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This paper presents the novel Droop-e grid-forming inverter control strategy, which establishes an active power-frequency relationship based on an exponential function of the inverter power dispatch. The advantages of this control strategy include an increased utilization of available headroom, mitigated system frequency dynamics, and a natural limiting behavior, all of which are directly compared to the hitherto standard static droop approach. First, the small signal stability of the Droop-e control is assessed on a 3-bus system and found stable across all possible inverter power dispatches. Then, time-domain simulations show improved frequency dynamics at lower power dispatches, and a limiting behavior at higher dispatches. Finally, a novel secondary control scheme is introduced that achieves power sharing following the primary Droop-e response to load perturbations, which is shown to be effective in time-domain simulations of the 3- and 9-bus systems; comparative simulations with a static 5% droop yields unacceptable frequency deviations, highlighting the superiority of the Droop-e control.