Multicriteria Interval Goal Optimization in the Regulation of Lake-River Systems

1

S ystemsAnalysis LaboratoryHelsinki University of Technology

Multicriteria Interval Goal Optimization in the Regulation of Lake-River Systems

Raimo P. Hämäläinen and Otso OjanenSystems Analysis Laboratory

Helsinki University of Technology

www.hut.fi/Units/SAL

[email protected]

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Lake Päijänne and River Kymijoki in Finland

3


Päijänne-Kymijoki lake river system

4:th largest in Finland

Control: Outflow from Päijänne to

the river Kymijoki

Inflows: forecasted

Regulation policies:

Water levels at six time points

LakePyhäjärvi

Lake Päijänne

Inflow

xp(t)A p(t)

9 1011

2

8

7

6

4

3

12

q(t) = Control

qL1 (t)

LakesRuotsalainen and Konnivesi

1

qp(t)

q2(t)

q21 (t)

5

Gulf of Finland

q in (t)

x(t)

A(t)

q23 (t)q22 (t)

q212 (t)q211 (t)

x(t)

A(t)

Inflow

dam

lakewater flowpower plant

qL2 (t)Inflow

4


Need for modelling

Development of feasible regulation strategies is a dynamic control problem– No intuitive solutions

– Planning againts long historical inflow data

– Interest in optimal regulation

– Interactive analysis of impacts

– Many interest groups

Interactive dynamic multicriteria optimization

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Goal programming

• Goal = Utopia point/set• Problem: Find a point in the

feasible set closest to the goal point/set minimize distance d

• New aspects:– Dynamic problem

– Goal interval (set)

d

Goal point/set

cost function

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Why goal programming ?

• Economic, social and environmental impacts 19 primary + 27 secondary = 48 different impacts

• For example: Power production, flood damages, number of destroyed loon nests

• Some impacts are interdependent:energy produced and the value of energy

Direct use of tradeoff comparisons is difficult

7


Modeling Principles

• Lake dynamics

• Optimization against four year history data

• Lower dam regulation by a given rule

• Regulator uses a rolling two goal optimization strategy

• Adjustment rules

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Interactive decision support

Utopia outcomes

Set of goal points

Reference weatherhistory

Constraints

Normal scenario

Risk scenario

Interest groups

Multicriteria outcomes

ISMO goaloptimization

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Goals in water levels

Users give desired water levels at:– six different points during one year– ideal level + acceptable interval (min, max)

78.5

78.3

78.979.02

78.9179.02

77.35

77.15

77.44 77.4477.58

77.33

77

77.5

78

78.5

79

79.5

1.1

21

.1

11.2 1.3

21

.3

11.4 1.5

21

.5

11.6 1.7

21

.7

11.8 1.9

21

.9

11.1

0

1.1

1

21

.11

11.1

2

1.1

NN

+m Max

Goal

Min

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Dynamics of the lake Päijänne

T h e a p p r o x i m a t i o n o f t h e c h a n g e i n t h e w a t e r l e v e l i n t w o p h a s e s :I ) I n t i a l c h a n g e i n t h e w a t e r l e v e l :

( c h a n g e i n w a t e r r e s e r v e = q t q q t ti i ii n

i i i 1 )

~

A ~xq t

xii i

i

1

g i v e s ~ ~ ~x x xi i i 1

A n a c t u a l e s t i m a t e :

xq t

x x

2

ii i

i 1 i

A~ g i v e s x x xi i i 1

~x i x i 1

x i

x xi i 1 2~

A x xi i 1 2~x xi i 1

A x i 1

~x i q ti i q ti i

x i 1

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Constraints

Outflow from PäijänneMin/max flow:

Fixed and hard

Max change in outflow:Soft penalty

Water level in the midstream lake Pyhäjävi:

Fixed rule based regulationPart of the dynamics

q q qimin max

q q qi i 1 max

x x xpi

pmin max

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Criteria and penalty functions

Criterion for goal levels:Quadratic cost for differences of goal points from regulated

water levels

Penalty outside the goal interval:Quadratic difference from the limits (min or max)

Penalty for violation of change in outflow rate:Quadratic cost outside the maximum flow limit,

otherwise zero

F x xkgoal

kk

K

2

1

P max x xx x , xk

mink k k

max

k

K

2

1

Pq max q qii

N2

1

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Cost function minimized =Sum of deviations from goal + penalty outside goal intervals

cx = 10

cx = 1

cx = 0.01

MinGoal

Max

xgoalk

Interval

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Benefits of the interval goal formulation

• Relaxation of the rigidity of fixed target points

• Allows dynamic flexibility to the solution

• Softer solutions with smaller changes in the flow rate

• Can increase risk and sensitivity to unpredicted deviations in the inflows

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10 days

Optimal

Goal optimization

Beginning of month

Adjusted bymeasurement

Updating of inflow forecastGoal optimization

Beginning of month

Updating of inflow forecastGoal optimization

Beginning of month

Updating of inflow forecast

Beginning of month

Goal optimization

Goal

Generation of the optimal regulation strategy

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Minimizes deviations from goal levels and goal

intervals

Satisfies flow constraints

Simulates the regulator’s operating principles

Preference model: • Set of goal levels + acceptability intervals

• Optimization againts history data for a selected four year period

Modifiable parameters:• Flow constraints in the river

• steepness of the penalty function

ISMO - spreadsheet software

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Use of models in ISMOUser

Flow constraints

Goals

Hydrological Model(1 stage=10 days)

Weather

Annual inflowprediction updated

every month(=every third stage) Dynamic

optimization overperiod of 2 goal

points

Initial strategy

Adjustment ofthe stratetegy at

every stage

Flow measurementsat every stage

Impact models

Practical regulationstrategy

Multicriteria outcomesUser

User

User Updating Initialconditions each

month

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Inflows years 1980-1984

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

30.12 23.5 14.10 7.3 29.7 20.12 13.5 4.10 25.2 18.7 9.12

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Utopia solution

76.50

77.00

77.50

78.00

78.50

79.00

79.50

80.00

1.1 25.5 16.10 9.3 31.7 22.12 15.5 6.10 27.2 20.7 11.12

Goal levelMin levelMax levelwater level

Water level

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Utopia solution

0

100

200

300

400

500

600

700

30.12 23.5 14.10 7.3 29.7 20.12 13.5 4.10 25.2 18.7 9.12

Min flow

Max flow

Outflow

Outflow

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Realistic solution

76.50

77.00

77.50

78.00

78.50

79.00

79.50

80.00

1.1 25.5 16.10 9.3 31.7 22.12 15.5 6.10 27.2 20.7 11.12


Water level

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Realistic solution

0

100

200

300

400

500

600

700

30.12 23.5 14.10 7.3 29.7 20.12 13.5 4.10 25.2 18.7 9.12

Min flow

Max flow

Outflow

Outflow

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Utopia and Realistic Solutions years 1980-1984

76.50

77.00

77.50

78.00

78.50

79.00

79.50

80.00

1.1 25.5 16.10 9.3 31.7 22.12 15.5 6.10 27.2 20.7 11.12


Water level

76.50

77.00

77.50

78.00

78.50

79.00

79.50

80.00

1.1 25.5 16.10 9.3 31.7 22.12 15.5 6.10 27.2 20.7 11.12


Water level

0

100

200

300

400

500

600

700

30.12 23.5 14.10 7.3 29.7 20.12 13.5 4.10 25.2 18.7 9.12

Min flow

Max flow

Outflow

Outflow

0

100

200

300

400

500

600

700

30.12 23.5 14.10 7.3 29.7 20.12 13.5 4.10 25.2 18.7 9.12

Min flow

Max flow

Outflow

Outflow

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Impacts

• Nature– Spawning areas for pike fish– Water level when ice melts– number of destroyed loon nests

• Social– Recreational losses– Professional fishing: Reduction of

the water level during 10-Dec and 28-Feb

• Economic– Power production– Flood damages– Days infavourable for log floating

209,525,596219,030,188

217,181,184

- 50,000,000 100,000,000 150,000,000 200,000,000 250,000,000

Sähkön arvo (mk)

1,100,296

1,125,8581,134,028

- 200,000 400,000 600,000 800,000 1,000,000 1,200,000

Sähkön määrä (MWh)

Vesivoimantuotanto

Virkistyskäyttö

426,874335,528

359,066

- 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 450,000

Haitta Kymijoella (mk)

5,847,3333,866,198

4,081,041

- 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000

Haitta Päijänteellä (mk)

Rantojen käyttö

0.002.35

4.45

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50

Hauen lisääntymisalueidenkoko (ha)

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Comparison of impacts:

User evaluates and modifies goal levels

Aktiivinen Vertailu

Taloudelliset vaikutukset Mittari (luvut keskiarvoja/vuosi, jos ei muuta mainittu)Vesivoimantuotanto Sähkön määrä (MWh) 1,394,842 1,394,842

Sähkön arvo (mk) 272,353,166 272,353,166 Talvella tuotettu sähkö (MWh) (talvi=sähkön hinnoituksen mukainen) 631,268 631,268 Kesällä tuotettu sähkö (MWh) 763,574 763,574 Voimalaitosten ohijuoksutusten määrä kuukausittain (MWh) 12,450 12,450

Tulvavahingot Tarkastelujakson ylin vedenkorkeus Päijänteellä (NN+m) 79.16 79.16Tarkastelujakson ylin virtaama Päijänteeltä (m^3/s) 500 500

-Maatalous Vahinkojen määrä Päijänteellä (mk) 89,691 89,691 Vahinkojen määrä Kymijoella (mk) 27,167 27,167 Tulvapeltojen pinta-ala Päijänteellä (ha) 75 75Tulvan kesto Päijänteellä (vrk) 2.5 2.5Tulvan kesto Kymijoella (vrk) 99 99

-Yhdyskunnat Vahinkojen määrä Päijänteellä (mk) 1,014,704 1,014,704 Vahinkojen määrä Kymijoella (mk) 301,624 301,624 Tulvan kesto Päijänteellä (vrk) 48.5 48.5Tulvan kesto Kymijoella (vrk) 53 53Huutorajan Päijänteellä ylittävien päivien lkm (vrk) 30.5 30.5

Historia vertailuTesti

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• ISMO is implemented in MS Excel 7.0 – Solver provides optimization routines

– 10-20 minutes for one solution

• Benefits– Rapid development

– Simple data input, model modification, visualization and printing

• Users accept easily:– Excel is a commonly used office program

Spreadsheet modelling works

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Further development• Other optimization criteria:

– Energy

– Other impacts

• Different information patterns

• Iterative optimization of the goal levels to produce maximum amount/value of the energy

• Now used to develop new regulation policies. Could ISMO be developed for everyday operational regulation ?

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ReferencesHämäläinen R.P., Mäntysaari J., ”A Dynamic Interval Goal Programming Approach

to the Regulation of a Lake-River System”, Multi-Criteria Decision Analysis, Vol. 10, Issue 2, March-April (2001).

Hämäläinen, R.P., Mäntysaari J., ”Dynamic Multiobjective Heating Optimization”, European Journal of Operational Research, 142, (2002).

Hämäläinen R.P., Kettunen E., Marttunen M., Ehtamo, H., ”Evaluating a Framework for Multistakeholder Decision Support in Water Resources Management”, Group Decision and Negotiation, Vol. 10, No. 4, (2001).

Marttunen M., Hämäläinen R.P., ”The Decision Analysis Interview Apporach in the Collaborative Management of a Large Regulated Water Course”, Environmental Management, Vol. 42: 6 (2008).

Schniederjans M.J., ”Goal Programming – Methodology and Applications”, Kluwer Academic Publishers, (1995).

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Multicriteria Interval Goal Optimization in the Regulation of Lake-River Systems