Aggregate flexibility of a collection of loads

Ashutosh Nayyar, Josh Taylor, Anand Subramanian, Kameshwar Poolla, Pravin Varaiya

Research output: Chapter in Book/Report/Conference proceedingConference contribution

46 Scopus citations


We consider a collection of flexible loads. Each load is modeled as requiring energy E on a service interval [a; d] at a maximum rate of m. The collection is serviced by available generation g(t) which must be allocated causally to the various tasks. Our objective is to characterize the aggregate flexibility offered by this collection. In the absence of rate limits, we offer necessary and sufficient conditions for the generation g(t) to service the loads under causal scheduling without surplus or deficit. Our results show that the flexibility in the collection can be modeled as electricity storage. The capacity Q(t) and maximum charge/discharge rate m(t) of the equivalent storage can be computed in real time. Ex ante, these parameters must be estimated based on arrival/departure statistics and charging needs. Thus, the collection is equivalent a stochastic timevarying electricity storage. We next consider the case with charging rate limits. Here, we offer bounds on the capacity and rate of the equivalent electricity storage. We offer synthetic examples to illustrate our results.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages8
ISBN (Print)9781467357173
StatePublished - 2013
Externally publishedYes
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference52nd IEEE Conference on Decision and Control, CDC 2013

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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