Tutorial on Congestion Control in Multi-Area Transmission Grids via Online Feedback Equilibrium Seeking

Online feedback optimization (OFO) is an emerging control methodology for real-time optimal steady-state control of complex dynamical systems. This tutorial focuses on the application of OFO for the autonomous operation of large-scale transmission grids, with a specific goal of minimizing renewable generation curtailment and losses while satisfying voltage and current limits. When this control methodology is applied to multi-area transmission grids, where each area independently manages its congestion while being dynamically interconnected with the rest of the grid, a non-cooperative game arises. In this context, OFO must be interpreted as an online feedback equilibrium seeking (FES) scheme. Our analysis incorporates technical tools from game theory and monotone operator theory to evaluate the stability and performance of multi-area grid operation. Through numerical simulations, we illustrate the key challenge of this non-cooperative setting: on the one hand, independent multi-area decisions are suboptimal compared to a centralized control scheme; on the other hand, some areas are heavily penalized by the centralized decision, which may discourage participation in the coordination mechanism.