# Investigation of Electromagnetic Losses Considering Current Harmonics in High-Speed Permanent Magnet Synchronous Motor

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## Abstract

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## 1. Introduction

## 2. High-Speed Permanent Magnet Synchronous Motor with SVPWM Inverter

#### 2.1. Design Specifications of the HPMSM

#### 2.2. Dynamic Simulation Model with HPMSM and SVPWM Inverter

_{s}*) is given, the system automatically compares it with the actual speed (N

_{s}). When N

_{s}or the load torque (T

_{L}) changes, the reference d-q currents I

_{d}

^{e*}and I

_{q}

^{e*}immediately adjust the speed and torque. Simultaneously, N

_{s}should equal N

_{s}* and the motor operation achieves a steady-state characteristic. Moreover, the current loop forces the actual currents to track the commanded current [8,9,10]. The purpose of the PWM inverter is to implement a sinusoidal three-phase AC voltage using the DC link voltage. To obtain a sinusoidal three-phase voltage from a three-phase PWM inverter, a carrier wave is implemented from the time counter of the digital signal processor (DSP) and is compared with the reference voltage signal. The frequency of the carrier wave is known as the carrier frequency. Due to the limitations of power electronics and material technology, the carrier frequency is limited to 10–15 kHz. Therefore, the current contains harmonic components, and the main harmonic orders of the phase currents are described in [5]. For example, in the case of 25,000 rpm and f

_{c}= 12 kHz, f

_{c}/f

_{0}= 24. The orders of the main harmonics are presented in Table 3.

## 3. Electromagnetic Loss Components with Harmonic Current

#### 3.1. Copper Losses in the Stator Winding

_{ph}), DC resistance (R

_{dc}), and number of phases (m):

_{0}is the permeability of the vacuum, and s is the electrical conductivity of the conductor.

_{d}is a coefficient indicating the magnitude of the total copper loss compared to the DC copper loss.

#### 3.2. Eddy Current Losses in the Rotor Sleeve and PM

^{6}and 8.345 × 10

^{5}S/m, respectively. Eddy current losses in the rotor are caused by the time-varying magnetic vector potential in the conductive material, while there are three causes of the time-varying magnetic vector potential [12,18,19]. First, the spatial harmonics of the magnetic flux density generated from the PM are distorted by the tooth-slot structure, which generates eddy currents. Second, the distortion component of the spatial harmonics of the magnetomotive force generated from the stator windings by the stator winding arrangement also causes eddy currents. Finally, the current applied to the stator with high-order time harmonics by the PWM inverter causes eddy currents in the rotor region.

_{rot}is the conductivity of different parts of the rotor, J

_{n}is the eddy current density of the k

^{th}time harmonic, and V

_{rot}is the volume of the material.

_{act}) of the rotor sleeve is designed to be longer in the axial direction than the length (l

_{stk}) of the stator core of the HPMSM to couple with the shaft. Since the length of the sleeve does not affect the analysis of the electromagnetic performance (such as back electromotive force, inductance, and torque), the results for the 2D and 3D electromagnetic analyses are similar. However, since the current path changes in the rotor loss analysis, a 3D analysis is required to analyze the eddy current losses. The analysis of the eddy current loss density according to the sinusoidal current and PWM current applied to the stator winding‘ is displayed in Figure 8. As described previously, when the PWM current is applied to the stator winding, the eddy current loss is significantly enhanced due to the higher-order time harmonics.

#### 3.3. Core Losses in the Stator Core

_{h}), eddy current loss coefficient (k

_{e}), and excess eddy current loss coefficient (k

_{a}) were derived as a function of the frequency [22,23]. Third, the magnetic flux density in the stator shoe, tooth, and yoke regions was analyzed according to the sinusoidal and harmonic currents applied to the stator winding. As shown in Figure 10, the elliptic loci of the flux density in the normal and tangential directions were derived.

_{min}/B

_{max}) can be calculated according to the loci of the flux density through the FFT analysis for each harmonic [22,23]. When the axis ratio is >0.1, it is considered a rotating magnetic field, and when the axis ratio is ≤0.1, it is considered an alternating magnetic field.

_{core}is the volume of the stator core, ρ

_{steel}is the mass density of the electrical steel sheet, n represents the harmonic order, and A

_{const}compensates for any inaccuracies in the core loss coefficients derived based on the Epstein data. The values of A

_{const}are 1 and 2 in the alternating and rotating magnetic field regions, respectively.

## 4. Experimental Setup and Performance Evaluation

#### 4.1. No-Load Test

_{mec}

_{h}) occurred in the HPMSM because there was no magnetic field in the rotor. Then, experiments were performed under no-load conditions on a rotor with a magnetized PM, and the no-load loss (P

_{noload}) was measured.

_{core}) under no-load conditions (predicted from the measured torque and speed) can be expressed as the no-load loss (P

_{noload}) and the mechanical loss (P

_{mech}).

_{mech}). To verify the validity of the proposed core loss analysis, the commercial FE analysis results, proposed loss analysis results, and experimental results were compared according to the speed, as shown in Figure 14. Since the mechanical loss measured according to the speed from the experimental method proposed from the experimental results was valid, it was applied equally to the load analysis and experiment to measure the overall loss and efficiency.

#### 4.2. Load Test

_{rms}, and the resistive load for each phase was fixed at 6.67 Ohm. The load test was performed using the performance evaluation system depicted in Figure 3.

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Gerada, D.; Mebarki, A.; Brown, N.L.; Gerada, C.; Cavagnino, A.; Boglietti, A. High-speed electrical machines: Technologies, trends, and developments. IEEE Trans. Ind. Electron.
**2013**, 61, 2946–2959. [Google Scholar] [CrossRef] - Dong, J.; Huang, Y.; Jin, L.; Lin, H. Comparative study of surface-mounted and interior permanent-magnet motors for high-speed applications. IEEE Trans. Appl. Supercond.
**2016**, 26, 5200304. [Google Scholar] [CrossRef] - Bramerdorfer, G.; Tapia, J.A.; Pyrhönen, J.J.; Cavagnino, A. Modern Electrical Machine Design Optimization: Techniques, Trends, and Best Practices. IEEE Trans. Ind. Electron.
**2018**, 65, 7672–7684. [Google Scholar] [CrossRef] - Schwager, L.; Tuysuz, A.; Zwyssig, C.; Kolar, J.W. Modeling and comparison of machine and converter losses for PWM and PAM in high-speed drives. IEEE. Trans. Ind. Appl.
**2014**, 50, 995–1006. [Google Scholar] [CrossRef] - Zhang, C.; Chen, L.; Wang, X.; Tang, R. Loss Calculation and Thermal Analysis for High-Speed Permanent Magnet Synchronous Machines. IEEE Access
**2020**, 8, 92627–92636. [Google Scholar] [CrossRef] - Jumayev, S.; Merdzan, M.; Boynov, K.; Paulides, J.; Pyrhönen, J.; Lomonova, E. The effect of PWM on rotor eddy-current losses in high-speed permanent magnet machines. IEEE Trans. Magn.
**2015**, 51, 8109204. [Google Scholar] [CrossRef] - Miyama, Y.; Hazeyama, M.; Hanioka, S.; Watanabe, N.; Daikoku, A.; Inoue, M. PWM Carrier Harmonic Iron Loss Reduction Technique of Permanent Magnet Motors for Electric Vehicles. IEEE Trans. Ind. Appl.
**2016**, 52, 2865–2871. [Google Scholar] [CrossRef] - Gu, C.; Wang, X.L.; Deng, Z.Q. Evaluation of three improved space-vector-modulation strategies for the high-speed permanent magnet motor fed by a SiC/Si hybrid inverter. IEEE Trans. Power Electron.
**2021**, 36, 4399–4409. [Google Scholar] [CrossRef] - Zhuo, L.; Yang, D.; Sun, R.; Sun, L.; Zou, J. Accurate Calculation of Iron Loss of High-Temperature and High-Speed Permanent Magnet Synchronous Generator under the Conditions of SVPWM Modulation. Energies
**2022**, 15, 2315. [Google Scholar] [CrossRef] - Woo, J.H.; Bang, T.K.; Lee, H.K.; Kim, K.H.; Shin, S.H.; Choi, J.Y. Electromagnetic characteristic analysis of high-speed motors with rare-earth and ferrite permanent magnets considering current harmonics. IEEE Trans. Magn.
**2021**, 57, 8201805. [Google Scholar] [CrossRef] - Wrobel, R.; Mellor, P.H.; Popescu, M.; Staton, D.A. Power Loss Analysis in Thermal Design of Permanent-Magnet Machines—A Review. IEEE Trans. Ind. Appl.
**2016**, 52, 1359–1368. [Google Scholar] [CrossRef] [Green Version] - Huynh, C.; Zheng, L.; Acharya, D. Losses in High Speed Permanent Magnet Machines Used in Microturbine Applications. J. Eng. Gas Turbines Power
**2008**, 131, 022301. [Google Scholar] [CrossRef] - Birnkammer, F.; Chen, J.; Pinhal, D.B.; Gerling, D. Influence of the Modeling Depth and Voltage Level on the AC Losses in Parallel Conductors of a Permanent Magnet Synchronous Machine. IEEE Trans. Appl. Supercond.
**2018**, 28, 0601705. [Google Scholar] [CrossRef] - Liu, J.; Fan, X.; Li, D.; Qu, R.; Fang, H. Minimization of AC copper loss in permanent magnet machines by transposed coil connection. IEEE Trans. Ind. Appl.
**2021**, 57, 2460–2470. [Google Scholar] [CrossRef] - Popescu, M.; Dorrell, D.G. Proximity Losses in the Windings of High-Speed Brushless Permanent Magnet AC Motors With Single Tooth Windings and Parallel Paths. IEEE Trans. Magn.
**2013**, 49, 3913–3916. [Google Scholar] [CrossRef] - Gonzalez, D.A.; Saban, D.M. Study of the Copper Losses in a High-Speed Permanent-Magnet Machine with Form-Wound Windings. IEEE Trans. Ind. Electron.
**2013**, 61, 3038–3045. [Google Scholar] [CrossRef] - Du, G.; Ye, W.; Zhang, Y.; Wang, L.; Pu, T. Comprehensive Analysis of Influencing Factors of AC Copper Loss for High-Speed Permanent Magnet Machine with Round Copper Wire Windings. Machines
**2022**, 10, 731. [Google Scholar] [CrossRef] - Han, T.; Wang, Y.C.; Shen, J.X. Analysis and Experiment Method of Influence of Retaining Sleeve Structures and Materials on Rotor Eddy Current Loss in High-Speed PM Motors. IEEE Trans. Ind. Appl.
**2020**, 56, 4889–4895. [Google Scholar] [CrossRef] - Kim, J.H.; Kim, D.M.; Jung, Y.H.; Lim, M.S. Design of ultra-high-speed motor for fcev air compressor considering mechanical properties of rotor materials. IEEE Trans. Energy Convers.
**2021**, 36, 2850–2860. [Google Scholar] [CrossRef] - Shin, K.; Park, H.; Cho, H.; Choi, J. Semi-three-dimensional analytical torque calculation and experimental testing of an eddy current brake with permanent magnets. IEEE Trans. Appl. Supercond.
**2018**, 28, 5203205. [Google Scholar] [CrossRef] - Ansys GRANTA Multi Campus Solution Software; ANSYS, Inc.: Cambridge, UK, 2022; Available online: http://www.ansys.com/materials (accessed on 15 October 2022).
- Shin, K.H.; Hong, K.; Cho, H.W.; Choi, J.Y. Core Loss Calculation of Permanent Magnet Machines Using Analytical Method. IEEE Trans. Appl. Supercond.
**2018**, 28, 5205005. [Google Scholar] [CrossRef] - Kim, C.W.; Koo, M.M.; Kim, J.M.; Ahn, J.H.; Hong, K.Y.; Choi, J.Y. Core Loss Analysis of Permanent Magnet Synchronous Generator with Slotless Stator. IEEE Trans. Appl. Supercond.
**2018**, 28, 5204404. [Google Scholar] [CrossRef] - Zhu, S.; Cheng, M.; Dong, J.; Du, J. Core loss analysis and calculation of stator permanent-magnet machine considering dc-biased magnetic induction. IEEE Trans. Ind. Electron.
**2014**, 61, 5203–5212. [Google Scholar] [CrossRef] - Okamoto, S.; Denis, N.; Kato, Y.; Ieki, M.; Fujisaki, K. Core Loss Reduction of an Interior Permanent-Magnet Synchronous Motor Using Amorphous Stator Core. IEEE Trans. Ind. Appl.
**2016**, 52, 2261–2268. [Google Scholar] [CrossRef] - Yao, A.; Sugimoto, T.; Odawara, S.; Fujisaki, K. Core losses of a permanent magnet synchronous motor with an amorphous stator core under inverter and sinusoidal excitations. AIP Adv.
**2018**, 8, 056804. [Google Scholar] [CrossRef] [Green Version] - Denis, N.; Kato, Y.; Ieki, M.; Fujisaki, K. Core losses of an inverter-fed permanent magnet synchronous motor with an amorphous stator core under no-load. AIP Adv.
**2016**, 6, 055916. [Google Scholar] [CrossRef]

**Figure 4.**Comparison of current waveforms and fast Fourier transform (FFT) analysis results: (

**a**) estimated and (

**b**) measured currents.

**Figure 5.**Distribution of magnetic flux and current density in the stator winding according to the current waveform: (

**a**) sinusoidal and (

**b**) PWM current.

**Figure 6.**Distribution of copper loss density in the stator winding according to the current waveform: (

**a**) sinusoidal and (

**b**) PWM current.

**Figure 7.**Distribution of eddy current density according to the current waveform: (

**a**) sinusoidal and (

**b**) PWM current.

**Figure 8.**Distribution of eddy current loss according to the current waveform: (

**a**) sinusoidal and (

**b**) PWM current.

**Figure 10.**Elliptic loci of flux density in the normal and tangential directions: (

**a**) sinusoidal and (

**b**) PWM current applied to the stator winding.

**Figure 11.**Analysis results of core loss according to magnetic flux density harmonics with sinusoidal current applied to the stator winding: (

**a**) stator shoe, (

**b**) stator tooth, and (

**c**) stator yoke.

**Figure 12.**Analysis results of core loss according to magnetic flux density harmonics with PWM current applied to the stator winding: (

**a**) stator shoe, (

**b**) stator tooth, and (

**c**) stator yoke.

**Figure 15.**Measured input current under load conditions: (

**a**) 10,000 rpm, (

**b**) 15,000 rpm, (

**c**) 20,000 rpm, (

**d**) 25,000 rpm.

**Figure 16.**Comparison of analysis and experimental results according to speed and loss components: (

**a**) analysis with sinusoidal current, (

**b**) analysis with PWM current, and (

**c**) experiment.

Parameters | Values | Parameters | Values |
---|---|---|---|

Pole number | 2 | Shaft outer diameter | 16 mm |

Slot number | 6 | Stack length | 84 mm |

Slot opening | 3 mm | Airgap length | 1 mm |

Rotor outer diameter | 37 mm | Stator outer diameter | 90 mm |

PM thickness | 8.5 mm | Turns per phase | 72 |

Sleeve thickness | 2 mm | Parallel branches | 2 |

Material of stator core | 20PN1500 | Material of PM | Sm2Co17 |

Material of shaft core | STS420J2 | Material of sleeve | Inconel |

Parameters | Analytical and FE Analysis | Measurement | |
---|---|---|---|

Phase resistance [mΩ] | 52.7 | 53.2 | |

Inductance [mH] | Self | 0.334 | 0.34 |

Mutual | 0.23 | 0.26 | |

Fluxlinkage [Wb] | 0.0389 | 0.0387 |

i | (2i − 1)f_{c}/f_{0}− 2 | (2i − 1) f_{c}/f_{0}+ 2 | (2i − 1) f_{c}/f_{0}− 4 | (2i − 1) f_{c}/f_{0}+ 4 |

1 | 26.8 | 30.8 | 24.8 | 32.8 |

2 | 84.4 | 88.4 | 82.4 | 90.4 |

3 | 142 | 146 | 140 | 148 |

i | 2i f_{c}/f_{0}− 1 | 2i f_{c}/f_{0}+ 1 | 2i f_{c}/f_{0}− 5 | 2i f_{c}/f_{0}+ 5 |

1 | 56.6 | 58.6 | 52.6 | 62.6 |

2 | 114.2 | 116.2 | 110.2 | 120.2 |

3 | 171.8 | 173.8 | 167.8 | 177.8 |

_{0}is the fundamental frequency [5].

Speed [rpm] | Input Power [W] | Output Power [W] | Mech. Loss [W] | Elec. Loss [W] |
---|---|---|---|---|

10,000 | 547.44 | 477.00 | 11.23 | 59.21 |

15,000 | 1138.90 | 1015.48 | 20.70 | 102.72 |

20,000 | 1951.81 | 1757.48 | 33.60 | 160.73 |

25,000 | 2865.47 | 2563.00 | 45.47 | 257.00 |

Speed (rpm) | Torque (N∙m) | Hybrid Analysis with Sinusoidal Current | Hybrid Analysis with Harmonic Current | Experiment | |||
---|---|---|---|---|---|---|---|

Loss [W] | Eff. [%] | Loss [W] | Eff. [%] | Loss (W) | Eff. (%) | ||

10,000 | 0.45 | 38.94 (44.72) | 92.24 (5.86) | 69.30 (1.62) | 87.04 (0.1) | 70.44 | 87.13 |

15,000 | 0.65 | 73.90 (40.12) | 93.24 (4.58) | 127.91 (3.64) | 88.85 (0.35) | 123.42 | 89.16 |

20,000 | 0.84 | 110.70 (43.06) | 94.11 (4.52) | 188.80 (2.85) | 90.34 (0.33) | 194.33 | 90.04 |

25,000 | 0.98 | 159.14 (47.39) | 94.15 (5.27) | 304.58 (0.69) | 89.37 (0.08) | 302.47 | 89.44 |

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**MDPI and ACS Style**

Lee, J.-H.; Sung, S.; Cho, H.-W.; Choi, J.-Y.; Shin, K.-H.
Investigation of Electromagnetic Losses Considering Current Harmonics in High-Speed Permanent Magnet Synchronous Motor. *Energies* **2022**, *15*, 9213.
https://doi.org/10.3390/en15239213

**AMA Style**

Lee J-H, Sung S, Cho H-W, Choi J-Y, Shin K-H.
Investigation of Electromagnetic Losses Considering Current Harmonics in High-Speed Permanent Magnet Synchronous Motor. *Energies*. 2022; 15(23):9213.
https://doi.org/10.3390/en15239213

**Chicago/Turabian Style**

Lee, Ju-Hyeong, Soyoung Sung, Han-Wook Cho, Jang-Young Choi, and Kyung-Hun Shin.
2022. "Investigation of Electromagnetic Losses Considering Current Harmonics in High-Speed Permanent Magnet Synchronous Motor" *Energies* 15, no. 23: 9213.
https://doi.org/10.3390/en15239213