# Research on Control of Levitation Force and Torque of a Maglev Device for Water-Turbine Generator Set

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure and Principle of the Maglev Device

## 3. Torque Offsetting Design

## 4. Calculation and Relationship of the Levitation Force and Torque

#### 4.1. Analytic Calculation of the Levitation Force and Torque

#### 4.2. Relationship of the Levitation Force and Torque

## 5. Control of the Normal Force and the Torque

#### 5.1. Dynamic Mathematical Model of the Torque

#### 5.2. Dynamic Mathematical Model of the Normal Lift Force

#### 5.3. Control Strategy of the Normal Force and the Torque

## 6. Simulation and Experimental Verification of Control Strategy

#### 6.1. Simulation Verification of Control Strategy

#### 6.2. Experimental Verification of Control Strategy

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- National Energy Administration of China. Notification on the Completion of the Duty Weighting of Renewable Energy Electricity Consumption; National Energy Administration of China: Beijing, China, 2021.
- Chen, Y.Q.; Hu, W.M. New progress in research on 1000MW hydropower unit. Electr. Power Constr.
**2011**, 32, 62–66. [Google Scholar] - Liu, Q.Y.; Fu, Y.C.; Wu, Z.D. Thrust bearing tile temperature of large hydraulic generator. Large Electr. Mach. Hydraul. Turbine
**2010**, 4, 14–15. [Google Scholar] - Yu, K.S. Discussion on thrust bearing support structure and principle of hydrogenator. Mech. Electr. Tech. Hydropower Stn.
**1996**, 1, 1–7. [Google Scholar] - Liu, J.; Ma, H.Z.; Zhang, Q.; Zhang, L.J.; Cai, B.P. Design and optimization of a magnetic levitation load reduction device for a hydropower unit. IEEE Access
**2021**, 9, 32019–32029. [Google Scholar] [CrossRef] - Liu, J.; Wang, R.B.; Hu, J.L.; Zhang, Q.; Ma, H.Z.; Zhang, L.J.; Cai, B.P. Study on Improving the Levitation Force for a Maglev Load Reduction Machine. IEEE Trans. Appl. Supercond.
**2021**, 31, 4400805. [Google Scholar] [CrossRef] - Morizane, T.; Tsujikawa, K.; Kimura, N. Control of Traction and Levitation of Linear Induction Motor Driven by Power Source with Frequency Component Synchronous with the Motor Speed. IEEE Trans. Magn.
**2011**, 47, 4302–4305. [Google Scholar] [CrossRef] - Ghosh, M.K.; Gao, Y.; Dozono, H.; Muramatsu, K.; Guan, W.; Yuan, J.; Tian, C.; Chen, B. Proposal of Maxwell Stress Tensor for Local Force Calculation in Magnetic Body. IEEE Trans. Magn.
**2018**, 54, 7206204. [Google Scholar] [CrossRef] - Long, X.L. Theory and Magnetic Design Method of Linear Induction Motor; Science: Beijing, China, 2006. [Google Scholar]
- Burnham, D.C. Asymptotic Lift to Drag Ratios for Magnetic Suspension Systems. J. Appl. Phys.
**1971**, 42, 3455–3457. [Google Scholar] [CrossRef] - Gang, L. Research on Decoupling Optimal Control of Linear Induction Motor; Beijing Jiaotong University: Beijing, China, 2007; pp. 84–135. [Google Scholar]
- Reitz, J.R.; Davis, L.C. Force on a Rectangular Coil Moving above a Conducting Slab. J. Appl. Phys.
**1972**, 43, 1547–1553. [Google Scholar] [CrossRef] - Wang, H.; Bao, J.; Xue, B.; Liu, J. Control of Suspending Force in Novel Permanent-Magnet-Biased Bearingless Switched Reluctance Motor. IEEE Trans. Ind. Electron.
**2015**, 62, 4298–4306. [Google Scholar] [CrossRef] - Li, X.; Wang, X.; Gao, P.; Gu, Y. Model Predictive Current Control Algorithm Based on Joint Modulation Strategy for Low-Inductance PMSM. IEEE Trans. Power Electron.
**2022**, 37, 806–819. [Google Scholar] [CrossRef] - Cruz, S.M.A.; Marques, G.D.; Gonçalves, P.F.C.; Iacchetti, M.F. Predictive Torque and Rotor Flux Control of a DFIG-DC System for Torque Ripple Compensation and Loss Minimization. IEEE Trans. Ind. Electron.
**2018**, 65, 9301–9310. [Google Scholar] [CrossRef] [Green Version] - Hao, Z.; Yu, Q.; Cao, X.; Deng, X.; Shen, X. An Improved Direct Torque Control for a Single-Winding Bearingless Switched Reluctance Motor. IEEE Trans. Energy Convers.
**2020**, 35, 1381–1393. [Google Scholar] [CrossRef] - Cho, Y.; Bak, Y.; Lee, K.-B. Torque-Ripple Reduction and Fast Torque Response Strategy for Predictive Torque Control of Induction Motors. IEEE Trans. Power Electron.
**2018**, 33, 2458–2470. [Google Scholar] [CrossRef]

**Figure 3.**The normal force from the analytical method and FEA. (

**a**) Normal force via the exciting current, (

**b**) Normal force via the power frequency, (

**c**) Normal force via the plate thickness, (

**d**) Normal force via the air gap length.

**Figure 7.**Dynamic features under the flux-linkage adjustment. (

**a**) Rotor flux linkage via time, (

**b**) Positive torque via time, (

**c**) Resultant torque via time, (

**d**) Resultant lift force via time, (

**e**) i

_{sq}via time, (

**f**) i

_{sd}via time.

**Figure 8.**Dynamic features under the rotor-speed fluctuation. (

**a**) Phase current via time, (

**b**) Resultant lift force via time, (

**c**) Resultant torque via time.

**Figure 9.**Dynamic features under the axial load disturbance. (

**a**) Pressure via time under disturbance, (

**b**) i

_{sq}

^{*}via time under disturbance, (

**c**) Lift force via time under disturbance.

**Figure 10.**Dynamic features under the axial-load disturbance and the flux-linkage adjustment with cascade control. (

**a**) Lift force via time, (

**b**) Resultant torque via time.

**Figure 12.**Tested levitation force with the shaft rotating at some speed. (

**a**) The tested levitation force for a long time; (

**b**) details of (

**a**).

**Figure 13.**Tested torque with the rotor blocked. (

**a**) The positive torque via power frequency, (

**b**) The reverse torque via power frequency.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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**

Liu, J.; Xu, C.; Zhu, J.; Huang, L.; Ma, H.
Research on Control of Levitation Force and Torque of a Maglev Device for Water-Turbine Generator Set. *Sustainability* **2022**, *14*, 8742.
https://doi.org/10.3390/su14148742

**AMA Style**

Liu J, Xu C, Zhu J, Huang L, Ma H.
Research on Control of Levitation Force and Torque of a Maglev Device for Water-Turbine Generator Set. *Sustainability*. 2022; 14(14):8742.
https://doi.org/10.3390/su14148742

**Chicago/Turabian Style**

Liu, Jing, Chongwang Xu, Jinnan Zhu, Lei Huang, and Hongzhong Ma.
2022. "Research on Control of Levitation Force and Torque of a Maglev Device for Water-Turbine Generator Set" *Sustainability* 14, no. 14: 8742.
https://doi.org/10.3390/su14148742