Andy Philpott

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

• 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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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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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 t1,2,,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))
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DOASA
Cutting plane coefficients come from LP dual
solutions
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How DOASA samples the scenario tree
w2(2)
w2(1)
w3(3)
w1(2)
w2(2)
w1(1)
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(2)
w2(1)
w1(3)
w1(2)
p21
w2(2)
w1(1)
w3(2)
p11
p21
w2(1)
p13
w1(2)
p21
w2(2)
w3(1)
w3(2)
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EDF Policy uses reduction to single reservoirs
Convert water values into one-dimensional cuts
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Results for parallel system
Upper bound from DOASA with 100 iterations
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Results for parallel system
Difference in value DOASA
Difference in value DOASA - EDF policy
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Results cascade system
Upper bound from DOASA with 100 iterations
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Results cascade system
Difference in value DOASA - EDF policy
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Case studies
New assumptions

• weekly stages t1,2,,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 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)bEh(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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Motivation
Part 2 EMBER

• 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
Source CC Report, p 200
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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
N
H
S
demand
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Application to NZEM
Rolling horizon counterfactual

• Set s0
• At ts1, solve a DOASA model to compute a weekly
  centrally-planned generation policy for
  ts1,,s52.
• In the detailed 18-node transmission system and
  river-valley networks successively optimize weeks
  ts1,,s13, using cost-to-go functions from
  cuts at the end of each week t, and updating
  reservoir storage levels for each t.
• Set ss13.

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Application to NZEM
We simulate an optimal policy in this detailed
system
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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
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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Savings in annual fuel cost
New Zealand electricity market
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
2007
2008
2009
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FIN