7/31/2019 Object-Oriented Modeling of Electrical Machines Part I
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Object-oriented modeling of electrical machines:
Modelica.Electrical.Machines
Anton Haumer
arsenal research, Vienna
03.03.2008
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Contents
• Common Mechanical Components
• DC Machines• Induction Machines
• Asynchronous Induction Machines
• Synchronous Induction Machines
• Transformers
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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
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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
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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;
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Permanent Magnet DC Machine• What’s missing:
excitation
• PM acts likeconstant excitation current
• turnsRatio * Ie:
determined byinduced armature voltageat nominal speedand no-load
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DC Machines: Example 1• Starting from standstill,
applying an armature voltage ramp
• Followed by a torque step
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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
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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
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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
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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
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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⋅⋅
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AIM Squirrel Cage• What’s missing:
squirrel cage
• resistance and inductanceof squirrel cage:w.r.t. stator
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AC Machines: Example 1• AIM with squirrel cage
• Starting from standstill
• Quadratic load torque
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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
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AC Machines: Example 2• SM with electrical excitation
• Driven with constant speed
• Constant excitation
• Varying load angle
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AC Machines: Example 3• SM with permanent magnet
• Simple open-loop inverter
• Load torque step
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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
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Transformers: Example 1• 12-pulse rectifier
• Transformer Dy1 + Dd0
• Significant reductionof harmonic currents
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Thank you for your attention.
mail: [email protected]
web: www.arsenal.ac.at
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