# Robust Sliding Mode Control of Permanent Magnet Synchronous Generator-Based Wind Energy Conversion Systems

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## Abstract

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## 1. Introduction

## 2. Wind Energy Conversion PMSG Model

#### 2.1. Ideal Actuator Disk Model

#### 2.2. Performance of a Non-Ideal Wind Turbine

#### 2.3. Permanent Magnet Synchronous Generator Model

## 3. Sliding Mode Control

#### 3.1. First-Order Sliding Mode Control

#### 3.1.1. Sliding Surfaces

#### 3.1.2. Reachability

#### 3.1.3. Parameter Variations

#### 3.1.4. Direct Axis Current Control Design

#### 3.1.5. Quadrature Axis Control Design

#### 3.1.6. Control Design Based on Rotational Speed Dynamics

#### 3.2. Higher Order Sliding Mode Design Using Super Twisting Algorithm

#### 3.2.1. Direct Axis Control Design

#### 3.2.2. Quadrature Axis Control Design

#### 3.2.3. Quadrature Axis Current Reference Control Design

## 4. Computer Simulation Results

#### 4.1. Piecewise Affine Wind Speed Input

#### 4.2. Stochastic Wind Speed Input

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Model of actuator disk interaction with wind [28].

**Figure 2.**Simplified diagram of a permanent magnet synchronous generator (PMSG)-WECS [28].

**Figure 7.**The direct axis current ${i}_{d}$ state trajectory controlled by the sliding mode control (SMC).

Property | Parameter Value |
---|---|

Rotor radius | ${R}_{t}=3$ m |

Stator Resistance | ${R}_{s}=3.5$ Ω |

d-axis inductance | ${L}_{q}=35$ mH |

q-axis inductance | ${L}_{d}=35$ mH |

Flux linkage | ${\mathsf{\Psi}}_{m}=0.3$ Wb |

Poles | $P=6$ |

Inertia | $J=1$ |

Stiffness | $B=0.001$ |

© 2016 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 (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Zhuo, G.; Hostettler, J.D.; Gu, P.; Wang, X. Robust Sliding Mode Control of Permanent Magnet Synchronous Generator-Based Wind Energy Conversion Systems. *Sustainability* **2016**, *8*, 1265.
https://doi.org/10.3390/su8121265

**AMA Style**

Zhuo G, Hostettler JD, Gu P, Wang X. Robust Sliding Mode Control of Permanent Magnet Synchronous Generator-Based Wind Energy Conversion Systems. *Sustainability*. 2016; 8(12):1265.
https://doi.org/10.3390/su8121265

**Chicago/Turabian Style**

Zhuo, Guangping, Jacob D. Hostettler, Patrick Gu, and Xin Wang. 2016. "Robust Sliding Mode Control of Permanent Magnet Synchronous Generator-Based Wind Energy Conversion Systems" *Sustainability* 8, no. 12: 1265.
https://doi.org/10.3390/su8121265