Dynamic adaptive streaming over HTTP (DASH) technique, the most popular streaming method, requires a large number of hard disk drives (HDDs) to store multiple bitrate versions of many videos, consuming significant energy. A solid-state drive (SSD) can be used to cache popular videos, thus reducing HDD energy consumption by allowing I/O requests to be handled by an SSD, but this requires effective HDD power management due to limited SSD bandwidth. We propose a new SSD cache management scheme to minimize the energy consumption of a video storage system with heterogeneous HDDs. We first present a technique that caches files with the aim of saving more HDD energy as a result of I/O processing on an SSD. Based on this, we propose a new HDD power management algorithm with the goal of increasing the number of HDDs operated in low-power mode while reflecting the heterogeneous HDD power characteristics. For this purpose, it assigns a separate parameter value to each I/O task based on the ratio of HDD energy to bandwidth and greedily selects the I/O tasks handled by the SSD within limits on its bandwidth. Simulation results show that our scheme consumes between 12% and 25% less power than alternative schemes under the same HDD configuration.