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 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.

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 July 2009
1 Jan 2012
1 July 2009
1 Jan 2012
1 July 2009
1 Jan 2012
NI lakes only utilising upper half of range
Waikaremoana, “Hawea and Clutha”, and Manapouri running too high - excessive spill.
Note – “Manapouri” is combined storage of Lakes Manapouri and Te Anau
6/12 (NI/SI) storage grid
Original IU’s when EC inherited the model
IU = Incremental Utilisation curve – allows tuning of relative fullness of lakes within the island

17. 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

18. SPECTRA Lake Levels (GWh) – “optimised”
1 July 2009
1 Jan 2012
1 July 2009
1 Jan 2012
1 July 2009
1 Jan 2012
1 July 2009
1 Jan 2012
Much improved storage range utilisation
Reduced spill
Note – Sudden increase in Hawea in 2011 is due to commissioning of future Control Gates station
Si in phase with actual
NI a bit delayed from actual

19. SDDP Lake Levels (hm3) 1 Jan 2008 1 Jan 2012 1 Jan 2008 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
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?)
Since Meridian use SPECTRA and they control the major hydro storage lakes

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
Lake level trajectory tends to track around base of the “hills”
Reaches minimum level about October/November
Maximum about May/June
High peak cost in dry year winters – constrained ability to transfer power back from NI to SI
1 July 2008
1 July 2010
(NI level = 50%)

24. SPECTRA Water Value Surface - NI
Lake level trajectory tends to track around base of the “hills”
Reaches minimum level about August
Maximum about January/February
Note phase shift relative to SI
Dry year peak cost less severe due to thermal firming plant in NI
1 July 2008
1 July 2010
(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 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?
RHS of constraint appears to be output to 5 sig. figs.
But for long studies the FCF gets very large so the relative precision becomes quite poor
Possibly only affects the output text file not the actual internal calculations

27. (All lakes equally full, Mean inflow sequence)
SDDP Water Value Surface – Lake Pukaki (inactive cuts eliminated after 4 iterations)
Water values are effectively extrapolated from the cut point over almost the entire storage range of the reservoir
(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)
Since main South Island lakes are synchronised, assuming equally full is best option (especially since this is what SPECTRA does)
Effect of NI levels is not so important
Lake level trajectory tends to track around base of the “hills”
Other South Island lakes show very similar pattern
Note – SDDP year starts in January (SPECTRA in July)
Not too dissimilar to SPECTRA, though less smooth
(All lakes equally full , Mean inflow sequence)

30. SDDP Water Value Surface – Lake Taupo (all cuts kept)
Since NI and SI hydrology is not synchronised, assuming other lakes at 50% (or mean trajectory) is probably the best option
Not a particularly well-defined surface
Not consistent with observed lake level trajectories
(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)
Keeping all cuts appears to give several improvements:
Lakes Tekapo and Taupo pull away from the upper bound (less spill)
Lake Pukaki percentiles more evenly spread
However, since the “keep cuts” study was only run for 2 years, some lakes tend to get drawn down towards the end (not comparing apples with apples)
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
Observe that SPECTRA and SDDP have essentially the same flat sections which correspond to particular thermal generators being marginal.
However, in SPECTRA, each thermal generator spends more time on the margin.
SDDP’s more extreme prices are consistent with its less conservative reservoir management.
Recall that in SPECTRA the North Island reservoirs almost never spill or run out, while in SDDP both spill and shortage occur much more frequently.
Very low prices correspond to spill while very high prices correspond to shortage.
SDDP’s less conservative strategy reduces average price except in very dry tears
spill

35. South Island Price Duration Curves
shortage
SDDP is generally slightly cheaper except at the very high end, which drags up the mean price.
Again SDDP has more extreme prices than SPECTRA though the difference between the models is less pronounced than for the North island.
Again this is consistent with SPECTRA’s more conservative reservoir management.
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 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

37. A sample of Generation Duration Curves
Actual generation over recent years
Simulated generation over same years with actual historical inflows

38. Waikato scheme 1998 through 2005
SPECTRA Avg 523 MW SDDP Avg 494 MW Actual Avg 461 MW MW
SPECTRA has too much energy, not enough spill?
SPECTRA is too schedulable.
SPECTRA spinning reserve function is using up too much peak capacity.

39. Waikaremoana scheme 1998 through 2005
SPECTRA Avg 37 MW SDDP Avg 40 MW Actual Avg 48 MW MW
Both models have too little energy.
Both models, especially SPECTRA are too schedulable.
Model peak too low

40. Ohau / Lower Waitaki schemes 1998 through 2005
SPECTRA Avg 756 MW SDDP Avg 743 MW Actual Avg 746 MW MW
SPECTRA has a little too much energy.
SPECTRA peak too low.
Schedulability about right.
SPECTRA spinning reserve function may be using up too much peak capacity.

41. Manapouri scheme 2003 through 2007
SPECTRA Avg 528 MW SDDP Avg 562 MW Actual Avg 566 MW MW
SPECTRA has too little energy (too much spill?)
Too Schedulable – eg. model as uncontrolled inflows with low pass filter?

42. Huntly E3P 2008 SPECTRA Avg 319 MW SDDP Avg 311 MW Actual Avg 344 MW
Note the sloping top in the actual curve
This occurs in all three CCGT’s
It is due to the seasonal temperature effect on output limit

43. CCGT seasonal temperature effect
Huntly E3P Otahuhu B TCC 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