Frequency Regulation using Sparse Learned Controllers in Power Grids with Variable Inertia due to Renewable Energy

Inertia from rotating masses of generators in power systems influence the instantaneous frequency change when an imbalance between electrical and mechanical power occurs. Renewable energy sources (RES), such as solar and wind power, are connected to the grid via electronic converters. RES connected through converters affect the system's inertia by decreasing it and making it time-varying. This new setting challenges the ability of current control schemes to maintain frequency stability. Proposing adequate controllers for this new paradigm is key for the performance and stability of future power grids. The contribution of this paper is a framework to learn sparse time-invariant frequency controllers in a power system network with a time-varying evolution of rotational inertia. We model power dynamics using a Switched-Affine hybrid system to consider different modes corresponding to different inertia coefficients. We design a controller that uses as features, i.e. input, the systems states. In other words, we design a control proportional to the angles and frequencies. We include virtual inertia in the controllers to ensure stability. One of our findings is that it is possible to restrict communication between the nodes by reducing the number of features in the controller (from 22 to 10 in our case study) without disrupting performance and stability. Furthermore, once communication between nodes has reached a threshold, increasing it beyond this threshold does not improve performance or stability. We find a correlation between optimal feature selection in sparse controllers and the topology of the network.