  Increasing penetrations of electric vehicles (EVs) presents a large source of
flexibility, which can be used to assist balancing the power grid. The
flexibility of an individual EV can be quantified as a convex polytope and the
flexibility of a population of EVs is the Minkowski sum of these polytopes. In
general computing the exact Minkowski sum is intractable. However, exploiting
symmetry in a restricted but significant case, enables an efficient computation
of the aggregate flexibility. This results in a polytope with exponentially
many vertices and facets with respect to the time horizon. We show how to use a
lifting procedure to provide a representation of this polytope with a reduced
number of facets, which makes optimising over more tractable. Finally, a
disaggregation procedure that takes an aggregate signal and computes dispatch
instructions for each EV in the population is presented. The complexity of the
algorithms presented is independent of the size of the population and
polynomial in the length of the time horizon. We evaluate this work against
existing methods in the literature, and show how this method guarantees
optimality with lower computational burden than existing methods.
