Transcript sal.aalto.fi

A Dynamic Interval Goal
Programming Approach
to the Regulation of
a Lake-River System
Raimo P. Hämäläinen
Juha Mäntysaari
Systems Analysis Laboratory
Helsinki University of Technology
www.sal.hut.fi
S ystems
Analysis Laboratory
Helsinki University of Technology
Päijänne-Kymijoki lake river system
Jyväskylä
LAKE
PÄIJÄNNE
Finland
RUOTSALAINEN
KONNIVESI
LAKE
PYHÄJÄRVI
Lahti
RIVER
KYMIJOKI
0 10 20 30 40 50
km
Kotka
Päijänne-Kymijoki lake river system
Lake Päijänne
x(t)
x(t)
Inflow
q(t) = Control
qin(t)
4:th largest in Finland
A(t)
A(t)
Lakes
Ruotsalainen and Konnivesi
Control: Outflow from Päijänne
to the river Kymijoki
Inflows: forecasted
Inflow
qL1(t)
Lake
Pyhäjärvi
1
2
xp(t)
Ap(t)
qp(t)
lake
water flow
power plant
dam
3
4
q2(t)
5
Regulation policies:
Water levels at six time points
6
q21(t)
7
8
211
q
Inflow
qL2(t)
212
(t)
q
9
10
q22(t)
(t)
11
Gulf of Finland
q23(t)
12
Need for modelling
Development of feasible regulation strategies is a
dynamic control problem
– No intuitive solutions
– Planning againts long historical inflow data
– Analysis of regulation impacts
– Many interest groups
 multicriteria optimization in a dynamic system
Goals in terms of water levels
Users give desired water levels at:
– six different points during one year
– ideal level + acceptable interval (min, max)
79.5
79.02
79
78.5
NN+m
78.5
79.02
78.91
78.9
Max
78.3
Goal
78
Min
77.58
77.5
77.44
77.35
77.44
77.33
77.15
1.1
11.12
21.11
1.11
11.10
21.9
1.9
11.8
21.7
1.7
11.6
21.5
1.5
11.4
21.3
1.3
11.2
21.1
1.1
77
Constraints
Outflow from Päijänne:
Min/max flow
Fixed and hard
qmin  qi  qmax
Max change in outflow:
qi  qi1  qmax
Soft, violation penalties
p
p
Water level in the lake Pyhäjärvi: xmin  xi  xmax
Fixed rule based regulation
Part of the dynamics
Criteria and penalty functions
K
Criterion for goal levels:

F x
k 1
goal
k
 xk

2
Quadratic cost for differences of goal points from
regulated water levels
Penalty outside the goal interval:
K
 
Px   max x kmin  x k , x k  x kmax
k 1
Quadratic difference from the limits (min or max)
Penalty for violation of change
in outflow rate:
N
Pq    qi  qmax 
i 1
Quadratic cost outside the maximum flow limit,
otherwise zero
2

2
Criteria and penalty functions
Cost function minimized =
Sum of deviations from goal +
penalty outside goal intervals
cx = 10
cx = 1
cx = 0.01
Min
Max
Goal
goal
k
x
Interval
Model assumptions
•
•
•
•
Lake dynamics
Optimization against one to four year history
Lower dam regulation by a given rule
Regulator uses a rolling two goal optimization
principle
• Adjustment rules
Generation of the optimal regulation strategy
Updating of inflow forecast
Goal optimization
Beginning of month
Updating of inflow forecast
Goal optimization
Beginning of month
Updating of inflow forecast
Goal optimization
Beginning of month
Optimal
Adjusted by
measurement
Goal
Goal optimization
Beginning of month
10 days
Goal programming
• Goal (infeasible point)
• Problem: Find a point in the feasible set closest to
the goal point/set
 Weighted, Min Max, Lexicographic
• Aspects in regulation:
– Dynamic problem
– Goal interval (set)
Why goal programming ?
• Economic, social and environmental impacts
37 primary + 20 secondary
= 57 different impacts
• For example: Power production, flood damages,
number of destroyed loon nests
• Some impacts are interdependent:
energy produced and the value of energy
Use of tradeoff comparison questions or
criteria classification becomes difficult
ISMO spreadsheet application
ISMO spreadsheet application
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 one to four
year period
Modifiable parameters
• Flow constraints in the river
• steepness of the penalty function
Use of ISMO
User
Weather
Annual inflow
prediction updated
every month
(=every third stage)
Hydrological Model
(1 stage=10 days)
Impact models
Dynamic
optimization over
period of 2 goal
points
Initial strategy
User
User
Multicriteria outcomes
Flow constraints
User
Updating Initial
conditions each
month
Goals
Flow measurements
at every stage
Adjustment of
the stratetegy at
every stage
Practical regulation
strategy
ISMO example
Inflow 1980-1984
700.00
600.00
500.00
400.00
300.00
200.00
100.00
0.00
30.12
23.5
14.10
7.3
29.7
20.12
13.5
4.10
25.2
18.7
9.12
Utopia and realistic solutions
79.5
900
79.0
800
78.5
700
Meters
Goal points
78.0
600
Inflow
77.5
500
77.0
400
76.5
300
76.0
200
75.5
100
75.0
1-Jan-80
31-Dec-80
31-Dec-81
31-Dec-82
0
31-Dec-83
Cubic meters per second
Water level
80.0
Total outflows
80
80
550
Max flow
500
79
450
79
400
78
78
350
77
300
77
250
76
200
76
75
1-Jan-80
31-Dec-80
31-Dec-81
31-Dec-82
150
31-Dec-83
Cubic meters per second
Meters
Utopia and realistic solutions
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
Comparison of impacts:
Taloudelliset vaikutukset Mittari (luvut keskiarvoja/vuosi, jos ei muuta mainittu)
Vesivoimantuotanto
Sähkön määrä (MWh)
Sähkön arvo (mk)
Talvella tuotettu sähkö (MWh) (talvi=sähkön hinnoituksen mukainen)
Kesällä tuotettu sähkö (MWh)
Voimalaitosten ohijuoksutusten määrä kuukausittain (MWh)
Tulvavahingot
Tarkastelujakson ylin vedenkorkeus Päijänteellä (NN+m)
Tarkastelujakson ylin virtaama Päijänteeltä (m^3/s)
Vahinkojen määrä Päijänteellä (mk)
Vahinkojen määrä Kymijoella (mk)
Tulvapeltojen pinta-ala Päijänteellä (ha)
Tulvan kesto Päijänteellä (vrk)
Tulvan kesto Kymijoella (vrk)
Vahinkojen määrä Päijänteellä (mk)
Vahinkojen määrä Kymijoella (mk)
Tulvan kesto Päijänteellä (vrk)
Tulvan kesto Kymijoella (vrk)
Huutorajan Päijänteellä ylittävien päivien lkm (vrk)
-Maatalous
-Yhdyskunnat
Aktiivinen
Testi
Vertailu
Historia vertailu
1,394,842
272,353,166
631,268
763,574
12,450
1,394,842
272,353,166
631,268
763,574
12,450
79.16
500
89,691
27,167
75
2.5
99
1,014,704
301,624
48.5
53
30.5
79.16
500
89,691
27,167
75
2.5
99
1,014,704
301,624
48.5
53
30.5
User evaluates and modifies goal levels
Spreadsheet modelling works !
• ISMO is implemented in MS Excel 7.0
(MS Office 95)
– Solver provides optimization routines
– 10-20 minutes for one solution
• Benefits
– Rapid development
– Easy: data input, model modification,
visualisation and printing
• Users accept easily
– Excel is a commonly used office program
Added value
• Generation of alternative regulation strategies
• Impact tables of regulation
– a key info material in decision analysis
interviews and conferences
• Sensitivity tool
– individual changes for water levels and
related impacts
– helps representatives to better understand
the restrictions of the system
Further development
• Different information patterns
• Iterative optimization of the goal levels to
produce maximum amount/value of the energy
• Now used to develop new regulation policies
and their impacts
References
– Marttunen, M., Järvinen, E. A., Saukkonen, J. and Hämäläinen, R. P.,
“Regulation of Lake Päijänne - a Learning Process Preceding
Decision-Making”, Finnish Journal of Water Economy, 6:29-37,
1999.
– Hämäläinen, R. P., Kettunen, E., Marttunen, M. and Ehtamo, H.,
“Evaluating a framework for multi-stakeholder decision support in
water resources management”, Manuscript, 1999. (Downloadable
from http://www.sal.hut.fi/Publications/pdf-files/mhamb.pdf)
– Hämäläinen, R. P. and Mäntysaari, J., “A Dynamic Interval Goal
Programming Approach the Regulation of a Lake-River System”,
Manuscript, 2000. (Downloadable from http://www.sal.hut.fi/
Publications/pdf-files/mhama.pdf)
– Hämäläinen, R. P., “Interactive Multiple Criteria Decision Analysis in
Water Resources Planning”, Home pages of the Lake Päijänne project,
www.paijanne.hut.fi
1998,