192021 10 Advances in DOASA Andy Philpott EPOC

19/2021 10 Advances in DOASA Andy Philpott EPOC (www. epoc. org. nz) joint work with Vitor de Matos, Ziming Guan EPOC Winter Workshop, October 26, Slide 1 of 31

DOASA 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) 19/2021 10 – Written in C++/Cplex – Time-consistent risk aversion – Takes 8 hours for 5000 cuts on NZEM problem EPOC Winter Workshop, October 26, Slide 2 of 31

DOASA 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. • We don’t have access to SDDP. • We seek ways that SDDP can be improved. 19/2021 10 EPOC Winter Workshop, October 26, Slide 3 of 31

The Wolak benchmark Counterfactual 1 19/2021 10 EPOC Winter Workshop, October Source: 26, CC Report, p 200 Slide 4 of 31

The Wolak benchmark 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]. 19/2021 10 (* Borenstein, Bushnell, Wolak, American Economic Review, 92, 2002) EPOC Winter Workshop, October 26, Slide 5 of 31

Counterfactual 1 What about uncertain inflows? 19/2021 10 wet dry summer winter 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. 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). EPOC Winter Workshop, October 26, Slide 6 of 31

EPOC Counterfactual Yearly problem represented by this system 19/2021 10 demand WKO N MAN H S HAW demand EPOC Winter Workshop, October 26, Slide 7 of 31

DOASA Cost-to-go recursion 19/2021 10 EPOC Winter Workshop, October 26, Slide 8 of 31

DOASA: Cutting planes define the future cost function 19/2021 10 EPOC Winter Workshop, October 26, Slide 9 of 31

DOASA SDDP versus DOASA SDDP (literature) DOASA Fixed sample of N openings Fixed sample of forward pass scenarios (50 or 200) Resamples forward pass scenarios (1 at a time) High fidelity physical model Low fidelity physical model Weak convergence test Stricter convergence criterion Risk model (Guigues) Risk model (Shapiro) 19/2021 10 EPOC Winter Workshop, October 26, Slide 10 of 31

How DOASA samples the scenario tree 19/2021 10 w 2(1) w 2(2) w 3(3) w 1(2) w 1(1) p 11 p 12 w 2(2) w 3(2) w 2(1) p 13 w 3(1) EPOC Winter Workshop, October 26, Slide 11 of 31

How DOASA samples the scenario tree 19/2021 10 w 1(1) p 11 p 12 w 2(1) p 13 w 3(1) EPOC Winter Workshop, October 26, Slide 12 of 31

How DOASA samples the scenario tree 19/2021 10 w 2(1) w 2(2) p 21 w 1(2) w 2(2) w 1(1) p 11 w 1(3) w 3(2) p 21 w 2(1) p 13 p 21 w 1(2) w 2(2) w 3(1) EPOC Winter Workshop, October 26, w 3(2) Slide 13 of 31

DOASA run times 19/2021 10 EPOC Winter Workshop, October 26, Slide 14 of 31

Why do it this way? Lower bounds converge faster 19/2021 10 EPOC Winter Workshop, October 26, Slide 15 of 31

Why do it this way? Upper bound convergence: 5000 forward simulations 19/2021 10 EPOC Winter Workshop, October 26, Slide 16 of 31

SDDP Takeaways • 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. 19/2021 10 EPOC Winter Workshop, October 26, Slide 17 of 31

Application to NZEM Rolling horizon counterfactual 19/2021 10 – 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. EPOC Winter Workshop, October 26, Slide 18 of 31

Application to NZEM We simulate an optimal policy in this detailed system WKO MAN 19/2021 10 HAW EPOC Winter Workshop, October 26, Slide 19 of 31

Application to NZEM Gas and diesel industrial price data ($/GJ, MED) 19/2021 10 EPOC Winter Workshop, October 26, Slide 20 of 31

Application to NZEM Heat rates 19/2021 10 EPOC Winter Workshop, October 26, Slide 21 of 31

Application to NZEM Load curtailment costs 19/2021 10 EPOC Winter Workshop, October 26, Slide 22 of 31

New Zealand electricity market Market storage and centrally planned storage 19/2021 10 EPOC Winter Workshop, October 26, Slide 23 of 31

New Zealand electricity market Estimated daily savings from central plan 19/2021 10 =(NZ)$12. 9 million per year (=2. 8% of historical fuel cost) EPOC Winter Workshop, October 26, Slide 24 of 31

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) 19/2021 10 EPOC Winter Workshop, October 26, Slide 25 of 31

Application to NZEM The next steps 19/2021 10 How does risk aversion affect prices and efficiency? How to model this? Use CVa. R (Rockafellar and Urysayev, 2000) Actually, need a time-staged version of this. (Ruszczynzki, 2010), (Shapiro, 2010) EPOC Winter Workshop, October 26, Slide 26 of 31

Application to NZEM CVa. R 1 -a = Conditional value at risk (tail average) 19/2021 10 Va. R 0. 9= $420 M CVa. R 0. 9= $460 M 90% 10% EPOC Winter Workshop, October 26, Slide 27 of 31

A risk-averse central planner Average 2006 storage trajectories minimizing (1 -l)E[Z]+l. CVar(Z) 19/2021 10 EPOC Winter Workshop, October 26, Slide 28 of 31

A risk-averse central planner “Fuel and shortage cost – residual water value” CDF 1 0 19/2021 10 EPOC Winter Workshop, October 26, Slide 29 of 31

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 $50 M 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? 19/2021 10 EPOC Winter Workshop, October 26, Slide 30 of 31