SDDP, SPECTRA and Reality A comparison of hydro-thermal generation system management Roger Miller, Electricity Commission 3 September 2009

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.

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

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

Actual Levels - Lake Pukaki

Actual Levels – Lake Tekapo

Actual Levels - Lake Hawea

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

Actual Levels - Lake Te Anau

Actual Levels - Lake Manapouri

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

Actual Levels - Lake Taupo

Actual Levels - Lake Waikaremoana

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

Simulated Lake Levels

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

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

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

SDDP Lake Levels (hm3) 1 Jan 2008 1 Jan 2012 1 Jan 2008 1 Jan 2012

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

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

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

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%)

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%)

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

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

(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)

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

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)

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)

Effect of cut elimination on SDDP simulation

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)

Price Duration Curves For study year 2010 Inflow sequences 1932 through 2005

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

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

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

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

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.

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

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.

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?

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

CCGT seasonal temperature effect Huntly E3P Otahuhu B TCC MW

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?

Possible program enhancements to SPECTRA / RESOP Schedulable thermals in the South Island? Pumped storage hydros? More explicit hydro reservoirs in RESOP?

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