sddp generation and transmission planning model · tom halliburton - energy modeling consultants...

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


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


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


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


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


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


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


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


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


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



• 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



• 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



• 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



• 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



• 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 transmissionsystem model


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


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


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


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


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


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


MW Flow

North Makerew a Thermal

Marsden Thermal


Mangamaire - Woodville Line Flow

-40

-30

-20

-10

0

10

20

30

0 0.2 0.4 0.6 0.8 1


MW


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


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 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


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


Add a plane to cost to go function ateach storage point

Lake Storage

Costto go


• 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


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


• 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


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

sddp generation and transmission planning model · tom halliburton - energy modeling consultants...

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