Abstract
In this paper, a new analytical approach is proposed to investigate the electrical and mechanical behavior of a low-power permanent magnet synchronous generator (PMSG) in the presence of a wind gust. The proposed model for the wind gust and wind power system was analytically investigated using the optimal auxiliary functions method (OAFM), which has proven to be a reliable tool. The reaction of the system to a wind gust was explicitly obtained, which is useful for stability analysis, protection issues, and risk assessment concerning the PMSG. A substantial reduction of computations in analytically analysing a complicated dynamical system is ensured by this new approach, through some auxiliary functions and convergence-control parameters.
Highlights
Wind turbine dynamics recently became a subject of great interest for scientists [1,2], with the increasing importance of renewable, green energy harvesting technologies and their installations.It is a known reality that both mechanical and electrical loads are greatly influenced by the action of the wind speed and its variations, which simultaneously affect the tower/nacelle and blade system, and the electrical parameters or the mechanical behavior of the stator/rotor system
Other works reveal the dynamic response of permanent magnet synchronous generators (PMSGs) to specific wind speed profiles in order to assess both the electrical and mechanical stress of different components of the wind power station [5] or propose some modeling procedures for wind speed simulation, which are needed in the investigation of wind power systems [6]
The jumps in wind speed represented by wind gusts are often present in real operating conditions and can produce mechanical and electrical shocks, which can lead to damages from both mechanical and electrical points of view
Summary
Wind turbine dynamics recently became a subject of great interest for scientists [1,2], with the increasing importance of renewable, green energy harvesting technologies and their installations. Bystryk and Sullivan [9] analyzed control strategies for a small-scale wind turbine in intermittent wind gusts using a computer model Such developments need some reliable models, which must obey the theory of electrical machines [10,11,12,13]. Two other improved homotopic approaches are the optimal homotopy perturbation method (OHPM) [21] and the optimal homotopy asymptotic method (OHAM) [22,23], which are endowed with a rigorous and reliable procedure for convergence control, which lead to an increase in accuracy at a reduced number of iterations Among these new and emerging approaches intended for solving non-linear problems can be mentioned the modified differential transform method (MDTM) [24], which is used mainly in solving boundary values problems.
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