  Flexible demand response (DR) resources can be leveraged to accommodate the
stochasticity of some distributed energy resources. This paper develops an
online learning approach that continuously estimates price sensitivities of
residential DR participants and produces such price signals to the DR
participants that ensure a desired level of DR capacity. The proposed learning
approach incorporates the dispatch decisions on DR resources into the
distributionally robust chance-constrained optimal power flow (OPF) framework.
This integration is shown to adequately remunerate DR resources and co-optimize
the dispatch of DR and conventional generation resources. The distributionally
robust chance-constrained formulation only relies on empirical data acquired
over time and makes no restrictive assumptions on the underlying distribution
of the demand uncertainty. The distributional robustness also allows for
robustifying the optimal solution against systematically misestimating
empirically learned parameters. The effectiveness of the proposed learning
approach is shown via numerical experiments. The paper is accompanied by the
code and data supplement released for public use, see [27].
