Copyright © 2010 KSAE 1229−9138/2010/051−17
International Journal of Automotive Technology, Vol. 11, No. 2, pp. 277−282 (2010)
DOI 10.1007/s12239−010−0035−z
SIMPLE DESIGN APPROACH FOR IMPROVING CHARACTERISTICS OF INTERIOR PERMANENT MAGNET SYNCHRONOUS MOTORS FOR ELECTRIC AIR-CONDITIONER SYSTEMS IN HEV *
S. I. KIM, G. H. LEE, J. J. LEE and J. P. HONG
Department of Automotive Engineering, Hanyang University, Seoul 133-791, Korea (Received 18 February 2009; Revised 20 July 2009)
ABSTRACT−In this paper, a simple design method for improving the performance of an interior permanent magnet synchronous motor (IPMSM), for driving the air-conditioning compressor used in hybrid electric vehicles, is presented. There are many design methods that optimize the IPMSM. Each method deals with a variety of design factors, such as slot opening, pole arc, and rotor shape. However, as the number of design variables increases, a lot of modeling and analysis time is needed in order to improve the characteristics of an IPMSM. This paper demonstrates that the optimization of a double-layer IPMSM, satisfying the given design conditions, is possible with only a flux barrier shape design. Then, response surface methodology is applied as the optimization method, and the validity of the design approach is verified by comparison with test results. KEY WORDS : Air-conditioning compressor, IPMSM, Optimization, Response surface methodology to many design factors and the interactions between them. Unfortunately, there are very few technical papers that discuss how variations of design variables effect torque ripple, cogging torque and harmonics of back-EMF. The small number of papers that have appeared (Kioumarusi ., 2006; Sanada ., 2004) offer a design method for mitigating overall torque pulsation under various load conditions. The goal of this paper is to present a relatively simple and feasible design approach that will facilitate an improvements in the above mentioned characteristics without any sacrifice to other performance characteristics of the doublelayer IPMSM. The method employs the response surface method (RSM) and considers the flux barrier as the only design factor. RSM is well suited for making empirical models that relate the performance of a motor to the design parameters. With these empirical models, the objective functions with restraints are easily created and a lot of computational time can be saved (Jeon ., 2006; Qinghua ., 2004). Furthermore, an obtained response surface
1. INTRODUCTION
Idling stop systems to reduce fuel consumption are of interest for developers of hybrid electric vehicles (HEV). In order to adapt to the idling stop system, the automobile airconditioner must continue to work even while the engine is stopped. As such, conventional engine-driven compressors are gradually being replaced with electric motor-driven models. The motors for driving air-conditioning compressors in HEVs must be miniature, lightweight, and highly efficient. Interior permanent magnet synchronous motors (IPMSMs) are well suited to these design requirements due to their high power density, high efficiency and wide speed region (Murakami ., 2001). However, IPMSMs have limitations related to torque characteristics. Torque ripple and cogging torque are relatively large compared with a surface permanent magnet synchronous motor. These limitations are mainly the result of discontinuous reluctance variation between the rotor and stator (Kioumarusi ., 2006; Bianchi ., 2006; Islam ., 2005; Sanada ., 2004). Especially, because of d-axis current to utilize reluctance torque and increase the motor speed, the back-electromotive force (back-EMF) of the IPMSM operated in wide speed range contains many harmonics, and the torque ripple rises greatly when driven by a sinusoidal current (Lee ., 2008). Therefore, it is necessary to optimize the shape of the IPMSM in order to improve torque performance. This optimization is very complex and difficult due
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*
Corresponding author.
e-mail:
[email protected]
Figure 1. Configuration of initial designed model. 277
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S. I. KIM, G. H. LEE, J. J. LEE and J. P. HONG
Table 1. Dimension and specifications of double-layer IPMSM for electric air-conditioner system. Items Value Stator outer diameter 117.2 mm Rotor outer diameter 70.8 mm Stack length 15 mm Air-gap 0.6 mm 1.22~1.28 T Br (@20~25oC) Number of poles 6 Cooling method Refrigerant cooling DC link voltage 155 V Maximum terminal voltage 98.6 V Rated output power 2 kW Maximum current 17 Arms Base, Maximum speed 3500, 7500 rpm supplies a designer with a description of system responses based on the behavior of design parameters within a design space. Conventional optimization methods cannot provide this. In the end, the utility of the method for the flux barrier shape design is verified by test results.
2. CHARACTERISTICS OF INITIAL MODEL
vq
=
Ra
+ pLd
ω Ld
–ω L q R a + pLq
id iq
+ 0
id
ωψa
(1)
iq
= [ ψa iq + ( Ld – Lq ) id iq ]
T Pn
Lq
according to the current and to β .
and q as a function of current and β are shown in Figure 2. In (3), ψa and ψo are fundamental components calculated by Fourier analysis. The steady-state phasor diagram for the IPMSM is shown in Figure 3 (Morimoto ., 1990). ψ0cosα – ψa L =---------------ψ0sinαL = ---------------------------(3) et al
d
id
q
iq
where, ψo is the total flux linkage considering the armature reaction effects, and α is the phase difference between ψa and ψo. The characteristics of the initial model are predicted with d and q estimated as in (1) and (2). The following limitations on armature current and terminal voltage were considered: L
L
=
Va
=
2
id
+ i2q ≤ Iam 2
vd
+ v2q ≤ Vam
(4) (5)
(2)
where, d and q are components of armature current, d, q are components of terminal voltage ψa 3/2 ψf ; ψf : is the maximum flux linkage of the permanent magnet, a is the armature winding resistance, d, q are inductance along d-, and q-axis, = / , and n is the number of pole pairs. At the base and maximum speed, input armature current and current angle (β ) are required to estimate torque ripple by FEA (Kioumarusi ., 2006; Sanada ., 2004). To get these values, d and q should be computed according to the change of armature current and β. In this paper, they are obtained by FEA cubic spline interpolation and (3). d i
and
Figure 3. Phasor diagram of the IPMSM.
Ia
1 =PnψaIacosβ + --- ( Ld – Lq) Ia2sin2β 2
Ld
L
Figure 1 shows the initial configuration of the double-layer IPMSM designed for driving the compressor of a HEV. The constant power speed range (CPSR) of the initial model is 3500 rpm to 7500 rpm. The main dimensions and specifications are listed in Table 1. The characteristics of the model are estimated by finite element analysis (FEA) and the voltage and torque equation; mechanical and iron loss are ignored. The equations in normal operation are expressed in d-q coordinates as follows (Chin and Soulard, 2003): vd
Figure 2.
i
v
v
R
L
p
d dt
P
et al
L
L
et al
L
L
Figure 4. Speed versus torque and output performance of the initial model.
SIMPLE DESIGN APPROACH FOR IMPROVING CHARACTERISTICS OF INTERIOR PERMANENT MAGNET 279 where, am and am are peak values of current and voltage, respectively. The entire torque-speed operation region, considering the above control conditions, is acquired in the following manner. In the anterior region of base speed, maximum torque per ampere control is used. In the posterior region flux, weakening control is applied. Characteristics of the initial model, such as speed versus torque (Figure 4), torque waveforms at the base (Figure 5), and maximum speed and cogging torque estimated by FEA (Figure 6), are shown. Input currents were 15.3 A and 12.5 A, and β was 32.5o and 63.6o, respectively. The back-EMF of the initial model and its total harmonic distortion (THD) are given in Figure 7. I
V
Figure 7. Back-EMF and THD of initial model at 3500 rpm.
3. DESIGN OPTIMIZATION 3.1. Selection of Design Factors Section 2 demonstrated that the initial design of the IPMSM satisfied the given design conditions. In the IPMSM, the operating constraints on input current, terminal voltage, and CPSR critically depend on motor parameters, such as the flux linkage by the permanent magnet, as well as d- and q-axis inductance (Morimoto and Takeda, 2000). Therefore, in the initial model, the size and position of permanent magnet and air-gap length cannot be changed. Due to the fill factor and auto winding, the slot opening, the teeth, and the yoke width also should not be altered. As a result, the only design factor selected in this paper is the flux barrier angle. Figure 8, a magnified view of the region of Figure 1
Figure 5. Torque waveforms of initial model at the base and maximum speed.
Figure 8. Design variables of the initial model. surrounded by a dotted line, indicates the factors. In the shape optimization there are many limitations that make it difficult to consider all the design variables. 3.2. Application of RSM RSM is a set of statistical and mathematical techniques to find the “best fit” response of a physical system through experiment or simulation. RSM has recently been recognized as an effective approach for modeling the performance of electrical devices. In RSM, a polynomial model, called a fitted model, is usually constructed to represent the relationship between performance and design parameters. In this paper, RSM is used to make appropriate response models of torque ripple, cogging torque and THD of back-EMF of the initial model. A quadratic approximation function of the model is commonly used to construct the fitted response surface. In general, the response model can be written as follows: Y= b0+
k
k
i=1
i i+
i=1
2
ii i +
i≠j
ij i j + ε
(6)
where, o…ij are regression coefficients for design variables, and ε is a random error. In this paper, the least squares method is used to estimate unknown coefficients. The fitted coefficients and response model can be written as: b X Y –1 X T Y (7) Y =Xb (8) Where, is matrix notation for the levels of the indepenb
′= ( ′
Figure 6. Cogging torque waveform of initial model.
k
∑bx ∑b x ∑b x x
′
)
′
X
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S. I. KIM, G. H. LEE, J. J. LEE and J. P. HONG
Table 2. Design space of CCD. Levels of design factor Design factors −α −1 0 1 o 60 90 120 θ1 [ ] 39.5 50 60 70 θ2 [ o ] 43.2 40 45 50 θ3 [ o ] 36.6 Table 3. FEA results based on CCD. θ1 [ o ] θ2 [ o ] θ3 [ o ] YAT YTr_B YTr_M 60 50 40 5.65 9.56 28.90 120 50 40 5.69 10.54 25.0 60 70 40 5.70 13.51 32.85 120 70 40 5.74 14.60 27.03 60 50 50 5.68 12.50 32.30 120 50 50 5.73 12.57 29.78 60 70 50 5.76 15.23 36.03 120 70 50 5.80 15.86 31.34 39.5 60 45 5.69 11.07 31.45 140.4 60 45 5.77 10.75 24.49 90 43.2 45 5.67 10.41 28.57 90 76.8 45 5.62 14.41 31.52 90 60 36.6 5.62 14.23 31.47 90 60 53.4 5.75 15.83 35.07 90 60 45 5.74 12.89 30.25
a 140.4 76.8 53.4
YCogT 0.084 0.087 0.150 0.055 0.090 0.088 0.156 0.055 0.140 0.176 0.054 0.087 0.087 0.092 0.091
YTHD 5.39 4.84 4.57 3.61 3.96 3.32 4.04 3.05 4.41 4.08 4.38 5.01 5.0 3.55 4.22
Table 4. Fitted coefficients and response models. Coeffi′AT ′Tr_B ′Tr_M ′CogT cients β′0 3.8020 35.75 85.39 −0.8250 −0.0002 0.1690 0.1009 0.0007 β′1 0.0270 0.4860 0.4458 0.020 β′2 0.0410 −2.3710 −3.584 0.0118 β′3 0 −0.0007 −0.0009 0 β′11 β′22 −0.0003 −0.0011 −0.0008 −0.0001 β′33 −0.0005 0.0325 0.0424 −0.0001 0 0.0003 −0.0017 −0.0001 β′12 0 −0.0011 0.0021 0 β′13 0.0001 −0.0050 −0.0017 0 β′23 Y
Y
Y
Table 5. Optimal condition. Design factors Initial model o 60 θ1 [ ] 60 θ [ o] 45 θ [ o] 2
3
Y
′THD
Y
19.50 0.0262 −0.3102 −0.1928 −0.0001 0.0010 −0.0019 −0.0003 −0.0001 0.0047
Optimized model 140.4 52.2 45
*YAT: average torque at the base speed; YTr_B and YTr_M : torque ripple at the base and maximum speed; YCogT: peak to peak of cogging torque; YTHD : THD of back-EMF.
dent variables, is the transpose of the matrix , and is the vector of the observations. Central composite design (CCD) was used as the experimental design method, to estimate the fitted model of each response (Montgomery, 2001). CCD consists of three portions: 1) a complete 2 factorial design in which the factor levels are coded into –1 and 1, 2) axial points at a distance α from the center point, and 3) one design center point. Table 2 shows the design area of CCD. The FEA results, based on CCD, are listed in Table 3. Input current and current angle at the base and maximum speed are the same those of the initial IPMSM. Finally, the fitted models, obtained by the results of Table 3, (7) and (8) are shown in Table 4. The flux barrier design with the fitted models was performed. The design objectives and constraints are as follows: • Design objectives: YTr_B 10% , YTr_M 30% , YCogT 0.16 Nm , YTHD 4% • Subject to: YAT 5.5 Nm , Output power ≥ 2 kW Table 5 shows the optimal point satisfying the design X
T
X
k
′
≤
′
′
≤
′
′
Y
Figure 9. Responses of each fitted model according to the design factors. objectives, and Figure 9 describes the results of each fitted model corresponding to the point. Each model response varies greatly according to the variation of design factors. This means that it is difficult to find the optimal condition that minimizes every response. Thus, a proper trade-off is required, according to the application field of the IPMSM.
≤
≤
≥
Figure 10. Optimized model.
SIMPLE DESIGN APPROACH FOR IMPROVING CHARACTERISTICS OF INTERIOR PERMANENT MAGNET 281 4. TEST RESULTS
The optimized double-layer IPMSM was fabricated as shown in Figure 10 and tested in order to verify the validity of the results acquired through the optimization method. Figure 11(a) shows a testing apparatus for measuring torque ripple. Torque ripple results are displayed in Figures 11(b) and (c). The voltage amplitude obtained was 1 Nm per V. The torque ripple of the optimized IPMSM, at the load condition of base and maximum speed, was measured as 7.82% and 12.55%, while the FEA results were 10.0% and 24.7%, respectively. The difference between the test results and the FEA results may have been caused by the influence of the motor and reduction gear inertia. The measured and estimated cogging torques are given in Figure 12. The measured magnitude and wave-shape of the cogging torques are quite similar to the FEA predicted results. Back-EMF, measured and calculated at 3500 rpm, and its THD are shown in Figure 13. The waveforms of the measured and computed back-EMF are slightly different. We hypothesize that the difference is created by the manufacturing error generated in the barrier angle, slot opening, and tooth tip. In the end, the accuracy of the predicted values, obtained by each fitted response model, were proved through the test and FEA results (Figure 9). 5. CONCLUSION
In this paper, RSM was presented as an optimization method for the flux barrier shape design to improve the
Figure 11. Test and FEA results with respect to the torque ripple of the optimized model.
Figure 12. Test and FEA results with respect to the cogging torque of the optimized model.
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4 2
41 4
1 4
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11
Figure 13. Back-EMF measured and computed at 3500 rpm and THD. characteristics of initially designed double-layer IPMSM. Performance variations according to changes of design factors were easily predicted by the method, and the optimal condition to satisfy multiple design objectives was detected. However, the optimal points of each response could not minimize torque ripple at the base, torque ripple at maximum speed, cogging torque, and THD of back-EMF simultaneously. Moreover, the optimal conditions for torque ripple conflict with the optimal conditions for cogging torque. Thus, RSM is a useful method for finding an appropriate trade-off. Finally, the validity of the design method was verified by comparison with test results of the fabricated optimal model.
REFERENCES Bianchi, N., Pre, M. D. and Bolognani, S. (2006). Design of a fault-tolerant IPM motor for electric power steering.
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