Power system inertia is falling as more energy is supplied by renewable generators, and there are concerns about the frequency controls required to guarantee satisfactory system performance. The majority of research into the negative effect of low inertia has focused on poor dynamic response following major disturbances, when the transient frequency dip can become unacceptable. However, another important practical concern - keeping average frequency deviations within acceptable limits - was mainly out of the sight of the research community. In this manuscript, we present a method for finding the frequency probability density function (PDF) for a given power system. We pass from an initial stochastic dynamic model to deterministic equations for the frequency PDF, which are analyzed to uncover key system parameters influencing frequency deviations. We show that system inertia has little effect on the frequency PDF, making virtual inertia services insufficient for keeping frequency close to nominal under ambient load fluctuations. We establish that aggregate system droop and deadband width are the only parameters that have major influence on the average frequency deviations, suggesting that energy storage might be an excellent solution for tight frequency regulation. We also show that changing the governor deadband width does not significantly affect generator movement.
Bibliographical noteFunding Information:
Manuscript received July 13, 2018; revised December 6, 2018; accepted January 9, 2019. Date of publication January 25, 2019; date of current version June 18, 2019. This work was supported in part by Skoltech-MIT Next Generation program, in part by MIT Undergraduate Research Opportunities Program, and in part by the Engineering and Physical Sciences Research Council under Grant EP/K002252/1. Paper no. TPWRS-01082-2018. (Corresponding author: Petr Vorobev.) P. Vorobev and J. W. Bialek are with the Skolkovo Institute of Science and Technology (Skoltech), Moscow 121205, Russia (e-mail:, p.vorobev@ skoltech.ru; J.Bialek@skoltech.ru).
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- droop control
- Frequency control
- frequency fluctuations
- low inertia grids