Modern computational systems have adopted heterogeneous multiprocessors to increase their computation capability. As the performance increases, the energy consumption in these systems also increases significantly. Dynamic Voltage and Frequency Scaling (DVFS), which allows processors to dynamically adjust their supply voltages and execution frequencies to work on different power/energy levels, is considered an efficient scheme to achieve the goal of saving energy. In this paper, we consider scheduling frame-based tasks on DVFS-enabled heterogeneous multiprocessor platforms with the goal of achieving minimal overall energy consumption. We consider three types of heterogeneous platforms, namely, dependent platforms without runtime adjusting, dependent platforms with runtime adjusting, and independent platforms. For all of these three platforms, we first introduce a Relaxation-based Naive Rounding Algorithm (RNRA), which can produce good solutions for some cases, but may be unstable under other situations. Then, we propose a Relaxation-based Iterative Rounding Algorithm (RIRA). Experiments and comparisons show that our RIRA produces a better performance than RNRA and other existing methods, and achieves near-optimal scheduling under most cases.