Design Optimization of IPMSM for 42 V Integrated ... - IEEE Xplore

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

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Design Optimization of IPMSM for 42 V Integrated Starter Alternator Using Lumped Parameter Model and Genetic Algorithms Hooshang 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 parameter model and genetic algorithms for 42 V integrated starter alternator application. The aim of the optimization is to increase starting torque while keeping torque ripple below 10% and increasing power output in generating mode at high speed and reducing the permanent 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. I NTRODUCTION

T

O COPE with the increase of electric power demand in cars, the automotive industry has substituted the 14 V voltage systems with 42 V systems [1], [2]. This new voltage level provides engineers with a good opportunity for integrating the automotive starter and alternator into a new single piece of equipment, namely an integrated starter alternator (ISA) [3]. Among the existing electrical machines, the interior permanent magnet synchronous machine (IPMSM) is an attractive 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-power speed range [1], [2]. Since finite-element analysis is highly time consuming for machine design and optimization process [4], researchers have always been looking for analytical methods that could be used for the purpose of machine optimization. The existing methods such as Laplacian or quasi-Poissonian methods solve the field equations for surface permanent magnet (SPM) machine [5] or inset PM machine [6] directly and use the conformal mapping for considering the effects of slots into consideration [7]. Anyhow, because of the leakage flux, saturation in different parts, and the complicated structure of the IPMSM, it is not possible to use this analytical method for the optimization purposes [5], [8]. The magnetic equivalent circuits method that is used for calculation of no- and full-load field in inductions machines [9], switched reluctance [10], salient-pole synchronous machines [11], SPM [12], and even IPMSM [13] is not an appropriate approach for optimization purposes due to its complication and being time consuming. The saturating lumped parameter model (LPM) is one of the most efficient methods for optimization of IPM machines especially in highload conditions [14], [15] since it can consider machine

Manuscript received May 25, 2013; revised August 7, 2013 and October 2, 2013; accepted October 3, 2013. Date of publication October 10, 2013; date of current version March 14, 2014. Corresponding author: H. Mirahki (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2013.2285358

complex geometry and also the saturation in stator and rotor cores [16]. Due to its fast and accurate results in calculating machine parameters, LPM could be used in an optimization process that needs thousands of iterations for finding an optimal solution. In this method, three different lumped parameter models are used for calculation of power and torque [17]. First, an LPM is used for calculation of linkage flux in PM [14], [16]. For simplicity, the reluctances of the rotor and stator yokes could be easily ignored compared with the reluctance of the air gap [4], [5], [8], [16], [18]. Two other lumped parameter models could be used for calculation of D- and Q-axis inductances. Since the effective air gap in D-axis is large [19], the reluctances of the rotor and stator yokes could be easily ignored. Carter coefficient could be used for considering the effects of slots [5], [8]. Evolutionary algorithms have been widely used in the last decade for solving optimization problems. According to the no free lunch theorem, evolutionary algorithms may show different peculiarity answers in different problems [20], [21]. To have a better perspective in choosing the type of optimization algorithm, we can divide the problems into two general categories according to the dimension of the solution space, namely high- and low-dimension solution spaces [21]. The optimization problem in this paper is of high-dimension solution space type. Therefore, according to [21], genetic algorithms (GAs) yield better results than other evolutionary algorithms. The GAs are quite popular for solving nonlinear, nondifferentiable models due to their high efficiency in finding global or near global optimum point of objective functions [22]. The GAs have been used for optimization of the structure of many different machines. In some cases, a combination of the finite-element and the evolutionary algorithms has been used [23], [24]. Using the finite-element method (FEM) in the process of optimization increases the time of the optimization process and may lead to inappropriate results. Combining the GA with an analytical method could reduce the optimization time significantly and improvethe results [15]. Therefore, in this paper, we have used the combined GA and lumped parameter method (LPM). Because of the inability of the LPM in calculation of transients, the final result of

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TABLE I VARIABLES OF O PTIMIZATIONS

each optimization process is simulated with the FEM for the purpose of reducing the torque ripple. As a result, with proper combination of these two methods (finite element and lumped parameters), the transients are also considered in addition to the reduction in the optimization time. In this paper, an objective function is proposed for optimization of a three-layer IPM machine’s main parameters for use in 42 V ISA applications. The GA is used to solve the optimization problem. In addition to fulfilling the standards proposed by the MIT Consortium, we have succeeded in increasing the starting torque and the power in generating mode at high speed (6000 r/min) beyond the measures proposed by the Consortium [25]. II. ISA P ERFORMANCE C RITERIA The ISA is connected directly to cranking shaft as a starter and generator. The MIT/Industry Consortium on Advanced Automotive Electrical/Electronic Components has proposed a set of performance criteria on voltage [25], power, and starting torque that are considered as the groundwork for machine design and optimization in this paper. The Consortium suggestions are as follows. 1) DC link voltage connected to ISA is 42 V. Therefore, the ISA should be able to produce a constant voltage of 19.3 rms per phase in a wide range of speed (from 600 to 6000 r/min) in the generation mode. 2) For the purpose of direct connection, the starting torque of IPMSM should not fall below 150 N·m. 3) The generated power at the speed of 6000 r/min should not be less than 6 kW. In this paper, due to limitations of converter and magnet material (ferrite magnet), the maximum steady-state postfault voltage in generator mode is selected to be 55 VDC. In addition, since the ISA is directly connected to cranking shaft, (no flywheel) the torque ripple should be low, and therefore we selected the torque ripple to be less than 10%. III. O BJECTIVE F UNCTION The objective function is targeted at increasing the power in generator mode at 6000 r/min, increasing the starting torque and also decreasing the torque ripple. Torque ripple is defined as the ratio of peak-peak torque to the average torque in starting mode. The magnet weight used in our preliminary design is half of the amount used in [17]; therefore, it is not considered as an optimization variable. The proposed objective function is as follows: 6000(w) − Peg 150(N · m) − Tem + λ2 (1) F(z) = λ1 150(N · m) 6000(w) where z is the vector of optimization variables and λ1 and λ2 are the penalty factors, which can be chosen based on the importance of the starting torque or power at maximum speed by the designer. In this paper, because of the equal importance of starting torque and power at maximum speed (6000 r/min), we consider λ1 and λ2 equal. Tem is the starting torque in motoring mode and Peg is the power in generator mode at the speed of 6000 r/min.

Fig. 1.

Details of IPMSM structure.

Torque ripple is calculated using FEM in each iteration of optimization procedure and in case the torque ripple is less than 10%, the process will be terminated. Otherwise, the chromosomes with high torque ripple are removed from the population in the next iteration using λ1 and λ2 penalty factors and the process continues until the desired ripple level is obtained. Considering the no-load voltage limitation (E a ) and the generator voltage (Va ) limit at 6000 r/min, the following two nonlinear constraints are exerted on the objective function 1 : E arms6000rpm < 24Vrms

(2)

2 : Varms6000rpm < 19.3Vrms.

(3)

The optimization variables are listed in Table I. These variables are bounded to predetermined values to speed up the convergence of the optimization process. Fig. 1 shows the detail of machine cross section. Since the lengths of flux barriers are functions of magnet span angle, no additional bounds are considered for flux barrier lengths. IV. L UMPED PARAMETER M ETHOD In this paper, saturated LPM is used for modeling of IPMSM. In this method, IPMSM is modeled to obtain machine basic parameters such as magnet linkage flux, D-axis inductance, Q-axis inductance, stator winding resistance, and the stator leakage inductance. Then, using these parameters, the objective function and the nonlinear constraints are calculated and results are used in the GA optimization process. Calculation of winding resistance and leakage inductance is detailed in [17] and [19] and will not be further discussed in this paper.

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

Fig. 2.

Lumped circuit for flux linkage calculation.

1) Flux Linkage Calculation: Flux linkage is calculated using the method presented in [2]. In this method, an equivalent LPM is offered using FE results of the calculated flux lines. Using this method, the equivalent flux tubes are obtained, as shown in Fig. 2. In Fig. 2, reluctances can be calculated by the following equations: ge (4) Rgk = μ0 A gk h mk Rmok = (5) μ0 μr wmk L 2h mk Rkml1 = μ0 L(h n + h n+1 ) (k = 1, n = 1), (k = 2, n = 3), (k = 3, n = 5) (6) 4h m3 (7) R3ml2 = μ0 L(h 7 + h 8 ) ϕrk = Br wmk L (8) (9) ϕmbk = Bsat k wc L 2π(Rsi − ge /2) A gk = (α p(k) − α p(k−1) ) L, (k = 2, 3) (10) Np 2π(Rsi − ge /2) A gk = (α p1 ) L, (k = 1). (11) Np The geometrical parameters for these equations are shown in Fig. 1. L, N p , k, ge , and α p(k) are effective length, number of poles, number of magnet layers, the effective air-gap length, and pole-arc to pole pitch ratio of machine, respectively. Equation (8) pertains to flux source and (9) pertains to saturation flux source of air bridges. Since a part of flux lines of the third magnet flows through its own flux barrier and a part of it flows commonly through its own flux barrier and the flux barrier of the adjacent magnet, its flux barrier is divided into two parts. Ignoring the reluctances of stator and rotor iron compare with air gap reluctance and using Kirchhoff’s law, the air-gap flux density could be calculated with a high accuracy. Using the first harmonic of flux density in the air gap, the flux linkage can be calculated. 2) D-Axis Inductance Calculation: D-axis inductance is comprised of magnetizing and leakage inductances. Leakage

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

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

inductance is calculated using the method described in [17]. Magnetizing inductance is calculated using the method presented in [19]. Since the effective air gap of D-axis flux is high, the variation of D-axis current has no effect on D-axis inductance. Therefore, using an equivalent per unit magnetic circuit and the relationships presented in [15] and [19], D-axis magnetizing inductance could be calculated. The equivalent per unit magnetic circuit of D-axis is shown in Fig. 3. A few parameters should be defined for calculation of D-axis inductance. Considering Fig. 3, αk = αk − αk−1 and slot span area is As = 2π L Rsi /Q s, where Q s is the number of stator slots h mk As gelmk L αs = αk cos(αk−1 ) − cos(αk ) = . αk

rmk =

(12)

r gk

(13)

f dsk

(14)

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Fig. 5.


Flowchart for calculation of Q-axis inductance. Fig. 6.

Finally, the D-axis inductance could be calculated as follows [6]: 4 4 2 αk f dsk + f dsk ( f dsk − f drk )αk L ag . L dm = 1− π π k

k

(15) In (15), L ag 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 and rotor cores. Therefore, Q-axis inductance is highly dependent on stator current variations. Saturated LPM presented in [15] is used for calculation of Q-axis inductance. Considering an equivalent magnetic circuit for the Q-axis flux (as shown in Fig. 4) and the iterative method presented in flowchart 5, Q-axis inductance can be calculated. Na and K a1 are the number of series turns per phase and fundamental component of winding factor, respectively.

Flowchart of GA optimization.

V. O PTIMIZATION P ROCESS For GA optimization process, the population size is selected as 20 and evaluation of fitness and constraint function are in series. For termination, the function tolerance, generations, and nonlinear constraint tolerance are selected as 10−6 , 50, and 10−6 , respectively. For calculation of torque ripple in each iteration of optimization, the designed machine is simulated using FEM. The schematic view of the GA optimization process is shown in Fig. 6. VI. R ESULTS AND D ISCUSSION Fig. 7 shows fitness value including best fitness and mean fitness versus generation. Fig. 8 shows the optimized machine. Table II shows machine parameters obtained from optimization process. Table III shows the results of optimal design using FEM with the parameters obtained from optimization method in

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

Fig. 7.

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Fig. 9.

Fitness value.

Starter torque.

VII. C ONCLUSION In this paper, GA optimization method for IPMSM design in ISA application is proposed. The proposed design method resulted in a machine with 26% increase in power at generating mode and 3% increase in starting torque without increasing the current, compared with the MIT Consortium suggestions. Furthermore, the proposed design resulted in a 50% decrease of magnet weight compared with the design presented in [17]. FEM is used for verification of the optimal design. Comparison of the simulation results validates the proposed design method. R EFERENCES

Fig. 8.

Optimized 12-pole IPM machine. TABLE II O PTIMIZED PARAMETERS

TABLE III P ERFORMANCE R ESULTS OF O PTIMAL IPMSM

different operating points. Results show that in addition to fulfilling the constraints required by the Consortium, the designed machine generates an extra 1.6 kW power in generating mode at high speed and 4.3 N·m extra starting torque. Fig. 9 shows the starter torque. It can be observed that the starter torque ripple is less than 10%.

[1] T. J. E. Miller, Brushless Permanent-Magnet and Reluctance Motor Drives. New York, NY, USA: Oxford University Press, 1989. [2] I. Boldea, Reluctance Synchronous Machines and Drives. New York, NY, USA: Oxford University Press, 1996. [3] B. H. Bae and S. K. Sul, “Practical design criteria of interior permanent magnet synchronous motor for 42V integrated starter-generator,” in Proc. IEEE IEMDC, vol. 2. Jun. 2003, pp. 656–662. [4] C. Mi, M. Filippa, W. Liu, and R. Ma, “Analytical method for predicting the air-gap flux of interior-type permanent-magnet machines,” IEEE Trans. Magn., vol. 40, no. 1, pp. 50–58, Jan. 2004. [5] Z. Zhu, D. Howe, E. Bolte, and B. Ackermann, “Instantaneous magnetic field distribution in brushless permanent magnet DC motors. I. opencircuit field,” IEEE Trans. Magn., vol. 29, no. 1, pp. 124–135, Jan. 1993. [6] Z. Zhu, D. Howe, and Z. Xia, “Prediction of open-circuit airgap field distribution in brushless machines having an inset permanent magnet rotor topology,” IEEE Trans. Magn., vol. 30, no. 1, pp. 98–107, Jan. 1994. [7] D. Zarko, D. Ban, and T. Lipo, “Analytical solution for cogging torque in surface permanent-magnet motors using conformal mapping,” IEEE Trans. Magn., vol. 44, no. 1, pp. 52–65, Jan. 2008. [8] C. C. Hwang and Y. H. Cho, “Effects of leakage flux on magnetic fields of interior permanent magnet synchronous motors,” IEEE Trans. Magn., vol. 37, no. 4, pp. 3021–3024, Jul. 2001. [9] M. Amrhein and P. Krein, “Induction machine modeling approach based on 3-D magnetic equivalent circuit framework,” IEEE Trans. Energy Convers., vol. 25, no. 2, pp. 339–347, Jun. 2010. [10] J. Kokernak and D. Torrey, “Magnetic circuit model for the mutually coupled switched-reluctance machine,” IEEE Trans. Magn., vol. 36, no. 2, pp. 500–507, Mar. 2000. [11] M. Bash and S. Pekarek, “Modeling of salient-pole wound-rotor synchronous machines for population-based design,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 381–392, Jun. 2011. [12] M. F. Hsieh and Y. C. Hsu, “A generalized magnetic circuit modeling approach for design of surface permanent-magnet machines,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 779–792, Feb. 2012.

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[13] A. Tariq, C. Nino Baron, and E. Strangas, “Iron and magnet losses and torque calculation of interior permanent magnet synchronous machines using magnetic equivalent circuit,” IEEE Trans. Magn., vol. 46, no. 12, pp. 4073–4080, Dec. 2010. [14] Z. Zhu, D. Howe, and C. Chan, “Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines,” IEEE Trans. Magn., vol. 38, no. 1, pp. 229–238, Jan. 2002. [15] E. Lovelace, T. Jahns, and J. H. Lang, “A saturating lumped-parameter model for an interior PM synchronous machine,” IEEE Trans. Ind. Appl., vol. 38, no. 3, pp. 645–650, May/Jun. 2002. [16] L. Zhu, S. Z. Jiang, Z. Zhu, and C. Chan, “Analytical modeling of open-circuit air-gap field distributions in multisegment and multilayer interior permanent-magnet machines,” IEEE Trans. Magn., vol. 45, no. 8, pp. 3121–3130, Aug. 2009. [17] E. C. F. Lovelace, “Optimization of a magnetically saturable interior permanent-magnet synchronous machine drive,” Ph.D. dissertation, Dept. Electr. Eng. Comput. Sci., Massachusetts Inst. Technol., Cambridge, MA, USA, 2000. [18] M. Rahman, T. Little, and G. Slemon, “Analytical models for interiortype permanent magnet synchronous motors,” IEEE Trans. Magn., vol. MAG-21, no. 5, pp. 1741–1743, Sep. 1985. [19] A. Fratta, A. Vagati, and F. Villata, “Design criteria of an ipm machine suitable for field-weakened operation,” in Proc. Int. Conf. Electr. Mach., 1999, pp. 1059–1065. [20] D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput., vol. 1, no. 1, pp. 67–82, Apr. 1997. [21] F. Fulginei and A. Salvini, “Comparative analysis between modern heuristics and hybrid algorithms,” Int. J. Comput. Math. Electr. Electron. Eng., vol. 26, no. 2, pp. 259–268, 2007. [22] D. E. Goldenberg, Genetic Algorithm in Search, Optimization and Machine Learning. Reading, MA, USA: Addison-Wesley, 1989. [23] J. H. Seo, S. M. Kim, and H. K. Jung, “Rotor-design strategy of IPMSM for 42 V integrated starter generator,” IEEE Trans. Magn., vol. 46, no. 6, pp. 2458–2461, Jun. 2010. [24] J. Legranger, G. Friedrich, S. Vivier, and J. Mipo, “Combination of finite-element and analytical models in the optimal multidomain design of machines: Application to an interior permanent-magnet starter generator,” IEEE Trans. Ind. Appl., vol. 46, no. 1, pp. 232–239, Jan./Feb. 2010. [25] Mit/industry consortium on advanced automotive electrical/electronic components and systems, Discussion with Automotive OEMs about Typical Future Vehicle Requirements. Toulouse, France: Centre de Conrès Pierre Baudis, 1996.


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

Mehdi Moallem (SM’90) received the Ph.D. degree in electrical engineering from Purdue University, West Lafayette, IN, USA, in 1989. He is currently a Full Professor with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran. He has authored more than 150 journal and conference papers. His current research interests include the design and optimization of electromagnetic devices, the application of advance numerical techniques and expert systems to 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 engineering from the Sharif University of Technology, Tehran, Iran, and the M.Sc. degree in 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 current research interests include the application of evolutionary algorithms in power systems.