LPV polytopic modelling and stability analysis of a DFIG for a wind energy conversion system based on LMI approach

A state space model of a dynamical system is commonly obtained from algebraic handling of its physic equations, which involve often-approximate parameter values due to imperfect knowledge of system components or variable parameters in time. These parameters are referred to as uncertainties. The modelling of uncertain systems is relevant in stability analysis methods such as Lyapunov theory. In addition, in robust control synthesis, the more information the model gives about uncertain parameter dynamics i.e. its value bounds and its variation rates, the best their performances are enhanced. Since the Linear Matrix Inequalities (LMI) approach has been introduced in the analysis and the control of complex systems, modelling parameter dependent systems is also relevant in the formulation and the resolution of LMIs. This paper is focused on the equivalence between Linear Parameter Varying (LPV) modelling of a Doubly Fed Induction Generator (DFIG) of a Wind Energy Conversion System use under both affine and polytopic structures. The stability analysis based on LMI approach is also carried out.