Optimal Design of Interior Permanent Magnet Synchronous Motor Considering Various Sources of Uncertainty
Abstract
:1. Introduction
1.1. Literature Review
1.2. Contribution
2. Method
- Definition of a design of experiments (DoE);
- Thermal and electromagnetic MotorCAD finite element analysis simulations of operating points;
- Selection of a tolerance range for each input, with each assumed to be normally distributed and independent from the others;
- Estimation of the standard deviation of each input from the tolerance range;
- Feedforward neural network training with the outputs of the simulations;
- Estimation of the expected values, the standard deviation of the objective, and constraint functions with the neural network;
- Multi-objective constrained optimizations with a genetic algorithm.
2.1. DoE
2.2. Simulation
2.3. Neural Network
2.4. Formulation of the Optimization Problem
2.4.1. Multi-Objective Deterministic Optimization
2.4.2. -Efficient Formulation
2.4.3. Multi-Objective Minimization of the Standard Deviation (MOMSD)
2.5. Determination of the Optimal Solutions
Algorithm 1 Non-dominated sorting genetic algorithm |
|
3. Case Study
3.1. Design Variables
3.2. Additional Sources of Uncertainty
3.3. Constraints
3.4. Performance Indexes
3.5. Neural Networks
4. Results
4.1. Accuracy of the Estimates of the Expected Values of Objective and Constraint Functions
4.2. Accuracy of the Estimates of the Standard Deviation of Objective and Constraint Functions
4.3. Optimization
4.3.1. Comparison Between MOMSD Solutions and Deterministic Optimal Solutions
4.3.2. Comparison Between -Efficient Approach and Deterministic Optimal Solutions
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Article | Electric Motor | Manufacturing Tolerances | Temperature Variation | Magnetic Material Variability | Multi-Objective Optimization | NNVE |
---|---|---|---|---|---|---|
[26] | X | X | ||||
[25] | X | X | X | X | ||
[24] | X | X | X | |||
[21] | X | X | X | |||
[20] | X | X | X | |||
[22] | X | X | X | X | ||
[23] | X | X | ||||
[27] | X | X | ||||
This article | X | X | X | X | X | X |
Design Variable | Reference | Tolerance | Min | Max |
---|---|---|---|---|
Airgap | 1 mm | mm | 0.7 mm | 1.3 mm |
Slot opening | 2 mm | mm | 1.4 mm | 2.6 mm |
Magnet thickness | 4 mm | mm | 2.8 mm | 5.2 mm |
Magnet width | 23 mm | mm | 16.1 mm | 23 mm |
Tooth width | 6.76 mm | mm | 4.73 mm | 8.79 mm |
Bridge thickness | 0.5 mm | mm | 0.35 mm | 0.65 mm |
Web thickness | 9 mm | mm | 6.3 mm | 11.7 mm |
Pole V angle | 158° | ° | 130° | 160° |
Number of turns | 29 | / | 20 | 36 |
Number of strands in hand | 9 | / | 5 | 13 |
Dimension | Reference | Variation Range | Min | Max |
---|---|---|---|---|
120 °C | °C | 90 °C | 150 °C | |
120 °C | °C | 90 °C | 150 °C | |
1.37 T | T | 1.36 T | 1.38 T |
Parameter | Limit Value |
---|---|
150 °C | |
180 °C | |
650 V |
Parameter | Value | Parameter | Value |
---|---|---|---|
Number of levels per variable | 5 | Number of levels per variable | 4 |
(DoE electromagnetic) | (DoE thermal) | ||
Number of hidden layers | 1 | Number of hidden layers | 1 |
(ANN electromagnetic) | (ANN thermal) | ||
Number of neurons per hidden | 34 | Number of neurons per hidden | 65 |
layer (ANN electromagnetic) | layer (ANN thermal) | ||
Activation function | Log- | Activation function | Log- |
(ANN electromagnetic) | sigmoid | layer (ANN thermal) | sigmoid |
Population size | Bits per design | 10 | |
(Genetic algorithm) | variable (Genetic algorithm) | ||
Mutation probability | 0.5% | Max number of generations | 1000 |
(Genetic algorithm) | (Genetic algorithm) |
Average absolute differences between Monte Carlo method and NNVE | |||
0.02% | 0.08% | ||
0.7% | 1% | ||
0.04% | 0.06% |
Deterministic | - (95%) | - (99%) | MOMSD | |
---|---|---|---|---|
Airgap | 0.716 mm | 0.717 mm | 0.75 mm | 1.23 mm |
Slot opening | 1.84 mm | 1.56 mm | 1.44 mm | 1.45 mm |
Magnet thickness | 5.2 mm | 5.11 mm | 5.09 mm | 5.17 mm |
Magnet width | 21.52 mm | 21.63 mm | 21.84 mm | 19.4 mm |
Tooth width | 6.51 mm | 6.45 mm | 6.18 mm | 7.73 mm |
Bridge thickness | 0.46 mm | 0.46 mm | 0.61 mm | 0.57 mm |
Web thickness | 11.66 mm | 11.55 mm | 11.55 mm | 7.52 mm |
Pole V angle | 153.4° | 148.6° | 150.1° | 130.6° |
Number of turns | 27 | 27 | 28 | 20 |
Number of strands in hand | 12 | 12 | 12 | 13 |
25.1 Nm | 25.5 Nm | 24.5 Nm | 27.15 Nm | |
Eff | 97.1% | 97.1% | 97% | 97% |
T | 205 Nm | 205 Nm | 205 Nm | 142 Nm |
507 V | 512 V | 526 V | 349.8 V | |
139 °C | 137 °C | 144 °C | 99 °C | |
153 °C | 152 °C | 159 °C | 105 °C | |
0.55 Nm | 0.51 Nm | 0.57 Nm | 0.19 Nm | |
0.008% | 0.008% | 0.008% | 0.007% | |
1.32 Nm | 1.33 Nm | 1.37 Nm | 0.93 Nm |
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Guidotti, G.; Barri, D.; Soresini, F.; Gobbi, M. Optimal Design of Interior Permanent Magnet Synchronous Motor Considering Various Sources of Uncertainty. World Electr. Veh. J. 2025, 16, 79. https://doi.org/10.3390/wevj16020079
Guidotti G, Barri D, Soresini F, Gobbi M. Optimal Design of Interior Permanent Magnet Synchronous Motor Considering Various Sources of Uncertainty. World Electric Vehicle Journal. 2025; 16(2):79. https://doi.org/10.3390/wevj16020079
Chicago/Turabian StyleGuidotti, Giacomo, Dario Barri, Federico Soresini, and Massimiliano Gobbi. 2025. "Optimal Design of Interior Permanent Magnet Synchronous Motor Considering Various Sources of Uncertainty" World Electric Vehicle Journal 16, no. 2: 79. https://doi.org/10.3390/wevj16020079
APA StyleGuidotti, G., Barri, D., Soresini, F., & Gobbi, M. (2025). Optimal Design of Interior Permanent Magnet Synchronous Motor Considering Various Sources of Uncertainty. World Electric Vehicle Journal, 16(2), 79. https://doi.org/10.3390/wevj16020079