Cross-gramian-based dynamic equivalence of wind farms

This study presents dynamic equivalence of wind farms using the cross-gramian (CG)-based model order reduction method. For the purpose of wind fluctuation simulation, the dynamic model of wind farms can be described as a high-order linear input–output system, whose input is the wind speed and output is the active power injected from point of common coupling (PCC). The main input–output behaviours of the system can be measured by its CG. The right and left eigenspaces associated with large eigenvalues of CG are used to obtain a low-order model. Frequency-domain analysis of wind farms consisted of doubly-fed induction generators shows that the proposed method is rapid and numerically stable. The non-linear dynamic simulation also confirms that the reduced model is capable of retaining the dynamic relationship between the input and output of original wind farms. The proposed method offers a potential solution to dynamic simulation of the power system with large-scale wind farms.

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