# Analysis of the Propagation Characteristic of Subsynchronous Oscillation in Wind Integrated Power System

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## Abstract

**:**

## 1. Introduction

## 2. Dynamic Model of Wind Integrated Power System

_{W}is the DFIG bus voltage; I

_{W}is the DFIG bus injection current. The positive direction of the physical quantity uses the generator convention.

## 3. Oscillation Propagation Factor

#### 3.1. The Linearization Model

#### 3.2. Oscillation Propagation Factor

## 4. Simulation Results and Analysis

#### 4.1. Two Area Four Machine System

#### 4.1.1. Frequency Domain Simulation Results

#### 4.1.2. Time Domain Simulation Results

#### 4.2. New England 39 Bus System

#### 4.2.1. Frequency Domain Simulation Results

#### 4.2.2. Time Domain Simulation Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Leon, A.E. Integration of DFIG-Based Wind Farms Into Series-Compensated Transmission Systems. IEEE Trans. Sustain. Energy
**2017**, 7, 451–460. [Google Scholar] [CrossRef] - Liu, H.; Xie, X.; Zhang, C.; Li, Y.; Liu, H.; Hu, Y. Quantitative SSR analysis of series-compensated DFIG-based wind farms using aggregated RLC circuit model. IEEE Trans. Power Syst.
**2017**, 32, 474–483. [Google Scholar] [CrossRef] - Gao, F.; He, Q.; Hao, Z.; Zhang, B. The research of subsynchronous oscillation in PMSG wind farm. In Proceedings of the IEEE PES AsiaPacificPower and Energy Engineering Conference (APPEEC), Xi’an, China, 25–28 October 2016; pp. 1883–1887. [Google Scholar]
- Dincer, I. Renewable energy and sustainable development: A crucial review. Renew. Sustain. Energy Rev.
**2000**, 4, 157–175. [Google Scholar] [CrossRef] - Khan, M.A.A.; Shahriar, M.M.; Islam, M.S. Power quality improvement of DFIG and PMSG based hybrid wind farm using SMES. In Proceedings of the International Conference on Electrical & Electronic Engineering (ICEEE), Ankara, Turkey, 8–10 April 2017; pp. 1–4. [Google Scholar]
- Fan, L.; Yuvarajan, S.; Kavasseri, R. Harmonics analysis of a DFIG for a wind energy conversion system. IEEE Trans. Energy Convers.
**2010**, 25, 181–190. [Google Scholar] [CrossRef] - Djurović, S.; Vilchis-Rodriguez, D.S.; Smith, A.C. Supply induced interharmonic effects in wound rotor and doubly-fed induction generators. IEEE Trans. Energy Convers.
**2015**, 30, 1397–1408. [Google Scholar] [CrossRef] - Wen, T.; Huang, Y.; Zhao, D.; Zhu, L.; Wang, X. Mechanism of Sub-synchronous Interaction caused by inter-harmonics in DFIG. J. Eng.
**2017**, 13, 892–896. [Google Scholar] [CrossRef] - Dong, X.; Zang, W.; Dong, C.; Xu, T. SSR characteristics study considering DFIGs at different locations in large wind farm. In Proceedings of the China International Conference on Electricity Distribution (CICED), Xi’an, China, 10–13 August 2016; pp. 1–6. [Google Scholar]
- Leon, A.E.; Solsona, J.A. Sub-synchronous interaction damping control for DFIG wind turbines. IEEE Trans. Power Syst.
**2015**, 30, 419–428. [Google Scholar] [CrossRef] - Cheng, Y.; Sahni, M.; Muthumuni, D.; Badrzadeh, B. Reactance scan crossover-based approach for investigating SSCI concerns for DFIG-based wind turbines. IEEE Trans. Power Deliv.
**2013**, 28, 742–751. [Google Scholar] [CrossRef] - Suriyaarachchi, D.H.R.; Annakkage, U.D.; Karawita, C.; Jacobson, D.A. A Procedure to Study Sub-Synchronous Interactions in Wind Integrated Power Systems. IEEE Trans. Power Syst.
**2013**, 28, 377–384. [Google Scholar] [CrossRef] - Fan, L.; Miao, Z. Nyquist-stability-criterion-based SSR explanation for type-3 wind generators. IEEE Trans. Energy Conv.
**2012**, 27, 807–809. [Google Scholar] [CrossRef] - Sun, J. Impedance-based stability criterion for grid-connected inverters. IEEE Trans. Power Electron.
**2011**, 26, 3075–3078. [Google Scholar] [CrossRef] - Cespedes, M.; Sun, J. Modeling and mitigation of harmonic resonance between wind turbines and the grid. In Proceedings of the IEEE Energy Conversion Congress and Exposition, Phoenix, AZ, USA, 17–22 September 2011; pp. 2109–2116. [Google Scholar]
- Wu, F.; Zhang, X.; Godfrey, K.; Ju, P. Modeling and Control of Wind Turbine with Doubly Fed Induction Generator. In Proceedings of the IEEE PES Power Systems Conference and Exposition, Atlanta, GA, USA, 29–31 October 2006; pp. 1404–1409. [Google Scholar]
- Qiao, W. Dynamic modeling and control of doubly fed induction generators driven by wind turbines. In Proceedings of the IEEE PES Power Systems Conference and Exposition, Seattle, WA, USA, 15–18 March 2009; pp. 1–8. [Google Scholar]
- Erdogan, N.; Henao, H.; Grisel, R. A proposed Technique for Simulating the Complete Electric Drive Systems with a Complex Kinematics Chain. In Proceedings of the 2007 IEEE International Electric Machines & Drives Conference, Antalya, Turkey, 3–5 May 2007; pp. 1240–1245. [Google Scholar]
- Abad, G.; Rodriguez, M.A.; Iwanski, G.; Poza, J. Direct Power Control of Doubly Fed Induction Generator based Wind Turbines under Unbalanced Grid Voltage. IEEE Trans. Power Electron.
**2010**, 25, 442–452. [Google Scholar] [CrossRef] - Jiang, J.; Chao, Q.; Chen, J.; Chang, X. Simulation study on frequency response characteristic of different wind turbines. Renew. Energy Resour.
**2010**, 28, 24–28. [Google Scholar] - Skogestad, S.; Postlethwaite, I. Multivariable Feedback Control: Analysis and Design; John Wiley & Sons: Hoboken, NJ, USA, 2005. [Google Scholar]
- Kundur, P. Power System Stability and Control; Balu, N.J., Lauby, M.G., Eds.; McGraw-Hill: New York, NY, USA, 1994; Volume 7. [Google Scholar]
- Holmes, D. Pulse Width Modulation for Power Converters: Principles and Practice; JohnWiley & Sons: Hoboken, NJ, USA, 2003. [Google Scholar]
- Pai, M.A. Energy Function Analysis for Power System Stability; Kluwer Academic Publishers: Boston, MA, USA, 1989. [Google Scholar]
- Xie, X.; Liu, W.; Liu, H.; Du, Y.; Li, Y. A system-wide protection against unstable SSCI in series-compensated wind power systems. IEEE Trans. Power Deliv.
**2018**, 33, 3095–3104. [Google Scholar] [CrossRef]

Mode | Eigenvalue | Angular Frequency (Rad/s) | Damping Ratio |
---|---|---|---|

1 | −0.3364 ± 90.8578j | 90.8578 | 0.0037 |

2 | −0.1806 ± 89.5917j | 89.5917 | 0.0020 |

3 | −0.1297 ± 75.1461j | 75.1461 | 0.0017 |

4 | −0.2758 ± 74.9510j | 74.9510 | 0.0037 |

5 | −0.0368 ± 13.3422j | 13.3422 | 0.0028 |

6 | −0.0403 ± 12.4648j | 12.4648 | 0.0032 |

7 | −0.0355 ± 6.5300j | 6.5300 | 0.0054 |

Mode | Eigenvalue | Angular Frequency (Rad/s) | Damping Ratio |
---|---|---|---|

1 | −0.2973 ± 90.9755j | 90.9755 | 0.0033 |

2 | −0.2285 ± 89.8449j | 89.8449 | 0.0025 |

3 | −0.2367 ± 75.1553j | 75.1553 | 0.0031 |

4 | −0.2539 ± 74.9392j | 74.9392 | 0.0034 |

5 | −0.0373 ± 13.3797j | 13.3797 | 0.0028 |

6 | −0.0403 ± 12.4733j | 12.4733 | 0.0032 |

7 | −0.0395 ± 6.3194j | 6.3194 | 0.0062 |

Mode | Eigenvalue | Angular Frequency (Rad/s) | Damping Ratio |
---|---|---|---|

1 | −0.5060 ± 90.4108j | 90.4108 | 0.0056 |

2 | −0.5494 ± 91.0655j | 91.0655 | 0.0060 |

3 | −0.4586 ± 74.7992j | 74.7992 | 0.0061 |

4 | −0.5610 ± 75.0893j | 75.0893 | 0.0075 |

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**MDPI and ACS Style**

Wen, Z.; Peng, S.; Yang, J.; Deng, J.; He, H.; Wang, T.
Analysis of the Propagation Characteristic of Subsynchronous Oscillation in Wind Integrated Power System. *Energies* **2019**, *12*, 1081.
https://doi.org/10.3390/en12061081

**AMA Style**

Wen Z, Peng S, Yang J, Deng J, He H, Wang T.
Analysis of the Propagation Characteristic of Subsynchronous Oscillation in Wind Integrated Power System. *Energies*. 2019; 12(6):1081.
https://doi.org/10.3390/en12061081

**Chicago/Turabian Style**

Wen, Zhiping, Shutao Peng, Jing Yang, Jun Deng, Hanqing He, and Tong Wang.
2019. "Analysis of the Propagation Characteristic of Subsynchronous Oscillation in Wind Integrated Power System" *Energies* 12, no. 6: 1081.
https://doi.org/10.3390/en12061081