Embedded Multiprocessor Systems-on-Chip (MPSoCs) commonly run multiple applications at once. These applications may have different time criticalities, i.e. non real-time, soft real-time, and firm or hard real-time. Application-level composability is used to provide each application with its own virtual platform, such that each application may be developed, verified, and executed independently, given its virtual platform specification. Composability of functional and temporal properties has been demonstrated in previous work. In this paper, we extend composability to include power management, where each application can manage its energy usage independently. Each application receives an independent energy and/or power budget, which it can manage as it sees fit, with its own application-specific power-management policy. Time, energy, and power budgets allocated to each application ensure that its power-management policy cannot cause any interference to the functional, timing, and power behaviours of other applications. We implement our technique on an existing composable and predictable hardware platform (CompSoC), and extend its Real-Time Operating System (OS) with a power-management infrastructure. Applications use a power-management API to communicate with the OS that implements time, energy, and power budgets. We demonstrate the applicability of our techniques by running several concurrent applications with their own power managers on an FPGA prototype.