reduced basis finite element modelling of electrical machines with multi-conductor windings

Research Group of Electromechanics AaltoElectromechanics AaltoEM

Reduced Basis Finite Element Modelling ofElectrical Machines with Multi-ConductorWindingsAntti LehikoinenAalto University School of Electrical Engineeringantti.lehikoinen@aalto.fiwww.anttilehikoinen.fi

September 7, 2016

Research Group of Electromechanics AaltoElectromechanics AaltoEM

Reduced Basis FEM of WindingsICEM 2016

2/15

Wait - what?

Reduced Basis...=

Faster computation of windinglosses

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

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.

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.

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

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?

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.

Research Group of Electromechanics AaltoElectromechanics AaltoEM

Reduced Basis FEM of WindingsICEM 2016

9/15

Reduced-Basis Approach - ExampleResponse to coupling potential 1.

Research Group of Electromechanics AaltoElectromechanics AaltoEM

Reduced Basis FEM of WindingsICEM 2016

10/15

Reduced-Basis Approach - ExampleResponse to coupling potential 2.

Research Group of Electromechanics AaltoElectromechanics AaltoEM

Reduced Basis FEM of WindingsICEM 2016

11/15

Reduced-Basis Approach - ExampleCombined response.

= +

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

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

Research Group of Electromechanics AaltoElectromechanics AaltoEM

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

Research Group of Electromechanics AaltoElectromechanics AaltoEM

Reduced Basis FEM of WindingsICEM 2016

15/15

Epilogue

Thank you for your attention!

Questions?

Contact:antti.lehikoinen@aalto.fiwww.anttilehikoinen.fi