SDDP Generation and Transmission Planning Model

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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


0.8

1

Mangamaire - Woodville Line Flow 30 20 10

MW

0 0

0.2

0.4

0.6

-10 -20 -30 -40


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


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


SDDP Algorithm


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


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


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


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
