Disturbance Margin for Quantifying Limits on Power Smoothing by Wind Turbines

Wind turbines can, in principle, be operated to smooth wind power fluctuations by allowing wider variations in turbine speed and generator torque to store and release energy. This ability must be constrained by turbine speed and generator torque limits. To present, work in the literature is conceptual and does not indicate what extent of smoothing is possible before component limits are reached, nor does it quantify sensitivity to variations in the input wind speed. This paper introduces a method for quantifying how much wind variation a wind turbine can absorb in variable speed mode while still being guaranteed to operate within its component limits. One can apply this method to obtain the dependence of maximum tolerable wind disturbance on the smoothing time constant, and thus make design decisions. This paper shows that the analysis of torque speed intersections, as standardly applied in electric machine theory, is of limited use for studying power smoothing. The new conclusions and design choices made available by the proposed method are illustrated with a series of computation examples. The method is shown to agree asymptotically with two limiting cases that can be calculated based on torque-intersection analysis. The method is based on new theory for computing invariance kernels for nonlinear planar systems, and can be adapted to assess the robustness of other control laws.