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Satisfiability of Elastic Demand in the smart grid

Jean-Yves Le Boudec, Joint work with Dan- Cristian Tomozei EPFL Feb 2 nd , 2011. Satisfiability of Elastic Demand in the smart grid. Contents. The Grid and Elastic Demand One Day in the life of Robert Longirod Modelling Approach Conclusions.

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Satisfiability of Elastic Demand in the smart grid

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  1. Jean-Yves Le Boudec, Joint work with Dan-CristianTomozei EPFL Feb 2nd, 2011 Satisfiability of Elastic Demand in the smart grid 1

  2. Contents • The Grid and ElasticDemand • One Day in the life of Robert Longirod • ModellingApproach • Conclusions [arXiv:1011.5606v1]Jean-Yves Le Boudec and Dan-CristianTomozei « Satisfiability of Elastic Demand in the Smart Grid », Nov 2010, arxiv.org 2

  3. The SwissDream… • 2000 W society = energyexpenditure per capita as itwas in 1960 in Western Europe (in CH; = 63.1 GJ per year per capita) • Today: 5000 – 6000 W  • Realistic Goal for 2050: 3500 W[The 2000 Watt Society –Standard or Guidepost? Energiespiegel Nr 18, April 2007, PSI, Switzerland] 3

  4. The British Dream… • David MacKay 2009 « Sustainable Energy without the Hot Air » • An aggressive, though not unrealistic plan requires ca 3000W, ¾ of whichis by the electricalgrid 4

  5. Volatility in demand • Increasedvolatility in supply • Calls for intelligent demand and supply « Adaptive Appliances » 5

  6. Management of EnergyDemand • Managing End-User Preferences in the Smart Grid, C. Wang and M. d. Groot, E-energy 2010, Passau, Germany, 2010 • Demandresponse by loadswitch • For thermal loadwww.voltalis.com 6

  7. BeyondDemandResponse • Tomorrow (2050) adapt to wind, tidal, solaretc over severaldays • Demandresponse = shave the peakmeandoes not adapt Wind energy production in MW of Eire in 2006. Source: Sustainable Energy - without the hot air  by David JC MacKay (online) 7

  8. One Day in the Life of Robert Longirod 8

  9. One Day in the Life of Robert Longirod • We are in May 2050, in the 3500W society • Robert Longirodistelecomengineerat the swissbranch of Huawei Technologies 9

  10. A fatal exception 8E has occurredat 0028:C881E33670F in UXD DXC 32 883FA2332EBD. The current application willbeterminated. . Robert wakes up at 6:45 Walks to the bathroom to take a shower No hot water ! Home automation controllerhungyesterday night. Hot water was not replenishedovernight.

  11. Robert is a philosoph and takes a cold shower. Nowis time for a good, hot, espresso. Robert imagines the smell of the first coffee of the day and smiles … …but no coffee !

  12. Robert re-programmedhis end user preferences in the smart gridyesterday night and made a mistake ! Fortunately, the fridgeworks and thereissome orange juiceleft.

  13. Robert nowwalks to hislounge and prepares to work. Today, Robert istelecommuting – thissaves time and energy. Strange, the loungeisdark – shutters are blockedclosed … the home automation controller, of course !

  14. Not a seriousproblemanyhow; the shutterscanbeopenedmanually. Robert sitsathis table and opens his desktop …

  15. The femtocell has burnt, no internet access …

  16. Robert is a bit worried. There is an important meeting at 10:00 scheduledwithtwoco-workers. « If I am not atthat meeting, itis George whowillget the work. I must bethere » Robert decides to do somethingexceptional: drive to work !

  17. In the garage … The e-car is not charged. The batteries wereused to power the grid. Normal, Robert did not plan to go anywheretoday…

  18. Robert cycles to work Whilepedalling back home in the evening, hehopesthat the washing machine didits job…

  19. Intelligent Demand Management must Be Simple, Adaptive and Distributed • Global, optimal schedules • are hard, • errorprone • and do not account for last minute changes • More realisticis • elasticdemand, • with best effort service withstatisticalguarantees. • [Keshav and Rosenberg 2010] 19

  20. Possible Directions for Distributed Control Network Users Delay / reducedemand Deferheating / cooling /batteryloading Substitute local source Substitute battery • Signals marginal price to users • Whether a trueprice or a congestion signal is an issue 20

  21. ModellingApproach 21

  22. A Preliminary Issue isStability • Wewant first to study if elasticdemand / adaptation isfeasible • Assume supplyisrandom and loadiselastic • Usersact a distributed buffer • Hot water tanks, batteries • Weleave out (for now) the details of signals and algorithms • A verycoarse, but fundamentalcriterion: isthere a control mechanismthatcanstabilizedemand • Instabilitycanbegenerated by • Delays in demand • Increase in demand due to delay 22

  23. A Demand / Supply Model Supply Ga(t) • Inspired by [Meyn et al 2010] volatility Natural Demand Da(t) forecast ExpressedDemandEa(t) Evaporation μ Z(t) + . Latent Backlogged Demand Z(t) Satisfied Demand ReturningdemandB(t) = λ Z(t) FrustratedDemand F(t) evaporation delay 23

  24. The Control Problem Supply Ga(t) • Control variable: G(t-1), production bought one second ago in real time market • Controller seesonlysupply Ga(t) and expresseddemandEa(t) • Our (initial) problem: keep Z(t) stable • Assume ramp-up constraintonly G(t)-G(t-1) ≤ ζ Natural Demand Da(t) ExpressedDemandEa(t) Evaporation μ Z(t) + . Latent Backlogged Demand Z(t) Satisfied Demand ReturningdemandB(t) = λ Z(t) FrustratedDemand F(t) 24

  25. ThresholdBasedPolicies Forecastsupplyisadjusted to forecastdemand R(t) := reserve = excess of demand over supply • Thresholdpolicy: • if R(t) < r* increasesupply as much as possible (consideringramp up constraint) • else set R(t)=r* 25

  26. 26

  27. Findings • If evaporationμis positive, the system is stable (ergodic, positive recurrent Markov chain) for anythreshold r* • If evaporationisnegative, the system isunstable for anythreshold r* • Delay does not play a role in stability • Nor do ramp-up constraint and size of reserves 27

  28. The Role of Negative Evaporation • Negative Evaporation means • The simple fact of delaying a demandmakes the returningdemandlargerthan the original one.(do not confuse with the sum of returningdemand + currentdemand, whichisalwayslargerthancurrentdemand) • Couldthathappen ? 28

  29. Evaporation: HeatingAppliances • Assume the model [MacKay 2009]thendelayedheatingislessheating (thisiswhatmakesVoltalisbeaccepted by French households) • Pure thermal load = positive evaporation • This istrue for heatprovided, is not necessarilytrue for energyconsumed • Dependswhether coefficient of performance e is constant or not; true for resistancebasedheating • Delayedheatingwith air heatpumpwith cold air may have negativeevaporation (bad coefficient of performance when air is cold) heatprovided to building leakiness outside inertia 29

  30. Conclusions • A first model of adaptive applianceswith volatile demand and supply • Suggeststhatnegativeevaporationmakes system unstable, • thusdetailedanalysisisrequired to avoidit • Model canbeused to quantify more detailedquantities • E.g. amount of backlog 30

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