# Low-frequency oscillations of wind power systems caused by doubly-fed induction generators

## Highlights

The state equations of the DFIGs with the stator voltage transient are newly proposed.

The participation ratios are defined by the DFIGs to find the LFO caused by the DFIGs.

The multi-step derivatives are proposed to derive the sensitivity of the LFO.

The sensitivity-based damping scheme is proposed by changing parameters of the converters.

## Abstract

The existing researches on the wind power systems do not specify whether of the low-frequency oscillations are caused by the synchronous generators or the wind turbine generators. In this paper, the low-frequency oscillation caused by the doubly-fed induction generators (DFIGs) is studied. The linearized state equations of the DFIGs with the stator voltage transient are newly proposed, where the stator voltages as algebraic variables are expressed by the state variables. The low-frequency oscillation modes, usually caused by the synchronous generators, are newly defined by the mechanical parameters of the DFIGs to derive the participation ratios and find the low-frequency oscillation modes caused by the DFIGs. The low-frequency oscillation modes caused by the DFIGs are validated by the dynamic response using the band-pass/low-pass filter. The multi-step derivatives are proposed to quantify the sensitivity of the oscillation modes caused by the DFIGs to the parameters of the DFIGs and the synchronous generators. The damping schemes are derived by comparing the sensitivity and the accuracy is validated. The numerical results on the IEEE RTS system and a regional system show the error due to neglect to the stator voltage transient. The low-frequency oscillations caused by the DFIG have longer period, and converge more slowly than those caused by the synchronous generators.

## Keywords

• Low-frequency oscillation;
• Doubly-fed induction generator;
• Stator voltage transient;
• Sensitivity;
• Oscillation damping