sddp generation and transmission planning model · tom halliburton - energy modeling consultants...
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Tom Halliburton - Energy Modeling Consultants Ltd
SDDPGeneration and Transmission
Planning Model
Tom HalliburtonEnergy Modeling Consultants Ltd
for
Electric Power Optimization CentreWinter Workshop 2003
16 July, 2003
Tom Halliburton - Energy Modeling Consultants Ltd
Stochastic Dual DynamicProgramming
• What is SDDP• Purpose of this project• Other users• Why was SDDP selected• Main Features• Typical outputs and applications• How it works
Tom Halliburton - Energy Modeling Consultants Ltd
What is SDDP?• Stochastic Dual Dynamic Programming
• Very detailed hydro-thermal power systemoptimal dispatch
• Detailed in both generation & transmissionaspects
• Global optimum, as would be determined bya central dispatcher
Tom Halliburton - Energy Modeling Consultants Ltd
Project Objectives• Assemble a data base
– no comprehensive publicly available data base ofelectricity system parameters
• Demonstrate the capabilities of a detailedmodel
• Make available a resource for planningstudies within Transpower and elsewhere
• Enable Transpower to fulfill new roles
Tom Halliburton - Energy Modeling Consultants Ltd
Other Users of SDDP• First used to analyse the six Central
American countries - World Bank study• Consultants, generation companies, grid
operators, regulators, government planners• Licenced in:
Argentina, Austria, Bolivia, Brasil*, Chile, China,Colombia*, Costa Rica, Dominican Republic*,Ecuador, El Salvador*, Guatemala*, Honduras,Nicaragua, Panama*, Scandanavia*, Spain, USPacific Northwest*, Venezuala, United States bycompanies with international portfolios
Tom Halliburton - Energy Modeling Consultants Ltd
Scenarios Analysis and Simulation Results: Energy Exchanges Between Countries under Scenario 1 --- 2010 (GWh)
317 1791
445
2027
639
151
1524364572290
1017
4892169
1857
1074668
7564 622
3902244
35643834
3337
25331004
2734
35
1786
739
6431
8954823
1333
Tom Halliburton - Energy Modeling Consultants Ltd
Why SDDP was Selected• Tested by ECNZ 1995• Stochastic• Multi-reservoir• Generation & transmission• Provides most features required
– some of these added 1994/95 for ECNZ• Extensive use elsewhere & on-going support• Ease of testing - demonstration copy,
documentation, available at no cost• Good relationship with vendor
Tom Halliburton - Energy Modeling Consultants Ltd
Selection of SDDP (continued)
• Model information available is most unusual– algorithm published in Mathmatical Programming– manuals describe the maths in detail– source code has been studied– vendors answer every question
• Usually only a functional specificationavailable, but no implementation details
• Source code usually kept secret
Tom Halliburton - Energy Modeling Consultants Ltd
Stochastic Model• Two main categories of stochastic models
– stochastic LP solves a scenario tree structure– stochastic dynamic programming generally not
practicable beyond three dimensions due tocomputation requirements
• SDDP overcomes dimensionality problem bysampling - build an accurate function onlywhere it is needed
• Iteratively builds a function for each time step– cost-to-go as a function of reservoir level and last
week’s inflows
Tom Halliburton - Energy Modeling Consultants Ltd
Solution Methodology• Rigorous mathematical basis• Solve a large number of one week optimal
dispatch problems using linear program• LP gives
– sensitivity information– consistent results
• Mathematics aids understanding
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Capabilities (1)
• Weekly or monthly time step– weekly for NZ study
• Time horizon 360 stages (or more)– limits set at compile time
• Load duration curve, up to 5 blocks– NZ not peak capacity constrained, 5 blocks
adequate• HVDC and AC transmission system
– various options for AC model
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Capabilities (2)
• Each large hydro reservoir modeled– no aggregation of reservoirs
• Each hydro station included, actual flow paths– Tekapo spills to Benmore– Residual flows for Project Aqua
• Roxburgh - part on 220 kV, part 110 kV• Seasonal variations in
– lake maximum levels– minimum flows
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Capabilities (3)
• Inflow data from the “Power Archive”– 71 year record– Mangahao data not released– Tongariro total diversion only since 1997– Waikaremoana data not available last 18 months
• Synthetic inflows for optimization– spatial correlation– auto correlation (correlation in time)
• Final simulation with historical record
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Capabilities (4)
• Each thermal plant modeled– constraints on fuels shared by several stations
• Multiple fuels possible at each station• Unit commitment• Huntly coal stockpile modeled as a hydro
reservoir with specified inflows• Maintenance generally modeled as a derating
– put in explicit schedules if known
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Capabilities (5)
• Transmission system model similar to SPD• DC link handled directly by LP• AC system represented by DC power flow
– Solve one stage dispatch, then solve DC loadflow,identify constrained lines, add these to thedispatch optimization
– optional AC system loss calculation, piecewiselinear, iterative solution
– nodal prices available
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Capabilities (6)
• 300 lines, 120 busses in simplified system– most of 220 & 110 kv systems– more lines & busses if required
• Contingency constraints– outages studied for up to 10 lines– examine up to 5 lines in each case for overload
Tom Halliburton - Energy Modeling Consultants Ltd
Software Configuration• Runs on a Windows PC• Fortran executable• VB interface• Output:
– summary report, text– select from 98 csv files
• 4 year optimization (weekly) approx 19 hours(1.8 GHz laptop)
• Simulation approx 2.7 hours with transmissionsystem model
Tom Halliburton - Energy Modeling Consultants Ltd
NI Marginal Cost, Weekly Average
0
50
100
150
200
250
300
2003
/1820
03/26
2003
/3420
03/42
2003
/5020
04/06
2004
/1420
04/22
2004
/3020
04/38
2004
/4620
05/02
2005
/10
$/MWh
Average10 Percentile90 Percentile
Tom Halliburton - Energy Modeling Consultants Ltd
Taupo Storage
Spaghetti chart
Taupo Final storage (Hm3)
0
100
200
300
400
500
600
700
800
900
2003
/18
2003
/22
2003
/26
2003
/30
2003
/34
2003
/38
2003
/42
2003
/46
2003
/50
2004
/02
2004
/06
2004
/10
2004
/14
2004
/18
2004
/22
2004
/26
2004
/30
2004
/34
2004
/38
2004
/42
2004
/46
2004
/50
2005
/02
2005
/06
2005
/10
2005
/14
Stage
Hm3
Tom Halliburton - Energy Modeling Consultants Ltd
L Hawea Storage
Spaghetti chart
L H aw ea F ina l s to rage (H m 3)
700
900
1100
1300
1500
1700
1900
2100
2300
2003
/1820
03/22
2003
/2620
03/30
2003
/3420
03/38
2003
/4220
03/46
2003
/5020
04/02
2004
/0620
04/10
2004
/1420
04/18
2004
/2220
04/26
2004
/3020
04/34
2004
/3820
04/42
2004
/4620
04/50
2005
/0220
05/06
2005
/1020
05/14
S tage
H m 3
Tom Halliburton - Energy Modeling Consultants Ltd
Number of Sequences with Shortfall
0
2
4
6
8
10
12
14
2003
/2420
03/36
2003
/4820
04/08
2004
/2020
04/32
2004
/4420
05/04
2005
/1620
05/28
2005
/4020
05/52
2006
/1220
06/24
2006
/3620
06/48
2007
/0820
07/20
Number of
Sequences
Tom Halliburton - Energy Modeling Consultants Ltd
New CT Annual Plant Factor 2004/05
0%
10%
20%
30%
40%
50%
60%
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability of Exceedance
Plant Factor
Tom Halliburton - Energy Modeling Consultants Ltd
Clyde - Twizel Line flow for 2007
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 0.2 0.4 0.6 0.8 1
Probability of Exceedance
MW Flow
North Makerew a Thermal
Marsden Thermal
Tom Halliburton - Energy Modeling Consultants Ltd
Mangamaire - Woodville Line Flow
-40
-30
-20
-10
0
10
20
30
0 0.2 0.4 0.6 0.8 1
Probability of Exceedance
MW
Tom Halliburton - Energy Modeling Consultants Ltd
Bus Marginal Costs in the Wairarapa
-100
100
300
500
700
900
1100
1300
24/20
0336
/2003
48/20
0308
/2004
20/20
0432
/2004
44/20
0404
/2005
16/20
0528
/2005
40/20
0552
/2005
12/20
0624
/2006
36/20
0648
/2006
08/20
0720
/2007
$/MWh
MGM110 Upper 10 percentileWDV110 AverageWDV110 Upper 10 percentile
Tom Halliburton - Energy Modeling Consultants Ltd
Where to now?• Useful to outside organizations• Anyone can buy or lease the model• All data is in public domain, except some flow
data• Transpower lease of the model for the
remainder of this year
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Algorithm
Tom Halliburton - Energy Modeling Consultants Ltd
Begin with backward passas for conventional stochastic DP
00.10.20.30.40.50.60.70.80.9
1
0 1 2 3 4 5 6 7Stages
Lake Level
Tom Halliburton - Energy Modeling Consultants Ltd
LP solved for each flow outcome
0
0.5
1
0 0.2 0.4 0.6 0.8 1Generation this Period
Cost
Immediate Cost(this period) Future cost
• Deterministic• Minimise sum
of immediatecost (thisperiod) + futurecost
• Trades off useof water nowwith storage forlater use
Tom Halliburton - Energy Modeling Consultants Ltd
Add a plane to cost to go function ateach storage point
Lake Storage
Costto go
Tom Halliburton - Energy Modeling Consultants Ltd
• Generate (eg 15) random inflow outcomesusing a multivariate autoregressive model
• Consistent with flow outcome for precedingtime period, ie autocorrelation preserved
• Solve for each inflow outcome using LP• Store average slope in each dimension =
average multiplier on flow balance equation,and cost axis intercept
• Typically 50 points per time period, 15 flowoutcomes
At each storage point
Tom Halliburton - Energy Modeling Consultants Ltd
Forward simulation• Used to determine upper bound• Storage values passed through form new
points for next backward optimisation pass• Can use different flows, plant availability, etc
using existing policy (result of anoptimisation) to simulate changes in thesystem
Tom Halliburton - Energy Modeling Consultants Ltd
• Optimise in backward direction.• Simulate in forward direction using this policy
- cost must be higher than optimal as have asub-optimal policy.
• Optimise again, backward, using storagelevels that the simulations passed through.Gives a lower bound.
• Each optimisation adds more information tothe cost-to-go function. When detailedenough, process is converged.
Iterative Process
Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Recursive EquationFor each time step, each point in state space,
each flow outcome
Costtk(vt)= Min ct(ut) + αt+1
subject to vt+1 = vt-ut-st+atk water balance
vt+1 ≤ vmax max volumeut ≤ umax max flow αt+1 ≥ ϕn
t+1vt+1 + δnt+1 future cost