PRIME: Fast Primal-Dual Feedback Optimization for Markets with Application to Optimal Power Flow

Online Feedback Optimization (OFO) controllers iteratively drive a plant to an optimal operating point that satisfies input and output constraints, relying solely on the input-output sensitivity as model information. This paper introduces PRIME (PRoximal Iterative MarkEts), a novel OFO approach based on proximal-point iterations. Unlike existing OFO solutions, PRIME admits a market-based implementation, where self-interested actors are incentivized to make choices that result in a safe and efficient operation, without communicating private costs or constraints. Furthermore, PRIME can cope with non-smooth objective functions, achieve fast convergence rates and rapid constraint satisfaction, and reject measurement noise. We demonstrate PRIME on an AC optimal power flow problem, obtaining an efficient real-time nonlinear local marginal pricing scheme.