Transient computing systems do not have energy storage, and operate directly from energy harvesting. These systems are often faced with the inherent challenge of low-current or transient power supply. In this paper, we propose "power-neutral" operation, a new paradigm for such systems, whereby the instantaneous power consumption of the system must match the instantaneous harvested power. Power neutrality is achieved using a control algorithm for dynamic frequency scaling, modulating system performance gracefully in response to the incoming power. Detailed system model is used to determine design parameters for selecting the system voltage thresholds where the operating frequency will be raised or lowered, or the system will be hibernated. The proposed control algorithm for power-neutral operation is experimentally validated using a microcontroller incorporating voltage threshold-based interrupts for frequency scaling. The microcontroller is powered directly from real energy harvesters; results demonstrate that a power-neutral system sustains operation for 4%-88% longer with up to 21% speedup in application execution.