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Computational Problems in Simulation of Electrical Machines
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School of Science |
Doctoral thesis (article-based)
| Defence date: 2021-01-22
Electronic archive copy is available via Aalto Thesis Database.
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en
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41 + app. 67
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Aalto University publication series DOCTORAL DISSERTATIONS, 200/2020
Abstract
This thesis deals with computational challenges related to simulation of electrical machines. Electromagnetic fields and heat conduction in the machines are modeled by partial differential equations (PDEs), which are treated numerically by using the finite element (FE) method combined with appropriate time integration schemes. The uniting theme of this work is the prediction of iron losses in electrical machines.
Simulating energy losses and mechanical torque in an electrical machine involves computation of the energy in the system, and a time integration method may introduce numerical errors in such computations. Additional complications are caused by a moving subdomain in a machine, and the fact that the resulting discretized problem does not lead into a system of ordinary differential equations (ODEs), but to a differential-algebraic equation (DAE). All this has to be taken into account to construct proper time integration schemes, which is the first topic of thesis.
A core of an electrical machine often consists of a hysteretic ferromagnetic material. Conventionally, hysteresis is neglected in electromagnetic simulations, as its inclusion is complicated and computationally expensive. In this thesis, we propose and test numerically a method to incorporate the Jiles-Atherton magnetic hysteresis model into a FE simulation.
The last article approaches the iron loss prediction from an inverse problem perspective. The iron loss acts as an unknown heat source term in the heat equation, and the source is reconstructed from a limited number of temperature measurements conducted on and inside the machine. A computational framework and temperature sensor placement optimization is proposed and numerically tested in the thesis.
TƤssƤ vƤitƶskirjassa kƤsitellƤƤn sƤhkƶkoneiden mallintamiseen liittyviƤ laskennallisia haasteita. Koneissa esiintyviƤ sƤhkƶmagneettisia kenttiƤ ja lƤmmƶnjohtumista kuvataan osittaisdifferentiaaliyhtƤlƶillƤ (ODY), joita ratkaistaan numeerisesti elementtimenetelmƤn ja sopivan aikaintegrointimenetelmƤn avulla. TƤtƤ kirjaa yhdistƤvƤ teema on sƤhkƶkoneissa esiintyvien rautahƤviƶiden mallinnus.
SƤhkƶkoneen energiahƤviƶiden ja vƤƤntƶmomentin laskeminen edellyttƤƤ systeemin energian laskentaa numeerisesti. TƤmƤ liittyy kƤytettyihin aikaintegroimismenetelmiin, jotka voivat aiheuttaa numeerista virhettƤ energian laskennassa. Ongelman monimutkaisuutta lisƤƤ muuttuva laskenta-alue pyƶrivƤssƤ sƤhkƶkoneessa, ja se, ettƤ diskretisaatiosta seuraava ongelma ei ole tavallinen differentiaaliyhtƤlƶ, vaan differentiaalialgebrallinen yhtƤlƶ. NƤiden asioiden huomioonottaminen on yksi tƤmƤn kirjan aiheista.
SƤhkƶkoneen ydin koostuu usein hystereettisestƤ ferrogmagneettisesta materiaalista. Tavallisesti, tƤtƤ ei oteta simulaatioissa suoraan huomioon, koska se vaatii huomattavaa laskennallista lisƤtyƶtƤ. TƤssƤ tyƶssƤ ehdotamme ja testaamme numeerisesti uutta laskennallista menetelmƤƤ, jonka avulla Jiles-Atherton hystereesimallia voidaan kƤyttƤƤ elementtimenetelmƤƤn perustuvassa simulaatiossa.
Kirjan viimeisessƤ artikkelissa rautahƤviƶn mƤƤrittƤminen muotoillaan inversio-ongelmana. RautahƤviƶtƤ kƤsitellƤƤn lƤmpƶyhtƤlƶn tuntemattomana lƤhdeterminƤ, ja tƤmƤ lƤhde pyritƤƤn rekonstruoimaan rajallisesta mƤƤrƤstƤ lƤmpƶtilamittauksia koneen pinnalla ja sen sisƤllƤ. Inversio-ongelman ratkaisuun ja lƤmpƶtilamittauksien sijainnin optimointiin annetaan laskennalliset puitteet, ja menetelmiƤ testataan numeerisesti.
Description
Supervising professor
Hannukainen, Antti, Asst. Prof., Aalto University, Department of Mathematics and Systems Analysis, FinlandOther note
Parts
- [Publication 1]: Paavo Rasilo, Lauri Perkkiƶ, Antti Hannukainen, Bishal Silwal, Timo Eirola, Antero Arkkio. Instantaneous Power Balance in Finite-Element Simulation of Electrical Machines. IEEE Transactions on Magnetics, Vol. 50, May 2014.
DOI: 10.1109/TMAG.2013.2294945 View at publisher
- [Publication 2]: Lauri Perkkiƶ, Paavo Rasilo, Bishal Silwal, Antti Hannukainen, Antero Arkkio, Timo Eirola. Energy-Preserving Methods and Torque Computation From Energy Balance in Electrical Machine Simulations. IEEE Transactions on Magnetics, Vol. 52, August 2016.
DOI: 10.1109/TMAG.2016.2537263 View at publisher
- [Publication 3]: Lauri Perkkiƶ, Brijesh Upadhaya, Antti Hannukainen, Paavo Rasilo. Stable Adaptive Method to Solve FEM Coupled With JilesāAtherton Hysteresis Model. IEEE Transactions on Magnetics, Vol. 54, February 2018.
DOI: 10.1109/TMAG.2017.2782214 View at publisher
- [Publication 4]: Antti Hannukainen, Nuutti Hyvƶnen, Lauri Perkkiƶ. Inverse Heat Source Problem and Experimental Design for Determining Iron Loss Distribution.Submitted to SIAM Journal on Scientiļ¬c Computing, April 6th 2020