  Energy prices and net power injection limitations regulate the operations in
distribution grids and typically ensure that operational constraints are met.
Nevertheless, unexpected or prolonged abnormal events could undermine the
grid's functioning. During contingencies, customers could contribute
effectively to sustaining the network by providing services. This paper
proposes an incentive mechanism that promotes users' active participation by
essentially altering the energy pricing rule. The incentives are modeled via a
linear function whose parameters can be computed by the system operator (SO) by
solving an optimization problem. Feedback-based optimization algorithms are
then proposed to seek optimal incentives by leveraging measurements from the
grid, even in the case when the SO does not have a full grid and customer
information. Numerical simulations on a standard testbed validate the proposed
approach.
