Prof Graeme Dandy (PDF 1.3mb)

Optimisation of Urban Water Management Prof Graeme Dandy University of Adelaide

Outline • Framework for Optimisation Models • Multi-Objective Optimisation • Case Study #1: Multi-Objective Optimisation of Canberra’s Water Supply System • Case Study #2: Melbourne’s Water Supply System • Case Study #3: Water Supply Options for Adelaide: Cost vs Greenhouse Gas Tradeoffs • Case Study #4: Urban Water Management at the Cluster Scale • Conclusions

Types of Models • Descriptive – How does the system behave? – What will be the consequences of certain actions? Simulation Models

• Prescriptive – What are the best actions to achieve a particular objective or set of objectives? Optimisation models

Informed actions

Stakeholder preferences

Support for good decisions

Multi criteria analysis

Controls

Multi-objective optimisation

Data & uncertainty

P1

P2

Pn

Performance prediction models

P = performance

R1

R2

Rn

Risk assessment Uncertainty & likelihood

R = risk

(Ref: Blackmore et al., 2009)

Additional data & Knowledge

Optimisation Methodology • Systems approach Selection of Objectives Selection of Alternative Simulation of Alternative Evaluation of Alternative Results

Optimisation Module

Form of an Optimisation Model • Choose values for a set of decision variables so as to maximise (or minimise) a particular set of objectives Subject to a set of constraints

Genetic Algorithm Optimisation

What Are Genetic Algorithms ? • Guided search procedures that work by analogy to natural selection • Include embedded computer simulation • Each solution is represented by a string of numbers • Work with a population of solutions • Algorithm can run for any length of time • Can’t prove that you have reached the optimum solution

Typical GA string

Distribution Network Pipe Material

Distribution Network Pipe Diameters

Collection Network Pipe Pump Size Material

Repeat Towards Convergence Solution Cost ($ million)

100 90

The GA conducts a directed search for optimal solutions

80 70 60 50 40 30 0

50,000

100,000 150,000 Number of Solution Evaluations

200,000

Multi-Objective Optimisation

Multi-Objective Optimisation

Pareto Optimal Front

Multi-Objective Optimisation: Articulation of Preferences (MCA)

Pareto Optimal Front

Advantages of Genetic Algorithms for Multi-Objective Optimisation • GAs deal with a population of solutions that are spread over the solution space • In one GA run, these solutions can be “spread” along the Pareto front by using various techniques such as the Dominance Rank Sorting Algorithm • Thus the population can be made to approximate the Pareto optimal front upon convergence

Case Study #1: MultiObjective Optimisation Of Canberra’s Water Supply System

The Canberra Water Supply System Canberra and Queanbeyan

Canberra Network in WATHNET

Data/Model Used • Monthly rainfall and flow data for period 1871 to 2008 • Current demands increased by 75% • Modified NSGA II with WATHNET

Scenario #1: Objectives • Objective 1: Average number of months per year of restrictions (reliability measure) • Objective 2: Cost

Scenario #1: Decision Variables • Decision Variable 1: Googong base reservoir gain (BG)

Cost ( j ) BG ( j 1) * IG j 1,, n • Decision Variable 2: Googong incremental reservoir gain (IG)

Pareto Optimal Front (Scenario 1) case 1 - 175% demand Googong base gain, Googong incremental gain

5

7.82

x 10

7.8

cost ($/month average)

7.78 7.76 7.74 7.72 7.7 7.68 7.66 7.64 7.62 6.8

6.85

6.9

6.95 7 7.05 7.1 7.15 restrictions (months/year)

7.2

7.25

7.3

Scenario #2: Objectives • Objective 1: Number of months per year of restrictions (reliability measure) • Objective 2: Cost • Objective 3: Months/year with less than 20% storage (vulnerability measure)

Scenario #2: Decision Variables • Decision Variable 1: Googong base reservoir gain (BG)

Cost ( j ) BG ( j 1) * IG j 1,, n • Decision Variable 2: Googong incremental reservoir gain (IG) • Decision Variable 3: Canberra level 1 trigger (for restrictions)

Canberra Case Study

Pareto Front

Case Study #2: Melbourne’s Water Supply System (Ref: Optimatics, 2010)

Melbourne Water System

(Ref: Kularathne et al., 2011)

Simplified REALM Model

Melbourne Water System 30-year Operations Optimisation Problem

Operating Decision Annual desal order Yarra pumping rate Tarago output rate Transfers

Decisions 30 360 360 3000+

Options 5 5 5 5

Total possible combinations: 530 * 5360 * 5360 * 53000 = 53750

Components of Water Supply Security Relative Weights: 0.25 1

b)

1

c)

0.6 0.4

1 0.8

0.8

Utility

Utility

0.8

0.25

Utility

a)

0.5

0.6 0.4

0.6 0.4

0.2

0.2

0.2

0

0

0

0%

50% Reliability

100%

0

6

12

18

24

Duration (months)

0

1

2

3

Restriction Level

4

Pareto Optimum Front 0.6

E

Security Water SupplySecurity Water Supply

0.5

0.4

C

D

0.3

B 0.2

A

0.1

0 0

20

40

60

Annual Operating Cost Annual Operating Cost ($million)

80

100

120

Spider Graphs for Options D and E

d)

e)

Desalination Costs 1

Severity

Desalination Costs 1

0.8

0.8

0.6

0.6 Other Costs

0.4 0.2

Severity

Other Costs

0.4 0.2 0

0

Duration

Reliability

D: Poor value for money

D

Duration

Reliability

E: Expensive, High Security

E

Spider Graphs for Options A and B

a)

b)

Desalination Costs 1

Severity

Desalination Costs 1

0.8

0.8

0.6

0.6

Other Costs

0.4 0.2

Severity

Other Costs

0.4 0.2 0

0

Duration

Reliability

A: Inexpensive, Low Security

A

Duration

Reliability

B: Balanced (less expensive)

B

Pareto Optimum Front 0.6

E

Security Water SupplySecurity Water Supply

0.5

0.4

C

D

0.3

B 0.2

A

0.1

0 0

20

40

60

Annual Operating Cost Annual Operating Cost ($million)

80

100

120

An Example of Weights in a MultiCriteria Analysis

(Ref: Smith et al., 2012)

Case Study #3: Water Supply Options for Adelaide. Cost vs GHG Tradeoffs (Ref: Baulis et al, 2008)

TEMPORAL SCENARIOS SUPPLY TYPE ALTERNATIVES

Risk Based Performance Assessment

2020 – 72ML/day 2060 – 225ML/day 2100 – 300ML/day

0KL

< 30GL/yr

Water Simulation Model (WaterCress) Run Check simulation constraints model

Output results

Calculate: - Reliability - Resilience - Vulnerability

Risk Based Performance Assessment - 2060 90 80

Myponga Reservoir

Water Supply (GL/yr)

70 60

Happy Valley Reservoir

50

River Murray

40

The 30amount of water 20 supplied by each supply type for the 10 Southern system for 0 2060 2015 2020 2010

Desalination Plant Maximum River Murray Flow

2025

2030

2035

2040

2045

2050

2055

2060

Date

Reliability

225ML/day

0KL

85%

Resilience Vulnerability -1 (GL) (years )

0.63

26.0

Optimisation • Objectives: – Minimise present value of total system cost – Minimise (discounted) greenhouse gas emissions

• Constraint: – Availability of water from the Murray (30 GL/year)

• Decision Variables: – Capacity of desalination plant (ML/day) – Size of rainwater tanks for all households (kL) – Operating rules for the system

Optimisation Process

Optimisation Process GHG emissions (Megatonnes of CO2-e)

2060 trade-offs 27.00

Feasible (300ML/day, 5KL)

25.00 23.00 21.00 19.00 Infeasible

(225ML/day,

0KL)

17.00 15.00 4.000

5.000 6.000 7.000 8.000 Cost ($2007 billion)

9.000

Optimisation Process GHG emissions (Megatonnes of CO2-e)

2060 trade-offs 27.00 Feasible (300ML/day, 5KL)

25.00 23.00 21.00 Pareto Optimal Front

19.00 17.00

Infeasible

(225ML/day,

0KL)

15.00 4.000

5.000 6.000 7.000 8.000 Cost ($2007 billion)

9.000

Optimisation Process 2060 results

25.00 23.00 21.00 19.00

The 2060 Pareto Front

17.00 15.00 4.0

GHG emissions (Megatonnes of CO 2 -e)

GHG emissions (Megatonnes of CO 2-e)

27.00

21.84

6.0 8.0 21.82 Cost ($2007 billion)

10.0 Breakpoint (250ML/day, 2KL)

21.80 21.78 21.76 6.990

7.000 7.010 Cost ($2007 billion)

7.020

Optimisation Process 2060 results

25.00 23.00 21.00 19.00

The 2060 Pareto Front

17.00 15.00 4.0

GHG emissions (Megatonnes of CO 2 -e)

GHG emissions (Megatonnes of CO 2-e)

27.00

21.84

6.0 8.0 21.82 Cost ($2007 billion)

10.0

$45/tonne

Breakpoint (250ML/day, 2KL)

21.80 21.78 21.76 6.990

$1000/tonne

7.000 7.010 Cost ($2007 billion)

7.020

Optimisation Process 2060 results

25.00 23.00 21.00 19.00

The 2060 Pareto Front

17.00 15.00 4.0

GHG emissions (Megatonnes of CO 2 -e)

GHG emissions (Megatonnes of CO 2-e)

27.00

21.84 (251ML/day, 1.8KL)

6.0 8.0 21.82 Cost ($2007 billion)

10.0

$45/tonne

Breakpoint (250ML/day, 2KL)

21.80 21.78 21.76 6.990

$1000/tonne (248ML/day, 2.6KL)

7.000 7.010 Cost ($2007 billion)

7.020

Optimisation Process Range depends on optimal rainwater tank size, which depends on average yearly water supply per tank:

Average yearly water supply per tank 1KL

24KL

$3.08/KL

0.96kgCO2-e/KL

20KL

48KL

$3.27/KL

3.34kgCO2-e/KL

247.7 251.6

Economic Discount Rate

245.5

Social Discount Rate

512.0

168.0

Demand

Sensitivity Analysis of the Optimisation Process

251.0

296.0

206.7

River Murray Supply Constraint

247.8

Climate Change Impacts

241.9

Lifetime of Rainwater Tanks

287.0

251.1

247.1 251.1

Lifetime of the Desalination Plant 0

200

400

600

Desalination Plant Size (ML/day)

Economic Discount Rate

1.7

Social Discount Rate

1.7

Demand

1.8

2.8 3.6 2.9

1.1

River Murray Supply Constraint

3.2 2.9

0.9

Climate Change Impacts Lifetime of Rainwater Tanks

1.8

Lifetime of the Desalination Plant

1.8 0

5.3 3.1 2

4

Tank Size (KL)

6

Case Study #4: Urban Water Management at the Cluster Scale

Woden Case Study (Canberra)

Urban Developer Case Study

• Collier Street – 39 Houses

• Measured roof areas • Census data used for number of occupants

Urban Developer Case Study

Occupants 2 3 4 5

Number of Houses 18 8 10 3

Urban Developer Case Study • Households vary between 2-5 people • 5 different sizes of rainwater tank: – 1kL, 2kL, 5.5kL, 9kL,10kL

• Water consumption data: – From “Domestic Water Use in the ACT” (Troy et al., 2006)

Objectives • Set in collaboration with ACT government and ACTEW – Reduce potable water demand – Reduce total water consumption

• Further objectives – Cost (minimize) – Energy use (minimize) – Ecological objectives

Decision Variables • Inputs into the model that can be changed in order to meet objectives: – Number of houses with rainwater tanks of various sizes – Uptake of water efficient appliances (WELS 1 to 5)

• Three Scenarios corresponding to water prices of $2, $3 and $4 per kL up to 548 kL per year (scenarios 0,1,2)

Average annual water use (kL/household)

Multi-Objective Tradeoffs

304

Scenario 0 Scenario 1 Scenario 2

302 300 298 296 294 292 290 300

2500

280 2000 260 Average annual mains water use 240 (kL/household)

1500 1000

Average annual household cost ($)

Tradeoffs in Terms of Two Objectives

Average annual water use (kL/household)

310

300

290

280

270

260

Scenario 0 Scenario 1 Scenario 2

250

240 1000

1200

1400

1600 1800 2000 Average annual household cost ($)

2200

2400

Tradeoffs in Terms of Two Objectives

Average annual mains water use (kL/household)

310 Scenario 0 Scenario 1 Scenario 2

300

290

280

270

260

250

240 1000

1200

1400

1600 1800 2000 Average annual household cost ($)

2200

2400

Distribution of Rainwater Tank Sizes Scenario 0 40 35 30 25 20 15 10 5 0 no tank

1kL

2kL

5.5kL

9kL

10kL

Distribution of Rainwater Tank Sizes Scenario 2 35 30 25 20 15 10 5 0 no tank

1kL

2kL

5.5kL

9kL

10kL

Distribution of WELS Ratings Scenario 0 40 35 30 25 20 15 10 5 0 1 star

2 star

3 star

4 star

5 star

Distribution of WELS Ratings Scenario 2 45 40 35 30 25 20 15 10 5 0 1 star

2 star

3 star

4 star

5 star

Conclusions (1) • Urban Water Systems are inherently complex with many objectives and many options • Multi-objective optimization (MOO) enables the exploration of a wide range of options for these systems • MOO can be used to produce a Pareto optimal front which provides a range of efficient options from which the decision-maker can choose

Conclusions (2) • Multi-objective optimisation (MOO) has a key role to play in providing decision support for the planning and operations of major water supply systems • Tradeoffs between cost and system security or greenhouse gas emissions can be developed • The combination of MOO and MCDA enables efficient outcomes that satisfy the preferences of stakeholders

Acknowledgements • H.Maier, J.Ravalico, F.Paton, J.Baulis, L. Lloyd, B. Staniford (University of Adelaide) • G.Kuczera, L.Cui (University of Newcastle) • J. Blackmore (CSIRO) • D.McIver, D.Broad, H.Schultz-Byard, T.Rowan, P.Smith (Optimatics Pty Ltd) • U.Kularathna, B.Rhodes, D.Flower, B.Baker (Melbourne Water)

References •

Baulis, J., Lloyd, L., Paton, F. and Staniford, B. (2008) “Multi-Objective Optimisation of Urban Water Supply Systems at the Regional Scale Incorporating Sustainability” Final Year Honours Presentation, School of Civil, Environmental and Mining Engineering, University of Adelaide.

•

Blackmore, J.M., Dandy, G.C., Kuczera, G. and Rahman J. (2009) “Making the most of modelling: A decision framework for the water industry”. In Anderssen, R.S., R.D. Braddock and L.T.H. Newham (eds) 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, July.

•

Kularathna, M.D.U.P., Rowan, T.S.C., Schultz-Byard, H., Broad, D.R., McIver D., Flower, D., Baker, B., Rhodes, B.G. and Smith , P. J. (2011) “Multi-Objective Optimisation using Optimizer WSS to Support Operation and Planning Decisions of Melbourne Water Supply System”, Proceedings,19th International Congress on Modelling and Simulation, Perth, Dec.

•

Optimatics Pty Ltd (2010) “Water Supply System Optimisation. Feasibility Study Report” prepared for Victorian Smart SMEs Market Validation Program. Host Institution: Melbourne Water, April 2010

•

Smith, P. J., Kularathna, M. D. U. P., Rhodes, B., Broad, D. R., Schultz-Byard, H. (2012) “Decision Support for Management of Melbourne’s Water Supply System”, Proceedings, Ozwater’12, Sydney, May.