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The rigid timing requirement of real-time applications biases the analysis to focus on the worst-case performances. Such a focus cannot provide enough information to optimize the system’s typical resource and energy consumption. In this work, we study the real-time scheduling of parallel tasks on a multi-speed heterogeneous platform while minimizing their typical-case CPU energy consumption. Dynamic power management (DPM) policy is integrated to determine the minimum number of cores required for each task while guaranteeing worst-case execution requirements (under all circumstances). A Hungarian Algorithm-based task partitioning technique is proposed for clustered multi-core platforms, where all cores within the same cluster run at the same speed at any time, while different clusters may run at different speeds. To our knowledge, this is the first work aiming to minimize typical-case CPU energy consumption (while ensuring the worst-case timing correctness for all tasks under any execution condition) through DPM for parallel tasks in a clustered platform. We demonstrate the effectiveness of the proposed approach with existing power management techniques using experimental results and simulations. The experimental results conducted on the Intel Xeon 2680 v3 12-core platform show around 7%-30% additional energy savings.