Aggregate flexibility of a collection of loads

TitleAggregate flexibility of a collection of loads
Publication TypeConference Paper
Year of Publication2013
AuthorsAshutosh Nayyar, Josh Taylor, Anand Subramanian, Kameshwar Poolla, Pravin Varaiya
Conference Name2013 IEEE 52nd Annual Conference on Decision and Control (CDC)
Date Published12/2013
Conference LocationFirenze
ISBN Number978-1-4673-5714-2
Keywordsload modeling, load regulation, reliability and markets, RM11-006

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 time-varying 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.