An Equivalent Model of Wind Farms for Torsional Vibration Analysis

Abstract

Torsional vibration of wind turbines can be excited by the small electrical disturbance from the power system, which can cause damage to the shaft. In this paper, based on the established model of fixed speed induction generator (FSIG), the small signal model of the FSIG-based wind farm is developed according to the step by step transfer of the state variables of the differential equations. Then through similarity transformation of the state matrix, a novel equivalent model of the multi-machine infinite-bus system is derived. In this model, the original N–FSIG wind farm is decomposed into N-1 identical independent single-machine infinite-bus subsystems and one modified single-machine infinite-bus subsystem. Finally, simulations are performed in Matlab/Simulink and results comparison between the small signal model without equivalence and the proposed equivalent model is conducted extensively. The results show that the torsional vibration modes are reserved completely in the reduced order equivalent model. In addition, the obtained torsional vibration frequencies match well with those from the small signal model without equivalence, indicating the effectiveness and robustness of the equivalent model. Through modal analysis, it is also found that the torsional vibration is excited in both the disturbed FSIGs and the undisturbed ones. Besides, the obtained results are also verified through time-domain simulation.