Distributed Frequency Control via Randomized Response of Electric Vehicles in Power Grid

In this paper, we propose a new distributed frequency control scheme for electric vehicles (EVs) to help restore the power grid frequency upon a contingency of supply-demand imbalance. Under our scheme, each EV independently monitors the grid frequency at discrete times and responds by switching among its charging, idle, and discharging operational modes according to a simple threshold-based switching algorithm. To recover the grid frequency smoothly and prevent an undesired frequency overshoot/undershoot due to simultaneous response of EVs, we design the inter-response times of any EV to follow an exponentially distributed random variable with a certain mean value at each operational mode. To draw insights into the performance of our scheme, we characterize its impacts on the grid frequency in various aspects, including the mean and variance of the resulting grid frequency over time, the mean frequency recovery time, the average number of EV switching their modes, and the probability of frequency overshoot/undershoot. Accordingly, we formulate an optimization problem for the grid operator to minimize the expected cost of implementing our frequency control scheme by designing EVs' response rates subject to their requested incentive prices and the given grid performance guarantees. Finally, we validate our analysis via simulations on the IEEE 9-Bus test system and the Ireland power system, where it is observed that our frequency control scheme can be used as a reliable and cost-efficient alternative for the conventional primary reserve service.