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SUMMARY:State Space Collapse in Resource Allocation for Demand Dispatch - 
 Sean Meyn (University of Florida\; University of Illinois)
DTSTART:20190503T123000Z
DTEND:20190503T133000Z
UID:TALK123634@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The term demand dispatch refers to the creation of virtual ene
 rgy storage from deferrable loads. The key to success is automation: an ap
 propriate distributed control architecture ensures&nbsp\;that bounds on qu
 ality of service (QoS) are met and simultaneously&nbsp\;ensures that the l
 oads provide aggregate grid services&nbsp\;comparable to a large battery s
 ystem. A question addressed in our 2018 CDC paper is how to control&nbsp\;
 a large collection of heterogeneous loads. This is in part&nbsp\;a resourc
 e allocation problem\, since different classes of loads&nbsp\;are more val
 uable for different services. The evolution of QoS&nbsp\;for each class of
  loads is modeled via a state of charge surrogate\, which is a part of the
  leaky battery model for the load&nbsp\;classes. The goal of this paper is
  to unveil the structure of the optimal solution&nbsp\;and investigate sho
 rt term market implications. The following&nbsp\;conclusions are obtained:
 <br>(i) Optimal power deviation for each of the M &#21\; 2 load classes&nb
 sp\;evolves in a two-dimensional manifold.<br>(ii) Marginal cost for each 
 load class evolves in a two-dimensional subspace: spanned by a co-state pr
 ocess and its derivative.<br>(iii) The preceding conclusions are applied t
 o construct a dynamic competitive equilibrium model\, in which the consume
 r utility&nbsp\;is the negative of the cost of deviation from ideal QoS. I
 t is found that a competitive equilibrium exists\, and that the resulting&
 nbsp\;price signals are very different than what would be obtained&nbsp\;b
 ased on the standard assumption that the utility is with&nbsp\;respect to 
 power consumption. It is argued that price signals are not useful for cont
 rol of the grid&nbsp\;since they are inherently open loop. However\, the a
 nalysis may&nbsp\;inform the creation of heuristics for payments within th
 e context&nbsp\;of contracts for services with consumers.
LOCATION:Seminar Room 1\, Newton Institute
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