Order reduction of a wind turbine energy system via the methods of system balancing and singular perturbations

Abstract

In this paper we study the order reduction of a wind turbine model using the methods of balancing transformation and singular perturbations. We show that the order of the considered wind turbine model can be reduced from eight to six via the balancing transformation. Further reduction via the aforementioned method results in a significant jump in the error bound. In contrast, the method of singular perturbations shows that the order of the model can be further reduced to four, or two, and still provide very good approximations to the system model, in terms of its transient step response. Moreover, we show that the reduction in model order achieved via singular perturbations is superior to that achieved via balancing, when the linear-quadratic near-optimal controllers are considered and when wind turbulence and a large-signal disturbance are applied to the system.