsheet ...................................................................................... 4 1.3 Specification of inertia .......................................................................................... 7 1.4 Torque specification.............................................................................................. 7 1.5 Assumed stator losses ........................................................................................... 8 1.6 Stator reactance ..................................................................................................... 8 1.7 Factor K................................................................................................................. 8 1.8 Convergence problems.......................................................................................... 9

2 RECOMMENDED VERIFICATION ............................................................................ 10

3 APPENDIX A: MATHCAD SPREADSHEET.............................................................. 12

Mathcad spreadsheet dedicated for induction motor model parameter estimationObjectiveIllustartion of modelInput data to spreadsheetOutput dataAdditional input dataEffect of the artifical factor KVerification