Modelling incentives and regulation in wholesale electricity markets

1
Modelling incentives and regulation in
wholesale electricity markets
Andy Philpott Electric Power Optimization
Centre The University of Auckland (www.esc.auckl
and.ac.nz/epoc)? (with acknowlegements to Geoff
Pritchard and Golbon Zakeri)?
2
What is the purpose of this talk?

• New Zealand faces some huge technical challenges
  in energy supply and delivery.
• This needs lots of research and development into
  new technology which is where NERI is currently
  focused.
• But technology is not enough we need to
  understand the economic institutions for
  implementing this technology.
• Our work at EPOC studies how these institutions
  (e.g. taxes, trading schemes, regulations etc.)
  work using models.
• These models try to help us design mechanisms
  that will induce optimal behaviour in the
  agents of wholesale electricity markets i.e. we
  study incentives and how they work.

3
Summary

• What is the wholesale electricity market?
• Examples of incentive/regulation problems
• Generator offering
• Transmission planning
• Wind power
• Emissions trading
• Takeaway new energy technology is necessary but
  not sufficient without understanding the market
  mechanisms under which we expect it to be
  adopted.

4
NZEM is a uniform price auction (e.g. single
node)
price
T2(q)?
p
quantity
price
combined offer stack
p
quantity
5
Example
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
Thermal B 400 _at_ 50
Load 500
6
Least-cost dispatch
100
150
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
7
Least-cost dispatch with nodal prices
45
100
150
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
50

• Load pays 25000 (50500)?
• Hydro makes profit 4000 and Wind makes profit
  4500
• System operator makes congestion rent of 1250
• The dispatch has total cost 15250

8
The actual NZEM

• Generators specify supply curves defining prices
  at which they will generate.
• Curves fixed for each (1/2) hour
• Linear programming model runsevery five minutes
  to determine
• who produces how much
• electricity flows in grid
• spot price of electricity at each grid exit point
  around the country (244 of these)?

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Wholesale electricity prices
Five Minute Wholesale Electricity Prices on
28/08/06 (/MWh)?
Source comitfree
Otahuhu
Benmore
Time of Day
11
Example 1 Dispatch with strategic bidding
45
100
150
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
50

• Load pays 19500 extra (39500)?
• Hydro makes extra 7800 and Thermal B makes extra
  1950
• System operator makes extra congestion rent of
  9750
• The dispatch is exactly the same, with cost
  15250

12
Example 2 Dispatch with strategic withholding
45
100
150
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
50

• Load pays no extra money
• System operator congestion rent goes down by
  1250 to 0
• Wind makes 500 more, Thermal A makes 745 more

Total cost of dispatch is 15255 which is 5 more
than original cost!!
13

• What can we learn from this example?

• Strategic behaviour by firms can result in higher
  prices and a wealth transfer between agents.
• Strategic behaviour by firms can result in
  dispatch inefficiency.
• Prices that do not truly represent the cost of
  shortage can lead to inefficiencies in the wider
  economy.
• Dispatch inefficiency is a deadweight loss (5 in
  example)?
• Q How bad can it get?
• Q How do we prevent it?

14
J.F. Nash Jr., Equilibrium points in n-person
games, Proc Nat. Acad. Sci. USA, 36 (1950) 48-49.
15
If generators offer at marginal cost
Load 500 - p

• Expect the price to be 50
• a450
• b450
• Line contains no flow.
• Thermals make no profit.
• Load has high welfare.

Thermal A 500 _at_ 50
a
Capacity 1000 lossless
Thermal B 500 _at_ 50
b
Load 500 - p
16
If generators withhold strategically
Load 500 - p
Total load 1000-2p p 500-(ab)/2 A
solves max (p-50)a B solves max (p-50)b
Thermal A 500 _at_ 50
a
Capacity 1000 lossless
Thermal B 500 _at_ 50
(500-(ab)/2-50)a has maximum at a
450-b/2 (500-(ab)/2-50)b has maximum at b
450-a/2
b
Load 500 - p
17
Example of Cournot-Nash equilibrium
Load 500 - p
200
Total load 1000-2p p 500-(ab)/2 A
solves max (p-50)a B solves max (p-50)b
Thermal A 500 _at_ 50
300
Capacity 1000 lossless
Thermal B 500 _at_ 50
(500-(ab)/2-50)a has maximum at a
450-b/2 (500-(ab)/2-50)b has maximum at b
450-a/2
300
Load 500 - p
200
18
Example of Cournot-Nash equilibrium
Price 200
Load 500 - p
200
Thermal A 500 _at_ 50
300
Deadweight loss is 11250 x 2
No flow in the line
Capacity 1000 lossless
Thermal B 500 _at_ 50
300
Load 500 - p
200
19
What if the line has zero capacity?
Load 500 - p
Each load 500-p p 500-a A solves max
(p-50)a
Thermal A 500 _at_ 50
a
Capacity 0 lossless
(500-a-50)a has maximum at a 225 (500-b-50)b
has maximum at b 225
Thermal B 500 _at_ 50
b
Load 500 - p
20
What if the line has zero capacity?
Load 500 - p
275
Each load 500-p p 500-a A solves max
(p-50)a
Thermal A 500 _at_ 50
225
Capacity 0 lossless
(500-a-50)a has maximum at a 225 (500-b-50)b
has maximum at b 225
Thermal B 500 _at_ 50
225
Load 500 - p
275
21
What if the line has zero capacity?
Price 275
Load 500 - p
275
Thermal A 500 _at_ 50
225
Deadweight loss is 25312.50 x 2
Capacity 0 lossless
Thermal B 500 _at_ 50
225
Load 500 - p
275
The transmission line has significant value in
encouraging competition even though it might
never transport any electricity.
22
Does this matter in practice?

• Clause 10 of the Grid Investment Test states
• Competition Benefits may be included in the
  market benefits of a proposed investment or
  alternative project if the Board reasonably
  considers this appropriate, provided the
  competition benefits can be separately identified
  and calculated
• NZ Electricity Commission 2006, Grid Investment
  Test.

23
New Zealand example (Downward 2007)?
Northland/Auckland Demand 2010 2288
MW 2015 2631 MW 2020 2987 MW Strategic
Generators Huntly E3P (1413 MW)? Otahuhu B
(390 MW)?
Central North Island Demand 2010 1794
MW 2015 1954 MW 2020 2109 MW Strategic
Generators Waikato Hydro (776 MW)?
Lower North Island and South Island Demand 2010
3211 MW 2015 3492 MW 2020 3721
MW Strategic Generators Taranaki CC (365
MW)? Waitaki Hydro (2718 MW)? Clutha Hydro
(1000MW)?
24
New Zealand example
Source Anthony Downward, EPOC
25
Incentives for wind generation
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
Thermal B 400 _at_ 50
Load 500
Source Geoff Pritchard, EPOC WW2007
26
Least-cost dispatch
100
150
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
The best solution, on the assumption that the
wind forecast is accurate.
Source Geoff Pritchard, EPOC WW2007
27
Wind above forecast
100
150
Thermal A 400 _at_ 45
Wind 120 actual, _at_ 0
spill 20
250
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
200
50
Thermal B 400 _at_ 50
Load 500
Wind is spilled cheap energy is lost.
Source Geoff Pritchard, EPOC WW2007
28
Wind below forecast
80
150
Thermal A 400 _at_ 45
Wind 80 actual, _at_ 0
230
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
220
50
Thermal B 400 _at_ 50
Load 500
Wind shortfall is made up with expensive water.
Source Geoff Pritchard, EPOC WW2007
29
Are better forecasts needed?
Electricity Commission WGIP report June 2007
30
A flexible dispatch
100
125
Thermal A 400 _at_ 45
Wind 100 forecast, _at_ 0
225
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
175
100
Thermal B 400 _at_ 50
Load 500

• Spare capacity on transmission line.
• Spare capacity in cheap hydro offer.

Source Geoff Pritchard, EPOC WW2007
31
Wind above forecast
120
125
Thermal A 400 _at_ 45
Wind 120 actual, _at_ 0
245
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
155
100
Thermal B 400 _at_ 50
Load 500
Surplus wind is matched to hydro decrease.
Source Geoff Pritchard, EPOC WW2007
32
Wind below forecast
80
125
Thermal A 400 _at_ 45
Wind 80 actual, _at_ 0
205
Capacity 250 lossless
Hydro 200 _at_ 30, 200 _at_ 90
195
100
Thermal B 400 _at_ 50
Load 500
Lack of wind is matched by hydro.
Source Geoff Pritchard, EPOC WW2007
33
Optimizing dispatch as a stochastic LP

• Generators offer to sell quantities qi , ask
  prices pi ,regulation margins ri
• We find dispatches xi and Zi to
• minimize ? (pi xi E???pi ? ri??Zi
  ??xi??????pi ? ri??Zi ??xi???? )
• (expected cost of power, at offered prices,
  including re-dispatch)?
• so that
• demand is met (at both 1st and 2nd stages)?
• transmission network is operated within capacity
• (xi , Zi ) satisfy plant constraints

Source Geoff Pritchard, EPOC WW2007
34
Example
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)?
Hydro 2 40 _at_ 40 (/- 5)?
Load 60

• Ensemble forecast for wind. Most likely scenario
  is 0.
• Hydros compete on both energy and regulation.
• What to dispatch?

Source Geoff Pritchard, EPOC WW2007
35
Optimal hedged dispatch (initial)?
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)?
30
10
20
Hydro 2 40 _at_ 40 (/- 5)?
Load 60

• Hydros dispatched out of order to keep
  regulation cost down.

Source Geoff Pritchard, EPOC WW2007
36
Optimal hedged re-dispatch
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)?
0, 10, 20, 30
40, 30, 20, 10
Hydro 2 40 _at_ 40 (/- 5)?
20
Load 60

• Hydro 1 wins the regulation business.

Source Geoff Pritchard, EPOC WW2007
37
Initial dispatch prices

• ? the marginal cost of an additional unit of
  load
• in the initial dispatch.
• This is an appropriate price at which to trade
  energy,
• where that energy was present in the
  initial dispatch.
• Applies to
• inflexible load and generation
• some flexible and intermittent generation

Source Geoff Pritchard, EPOC WW2007
38
Re-dispatch prices

• ?R the marginal cost of an additional unit of
  load
• in a re-dispatch.
• This is an appropriate price at which to trade
  energy,
• where that energy was added in a
  re-dispatch.
• Applies to
• some flexible and intermittent generation (both
  hydro wind)?

Source Geoff Pritchard, EPOC WW2007
39
Example initial dispatch prices
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)?
30
10
20
Hydro 2 40 _at_ 40 (/- 5)?
40
Load 60

• Marginal additional load would be met by Hydro
  2.
• The quantities xi are sold _at_ 40 load pays 40.
  

Source Geoff Pritchard, EPOC WW2007
40
Example re-dispatch prices
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)?
0, 10, 20, 30
40, 30, 20, 10
Hydro 2 40 _at_ 40 (/- 5)?
10
30
20
41, 41, 37, 37
Load 60

• 1st scenario Wind buys back 10 _at_ 41 Hydro 1
  sells 10 _at_ 41
• 2nd scenario no re-dispatch
• 3rd scenario Wind sells 10 _at_ 37 Hydro 1 buys
  back 10 _at_ 37
• 4th scenario Wind sells 20 _at_ 37 Hydro 1 buys
  back 20 _at_ 37

Source Geoff Pritchard, EPOC WW2007
41
Average selling prices
Wind capacity 40, _at_ 0 scenarios 0, 10, 20,
30 probabilities 0.5, 0.2, 0.2, 0.1
Hydro 1 40 _at_ 39 (/- 2)?
0, 10, 20, 30
40, 30, 20, 10
Hydro 2 40 _at_ 40 (/- 5)?
20
41, 41, 37, 37
Load 60

• Average selling price achieved
• (expected revenue) / (expected
  generation)?
• Wind 38.11
• Hydro 1 40.55
• Hydro 2 40

Source Geoff Pritchard, EPOC WW2007
42
A price for uncertainty

• Prices earned by less predictable wind generation
  are lower on average.
• Prices earned by flexible generation are higher
  on average.
• Prices paid by less predictable loads are higher
  on average.
• New wind generation that decreases variation will
  increases price for all.
• Revenue adequate dispatch model means that wind
  backup can be suitably rewarded.

43
Emissions trading

• NZ ETS is a cap-and-trade scheme.
• How can generators act strategically in this
  setting?
• Little work done here, but see e.g. Chen, Hobbs
  et al 2007.
• Conjecture withholding generation decreases
  emissions so that emission permits become cheaper
  and are acquired by competitive firms who will
  increase output in equilibrium.
• What about a carbon tax?

44
Least-cost dispatch
Load 500 - p

• Expect the price to be 50
• a450
• b450
• Line contains no flow.
• Thermals make no profit.
• Load has high welfare.

50
Thermal A 500 _at_ 50
a
Capacity 1000 lossless
GEOThermal B 500 _at_ 50
b
Load 500 - p
50
45
Least-cost dispatch with CO2 tax
Load 500 - p
70
Thermal A 500 _at_ 50 plus 20 CO2 tax
Capacity 1000
GEOThermal B 500 _at_ 50
Load 500 - p
70
Price increases by 20. The carbon tax has been
transferred to consumers. GEOThermal B makes
10000 profit.
46
Cournot-Nash equilibrium
Load 500 - p
200
Total load 1000-2p p 500-(ab)/2 A
solves max (p-50)a B solves max (p-50)b
Thermal A 500 _at_ 50
300
Capacity 1000 lossless
GEOThermal B 500 _at_ 50
(500-(ab)/2-50)a has maximum at a
450-b/2 (500-(ab)/2-50)b has maximum at b
450-a/2
300
Load 500 - p
200
47
Cournot-Nash equilibrium with CO2 tax
Load 500 - p
206.66
Total load 1000-2p p 500-(ab)/2 A
solves max (p-5020)a B solves max (p-50)b
Thermal A 500 _at_ 50 plus 20 CO2 tax
Capacity 1000
GEOThermal B 500 _at_ 50
(500-(ab)/2-70)a has maximum at a
430-b/2 (500-(ab)/2-50)b has maximum at b
450-a/2
Load 500 - p
206.66
Price increases by only 6.66.
48
The takeaways

• Markets are intended to provide incentives for
  agents to make optimal decisions.
• Understanding these is essential to formulating
  energy policy.
• For a poor market design, strategic behaviour
  might make decisions inefficient.
• Regulation is intended to restore some
  efficiency.
• Nash equilibrium models are indispensible in
  understanding whether incentives and or
  regulation will deliver the desired outcomes.

49
The last word is incentives
Robert Aumann Nobel Prize Lecture December 8 2005
50
The End
51
The End
52
Why study Nash Equilibria?
Roger Myerson, JEL, 1999
53
Single-period Nash equilibrium models

• Classical model (Cournot, 1838)?
• Generator i offers quantity Q(i) at price 0
• Deterministic
• A demand curve determines the clearing price
• Transmission network can be modelled (to some
  extent)?
• Non identical players can be modelled
• Solve using calculus or a numerical method (e.g.
  PATH)?
• Supply-function model (Klemperer Meyer, 1989)?
• Players offer supply functions (marginal cost
  curves)?
• Uncertainty in demand
• Demand can be elastic or inelastic (Anderson
  Philpott, 2002)?
• Difficult to model and compute with

54

• Models for imperfect competition

• User optimal not system optimal
• Minimizing cost becomes maximizing profit.
• Imperfect competition
• Generator offers affect the price and hence
  profit
• Why is this bad?
• How bad can it get?
• How do we prevent it?

55
The hydro system
56
Sources of inefficiency

• Market power
• Most popular target from demand side
• Higher prices mean loss of consumer welfare
• User optimization versus system optimization
• Price of anarchy (e.g. traffic networks)?
• Pool prices are theoretically efficient in each
  trading period in perfectly competitive case.
• But what about reservoir operation?
• Risk
• Central plan has a different risk measure than
  generators.
• Central plan can pool risk, e.g. by trading off
  reservoir shortages.
• Information structure
• counterfactual solution may have access to more
  information than market solution

57
We have four models

• A single-period dispatch and nodal pricing model
  (HOUR) that models the real WEM dispatch process
  for any given trading period (18 node model).
• A national river-chain dispatch model (DAY) that
  minimizes thermal fuel costs subject to river
  scheduling constraints and transmission
  constraints over 48 trading periods (day).
• A national river-chain dispatch model (WEEK) that
  minimizes thermal fuel costs subject to river
  scheduling constraints and transmission
  constraints over 336 trading periods (week).
• A hydro-thermal scheduling model (YEAR) for
  centrally planning hydro-electricity releases to
  minimize expected fuel costs over 52 weeks. This
  is based on a SDDP sampling approach.

58
Related work

• Measuring market power in poolcos (ex-ante )?
• Market concentration indices (Herfindahl-Hirschman
  Index)?
• Cournot and SFE models (many)?
• Compare prices with marginal cost (e.g. Lerner
  index)?
• Agent-based market simulations (e.g. V.Smith,
  Bunn)?
• Price-of-anarchy models (e.g. Johari)?
• Hydro models (e.g. Bushnell, Scott and Read)?
• Empirical studies (e.g. Wolak) focus on price
  markups (ex-post)?
• In NZ, contracts not public knowledge, so
  analysis of prices presents some difficulties.
• However we can see if the market gives an
  inefficient dispatch.

59
HOUR model
?i
60
DAY (WEEK) model
61
YEAR model
62
Outer approximation of Ct1(y)?
T(t1)?
?t1 at1(k) ßt1(k)Ty, ?k
Reservoir storage, x(t1)?
63
YEAR model simplified network
demand
N
S
demand
64
Experiment 1

• Use YEAR to derive a (water value) policy for
  water release in week 1 (i.e. a function of
  current reservoir storage)?
• For months 1 to 12 do (a rolling horizon)?
• For weeks in current month, simulate the policy
  in WEEK using
• historical inflows
• historical demand
• fuel costs for thermal plant
• cuts computed in YEAR defining water value
• Re-solve YEAR to derive new water value (and
  policy) for next month. Increment month and do
  previous steps simulation.
• Dispatch historical generation offers in the DAY
  model using the same data for 365 days.
• Compare the amount/cost of fuel consumed over 365
  days.

65
Preliminary results for 2005/2006
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Preliminary results for 2005/2006
These results are wrong too much fuel burnt
Cogeneration plant has been dispatched at capacity
72
What is wrong with these results?

• Reservoir levels are allowed to get lower than
  Minzone targets.
• All cogeneration plant is dispatched at capacity
  at zero offer price.
• With minzone and cogen plant correctly accounted
  for the cost increases to (NZ)300M.
• What is the source of (NZ)200M inefficiency?
• Inefficient use of reservoir storage? and/or
• Misallocation of resources in short term?
• Use the WEEK model to study the latter.

73
Experiment 2 April 23-29, 2006

• For every trading period in the week we
• solved HOUR model using historical generation
  offers
• compute the amount/cost of fuel consumed MARKET
  FUEL COST
• For every day in the week we solved the DAY model
  
• generation targets set to those from the hour
  model
• block dispatch for Waikato and Waitaki
• Record daily reservoir releases and PLAN DAILY
  FUEL COST
• Sum the reservoir releases over the week to give
  target levels.
• Solve the WEEK model with
• historical inflows
• historical demand
• fuel costs for thermal plant
• target reservoir levels
• Compute PLAN WEEKLY FUEL COST
• Compare the amount/cost of fuel consumed over the
  week.

74
RESULTS
2.7M in one week amounts to 140M p.a.
75
Huntly
76
Otahuhu
77
Caveats and Conclusions

• Modelling improvements are needed before making
  results public.
• Need to extend simulation to seven years.
• YEAR is a very simple hydro-thermal model
• e.g. assumes stage-wise independent inflows.
• Central-plan policies are risk-neutral, and so
  can be extreme.
• Our simulation of policies
• Ignores many transmission constraints/outages
• Ignores voltage support constraints
• Ignores spinning reserve
• Ignores plant reliability
• Ignores ramping and startup costs

78
The end
79
Experiment 3 Day comparison

• Select a single day (or several sample days).
• For every trading period in the day
• solve HOUR model using historical generation
  offers
• record reservoir releases
• compute the amount/cost of fuel consumed.
• Sum the reservoir releases over the day to give a
  target level.
• Solve the DAY model with
• historical inflows
• historical demand
• fuel costs for thermal plant
• target reservoir levels
• Compare the amount/cost of fuel consumed over the
  day.
• Overcomes water-target problem and most of
  anticipation in WEEK that market model does not
  have available. Does not identify inefficiencies
  in long-term water allocation.

80
Uniform price auction (single node)
price
T2(q)?
p
quantity
price
combined offer stack
p
quantity
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Experiment 2 Week comparison

• Select a single week (or several sample weeks).
• For every trading period in the week
• solve HOUR model using historical generation
  offers
• record reservoir releases
• compute the amount/cost of fuel consumed.
• Sum the reservoir releases over the week to give
  target levels.
• Solve the WEEK model with
• historical inflows
• historical demand
• fuel costs for thermal plant
• target reservoir levels
• Compare the amount/cost of fuel consumed over the
  week.

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Computational results NZ model

• 10 reservoirs
• 52 weekly stages
• 30 inflow outcomes per stage
• Model written in AMPL/CPLEX
• Takes 100 iterations and 2 hours on a standard
  Windows PC to converge
• Larger models have slow convergence

86
2005-2006 policy simulated with historical inflow
sequences
87
Simplifying assumptions

• Small number of storage reservoirs (9)?
• Inflows are the only uncertain parameter
• Relatively complete recourse.
• Stage-wise independence of inflow process.
• A convex dispatch problem in each stage.

88
Outer approximation
89
Sampling algorithm
90
Cut calculation
91
??????
??????
??????
??????
??????
??????
??????
p11
p12
??????
p13
??????
92
??????
p11
p12
??????
p13
??????
93
??????
??????
??????
??????
p21
??????
??????
??????
p11
p21
??????
p13
??????
p21
??????
??????
??????
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??????
??????
??????
??????
p21
??????
??????
??????
p11
p21
??????
p13
??????
p21
??????
??????
??????
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New Zealand system
96
The experiment

• Hope to mirror how central planning might be done
  in practice.
• DOASA solved monthly to update the hydro release
  policy.
• Aim to simulate over 1999-2007.
• Demand data missing for some years so we need to
  proxy data by pro-rating.
• Full data set available for 2005/2006
• Report a preliminary result for
• June 1 2005 to May 31 2006

97
DAY (WEEK) model
98
Experiment 1

• Use YEAR to derive a policy for water release
  (i.e. a function of current reservoir storage and
  week of year).
• Simulate the policy weekly in WEEK using
• historical inflows
• historical demand
• fuel costs for thermal plant
• water values from YEAR (resolved regularly)?
• Simulate historical generation offers in DAY
  using the same data for 365 days.
• Compare the amount/cost of fuel consumed over 365
  days.