Multiobjective Optimization Design of a Brushless Excitation Synchronous Motor Based on the Taguchi Method

Considering the issue of significant total harmonic distortion in the no-load back electromotive force (EMF) and torque ripple of a brushless excitation synchronous motor (BESM) used in a compressor, a multiobjective optimization design method of a BESM based on the Taguchi method was proposed. By selecting the polar arc coefficient, stator slot width, damping winding pitch, and air gap length as the optimization parameters, the maximum no-load back EMF, minimum back EMF total harmonic distortion rate, and minimum torque ripple are selected as the optimization objectives. Then, the Taguchi method was employed to construct an orthogonal table to enhance the performance of the optimization objectives. This approach facilitated the determination of the optimal parameter combination for optimization. Finally, the simulation results indicate significant enhancements in each optimized aspect of the motor’s performance following the optimization process. This outcome serves as validation for the efficacy of the Taguchi method in achieving an optimal design for the BESM.


Introduction
Synchronous motors have gained widespread prominence in electric power and power generation applications due to their high efficiency, adjustable power factor, and high overload capacity [1][2] .Brushless excitation synchronous motors (BESM) [3 -4] are widely used in special occasions of flame and explosion protection due to the elimination of brushes and slip rings, which makes BESM easy to maintain and highly reliable.Therefore, the optimized design of BESM has certain theoretical significance and practical engineering value.
Motor optimization algorithms are mainly global optimization and local optimization [5][6][7][8] .The global optimization algorithm can consider all the uncertainties, but the objective function is difficult to establish, the solution cycle is long, and it has some limitations.The local optimization algorithm has a short computation period and good convergence, but it has significant limitations when applied to multiobjective optimization.The Taguchi method [9][10][11] , as a form of local optimization algorithm, distinguishes itself from other similar algorithms by its capability to facilitate multiobjective optimization designs.This approach minimizes the required number of tests and experimental data to obtain the optimal parameter combination for multiple objectives, ultimately reducing optimization time and enhancing efficiency.This method has gained significant attention in recent years in motor optimization studies.
Considering the issue of significant total harmonic distortion in the no-load back (EMF) and torque ripple of a BESM used in a compressor, this is achieved by selecting optimization parameters, including the polar arc coefficient, stator slot width, damping winding pitch, and air gap length.Additionally, optimization objectives are defined as maximizing the no-load back EMF, minimizing the rate of back EMF total harmonic distortion, and reducing torque ripple to a minimum.Then, the orthogonal experiment table was established by the Taguchi method, followed by finite element simulations.These simulations analyzed the impact of each optimization variable on the optimization objective, facilitating the determination of the optimal combination of optimization parameters.Ultimately, the validity of the proposed approach was further affirmed through finite element simulation.

Synchronous motor model and main parameters
This paper focuses on the optimization of a 216-slot 18-pole brushless excitation convex pole synchronous motor.A two-dimensional model representing the motor is established, as illustrated in Figure 1.Key motor parameters are presented in Table 1.

Taguchi method motor optimization design
The Taguchi method, developed by the Japanese expert Genichi Taguchi, is a form of local optimization design geared toward multiobjective optimization.Unlike global optimization methods, the Taguchi approach achieves the optimal parameter combination for multiobjective optimization using minimal experimentation and experimental data.This is achieved through the design and creation of an orthogonal table, which subsequently reduces optimization time and enhances efficiency

Determine the optimization objective and optimization parameters
Considering the issue of significant total harmonic distortion in the no-load back electromotive force (EMF) and torque ripple of a BESM used in a compressor, optimization goals are set to maximize the no-load back EMF, minimize the rate of back EMF total harmonics distortion (THD), and reduce torque ripple to a minimum (K mb ).
Since the stator slot size, damping winding parameters and length of the air gap have a great influence on the performance of the motor.Four parameters, namely, the polar arc coefficient α p , stator slot width b s1 , damping winding pitch t 2 and air gap δ, are selected as the optimization parameters in this paper.
The harmonic distortion rate of the back EMF can be expressed as: where n is the number of harmonics and U i is the i-th harmonic amplitude of the back EMF.

Determine the optimal range and level values of optimization parameters
Through the utilization of Ansys FEA software, iterative adjustments of the optimization parameters are executed, followed by the conduction of finite element simulations.These simulations aim to determine the optimal sensitivity range of the optimization objective to the optimization parameters.Subsequently, based on the determined value range of the optimization parameters, four discrete-level values are selected.A comprehensive depiction of the value ranges and corresponding level values for each optimization parameter is presented in Table 2.

Experimental analysis
(1) Mean value analysis First, the total average value of the finite element simulation outcomes for each optimization goal is computed, and the calculated results based on Equation (2) are displayed in Table 4. Next, an examination is conducted on the mean of the finite element simulation outcomes for a specific level of each optimization parameter.For instance, considering the test data for the maximum no-load back electromotive force (E) of the targeted motor under the optimization parameter's polar arc coefficient (α p ) at level value 2, denoted as E 1 , E 2 , E 3 , and E 4 , the average value is calculated using Equation (3).The computational results are displayed in Table 5.  4), the relative impact proportion of each optimization parameter optimization objective can be deduced.This deduction involves a consideration of both the combined mean value of each motor optimization objective from Table 4 and the mean value of the motor's optimization objective across various parameter levels, as provided in Table 5.The resulting calculation outcomes are displayed in Table 6.

ETAI-2023
where SS is the variance value of the optimization objective; X is the optimization parameter; S is the optimization objective; m(S) is the overall mean value of the optimization objective; and m Xi (S) corresponds to the mean value of the optimization objective at the specific level value i of the optimization parameter X.  6, it can be seen that the polar arc coefficient α p , damping winding pitch t 2 , and air gap δ have a substantial impact on the amplitude of no-load back EMF; the damping winding pitch t 2 displays the most prominent impact on the harmonic distortion rate of no-load back EMF; additionally, both the damping winding pitch t 2 and air gap δ have considerable impacts on the motor's torque ripple.
Therefore, the polar arc coefficient α p is chosen to maximize the level value of the no-load back EMF; the damping winding pitch t 2 is chosen to minimize the level value of the harmonic distortion rate of the no-load back EMF; and the stator slot width bs1 along with the air gap δ are optimized to minimize the level value of the motor's torque ripple.In summary, the combination of parameters that make the motor optimization objective optimal is α p (1)b s1 (3)t 2 (1)δ(4).

Comparative analysis of simulation
Table 7 displays the comparative data of the optimization objectives before and after fine-tuning the motor's parameters.The data demonstrate that following the optimization process, the maximum noload reverse electromotive force escalates from 7.43 KV to 7.92 KV, marking an increase of 0.49 KV.Simultaneously, the harmonic distortion rate of the reverse electromotive force diminishes from 4.16% to 3.16%, resulting in a smoother output waveform.Additionally, optimization leads to a substantial reduction in motor torque pulsation, contributing to a more stabilized motor output.Figure 2 reveals that the fundamental amplitude of the no-load back EMF in the optimized motor experiences a certain degree of increase.The third harmonic as well as the first-and second-order tooth harmonics are weakened, but the higher harmonics also increase.This optimization is further demonstrated by a reduction in the harmonic distortion rate as per Equation ( 1), leading to a smoother graph.The evident optimization effect underscores the success of the proposed approach.In summary, the simulation and comparison analysis demonstrate that the multiobjective optimization of the performance indices for the designed BESM, carried out using the Taguchi method, yields a noticeable optimization effect.This result underscores the efficacy and validity of the suggested approach.
In summary, the simulation and comparative analysis unequivocally indicate the pronounced optimization effect achieved through the Taguchi method for the multiobjective optimization of performance indices in the designed BESM.This outcome underscores the efficacy and soundness of the proposed methodology.

Conclusions
Considering the issue of significant total harmonic distortion in the no-load back electromotive force (EMF) and torque ripple of a BESM used in a compressor, the polar arc coefficient, stator slot width, damping winding pitch, and air gap length are selected as the optimization parameters, and the maximum no-load back EMF, minimum back EMF total harmonic distortion rate, and minimum torque ripple are selected as the optimization objectives.Then, by employing a combination of the Taguchi method and finite element simulation for motor optimization, substantial improvements are achieved in various performance indicators of the motor after the optimization process.The preceding analysis serves to confirm the efficacy of the Taguchi method in achieving an optimal design for BESM.

Figure. 2
Figure. 2 Comparison of no-load back EMF and harmonics before and after optimization

Table 1
Basic dimensional parameters of the brushless excitation synchronous motor

Table 2
4ange of values and level values of motor optimization parameters Orthogonal experimental design and finite element simulationUtilizing the four-level values determined for the four optimization parameters from Table2, an L 16 (44) orthogonal array is constructed following the experimental design principles of orthogonal methodology.This approach enables the accomplishment of a multiobjective, multivariable optimization design through a mere 16 experimental trials, thereby reducing the number of experiments and saving valuable time and costs.The orthogonal array and finite element simulation results are presented in Table3.Table3Orthogonal table and simulation results

Table 4
Total average value of each optimization objective of the motor

Table 6
Effect of each optimization factor on motor performance

Table 7
Optimization parameter optimization objective comparison before and after optimization