Real-time Flexibility Feedback for Closed-loop Aggregator and System Operator Coordination

Consider a system operator that wishes to optimize its objectives over time subject to operational constraints as well as private constraints of controllable loads managed by an aggregator. In this paper, we design a real-time feedback signal for the aggregator to quantify and communicate its available flexibility to the system operator. The proposed feedback signal at each time is the conditional probability of future feasible trajectories that will be enabled by the operator's decision. We show that it is the unique distribution that maximizes a system capacity for flexibility. It allows the system operator to maintain feasibility and enhance future flexibility while optimizing its objectives. We illustrate how the design can be used by the system operator to perform online cost minimization and real-time capacity estimation, while provably satisfying the private constraints of the loads.