Jul 16, 2003 ... SDDP. Generation and Transmission. Planning Model. Tom Halliburton. Energy
Modeling Consultants Ltd for. Electric Power Optimization ...
SDDP Generation and Transmission Planning Model Tom Halliburton Energy Modeling Consultants Ltd for Electric Power Optimization Centre Winter Workshop 2003 16 July, 2003 Tom Halliburton - Energy Modeling Consultants Ltd
Stochastic Dual Dynamic Programming • • • • • • •
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 system optimal dispatch • Detailed in both generation & transmission aspects • Global optimum, as would be determined by a central dispatcher Tom Halliburton - Energy Modeling Consultants Ltd
Project Objectives • Assemble a data base – no comprehensive publicly available data base of electricity system parameters
• Demonstrate the capabilities of a detailed model • Make available a resource for planning studies 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, US Pacific Northwest*, Venezuala, United States by companies with international portfolios Tom Halliburton - Energy Modeling Consultants Ltd
Scenarios Analysis and Simulation Results: Energy Exchanges Between Countries under Scenario 1 --- 2010 (GWh)
1333
2533
1004
3337
3564 4668
895
3834 4823
3902
107
244 739
151 2290
7564
622 317
6431 445
15243
6457 2734
1791 2027
35 1786
489
1857 2169
1017
639
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 specification available, 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 to computation requirements
• SDDP overcomes dimensionality problem by sampling - build an accurate function only where 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 the dispatch optimization – optional AC system loss calculation, piecewise linear, 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 transmission system model Tom Halliburton - Energy Modeling Consultants Ltd
NI Marginal Cost, Weekly Average Average
300
10 Percentile 250
90 Percentile
200 150 100 50
05 20
05
0 /1
2 /0
6 /4
20
Tom Halliburton - Energy Modeling Consultants Ltd
20
04
/3 04
20
04
8
0 /3
2 /2 20
04 20
04 20
04 20
4 /1
6 /0
0 /5
03 20
03 20
03
2 /4
4 /3
6 20
03 20
03
/1
/2
8
0
20
$/MWh
Stage
Tom Halliburton - Energy Modeling Consultants Ltd
2005/14
2005/10
2005/06
2005/02
2004/50
2004/46
2004/42
2004/38
2004/34
2004/30
2004/26
2004/22
2004/18
2004/14
2004/10
2004/06
2004/02
500
2003/50
600
2003/46
2003/42
2003/38
2003/34
2003/30
2003/26
2003/22
2003/18
Taupo Storage Taupo Final storage (Hm3)
900
800
700
Spaghetti chart
Hm3 400
300
200
100
0
Hm3
20 03 /1 20 8 03 /2 20 2 03 /2 20 6 03 /3 20 0 03 /3 20 4 03 /3 20 8 03 /4 20 2 03 /4 20 6 03 /5 20 0 04 /0 20 2 04 /0 20 6 04 /1 20 0 04 /1 20 4 04 /1 20 8 04 /2 20 2 04 /2 20 6 04 /3 20 0 04 /3 20 4 04 /3 20 8 04 /4 20 2 04 /4 20 6 04 /5 20 0 05 /0 20 2 05 /0 20 6 05 /1 20 0 05 /1 4
L Hawea Storage L H a w e a F in a l s to ra g e (H m 3 )
2300
2100
1900
1700
Spaghetti chart
1500
1300
1100
900
700
S ta g e
Tom Halliburton - Energy Modeling Consultants Ltd
20 03 /2 4 20 03 /3 6 20 03 /4 8 20 04 /0 8 20 04 /2 0 20 04 /3 2 20 04 /4 4 20 05 /0 4 20 05 /1 6 20 05 /2 8 20 05 /4 0 20 05 /5 2 20 06 /1 2 20 06 /2 4 20 06 /3 6 20 06 /4 8 20 07 /0 8 20 07 /2 0
Number of Sequences with Shortfall 14
12
10
Number of Sequences 6 8
4
2
0
Tom Halliburton - Energy Modeling Consultants Ltd
New CT Annual Plant Factor 2004/05 60% 50% 40%
Plant 30% Factor 20% 10% 0% 0
0.1
0.2
0.3
0.4
0.5
0.6
Probability of Exceedance Tom Halliburton - Energy Modeling Consultants Ltd
0.7
0.8
0.9
1
Clyde - Twizel Line flow for 2007 500
North Makerew a Thermal
400
Marsden Thermal
300 200
MW Flow
100 0
-100 0
0.2
0.4
0.6
-200 -300 -400 -500
Probability of Exceedance Tom Halliburton - Energy Modeling Consultants Ltd
0.8
1
Mangamaire - Woodville Line Flow 30 20 10
MW
0 0
0.2
0.4
0.6
-10 -20 -30 -40
Probability of Exceedance Tom Halliburton - Energy Modeling Consultants Ltd
0.8
1
Bus Marginal Costs in the Wairarapa 1300
1100
MGM110
Upper 10 percentile
WDV110
Average
WDV110
Upper 10 percentile
900
$/MWh 700
500
300
100
24 /2 00 36 3 /2 00 48 3 /2 00 08 3 /2 00 20 4 /2 00 32 4 /2 00 44 4 /2 00 04 4 /2 00 16 5 /2 00 28 5 /2 00 40 5 /2 00 52 5 /2 00 12 5 /2 00 24 6 /2 00 36 6 /2 00 48 6 /2 00 08 6 /2 00 20 7 /2 00 7
-100
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 pass as for conventional stochastic DP
Lake Level
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
1
2
3
4
Stages
Tom Halliburton - Energy Modeling Consultants Ltd
5
6
7
LP solved for each flow outcome • Deterministic • Minimise sum of immediate cost (this period) + future cost • Trades off use of water now with storage for later use
Cost 1
Immediate Cost (this period)
Future cost
0.5
0 0
0.2
0.4
0.6
Generation this Period
Tom Halliburton - Energy Modeling Consultants Ltd
0.8
1
Add a plane to cost to go function at each storage point
Cost to go
Lake Storage Tom Halliburton - Energy Modeling Consultants Ltd
At each storage point • Generate (eg 15) random inflow outcomes using a multivariate autoregressive model • Consistent with flow outcome for preceding time 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 flow outcomes 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 an optimisation) to simulate changes in the system
Tom Halliburton - Energy Modeling Consultants Ltd
Iterative Process • Optimise in backward direction. • Simulate in forward direction using this policy - cost must be higher than optimal as have a sub-optimal policy. • Optimise again, backward, using storage levels that the simulations passed through. Gives a lower bound. • Each optimisation adds more information to the cost-to-go function. When detailed enough, process is converged. Tom Halliburton - Energy Modeling Consultants Ltd
SDDP Recursive Equation For 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 vt+1 ≤ vmax ut ≤ umax αt+1 ≥ ϕnt+1vt+1 + δnt+1
water balance max volume max flow future cost
Tom Halliburton - Energy Modeling Consultants Ltd