  Bundling a large number of distributed energy resources through a load
aggregator has been advocated as an effective means to integrate such resources
into whole-sale energy markets. To ease market clearing, system operators allow
aggregators to submit bidding models of simple prespecified polytopic shapes.
Aggregators need to carefully design and commit to a polytope that best
captures their energy flexibility along a day-ahead scheduling horizon. This
work puts forth a model-informed data-based optimal flexibility design for
aggregators, which deals with the time-coupled, uncertain, and non-convex
models of individual loads. The proposed solution first generates efficiently a
labeled dataset of (non)-disaggregatable schedules. The feasible set of the
aggregator is then approximated by an ellipsoid upon training a convex
quadratic classifier using the labeled dataset. The ellipsoid is subsequently
inner approximated by a polytope. Using Farkas lemma, the obtained polytope is
finally inner approximated by the polytopic shape dictated by the market.
Numerical tests show the effectiveness of the proposed flexibility design
framework for designing the feasible sets of small- and large-sized aggregators
coordinating solar photovoltaics, thermostatically-controlled loads, batteries,
and electric vehicles. The tests further demonstrate that it is crucial for the
aggregator to consider time-coupling and uncertainties in optimal flexibility
design.
