Analytic video surveillance system is one of the fastest-growing cyber-physical applications worldwide. A video surveillance system must have a scalable storage backend to simultaneously ingest video frames and serve read requests for video analytics. As a result, 3D NAND flash-based storage devices, i.e., Solid-State Drives (SSD), are gradually regarded as promising candidates thanks to their rapidly growing density and parallelism. However, when deployed in power-constrained environments like the network edges, SSDs' parallelism often cannot be fully unleashed. In edge video analytics systems, the lost parallelism can cause video frame drop and untimely analytics. To tackle this limitation, we first reveal that a flash program operation's power usage is over-estimated in the conventional SSD design, leading to a limited degree of I/O parallelism. Based on the observation, we propose a novel command set, RVO (Read-Verify Overlap), which reclaims the unused power from the overestimation to amend the lost parallelism. To realize feasible fine-grained power management, we further accompany RVO with a generic power-aware scheduler. Through experiments, we show how video analytics systems equipped with RVO can achieve zero frame drop while ensuring compliance with industrial read latency requirements, even in write-intensive workloads.