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Online feedback optimization (OFO) is an emerging control methodology forreal-time optimal steady-state control of complex dynamical systems. Thistutorial focuses on the application of OFO for the autonomous operation oflarge-scale transmission grids, with a specific goal of minimizing renewablegeneration 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 dynamicallyinterconnected with the rest of the grid, a non-cooperative game arises. Inthis context, OFO must be interpreted as an online feedback equilibrium seeking(FES) scheme. Our analysis incorporates technical tools from game theory andmonotone operator theory to evaluate the stability and performance ofmulti-area grid operation. Through numerical simulations, we illustrate the keychallenge of this non-cooperative setting: on the one hand, independentmulti-area decisions are suboptimal compared to a centralized control scheme;on the other hand, some areas are heavily penalized by the centralizeddecision, which may discourage participation in the coordination mechanism.

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