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Latency or delay in remote feedback signals can adversely affect the closed-loop damping performance. Accurate time-stamp information at both (PMU location and control center) ends offers a possibility to continuously compensate for time-varying latency. In this paper, an adaptive phasor power oscillation damping controller (APPOD) is proposed wherein the rotating coordinates for phasor extraction are adjusted to account for the change in phase caused due to the delay. The oscillatory component of the original signal is thus retrieved out of the delayed signal received at the control center. Unlike conventional phasor POD, which uses a fixed phase shift to generate damping control signal, an adaptive phase shift algorithm is used here to suit varying signal locations and operating conditions. Case studies confirm the effectiveness of the proposed technique, both in terms of robustness and handling continuously varying delays. A comparison with a conventional gain scheduled POD (CGPOD) and a Unified Smith Predictor (USP) approach is also presented.