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Stochastic optimization and control for Energy Management

Nicolas Gast Joint work with Jean-Yves Le Boudec , Dan- Cristian Tomozei March 2013. Stochastic optimization and control for Energy Management. Design of control policies Online algorithms Dynamic optimization Performance guarantees. Randomness due to: Volatility

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Stochastic optimization and control for Energy Management

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  1. Nicolas Gast Joint work with Jean-Yves Le Boudec, Dan-CristianTomozei March 2013 Stochastic optimization and control for Energy Management 1

  2. Design of control policies • Online algorithms • Dynamic optimization • Performance guarantees • Randomness due to: • Volatility • Forecast errors Stochastic optimization and control for Energy Management • Storage Management • Energyscheduling 2

  3. 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 maintainstoragelevelat ½ of itscapacityusingupdatedforecasts • Stochasticapproach • Use statistics of pasterrors. load renewables renewables + storage Pump hydro, Cycle efficiency 3

  4. Energy scheduling with delays Unmatcheddemand Reserve (Fast ramping generators) Production surplus production (control) schedule Losses (e.g. wind curtailements) Easily dispatchable Used last-minute Storage time Renewables Forecastuncertainties Non-dispatchable «Large» system (national level) 4 Wind forecast Demand forecast

  5. Example of schedulingheuristics Fixed offset policy Offset Forecastedneeded power Neededgeneration Alreadycommitedgeneration Max ? Forecastedstoragelevel Max/2 Schedule Future Past Time Fixedstoragelevelpolicy Storage level Max Forecastedstoragelevel Max/2 Max Forecastedstoragelevel Max/2 Time Time t+n Time t 5

  6. Metric and performance (large storage) Fixed offset • 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 Target=50% FO +200 Max Max/2 FO -200 FO +0 Fixedstorage Max • 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: Forecastedstoragelevel • canwe do better? • How to compute optimal offset? Max/2 6

  7. Fixed offset is optimal for large storage Let with • Theorem. If the forecast error is distributed as . Then: • (l,g) 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% Lowerbound • Uses distribution of error • FixedreserveisPareto-optimal Optimal fixed offset FO +50 FO 7 7

  8. 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 8

  9. DO 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 9

  10. Conclusion • Maintain the storage at fixed level is not optimal • Statistics of forecast error are important • Our heuristics are close to optimal (and optimal for large capacity) • Social planner point of view • Provide a baseline • Guidelines to design a market structure? • Can be used to dimension storage • Other work: • Economic implications of storage • Does the market leads to a socially optimal use of storage? (partially yes) • Algorithmic aspects for charging EV (Distributed storage systems) 10

  11. Questions ? [1] Nicolas Gast, Dan-Christian Tomozei, Jean-Yves Le Boudec. Optimal Storage Policies with Wind Forecast Uncertainties. Greenmetrics 2012, London, UK. Relatedwork: [2] Nicolas Gast, Jean-Yves Le Boudec, Alexandre Proutière, Dan-Christian Tomozei. Impact of Storage on the Efficiency and Prices in Real-Time Electricity Markets. ACM E-Energy 2013 [3] Bejan, Gibbens, Kelly, Statistical Aspects of Storage SystemsModelling in Energy Networks.46th AnnualConference on Information Sciences and Systems, 2012, Princeton University, USA. [4] Cho, Meyn – Efficiency and marginal cost pricing in dynamic competitive markets with friction, Theoretical Economics, 2010

  12. Computing the optimal storage • Losses & Gaz useddecreases • As capacityincreases • As maximum power increases • Developtworules-of-thumb to compute optimal storagecharacteristics: • Optimal power C iswhen P(forecasterror >= C) < 1%. • Optimal capacity B, when P(sum of errors over n slots >= B/2) < 1%. optimal capacity B Losses + Fastrampinggeneration Storage capacity(in AverageWindPower-hour) 12

  13. Optimal storage and time horizon • Optimal storage power • Optimal storagecapacity Weschedule the base production n hoursin advance 13

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