This paper proposes the multi-objective topology optimization of an Electrically Controlled Permanent-Magnet Synchronous Machine (ECPMSM) using the Level Set Method (LSM) and the Weighted Average Method (WAM) in order to reduce both the electromagnetic losses and the Cogging Torque (CT). Additionally, the back-electromotive force (the back-EMF) is approximately taken into account in the optimization process. For a shape sensitivity of a cost functional we elaborate the Continuum Design Sensitivity Analysis (CDSA). Our main contribution is to formulate and provide the solution to the nonlinear magnetoquasistatic interface problem. Simulation outcomes show that the applied method leads to a significant reduction of the losses and of the CT and, additionally, minimizes the higher harmonics in the back-EMF.
BachingerF., LangerU. and SchöberlJ., Numerical Analysis of Nonlinear Multiharmonic Eddy Current Problems, Numer. Math.100 (2005), 593-616.
2.
BertottiG., General properties of power losses in soft ferromagnetic materials, IEEE Trans. on Magn.24 (1988), 621-630.
3.
Di BarbaP., Multi-objective shape design in electricity and magnetism, Springer, 2010.
4.
Di BarbaP., BonisƚawskiM., PaƚkaR., PaplickiP. and WardachM., Design of Hybrid Excited Synchronous Machine for Electrical Vehicles, IEEE Trans. on Mag.51 (2015), 8107206.
5.
ChuW.Q. and ZhuZ.Q., On-Load Cogging Torque Calculation in Permanent Magnet Machines, IEEE Trans. on Magn.49 (2013), 2982-2989.
6.
CimrakI., Material and shape derivative method for quasi-linear elliptic systems with applications in inverse electromagnetic interface problems, SIAM Journal of Numerical Analysis50 (2012), 1086-1110.
7.
GierasF. and WingM., Permanent magnet motor technology, John Wiley & Sons Ltd., 2008.
8.
KimD., LowtherD. and SykulskiJ., Efficient force calculation based on continuum sensitivity analysis, IEEE Trans. on Magn.41 (2005), 1404-1407.
9.
KimD., ShipK. and SykulskiJ., Applying Continuum Design Sensitivity Analysis combined with standard EM software to shape optimization in magnetostatic problems, IEEE Trans. on Magn.40 (2004), 1156-1159.
10.
LimS., MinS. and HongJ.P., Low torque ripple rotor design of the interior permanent magnet motor using the multi-phase level-set and phase-field concept, IEEE Trans. on Magn.48 (2012), 907-909.
11.
MahdiA., YasserM. and Abdel-RadyI., Multi-objective shape optimization of segmented pole PM-synchronous machines with improved torque characteristics, IEEE Trans. on Magn.47 (2011), 795-804.
12.
MakniZ., BesbesM. and MarchandC., Multiphysics design methodology of Permanent-Magnet synchronous motors, IEEE Trans. on Vehic. Techn.56 (2007), 1524-1530.
13.
MarlerR.T. and AroraJ.S., Survey of multi-objective optimization methods for engineering, Structural and Multidisciplinary Optimization26 (2004), 369-395.
14.
MoehleN. and BoydS., Optimal Current Waveforms for Brushless Permanent Magnet Motors, International Journal of Control88 (2015), 1389-1399.
15.
OsherS.J. and SethianJ.A., Fronts Propagating With Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi formulations, Journal of Comput. Phys.79 (1988), 12-49.
16.
ParkI.H., LeeH.B., KwakI.G. and HahnS.Y., Design Sensitivity Analysis for nonlinear magnetostatic problems using finite element method, IEEE Trans. on Magn.28 (1992), 1533-1536.
17.
ParkI.H., LeeH.B., KwakI.G. and HahnS.Y., Design Sensitivity Analysis for Steady State Eddy Current Problems by Continuum Approach, IEEE Trans. on Magn.30 (1994), 3411-3414.
18.
PaplickiP., The new generation of electrical machines applied in hybrid drive car, Electrical Review86 (2010), 101-103.
19.
PaplickiP., Design optimization of the electrically controlled permanent magnet excited synchronous machine to improve flux control range, Electronika ir Electrotechnika20 (2014), 17-22.
20.
PutekP., PaplickiP., SlodičkaM., et al., Application of topological gradient and continuum sensitivity analysis to the multi-objective design optimization of a permanent-magnet excited synchronous machine, Electrical Review88 (2012), 256-260.
21.
PutekP., PaplickiP. and PaƚkaR., Low cogging torque design of Permanent-Magnet machine using modified multi-level set method with total variation regularization, IEEE Trans. on Magn.50 (2014), 657-660.
22.
PutekP., PaplickiP. and PaƚkaR., Topology Optimization of rotor poles in a Permanent Magnet machine using level set method and continuum design sensitivity analysis, COMPEL33 (2014), 711-728.
23.
PutekP., PaplickiP., SlodičkaM. and PaƚkaR., Minimization of cogging torque in permanent magnet machines using the topological gradient and adjoint sensitivity in multi-objective design, JAEM39 (2012), 933-940.
24.
PutekP., Mitigation of the cogging torque and loss minimization in a permanent magnet machine using shape and topology optimization, Engineering Computations33 (2016), 831-854.
25.
PutekP., PulchR., BartelA., ter MatenE.J.W., GüntherM. and GawrylczykK.M., Shape and topology optimization of a permanent-magnet machine under uncertainties, J. Math.Industry6 (2016), 1-19. https://mathematicsinindustry. springeropen.com/articles/10.1186/s13362-016-0032-6.
26.
PutekP., GauslingK., BartelA., GawrylczykK.M., ter MatenE.J.W., PulchR. and GüntherM., Robust topology optimization of a permanent magnet synchronous machine using multi-level set and stochastic collocation methods, In: Scientific Computing in Electrical Engineering SCEE 2014. Mathematics in Industry, BartelA., ClemensM., GüntherM., ter MatenE.J.W., eds, Vol. 23, Springer, Berlin (2016), pp. 233-242.
27.
RuohoS., DlalaE. and ArkkioA., Comparison of Demagnetization Models for Finite-Element Analysis of Permanent-Magnet Synchronous Machines, IEEE Trans. on Magn.43 (2007), 3964-3968.
28.
VeseL.A. and ChanT.F., A multiphase level set framework for image segmentation using the Mumford and Shah model, Int. J. Comput. Vis.50 (2002), 271-293.
29.
YamazakiK., FukushimaY. and SatoM., Loss Analysis of Permanent-Magnet Motors With Concentrated Windings-Variation of Magnet Eddy-Current Loss Due to Stator and Rotor Shapes, IEEE Trans. on Indus. Appli.45 (2009), 1334-1342.
