۱- Introduction

۲- The model

۳- Global boundedness under control limits

۴- Hopf bifurcation and periodic attractors

۵- Conclusion

References

Abstract

In this paper we investigate whether continuous oscillations are probable for the wind turbines dynamics when connected to the grid. This can have negative consequences on the mechanical parts of the system, the power grid and, possibly, on other power systems connected to the same grid. We consider the wind turbine when the pitch control is activated, exposing it to higher wind speeds. In order to find out if there are continuous oscillations in the state variables that may realistically occur, we investigate if there are periodic attractors for the dynamics that are still allowed within the control limits suggested by many in industry, such as, and not limited to General Electric. The paper provides rigorous mathematical proofs for boundedness of the systems state variables and their derivatives under the imposed control limits by industry. This establishes the existence of attractors in a bounded system under the controls. We then find that there is a Hopf bifurcation in which periodic attractors within the control limits exist. The results are supported by simulations. The nonlinear model used in the analysis is validated versus a real measured data to magnify the finding of this paper. The conclusion of this paper is significant for the nonlinear dynamics and control literature for wind turbines complex system, and the possible consequences on studying/questioning the control limits (limeters) suggested by industry.

Introduction

According to the US Department of Energy [1], wind is the fastest growing energy resource being used. This rapid expansion requires more scientific research and studies to comprehend the dynamics of Wind Turbine Generators (WTGs), if we are to gain the most from this valuable resource. Governments and corporations are working on understanding the challenges and consequences of integrating WTGs within large cities with/without other power systems. As a result of the complexities of the WTG mechanical and electrical systems, dynamic and control studies have increased recently. This has been observed by the comprehensive review article [2]. Additionally, the reader may consider [3,4] for studies that are looking into the challenges facing the future of power grid with large share of wind and renewable energies. According to [5], three-bladed (type-3) WTGs are more efficient in extracting power from the air streams, when compared to other types. Coefficients of Performance ( curves) of type-3 can go to up 0.4-0.5 efficiency (also see [6]). Most agree that Doubly Fed Asynchronous/Induction Generator (DFAG/DFIG) is mostly the technology used with WTGs systems. A detailed study describing this can be found in the literature review of [2] with citations to many sources in the literature that focus mainly on investigating the implementation and advantageous of DFAG/DFIG technologies.