## Effect of PI controllers’ parameters on machine-network interaction of grid-connected PMSG system

In order to study the oscillation problem of grid-connected permanent magnet direct drive wind power generation (PMSG) system, a small-signal model of PMSG system based on PQ (active and reactive powers) decoupling control is established. All the oscillation modes of the system are found out, by using eigenvalue analysis and correlation factor analysis. The characteristic frequency and the dominant state variables of each oscillation mode are considered, the optimal parameter combination of proportional–integral (PI) controller is obtained by using the distribution estimation algorithm based on Copula theory. The time-domain simulation of the MATLAB/Simulink platform verifies the existence of various modes of oscillation. The control parameters of the converter are changed in turn without changing the stability of the system, the subsynchronous control interaction; the subsynchronous oscillation and the low-frequency oscillation mode of the system are studied. The modal analysis of the PMSG system model is carried out by using the optimal PI controller parameters, and the simulation results verify the correctness of the proposed model. This type of theoretical/practical approach has not been taken before to resolve the oscillation problems of grid-connected PMSG.