As real-time systems are safety critical, guaranteeing a high reliability threshold is as important as meeting all deadlines. Periodic tasks are replicated to mitigate the negative impact of transient faults, which leads to redundancy and high energy consumption. On the other hand, energy saving is widely identified as increasingly relevant issues in real-time systems. In this paper, we formalize this challenging tri-criteria optimization problem, i.e., minimizing the expected energy consumption while enforcing the reliability threshold and meeting all task deadlines, and propose several mapping and scheduling heuristics to solve it. Specifically, a novel approach is designed to (i) map an arbitrary number of replicas onto processors, (ii) schedule each replica of each task instance on its assigned processor with less temporal overlap. The platform is composed of processing units with different characteristics, including speed profile, energy cost and fault rate. The heterogeneity of the computing platform makes the problem more complicated, because different mappings achieve different levels of reliability and consume different amounts of energy. Moreover, scheduling plays an important role in energy saving, as the expected energy consumption is the average over Minimizing energy consumption for real-time tasks all failure scenarios. Once a task replica is successful, the other replicas of that task instance can be canceled, which calls for minimizing the overlap between any replica pair. Finally, to quantitatively analyze our methods, we derive a theoretical lower-bound for the expected energy consumption. Comprehensive experiments are conducted on a large set of execution scenarios and parameters. The comparison results reveal that our strategies perform better than the random baseline under almost all settings, with an average gain in energy consumption of more than 40%, and our best heuristic achieves an excellent performance: its energy saving is only 2% less than the lower-bound on average.