sddp, spectra and reality
DESCRIPTION
SDDP, SPECTRA and Reality. A comparison of hydro-thermal generation system management Roger Miller, Electricity Commission 3 September 2009. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
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SDDP, SPECTRA and Reality
A comparison of hydro-thermal generation system management
Roger Miller, Electricity Commission3 September 2009
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2
Introduction• SDDP (Stochastic Dual Dynamic Programming Model) and
SPECTRA (System, Plant, and Energy Co-ordination using Two Reservoir Approach) are two hydro-thermal generation coordination programs.
• The Electricity Commission uses SDDP in conjunction with GEM (Generation Expansion Model) to model power system operation under possible future generation expansion scenarios.
• SDDP allows quite flexible and detailed modelling of generation and transmission constraints (though the EC doesn’t use most of these features), but takes many hours to solve a typical multi-year optimisation problem.
• SPECTRA, is less flexible and detailed, but can solve an equivalent problem in a matter of minutes.
• In order to assess the usefulness of SPECTRA as a replacement and/or supplement to SDDP, a comparison has been carried out between the outputs of the two models, and with the actual generation patterns observed in the NZ system over recent years.
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Overview
• Hydro Lake Level Contours• Incremental Water Value Surfaces• Price Duration Curves• Generation Duration Curves• Possible improvements
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Hydro Lake Level Contours
• Actual - One trajectory per year• Simulations
• One trajectory per inflow sequence• Shows study period up to December 2011
• 5th, 25th, 50th, 75th, 95th percentiles and mean
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Actual Levels - Lake Pukaki Lake Pukaki - Actual Lake Levels
(Lake Limits: 518 to 532.5 m)
0%
20%
40%
60%
80%
100%
120%
0 92 184 276 368
Day of Year
Per
cen
t F
ull
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Actual Levels – Lake Tekapo Lake Tekapo - Actual Lake Levels
(Lake Limits: 701.8 to 710.9 m)
-20%
0%
20%
40%
60%
80%
100%
120%
0 92 184 276 368
Day of Year
Pe
rce
nt
Fu
ll
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Actual Levels - Lake Hawea Lake Hawea - Actual Lake Levels
(Lake Limits: 338 to 346 m)
-20%
0%
20%
40%
60%
80%
100%
120%
0 92 184 276 368
Day of Year
Pe
rce
nt
Fu
ll
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Observations – Actual levels
Pukaki, Tekapo and Hawea
• all have similar annual cycles• Drawn down through winter reaching a
minimum level around September/October in time for spring snow melt
• Reach Max Level 5 to 25% of the time in first half of year
• Occasionally get very low in spring
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Actual Levels - Lake Te AnauLake Te Anau - Actual Lake Levels (controlled post 1974)
(Lake Limits: 201.5 to 202.7 m)
-100%
-50%
0%
50%
100%
150%
200%
250%
300%
0 92 184 276 368
Day of Year
Perc
ent F
ull
1974 1975 1976 1977
1978 1979 1980 1981
1982 1983 1984 1985
1986 1987 1988 1989
1990 1991 1992 1993
1994 1995 1996 1997
1998 1999 2000 2001
2002 2003 2004 2005
2006 2007 2008 5%
25% 50% 75% 95%
avg
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Actual Levels - Lake ManapouriLake Manapouri - Actual Lake Levels
(Lake Limits: 518 to 532.5 m)
-100%
-50%
0%
50%
100%
150%
200%
250%
300%
0 92 184 276 368
Day of Year
Pe
rce
nt
Fu
ll
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Observations – Actual levels
Manapouri and Te Anau
• Less pronounced annual cycle• Much more variable throughout most of year• Smaller storage relative to their mean inflows• Regularly exceed maximum control level• SDDP/SPECTRA model a hard upper limit at
which forced release occurs (high spill)• In reality levels subside over several weeks
(less spill)• Potential for improved modelling
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Actual Levels - Lake Taupo Lake Taupo - Actual Lake Levels
(Lake Limits: 355.85 to 357.25 m)
-20%
0%
20%
40%
60%
80%
100%
120%
140%
0 92 184 276 368
Day of Year
Per
cen
t F
ull
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Actual Levels - Lake Waikaremoana Lake Waikaremoana - Actual Lake Levels
(Lake Limits: 580.29 to 583.29 m)
-40%
-20%
0%
20%
40%
60%
80%
100%
120%
140%
160%
0 92 184 276 368
Day of Year
Pe
rce
nt
Fu
ll
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Observations – Actual levels
Taupo and Waikaremoana
• Different cycle to South Island lakes• Reach minimum level around May and fill
through the winter• Utilise most of their range but seldom spill or
run out
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Simulated Lake Levels
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SPECTRA Lake Levels (GWh) – 1st attempt
52 78 104 130 156 1820
100
200
300
400
500
600
SPECTRA Lake Levels (GWh)
TPO min outflow 90 cumecs; Original IU's; Post Tax NPV $7820.4M
North Island
study week52 78 104 130 156 182
0
500
1000
1500
2000
2500
3000
South Island
study week52 78 104 130 156 182
0
50
100
150
200
250
300
350
400
450
500Taupo & Waikato
study week52 78 104 130 156 182
0
20
40
60
80
100
120
Waikaremoana
study week
52 78 104 130 156 1820
50
100
150
200
250
300Hawea & Clutha
study week52 78 104 130 156 182
0
50
100
150
200
250
300
350
400Manapouri
study week52 78 104 130 156 182
0
200
400
600
800
1000
1200
1400
1600Waitaki Pukaki
study week52 78 104 130 156 182
0
100
200
300
400
500
600
700
Waitaki TEKAPO
study week
1 Jan 20121 July 2009 1 Jan 20121 July 2009 1 Jan 20121 July 2009 1 Jan 20121 July 2009
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Improvements made:
• Reduced Taupo minimum outflow from 90 to 50 cumecs (resource consent)
• All IU’s set back to neutral except for Manapouri (biased downwards)
• Introduced 20/20 storage grid (NI/SI)• Resulted in 3% saving in fuel costs• Further room for fine tuning
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SPECTRA Lake Levels (GWh) – “optimised”
52 78 104 130 156 1820
100
200
300
400
500
600
SPECTRA Lake Levels (GWh)
TPO min outflow 50 cumecs; Manapouri IU Bias 0.7; 20/20 grid; Post Tax NPV $7602.3M
North Island
study week52 78 104 130 156 182
0
500
1000
1500
2000
2500
3000
South Island
study week52 78 104 130 156 182
0
50
100
150
200
250
300
350
400
450
500Taupo & Waikato
study week52 78 104 130 156 182
0
20
40
60
80
100
120
Waikaremoana
study week
52 78 104 130 156 1820
50
100
150
200
250
300Hawea & Clutha
study week52 78 104 130 156 182
0
50
100
150
200
250
300
350
400Manapouri
study week52 78 104 130 156 182
0
200
400
600
800
1000
1200
1400
1600Waitaki Pukaki
study week52 78 104 130 156 182
0
100
200
300
400
500
600
700
Waitaki TEKAPO
study week
1 Jan 20121 July 2009 1 Jan 20121 July 2009 1 Jan 20121 July 2009 1 Jan 20121 July 2009
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SDDP Lake Levels (hm3)
6 12 18 24 30 36 42 480
100
200
300
400
500
600
700
SDDP Lake Levels (hm3)Lake Taupo
study month6 12 18 24 30 36 42 48
0
20
40
60
80
100
120
140
160L Waikaremo
study month6 12 18 24 30 36 42 48
0
100
200
300
400
500
600
Lake Tekapo
study month
6 12 18 24 30 36 42 480
250
500
750
1000
1250
1500
1750
2000
Lake Pukaki
study month6 12 18 24 30 36 42 48
0
100
200
300
400
500
600
700
800
900
1000
1100
Lake Hawea
study month6 12 18 24 30 36 42 48
0
100
200
300
400
500
600
700
800
900
1000
Manapouri
study month
1 Jan 20121 Jan 2008 1 Jan 20121 Jan 2008 1 Jan 20121 Jan 2008
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SDDP/SPECTRA lake level comparison• SDDP drives lakes up and down more
aggressively! (less conservative)
• Most lakes have a high probability of both running out of water and of spilling
• SDDP trajectories vary significantly from year to year – most apparent in Waikaremoana
• Doesn’t appear to make economic sense
• Possibly due to cut elimination (discussed later)
• SPECTRA settles down to a regular pattern
• SPECTRA more similar to reality (possibly a self-fulfilling prophecy?)
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Water Value Surfaces
• Represents the expected future value of holding an additional unit of water in storage
• Averaged over historical inflow sequences (in this case 1932 through 2005)
• Gives controlled hydro storage an effective “fuel price” (opportunity cost)
• Function of time of year due to annual inflow and demand patterns
• Function of storage level in all reservoirs
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Water Value Surfaces (SPECTRA)
• Produced by RESOP (Reservoir Optimisation) module
• 2-reservoir model ( NI and SI lumped model)• Directly calculated for all combinations of
storage (eg. 6x12 or 20x20)• Uses Incremental Utilisation (IU) Curves to
approximately split out into individual reservoirs• Uses heuristic to account for serial inflow
correlation
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SPECTRA Water Value Surface - SI
1 14 27 40 53 66 79 92
0246810121416
18
20050
100150200250300350400450500550600650700750800850900950
100010501100115012001250
Water Value [$/MWh]
week number
SI Level
(NI level = 50%)
1 July 2008 1 July 2010
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SPECTRA Water Value Surface - NI
(SI level = 50%)
1 14 27 40 53 66 79 92
02468101214
16
18
200
25
50
75
100
125
150
175
200
225
250
275
300
325
Water Value [$/MWh]
week number
NI Level
1 July 2008 1 July 2010
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Water Value Surfaces (SDDP)
• Multi-reservoir model• Serial inflow correlation explicitly modelled• Water value implied by slope of Future Cost Function (FCF)• FCF is a multi-dimensional non-linear hyper-surface• Approximated by tangent hyper-planes known as “cuts”
which act as linear constraints in the optimisation• Extra cuts are added at each iteration at the storage and
inflow combinations that occur in the simulation (each time step gets one new cut for every inflow sequence)
• To reduce dimensionality, inactive (non-binding) cuts can be eliminated after a specified number of iterations
• Implied water values tend to be lumpy and not well defined over the whole solution space, especially if cuts are eliminated
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Obtaining Water Values from SDDP• Tom Halliburton has written a utility to extract
water values from an FCF output text file• Electricity Commission has traditionally
eliminated inactive cuts after 4 iterations• This doesn’t yield meaningful water value
surfaces• Water values are effectively extrapolated from
the cut point over almost the entire storage range of the reservoir
• I suspect there may also be data precision issues in the FCF text file for long studies?
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SDDP Water Value Surface – Lake Pukaki(inactive cuts eliminated after 4 iterations)
(All lakes equally full, Mean inflow sequence)
Jan-
08
Feb
-08
Mar
-08
Apr
-08
May
-08
Jun-
08
Jul-0
8
Aug
-08
Sep
-08
Oct
-08
Nov
-08
Dec
-08
Jan-
09
Feb
-09
Mar
-09
Apr
-09
May
-09
Jun-
09
Jul-0
9
Aug
-09
Sep
-09
Oct
-09
Nov
-09
25,463
21,442
17,422
13,402
9,381
5,3611,340
0
50
100
150
200
250
300
350
400
450
500
550
Water Value($/MWh)
Storage(CMD)
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Obtaining Water Values from SDDP (2)
To obtain meaningful Water Value Surfaces:• SDDP was rerun without eliminating any cuts• This significantly increases solution time, so• Study was limited to only 2 years• Risk of end effects
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Jan-
08
Feb
-08
Mar
-08
Apr
-08
May
-08
Jun-
08
Jul-0
8
Aug
-08
Sep
-08
Oct
-08
Nov
-08
Dec
-08
Jan-
09
Feb
-09
Mar
-09
Apr
-09
May
-09
Jun-
09
Jul-0
9
Aug
-09
Sep
-09
Oct
-09
Nov
-09
25,463
21,442
17,422
13,402
9,381
5,361
1,340
050
100150200250300350400450500550600650700750800850900950
100010501100115012001250130013501400145015001550160016501700175018001850
Water Value($/MWh)
Storage(CMD)
SDDP Water Value Surface – Lake Pukaki(all cuts kept)
(All lakes equally full , Mean inflow sequence)
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SDDP Water Value Surface – Lake Taupo(all cuts kept)
(All other lakes 50% full, Mean inflow sequence)
Jan-
08
Feb
-08
Mar
-08
Apr
-08
May
-08
Jun-
08
Jul-0
8
Aug
-08
Sep
-08
Oct
-08
Nov
-08
Dec
-08
Jan-
09
Feb
-09
Mar
-09
Apr
-09
May
-09
Jun-
09
Jul-0
9
Aug
-09
Sep
-09
Oct
-09
Nov
-09
8,796
7,407
6,019
4,630
3,241
1,852463
0
50
100
150
200
250
300
Water Value($/MWh)
Storage(CMD)
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Effect of cut elimination on SDDP simulation
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6 12 180
100
200
300
400
500
600
700
SDDP Lake Levels (hm3)Lake Taupo
study month6 12 18
0
20
40
60
80
100
120
140
160L Waikaremo
study month6 12 18
0
100
200
300
400
500
600
Lake Tekapo
study month
6 12 180
250
500
750
1000
1250
1500
1750
2000
Lake Pukaki
study month6 12 18
0
100
200
300
400
500
600
700
800
900
1000
1100Lake Hawea
study month6 12 18
0
100
200
300
400
500
600
700
800
900
1000
Manapouri
study month
6 12 180
100
200
300
400
500
600
700
SDDP Lake Levels (hm3)Lake Taupo
study month6 12 18
0
20
40
60
80
100
120
140
160L Waikaremo
study month6 12 18
0
100
200
300
400
500
600
Lake Tekapo
study month
6 12 180
250
500
750
1000
1250
1500
1750
2000
Lake Pukaki
study month6 12 18
0
100
200
300
400
500
600
700
800
900
1000
1100
Lake Hawea
study month6 12 18
0
100
200
300
400
500
600
700
800
900
1000
Manapouri
study month
inactive cuts eliminated after 4 iterations(36 year study)
keep all cuts(2 year study)
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Price Duration Curves
• For study year 2010• Inflow sequences 1932 through 2005
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North Island Price Duration Curves
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
20
30
40
50
60
708090
100
200
300PDC - North Island, pds=79:130, Avg MC=$62.7/MWh
Ma
rgin
al C
ost
$/M
Wh
Spectra - Avg MC $62.7/MWh
SDDP - Avg MC $58.3/MWh
spill
shortage
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South Island Price Duration Curves
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
20
30
40
50
60
708090
100
200
300PDC - South Island, pds=79:130, Avg MC=$52.6/MWh
Ma
rgin
al C
ost
$/M
Wh
Spectra - Avg MC $52.6/MWh
SDDP - Avg MC $55.1/MWh
shortage
spill
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• In SI, SPECTRA is $2.50 cheaper.• In NI, SPECTRA is $4.40 more expensive• Since NI is bigger, overall SDDP comes out
cheaper.• This perhaps suggests that on purely economic
grounds SPECTRA’s extra conservatism may not be justified?
• Comes down to appetite for risk and valuation of shortage
• There may be other differences between the models causing this outcome, eg. different demand response/shortage prices
• Not a rigorous comparison
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A sample ofGeneration Duration Curves
• Actual generation over recent years• Simulated generation over same years with
actual historical inflows
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SPECTRAAvg 523 MW
SDDPAvg 494 MW
ActualAvg 461 MW
Waikato scheme1998 through 2005
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
1100Actual GDC for taupo for 01-Jan-1998:31-Dec-2005, Avg MW =461.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
1100Spectra GDC for delf.TAUP, pds 79-130, flows 1996-2003 Avg MW =523.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000
1100SDDP GDC - sim year=2010, inflow year=1996 to 2003, stn=TPO, Avg MW =494.3
MW
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SPECTRAAvg 37 MW
SDDPAvg 40 MW
ActualAvg 48 MW
Waikaremoana scheme1998 through 2005
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140Spectra GDC for delf.WAIK, pds 79-130, flows 1996-2003 Avg MW =37.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140SDDP GDC - sim year=2010, inflow year=1996 to 2003, stn=WKA, Avg MW =39.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140Actual GDC for GEN.Hydro.Waikaremoana for 01-Jan-1998:31-Dec-2005, Avg MW =48.4
MW
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SPECTRAAvg 756 MW
SDDPAvg 743 MW
ActualAvg 746 MW
Ohau / Lower Waitaki schemes1998 through 2005
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500Spectra GDC for delf.WAIT, pds 79-130, flows 1998-2005 Avg MW =756
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500SDDP GDC - sim year=2010, inflow year=1998 to 2005, stn=WTR, Avg MW =743
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500Actual GDC for pukaki for 01-Jan-2000:31-Dec-2007, Avg MW =746
MW
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SPECTRAAvg 528 MW
SDDPAvg 562 MW
ActualAvg 566 MW
Manapouri scheme2003 through 2007
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800Spectra GDC for delf.MANA, pds 79-130, flows 2001-2005 Avg MW =528
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800SDDP GDC - sim year=2010, inflow year=2001 to 2005, stn=MANA, Avg MW =562
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800Actual GDC for GEN.Hydro.Manapouri for 01-Jan-2003:31-Dec-2007, Avg MW =566
MW
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SPECTRAAvg 319 MW
SDDPAvg 311 MW
ActualAvg 344 MW
Huntly E3P 2008
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400Spectra GDC for delf2010.E3P, pds 79-130, flows 1932-2005 Avg MW =319
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400SDDP GDC - sim year=2010, inflow year=1932 to 2005, stn=e3p , Avg MW =311
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450Actual GDC for GEN.Thermal.Huntly.Gas for 01-Jan-2008:31-Dec-2008, Avg MW =344
MW
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Huntly E3P
Otahuhu B
TCC
CCGT seasonal temperature effect
2007 2008 20090
50
100
150
200
250
300
350
400
450Actual Time Series for GEN.Thermal.Huntly.Gas for 01-Jan-2007:31-Dec-2008, Avg MW =282
2006 2007 2008 20090
50
100
150
200
250
300
350
400Actual Time Series for GEN.Thermal.Otahuhu.B for 01-Jan-2006:31-Dec-2008, Avg MW =302
2005 2006 2007 2008 20090
50
100
150
200
250
300
350
400Actual Time Series for GEN.Thermal.Stratford.B for 01-Jan-2005:31-Dec-2008, Avg MW =257
MW
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Possible EC model improvements:• Modify HVDC loss model to include the effect of
DC transfer on AC losses • Update various station capacities• Update HVDC capacity• Update various lake level and outflow constraints• Seasonal variations in lake level limits• Seasonal temperature effect on CCGT capacity• Additional reservoirs (Waipori, Cobb, Coleridge …)• Fewer reservoirs (run Manapouri as uncontrolled?)• Reduce RESOP serial correlation heuristic?
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Possible program enhancements to SPECTRA / RESOP
• Schedulable thermals in the South Island?• Pumped storage hydros?• More explicit hydro reservoirs in RESOP?
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Conclusion
• SDDP and SPECTRA currently each have advantages and disadvantages
• Potential to fine tune both EC models• SDDP execution options (cut elimination
strategy, convergence tolerance, max iterations)
• SPECTRA IU curves, trib schedulability, serial correlation
• Model details (ratings, constraints etc)• Possible SPECTRA program enhancements