Transcript Document

Recent Applications of
DOASA
Andy Philpott
EPOC
(www.epoc.org.nz)
joint work with
Anes Dallagi, Emmanuel Gallet, Ziming Guan
EPOC Optimization Workshop, July 8, 2011
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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)
– Written in C++/Cplex with NZEM focus
– Time-consistent risk aversion
– Takes 8 hours for 5000 cuts on NZEM problem
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DOASA used for reservoir optimization
Notation
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Hydro-thermal scheduling problem
Classical hydro-thermal formulation
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Hydro-thermal scheduling
SDDP versus DOASA
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 model
Low fidelity physical model
Weak convergence test
Stricter convergence criterion
Risk model (Guigues)
Risk model (Shapiro)
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Two Applications of DOASA
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)
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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?
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Case study 1
A parallel system of three reservoirs
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Case study 2
A cascade system of four reservoirs
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Case studies
Initial assumptions
• 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
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Mid-term scheduling of river chains
Revenue maximization model
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DOASA stage problem SP(x,w(t))
Outer approximation using cutting planes
V(x,w(t)) =
Θt+1
Reservoir storage, x(t+1)
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DOASA
Cutting plane coefficients come from LP dual solutions
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How DOASA samples the scenario tree
w2(1)
w2(2)
w3(3)
w1(2)
w1(1)
w2(2)
w3(2)
p11
p12
w2(1)
p13
w3(1)
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How DOASA samples the scenario tree
w1(1)
p11
p12
w2(1)
p13
w3(1)
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How DOASA samples the scenario tree
w2(1)
w2(2)
p21
w1(2)
w2(2)
w1(1)
p11
w1(3)
w3(2)
p21
w2(1)
p13
p21
w1(2)
w2(2)
w3(1)
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w3(2)
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EDF Policy uses reduction to single reservoirs
Convert water values into one-dimensional cuts
xi0
xi1
xi2
xi3
i0+i0 xi1
i1
i0
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Results for parallel system
Upper bound from DOASA with 100 iterations
460
455
450
445
440
435
430
0
10
20
30
40
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50
60
70
80
90
100
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Results for parallel system
Difference in value DOASA - EDF policy
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
-0.300
-0.200
-0.100
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0
0.000
0.100
0.200
0.300
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Results cascade system
Upper bound from DOASA with 100 iterations
745
740
735
730
725
720
715
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
Difference in value DOASA - EDF policy
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-1
0
1
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2
3
4
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Case studies
New assumptions
• 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
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Modelling head effects
Piecewise linear turbine curves vary with volume
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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.
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Modelling head effects
Convexification
• assume that the slopes of the turbine
curves increase linearly with head volume
Dslope = Dvolume
• 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(w)] to the
marginal water value at volume x.
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Modelling head effects: cascade system
Difference in value: DOASA - EDF policy
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Modelling head effects: casade system
Top reservoir volume - EDF policy
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Modelling head effects: casade system
Top reservoir volume - DOASA policy
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Part 2: EMBER
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.
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The Wolak benchmark
Counterfactual 1
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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].
(* Borenstein, Bushnell, Wolak, American Economic Review, 92, 2002)
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EPOC Counterfactual
Yearly problem represented by this system
demand
demand
WKO
N
MAN
H
S
HAW
demand
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Application to NZEM
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.
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Application to NZEM
We simulate an optimal policy in this detailed system
WKO
MAN
HAW
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Application to NZEM
Thermal marginal costs
Gas and diesel prices ex MED estimates
Coal priced at $4/GJ
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Application to NZEM
Gas and diesel industrial price data ($/GJ, MED)
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Application to NZEM
Load curtailment costs
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New Zealand electricity market
Market storage and centrally planned storage
2005
2006
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2007
2008
2009
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New Zealand electricity market
Estimated daily savings from central plan
$481,000 extra is saved from anticipating inflows during this week
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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)
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New Zealand electricity market
Benmore half-hourly prices over 2008
2005
2006
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2007
2008
2009
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FIN
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