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Andy Philpott EPOC (epoc.nz) joint work with Anes Dallagi, Emmanuel Gallet, Ziming Guan

Recent Applications of DOASA. Andy Philpott EPOC (www.epoc.org.nz) joint work with Anes Dallagi, Emmanuel Gallet, Ziming Guan. 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

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Andy Philpott EPOC (epoc.nz) joint work with Anes Dallagi, Emmanuel Gallet, Ziming Guan

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  1. Recent Applications of DOASA Andy Philpott EPOC (www.epoc.org.nz) joint work with Anes Dallagi, Emmanuel Gallet, Ziming Guan

  2. 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 What is it?

  3. DOASA used for reservoir optimization Notation

  4. Hydro-thermal scheduling problem Classical hydro-thermal formulation

  5. Hydro-thermal scheduling SDDP versus DOASA

  6. 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. Mid-term scheduling of river chains What is the problem? • 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. Case study 1 A parallel system of three reservoirs

  9. Case study 2 A cascade system of four reservoirs

  10. 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. Mid-term scheduling of river chains Revenue maximization model

  12. DOASA stage problem SP(x,w(t)) Θt+1 Reservoir storage,x(t+1) Outer approximation using cutting planes V(x,w(t)) =

  13. DOASA Cutting plane coefficients come from LP dual solutions

  14. How DOASA samples the scenario tree w2(1) w2(2) w3(3) w1(2) w2(2) w1(1) w3(2) p11 p12 w2(1) p13 w3(1)

  15. How DOASA samples the scenario tree w1(1) p11 p12 w2(1) p13 w3(1)

  16. How DOASA samples the scenario tree w2(1) w2(2) w1(3) p21 w1(2) w2(2) w1(1) w3(2) p11 p21 w2(1) p13 w1(2) p21 w2(2) w3(1) w3(2)

  17. EDF Policy uses reduction to single reservoirs Convert water values into one-dimensional cuts

  18. Results for parallel system Upper bound from DOASA with 100 iterations

  19. Results for parallel system Difference in value DOASA - EDF policy Difference in value DOASA

  20. Results cascade system Upper bound from DOASA with 100 iterations

  21. Results: cascade system Difference in value DOASA - EDF policy

  22. 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. Modelling head effects Piecewise linear turbine curves vary with volume

  24. 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. assume that the slopes of the turbine curves increase linearly with head volume Dslope = bDvolume 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)*b*E[h(w)] to the marginal water value at volume x. Modelling head effects Convexification

  26. Modelling head effects: cascade system Difference in value: DOASA - EDF policy

  27. Modelling head effects: casade system Top reservoir volume - EDF policy

  28. Modelling head effects: casade system Top reservoir volume - DOASA policy

  29. 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 Motivation

  30. The Wolak benchmark Counterfactual 1 Source: CC Report, p 200

  31. 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 What is counterfactual 1?

  32. EPOC Counterfactual HAW MAN WKO Yearly problem represented by this system demand demand N H S demand

  33. 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 Rolling horizon counterfactual

  34. Application to NZEM HAW MAN WKO We simulate an optimal policy in this detailed system

  35. Application to NZEM Thermal marginal costs Gas and diesel prices ex MED estimates Coal priced at $4/GJ

  36. Application to NZEM Gas and diesel industrial price data ($/GJ, MED)

  37. Application to NZEM Load curtailment costs

  38. New Zealand electricity market Market storage and centrally planned storage 2005 2006 2007 2008 2009

  39. New Zealand electricity market Estimated daily savings from central plan $481,000 extra is saved from anticipating inflows during this week

  40. New Zealand electricity market 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)

  41. New Zealand electricity market Benmore half-hourly prices over 2008 2005 2006 2007 2008 2009

  42. FIN

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