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The complex interactions between renewables and AC/DC networks have brought new oscillation issues. To effectively monitor and suppress these oscillations, the observability and controllability of the oscillatory modes at different locations of the system must be investigated. To achieve this, the paper first defines the concept of modal observability and controllability using the responses of unit-pulse perturbations. Then an eigenvalue-decomposition based method is proposed to calculate these two indexes with the impedance network model (INM) as the input. The obtained modal observability(controllability) has many important applications and one of them is to facilitate the aggregation of the INM. The paper investigates this application by selecting an optimal aggregation port to ensure that the aggregated impedance can reflect the complete system dynamics. Finally, the proposed method is verified on a simple passive circuit and a practical wind power system that experienced actual subsynchronous resonance incidents. Theoretical results as well as EMT simulations demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper analytically examines how the condition of weak grid connection affects the torsional sub-synchronous oscillations (SSOs) induced by a grid-connected DFIG in a power system. The examination focuses on the SSO mode of grid-connected DFIG, which is dominated by the phase locked loop (PLL) or DC voltage control. Theoretical analysis is carried out to prove that the condition of weak grid connection amplifies the impact of modal resonance between the DFIG and torsional dynamics of synchronous generators. The amplifying effect of weak grid connection exhibits as the decrease of damping of SSO mode of DFIG and increase of the associated residue when the grid connection weakens. Consequently, the DFIG is more likely to induce torsional SSOs under the condition of weak grid connection, leading to system instability in the worst case. Analytical examination presented in the paper reveals the mechanism about how the condition of weak grid connection plays a key role for the DFIG to induce the torsional SSOs. An example multi-machine power system with the grid-connected DFIG is presented. Results of modal analysis and non-linear simulation using detailed model of DFIG validate the analysis and conclusions made in the paper. [ABSTRACT FROM AUTHOR]