advanced parametric environment for electrical machines design optimization

Proceedings of the 2008 International Conference on Electrical Machines Paper ID1133

978-1-4244-1736-0/08/$25.00 ©2008 IEEE 1

Advanced Parametric Environment for ElectricalMachines Design Optimization

1Konstantinos G. Papadopoulos and 1Christos Mademlis2Alexandros M. Michaelides, 2Christopher P. Riley, 2 Nick Robertson and 2Isabel Coenen

1Aristotle University of Thessaloniki,Department of Electrical and Computer Engineering, Thessaloniki, 54124, Greece

Tel & Fax: +30 2310 996234, e-mail: [email protected]

2Vector Fields, 24 Bankside, Kidlington, Oxford OX5 1JE, UKTel: +44 (0)1865 370151, fax: +44 (0)1865 370277, e-mail: [email protected]

Abstract- The paper describes a template-style front-end to ageneric electromagnetic modeling tool, for the analysis and opti-mization of Electrical Machines. A two and three-dimensionalFEA model for a generator and motor can be created in minutes,using templates with 'fill in the blanks' style screens. Accuratevirtual prototypes can then be produced to help engineers provideanswers on the performance of specific machine designs rapidly,and perform searching 'what-if?' investigations to identify thedesign characteristics of the perfect machine. Optimization toolsare also available within the Environment, enabling engineers tofind the 'best' solution automatically. Equally important is thatthe Environment is structured to allow creation and analysis ofcustomised geometries, including special proprietary features.

I. INTRODUCTION

Many engineers designing rotating electrical machines cur-rently employ analytic computer programs as the starting pointfor new designs. Such software solves electromagnetic equa-tions for specific geometries, and is typically inexpensive andvery quick to run. However, analytic solutions can compro-mise accuracy and, more importantly, are “closed”systems thatcannot be modified except by the originators. Analytic pro-grams compute an average result for the overall geometry andonly approximating.

The alternative is a CAE tool employing, for example, FiniteElement Analysis (FEA). These programs typically offer flexi-ble GUIs, allowing users to simulate any design concept withsupreme precision and accuracy. Wider analysis options arealso on offer; for example, FEA programs can accurately com-pute eddy currents and naturally evaluate motional effects.

However, the time required for analysis using FEM soft-ware, with its three step approach of pre-processing, solvingand post-processing is unfavorable. While solution times havesteadily decreased over the years owing to steady technologicaladvances in computers, significant effort is still required by theuser at the pre-processing stage, that is, building the geometryand setting the right conditions for solution. Thus, severalworks have been presented for improving the design environ-ment enhancing the electromagnetic analysis [1], [2], adaptingthe dimensional model of the electromagnetic devices [3] and

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

developing an object oriented build up design environment [4]and with sensitivity analysis [5].

The present approach aims to develop a design environmentfor two and three dimensional analysis of electric motors andgenerators that could fulfill the needs of both the experiencedand less experienced designer. The user provides the necessarygeometric and electrical data for the machine through friendlydialog windows. The software builds the resulting machinemodel, performs the necessary solutions and provides simula-tion results at selected operating conditions. Variation of thegiven design parameters allows different scenarios to be testedand through an iteration process the user could arrive at anoptimal machine design. Alternatively, the parametric modelcan be used to drive an optimization tool within the software,setting specific objective functions for the software to achieve.

II. IMPLEMENTATION AND SIMULATION EXAMPLES

The Electrical Machines Environment is an add-on ‘toolbox’available with the established commercial packages, Opera-2dand Opera-3d. Within the Environment, a FEA model for agenerator or motor can be created in minutes using templateswith 'fill in the blanks' style screens. Templates have been de-signed for most common electrical machine types, as listed inTable I. As with analytic computer programs, these templatesrepresent the most characteristic geometries used in rotating

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Proceedings of the 2008 International Conference on Electrical Machines

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(a)

(b)

Fig. 1. Dialog window requesting information for: (a) the stator and (b) therotor of the SRM

Fig. 2. 4-phase, 8/6 SRM 3d-model

machinery.One important feature of the Environment is that templates

are built using generic scripting and parameterisation tech-niques and the underlying code can easily be modified by us-ers, providing the freedom to create and analyse customizedgeometries, including special proprietary features such as pro-filed stator teeth in SRMs or flux weakening features in PMmachines.

Fig. 3. Graph of electromagnetic torque versus rotor angle of a 4-phase, 8/6SRM (typical simulation results)

Figs. 1(a) and (b) show one such example for the definitionof a 4-pahse, 8/6 Switched Reluctance Motor (SRM). All ma-chine geometry information including teeth numbers, lengths,and angles are parameterised providing geometric flexibility.The program builds the machine geometry based on these pa-rameters (Fig. 2). If the user is satisfied with the geometry cre-ated, they may proceed to analysis. Analysis data, specific toeach type of machine is subsequently entered, as well as solu-tion details, including mesh density and the required resolutionin the results.

The program proceeds with solutions to multiple cases andmachine specific post-processing. One such example of results,the SRM electromagnetic torque Vs mechanical rotor anglecurve is shown in Fig. 3. All output data is stored into namedfolders so that users are able to recover and further examineresults.

As an additional example, sequential dialog windows for thedefinition of the brushless PM synchronous machine rotor areillustrated in Figs. 4 and 5, respectively. A sample result of themodel solution is shown in Fig. 6 representing the graph ofstatic torque versus rotor angle on a 3-phase, 8-pole surfacemount magnet PM synchronous motor.

(a)


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(b)

(c)

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

Fig. 5 PM synchronous motor 3d-model (3-phase, 8-poles, surface mountmagnet type PM synchronous machine)

III. MANIPULATING DESIGN CONSTRAINTS

The structure of the Environment is open to the user. Theuser is able to examine the logical organisation of the models

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

Fig. 7. Dialog window informing the user of insufficient room for stator toothconstruction.

and analysis settings and change or add specific features. Addi-tion of features can range from the addition of minor geometri-cal features, winding arrangements, complete stator or rotorstructures or alternative analysis and post-processing requests

The design of the machine is subject to constraints which areactivated during the model definition. These are geometricalconstraints and are derived from the technical drawing. A setof algebraic expressions have been assigned for each designparameter so that the respective design constraint is imple-mented. When the input value of a geometric parameter is outof the range specified to each parameter & model, the softwareresponds with an error message and prompts the user to alterthe input value through a technical drawing. Such constraintssimplify the desired parameterization within a machine modeland avoid the cost of aimless designing iterations. The use ofvariables and expressions in the design constraints allowschanges to the geometric dimensions to be made quickly.


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All constraints can be adjusted/altered by the user, who canalso provide additional constraints pertinent to the particularelectric machine variant designed. In similar fashion, post-processing can also be modified or added-to matching the ex-pectations of the user.

IV. OPTIMISATION

Once the user has produced a design using the ElectricalMachines Environment they can chose to optimise it automati-cally using the general purpose Opera Optimiser. The optimi-sation process takes the original geometry, adjusts it automati-cally, solves the model using finite elements, checks the resultsfor improvements and carefully selects a new geometry with ahigh likelihood of further improvements to the design.

During a simple interactive set-up procedure (Fig. 8) the useris able to select important input parameters from the design

Fig. 8. Optimiser dialog window displaying the constraints tab.

environment; these will be adjusted as the optimiser createsnew geometries in its search for a global minimum. A post-processing analysis with resulting parameters can be created toallow the optimiser to define the quality of the generatedmodel.

Input parameters can be assigned upper and lower limits, toprevent the construction of infeasible models and to define thesize and shape of the input parameter space. However, due tothe automatic geometry checking within the Machines Envi-ronment the optimiser will not construct geometrically badmodels. These models are not simply ignored however; theoptimiser realises the implications upon this region of the inputparameter space.

Constraints can be imposed onto the optimisation by creatingfunctions of the input and output variables. Analysed modelgeometries can then be seen to satisfy the constraints in graphi-cal form as a function of the interaction number. Again, theoptimiser does not simply discard models which do not satisfythe constraints; it realises the implications on the input parame-

ter space.The optimiser begins by submitting a range of designs across

the input parameter space to the Opera batch processor, to gaina diffuse knowledge of the relationship with the objectivespace. The searching algorithm then begins to home in on re-gions of interest where minima occurs. However, exploratorymodels are also built in sparse regions of input space to reducethe likelihood of missing other small but potentially deep min-ima. A balance is therefore maintained between the two to pre-vent effort seeking tiny improvements on potentially false min-ima (see sample objective function evolution and Pareto spaceof Figs. 9 and 10).

The optimiser’s search algorithm analyses the stochasticproperties of the input space and utilises a Kriging-assistedsurrogate method to predict the shape of its solution surfaceand thus determine the position of the next model with thehighest likelihood of improvement. Where multiple objectivefunctions are specified, solutions are ranked according to theirlocation between Pareto surfaces in the objective space, [6],[7].

Fig. 9. The Evolution with iteration of: the two normalised objective func-tions (left); the normalised Fourier harmonic constraint, A5 < A3 (right).

Fig. 10. The location of the iteration inside the objective function space show-ing the nine first rank Pareto solutions.


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Synchronous machine example in OPERA-2d

In order to demonstrate the optimisation of an electrical ma-chine, a synchronous machine with thirty six stator teeth andan asymmetric six-bar, four-pole rotor (as shown in Fig. 11)was constructed in Opera-2D using the Electrical MachinesEnvironment.

Fig. 11. The example synchronous machine before optimisation.

The objectives of the optimisation were to minimise unde-sirable normalised Fourier harmonics of the radial magneticfield component on a 1800 arc along the gap region. High orderharmonics are produced by both the rotor bars and the statorteeth, while lower order harmonics are generated by the rotorshape. Thus, the A3 and A17 harmonics were selected as ob-jectives to be minimised. The harmonics were normalised tothe primary harmonic of the original model to maintain consis-tency.

Four critical input parameters were selected as optimisationvariables: the asymmetric radius of curvature of the rotor end;the width of the rotor end; the stator tooth width; and the innerstator coil width. Intelligent limits were chosen on the inputparameters to define the size of the four-dimensional inputspace. Constraints were also imposed on numerous none-objective Fourier harmonics so that they maintain their relative

Fig. 12. The change in rotor and stator tooth geometry between the original(left) and a Pareto solution (right).

Fig. 13. Radial B field component along a 180 degree arc inside the gap re-gion demonstrating the reduction in high order harmonics from the originaldesign (top) and a Pareto solution (bottom).

relationship to the objective harmonics found in the originalmodel. Thus, preventing their growth is a response to theminimisation of the objective harmonics. Fig. 9 shows the ob-jective functions and one of the constraints development as theoptimisation progresses.

The optimisation process converged to nine Pareto rank onesolutions after 117 iterations; it took approximately twelvehours on a relatively cheap dual processor desktop PC with2GB of memory. The majority of the time was spent, not insolving the finite element models since each of these took onlya few minutes, but in the optimiser’s Kriging algorithm be-tween iterations; due to the large four dimensional input spaceand subsequent matrix inversions.

The evolution of the objective functions and constraintsthrough the optimiser’s iterations can be displayed graphically(Fig. 9), as can the location of models within the input and ob-jective parameter spaces. Fig 10 displays the model locationsinside objective space and distinguishes between feasible, un-


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feasible and Pareto solutions. The resulting geometric changesto the machine are displayed in Fig. 12.

Examination of the nine first rank Pareto solutions showsthat the seventeenth order harmonic has been reduced to be-tween a third and a half of its original value depending on themodel. The constraints imposed on other harmonics resulted inthem being reduced also. The third order harmonic was seen tobe reduce by approximately ten percent from its original valuein most of the solutions. This implies that the rotor input pa-rameters selected do not provide sufficient control of this har-monic and that an intelligent replacement should be selected;thus, allowing the optimisation process to be repeated. Fig. 13reproduces the magnetic wave form inside the gap region anddemonstrates the improvement of a Pareto solution over theoriginal design due to it containing smaller high order Fourierharmonics.

The optimisation of this synchronous machine can be viewedas a demonstration of the type of route now available to ma-chine designers striving for the ultimate system design and thatfurther examinations are required with the aim of improvingthe purity of Fourier terms further.

Switched Reluctance machine example in OPERA-3d

In this example, the width of the stator and rotor teeth of a 1-phase 4/4 switched reluctance machine, shown in Fig. 14,were optimized to provide a sinusoidal change of stator fluxlinkage against angle, a feature that has been associated withsmoother torque variation and lower acoustic noise.

Fig. 14. The 1-phase 4/4 Switched reluctance motor topology

In examining this problem, the Optimiser needed to operateon a series of (instead of a single) OPERA-3d solutions. Fluxlinkage was measured at ten rotor positions

B(θ) , θ = 0º,5º,10º,… ,45ºFlux values are normalized, so they vary between 0 and 1. A

‘goodness of fit parameter, R2 was then constructed, whichcompared the normalized B(θ) to the standard cos(θ) function.R2 was therefore the objective function to be maximized, withan ideal value of 1. Fig. 15 illustrates the end result of the Op-timisation, always bearing in mind that the Optimiser wasworking within the user-specified variable constraints.

Fig. 15. Optimisation Results (initial R2 = 0.894, final R2 = 0.981)

V. CONCLUSIONS

This approach to design can deliver significant advantages intoday's market environment. The accuracy of FEA simulations,combined with the easy to interpret delivery of results, givesdesigners the means to rapidly make informed decisions -whether the need is simply to make the most cost-effectivesolution for a given application, or to come up with somethingnew. Currently, there's enormous pressure to improve energyefficiency for instance. FEA allows searching 'what-if?' inves-tigations to be performed rapidly, identifying the design char-acteristics of the right machine with great accuracy. Prelimi-nary design studies can be performed in minutes. Optimisationtools are also available within the Environment, enabling engi-neers to find the 'best' solution automatically.

VI. REFERENCES

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

[2] F. Deng and N.A. Demerdash, “Comprehensive salient-pole synchronousmachine parametric design analysis using time-step finite element-statespace modeling technique”, IEEE Trans Energy Conversion, vol. 13, no.3, pp. 221-229, Sept. 1998.

[3] R. Rong and D.A. Lowther, “Adapting design using dimensional modelsof 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 parameter-ized 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 parametric elec-tromagnetic 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 algorithm forcomputationally expensive electromagnetic design optimization.”COM-PEL: The International Journal for Computation and Mathematics inElectrical and Electronic Engineering, 26 (2). pp. 236-246, (2007).

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

advanced parametric environment for electrical machines design optimization

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