In smart substation, the stability control device as a cross-interval device needs to receive and process a plurality of spaced sampling quantities simultaneously. Aiming at the problem of multi-interval sampling synchronization in "direct sampling ", a synchronization and resampling interpolation combining processing method based on local time scale is proposed. The message time stamp is used as the stability control device in the "direct sampling " for multi-interval sampling synchronization and resampling reference. With the auxiliary clock, the sampling data is synchronized, resampling by linearly interpolated and analyzed the interpolation error. Finally, the digital sampling of the stability control device is realized by FPGA+DSP hardware platform, and the experimental system is built. The timeliness of the local time-scale based synchronization interpolation algorithm proposed in this paper is analyzed from the aspects of sampling accuracy and synchronization effectiveness. The feasibility is verified. The test results verify that the synchronous linear resampling based on local time scale can meet the real-time and accuracy requirements of the actual engineering of the stability control device.