Interaction among synchronous generator (SG)

wind farm

and high-voltage direct current (HVDC) adds risk of power system low-frequency oscillation (LFO). Installing the supplementary damping controller (SDC) at the doubly-fed induction generator (DFIG) can improve small-signal stability. Due to system requirement and installation cost

not all DFIGs have SDCs

which yields the heterogeneous wind farm (HWF). This paper proposes the equivalent wind-farm-grid oscillation model for the HWF

and quantifies the impact of interactions among HWF

SG

and HVDC on the LFO. At first

the non- diagonal state submatrices relating to SDCs are derived. With the same control effect of SDCs

equivalent HWF equations are proposed. Based on relation of the outputs of equivalent DFIGs and HWF

the equivalent wind-farm-grid oscillation model of the HWF is proposed. Then

substructure models of the HWF- SG-HVDC are derived

whose output currents are given by the superposition of interaction currents with equipments’ terminal voltage and transmission system admittance. The component connection method is used to derive state matrix considering the interactions. Finally

nonlinear interactive matrix is derived

whose F-norm is defined as interactive strength. With elements of interactive matrix as the intermediate variables

sensitivity of critical mode with respect to interactive strength is proposed

and an optimization model to suppress the LFO is derived. The simulation results show that after the optimization

the system interactive strength is reduced by 24.5%

and the damping ratio of critical mode is increased from 0.02 to 0.06.