Statistical modeling of the power grid from a wind farm standpoint

Abstract

In this study, we derive a statistical model of a power grid from the wind farm's standpoint based on dynamic principal component analysis. The main advantages of our model compared to the previously developed models are twofold. Firstly, our proposed model benefits from logged data of an offshore wind farm over several years which results in the development of a useful model for practical purposes. Secondly, the derived model is computationally inexpensive. Considering an arbitrary wind turbine generator, we show that the behavior of the power grid at the connection point can be represented by 4 out of 9 registered variables, i.e. 3-phase voltages, 3-phase currents, frequency, and generated active and reactive powers. We further prove that the dynamic nature of the system can be optimally captured by a time lag shift of two samples. To extend the derived model of a wind turbine generator to a wind farm, we propose an algorithm that optimally combines the principal components and scores. The principal components are estimated by the optimization of a cost function based on the modeling error while the scores are selected corresponding to the worst case scenario among the wind turbine generators. Our results show that the optimized principal components result in the modeling error less than 5% and the selected scores cover the variance of the data with probability higher than 95% among all generators in the wind farm.