SDDP, SPECTRA and Reality

1
SDDP, SPECTRA and Reality

• A comparison of hydro-thermal generation system
  management
• Roger Miller, Electricity Commission
• 3 September 2009

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 doesnt 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.

3
Overview

• Hydro Lake Level Contours
• Incremental Water Value Surfaces
• Price Duration Curves
• Generation Duration Curves
• Possible improvements

4
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

5
Actual Levels - Lake Pukaki
6
Actual Levels Lake Tekapo
7
Actual Levels - Lake Hawea
8
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

9
Actual Levels - Lake Te Anau
10
Actual Levels - Lake Manapouri
11
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

12
Actual Levels - Lake Taupo
13
Actual Levels - Lake Waikaremoana
14
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

15
Simulated Lake Levels
16
SPECTRA Lake Levels (GWh) 1st attempt
1 July 2009
1 Jan 2012
1 Jan 2012
1 Jan 2012
1 July 2009
1 July 2009
1 Jan 2012
1 July 2009
17
Improvements made

• Reduced Taupo minimum outflow from 90 to 50
  cumecs (resource consent)
• All IUs 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

18
SPECTRA Lake Levels (GWh) optimised
1 Jan 2012
1 July 2009
1 Jan 2012
1 Jan 2012
1 July 2009
1 July 2009
1 Jan 2012
1 July 2009
19
SDDP Lake Levels (hm3)
1 Jan 2008
1 Jan 2008
1 Jan 2008
1 Jan 2012
1 Jan 2012
1 Jan 2012
20
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
• Doesnt 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?)

21
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

22
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

23
SPECTRA Water Value Surface - SI
1 July 2010
1 July 2008
(NI level 50)
24
SPECTRA Water Value Surface - NI
1 July 2010
1 July 2008
(SI level 50)
25
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

26
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 doesnt 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?

27
SDDP Water Value Surface Lake Pukaki(inactive
cuts eliminated after 4 iterations)
(All lakes equally full, Mean inflow sequence)
28
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

29
SDDP Water Value Surface Lake Pukaki(all cuts
kept)
(All lakes equally full , Mean inflow sequence)
30
SDDP Water Value Surface Lake Taupo(all cuts
kept)
(All other lakes 50 full, Mean inflow sequence)
31
Effect of cut elimination on SDDP simulation
32
inactive cuts eliminated after 4 iterations(36
year study)
keep all cuts(2 year study)
33
Price Duration Curves

• For study year 2010
• Inflow sequences 1932 through 2005

34
North Island Price Duration Curves
shortage
spill
35
South Island Price Duration Curves
shortage
spill
36

• 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 SPECTRAs 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

37
A sample ofGeneration Duration Curves

• Actual generation over recent years
• Simulated generation over same years with actual
  historical inflows

38
Waikato scheme1998 through 2005
SPECTRAAvg 523 MWSDDPAvg 494
MWActualAvg 461 MW
MW
39
Waikaremoana scheme1998 through 2005
SPECTRAAvg 37 MWSDDPAvg 40
MWActualAvg 48 MW
MW
40
Ohau / Lower Waitaki schemes1998 through 2005
SPECTRAAvg 756 MWSDDPAvg 743
MWActualAvg 746 MW
MW
41
Manapouri scheme2003 through 2007
SPECTRAAvg 528 MWSDDPAvg 562
MWActualAvg 566 MW
MW
42
Huntly E3P 2008
SPECTRAAvg 319 MWSDDPAvg 311
MWActualAvg 344 MW
MW
43
CCGT seasonal temperature effect
Huntly E3POtahuhu BTCC
MW
44
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?

45
Possible program enhancements to SPECTRA / RESOP

• Schedulable thermals in the South Island?
• Pumped storage hydros?
• More explicit hydro reservoirs in RESOP?

46
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