Distributed Frequency Control in Power Grids with Low and Time-Varying Inertia

This paper presents a distributed frequency control method for power grids with high penetration of inverter-connected resources under low and time-varying inertia due to renewable energy (RE). We provide a distributed virtual inertia (VI) allocation method using the distributed subgradient algorithm. We implement our distributed control strategy under full and sparse communication architectures. The distributed full and sparse communication controllers achieve comparable performance to a centralized controller and stabilize the test system within 6~s. We study the sensitivity of the controller performance to varying objective function weights on phase angle versus frequency deviation, gradient step sizes, and allowed rate of change of inertia (RoCoI) coefficients. We observe that the settling time of the states and the controller performance and effort are susceptible to changes in the gradient step size and objective weights on the frequency and angle deviation. While a higher objective weight on angle versus frequency deviations positively affects their settling times, it negatively impacts controller performance and control effort. The impact of this work is to propose distributed control schemes as new mechanisms that act before or in alignment with primary and secondary control to safely regulate the frequency in future power grids.