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An energy harvesting system (EHS) delivers a nondeterministic power density over a range of explicit environmental conditions. The computational architecture is required to be tunable and optimized at run-time in order to adapt the power supply and, simultaneously, deliver optimal performance. In this paper, an important aspect of the supply-consumption relation inEHS is considered, that the transient peak power consumption of the load should be bounded by the energy supply rate, yet the average power utilisation should be maximised. A design flow is proposed in this paper for adjusting the concurrency degree of a system according to the available power, and choosing a runtime schedule for an EHS satisfying the optimisation purpose. In particular, a novel concurrency model named scheduling decision graph has been introduced, providing the flexibility of scheduling a system in decision steps with various concurrency degrees. Algorithms for deriving this graph from a system's data flow relations are proposed. A run-time schedule for the system is then extracted from the decision graph, using a simple dynamic scheduling method. Finally, the results of our design flow are demonstrated using a FIR filter circuit implemented in an FPG Adevice.