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

EPOC Optimization Workshop, July 8, 2011 Slide 2 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 3 of 41

NotationDOASA used for reservoir optimization

EPOC Optimization Workshop, July 8, 2011 Slide 4 of 41

Hydro-thermal scheduling problemClassical hydro-thermal formulation

EPOC Optimization Workshop, July 8, 2011 Slide 5 of 41

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)

EPOC Optimization Workshop, July 8, 2011 Slide 6 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 7 of 41

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?

EPOC Optimization Workshop, July 8, 2011 Slide 8 of 41

A parallel system of three reservoirs

Case study 1

EPOC Optimization Workshop, July 8, 2011 Slide 9 of 41

A cascade system of four reservoirs

Case study 2

EPOC Optimization Workshop, July 8, 2011 Slide 10 of 41

• 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

EPOC Optimization Workshop, July 8, 2011 Slide 11 of 41

Revenue maximization modelMid-term scheduling of river chains

EPOC Optimization Workshop, July 8, 2011 Slide 12 of 41

DOASA stage problem SP(x,(t))Outer approximation using cutting planes

Θt+1

Reservoir storage, x(t+1)

V(x,(t)) =

EPOC Optimization Workshop, July 8, 2011 Slide 13 of 41

Cutting plane coefficients come from LP dual solutionsDOASA

EPOC Optimization Workshop, July 8, 2011 Slide 14 of 41

p11

p13

p12

How DOASA samples the scenario tree

EPOC Optimization Workshop, July 8, 2011 Slide 15 of 41

p11

p13

p12

How DOASA samples the scenario tree

EPOC Optimization Workshop, July 8, 2011 Slide 16 of 41

p11

p13

p21

p21

p21

How DOASA samples the scenario tree

EPOC Optimization Workshop, July 8, 2011 Slide 17 of 41

xi0xi1 xi2

i0+i0 xi1

xi3

i0

i1

EDF Policy uses reduction to single reservoirsConvert water values into one-dimensional cuts

EPOC Optimization Workshop, July 8, 2011 Slide 18 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 19 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 20 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 21 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 22 of 41

• 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

EPOC Optimization Workshop, July 8, 2011 Slide 23 of 41

Modelling head effectsPiecewise linear turbine curves vary with volume

EPOC Optimization Workshop, July 8, 2011 Slide 24 of 41

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.

EPOC Optimization Workshop, July 8, 2011 Slide 25 of 41

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.

EPOC Optimization Workshop, July 8, 2011 Slide 26 of 41

Modelling head effects: cascade systemDifference in value: DOASA - EDF policy

EPOC Optimization Workshop, July 8, 2011 Slide 27 of 41

Modelling head effects: casade systemTop reservoir volume - EDF policy

EPOC Optimization Workshop, July 8, 2011 Slide 28 of 41

Modelling head effects: casade systemTop reservoir volume - DOASA policy

EPOC Optimization Workshop, July 8, 2011 Slide 29 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 30 of 41Source: CC Report, p 200

Counterfactual 1The Wolak benchmark

EPOC Optimization Workshop, July 8, 2011 Slide 31 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 32 of 41

Yearly problem represented by this system

S

N

demand

demandWKO

HAW

MAN

H

demand

EPOC Counterfactual

EPOC Optimization Workshop, July 8, 2011 Slide 33 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 34 of 41

We simulate an optimal policy in this detailed system

MAN

HAW

WKO

Application to NZEM

EPOC Optimization Workshop, July 8, 2011 Slide 35 of 41

Thermal marginal costs Application to NZEM

Gas and diesel prices ex MED estimatesCoal priced at $4/GJ

EPOC Optimization Workshop, July 8, 2011 Slide 36 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 37 of 41

Load curtailment costsApplication to NZEM

EPOC Optimization Workshop, July 8, 2011 Slide 38 of 41

Market storage and centrally planned storage New Zealand electricity market

2005 2006 2007 2008 2009

EPOC Optimization Workshop, July 8, 2011 Slide 39 of 41

New Zealand electricity marketEstimated daily savings from central plan

$481,000 extra is saved from anticipating inflows during this week

EPOC Optimization Workshop, July 8, 2011 Slide 40 of 41

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

EPOC Optimization Workshop, July 8, 2011 Slide 41 of 41

Benmore half-hourly prices over 2008 New Zealand electricity market

2005 2006 2007 2008 2009

EPOC Optimization Workshop, July 8, 2011 Slide 42 of 41

FIN