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Aiming at the TTC (Time to Collision) and derivative indicators' problems of unclear definition and missed/wrong judgments of traffic conflicts on curved road in the traditional Cartesian coordinate system, a new method that can better identify the conflicts on curved road is proposed. The method first establishes the Frenet coordinate system according to the road centerline (i.e., the reference line), and obtains the vehicle trajectory coordinates in the Frenet coordinate system. The Frenet coordinate system can simplify the calculation difficulty of vehicle trajectory and conflict under the curve road. Then determine the vehicle state in the Frenet coordinate system, and then use TTC to calculate rear-end and lane-change conflicts according to the state of the vehicle (non-lane-change/lane-change). Finally, a total of 4 hours of video data were collected based on the K283 of the lane-switch work zone of the Jiqing Highway. Subsequently, the continuous high-precision conflict data in the region was obtained through the video and conflict identification program, and the traditional method was compared with the new method. The results show that different methods have a significant impact on the identification of the number of serious conflicts. The new method can reduce the missed judgments of serious rear-end conflicts on curved road, especially at the junctions of curved and straight segments (segment 3/4/7/8/9), and can also reduce wrong judgments of serious lane-change conflicts. In addition, among the 125 added serious rear-end conflicts identified by the new method, the maximum deceleration of 10 conflicting vehicles during the conflict exceeds the dangerous state -4/-1.5m/s2, which explain that the new method can help us better identify the risks of curved road. The new method combines the Frenet coordinate system, vehicle state determination and TTC, which can reduce the missed/wrong judgments of conflicts on curved road, and expand the traffic conflict identification from previous straight road to full-line road alignment.