  The increasing prevalence of electric vehicles (EVs) in the transportation
sector will introduce a large number of highly flexible electric loads that EV
aggregators can pool and control to provide energy and ancillary services to
the wholesale electricity market. To integrate large populations of EVs into
electricity market operations, aggregators must express the aggregate
flexibility of the EVs under their control in the form of a small number of
energy storage (battery) resources that accurately capture the supply/demand
capabilities of the individual EVs as a collective. To this end, we propose a
novel multi-battery flexibility model defined as a linear combination of a
small number of base sets (termed batteries) that reflect the differing
geometric shapes of the individual EV flexibility sets, and suggest a
clustering approach to identify these base sets. We study the problem of
computing a multi-battery flexibility set that has minimum Hausdorff distance
to the aggregate flexibility set, subject to the constraint that the
multi-battery flexibility set be a subset of the aggregate flexibility set. We
show how to conservatively approximate this problem with a tractable convex
program, and illustrate the performance achievable by our method with several
numerical experiments.
