other components canals and diversions andrea castelletti politecnico di milano nrml13
TRANSCRIPT
Other componentscanals and diversions
Andrea CastellettiPolitecnico di Milano
NRMNRML13L13
2
Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
SAN GIACOMO (SG)
Irrigation District(CBN)
S. LUCIA (SL)
PROVVIDENZA (P)
3
Canal
• the peak’s propagation velocity w is greater than the average velocity v;
• the difference (w-v) increases with the depth H of the stream.
space
inst
anta
neou
s flo
w
4
• The peak time increases with the distance;
• The peak flow decreases with the distance;
• Hydrographs are a-symmetrical and widen;
Canal: storing effectsec. 1
sec. 2
sec. 3
control sections
elementary unit
time
inst
anta
neou
s flo
wsto
ring ef
fect
(flow buffe
ring)
storin
g effec
t
(flow buffe
ring)
5
Example: the Po river
l1
l2
l3
l4
l5
tSEP OCT NOV
Hydrometric plots for 5 stations (li)
h
6
Canal: causal network
qt+1v
q
t+?m
q
t+?m
at+1
qt+1v
at+1
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Canal: mechanistic model
qt+1v
q
t+1v =qt−τ +1
m + at+1
Travel time
x
t=qt
m qt−1m ... qt−τ +1
m Tstate
xt+1 =
01M0
00M0
..
..
..
..
..
..
00M1
00M0
xt +
10M0
qt+1m
q
t+1v = 0 0 ... 0 1 xt + at+1
internal representation
plug-flow
at+1
q
t+?m
8
Canal: the delay τ
qt+1v
q
t−τ +1m
q
t+1v =qt−τ +1
m + at+1
If τ = 0 the system is a non-dynamic one: the state does not exist.
To reduce the computing time in solving the design problem, the more convenient solution would be to fix in a way that τ be equal to zero.
But how to determine τ ? ....
plug-flow
at+1
9
Canal: how to determine τIf one is able to observe a flood wave ..
… but if this is not possible?
use the cross-correlogram
τ
τ
t
t
qtm
qtv
t
t qt
v
qtm
upstream
downstream
τ
computed using whitened series
10
correlation ρcorrelation ρ ρxy is a statistics of x and y measuring
the strenghtness of the link between x
and y
if x = α y → |ρxy| = 1
Correlation
−1< xy <1if x = α y + εwhite → |ρxy| < 1
if x = εwhite → ρxy = 0
provides an estimate of
rxy=
(xt −μx)∑ (yt −μy)
(xt −μx)∑⎡⎣ ⎤⎦2
(yt −μy)∑⎡⎣ ⎤⎦2 xy
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yt yt+τ
τ( )
τ
(Self)correlogram
It measures the correlation of the pair
1
… separated by different time intervals …… separated by different time intervals …
ττ
Pairs of variablesPairs of variables
( yt , yt+τ ) as a function of τ :( yt , yt+τ ) as a function of τ :
… of which we are interested in the strenghtness of the link.
… of which we are interested in the strenghtness of the link.
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1ta 1ta
Canal: leakage
qt+1v
q
t−τ +1m
q
t+1v =qt−τ +1
m + at+1
If the leakage does not change with the time
q
t+1v =qt−τ +1
m −at+1
q
t+1v =(1−α) qt−τ +1
m
If the leakage changes with the time
In this way is never negative even for very small value of the entring flow.
qt+1v
plug-flow
−αqt−τ +1
m
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Detention areas
Structural interventions that create a storage upstream where part of the inflow is retained when the flow rate is partuclarly high. They can be of 3 types::
• detention areas
Produce a narrowing of the riverbed
Produce an increase in the canal section when the flow is above a given value
They can be modeled as the aggregation of two components:
a reservoir and a canal
• detention basin
• dry dams
ht+1c
hts
at+1 h
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Detention areas
qt+1m
qt+1v
canal at+1
reservoir
st
qt+1v =qt+1
m −a qt+1m ,q,st( )
st+1 =st + a qt+1m ,q,st( )
If travel times can be neglected
Recession phase
ht+1c ht
s
at+1 h
Concentration phase
ht+1c
hts
at+1 h
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Detention areas
qt+1m
qt+1v
canal at+1
reservoir
st
By assuming that:
• stage-discharge curve of the canal is linear
, vale a dire ; qt+1
m > q
• the reservoir is cylindirc, i.e. ; st
=βhts
• The stage-discharge curve between the canal and the reservois is linear in the difference of the levels
qt+1v =qt+1
m + a qt+1m ,q,st( )
st+1 =st −a qt+1m ,q,st( )
at+1 =a qt+1
m ,q,st( ) =
0 if st=0 e q
t+1
m≤q
γq
t+1
m−q
α−
st
β
⎛⎝⎜
⎞⎠⎟ otherwise
⎧
⎨⎪
⎩⎪
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The model of a planned canal
If the canal is going to be planned its model should include up.
Each value of up correspond to a different alternative.
Typical situation: the canal has to be sized
In that case up is the maximum flow conveyable into the canal
q
t+1v =min qt+1
m ,up{ }
up = 0 is the business as usual alternative: do not do nothing
!
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Step-indicator of a canal
A step indicator is often associated to the canal
g
t+1 =gt qt+1m( )
For example:
• the damage produced by floods along the canal shores
• the environmental cost due to low flow rates
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Diversion (dam): structure
A branch point is usually an artificial work called diversion dam.
back-flow profile
spillway crest
bank of the water course bank of the
water course
inlet
dam
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qmax
Diversion (dam)
Features:
• entirely or partly channels the flow into a diversion canal
• can be equipped with mobile parts (usually sluice gates) for regulating the channelled flow.
riverbed
canal
• the diversion canal flow rate (qmax) is limited thorugh a crest spillways.
A branch point is usually an artificial work called diversion dam.
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Diversion (dam): causal network
qt+1
m
qt+1d
ut
qt+1v
qt+1v
qt+1m
ut qt+1d
1mtq
1dtq
1vtq
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Diversion (dam): mechanistic model
Non-regulated diversion
Regulated diversion:
qt+1d =min ut ,qt+1
m ,qmax⎡⎣ ⎤⎦
qt+1v =qt+1
m −qt+1d
⎧⎨⎪
⎩⎪
qt+1d =min qt+1
m ,qmax⎡⎣ ⎤⎦
qt+1v =qt+1
m −qt+1d
⎧⎨⎪
⎩⎪
q
t+1d =min ut ,(qt+1
m −qtMEF )+ ,qmax
⎡⎣ ⎤⎦
… diversion with a MEF:
q
max
qt+1m
qt+1d
qt+1m
qt+1d
q
max
ut
qt+1d ≠0 ut > 0 and
(qt+1m −qt
MEF ) > 0
only if:
−qt
DMV( )+
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Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
SAN GIACOMO (SG)
Irrigation district(CBN)
S. LUCIA (SL)
PROVVIDENZA (P)
23
Features of the reservoirs
4.954950 000Piaganini
5.5851 690 000Provvidenza
975.461.8217 000 000Campotosto
Ts [hours]
qmax [m3/sec]Vactive [m3]
T
s=
Vactive
qmaxtime for
emptying
3.530380 000V. Vomano
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Piaganini
25
Adriatic Sea
Fucino
VILLA VOMANO
PIAGANINI
PROVVIDENZA
CAMPOTOSTO
MONTORIO (M)
SAN GIACOMO (SG)
Irrigation district(CBN)
S. LUCIA (SL)
PROVVIDENZA (P)
26Adriatic Sea
VILLA VOMANO
PROVVIDENZA
(M)
(P)
(SG)
Irrigation district(SL)
PIAGANINI
CAMPOTOSTO
27Adriatic Sea
VILLA VOMANO
PROVVIDENZA
(M)
(P)
(SG)
Irrigationdistrict(SL)
PIAGANINI
CAMPOTOSTO
Ppumping
SGpumping
Problems:
• only ENEL is interested in the internal water cycling;
• a daily modelling time step is too large to accurately describe the phenomenon.
Problems:
• only ENEL is interested in the internal water cycling;
• a daily modelling time step is too large to accurately describe the phenomenon.
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P
SG
M
SL
DMV Fucino
MEF Vomano
PIAGANINI
CAMPOTOSTO PROVVIDENZA
VILLA VOMANODistretto irriguo(CBN)
P_pomp
SG+P_pomp
Acquedotto del Ruzzo
DMV Montorio
Schema logico corretto
Advantages:
• only the minimun value of release and pumping are decided, while ENEL is let free to increase these value to cope with the availability/demand of the national grid.
Advantages:
• only the minimun value of release and pumping are decided, while ENEL is let free to increase these value to cope with the availability/demand of the national grid.
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Pumping:
u2 ≤pMAX
SG
u1 +u2 ≤pMAX
Pr
Hydroelectric constraints
P
SG
M
SL
MEF2 Fucino
MEF1 Vomano
Irrigation district(CBN)
P_pump
SG+P_pump
Ruzzo Water Works
MEF Montorio
u2
u1
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Confluence point
The model of a confluence point is a simple algebraic expression.
q
t+1v = qt+1
m,i
i=1
n
∑
qt+1m,1
qt+1m,2
qt+1m,3
qt+1v
Being i=1,...,n in coming canals, the model has the following form:
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P
SG
M
SL
MEF Fucino
MEF Vomano
PIAGANINI
CAMPOTOSTO PROVVIDENZA
VILLA VOMANOIrrigation district(CBN)
P_pump
SG+P_pump
Ruzzo water works
MEF Montorio
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Reading
IPWRM.Theory Ch. 5