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In our recent work [1] , we constructed a reduced-order model of the Western Electricity Coordinating Council (WECC) power system using mathematically derived parameters from real Synchrophasor data. These parameters include inter and intra-area impedances, inertias, and damping factors for aggregate synchronous generators representing five geographical, and yet coherent, areas of WECC. In this paper, we use this reduced-order model as a tool to design a supplementary controller for a Static VAr Compensator (SVC), located at the terminal bus of one of the aggregate generators. Wide-area feedback consisting of phase angle and frequency measurements from Phasor Measurement Units (PMUs) in the other areas is used to design this controller. The objective is to damp the inter-machine oscillation modes of the reduced-order model, which in the full-order system corresponds to inter-area oscillations. The controller input is chosen via statistical variance analysis, and its parameters are tuned to improve the damping factors of the slow modes. The model is implemented in a real-time digital simulator, and validated using a wide range of disturbance scenarios. The closed-loop system is observed to be highly robust to all of these disturbances as well as the choice of operating points. Detailed experimental analyses of the capacity of the SVC to satisfy the damping specifications of supplementary control are also presented via multiple contingencies. The results are promising in aiding damping of inter-area modes in WECC, especially at a time of increasing penetration of wind and other renewable resources. [ABSTRACT FROM AUTHOR]