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REAL-TIME Storage and Demand Management

Jean-Yves Le Boudec (EPFL) , j oint work with Nicolas Gast (EPFL) Alexandre Proutière (KTH) Dan- Cristian Tomozei (EPFL) Energy Systems Week: Management of Variability and Uncertainty in Energy Systems April 2013, Newton Institute, Cambridge, UK .

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REAL-TIME Storage and Demand Management

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  1. Jean-Yves Le Boudec (EPFL), joint work with Nicolas Gast (EPFL) AlexandreProutière (KTH) Dan-CristianTomozei (EPFL) Energy Systems Week: Management of Variability and Uncertainty in Energy Systems April 2013, Newton Institute, Cambridge, UK REAL-TIME Storage and Demand Management 1

  2. INTroduction 2

  3. Storage and Demand Response can be used to mitigate volatility of renewables • Motivation: Swiss Nanoteragrid (M. Kayal, M. Paolone)use of storage in active distribution network as in [Bianchi et al, 2012] • In this talk: • can we use storage to compensate for renewable forecast errors ? • can we controlstorage with prices ? • can demand responsesubstitute for storage ? 3

  4. 1. [Bejan et al 2012] Bejan, Gibbens, Kelly, “Statistical aspects of storage systems modelling in energy networks,” 46th Annual Conference on Information Sciences and Systems 2012 [Gastet al 2012] Gast, Tomozei, Le Boudec. “Optimal Storage Policies with Wind Forecast Uncertainties”, GreenMetrics 2012 [Gastet al 2013] Gast, Tomozei, Le Boudec. “Optimal Energy Storage Policies with Renewable Forecast Uncertainties ”, submitted, 2013 USING STORAGE TO CopEwith RENEWABLE Volatility 4

  5. Production scheduling w. forecastserrors • Base load production scheduling • Deviationsfromforecast • Use storage to compensate • Social planner point of view • Quantify the benefit of storage • Obtain performance baseline • what could be achieved • no market aspects • Compare twoapproaches • Deterministicapproach • try to maintainstoragelevelate.g. ½ of itscapacityusingupdatedforecasts • Stochasticapproach • Use statistics of pasterrors. load renewables renewables + storage Pump hydro, Cycle efficiency 5

  6. Production scheduling with delays 1a. Forecastload and renewablesuppy1b. Schedule dispatchableproduction 2. Compensatedeviationsfromforecast by charging / discharging from storage load load renewables renewables storedenergy storedenergy 6

  7. Full compensation of fluctuations by storage may not be possible due to power / energy capacity constraints • Fast ramping energy source ( rich) is used when storage is not enough to compensate fluctuation • Energy may be wasted when • Storage is full • Unnecessary storage (cycling efficiency • Control problem: compute dispatched power schedule to minimize energy waste and use of fast ramping load renewables fastramping load spilledenergy renewables 7

  8. Example of schedulingpolicy: Fixed Offset • Fixed Offset policy: means excess production (expect to store)means deficit of production (expect to draw from storage) offset Actual Planned 8

  9. Example of schedulingpolicy: FixedLevel • target a fixedstoragelevel (e.g. ) • [Bejan et al 2012] Actual Planned load load renewables renewables storedenergy storedenergy targetlevel targetlevel 9

  10. Metric and performance (large storage) • Fast ramping energy sources ( rich) is used when storage is not enough to compensate fluctuation • Energy may be wasted when • Storage is full • Unnecessary storage (cycling efficiency FO +200 Target=80% Target=50% FO -200 FO +0 AWP = average wind power • Numerical evaluation: data from the UK (BMRA data archive https://www.elexonportal.co.uk/) • National data (windprod & demand) • 3 years • Corrected day ahead forecast: MAE = 19% • Questions: • Can we do better? • How to compute optimal offset? 10

  11. Fixed offset is optimal for large storage Let with • Theorem. If the forecast error is distributed as . Then: • () is a lowerbound: for anypolicy • FO is optimal for large storage: • The optimal offsetis for usuchthat: = Target=50% • Problemsolved for large capacity • What about small / medium capacity? Target=80% curve : Lowerbound • Uses distribution of error • FixedreserveisPareto-optimal Optimal fixed offset AWP FO 11 11

  12. SchedulingPolicies for Small Storage • Dynamic offset policy: • choose offset as a function of forecastedstoragelevel • Stochastic optimal control (generalidea) • Compute a value of being at storage level B • Computation of V: depends on problem • Here: solution of a fixed point equation: • Approximatedynamicprogramming if state spaceistoo large • Can beextended to more complicated state V(t,B,B’,…) Expectation on possible errors Instant cost (losses or fast-rampingenergy) Storage levelatnext time-slot 12

  13. Dynamic Offset outperformsotherheuristics • Large storagecapacity(=20h of average production of windenergy) • Power = 30% of averagewind power • Fixed Offset & Dynamic offset are optimal • Small storagecapacity(=3h of average production of windenergy) • Power = 30% of averagewind power • DO is the best heuristic Fixedstoragelevel Fixedstoragelevel Fixed Offset Fixed offset Dynamic offset Dynamic offset Lowerbound • Maintaining storage at fixed level: not optimal • There exist better heuristics 13

  14. Take Home Message • For “large” (i.e. one day) storage, there is an optimal value of fixed offset reserve, which can be computed from forecast error statistics • Can be used to dimension secondary reserve FO = 2% AWP 14

  15. 2. [Gastet al 2013] Gast, Le Boudec, Proutière, Tomozei, “Impact of Storage on the Efficiency and Prices in Real-Time Electricity Markets”, ACM e-Energy 2013, Berkeley, May 2013 Prices AND STORAGE inReal-Time Electricity Markets 15

  16. Storage and Real Time Prices • Impact of volatility on prices in real time market is studied by Meyn and co-authors, e.g.[Cho and Meyn, 2010] I. Cho and S. MeynEfficiency and marginal cost pricing in dynamic competitive markets with friction, Theoretical Economics, 2010 • We add storage to the model • Q1: how does storage impact volatility ? what is the required storage capacity ? • Q2: does the market provide optimal control ? 16

  17. A Macroscopic Model of Real Time Market with StorageExtension of [Cho and Meyn 2010] Control RampingConstraint Randomness Supply Day ahead Demand extracted (or stored) power Storage Storage constraints Power Capacity EnergyCapacity if if 0 Storage cycle efficiency(E.g. ) H: brownian motion 17

  18. Scenario A: Storage at Supplier Consumer • Consumer’s payoff • Supplier’s payoff • stochastic price process on real time market Supplier sell buy frustrated demand satisfied demand 18

  19. Definition of a Dynamic CompetitiveEquilibrium (Storage at Supplier)[Cho and Meyn 2010] Consumer • such that • maximizes welfare ( = expected discounted payoff) of consumer • maximizes welfare of supplier (given friction constraints)for the same price process • Without storage, there exists such an equilibrium [Cho and Meyn 2010] Supplier 19

  20. Scenario B: Storage at Consumer Consumer • Consumer’s payoff • Supplier’s payoff • Dynamic Competitive Equilibrium such that • maximizes consumer’s welfare • maximizes supplier’s welfarefor the same price process Supplier 20

  21. Consumer Scenario C: Stand-Alone Storage Operator • Consumer’s payoff • Supplier’s payoff • Storage Op’s payoff • Dynamic Competitive Equilibrium such that • maximizes consumer’s welfare • maximizes supplier’s welfare • maximizes storage op’s welfare • for the same price process Supplier 21

  22. Dynamic Competitive Equilibria exist and are essentially the same for the 3 Scenarios [Theorem 3, Gast et al 2013] 1 u.e. = 360 MWh1 u.p .= 600 MW= 0.6 GW2/h 2GW/hCmax=Dmax= 3 u.p. 22

  23. Social Optimality • Assume a social planner wants to maximize total payoff • Total payoff is same for all 3 scenarios and is independent of price process • Structure of optimally social control Let optimal control is such that if ) increase (t)if ) decrease (t) 23

  24. The Social Welfare Theorem [Gast et al., 2013] Any dynamic competitive equilibrium for any of the three scenarios maximizes social welfare 24

  25. The Invisible Hand of the Market may not be optimal • Any dynamic competitive equilibrium for any of the three scenarios maximizes social welfare • However, this assumes a given storage capacity. • Is there an incentive to install storage ? • No, stand alone operators or consumers have no incentive to install the optimal storage Expected welfare of stand alone operator Expected social welfare 25

  26. Scaling Laws • (steepness) being close to social welfare requires the optimal storage capacity • optimal storage capacity scales like increasevolatility and rampupcapacity by = increasestorage by 26

  27. Whatthissuggests about storage : • with a free and honestmarket, storagecanbeoperated by prices • however, theremay not beenoughincentive for storageoperators to install the optimal storage size • perhapspreferentialpricingshouldbedirectedtowardsstorage as much as towards PV 27

  28. 3. A MODEL OF REAL TIME DEMAND RESPONSE [Le Boudec and Tomozei 2013] Le Boudec, Tomozei, “Stability of a stochastic model for demand-response”, Stochastic Systems 2013, also available at http://infoscience.epfl.ch/record/185991 28

  29. Issue withDemandResponse: Grid Changes Load • Widespreaddemandresponsemaymakeload hard to predict loadwithdemandresponse «natural» load renewables 29

  30. A Macroscopic Model of Demand Response MacroscopicModel of [Cho and Meyn 2010] Control Ramping Constraint Supply Randomness Natural Demand Evaporation Expressed Demand update term Satisfied Demand Returning Demand Reserve (Excess supply) Frustrated Demand load is delayed Backlogged Demand demand response 30

  31. We obtain a 2-d Markov chain on continuous state space Control Ramping Constraint Randomness Supply Natural Demand Evaporation Expressed Demand Satisfied Demand Returning Demand Reserve (Excess supply) Frustrated Demand Backlogged Demand 31

  32. The Control Problem • Control variable: production bought one time slot ago in real time market • Controller seesonlysupplyand expresseddemand • Our Problem:keepbacklog stable • Ramp-up and ramp-down constraints 32

  33. ThresholdBasedPolicies Forecastsupplyisadjusted to forecastdemand R(t) := reserve = excess of demand over supply • Threshold policy: • ifincreasesupply to come as close toas possible (consideringramp up constraint) • elsedecreasesupply to come as close to as possible (consideringrampdown constraint) 33

  34. Simulations (evaporation) Backlog Reserve 34

  35. Simulations (evaporation) r* • meansreturningloadis, in average, less • Large excursions intonegativereserve and large backlogs are typicaland occuratrandom times 1 time step = 10mn 35

  36. Large backlogsmayoccurwithin a day, atany time (whenevaporation) t = 40 mn t = 400 mn t = 1280 mn Day 1 t = 40 mn t = 400 mn t = 1280 mn Day 2 Typical delay30 mn, all simulations withsameparameters as previousslide, 36

  37. ODE Approximation () explain large excursions into positive backlogs r* 37

  38. Simulations (evaporation) Backlog Reserve 38

  39. Simulations (evaporation) • meansreturningloadis, in average, more • Backloggrowsmore rapidly 1 time step = 10mn 39

  40. ODE Approximation () shows backlogisunstable 40

  41. Findings : StabilityResults • If evaporationis positive, system is stable (ergodic, positive recurrent Markov chain) for anythreshold • If evaporationisnegative, system unstable for anythreshold • Delay does not play a role in stability • Nor do ramp-up / ramp down constraints or size of reserve 41

  42. Whatthissuggests about DemandResponse: • Positive evaporationis essentialoccurswith thermal loads, might not alwaysoccur for all load • Model suggeststhat large backlogs are possible and unpredictible • Backloggedloadis a new threat to gridoperationNeed to measure and forecastbackloggedload loadwithdemandresponse «natural» load renewables 42

  43. Thank You ! [Cho and Meyn, 2010] I. Cho and S. MeynEfficiency and marginal cost pricing in dynamic competitive markets with friction, Theoretical Economics, 2010 [Bejanet al 2012] Bejan, Gibbens, Kelly, “Statistical aspects of storage systems modelling in energy networks,” 46th Annual Conference on Information Sciences and Systems 2012 [Gast et al 2012] Gast, Tomozei, Le Boudec. “Optimal Storage Policies with Wind Forecast Uncertainties”, GreenMetrics2012 [Gast et al 2013] Gast, Tomozei, Le Boudec. “Optimal Energy Storage Policies with Renewable Forecast Uncertainties ”, submitted, 2013 [Gast et al 2013] Gast, Le Boudec, Proutière, Tomozei, “Impact of Storage on the Efficiency and Prices in Real-Time Electricity Markets”, ACM e-Energy 2013, Berkeley, May 2013 [Le Boudecand Tomozei 2013] Le Boudec, Tomozei, “Stability of a stochastic model for demand-response”, Stochastic Systems 2013, also available at http://infoscience.epfl.ch/record/185991 [Bianchi et al. 2012] Bianchi, Borghetti, Nucci, Paolone and Peretto,“A Microcontroller-Based Power Management System for Standalone Microgrids With Hybrid Power Supply”, IEEE Transactions on Sustainable Energy, 2012

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