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Robust Multilevel Optimization of PMSM Using Design for Six Sigma

IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011, Page(s): 3248 ~ 3251

Adviser：Ming-Shyan Wang

Student： Ang-ting Wu

Student ID：MA120112

Xiangjun Meng, Shuhong Wang, Jie Qiu, Qiuhui Zhang, Jian Guo Zhu, Youguang Guo, and Dikai LiuState Key Laboratory of Electrical Insulation and Power Equipment, Faculty of Electrical Engineering, Xi’an Jiaotong

University, Xi’an 710049, ChinaXJ Flexible Transmission System Corporation Electric City, Xuchang 461000, China

Faculty of Engineering and Information Technology, University of Technology, Sydney NSW2007, Australia

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I. INTRODUCTION

II. MULTILEVEL GENETIC ALGORITHM

III. DFSS ROBUST OPTIMIZATION APPROACH

IV. ROBUST OPTIMIZATION MODEL OF PMSM

V. RESULTS

VI. CONCLUSION

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I. INTRODUCTION

NUMERICAL simulation technology and optimization method have been applied to improve the design quality and shorten the design cycle of the PMSM. However, the existence of fluctuation in design variables or operation conditions has a great influence on the motor performance.

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DFSS is an effective method to improve the design quality and decrease the sensitive of product quality to uncertainty. Y. Q. Li employs the six sigma design method to the optimization of sheet metal stamping [1] and deep-drawing sheet metal process combined with the dual response surface model and design of experiment [2]; the optimal results improve the reliability and robustness of the production and also increase the design efficiency.

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In order to estimate the effects of parameter perturbations in design and to improve the design efficiency, a robust optimization method based on design for six sigma (DFSS) is presented in this paper. The optimization result shows that the proposed optimization procedure can not only achieve better motor performance, but also improve significantly the reliability and robustness of the PMSM performance, comparing with those obtained by using GA and multilevel Genetic Algorithm.

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II. MULTILEVEL GENETIC ALGORITHM

In MLGA the design optimization variables are classified and allocated to different levels according to the relative importance among the variables and objective functions, constraints, as well as the practical engineering weight factor and optimization sequence. The variables on different levels are encoded independently. Each level may have multiple populations and each of them can adopt different dynamic genetic operators and parameters. Furthermore, the relationship between subproblems in multilevel problems can be handled by MLGA.

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In Fig. 1, the GA1 is the master GA module and GA2j,GA3j consist of a number of modules, in which each module corresponds to a subsystem. The subsystem in the multilevel structure is not independent for the interactions between the subsystems on upper and lower levels. The module in the upper level of the MLGA acts as a solver which affects GA of other subsystem.

Fig. 1. Block diagram of MLGA [9].

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The implementation process of MLGA is as follows. First, determine the objective functions, constraints and design variables. Second, make analysis using correlation analysis, then determine the architecture of MLGA. Third, allocate all the requirements and build up the relationships among different levels and different modules on each level. Each module corresponds to a genetic algorithm module. Forth, implement MLGA and feedback messages. Last, reach the termination criterion and end the total solving process.

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III. DFSS ROBUST OPTIMIZATION APPROACH

The six sigma methodology was proposed at Motolola [3] and developed into DFSS at General Electric (GE) [3]. DFSS is one of the robust optimization methods, and the term “sigma” here refers to standard deviation , which is a measure of dispersion. The performance level 6σ is equivalent to 3.4 defect parts per million (PPM), while at 3σ level (the average sigma level for most companied) the defect ratio is about 66800 PPM.

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In DFSS, six sigma and reliability are combined to define the robustness of disturbance, constraints and the original object function and constraints may be rewritten as [3]

LSL, USL, μƒ and σƒ are the lower bound, upper bound, mean value and standard deviation of the original function, respectively. Χ is the input design variables. ΧL,ΧU,μχ,σχ are the lower bound, upper bound, mean value and standard deviation of the variables, respectively. is the sigma level.

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IV. ROBUST OPTIMIZATION MODEL OF PMSM

A PMSM controlled by field oriented control (FOC), rated at 1000 W output power, 2000 rpm speed and 128 V line to line voltage is used to verify the MLGA and DFSS based robust optimization. The bilevel optimization model is defined as follows:

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output power and sƒ is fill factor, hm and bm are thickness and width of the permanent magnet. Ns and WindD are conductors per slot and the conductor diameter, hm and bm and WindD are selected as variables.

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V. RESULTS

Table I lists the robust optimization results when given different design variables disturbance scale and weighting factors ωμ and ωσ in the objective function (5).

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Figs. 3 and 4 are DFSS and MLGA optimization frequency histogram, respectively. It can be seen from those two figures that, when DFSS is used to the robust optimization, the range of the objective function is 0.266–0.274, and MLGA is 0.23–0.26. The range of MLGA is 0.03, which is bigger than that of DFSS, which is 0.08. It is suggested that “shrinked” distribution may improve robustness.

Fig. 3. DFSS optimization frequency histogram.

Fig. 4. MLGA optimization frequency histogram.

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A comparison of the quality improvement of the design results is listed in Table II. With MLGA algorithm, the mean value μƒ of the fitness function is 0.2530, the standard deviation σƒ of the fitness function is 6.706-e005 and the reliability of MLGA is 73.33%.

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Table III lists the optimization results for PMSM by using MLGA and DFSS respectively. Both optimization methods may provide better performance than that of the original design. Although the efficiency achieved by MLGA is little higher than that of DFSS, the cost of windings and permanent magnets optimized by DFSS is less than that calculated by using MLGA. It is crucial that the results optimized by DFSS possess higher reliability than those analyzed by MLGA.

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ACKNOWLEDGMENT

This work was supported by the Nation High Technology Research and Development Program of China (863 Program), Grant NO.2009AA01A131.

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REFERENCES

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