Facing constraints imposed by storage and bandwidth limitations, the vast volume of phasor measurement unit (PMU) data collected by the wide-area measurement system (WAMS) for power systems cannot be fully utilized. This limitation significantly hinders the effective deployment of situational awareness technologies for systematic applications. In this work, an effective curvature quantified Douglas-Peucker (CQDP)-based PMU data compression method is proposed for situational awareness of power systems. First, a curvature integrated distance (CID) for measuring the local flection and fluctuation of PMU signals is developed. The Douglas-Peucker (DP) algorithm integrated with a quantile-based parameter adaptation scheme is then proposed to extract feature points for profiling the trends within the PMU signals. This allows adaptive adjustment of the algorithm parameters, so as to maintain the desired compression ratio and reconstruction accuracy as much as possible, irrespective of the power system dynamics. Finally, case studies on the Western Electricity Coordinating Council (WECC) 179-bus system and the actual Guangdong power system are performed to verify the effectiveness of the proposed method. The simulation results show that the proposed method achieves stably higher compression ratio and reconstruction accuracy in both steady state and in transients of the power system, and alleviates the compression performance degradation problem faced by existing compression methods.