reduced basis finite element modelling of electrical machines with multi-conductor windings
TRANSCRIPT
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis Finite Element Modelling ofElectrical Machines with Multi-ConductorWindingsAntti LehikoinenAalto University School of Electrical [email protected]
September 7, 2016
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
2/15
Wait - what?
Reduced Basis...=
Faster computation of windinglosses
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
3/15
Problem Background
Consider an electrical machine:I Accurate computation of winding losses needed
I Skin effectI Proximity effectI Circulating currents
⇒ Numerical finite element (FE) analysis requiredI Extremely time-consuming
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
4/15
Why It’s Slow
I Dense mesh requiredaround the conductors
I Coarser sufficientelsewhere
I Huge number of DoFsI Long computation
times
Figure: Slot segment.
Figure: Winding mesh.
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
5/15
Problem Geometry
What might help?I Slots typically identicalI Interesting things happen
inside slotsI Boring boundary
I Linear behaviour
Figure: Phase belt.
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
6/15
Reduced Basis ApproachIDEA: only analyze one slot first
1. Pre-compute a set of solutions corresponding to different(Dirichlet) boundary conditions
2. StoreI Boundary conditionsI Solutions
3. Use solutions as shape functions in full-machine analysis
Sslot ← AT Sslot A
Pre-computed solutions
I Enforce continuity at slot boundary
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
7/15
Reduced Basis Approach
Why this works?I Solution uniquely defined by boundary valuesI Boundary values a linear combination of pre-computed
ones?⇒ entire solution is a linear combination
"How many" boundary conditions are there?
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
8/15
Reduced Basis Approach - BoundaryBoundary potential usually smooth→ representable by a fewdegrees-of-freedom
1. Define a few coupling potentials on the boundary atcoupling nodes
2. Interpolate in between
Figure: Coupling nodes.
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
9/15
Reduced-Basis Approach - ExampleResponse to coupling potential 1.
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
10/15
Reduced-Basis Approach - ExampleResponse to coupling potential 2.
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
11/15
Reduced-Basis Approach - ExampleCombined response.
= +
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
12/15
Simulation Example
A phase belt simulated:I High-speed machineI Linear harmonic analysisI 6000 HzI Finely meshed reference
solution
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Research Group of Electromechanics AaltoElectromechanics AaltoEM
Reduced Basis FEM of WindingsICEM 2016
13/15
Simulation Example
Computation times:I Reduced basis: 14 seconds on initialization + 0.15
seconds for the machine simulationI Reference: 8 minutes
Table: Error in total losses.
No. of coupling nodes P error (%)60 0.40294 0.315
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Reduced Basis FEM of WindingsICEM 2016
14/15
Conclusion
I Reduced basis method proposed for numerical windinganalysis
I Speed and accuracy demonstratedI Further work
1. Extension to time-domain2. Nonlinear problems
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Reduced Basis FEM of WindingsICEM 2016
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Epilogue
Thank you for your attention!
Questions?
Contact:[email protected]