# Torque Ripple and Mass Comparison between 20 MW Rare-Earth and Ferrite Permanent Magnet Wind Generators

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Generator Configuration

#### 2.2. Torque Ripple

#### 2.3. Brief Comparison between RPMG and FPMG

## 3. Results and Discussion

#### 3.1. Optimization Algorithm

#### 3.2. General Optimization Strategy

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

PM | Permanent magnet |

PMSG | Permanent magnet synchronous generator |

PSO | Particle swarm optimization |

MOPSO | Multi-objective particle swarm optimization |

RPMG | Rare-earth PM-based generator |

FPMG | Ferrite PM-based generator |

FEM | Finite element method |

## References

- Van Kuik, G.A.M.; Peinke, J.; Nijssen, R.; Lekou, D.; Mann, J.; Sørensen, J.N.; Ferreira, C.; van Wingerden, J.W.; Schlipf, D.; Gebraad, P.; et al. Long-term research challenges in wind energy—A research agenda by the European Academy of Wind Energy. Wind. Energy Sci.
**2016**, 1, 1–39. [Google Scholar] [CrossRef] - Chu, W.Q.; Zhu, Z.Q. Investigation of Torque Ripples in Permanent Magnet Synchronous Machines With Skewing. IEEE Trans. Magn.
**2013**, 49, 1211–1220. [Google Scholar] [CrossRef] - Yasa, Y.; Mese, E. Design and analysis of generator and converters for outer rotor direct drive gearless small-scale wind turbines. In Proceedings of the 2014 International Conference on Renewable Energy Research and Application (ICRERA), MilwaNuee, WI, USA, 19–22 October 2014; pp. 689–694. [Google Scholar] [CrossRef]
- Yaramasu, V.; Wu, B.; Sen, P.C.; Kouro, S.; Narimani, M. High-power wind energy conversion systems: State-of-the-art and emerging technologies. Proc. IEEE
**2015**, 103, 740–788. [Google Scholar] [CrossRef] - Cooperman, A.; Duffy, P.; Hall, M.; Lozon, E.; Shields, M.; Musial, W. Assessment of Offshore Wind Energy Leasing Areas for Humboldt and Morro Bay Wind Energy Areas, California; Technical Report; National Renewable Energy Laboratory: Washington, DC, USA, 2022. [Google Scholar]
- Nasiri-Zarandi, R.; Karami-Shahnani, A.; Toulabi, M.S. Performance Comparison between Rare-Earth and Ferrite-based PM Transverse Flux Generators for Small-Scale Direct-Drive Wind Turbine. In Proceedings of the IECON 2021—47th Annual Conference of the IEEE Industrial Electronics Society, Toronto, ON, Canada, 13–16 October 2021; pp. 1–6. [Google Scholar] [CrossRef]
- Polinder, H.; van der Pijl, F.; de Vilder, G.J.; Tavner, P. Comparison of direct-drive and geared generator concepts for wind turbines. IEEE Trans. Energy Convers.
**2006**, 21, 725–733. [Google Scholar] [CrossRef] - Prakht, V.; Dmitrievskii, V.; Kazakbaev, V.; Ibrahim, M.N. Comparison between rare-earth and ferrite permanent magnet flux-switching generators for gearless wind turbines. Energy Rep.
**2020**, 6, 1365–1369. [Google Scholar] [CrossRef] - Akuru, U.B.; Kamper, M.J. Design and Investigation of Low-cost PM Flux Switching Machine for Geared Medium-speed Wind Energy Applications. Electr. Power Compon. Syst.
**2018**, 46, 1084–1092. [Google Scholar] [CrossRef] - Bharathi, M.; Akuru, U.B.; Kumar, M.K. Comparative Design and Performance Analysis of 10 kW Rare-Earth and Non-Rare Earth Flux Reversal Wind Generators. Energies
**2022**, 15, 636. [Google Scholar] [CrossRef] - Hoang, T.K.; Queval, L.; Vido, L.; Berriaud, C. Impact of the rotor blade technology on the levelized cost of energy of an offshore wind turbine. In Proceedings of the 2017 International Conference on Optimization of Electrical and Electronic Equipment (OPTIM) & 2017 Intl Aegean Conference on Electrical Machines and Power Electronics (ACEMP), Brasov, Romania, 25–27 May 2017; pp. 623–629. [Google Scholar] [CrossRef]
- Roshanfekr, P.; Thiringer, T.; Alatalo, M.; Lundmark, S. Performance of two 5 MW permanent magnet wind turbine generators using surface mounted and interior mounted magnets. In Proceedings of the 2012 XXth International Conference on Electrical Machines, Marseille, France, 2–5 September 2012; pp. 1041–1047. [Google Scholar] [CrossRef]
- Libert, F.; Soulard, J. Design Study of Different Direct-Driven Permanent-Magnet Motors for a Low Speed Application. In Proceedings of the Nordic Workshop on Power and Industrial Electronics (NORpie), Trondheim, Norway, 14–16 June 2004. [Google Scholar]
- Haraguchi, H.; Morimoto, S.; Sanada, M. Suitable design of a PMSG for a small-scale wind power generator. In Proceedings of the 2009 International Conference on Electrical Machines and Systems, Tokyo, Japan, 15–18 November 2009; pp. 1–6. [Google Scholar] [CrossRef]
- Chen, H.; Qu, R.; Li, J.; Zhao, B. Comparison of interior and surface permanent magnet machines with fractional slot concentrated windings for direct-drive wind generators. In Proceedings of the 2014 17th International Conference on Electrical Machines and Systems (ICEMS), Hangzhou, China, 22–25 October 2014; pp. 2612–2617. [Google Scholar]
- McDonald, A.; Bhuiyan, N.A. On the Optimization of Generators for Offshore Direct Drive Wind Turbines. IEEE Trans. Energy Convers.
**2017**, 32, 348–358. [Google Scholar] [CrossRef] - Frosini, L.; Pastura, M. Analysis and Design of Innovative Magnetic Wedges for High Efficiency Permanent Magnet Synchronous Machines. Energies
**2020**, 13, 255. [Google Scholar] [CrossRef] - Manwell, J.F.; Mcgowan, J.G.; Rogers, A.L. Wind Energy Explained; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2010. [Google Scholar]
- Sethuraman, L.; Dykes, K. GeneratorSE: A Sizing Tool forVariable-Speed Wind TurbineGenerators; Technical Report; National Renewable Energy Laboratory: Washington, DC, USA, 2017. [Google Scholar]
- Grauers, A. Design of Direct-Driven Permanent Magnet Generators for Wind Turbines. Ph.D. Thesis, Chalmers University of Technology, Gothenburg, Sweden, 1996. [Google Scholar]
- Gieras, J.F.; Wang, C.; Lai, J.C. Noise of Polyphase Electric Motors; Taylor & Francis: Boca Raton, FL, USA, 2005. [Google Scholar]
- VuXuan, H.; Lahaye, D.; Ani, S.; Polinder, H.; Ferreira, J.A. Effect of design parameters on electromagnetic torque of PM machines with concentrated windings using nonlinear dynamic FEM. In Proceedings of the 2011 IEEE International Electric Machines and Drives Conference (IEMDC), Niagara Falls, ON, Canada, 15–18 May 2011; pp. 383–388. [Google Scholar] [CrossRef]
- Fei, W.; Luk, P.C.K. Torque Ripple Reduction of a Direct-Drive Permanent-Magnet Synchronous Machine by Material-Efficient Axial Pole Pairing. IEEE Trans. Ind. Electron.
**2012**, 59, 2601–2611. [Google Scholar] [CrossRef] - Herlina; Setiabudy, R.; Rahardjo, A. Cogging torque reduction by modifying stator teeth and permanent magnet shape on a surface mounted PMSG. In Proceedings of the 2017 International Seminar on Intelligent Technology and Its Applications (ISITIA), Surabaya, Indonesia, 28–29 August 2017; pp. 227–232. [Google Scholar] [CrossRef]
- Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the ICNN’95—International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December 1995; Volume 4, pp. 1942–1948. [Google Scholar] [CrossRef]
- Reddy, M.J.; Kumar, D.N. Multi-objective Particle Swarm Optimization for Generating Optimal Trade-offs in Reservoir Operation. Hydrol. Process.
**2007**, 21, 2897–2909. [Google Scholar] [CrossRef] - Wang, D.; Tan, D.; Liu, L. Particle swarm optimization algorithm: An overview. Soft Comput.
**2018**, 22, 387–408. [Google Scholar] [CrossRef] - Baumgartner, U.; Magele, C.; Renhart, W. Pareto optimality and particle swarm optimization. IEEE Trans. Magn.
**2004**, 40, 1172–1175. [Google Scholar] [CrossRef] - Sethuraman, L.; Maness, M.; Dykes, K. Optimized Generator Designs for the DTU 10-MW Offshore Wind Turbine Using GeneratorSE; Technical Report; National Renewable Energy Laboratory: Washington, DC, USA, 2017. [Google Scholar]
- Bergen, A.; Andersen, R.; Bauer, M.; Boy, H.; ter Brake, M.; Brutsaert, P.; Buhrer, C.; Dhalle, M.; Hansen, J.; ten Kate, H.; et al. Design and in-field testing of the worlds first ReBCO rotor for a 3.6 MW wind generator. Supercond. Sci. Technol.
**2019**, 32, 125006. [Google Scholar] [CrossRef] - Zhu, Z.; Howe, D. Influence of design parameters on cogging torque in permanent magnet machines. IEEE Trans. Energy Convers.
**2000**, 15, 407–412. [Google Scholar] [CrossRef] - Wu, D.; Zhu, Z. Design trade-off between cogging torque and torque ripple in fractional slot surface-mounted permanent magnet machines. In Proceedings of the 2015 IEEE International Magnetics Conference (INTERMAG), Beijing, China, 11–15 May 2015; p. 1. [Google Scholar] [CrossRef]
- Popescu, M.; Cistelecan, M.V.; Melcescu, L.; Covrig, M. Low Speed Directly Driven Permanent Magnet Synchronous Generators for Wind Energy Applications. In Proceedings of the 2007 International Conference on Clean Electrical Power, Capri, Italy, 21–23 May 2007; pp. 784–788. [Google Scholar]

**Figure 4.**Comparison of radial air-gap flux density between RPMG and FPMG at no-load condition. $\tau $ is the generator’s pole pitch.

**Figure 8.**Optimization results by Pareto-fronts. (

**a**) FPMG result: Asterisk—all solutions through iterations. Triangle—Solutions of the last iteration. (

**b**) RPMG result: Asterisk—all solutions through iterations. Circle—Solutions of the last iteration.

**Figure 10.**Optimization results by non-dominated Pareto-front. Red triangles F1 and F2: FPMG solutions with the lowest torque ripple and mass, respectively. Red squares R1 and R2: RPMG solutions with the lowest torque ripple and mass, respectively.

**Figure 11.**Four generators marked in Figure 10. (

**a**) Overall generator. (

**b**) Models with one pole pair.

Parameter | Description | Value |
---|---|---|

${v}_{n}$ | Nominal wind speed | 11.4 m/s |

${\rho}_{air}$ | Air density | 1.225 kg/m${}^{3}$ |

${P}_{n}$ | Rated power | 20 MW |

${C}_{p}$ | Power coefficient | 0.48 |

${R}_{\mathrm{blade}}$ | Blade length | 120.9 m |

$\lambda $ | Tip speed ratio | 7 |

${\omega}_{\mathrm{shaft}}$ | Shaft speed | 6.303 rpm |

${U}_{p}$ | Rated line-to-line voltage | 3.3 kV |

${I}_{rms}$ | Phase current (rms) | 3499 A |

${k}_{\mathrm{fill}}$ | Filling factor | 0.65 |

Variable | Description |
---|---|

p | Number of pole pairs |

${N}_{a}$ | Number of armature winding turns |

${R}_{i}$ | Shaft radius |

${t}_{r}$ | Rotor yoke height |

${t}_{pm}$ | PM height |

${\alpha}_{pm}$ | PM arc ratio |

${l}_{t}$ | Stator tooth height |

${\alpha}_{t}$ | Tooth width ratio |

${t}_{s}$ | Stator yoke height |

${K}_{\mathrm{rad}}$ | Aspect ratio |

Variable | Value |
---|---|

p | 22 |

${N}_{a}$ | 2 |

${R}_{i}$ | 3.516 m |

${t}_{r}$ | 0.106 m |

${t}_{pm}$ | 0.157 m |

${\alpha}_{pm}$ | 0.72 |

${l}_{t}$ | 0.317 m |

${\alpha}_{t}$ | 0.449 |

${t}_{s}$ | 0.108 m |

${K}_{\mathrm{rad}}$ | 0.235 |

Variable | Value |
---|---|

p | 22 |

${N}_{a}$ | 2 |

${R}_{i}$ | 3.516 m |

${t}_{r}$ | 0.106 m |

${t}_{pm}$ | 0.157 m |

${\alpha}_{pm}$ | 0.1 ÷ 0.9 |

${l}_{t}$ | 0.317 m |

${\alpha}_{t}$ | 0.1 ÷ 0.9 |

${K}_{\mathrm{rad}}$ | 0.235 |

**Table 5.**Summary of four generators marked in Figure 10.

F1 | F2 | R1 | R2 | |
---|---|---|---|---|

Torque ripple [%] | 0.12 | 0.25 | 0.58 | 0.75 |

Mass [ton] | 326.6 | 246.8 | 125.9 | 116.2 |

Air-gap length [mm] | 12.26 | 12.28 | 9.01 | 8.90 |

Power [MW] | 21.39 | 20.00 | 21.32 | 20.00 |

Variables | Unit | F1 | F2 | R1 | R2 |
---|---|---|---|---|---|

p | - | 51 | 49 | 39 | 39 |

${N}_{a}$ | - | 1 | 1 | 1 | 1 |

${R}_{i}$ | m | 6 | 5.99 | 4.35 | 4.30 |

${t}_{r}$ | m | 0.036 | 0.030 | 0.039 | 0.044 |

${t}_{pm}$ | m | 0.091 | 0.112 | 0.117 | 0.099 |

${\alpha}_{pm}$ | - | 0.780 | 0.777 | 0.678 | 0.680 |

${l}_{t}$ | m | 0.255 | 0.178 | 0.126 | 0.130 |

${\alpha}_{t}$ | - | 0.481 | 0.330 | 0.416 | 0.396 |

${t}_{s}$ | m | 0.051 | 0.056 | 0.078 | 0.064 |

${K}_{\mathrm{rad}}$ | m | 0.22 | 0.20 | 0.20 | 0.20 |

Stack length | m | 2.748 | 2.455 | 1.802 | 1.780 |

Outer diameter | m | 12.88 | 12.76 | 9.43 | 9.29 |

F1 | F2 | R1 | R2 | |
---|---|---|---|---|

Cogging torque [kNm] | 33.75 | 28.46 | 53.91 | 133.68 |

${T}_{\mathrm{mean}}$ [MNm] | 32.44 | 30.32 | 32.30 | 30.29 |

Cogging torque [% of ${T}_{\mathrm{mean}}$] | 0.103 | 0.09 | 0.17 | 0.44 |

Torque density [MNm/m${}^{3}$] | 0.074 | 0.083 | 0.200 | 0.080 |

Efficiency at nominal wind speed [%] | 92.1 | 92.0 | 92.0 | 92.0 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hoang, T.-K.; Vido, L.; Tchuanlong, C.
Torque Ripple and Mass Comparison between 20 MW Rare-Earth and Ferrite Permanent Magnet Wind Generators. *Machines* **2023**, *11*, 1063.
https://doi.org/10.3390/machines11121063

**AMA Style**

Hoang T-K, Vido L, Tchuanlong C.
Torque Ripple and Mass Comparison between 20 MW Rare-Earth and Ferrite Permanent Magnet Wind Generators. *Machines*. 2023; 11(12):1063.
https://doi.org/10.3390/machines11121063

**Chicago/Turabian Style**

Hoang, Trung-Kien, Lionel Vido, and Celia Tchuanlong.
2023. "Torque Ripple and Mass Comparison between 20 MW Rare-Earth and Ferrite Permanent Magnet Wind Generators" *Machines* 11, no. 12: 1063.
https://doi.org/10.3390/machines11121063