Andrea Castelletti Dept. of Electronics, Information, and Bioengineering, Politecnico di Milano, Italy Institute of Environmental Engineering ETH-Zurich, Switzerland QUEBĖC CITY, CA 17.09 19.09 2014 FROM OPERATIONAL HYDROLOGICAL FORECAST TO RESERVOIR MANAGEMENT OPTIMIZATION On the direct use of hydroclimatic information to better inform water reservoir operation
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Direct use of hydroclimatic information for reservoir operation
Direct use of hydroclimatic information for reservoir operation - Plenary Talk at the Conference "From operational hydrological forecast to reservoir management optimization" Québec City, Québec, Canadahttp://acrhrta2014.ouranos.ca/program.html
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Andrea Castelletti Dept. of Electronics, Information, and Bioengineering, Politecnico di Milano, Italy Institute of Environmental Engineering ETH-Zurich, Switzerland
QUEBĖC CITY, CA 17.09 -‐ 19.09 2014
FROM OPERATIONAL HYDROLOGICAL FORECAST TO RESERVOIR MANAGEMENT
OPTIMIZATION
On the direct use of hydroclimatic information to better inform water reservoir operation
Contributors
FRANCESCA PIANOSI MATTEO GIULIANI SIMONA DENARO
Towards pervasive sensing of the hydrological cycle
CITIZEN SCIENCE
SMART SENSORS
HUMAN SENSORS
LABS ON CHIP
ENVINODES SMART DUST
VIRTUAL SENSORS
REMOTE SENSING
CYBERINFRASTRUCTURES
CROWNSOURCING
Towards pervasive sensing of the hydrological cycle
ground sensors
“Torrent of information”, Economist, 17th Feb 2010
Towards pervasive sensing of the hydrological cycle
remote sensors
ground sensors
“Torrent of information”, Economist, 17th Feb 2010
Towards pervasive sensing of the hydrological cycle
remote sensors
ground sensors
virtual sensors
“Torrent of information”, Economist, 17th Feb 2010
Towards pervasive sensing of the hydrological cycle
remote sensors
ground sensors
virtual sensors
smart sensors
“Torrent of information”, Economist, 17th Feb 2010
Pareto front with BASIC Information e.g. - doy (RULE CURVE) or - doy + s(t) (OPERATING POLICY)
More information = smarter decisions (?)
FLOODS
HY
DRO
POW
ER
1. CAN WE DO BETTER?
2. HOW MUCH BETTER?
3. HOW?
Pareto front with BASIC Information e.g. - doy (RULE CURVE) or - doy + s(t) (OPERATING POLICY)
Can we do better?
FLOODS
HY
DRO
POW
ER
Pareto front with PERFECT foresight i.e. - doy, s(t), q(t+1), q(t+2), … q(t+h) (IDEAL POLICY)
Pareto front with BASIC Information e.g. - doy (RULE CURVE) or - doy + s(t) (OPERATING POLICY)
The upper bound performance (perfect foresight)
How much better?
FLOODS
HY
DRO
POW
ER
VALUE of EXOGENOUS INFORMATION (VEI)
Pareto front with BASIC Information e.g. - doy (RULE CURVE) or - doy + s(t) (OPERATING POLICY)
Pareto front with PERFECT foresight i.e. - doy, s(t), q(t+1), q(t+2), … q(t+h) (IDEAL POLICY)
The Value of Exogenous Information
How?
FLOODS
HY
DRO
POW
ER
Pareto front with BASIC Information e.g. - doy (RULE CURVE) or - doy + s(t) (OPERATING POLICY)
Pareto front with PERFECT foresight i.e. - doy, s(t), a(t+1), a(t+2), … a(t+h) (IDEAL POLICY)
Selecting appropriate exo information
Pareto front with EXOGENOUS INFO
VALUE of EXOGENOUS INFORMATION (VEI)
on a more technical ground …
1. How to get the upper bound?
Solve a deterministic optimization problem assuming perfect foresight of the future system inputs (here inflows).
q1, q2, . . . , qh
s.t. future inflow time series
minut
[J1 J2]
HY
DRO
POW
ER
FLOODS
IDEAL front
BASIC front
qt+1
st
FLOODS
qt
st
utHYDROPOWER
1. How to get the upper bound?
Solve a deterministic optimization problem assuming perfect foresight of the future system inputs (here inflows).
q1, q2, . . . , qh
s.t. future inflow time series
minut
[J1 J2]
HY
DRO
POW
ER
FLOODS
ideal release trajectories
ideal storage trajectories
IDEAL front
TARGET
BASIC front
qt+1
st
FLOODS
qt
st
utHYDROPOWER
2. How to estimate the potential improvement (VEI)?
Three metrics to quantify the operational Value of Exogenous Information (VEI)
1. Minimum distance from the target ideal point
2. Average distance from the target ideal point
3. Hypervolume
FLOODS
HY
DRO
POW
ER
IDEAL front
BASIC front
FLOODS
HY
DRO
POW
ER
IDEAL front
TARGET
BASIC front
FLOODS
HY
DRO
POW
ER
IDEAL front
TARGET
BASIC front
1 Min distance 2 Ave distance 3 Hypervolume
3. How to select the best exogenous information?
The ideal release sequence is equivalent to an operating policy whose arguments are t, s(t) and the entire sequence of future inflows
u⇤1, u⇤2, . . . , u
⇤h
ut = m(t, st, )qt, qt+1, qt+2, . . . , qh
'
HY
DRO
POW
ER
FLOODS
ideal release trajectories
ideal storage trajectories
IDEAL front
TARGET
BASIC front
3. How to select the best exogenous information?
The ideal release sequence is equivalent to an operating policy whose arguments are t, s(t) and the entire sequence of future inflows
u⇤1, u⇤2, . . . , u
⇤h
ut = m(t, st, )qt, qt+1, qt+2, . . . , qh
'
ut = m(t, st, )It
IDEA: use the hydrometeorologic information available at time t that better works as a surrogate of the future inflow sequence
HY
DRO
POW
ER
FLOODS
ideal release trajectories
ideal storage trajectories
IDEAL front
TARGET
BASIC front
3. How to select the best exogenous information?
The ideal release sequence is equivalent to an operating policy whose arguments are t, s(t) and the entire sequence of future inflows
u⇤1, u⇤2, . . . , u
⇤h
ut = m(t, st, )qt, qt+1, qt+2, . . . , qh
'
ut = m(t, st, )It
IDEA: use the hydrometeorologic information available at time t that better works as a surrogate of the future inflow sequence
HY
DRO
POW
ER
FLOODS
ideal release trajectories
ideal storage trajectories
IDEAL front
TARGET
BASIC front
streamflow prediction
(model based)
3. How to select the best exogenous information?
The ideal release sequence is equivalent to an operating policy whose arguments are t, s(t) and the entire sequence of future inflows
u⇤1, u⇤2, . . . , u
⇤h
ut = m(t, st, )qt, qt+1, qt+2, . . . , qh
'
ut = m(t, st, )It
IDEA: use the hydrometeorologic information available at time t that better works as a surrogate of the future inflow sequence
streamflow prediction
(model based)
select from available hydroclimatic data
(model free)
HY
DRO
POW
ER
FLOODS
ideal release trajectories
ideal storage trajectories
IDEAL front
TARGET
BASIC front
Automatic feature selection
With multiple, possibly redundant informations, and spatial variability, the number of candidate variables can be very high and an empirical selection is not always effective
Automatic feature selection
With multiple, possibly redundant informations, and spatial variability, the number of candidate variables can be very high and an empirical selection is not always effective
IDEA: AUTOMATIC FEATURE SELECTION algorithm
output candidate inputs
ut = m(t, st, )It
For example:
• Partial Mutual Information index (Sharma 2000; Bowden et al. 2005)
• minimum redundancy Maximum Relevance (Heiazi and Cai, 2009)
Greer, B.H., S. Galelli, H.R. Maier, A. Castelletti, G.C. Dandy, M.S. Gibbs, An evaluation framework for input variable selection algorithms for environmental data-driven models, EMS.
http://ivs4em.deib.polimi.it
A Control Theory interpretation
delay
t m(·) ut st+1reservoir reservoir
qt
It
catchment
Feedback + feedforward control
scheme
inflow predictor
qt qt+1ut = m(t, st, , , . . .)
Model-based control
A Control Theory interpretation
delay
t m(·) ut st+1reservoir reservoir
qt
It
catchment
Feedback + feedforward control
scheme
inflow predictor
delay
t m(·) ut st+1reservoir reservoir
qt
It
catchment
Feedback + model free control scheme
info selecUon
It
qt qt+1ut = m(t, st, , , . . .) ut = m(t, st, )It
Model-based control
Model-free control
Summary of the procedure
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
1. COMPUTE the UPPER BOUND
Summary of the procedure
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
Summary of the procedure
automatic feature
selection
selected policy
arguments
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
Summary of the procedure
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO 4. REOPTIMIZE the POLICY
Summary of the procedure
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
ex post VEI estimation
5. re-ESTIMATE the VEI
4. REOPTIMIZE the POLICY
NUMERICAL RESULTS Hoa Binh - Vietnam
Hanoi
HoaBinh
TaBu
LaiChau
TamDuong
NamGiang
MuongTe
VuQuangYenBai
BaoLacHaGiang
BacMe
VIETNAM
CHINA
LAOS
CAMBODIA
THAILAND
Da
Thao Lo
Red-Thai Binh River System - Vietnam
Hoa Binh reservoir - Vietnam
Main characteristics
• Catchment area 52,000 km2
• Active capacity 6 x 109 m3
• 8 penstocks 2,360 m3/s (240 MW)
• 12 bottom gates 22,000 m3/s
• 6 spillways 14,000 m3/s
• 15% national energy (7,800 GWh)
source: IWRP2008
Operating objectives • Hydropower production
• Flood control (Hanoi)
RESERVOIR
CATCHMENT
POWER PLANT
DIVERSION DAM
COMSUMPTIVE USE THAO
LO
DA
HOABINH
Experiment setting
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
ex post VEI estimation
5. re-ESTIMATE the VEI
4. REOPTIMIZE the POLICY
Experiment setting
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
ex post VEI estimation
5. re-ESTIMATE the VEI
4. REOPTIMIZE the POLICY
Deterministic Dynamic Programming
Experiment setting
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
ex post VEI estimation
5. re-ESTIMATE the VEI
4. REOPTIMIZE the POLICY
Deterministic Dynamic Programming
Tree Based Input variable selection (Galelli & Castelletti, 2013)
Experiment setting
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
ex post VEI estimation
5. re-ESTIMATE the VEI
4. REOPTIMIZE the POLICY
Deterministic Dynamic Programming
Tree Based Input variable selection (Galelli & Castelletti, 2013)
Multi-Objective Evolutionary Direct
Policy Search (Giuliani et al. 2014)
MONSOON
Upper bound (perfect foresight)
floods [cm2]
50 100 150 200 250 300 3503
4
5
6
7
8
9
10 x 109
0
sto
rag
e [
m3 ]
doy
average storage 6
7
8
9
10
11
12
13
7/16/2002 7/26/2002 8/05/2002 8/15/2002 8/25/2002
1st flood alarm level @ Hanoi
leve
l [m
]
behaviour on a flood
0 100 200 300 400 500 600 700 800 9002.1
2.15
2.2
2.25
2.3
2.35
2.4
2.45
2.5
2.55 x 107
Pareto frontier
hyd
rop
ow
er
[kW
h]
RESERVOIR
CATCHMENT
POWER PLANT
DIVERSION DAM
COMSUMPTIVE USE THAO
LO
DA
HOABINH
Candidate variable selection
Hanoi
HoaBinh
TaBu
LaiChau
TamDuong
NamGiang
MuongTe
VuQuangYenBai
BaoLacHaGiang
BacMe
VIETNAM
CHINA
LAOS
CAMBODIA
THAILAND
Da
Thao Lo
• precipitations
• areal precipitation
• streamflows
• doy and storage
Candidate variable selection
Hanoi
HoaBinh
TaBu
LaiChau
TamDuong
NamGiang
MuongTe
VuQuangYenBai
BaoLacHaGiang
BacMe
VIETNAM
CHINA
LAOS
CAMBODIA
THAILAND
Da
Thao Lo
• precipitations
• areal precipitation
• streamflows
• doy and storage
0
0.1
0.2
0.3
0.4
0.5
0.6
0.70.75
R2
doy s(t) qV(t) qTB(t) ….
50 100 150 200 250 300 3503
4
5
6
7
8
9
10 x 109
06
7
8
9
10
11
12
13
7/16/2002 7/26/2002 8/05/2002 8/15/2002 8/25/2002
0 100 200 300 400 500 600 700 800 9002.1
2.15
2.2
2.25
2.3
2.35
2.4
2.45
2.5
2.55 x 107
MONSOON
Basic information (doy, i.e. rule curve)
floods [cm2]
50 100 150 200 250 300 3503
4
5
6
7
8
9
10 x 109
0
sto
rag
e [
m3 ]
doy
average storage
Pareto frontier
hyd
rop
ow
er
[kW
h]
1st flood alarm level @ Hanoi
leve
l [m
]
behaviour on a flood
0
0.1
0.2
0.3
0.4
0.5
0.6
0.70.75
R2 policy parameters
doy
MONSOON
0 100 200 300 400 500 600 700 800 9002.1
2.15
2.2
2.25
2.3
2.35
2.4
2.45
2.5
2.55 x 107
50 100 150 200 250 300 3503
4
5
6
7
8
9
10 x 109
06
7
8
9
10
11
12
13
7/16/2002 7/26/2002 8/05/2002 8/15/2002 8/25/2002
Basic information (doy + s(t))
floods [cm2]
sto
rag
e [
m3 ]
doy
average storage
Pareto frontier
hyd
rop
ow
er
[kW
h]
1st flood alarm level @ Hanoi
leve
l [m
]
behaviour on a flood
0
0.1
0.2
0.3
0.4
0.5
0.6
0.70.75
R2 policy parameters
doy s(t)
MONSOON
0 100 200 300 400 500 600 700 800 9002.1
2.15
2.2
2.25
2.3
2.35
2.4
2.45
2.5
2.55 x 107
50 100 150 200 250 300 3503
4
5
6
7
8
9
10 x 109
06
7
8
9
10
11
12
13
7/16/2002 7/26/2002 8/05/2002 8/15/2002 8/25/2002
Improved policy (doy + s(t) + qv(t))
floods [cm2]
sto
rag
e [
m3 ]
doy
average storage
Pareto frontier
hyd
rop
ow
er
[kW
h]
1st flood alarm level @ Hanoi
leve
l [m
]
behaviour on a flood
0
0.1
0.2
0.3
0.4
0.5
0.6
0.70.75
R2 policy parameters
doy s(t) qv(t)
MONSOON
0 100 200 300 400 500 600 700 800 9002.1
2.15
2.2
2.25
2.3
2.35
2.4
2.45
2.5
2.55 x 107
50 100 150 200 250 300 3503
4
5
6
7
8
9
10 x 109
06
7
8
9
10
11
12
13
7/16/2002 7/26/2002 8/05/2002 8/15/2002 8/25/2002
Improved policy (doy + s(t) + qv(t) + qtb(t))
floods [cm2]
sto
rag
e [
m3 ]
doy
average storage
Pareto frontier
hyd
rop
ow
er
[kW
h]
1st flood alarm level @ Hanoi
leve
l [m
]
behaviour on a flood
0
0.1
0.2
0.3
0.4
0.5
0.6
0.70.75
R2 policy parameters
doy s(t) qv(t) qtb(t)
Estimating the Value of Exogenous Information
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
c) hypervolumea) minimum (normalized)distance from targetsolution
b) average (normalized)distance from targetsolution
Our approach vs ISO
automatic feature
selection
stochastic optimization
selected policy
arguments
improved policy
candidate variable selection
hydroclimatic time series
candidate policy arguments
ideal release trajectories deterministic
optimization
future inflow time series
ideal storage trajectories
ex ante VEI estimation
1. COMPUTE the UPPER BOUND
2. ESTIMATE the VEI
3. SELECT the BEST INFO
ex post VEI estimation
5. re-ESTIMATE the VEI
4. REOPTIMIZE the POLICY
0 100 200 300 400 500 600 700 800 9002
2.1
2.2
2.3
2.4
2.5
2.6 x 107
flood
hydr
opow
er
DDPI = (doy)I = (doy,st)
I = (doy,st,Vq)I = (doy,st,Vq,Ta)
EMODPS ISO
targetsolution
Our approach vs ISO
NUMERICAL RESULTS Lake Como - Italy
Lake Como system - Italy
Main characteristics
• Catchment area 4,509 km2
• Active capacity 2.47 x 106 m3
• Average annual supply 4,4 x 109 m3
• Irrigated area 1,320 km2
• 52% maize (1.5 x 106 ton/year)
Operating objectives • Water supply
• Flood control (Como)
River Adda
River Adda
R1
R2
H2
H3
H1
Kilometers0 5 10 20 30 40 50
LegendCatchment area
Irrigated area
Hydropower plant
Reservoir
LakeComo
Lake Como system - Italy
Main characteristics
• Catchment area 4,509 km2
• Active capacity 2.47 x 106 m3
• Average annual supply 4,4 x 109 m3
• Irrigated area 1,320 km2
• 52% maize (1.5 x 106 ton/year)
Operating objectives • Water supply
• Flood control (Como)
J F M A M J J A S O N D50
100
150
200
250
Dem
and
[m3 /
s]
(a)
J F M A M J J A S O N D0
500
1000
1500
2000
2500
Pric
e [e
uro/
MW
]
(b)
J F M A M J J A S O N D−20’000
−10’000
0
10’000
20’000
30’000
Reve
nue [euro
/day]
(c)
Time [days]
FIG. 5. (a): Yearly pattern of water demand. (b): Yearly pattern of the energy price(each colour band represents the energy price in the j-th most profitable hour). (c):Di↵erence in daily hydropower revenue (14-days moving average over years 1996-2005)between centralized policy C6 and uncoordinated UC.
25
water demand
J F M A M J J A S O N D0
10
20
30
40
Flow
[m3 /s]
Inflow Release
J F M A M J J A S O N D50
100
150
200
250
Flow
[m3 /s]
Time [days]
(a)
(b)
FIG. 2. Historical inflow (dashed) and release (solid) of the hydropower reservoir R1(a) and lake Como (b) (14-days moving median over the period 1996-2005).
22
inflow/outflow
River Adda
River Adda
R1
R2
H2
H3
H1
Kilometers0 5 10 20 30 40 50
LegendCatchment area
Irrigated area
Hydropower plant
Reservoir
LakeComo
Upper bound (perfect foresight)
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
Pareto frontier
qt+1
st
FLOODS
qt
st
ut
IRRIGATION
Candidate variable selection
• doy
• lake level h(t)
• areal solid precipitation (t-1)
• areal rainfall (t-1)
• 0 °C isotherm (t-1)
Candidate variable selection
Hydropower reservoirs:
• Inflow q(t-1)
• Storage s(t)
• Release r (t-1)
Candidate variable selection
areal SWE and melting inferred from SWE stations
• total SWE(t)
• free SWE(t)
• total melting(t)
• free melting(t)
Candidate variable selection
• doy and h(t) Como
• precipitation rain and 0 °C isotherm
• HP reservoirs: q(t-1), s(t) and r(t-1)
• SWE(t) and melting(t)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
R2
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
R2
policy parameters Pareto frontier
Basic information (doy)
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
policy parameters
R2
Pareto frontier
Basic information (doy+h(t))
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
policy parameters
R2
Pareto frontier
Basic information (doy+h(t)+q(t-1))
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
policy parameters
R2
Pareto frontier
Basic information (doy+h(t)+q(t-1)+free SWE(t))
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
policy parameters
R2
Pareto frontier
Basic information (doy+h(t)+q(t-1)+free SWE(t)+prec(t-1))
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
policy parameters
R2
Pareto frontier
Basic information (doy+h(t)+q(t-1)+free SWE(t)+prec(t-1)+s(t))
Yearly days of flood [#]
Irrig
atio
n d
efic
it2 [
(m2 /
s)2 ]
Conclusions
§ Enlarging the information system used to make decision might be a way to
improve operation efficiency and ultimately reduce vulnerability
§ Tools and procedure to quantitatively assess the space for improvement
and identify the most informative variables are very useful.
§ Skipping the use of models and directly using raw information seems to be
an interesting option when streamflow prediction are not available ….