7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 1/20

Monitoring, Energy and Drive Technologies1

Object-oriented modeling of electrical machines:

Modelica.Electrical.Machines

Anton Haumer

arsenal research, Vienna

03.03.2008

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 2/20

Monitoring, Energy and Drive Technologies2

Contents

• Common Mechanical Components

• DC Machines• Induction Machines

• Asynchronous Induction Machines

• Synchronous Induction Machines

• Transformers

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 3/20

Monitoring, Energy and Drive Technologies3

Common Mechanical Components• Rotor’s moment of inertia

• Stator:

 –  useSupport = false:fixed

 –  useSupport = true:

moment of inertia+ connect support!

• Common parameters

• Common outputs

e.g. wMechanical, tauShaft• Icon

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 4/20

Monitoring, Energy and Drive Technologies4

DC Machines: Common Electrical Components• Armature pins

• Armature resistance +leakage inductance

• Common parameters for:

 –  PM DC machine

 –  Electrical excited DC machine –  Series excited DC machine

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 5/20

Monitoring, Energy and Drive Technologies5

DC Machines: Airgap• Calculates flux from

excitation current

• Induced armature voltage:~ psi * omega

• Induced excitation voltage:

~ der(psi)• Torque tau:

~ psi * armature current

• omega =

der(shaft.phi – support.phi);• tau = - shaft.tau;

tau = support.tau;

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 6/20

Monitoring, Energy and Drive Technologies6

Permanent Magnet DC Machine• What’s missing:

excitation

• PM acts likeconstant excitation current

• turnsRatio * Ie:

determined byinduced armature voltageat nominal speedand no-load

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 7/20

Monitoring, Energy and Drive Technologies7

DC Machines: Example 1• Starting from standstill,

applying an armature voltage ramp

• Followed by a torque step

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 8/20

Monitoring, Energy and Drive Technologies8

Induction Machines: Three-Phase Winding• Feeding

a three-phase winding,

i.e. shifted spatially by 120°,with three-phase current,i.e. shifted timely by 120°,gives a sinusoidal field,

rotating with f / p.• This rotating field

can be represented by a

space phasor.

+U +U +U +U -W -W -W -W +V +V +V +V -U -U -U -U +W +W +W +W -V -V -V -V

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 1 19 20 21 22 23 24

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

+U +U -W -W -W -W +V +V +V +V -U -U -U -U +W +W +W +W -V -V -V -V +U +U

4 4 2 2 0 0 0 0 0 0 2 2 4 4 2 2 0 0 0 0 0 0 2 2

4 3,9 1,7 1,4 0 0 0 0 0 0 1,7 1,9 4 3,9 1,7 1,4 0 0 0 0 0 0 1,7 1,90 1 1 1,4 0 0 0 0 0 0 -1 -1 -0 1 1 1,4 0 0 0 0 0 0 -1 -1

4 1 -2 -1 0 0 0 0 0 0 -2 0,5 4 1 -2 -1 0 0 0 0 0 0 -2 0,5

0 3,9 1 -1 0 0 0 0 0 0 -1 -2 -0 3,9 1 -1 0 0 0 0 0 0 -1 -2

4 - 1 -2 1,4 0 0 0 0 0 0 -2 - 1 4 -1 - 2 1,4 0 0 0 0 0 0 -2 - 1

0 3,9 -1 -1 0 0 0 0 0 0 1 -2 -0 3,9 -1 -1 0 0 0 0 0 0 1 -2

4 -4 1,7 -1 0 0 0 0 0 0 1,7 -2 4 -4 1,7 -1 0 0 0 0 0 0 1,7 -2

0 1 -1 1,4 0 0 0 0 0 0 1 -1 0 1 -1 1,4 0 0 0 0 0 0 1 -1

4 -4 1,7 -1 0 0 0 0 0 0 1,7 -2 4 -4 1,7 -1 0 0 0 0 0 0 1,7 -2

0 -1 1 -1 0 0 0 0 0 0 -1 0,5 -0 -1 1 -1 0 0 0 0 0 0 -1 0,5

4 8 11 14 16 18 18 18 16 14 11 8 4 0 -3 -6 -8 -10 -10 -10 -8 -6 -3 -00 4 7 10 12 14 14 14 12 10 7 4 0 -4 -7 -10 -12 -14 -14 -14 -12 -10 -7 -4

0 0,3 0,5 0,5 0,4 0,2 -0 -0 -1 -1 -1 -0 0 0,3 0,5 0,5 0,4 0,2 -0 -0 -1 -1 -1 -0

0 0,1 0,4 0,7 0,9 1,2 1,2 1,1 0,8 0,5 0,2 0 0 0,1 0,4 0,7 0,9 1,2 1,2 1,1 0,8 0,5 0,2 0

0 3,7 7,1 10 12 14 14 14 12 10 7,1 3,7 -0 -4 -7 -10 -12 -14 -14 -14 -12 -10 -7 -4

0 -0 -1 -0 0,9 0,7 -1 -1 0,1 0,8 0,2 -0 0 -0 -1 -0 0,9 0,7 -1 -1 0,1 0,8 0,2 -0

0 0,3 -0 -1 -0 0,9 0,9 -0 -1 -0 0,5 0,2 0 0,3 -0 -1 -0 0,9 0,9 -0 -1 -0 0,5 0,2

0 -0 -0 0,7 -0 -1 0,8 0,4 -1 0,1 0,5 -0 0 -0 -0 0,7 -0 -1 0,8 0,4 -1 0,1 0,5 -0

0 0,1 -1 0,1 0,8 -1 -1 0,9 0,1 -1 0,2 0,2 0 0,1 -1 0,1 0,8 -1 -1 0,9 0,1 -1 0,2 0,2

0 -0 0,2 -0 0,6 -1 0,8 -1 0,5 -0 0,2 -0 0 -0 0,2 -0 0,6 -1 0,8 -1 0,5 -0 0,2 -0

0 -0 0,3 -0 0,3 -0 -0 0,3 -0 0,5 -0 0,2 0 -0 0,3 -0 0,3 -0 -0 0,3 -0 0,5 -0 0,2

0 0,1 -0 0,4 -1 0,7 -1 0,6 -0 0,3 -0 0 0 0,1 -0 0,4 -1 0,7 -1 0,6 -0 0,3 -0 0

0 -0 0,3 -0 0,2 -0 -0 0,3 -0 0,4 -0 0,2 0 -0 0,3 -0 0,2 -0 -0 0,3 -0 0,4 -0 0,2

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 9/20

Monitoring, Energy and Drive Technologies9

Induction Machines: Space Phasors• Length ~ field magnitude

• Points to maximum of field

• i.e. rotating with f / p

• Space phasor transformation:

• coordinate system (2) rotated by the angle γ

against the original coordinate system (1):

[ ] [ ] [ ]( )

[ ] [ ] [ ]( )3va2va1va3

2V

3v2v1v3

1

V

210

0

⋅+⋅+⋅⋅=

++⋅=

[ ] ( )[ ] ( )[ ] ( )VaReV3v

VaReV2v

VaReV1v

1

0

2

0

0

0

⋅+=

⋅+=

⋅+=

⎟ ⎠

 ⎞⎜⎝ 

⎛  π⋅+⎟

 ⎠

 ⎞⎜⎝ 

⎛  π==

π

3

2sin j

3

2cosea 3

2 j

γ−⋅= j)1()2( eVV γ+⋅= j

)2()1( eVV

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 10/20

Monitoring, Energy and Drive Technologies10

Assumptions• Phase symmetric windings are assumed, as well as symmetry

of the whole machine structure.

• Only first harmonics (in space) of current coverage, fieldexcitation curve and flux density distribution are taken intoaccount.

• Waveform of all signals is not restricted.• Resistances and inductances are considered as constant

parameters.

• Eddy currents in solid iron as well as iron losses and friction

losses are neglected.• Skin effects are neglected.

• http://www.haumer.at/refimg/SpacePhasors.pdf

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 11/20

Monitoring, Energy and Drive Technologies11

AC Machines: Common Electrical Components• Stator plugs

• Stator resistances +leakage inductances

• Space phasor transformation

• Common parameters for:

 –  AIM squirrel cage –  AIM slip ring

 –  SM permanent magnet

 –  SM electrical excited –  SM reluctance

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 12/20

Monitoring, Energy and Drive Technologies12

AC Machines: Airgap• Calculates main flux from

stator + rotor current

• Common coordinate system:stator or rotor fixed

• Induced voltage: der(psi)

• Torque tau:

• omega =der(shaft.phi – support.phi);

• tau = - shaft.tau;tau = support.tau;

( )*

SSiImp2

mψ⋅⋅

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 13/20

Monitoring, Energy and Drive Technologies13

AIM Squirrel Cage• What’s missing:

squirrel cage

• resistance and inductanceof squirrel cage:w.r.t. stator

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 14/20

Monitoring, Energy and Drive Technologies14

AC Machines: Example 1• AIM with squirrel cage

• Starting from standstill

• Quadratic load torque

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 15/20

Monitoring, Energy and Drive Technologies15

SM Permanent Magnet• What’s missing:

excitation

• PM acts likeconstant excitation current

• turnsRatio * Ie:

determined byinduced stator voltageat nominal speedand no-load

• User can choose whetherdamper cage is present or not

• Different inductancesd-axis and q-axis

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 16/20

Monitoring, Energy and Drive Technologies16

AC Machines: Example 2• SM with electrical excitation

• Driven with constant speed

• Constant excitation

• Varying load angle

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 17/20

Monitoring, Energy and Drive Technologies17

AC Machines: Example 3• SM with permanent magnet

• Simple open-loop inverter

• Load torque step

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 18/20

Monitoring, Energy and Drive Technologies18

Transformers• Primary + secondary

resistance + leakage inductance

• No magnetizing current,no magnetizing losses

• Record TransformerData

helps to calculate parameters• All vector groups

 –  Yy

 –  Yd

 –  Yz

 –  Dy

 –  Dd

 –  Dz

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 19/20

Monitoring, Energy and Drive Technologies19

Transformers: Example 1• 12-pulse rectifier

• Transformer Dy1 + Dd0

• Significant reductionof harmonic currents

7/31/2019 Object-Oriented Modeling of Electrical Machines Part I

http://slidepdf.com/reader/full/object-oriented-modeling-of-electrical-machines-part-i 20/20

Monitoring, Energy and Drive Technologies20

Thank you for your attention.

mail: Anton.Haumer@arsenal.ac.at

web: www.arsenal.ac.at

Controlled / Inverter fed drives SmartElectricDrives Library