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This paper developed a dynamic voltage scaling (DVS) technique for the power management of the OLED display on mobile devices in video streaming applications. An optimal voltage control scheme is proposed under input constraints. Fine-grained DVS technique is applied to maximize the power saving by leveraging the locality of the display content. The display quality is retained by monitoring structural-similarity-index (SSIM) during the optimization, subject to the hardware constraints like voltage regulator response time. Simulation results on four typical video test benchmarks show that the proposed technique saves 19.05%~49.05% OLED power on average while maintaining a high display quality (SSIM >; 0.98) all the time. The power saving efficiency of the proposed technique varies at different display resolutions, refresh rates, and display contents.