IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014 8100306

Design Optimization of IPMSM for 42 V IntegratedStarter Alternator Using Lumped Parameter

Model and Genetic AlgorithmsHooshang Mirahki, Mehdi Moallem, and Sayyed Abbas Rahimi

Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran

In this paper, the design optimization of an interior permanent magnet synchronous machine is presented using lumped parametermodel and genetic algorithms for 42 V integrated starter alternator application. The aim of the optimization is to increase startingtorque while keeping torque ripple below 10% and increasing power output in generating mode at high speed and reducing thepermanent magnet weight. A finite-element method is used to verify and compare the optimized machine characteristics.

Index Terms— Genetic algorithms (GAs), integrated starter alternator (ISA), interior permanent magnet synchronous machine(IPMSM), lumped parameter model (LPM).

I. INTRODUCTION

TO COPE with the increase of electric power demand incars, the automotive industry has substituted the 14 V

voltage systems with 42 V systems [1], [2]. This new voltagelevel provides engineers with a good opportunity for integrat-ing the automotive starter and alternator into a new single pieceof equipment, namely an integrated starter alternator (ISA) [3].

Among the existing electrical machines, the interiorpermanent magnet synchronous machine (IPMSM) is anattractive candidate for automotive applications such as ISA.This is mainly due to its high efficiency, brushless design,high torque and power density, and wide constant-powerspeed range [1], [2].

Since finite-element analysis is highly time consuming formachine design and optimization process [4], researchers havealways been looking for analytical methods that could be usedfor the purpose of machine optimization. The existing methodssuch as Laplacian or quasi-Poissonian methods solve the fieldequations for surface permanent magnet (SPM) machine [5] orinset PM machine [6] directly and use the conformal mappingfor considering the effects of slots into consideration [7].Anyhow, because of the leakage flux, saturation in differentparts, and the complicated structure of the IPMSM, it is notpossible to use this analytical method for the optimizationpurposes [5], [8]. The magnetic equivalent circuits methodthat is used for calculation of no- and full-load field ininductions machines [9], switched reluctance [10], salient-polesynchronous machines [11], SPM [12], and even IPMSM [13]is not an appropriate approach for optimization purposes dueto its complication and being time consuming. The saturatinglumped parameter model (LPM) is one of the most efficientmethods for optimization of IPM machines especially in high-load conditions [14], [15] since it can consider machine

Manuscript received May 25, 2013; revised August 7, 2013 and October2, 2013; accepted October 3, 2013. Date of publication October 10, 2013;date of current version March 14, 2014. Corresponding author: H. Mirahki(e-mail: h.mirahky@yahoo.com).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2013.2285358

complex geometry and also the saturation in stator and rotorcores [16]. Due to its fast and accurate results in calculatingmachine parameters, LPM could be used in an optimizationprocess that needs thousands of iterations for finding an opti-mal solution. In this method, three different lumped parametermodels are used for calculation of power and torque [17].First, an LPM is used for calculation of linkage flux inPM [14], [16]. For simplicity, the reluctances of the rotorand stator yokes could be easily ignored compared with thereluctance of the air gap [4], [5], [8], [16], [18]. Two otherlumped parameter models could be used for calculation ofD- and Q-axis inductances. Since the effective air gap inD-axis is large [19], the reluctances of the rotor and statoryokes could be easily ignored. Carter coefficient could be usedfor considering the effects of slots [5], [8].

Evolutionary algorithms have been widely used in the lastdecade for solving optimization problems. According to theno free lunch theorem, evolutionary algorithms may showdifferent peculiarity answers in different problems [20], [21].To have a better perspective in choosing the type of opti-mization algorithm, we can divide the problems into twogeneral categories according to the dimension of the solutionspace, namely high- and low-dimension solution spaces [21].The optimization problem in this paper is of high-dimensionsolution space type. Therefore, according to [21], geneticalgorithms (GAs) yield better results than other evolutionaryalgorithms. The GAs are quite popular for solving nonlin-ear, nondifferentiable models due to their high efficiency infinding global or near global optimum point of objectivefunctions [22]. The GAs have been used for optimization of thestructure of many different machines. In some cases, a combi-nation of the finite-element and the evolutionary algorithmshas been used [23], [24]. Using the finite-element method(FEM) in the process of optimization increases the time ofthe optimization process and may lead to inappropriate results.Combining the GA with an analytical method could reduce theoptimization time significantly and improvethe results [15].Therefore, in this paper, we have used the combined GA andlumped parameter method (LPM). Because of the inabilityof the LPM in calculation of transients, the final result of

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8100306 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014

each optimization process is simulated with the FEM for thepurpose of reducing the torque ripple. As a result, with propercombination of these two methods (finite element and lumpedparameters), the transients are also considered in addition tothe reduction in the optimization time.

In this paper, an objective function is proposed for optimiza-tion of a three-layer IPM machine’s main parameters for use in42 V ISA applications. The GA is used to solve the optimiza-tion problem. In addition to fulfilling the standards proposedby the MIT Consortium, we have succeeded in increasing thestarting torque and the power in generating mode at highspeed (6000 r/min) beyond the measures proposed by theConsortium [25].

II. ISA PERFORMANCE CRITERIA

The ISA is connected directly to cranking shaft as a starterand generator. The MIT/Industry Consortium on AdvancedAutomotive Electrical/Electronic Components has proposed aset of performance criteria on voltage [25], power, and startingtorque that are considered as the groundwork for machinedesign and optimization in this paper. The Consortium sug-gestions are as follows.

1) DC link voltage connected to ISA is 42 V. Therefore,the ISA should be able to produce a constant voltage of19.3 rms per phase in a wide range of speed (from 600to 6000 r/min) in the generation mode.

2) For the purpose of direct connection, the starting torqueof IPMSM should not fall below 150 N·m.

3) The generated power at the speed of 6000 r/min shouldnot be less than 6 kW.

In this paper, due to limitations of converter and magnetmaterial (ferrite magnet), the maximum steady-state postfaultvoltage in generator mode is selected to be 55 VDC. Inaddition, since the ISA is directly connected to cranking shaft,(no flywheel) the torque ripple should be low, and thereforewe selected the torque ripple to be less than 10%.

III. OBJECTIVE FUNCTION

The objective function is targeted at increasing the power ingenerator mode at 6000 r/min, increasing the starting torqueand also decreasing the torque ripple. Torque ripple is definedas the ratio of peak-peak torque to the average torque instarting mode. The magnet weight used in our preliminarydesign is half of the amount used in [17]; therefore, it is notconsidered as an optimization variable. The proposed objectivefunction is as follows:

F(z) = λ1150(N · m) − Tem

150(N · m)+ λ2

6000(w) − Peg

6000(w)(1)

where z is the vector of optimization variables and λ1 and λ2are the penalty factors, which can be chosen based on theimportance of the starting torque or power at maximum speedby the designer. In this paper, because of the equal importanceof starting torque and power at maximum speed (6000 r/min),we consider λ1 and λ2 equal. Tem is the starting torque inmotoring mode and Peg is the power in generator mode at thespeed of 6000 r/min.

TABLE I

VARIABLES OF OPTIMIZATIONS

Fig. 1. Details of IPMSM structure.

Torque ripple is calculated using FEM in each iterationof optimization procedure and in case the torque ripple isless than 10%, the process will be terminated. Otherwise,the chromosomes with high torque ripple are removed fromthe population in the next iteration using λ1 and λ2 penaltyfactors and the process continues until the desired ripple levelis obtained.

Considering the no-load voltage limitation (Ea) and thegenerator voltage (Va) limit at 6000 r/min, the follow-ing two nonlinear constraints are exerted on the objectivefunction

1 : Earms6000rpm < 24Vrms (2)

2 : Varms6000rpm < 19.3Vrms. (3)

The optimization variables are listed in Table I. Thesevariables are bounded to predetermined values to speed upthe convergence of the optimization process. Fig. 1 shows thedetail of machine cross section.

Since the lengths of flux barriers are functions of magnetspan angle, no additional bounds are considered for flux barrierlengths.

IV. LUMPED PARAMETER METHOD

In this paper, saturated LPM is used for modeling ofIPMSM. In this method, IPMSM is modeled to obtain machinebasic parameters such as magnet linkage flux, D-axis induc-tance, Q-axis inductance, stator winding resistance, and thestator leakage inductance. Then, using these parameters, theobjective function and the nonlinear constraints are calculatedand results are used in the GA optimization process. Calcula-tion of winding resistance and leakage inductance is detailedin [17] and [19] and will not be further discussed in thispaper.

MIRAHKI et al.: DESIGN OPTIMIZATION OF IPMSM FOR 42 V ISA 8100306

Fig. 2. Lumped circuit for flux linkage calculation.

1) Flux Linkage Calculation: Flux linkage is calculatedusing the method presented in [2]. In this method, an equiv-alent LPM is offered using FE results of the calculatedflux lines. Using this method, the equivalent flux tubes areobtained, as shown in Fig. 2.

In Fig. 2, reluctances can be calculated by the followingequations:

Rgk = ge

μ0 Agk(4)

Rmok = hmk

μ0μrwmk L(5)

Rkml1 = 2hmk

μ0 L(hn + hn+1)(k = 1, n = 1), (k = 2, n = 3), (k = 3, n = 5) (6)

R3ml2 = 4hm3

μ0 L(h7 + h8)(7)

ϕrk = Brwmk L (8)

ϕmbk = Bsatkwc L (9)

Agk = (αp(k) − αp(k−1))2π(Rsi − ge/2)

NpL, (k =2, 3) (10)

Agk = (αp1)2π(Rsi − ge/2)

NpL, (k = 1). (11)

The geometrical parameters for these equations are shownin Fig. 1. L, Np , k, ge, and αp(k) are effective length, numberof poles, number of magnet layers, the effective air-gap length,and pole-arc to pole pitch ratio of machine, respectively. Equa-tion (8) pertains to flux source and (9) pertains to saturationflux source of air bridges. Since a part of flux lines of the thirdmagnet flows through its own flux barrier and a part of it flowscommonly through its own flux barrier and the flux barrier ofthe adjacent magnet, its flux barrier is divided into two parts.Ignoring the reluctances of stator and rotor iron compare withair gap reluctance and using Kirchhoff’s law, the air-gap fluxdensity could be calculated with a high accuracy. Using thefirst harmonic of flux density in the air gap, the flux linkagecan be calculated.

2) D-Axis Inductance Calculation: D-axis inductance iscomprised of magnetizing and leakage inductances. Leakage

Fig. 3. LPM equivalent circuit and details of dimensions for D-axisinductances.

Fig. 4. LPM equivalent circuit and details of dimensions for Q-axisinductance.

inductance is calculated using the method described in [17].Magnetizing inductance is calculated using the method pre-sented in [19]. Since the effective air gap of D-axis fluxis high, the variation of D-axis current has no effect onD-axis inductance. Therefore, using an equivalent per unitmagnetic circuit and the relationships presented in [15] and[19], D-axis magnetizing inductance could be calculated. Theequivalent per unit magnetic circuit of D-axis is shown inFig. 3.

A few parameters should be defined for calculation ofD-axis inductance. Considering Fig. 3, �αk = αk −αk−1 andslot span area is As = 2π L Rsi/Qs, where Qs is the numberof stator slots

rmk = hmk As

gelmk L(12)

rgk = �αs

�αk(13)

fdsk = cos(αk−1) − cos(αk)

�αk. (14)

8100306 IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 3, MARCH 2014

Fig. 5. Flowchart for calculation of Q-axis inductance.

Finally, the D-axis inductance could be calculated as fol-lows [6]:

Ldm =[1− 4

π

∑k

�αk f 2dsk + 4

π

∑k

fdsk( fdsk − fdrk)�αk

]Lag.

(15)

In (15), Lag is the round-rotor air-gap inductance [15].3) Q-Axis Inductance: Unlike the D-axis inductance,

Q-axis inductance depends on variations of stator current.Q-axis flux closes almost its whole path through stator androtor cores. Therefore, Q-axis inductance is highly dependenton stator current variations. Saturated LPM presented in [15]is used for calculation of Q-axis inductance. Considering anequivalent magnetic circuit for the Q-axis flux (as shown inFig. 4) and the iterative method presented in flowchart 5,Q-axis inductance can be calculated. Na and Ka1 are thenumber of series turns per phase and fundamental componentof winding factor, respectively.

Fig. 6. Flowchart of GA optimization.

V. OPTIMIZATION PROCESS

For GA optimization process, the population size is selectedas 20 and evaluation of fitness and constraint function are inseries. For termination, the function tolerance, generations, andnonlinear constraint tolerance are selected as 10−6, 50, and10−6, respectively. For calculation of torque ripple in eachiteration of optimization, the designed machine is simulatedusing FEM. The schematic view of the GA optimizationprocess is shown in Fig. 6.

VI. RESULTS AND DISCUSSION

Fig. 7 shows fitness value including best fitness and meanfitness versus generation.

Fig. 8 shows the optimized machine. Table II showsmachine parameters obtained from optimization process.

Table III shows the results of optimal design using FEMwith the parameters obtained from optimization method in

MIRAHKI et al.: DESIGN OPTIMIZATION OF IPMSM FOR 42 V ISA 8100306

Fig. 7. Fitness value.

Fig. 8. Optimized 12-pole IPM machine.

TABLE II

OPTIMIZED PARAMETERS

TABLE III

PERFORMANCE RESULTS OF OPTIMAL IPMSM

different operating points. Results show that in addition to ful-filling the constraints required by the Consortium, the designedmachine generates an extra 1.6 kW power in generating modeat high speed and 4.3 N·m extra starting torque.

Fig. 9 shows the starter torque. It can be observed that thestarter torque ripple is less than 10%.

Fig. 9. Starter torque.

VII. CONCLUSION

In this paper, GA optimization method for IPMSM designin ISA application is proposed. The proposed design methodresulted in a machine with 26% increase in power at generatingmode and 3% increase in starting torque without increasingthe current, compared with the MIT Consortium suggestions.Furthermore, the proposed design resulted in a 50% decreaseof magnet weight compared with the design presented in [17].FEM is used for verification of the optimal design. Comparisonof the simulation results validates the proposed design method.

REFERENCES

[1] T. J. E. Miller, Brushless Permanent-Magnet and Reluctance MotorDrives. New York, NY, USA: Oxford University Press, 1989.

[2] I. Boldea, Reluctance Synchronous Machines and Drives. New York,NY, USA: Oxford University Press, 1996.

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Hooshang Mirahki (S’09) was born in Tata-Rashid, Iran, in 1988. Hereceived the B.Sc. degree in electrical engineering from the University ofKurdistan, Kurdistan, Iran, and the M.Sc. degree in electrical engineeringfrom the Isfahan University of Technology, Isfahan, Iran, in 2010 and 2013,respectively, where he is currently pursuing the Ph.D. degree in electricalengineering. His current research interests include design, optimization, andderivation of electrical machinery and power electronics.

Mehdi Moallem (SM’90) received the Ph.D. degree in electrical engineeringfrom Purdue University, West Lafayette, IN, USA, in 1989.

He is currently a Full Professor with the Department of Electrical andComputer Engineering, Isfahan University of Technology, Isfahan, Iran. Hehas authored more than 150 journal and conference papers. His currentresearch interests include the design and optimization of electromagneticdevices, the application of advance numerical techniques and expert systemsto the analysis and design of electrical machines, and power quality.

Prof. Moallem was the recipient of many international and national awards.

Seyyed Abbas Rahimi received the B.Sc. degree in electrical engineeringfrom the Sharif University of Technology, Tehran, Iran, and the M.Sc. degreein power systems engineering from the Isfahan University of Technology,Isfahan, Iran, in 2010 and 2013, respectively.

He is currently with Arya Transformers Power Co., Iran. His currentresearch interests include the application of evolutionary algorithms in powersystems.