andy philpott epoc (epoc.nz) joint work with anes dallagi, emmanuel gallet, ziming guan
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
EPOC Optimization Workshop, July 8, 2011 Slide 1 of 41
Andy PhilpottEPOC
(www.epoc.org.nz)
joint work with
Anes Dallagi, Emmanuel Gallet, Ziming Guan
Recent Applications of DOASA
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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
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NotationDOASA used for reservoir optimization
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Hydro-thermal scheduling problemClassical hydro-thermal formulation
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SDDP versus DOASAHydro-thermal scheduling
SDDP (literature) DOASA
Fixed sample of N openingsin 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 model Low fidelity physical model
Weak convergence test Stricter convergence criterion
Risk model (Guigues) Risk model (Shapiro)
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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
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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?
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A parallel system of three reservoirs
Case study 1
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A cascade system of four reservoirs
Case study 2
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• 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 studiesInitial assumptions
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Revenue maximization modelMid-term scheduling of river chains
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DOASA stage problem SP(x,(t))Outer approximation using cutting planes
Θt+1
Reservoir storage, x(t+1)
V(x,(t)) =
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Cutting plane coefficients come from LP dual solutionsDOASA
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p11
p13
p12
How DOASA samples the scenario tree
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p11
p13
p12
How DOASA samples the scenario tree
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p11
p13
p21
p21
p21
How DOASA samples the scenario tree
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xi0xi1 xi2
i0+i0 xi1
xi3
i0
i1
EDF Policy uses reduction to single reservoirsConvert water values into one-dimensional cuts
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Upper bound from DOASA with 100 iterations Results for parallel system
430
435
440
445
450
455
460
0 10 20 30 40 50 60 70 80 90 100
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Difference in value DOASA
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-0.300 -0.200 -0.100 0.000 0.100 0.200 0.300
Difference in value DOASA - EDF policyResults for parallel system
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Upper bound from DOASA with 100 iterations Results cascade system
715
720
725
730
735
740
745
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96
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Results: cascade system
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1 0 1 2 3 4
Difference in value DOASA - EDF policy
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• 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 studiesNew assumptions
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Modelling head effectsPiecewise linear turbine curves vary with volume
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Modelling head effectsA 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.
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Modelling head effectsConvexification
• 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.
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Modelling head effects: cascade systemDifference in value: DOASA - EDF policy
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Modelling head effects: casade systemTop reservoir volume - EDF policy
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Modelling head effects: casade systemTop reservoir volume - DOASA policy
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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
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Counterfactual 1The Wolak benchmark
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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
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Yearly problem represented by this system
S
N
demand
demandWKO
HAW
MAN
H
demand
EPOC Counterfactual
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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
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We simulate an optimal policy in this detailed system
MAN
HAW
WKO
Application to NZEM
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Thermal marginal costs Application to NZEM
Gas and diesel prices ex MED estimatesCoal priced at $4/GJ
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Gas and diesel industrial price data ($/GJ, MED)Application to NZEM
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Market storage and centrally planned storage New Zealand electricity market
2005 2006 2007 2008 2009
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New Zealand electricity marketEstimated daily savings from central plan
$481,000 extra is saved from anticipating inflows during this week
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Savings in annual fuel costTotal fuel cost = (NZ)$400-$500 million per annum (est)
Total wholesale electricity sales = (NZ)$3 billion per annum (est)
New Zealand electricity market
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Benmore half-hourly prices over 2008 New Zealand electricity market
2005 2006 2007 2008 2009