Optimal Design of IPMSM for FCEV Using Novel Immune Algorithm Combined with Steepest Descent Method
Abstract
:1. Introduction
2. Conventional Immune Algorithm
- Problem definition: Objective function and restrictions are defined.
- Generation of antibody: Initial antibodies are generated randomly in the problem region and initial memory cells are selected according to antibody-antigen affinity. When the algorithm is applied to find peaks, the antibody-antigen affinity of an antibody (v) is defined as follows:
- Expectation calculation: The expectation of each antibody is calculated and antibodies with low expectations are removed. The expectation of antibody (i) is calculated as follows:
- Crossover, mutation: The antibody group is updated by replacing removed antibodies. Mutants are randomly generated in the entire problem area and crossover is done by the antibodies remaining from step 3.
- Affinity calculation: The antibody-antigen affinity of the new antibody group is calculated with (3). Additionally, the antibody-antibody affinity of the memory cell is calculated as follows:
- Memory cell renewal: Cells with high antibody-antibody affinity in memory cells are removed, and antibodies with high antibody-antigen affinity are added to the memory cell.
- Convergence check: If the value of the memory cell group is not changed by N iteration, it is judged that the convergence condition is satisfied, and the algorithm terminates and the optimal solutions are saved to the memory cell. If the convergence condition is not satisfied, each step is repeated from step 4, and the algorithm proceeds.
3. Proposed Algorithm
3.1. Multi-Jittered Sampling
3.2. Hybrid Steepest Descent Method
3.3. Antibody Radius
3.4. Flow Chart of the NIA
3.5. Verification of the Proposed Algorithm
4. Application to the Optimal Design of IPMSM for FCEV
4.1. Analysis Model and Design Variables
4.2. Optimization Results
4.3. Result Analysis of Optimum Design
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Point | Concentration | Expectation |
---|---|---|
A | 1/4 | 2 × 4/1 = 8 |
B | 2/4 | 3 × 4/2 = 6 |
C | 1/4 | 5 × 4/1 = 20 |
D | 2/4 | 3 × 4/2 = 6 |
Test Function 1 [11 Peaks] | Number of Function Call | Success Rate [%] |
IA | 2060.0 | 58.45 |
NGA | 1650 | 89.09 |
NIA | 1365.2 | 99.45 |
Test Function 2 [36 Peaks] | Number of Function Call | Success Rate [%] |
IA | 3390.0 | 84.0 |
NGA | 3140 | 94.44 |
NIA | 1878.1 | 99.64 |
Parameter | Unit | Value |
---|---|---|
Pole number | - | 6 |
Slot number | - | 27 |
Rated torque | [Nm] | 310 |
Rated power | [kW] | 97.4 |
Rotation speed | [rev/min] | 3000 |
Stator inner/outer diameter | [mm] | 172/240 |
Rotor inner/outer diameter | [mm] | 50/170 |
Air gap | [mm] | 1 |
Stacking length | [mm] | 240 |
Stator and rotor core material | - | JFE steel 35JN230 |
Permanent magnet material | - | NEOMAX-42 |
Variable | Unit | Range |
---|---|---|
θ1 | [degree] | 125–140 |
θ2 | [degree] | 100–150 |
length | [mm] | 12–18.5 |
Model | Initial Model | Model 1 | Model 2 | Model 3 |
---|---|---|---|---|
θ1 [degree] | 127.67 | 130.77 | 141.50 | 131.33 |
θ2 [degree] | 122.22 | 111.33 | 124.00 | 130.08 |
length [mm] | 13.0 | 18.5 | 12.0 | 17.0 |
Model | Initial Model | Model 1 | Model 2 | Model 3 |
---|---|---|---|---|
Torque Ripple [%] | 19.58 | 2.68 | 4.10 | 4.36 |
Average Torque [Nm] | 322.39 | 304.97 | 323.71 | 315.49 |
Cogging Torque [Nm] | 24.11 | 6.23 | 21.52 | 2.92 |
AC phase [degree] | 43 | 45 | 39 | 44 |
Model | Initial Model | Optimum Model |
---|---|---|
Iron loss [W] | 507.8 | 473.5 |
Copper loss [W] | 2162.7 | 2162.7 |
Total loss [W] | 2670.5 | 2636.1 |
Input power [kW] | 103.9 | 101.7 |
Output power [kW] | 101.3 | 99.1 |
Efficiency [%] | 97.4 | 97.4 |
Parameter | Value |
---|---|
Young’s modulus (Core/PM) | 210/120 [GPa] |
Poisson’s ratio (Core/PM) | 0.3/0.3 |
Density (Core/PM) | 7850/8400 [kg/m3] |
Rotation speed | 3000/6000 [rpm] |
Yield stress | 250 [MPa] |
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Son, J.-C.; Kang, Y.-R.; Lim, D.-K. Optimal Design of IPMSM for FCEV Using Novel Immune Algorithm Combined with Steepest Descent Method. Energies 2020, 13, 3395. https://doi.org/10.3390/en13133395
Son J-C, Kang Y-R, Lim D-K. Optimal Design of IPMSM for FCEV Using Novel Immune Algorithm Combined with Steepest Descent Method. Energies. 2020; 13(13):3395. https://doi.org/10.3390/en13133395
Chicago/Turabian StyleSon, Ji-Chang, Young-Rok Kang, and Dong-Kuk Lim. 2020. "Optimal Design of IPMSM for FCEV Using Novel Immune Algorithm Combined with Steepest Descent Method" Energies 13, no. 13: 3395. https://doi.org/10.3390/en13133395