1. EPOC Optimization Workshop, July 8, 2011 Slide 1 of 41 Andy Philpott EPOC (www.epoc.org.nz) joint work with Anes Dallagi, Emmanuel Gallet, Ziming Guan Recent Applications of DOASA

2. EPOC Optimization Workshop, July 8, 2011 Slide 2 of 41 What is it? EPOC version of SDDP with some differences Version 1.0 (P. and Guan, 2008) –Written in AMPL/Cplex –Very flexible –Used in NZ dairy production/inventory problems –Takes 8 hours for 200 cuts on NZEM problem Version 2.0 (P. and de Matos, 2010) –Written in C++/Cplex with NZEM focus –Time-consistent risk aversion –Takes 8 hours for 5000 cuts on NZEM problem DOASA

3. EPOC Optimization Workshop, July 8, 2011 Slide 3 of 41 Notation DOASA used for reservoir optimization

4. EPOC Optimization Workshop, July 8, 2011 Slide 4 of 41 Hydro-thermal scheduling problem Classical hydro-thermal formulation

5. EPOC Optimization Workshop, July 8, 2011 Slide 5 of 41 SDDP versus DOASA Hydro-thermal scheduling SDDP (literature) DOASA Fixed sample of N openings in each stage. Fixed sample of N openings in each stage. Fixed sample of forward pass scenarios (50 or 200) Resamples forward pass scenarios (1 at a time) High fidelity physical modelLow fidelity physical model Weak convergence testStricter convergence criterion Risk model (Guigues)Risk model (Shapiro)

6. EPOC Optimization Workshop, July 8, 2011 Slide 6 of 41 Mid-term scheduling of river chains (joint work with Anes Dallagi and Emmanuel Gallet at EDF) EMBER (joint work with Ziming Guan, now at UBC/BC Hydro) Two Applications of DOASA

7. EPOC Optimization Workshop, July 8, 2011 Slide 7 of 41 What is the problem? Mid-term scheduling of river chains EDF mid-term model gives system marginal price scenarios from decomposition model. Given uncertain price scenarios and inflows how should we schedule each river chain over 12 months? In NZEM: How should MRP schedule releases from Taupo for uncertain future prices and inflows?

8. EPOC Optimization Workshop, July 8, 2011 Slide 8 of 41 A parallel system of three reservoirs Case study 1

9. EPOC Optimization Workshop, July 8, 2011 Slide 9 of 41 A cascade system of four reservoirs Case study 2

10. EPOC Optimization Workshop, July 8, 2011 Slide 10 of 41 weekly stages t=1,2,…,52 no head effects linear turbine curves reservoir bounds are 0 and capacity full plant availability known price sequence, 21 per stage stagewise independent inflows 41 inflow outcomes per stage Case studies Initial assumptions

11. EPOC Optimization Workshop, July 8, 2011 Slide 11 of 41 Revenue maximization model Mid-term scheduling of river chains

12. EPOC Optimization Workshop, July 8, 2011 Slide 12 of 41 DOASA stage problem SP(x,  (t)) Outer approximation using cutting planes Θ t+1 Reservoir storage, x(t+1) V(x,  (t)) =

13. EPOC Optimization Workshop, July 8, 2011 Slide 13 of 41 Cutting plane coefficients come from LP dual solutions DOASA

14. EPOC Optimization Workshop, July 8, 2011 Slide 14 of 41                   p 11 p 13        p 12 How DOASA samples the scenario tree

15. EPOC Optimization Workshop, July 8, 2011 Slide 15 of 41          p 11 p 13 p 12 How DOASA samples the scenario tree

16. EPOC Optimization Workshop, July 8, 2011 Slide 16 of 41                            p 11 p 13 p 21        How DOASA samples the scenario tree

17. EPOC Optimization Workshop, July 8, 2011 Slide 17 of 41 EDF Policy uses reduction to single reservoirs Convert water values into one-dimensional cuts

18. EPOC Optimization Workshop, July 8, 2011 Slide 18 of 41 Upper bound from DOASA with 100 iterations Results for parallel system

19. EPOC Optimization Workshop, July 8, 2011 Slide 19 of 41 Difference in value DOASADifference in value DOASA - EDF policy Results for parallel system

20. EPOC Optimization Workshop, July 8, 2011 Slide 20 of 41 Upper bound from DOASA with 100 iterations Results cascade system

21. EPOC Optimization Workshop, July 8, 2011 Slide 21 of 41 Results: cascade system Difference in value DOASA - EDF policy

22. EPOC Optimization Workshop, July 8, 2011 Slide 22 of 41 weekly stages t=1,2,…,52 include head effects nonlinear turbine curves reservoir bounds are 0 and capacity full plant availability known price sequence, 21 per stage stagewise independent inflows 41 inflow outcomes per stage Case studies New assumptions

23. EPOC Optimization Workshop, July 8, 2011 Slide 23 of 41 Modelling head effects Piecewise linear turbine curves vary with volume

24. EPOC Optimization Workshop, July 8, 2011 Slide 24 of 41 Modelling head effects A major problem for DOASA? For cutting plane method we need the future cost to be a convex function of reservoir volume. So the marginal value of more water is decreasing with volume. With head effect water is more efficiently used the more we have, so marginal value of water might increase, losing convexity. We assume that in the worst case, head effects make the marginal value of water constant. If this is not true then we have essentially convexified C at high values of x.

25. EPOC Optimization Workshop, July 8, 2011 Slide 25 of 41 Modelling head effects Convexification assume that the slopes of the turbine curves increase linearly with head volume slope = volume in the stage problem the marginal value of increasing reservoir volume at the start of the week is from the future cost savings (as before) plus the marginal extra revenue we get in the current stage from more efficient generation. So we add a term p(t)**E[h()] to the marginal water value at volume x.

26. EPOC Optimization Workshop, July 8, 2011 Slide 26 of 41 Modelling head effects: cascade system Difference in value: DOASA - EDF policy

27. EPOC Optimization Workshop, July 8, 2011 Slide 27 of 41 Modelling head effects: casade system Top reservoir volume - EDF policy

28. EPOC Optimization Workshop, July 8, 2011 Slide 28 of 41 Modelling head effects: casade system Top reservoir volume - DOASA policy

29. EPOC Optimization Workshop, July 8, 2011 Slide 29 of 41 Motivation Market oversight in the spot market is important to detect and limit exercise of market power. –Limiting market power will improve welfare. –Limiting market power will enable market instruments (e.g. FTRs) to work as intended. Oversight needs good counterfactual models. –Wolak benchmark overlooks uncertainty –We use a rolling horizon stochastic optimization benchmark requiring many solves of DOASA. Part 2: EMBER

30. EPOC Optimization Workshop, July 8, 2011 Slide 30 of 41 Source: CC Report, p 200 Counterfactual 1 The Wolak benchmark

31. EPOC Optimization Workshop, July 8, 2011 Slide 31 of 41 What is counterfactual 1? –Fix hydro generation (at historical dispatch level). –Simulate market operation over a year with thermal plant offered at short-run marginal (fuel) cost. –“The Appendix of Borenstein, Bushnell, Wolak (2002)* rigorously demonstrates that the simplifying assumption that hydro-electric suppliers do not re-allocate water will yield a higher system-load weighted average competitive price than would be the case if this benchmark price was computed from the solution to the optimal hydroelectric generation scheduling problem described above” [Commerce Commission Report, page 190]. (* Borenstein, Bushnell, Wolak, American Economic Review, 92, 2002) The Wolak benchmark

32. EPOC Optimization Workshop, July 8, 2011 Slide 32 of 41 Yearly problem represented by this system S N demand WKOHAWMAN H demand EPOC Counterfactual

33. EPOC Optimization Workshop, July 8, 2011 Slide 33 of 41 Rolling horizon counterfactual –Set s=0 –At t=s+1, solve a DOASA model to compute a weekly centrally-planned generation policy for t=s+1,…,s+52. –In the detailed 18-node transmission system and river-valley networks successively optimize weeks t=s+1,…,s+13, using cost-to-go functions from cuts at the end of each week t, and updating reservoir storage levels for each t. –Set s=s+13. Application to NZEM

34. EPOC Optimization Workshop, July 8, 2011 Slide 34 of 41 We simulate an optimal policy in this detailed system MANHAW WKO Application to NZEM

35. EPOC Optimization Workshop, July 8, 2011 Slide 35 of 41 Thermal marginal costs Application to NZEM Gas and diesel prices ex MED estimates Coal priced at $4/GJ

36. EPOC Optimization Workshop, July 8, 2011 Slide 36 of 41 Gas and diesel industrial price data ($/GJ, MED) Application to NZEM

37. EPOC Optimization Workshop, July 8, 2011 Slide 37 of 41 Load curtailment costs Application to NZEM

38. EPOC Optimization Workshop, July 8, 2011 Slide 38 of 41 Market storage and centrally planned storage New Zealand electricity market 20052006200720082009

39. EPOC Optimization Workshop, July 8, 2011 Slide 39 of 41 New Zealand electricity market Estimated daily savings from central plan $481,000 extra is saved from anticipating inflows during this week

40. EPOC Optimization Workshop, July 8, 2011 Slide 40 of 41 Savings in annual fuel cost Total fuel cost = (NZ)$400-$500 million per annum (est) Total wholesale electricity sales = (NZ)$3 billion per annum (est) New Zealand electricity market

41. EPOC Optimization Workshop, July 8, 2011 Slide 41 of 41 Benmore half-hourly prices over 2008 New Zealand electricity market 20052006200720082009

42. EPOC Optimization Workshop, July 8, 2011 Slide 42 of 41 FIN