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Asymmetric IPMSM Optimization Using VDSE Methods

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The electrical machines optimization process is the study of various design parameters to achieve the best performance. The optimization objectives usually include maximizing the average torque while minimizing the ripple rate. In addition, it is important to efficiently use the material such as iron, copper or permanent magnets to maintain the manufacturing cost. Meanwhile, using unconventional structures such as Asymmetric IPMSM (AIPMSM) can help the electric machine design engineers investigate new possibilities for optimization purposes [1]. However, the computational cost including the model development, number of required simulations and the corresponding computational time might exceed the accessible software and hardware limitations. Therefore, a proper computer-based study procedure is necessary to obtain the best solution while reducing the required computation effort. In this regard, Virtual Design Space Exploration (VDSE) methods can be employed to achieve a computationally efficient optimum solution. Figure 1 below illustrates the components of the VDSE methods for electrical machine design and optimization.

VDSE Components for Electrical Machines Design and Optimization
Fig. 1. VDSE Components for Electrical Machines Design and Optimization

Problem Definition

An example multi-objective of AIPMSM has been defined to study the application of VDSE method in the electrical machines design and optimization. Figure 2 illustrates the geometrical dissimilarity between the symmetric IPMSM and the AIPMSM, as well as the design variables that shape their geometry. The optimization objectives and design variables have been identified to determine the optimal design.

Symmetric IPMSM, AIPMSM and Design Parameters
Fig. 2. Symmetric IPMSM, AIPMSM and Design Parameters

According to the geometrical parameters, the optimization problem, which encompasses the objectives and variables range, is hereby defined as follows.

Optimization Objectives and Design Variables

Fig. 3. Optimization Objectives and Design Variables

Increasing the Efficiency of VDSE-Based Optimization

As illustrated in Figure 1, the VDSE methods is mainly comprised of three key components, namely sampling, model development and search/optimization process. Accordingly, the established model for the optimization plays a significant role in deciding the required time and computational cost [2].

To have a computationally efficient optimization process, we will use a solution based upon surrogate modeling technique coupled with the EMWorks2D software product. Figure 4 below shows the workflow of the surrogate-based modeling and optimization. The measured torque waveform for the initial design before conducting the optimization shows a considerably high torque ripple rate. Therefore, the main target is going to tackle this issue while improving the average torque and reducing the magnet volume.


Workflow of the Surrogate-Based Optimization

Fig. 4. Workflow of the Surrogate-Based Optimization

To implement the VDSE method to solve defined multi-objective optimization problem based on surrogate modeling, steps below is going to be followed:

  1. Establish the FEM-model using EMWorks2D to obtain objectives and constraints based on variables
  2. Use a proper sampling method to retrieve data from design space (create training dataset)
  3. Train a surrogate model for each objective/constraint
  4. Combine optimization algorithm with the surrogate models and search the design space
  5. Find the optimum design

Implementation and Results

Figure 5 below shows the developed FEM model using EMWorks2D connecting the input and output parameters of the optimization problem:

EMWorks2D as the Main Tool for Accurate Performance Analysis of the Sample Designs
EMWorks2D as the Main Tool for Accurate Performance Analysis of the Sample Designs
Fig. 5. EMWorks2D as the Main Tool for Accurate Performance Analysis of the Sample Designs

At next step, full-factorial method has been used to create the training dataset containing 256 samples. EMWorks2D evaluated all samples and outputs stored in the datasheet. Then, the kriging modeling technique has been adopted to construct the surrogate models.

The non-dominated sorting genetic algorithm (NSGAII) has been used for solving the multi-objective optimization problem. Thanks to the fast and accurate surrogate models we have developed, 1500 samples (15 population size and 100 generations) were evaluated. 

Figure 6 shows the obtained pareto-front optimum solutions for the multi-objective optimization problem we solved.

Pareto Optimum Solutions

Fig. 6. Pareto Optimum Solutions

By analyzing the distribution of optimized designs, it is evident that studied objectives vary in a large range of values. However, it is necessary to select a final design to finish our optimization process. The torque ripple rate varies significantly compared to other ones. Therefore, the design with lowest ripple rate has been chosen from the optimized designs. Figures 7 and 8 below compares the performance of the initial and final optimum designs.

Design parameters located on machine cross section
Design parameters located on machine cross section [
Fig. 7. The Selected Optimum Design and its Torque Waveform (AIPSM) Compared to the Initial Design (IPMSM)

Parametric Comparison Between the Initial and Optimized Designs

Fig. 8. Parametric Comparison Between the Initial and Optimized Designs

By comparing the parameters related to the initial and optimized designs, it is observed that the ripple rate significantly reduced due to applied asymmetricity in the structure of rotor. The study proves that the asymmetric design can be an effective approach in tackling the ripple rate issue of the machine. Thanks to the VDSE method implemented, the optimization procedure completed leading to a considerably improved performance while the computational cost required reduced.


The investigation of the VDSE method and its application in the design and optimization of electrical machines has been thoroughly explored. To practically evaluate the effectiveness of the VDSE, a multi-objective optimization problem was defined with the aim of observing how asymmetry can enhance the performance of conventional IPMSMs. The optimization problem was successfully solved using the EMWorks2D and surrogate modeling method, with the NSGAII algorithm being adopted to comprehensively search the design space. Ultimately, a design was selected as the product of the conducted optimization process. The findings of this study have demonstrated that the introduction of asymmetry can significantly reduce the ripple rate of the machine, while simultaneously increasing the average torque.


[1] W. Ren, Q. Xu, Q. Li, and L. Zhou, “Reduction of Cogging Torque and Torque Ripple in Interior PM Machines with Asymmetrical V-Type Rotor Design,” IEEE Trans. Magn., vol. 52, no. 7, 2016, doi: 10.1109/TMAG.2016.2530840.
[2] F. Farshbaf Roomi, A. Vahedi, and A. Nobahari, “Electrical machines surrogate-based design optimization based on novel waveform targeting strategy with improvement of the computational efficiency,” IET Electr. Power Appl., vol. 16, no. 11, pp. 1286–1299, 2022