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Aggregations of flexible loads can provide several power system servicesthrough demand response programs, for example load shifting and curtailment.The capabilities of demand response should therefore be represented in systemoperators' planning and operational routines. However, incorporating models ofevery load in an aggregation into these routines could compromise theirtractability by adding exorbitant numbers of new variables and constraints. Inthis paper, we propose a novel approximation for concisely representing thecapabilities of a heterogeneous aggregation of flexible loads. We assume thateach load is mathematically described by a convex polytope, i.e., a set oflinear constraints, a class which includes deferrable loads, thermostaticallycontrolled loads, and generic energy storage. The set-wise sum of the loads isthe Minkowski sum, which is in general computationally intractable. Ourrepresentation is an outer approximation of the Minkowski sum. The newapproximation is easily computable and only uses one variable per time periodcorresponding to the aggregation's net power usage. Theoretical and numericalresults indicate that the approximation is accurate for broad classes of loads.

A concise, approximate representation of a collection of loads described by polytopes