1. STOCHASTIC OPTIMIZATION AND CONTROL FOR ENERGY MANAGEMENT Nicolas Gast Joint work with Jean-Yves Le Boudec, Dan-Cristian Tomozei March 2013 1

2. STOCHASTIC OPTIMIZATION AND CONTROL FOR ENERGY MANAGEMENT 2 Randomness due to: Volatility Forecast errors Design of control policies Online algorithms Dynamic optimization Performance guarantees Storage Management Energy scheduling

3. Production scheduling w. forecasts errors Base load production scheduling Deviations from forecast 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 two approaches 1.Deterministic approach try to maintain storage level at ½ of its capacity using updated forecasts 2.Stochastic approach Use statistics of past errors. 3 renewables load

4. Energy scheduling with delays 4 time Renewables production (control) Reserve (Fast ramping generators) Losses (e.g. wind curtailements) Production surplus Unmatched demand Storage Forecast uncertainties Non-dispatchable Easily dispatchable Used last-minute «Large» system (national level)

5. Example of scheduling heuristics 5 Time t Max/2 Time Needed generation Forecasted needed power Already commited generation PastFuture Time Storage level Max Time t+n Schedule ? Forecasted storage level Offset Max/2 Forecasted storage level Max Fixed offset policy Max/2 Forecasted storage level Max Fixed storage level policy

6. Metric and performance (large storage) 6 Max/2 Max Fixed offset FO -200 Target=50% can we do better? How to compute optimal offset? Max/2 Forecasted storage level Max Fixed storage Questions: FO +0 FO +200 Numerical evaluation: data from the UK (BMRA data archive https://www.elexonportal.co.uk/ ) https://www.elexonportal.co.uk/ National data (wind prod & demand) 3 years Corrected day ahead forecast: MAE = 19%

7. Fixed offset is optimal for large storage 77 = Uses distribution of error Fixed reserve is Pareto-optimal Target=50% Lower bound Optimal fixed offset Target=80% FO +50 Problem solved for large capacity What about small / medium capacity? FO

8. Scheduling Policies for Small Storage 8 Instant cost (losses or fast-ramping energy) Storage level at next time-slot Expectation on possible errors

9. DO outperforms other heuristics Large storage capacity (=20h of average production of wind energy) Power = 30% of average wind power Fixed Offset & Dynamic offset are optimal Small storage capacity (=3h of average production of wind energy) Power = 30% of average wind power DO is the best heuristic 9 Maintaining storage at fixed level: not optimal There exist better heuristics Fixed storage level Dynamic offset Fixed storage level Fixed Offset Dynamic offset Fixed offset Lower bound

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. [1] Nicolas Gast, Dan-Christian Tomozei, Jean-Yves Le Boudec. Optimal Storage Policies with Wind Forecast Uncertainties. Greenmetrics 2012, London, UK. Related work: [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 Systems Modelling in Energy Networks. 46th Annual Conference 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 11 Questions ?

12. Computing the optimal storage Losses & Gaz used decreases As capacity increases As maximum power increases Develop two rules-of-thumb to compute optimal storage characteristics: Optimal power C is when P(forecast error >= C) < 1%. Optimal capacity B, when P(sum of errors over n slots >= B/2) < 1%. 12 Storage capacity (in AverageWindPower-hour) Losses + Fast ramping generation optimal capacity B

13. Optimal storage and time horizon Optimal storage powerOptimal storage capacity 13 We schedule the base production n hours in advance