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Accelerating Electrical Machines Design1Konstantinos G. Papadopoulos and 1Christos Mademlis

2Alexandros M. Michaelides, 2Christopher P. Riley, 2Isabel Coenen, 2Nick Robertson1Aristotle University of Thessaloniki,

Department of Electrical and Computer Engineering, Thessaloniki, 54124, GreeceTel & Fax: +30 2310 996234, e-mail: mademlis@eng.auth.gr

2Vector Fields, 24 Bankside, Kidlington, Oxford OX5 1JE, UKTel: +44 (0)1865 370151, fax: +44 (0)1865 370277, e-mail: info@vectorfields.co.uk

Abstract- The paper describes a template-style front-end to ageneric electromagnetic modeling tool, for the analysis andoptimisation of Electrical Machines. A two and three-dimensional FEA model for a generator and motor can becreated in minutes, using templates with 'fill in the blanks'style screens. Accurate virtual prototypes can then be pro-duced to help engineers provide answers on the performanceof specific machine designs rapidly, and perform searching'what-if?' investigations to identify the design characteristicsof the perfect machine. Optimisation tools are also availablewithin the Environment, enabling engineers to find the 'best'solution automatically. Equally important is that the Envi-ronment is structured to allow creation and analysis of cus-tomised geometries, including special proprietary features.

I. INTRODUCTION

Many engineers designing rotating electrical machinescurrently employ analytic computer programs as thestarting point for new designs. Such software solveselectromagnetic equations for specific geometries, and istypically inexpensive and very quick to run. However,analytic solutions can compromise accuracy and, moreimportantly, are “closed”systems that cannot be modi-fied except by the originators. Analytic programs com-pute an average result for the overall geometry and onlyapproximating.

The alternative is a CAE tool employing, for example,Finite Element Analysis (FEA). These programs typi-cally offer flexible GUIs, allowing users to simulate anydesign concept with supreme precision and accuracy.Wider analysis options are also on offer; for example,FEA programs can accurately compute eddy currentsand naturally evaluate motional effects.

However, the time required for analysis using FEMsoftware, with its three step approach of pre-processing,solving and post-processing is unfavorable. While solu-tion times have steadily decreased over the years owingto steady technological advances in computers, signifi-cant effort is still required by the user at the pre-processing stage, that is, building the geometry and set-ting the right conditions for solution. Thus, severalworks have been presented for improving the design en-vironment enhancing the electromagnetic analysis [1],[2], adapting the dimensional model of the electromag-netic devices [3] and developing an object oriented

TABLE IOFFERED MACHINE TYPES

2d-version 3d-versionInduction Machine Induction MachineSynchronous Machine Synchronous MachineSwitched Reluctance Ma-chine

Switched Reluctance Ma-chine

Permanent Magnet DCMachine (rotor armature)

Permanent Magnet DC Ma-chine (rotor armature)

Brushless PM Machine(many variants)

Brushless PM Machine(many variants)

Axial Flux PM Machine

build up design environment [4] and with sensitivityanalysis [5].

The present approach aims to develop a design envi-ronment for two and three dimensional analysis of elec-tric motors and generators that could fulfill the needs ofboth the experienced and less experienced designer. Theuser provides the necessary geometric and electrical datafor the machine through friendly dialog windows. Thesoftware builds the resulting machine model, performsthe necessary solutions and provides simulation results atselected operating conditions. Variation of the given de-sign parameters allows different scenarios to be testedand through an iteration process the user could arrive atan optimal machine design. Alternatively, the parametricmodel can be used to drive an Optimisation tool withinthe Software, setting specific objective functions for thesoftware to achieve.

II. IMPLEMENTATION AND SIMULATION EXAMPLES

The Electrical Machines Environment is an add-on‘toolbox’ available with the established commercialpackages, Opera-2d and Opera-3d. Within the Environ-ment, a FEA model for a generator or motor can be cre-ated in minutes using templates with 'fill in the blanks'style screens. Templates have been designed for mostcommon electrical machine types, as listed in Table I.As with analytic computer programs, these templatesrepresent the most characteristic geometries used in ro-tating machinery.

One important feature of the Environment is that tem-plates are built using generic scripting and parameterisa-

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(a)

(b)

Fig. 1. Dialog window requesting information for: (a) the statorand (b) the rotor of the induction motor

Fig. 2. Induction motor 3d-model

tion techniques and the underlying code can easily bemodified by users, providing the freedom to create andanalyse customised geometries, including special pro-prietary features such as profiled stator teeth in SRMs orflux weakening features in PM machines.

Figs. 1(a) and (b) show one such example for the defi-nition of an Induction Motor. All lengths, angles andpoints positions are parameterised providing geometricflexibility. The program builds the machine geometrybased on these parameters (Fig. 2). If the user is satisfied

Fig. 3. Graph of torque versus rotor slip of the induction motor(typical simulation results)

with the geometry created, they may proceed to analysis.Analysis data, specific to each type of machine is subse-quently entered, as well as solution details, includingmesh density and the required resolution in the results.

The program proceeds with solutions to multiple casesand machine specific post-processing. One such exampleof results, the Induction Motor Torque Vs Speed curve isshown in Fig. 3. All output data is stored into namedfolders so that users are able to recover and further ex-amine results.

As an additional example, sequential dialog windowsfor the definition of the brushless PM synchronous ma-chine rotor are illustrated in Figs. 4 and 5, respectively.A sample result of the model solution is shown in Fig. 6representing the graph of static torque versus rotor angleon a 3-phase, 8-pole surface mount magnet PM synchro-nous motor.

(a)

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(b)

(c)

Fig. 4. Dialog window requesting information for: (a) the PMmotor type, (b) shape of the magnets and (c) dimensions for themagnets and retaining can of the rotor

Fig. 5 PM synchronous motor 3d-model (3-phase, 8-poles, sur-face mount magnet type PM synchronous machine)

Fig. 6. Graph of torque versus rotor angle of the PM synchronousmotor (simulation results)

III. MANIPULATING DESIGN CONSTRAINTS

The structure of the Environment is open to the user.The user is able to examine the logical organisation ofthe models and analysis settings and change or add spe-cific features. Addition of features can range from theaddition of minor geometrical features, winding ar-rangements, complete stator or rotor structures or alter-native analysis and post-processing requests

The design of the machine is subject to constraintswhich are activated during the model definition. Theseare geometrical constraints and are derived from thetechnical drawing. A set of algebraic expressions havebeen assigned for each design parameter so that the re-spective design constraint is implemented. When theinput value of a geometric parameter is out of the rangespecified to each parameter & model, the software re-sponds with an error message and prompts the user toalter the input value through a technical drawing. Theseconstraints simplify the desired parameterisation within amachine model and avoid the cost of aimless designingiterations. The use of variables and expressions in thedesign constraints allows changes to the geometric di-mensions to be made quickly.

Fig. 7 illustrates an error message informing the userfor insufficient room for stator tooth construction. Theuser is prompted to reduce the number of stator teeth orincrease the distance between the stator tooth and theorigin so that the stator tooth fits to the angle availablefor every tooth.

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Fig. 7. Dialog window informing the user of insufficient roomfor stator tooth construction.

Fig. 8. Dialog window informing the user of a pole & stator teethcombination that is not allowed in this example.

In the example of Fig. 8, the user asked for a perma-nent magnet synchronous motor consisting of 8 polesand 36 stator teeth. The software responded informingthat the current combination between poles and statorteeth cannot be constructed.

All constraints can be adjusted/altered by the user,who can also provide additional constraints pertinent tothe particular electric machine variant designed. In simi-lar fashion, post-processing can also be modified oradded-to matching the expectations of the user.

IV. OPTIMISATION

Once the user has produced a design using the Electri-cal Machines Environment they can chose to optimise itautomatically using the general purpose Opera Opti-miser. The optimisation process takes the original ge-ometry, adjusts it automatically, solves the model usingfinite elements, checks the results for improvements andcarefully selects a new geometry with a high likelihoodof further improvements to the design.

Fig. 9. Optimiser dialog window displaying the constraints tab.

During a simple interactive set-up procedure (Fig. 9)the user is able to select important input parameters fromthe design environment; these will be adjusted as theoptimiser creates new geometries in its search for aglobal minimum. A post-processing analysis with result-ing parameters can be created to allow the optimiser todefine the quality of the generated model.

Input parameters can be assigned upper and lower lim-its, to prevent the construction of unfeasible models andto define the size and shape of the input parameter space.However, due to the automatic geometry checkingwithin the Machines Environment the optimiser will notconstruct geometrically bad models. These models arenot simply ignored however; the optimiser realises theimplications upon this region of the input parameterspace.

Constraints can be imposed onto the optimisation bycreating functions of the input and output variables. Ana-lysed model geometries can then be seen to satisfy theconstraints in graphical form as a function of the interac-tion number. Again, the optimiser does not simply dis-card models which do not satisfy the constraints; it real-ises the implications on the input parameter space.

The optimiser begins by submitting a range of designsacross the input parameter space to the Opera batchprocessor, to gain a diffuse knowledge of the relation-ship with the objective space. The searching algorithmthen begins to home in on regions of interest where min-ima occur. However, exploratory models are also built insparse regions of input space to reduce the likelihood ofmissing other small but potentially deep minima. A bal-ance is therefore maintained between the two to preventeffort seeking tiny improvements on potentially falseminima.

The optimiser’s search algorithm analyses the stochas-tic properties of the input space and utilises a Kriging-assisted surrogate method to predict the shape of its solu-tion surface and thus determine the position of the nextmodel with the highest likelihood of improvement.

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Where multiple objective functions are specified, solu-tions are ranked according to their location betweenPareto surfaces in the objective space, [6],[7].

Fig. 10. The example synchronous machine before optimisation.

To demonstrate the optimisation of an electrical ma-chine a synchronous machine with thirty six stator teethand an asymmetric six-bar, four-pole rotor was con-structed in Opera-2D using the Electrical Machines En-vironment; shown in Fig 10. The objectives of the opti-misation were to minimise undesirable normalised Fou-rier harmonics of the radial magnetic field component ona 180O arc along the gap region. High order harmonicsare produced by both the rotor bars and the stator teeth,while lower order harmonics are generated by the rotorshape. Thus, the A3 and A17 harmonics were selectedas objectives to be minimised. The harmonics were nor-malised to the primary harmonic of the original model tomaintain consistency.

Fig. 11. The Evolution with iteration of: the two normalised ob-jective functions (left); the normalised Fourier harmonic con-straint, A5 < A3 (right).

Four critical input parameters were selected as optimi-sation variables: the asymmetric radius of curvature ofthe rotor end; the width of the rotor end; the stator toothwidth; and the inner stator coil width. Intelligent limitswere chosen on the input parameters to define the size ofthe four-dimensional input space. Constraints were also

imposed on numerous none-objective Fourier harmonicsso that they maintain their relative relationship to theobjective harmonics found in the original model. Thus,preventing their growth is a response to the minimisationof the objective harmonics. Fig. 11 shows the objectivefunctions and one of the constraints development as theoptimisation progresses.

Fig. 12. The location of the iteration inside the objective functionspace showing the nine first rank Pareto solutions.

The optimisation process converged to nine paretorank one solutions after 117 iterations; it took approxi-mately twelve hours on a relatively cheap dual processordesktop PC with 2GB of memory. The majority of thetime was spent, not in solving the finite element modelssince each of these took only a few minutes, but in theoptimiser’s Kriging algorithm between iterations; due tothe large four dimensional input space and subsequentmatrix inversions.

Fig. 13. The change in rotor and stator tooth geometry betweenthe original (left) and a Pareto solution (right).

The evolution of the objective functions and con-straints through the optimiser’s iterations can be dis-played graphically (Fig. 11), as can the location of mod-els within the input and objective parameter spaces. Fig12 displays the model locations inside objective spaceand distinguishes between feasible, unfeasible and

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Pareto solutions. The resulting geometric changes to themachine are displayed in Fig. 13.

Fig. 13. Radial B field component along a 180 degree arc insidethe gap region demonstrating the reduction in high order harmon-ics from the original design (top) and a parato solution (bottom).

Examination of the nine first rank Pareto solutionsshows that the seventeenth order harmonic has been re-duced to between a third and a half of its original valuedepending on the model. The constraints imposed onother harmonics resulted in them being reduced also.The third order harmonic was seen to be reduce by ap-proximately ten percent from its original value in mostof the solutions. This implies that the rotor input parame-ters selected do not provide sufficient control of thisharmonic and that an intelligent replacement should beselected; thus, allowing the optimisation process to berepeated. Fig. 13 reproduces the magnetic wave forminside the gap region and demonstrates the improvementof a Pareto solution over the original design due to itcontaining smaller high order Fourier harmonics.

The optimisation of this synchronous machine can beviewed as a demonstration of the type of route nowavailable to machine designers striving for the ultimatesystem design and that further examinations are requiredwith the aim of improving the purity of Fourier termsfurther.

V. CONCLUSION

This approach to design can deliver significant advan-tages in today's market environment. The accuracy ofFEA simulations, combined with the easy to interpretdelivery of results, gives designers the means to rapidlymake informed decisions - whether the need is simply tomake the most cost-effective solution for a given appli-cation, or to come up with something new. Currently,there's enormous pressure to improve energy efficiencyfor instance. FEA allows searching 'what-if?' investiga-tions to be performed rapidly, identifying the designcharacteristics of the right machine with great accuracy.Preliminary design studies can be performed in minutes.Optimisation tools are also available within the Envi-ronment, enabling engineers to find the 'best' solutionautomatically.

VI. REFERENCES

[1] C. F. Parker, J. K. Sykulski, S. C. Taylor, and C. S. Biddlecombe,“Parametric Environment for EM computer aided design,” IEEETrans. Magnetics, vol. 32, no. 3, pp. 1433-1437, May 1996.

[2] F. Deng and N.A. Demerdash, “Comprehensive salient-pole syn-chronous machine parametric design analysis using time-step finiteelement-state space modeling technique”, IEEE Trans Energy Con-version, vol. 13, no. 3, pp. 221-229, Sept. 1998.

[3] R. Rong and D.A. Lowther, “Adapting design using dimensionalmodels of electromagnetic devices”, IEEE Trans. Magnetics, vol. 32,no. 3, pp. 1437-1440, May 1996.

[4] M.B Norton, P.J. Leonard, “An object oriented approach to param-eterized electrical machine design”, IEEE Trans Magnetics, vol. 36,no. 4, pp. 1687-1691, July 2000.

[5] P.J. Weicker and D.A. Lowther, “A sensitivity-driven parametricelectromagnetic design environment”, IEEE Trans. Magnetics, vol.42, no. 4, pp. 1199-1202, April 2006.

[6] G.I. Hawe and J.K. Sykulski “A hybrid one-then-two stage algorithmfor computationally expensive electromagnetic design optimization.”COMPEL: The International Journal for Computation and Mathe-matics in Electrical and Electronic Engineering, 26 (2). pp. 236-246,(2007).

[7] G.I. Hawe and J.K. Sykulski, “Considerations of Accuracy and Un-certainty with Kriging Surrogate Models in Single-Objective Elec-tromagnetic Design Optimization.” IET Science, Measurement &Technology, 1 (1). pp. 37-47, (2007).