multicriteria interval goal optimization in the regulation of lake-river systems
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Multicriteria Interval Goal Optimization in the Regulation of Lake-River Systems. Raimo P. Hämäläinen and Otso Ojanen Systems Analysis Laboratory Helsinki University of Technology www.hut.fi/Units/SAL [email protected]. Lake Päijänne and River Kymijoki in Finland. - PowerPoint PPT PresentationTRANSCRIPT
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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
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Lake Päijänne and River Kymijoki in Finland
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S ystemsAnalysis LaboratoryHelsinki University of Technology
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
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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
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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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
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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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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
Goal levelMin levelMax levelwater level
Water level
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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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
Goal levelMin levelMax levelwater level
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
Goal levelMin levelMax levelwater level
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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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S ystemsAnalysis LaboratoryHelsinki University of Technology
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).