# A finite element based optimisation tool for electrical machines

Gerber, Stiaan (2011-03)

Thesis (MSc (Electrical and Electronic Engineering))--University of Stellenbosch, 2011.

Thesis

ENGLISH ABSTRACT: Knowledge of the magnetic fields in the domain of electrical machines is required in order to model machines accurately. It is difficult to solve these fields analytically because of the complex geometries of electrical machines and the non-linear characteristics of the materials used to build them. Thus, finite element analysis, which can be used to solve the magnetic field accurately, plays an important part in the design of electrical machines. When designing electrical machines, the task of finding an optimal design is not simple because the performance of the machine has a non-linear dependence on many variables. In these circumstances, numerical optimisation using finite element analysis is the most powerful method of finding optimal designs. In this thesis, the work of improving an existing finite element simulation package, formerly known as the Cambridge package among its users, and the use of this package in the optimisation of electrical machine designs, is presented. The work involved restructuring the original package, expanding its capabilities and coupling it to numerical optimisers. The developed finite element package has been dubbed SEMFEM: the Stellenbosch Electrical Machines Finite Element Method. The Cambridge package employed the air-gap element method, first proposed by Razek et. al. [2], to solve the magnetic field for different positions of the moving component in a time-stepped finite element simulation. Because many new machine topologies have more than one air-gap, the ability to model machines with multiple air-gaps is important. The Cambridge package was not capable of this, but during the course of this work, the ability to model machines with multiple air-gaps using the air-gap element method was implemented. Many linear electrical machines have tubular, axisymmetric topologies. The functionality to simulate these machines was newly implemented because the original program was not capable of analysing these machines. Amongst other things, this involved the derivation of the coefficients of an axisymmetric air-gap element’s stiffness matrix. This derivation, along with the original air-gap element derived by Razek et. al. [2] and the extension of the method to the Cartesian coordinate system by Wang et. al. [29, 30], completes the derivation of all two-dimensional air-gap elements. In order to speed the numerical optimisation process, which is computationally expensive, parallelisation was introduced in two areas: at the level of the finite element simulation and at the level of the optimisation program. The final product is a more powerful, more usable package, geared for the optimisation of electrical machines.

AFRIKAANSE OPSOMMING: Kennis van die magnetiese velde in die gebied van elektriese masjiene word benodig om masjiene akkuraat te modelleer. Dit is moeilik om hierdie velde analities op te los as gevolg die komplekse geometrieë van elektriese masjiene en die nie-lineêre karakteristieke van die materiale wat gebruik word om hulle te bou. Dus speel eindige element analise ’n belangrike rol in die ontwerp van elektriese masjiene omdat dit gebruik kan word om die magnetiese veld akkuraat te bepaal. Wanneer elektriese masjiene ontwerp word, is dit nie ’n eenvoudige taak om ’n optimale ontwerp te vind nie omdat die werkverrigting van die masjien nie-lineêr afhanklik is van baie veranderlikes. Onder hierdie omstandighede is numeriese optimering, tesame met eindige element analise, die kragtigste metode om optimale ontwerpe te vind. In hierdie tesis word die verbetering van ’n bestaande eindige element simulasie pakket, wat onder gebruikers van die pakket as die Cambridge pakket bekend staan, en die gebruik van hierdie pakket vir die optimering van elektriese masjiene, voorgelê. Die werk het die herstrukturering van die oorspronklike pakket, die uitbreiding van die pakket se vermoëns en die koppeling van die pakket aan numeriese optimeerders behels. Die ontwikkelde eindige element pakket word SEMFEM genoem: die Stellenbosch Elektriese Masjiene Finite Element Method. Die Cambridge pakket het van die lugspleet element metode, soos oorspronlik deur Razek et. al. [2] voorgestel, gebruik gemaak om die magnetiese veld vir verskillende posisies van die bewegende komponent in ’n tyd-stapsgewyse eindige element simulasie op te los. Omdat baie nuwe masjien topologieë meer as een lugspleet het, is die vermoë om masjiene met meer as een lugspleet te kan modelleer belangrik. Die Cambridge pakket was nie hier toe in staat nie, maar die vermoë om masjiene met meervoudige lugsplete te modelleer is gedurende hierdie werk geïmplementeer. Baie lineêre masjiene het tubulêre, assimmetriese topologieë. Die funksionaliteit om hierdie masjiene te simuleer is nuut geïmplementeer omdat die oorspronlike program nie in staat was om hierdie masjiene te analiseer nie. Dit het onder andere behels dat die koeffisiënte van ’n assimmetriese lugspleetelement se styfheidsmatriks afgelei moes word. Hierdie afleiding, tesame met die oorspronlike lugspleetelement afgelei deur Razek et. al. [2] en die uitbreiding na die Cartesiese koördinaatstelsel deur Wang et. al. [29, 30], voltooi die afleiding van alle twee-dimensionele lugspleet elemente. Om die numeriese optimeringsproses, wat tipies tydsgewys duur is, te versnel, is parallellisering op twee vlakke ingebring: op die vlak van die eindige element simulasie en op die vlak van die optimeringsprogram. Die finale produk is ’n kragtiger, meer bruikbare pakket, goed aangepas vir die optimering van elektriese masjiene.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/6635