  Aggregations of flexible loads can provide several power system services
through demand response programs, for example load shifting and curtailment.
The capabilities of demand response should therefore be represented in system
operators' planning and operational routines. However, incorporating models of
every load in an aggregation into these routines could compromise their
tractability by adding exorbitant numbers of new variables and constraints. In
this paper, we propose a novel approximation for concisely representing the
capabilities of a heterogeneous aggregation of flexible loads. We assume that
each load is mathematically described by a convex polytope, i.e., a set of
linear constraints, a class which includes deferrable loads, thermostatically
controlled loads, and generic energy storage. The set-wise sum of the loads is
the Minkowski sum, which is in general computationally intractable. Our
representation is an outer approximation of the Minkowski sum. The new
approximation is easily computable and only uses one variable per time period
corresponding to the aggregation's net power usage. Theoretical and numerical
results indicate that the approximation is accurate for broad classes of loads.
