Andy Philpott EPOC (epoc.nz) joint work with Vitor de Matos, Ziming Guan

1. Advances in DOASA Andy Philpott EPOC (www.epoc.org.nz) joint work with Vitor de Matos, 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 Time-consistent risk aversion Takes 8 hours for 5000 cuts on NZEM problem DOASA What is it?

3. 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. We don’t have access to SDDP. We seek ways that SDDP can be improved. DOASA Motivation

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

5. 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?

6. Counterfactual 1 What about uncertain inflows? Counterfactual 1 In the year under investigation, suppose all generators optimistically predicted high inflows and used all their water in summer. They were right, and no thermal fuel was needed at all. Counterfactual prices are zero. wet Stochastic program counterfactual The optimal generation plan burns thermal fuel in stage 1 in case there is a drought in winter. The competitive price is high (marginal thermal fuel cost) in the first stage, but zero in the second (if wet). dry summer winter

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

8. DOASA Cost-to-go recursion

9. DOASA DOASA: Cutting planes define the future cost function

10. DOASA SDDP versus DOASA

11. 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)

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

13. 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)

14. DOASA run times

15. Why do it this way? Lower bounds converge faster

16. Why do it this way? Upper bound convergence: 5000 forward simulations

17. In this case terminating SDDP after 4, or 5, or even 10 iterations (of 200 scenarios each) does NOT guarantee a close to optimal policy. Confidence intervals with 200 scenarios are 5 times bigger than with 5000 scenarios. Single forward pass is better as it does not duplicate cut evaluation. Iterations slow down as cut sets increase. Cut-set reduction needed. SDDP Takeaways

18. 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

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

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

21. Application to NZEM Heat rates

22. Application to NZEM Load curtailment costs

23. New Zealand electricity market Market storage and centrally planned storage

24. New Zealand electricity market Estimated daily savings from central plan =(NZ)$12.9 million per year (=2.8% of historical fuel cost)

25. 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)

26. Application to NZEM The next steps How does risk aversion affect prices and efficiency? How to model this? Use CVaR (Rockafellar and Urysayev, 2000) Actually, need a time-staged version of this. (Ruszczynzki, 2010), (Shapiro, 2010)

27. Application to NZEM CVaR1-a = Conditional value at risk (tail average) VaR0.9= $420M CVaR0.9= $460M 90% 10%

28. A risk-averse central planner Average 2006 storage trajectories minimizing (1-l)E[Z]+lCVar(Z)

29. A risk-averse central planner “Fuel and shortage cost – residual water value” CDF 1 0

30. Conclusions DOASA is well-tested tool for benchmarking. We now have a good empirical understanding of convergence behaviour. We can model risk aversion effectively. Next steps include 2008-2009 inflow data simulate central plans with different levels of risk aversion How much risk can be avoided for $50M fuel cost? Examine winter 2008 in more detail – especially price outcomes. Interested in feedback from participants – is this worth pursuing? If so how should industry fund it?