NAND flash-based storage devices (NFSDs) have been widely employed in various systems, including cloud servers as well as mobile devices. The core component of NFSDs is NAND flash memory (NFM) which has several advantages over the conventional hard disk drives (HDDs). An NFSD typically adopts a bunch of NFMs which are operated in parallel for maximizing the I/O throughput. However, optimizing for performance may not be desirable from the power budget (PB) perspective. In other words, concurrent operations of NFMs often drain inordinate current, which leads to the violation of the PB allocated for a storage device. In this article, we propose a novel power management scheme which maximizes concurrent operations of NFMs under the given power constraint. The proposed method quantizes the given power constraint of an NFSD. A quantum also called token is the basic unit of power management. The proposed power management scheme allocates tokens to NFMs and only the NFMs having enough tokens can perform their operations. We call this method multitoken-based power management (MTPM). The critical issue of MTPM is a deadlock which is resolved with the key allocation scheme. Furthermore, we enhance MTPM to improve performance. The extended method called keyless MTPM (KMTPM) improves the overall performance by relaxing the key acquisition requirement and allowing subatomic operations. In the experimental results, we confirm that the proposed methods always meet the given power constraint. The proposed KMTPM improves throughput by 22.85% compared to state of the art technique. In addition, KMTPM only incurs 3.8% of performance overhead and 0.015% of area overhead.