Damping To Low Frequency Oscillations Of DFIG-integrated Power System Based On Eigenvalue Sensitivity

With the low frequency oscillation of power systems affected by the grid-integrated doubly-fed induction generator(DFIG),the power oscillation damper(POD)is introduced to the converter of the DFIG to improve the system damping.Considering the nonlinear character of power systems,the functional sensitivity and second order eigenvalue sensitivity are applied to improve the accuracy of the sensitivity model,which may be regarded as the fundamental research of eigen-analysis and optimization to the POD parameters.It is found that the low frequency oscillation mode is introduced to the DFIG by the POD,which intensifies the oscillation of the former.According to the transfer function derived with the open-loop model of the DFIG,the impact of the POD on the DFIG is quantified,based on which,the optimization model of the POD parameters considering the stability of the DFIG is established.Combining the sliding mode control(SMC)and the eigenvalue sensitivity,the low frequency oscillation damping controller of the DFIG-integrated power system is proposed,which is robust to the variation of wind speeds.In this paper,the innovative work is as follow:(1)Considering the structure and control strategy of the DFIG,the state space equations of wind power systems including the transfer function of the POD is established,based on which,the functional sensitivity to the POD is newly derived by the derivations of coefficient matrices.The improved functional sensitivity model is proposed with a higher accuracy,in which,the eigenvalue increment is introduced to the iterative calculation of transfer function increment.With the functional eigenvalue sensitivity,the approximate results of the first and the second order derivatives of eigenvalue to the POD parameters is derived,based on which,the optimization to the POD parameters is carried out.(2)To solve the second order eigenvalue sensitivity,the eigenvector sensitivity is required whose difficulty lies in insufficient constraints of eigenvectors in the eigenanalysis model.Two constraints about the magnitude and angle of eigenvector elements are newly proposed,and the normalization conditions are derived to solve the eigenvector sensitivity and the second order eigenvalue sensitivity.Based on the first and the second order eigenvalue sensitivity,the optimization model of the POD parameters is established.(3)The optimization to POD parameters considering its impact on the DFIG is proposed.The open-loop subsystems of the DFIG with the POD and the rest part of power system are derived to describe the interaction between them.The transfer function of the DFIG is derived based on the open-loop model to study the impact of the POD on the DFIG.The balanced truncation method is used to reduce the transfer function of the DFIG and derive the analytical description to the oscillation of the DFIG.Considering the impact of the POD on the DFIG,the constraint to the DFIG is proposed and newly incorporated in the optimization model to the POD parameters,aiming to achieve the coordinated damping control of the oscillations of power system and the DFIG.(4)The low frequency oscillation damping controller is proposed based on the eigenvalue sensitivity and the SMC.According to the state space equation of DFIGintegrated power system,the time derivative of sliding surface is derived to find the relative degree,and the switch control law is designed with the super twisting algorithm.Then,the closed-loop model of power system with equivalent control is derived to analyze the damping effect and undesirable effect on the low frequency oscillation modes.The improved equivalent control is proposed,whose gain is optimized with the first and the second order eigenvalue sensitivities.