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

TL;DR

This paper introduces a simple, computationally efficient approximation method for representing the aggregate flexibility of diverse loads modeled as convex polytopes, aiding power system planning and operation.

Contribution

It proposes a novel outer approximation of the Minkowski sum for heterogeneous load aggregations, reducing complexity while maintaining accuracy.

Findings

The approximation is easily computable with one variable per time period.

The method is accurate for broad classes of loads.

The approach simplifies integration of load flexibility into system routines.

Abstract

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.