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While transmission expansions are planned to have positive impact on reliability of power grids, they could increase the risk and severity of some of the detrimental incidents in power grid mainly by virtue of changing system configuration, consequently electrical distance. This paper aims to evaluate and quantify the impact of transmission expansion projects on Sub-Synchronous Resonance (SSR) risk through a two-step approach utilizing outage count index and Sub-synchronous damping index. A graph-theory based SSR screening tool is introduced to quantify the outage count associated with all grid contingencies which results in radial connection between renewable generation resources and nearby series compensated lines. Moreover, a frequency-scan based damping analysis is performed to assess the impact of transmission expansion on the system damping in sub-synchronous frequency range. The proposed approach has been utilized to evaluate the impact of recently-built transmission expansion project on SSR risk in a portion of Electric Reliability Council of Texas (ERCOT) grid.

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This paper presents the design of a robust fixed-order H ∞ controller to damp out the inter-area oscillations and to enhance the stability of the power system. The proposed H ∞ approach is based on shaping the open-loop transfer function in the Nyquist diagram through minimizing the quadratic error between the actual and the desired open loop transfer functions in the frequency domain under linear constraints that guarantee robustness and stability. The proposed approach is robust with respect to multi-model uncertainty closed-loop sensitivity functions in the Nyquist diagram through the constraints on their infinity norm. The H ∞ constraints are linearized with the help of a desired open-loop transfer function. The controller is designed using the convex optimization techniques in which the difference between the open-loop transfer function and the desired one is minimized. The two-area four-machine test system is selected to evaluate the performance of the designed controller under different load conditions as well as different levels of wind penetrations.