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Steinmann, Victor
Learning Python
Commits
34b90daa
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34b90daa
authored
5 months ago
by
Steinmann
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redone flow requirement objectivbe
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optimierung_pymoo.ipynb
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34b90daa
...
...
@@ -219,7 +219,7 @@
},
{
"cell_type": "code",
"execution_count": 1
2
,
"execution_count": 1
6
,
"metadata": {},
"outputs": [
{
...
...
@@ -260,13 +260,14 @@
" ) for i in modell.pumps)\n",
"modell.Power_Objective = pyo.Objective(rule=PumpPower,sense=pyo.minimize)\n",
"def PumpFlow(modell,pump):\n",
" pump=np.dot(np.array([modell.Q[pump]**2,modell.n[pump]*modell.Q[pump],modell.n[pump]**2]),LR_H.coef_)\n",
" return pump>=sum(modell.Q_valve[node] for node in graph.successors(pump) if node in modell.valves)+sum(modell.Q[n] for n in graph.successors(node) if node in modell.pumps)\n",
"#modell.Flow_Objective = pyo.Objective(rule=PumpFlow,sense=pyo.as_boolean)\n",
" return np.dot(np.array([modell.Q[pump]**2,modell.n[pump]*modell.Q[pump],modell.n[pump]**2]),LR_H.coef_)\n",
"def Flow_req(modell,p):\n",
" return PumpFlow(modell,p) - pyo.summation(modell.Q,index=graph.successors(p))\n",
"modell.Flow_Objective = pyo.Objective(modell.pumps,rule=Flow_req,sense=pyo.minimize)\n",
"\n",
"#Constaints\n",
"def continuityRule(modell,node):\n",
" return
sum(modell.Q[i] for i in graph.predecessors(node))==sum(modell.Q[j] for j in
graph.successors(node))\n",
" return
pyo.summation(modell.Q, index=graph.predecessors(node))==pyo.summation(modell.Q, index=
graph.successors(node))\n",
"#alternative\n",
"def continuityRule2(modell,node):\n",
" return 0.==sum(graph[node][i][0]['weight'] for i in graph[node])\n",
...
...
@@ -303,7 +304,7 @@
},
{
"cell_type": "code",
"execution_count": 1
3
,
"execution_count": 1
7
,
"metadata": {},
"outputs": [],
"source": [
...
...
%% Cell type:markdown id: tags:
Formulieren der Optimierungsgleichung in pymoo
%% Cell type:markdown id: tags:
Es gilt die Kontinuitätsgleichung:
$
\S
igma
\d
ot{V}_k(t) = O$
und die aus der Topologie resultierende Inzidenzmatrix $A_i$
sowie die aus dem Pumpenkennfeld folgende Beziehung:
$
\D
elta p=
\a
lpha_1 Q^2+
\a
lpha_2 Q n+
\a
lpha_3 n^2 : n
\i
n
\{
0
\}
\c
up [n_{
\m
athrm{min}},n_{
\m
athrm{max}}] $
$P=
\b
eta_1 Q^3+
\b
eta_2 Q^2 n+
\b
eta_3 Q n^2+
\b
eta_4n^3+
\b
eta_5$
und die beziehung für den Druckverlust an den Ventilen:
$
\D
elta p_{
\m
athrm{loss}} = -
\f
rac{1}{2}
\v
arrho
\z
eta
\l
eft(
\f
rac{Q}{A}
\r
ight)^2 = -l Q^2 :l
\i
n [l_{
\m
athrm{min}}:
\i
nfty )$
nun soll für einen Gegebenen Volumenstrom $Q$ eine Optimale Drehzahl bestimmt werden, welche die Pumpenlesitung minimiert.
$$
\b
egin{align
*
}
\m
athrm{min}
\s
um_{p
\i
n
\m
athcal{P}} Po_{p}
\\
Q_{p,i}
\g
eq
\s
um_{strang} Q_v +
\s
um_{strang} Q_p
\\
Q_p , n
\e
psilon [n_{min},n_{max}]
\\
\o
verrightarrow{n} = (1,n,n^2,n^3)^T
\\
min P = A
\o
verrightarrow{n}
\\
-n
\l
eq n_{min}
\\
n
\l
eq n_{max}
\e
nd{align
*
}
$$
Förderhöhe als constraint continuität fomulieren pro strang
%% Cell type:code id: tags:
```
python
!
pip
install
pyomo
```
%% Output
Defaulting to user installation because normal site-packages is not writeable
Requirement already satisfied: pyomo in c:\users\steinmann\appdata\roaming\python\python312\site-packages (6.8.2)
Requirement already satisfied: ply in c:\users\steinmann\appdata\roaming\python\python312\site-packages (from pyomo) (3.11)
[notice] A new release of pip is available: 24.2 -> 25.0
[notice] To update, run: C:\Program Files\Python312\python.exe -m pip install --upgrade pip
%% Cell type:code id: tags:
```
python
#Pump-Powercurve and Pump-Hightcurve
import
regression_own
(
LR_H
,
LR_P
)
=
regression_own
.
regress_pump
()
```
%% Output
R^20.9998289611292903
R^20.9994449560888792
%% Cell type:code id: tags:
```
python
#Graph constroctor
#Alle Ventile sind direkt mit der Quelle/Senke Verbunden
import
multiDiGraph
as
gr
nodes
=
[
'
source
'
,
'
pump1
'
,
'
pump2
'
,
'
valveA
'
,
'
valveB
'
,
'
valveC
'
]
graph
=
gr
.
construct_graph
(
'
source
'
,(
'
source
'
,
'
pump1
'
,
0.
),(
'
pump1
'
,
'
pump2
'
,
0.
),(
'
pump2
'
,
'
valveA
'
,
0.
),(
'
pump2
'
,
'
valveB
'
,
0.
),
(
'
pump1
'
,
'
valveC
'
,
0.
),(
'
valveA
'
,
'
source
'
,
4.
),(
'
valveB
'
,
'
source
'
,
4.
),(
'
valveC
'
,
'
source
'
,
4.
))
#ist das notwendig?!?
for
node
in
graph
.
nodes
:
#definieren der Drehzahl für jede Pumpe im graphen
#inizieren des Durchflusses für jedes Ventil im Graphen
if
'
pump
'
in
node
:
graph
.
nodes
[
node
][
'
n
'
]
=
750
/
3600
else
:
graph
.
nodes
[
node
][
'
n
'
]
=
None
graph
.
nodes
[
node
][
'
flow
'
]
=
0.
if
'
valve
'
in
node
:
graph
.
nodes
[
node
][
'
flow
'
]
=
graph
[
node
][
'
source
'
][
0
][
'
weight
'
]
for
node
in
graph
.
nodes
:
#Berechnen des Durchflusses im Knoten
if
'
valve
'
in
node
:
continue
for
inF
in
graph
.
predecessors
(
node
):
graph
.
nodes
[
node
][
'
flow
'
]
+=
graph
[
inF
][
node
][
0
][
'
weight
'
]
#Berechnen des Durchflusses der abgehenden Kanten
tempF
=
graph
.
nodes
[
node
][
'
flow
'
]
SC
=
0
for
outF
in
graph
.
successors
(
node
):
if
'
valve
'
in
outF
:
graph
[
node
][
outF
][
0
][
'
weight
'
]
=
graph
.
nodes
[
outF
][
'
flow
'
]
tempF
=
tempF
-
graph
.
nodes
[
outF
][
'
flow
'
]
else
:
SC
+=
1
for
outF
in
graph
.
successors
(
node
):
if
SC
!=
0.
and
not
'
valve
'
in
outF
:
graph
[
node
][
outF
][
0
][
'
weight
'
]
=
tempF
/
SC
else
:
continue
print
(
graph
.
nodes
.
data
(
'
flow
'
))
```
%% Output
[('source', 12.0), ('pump1', 12.0), ('pump2', 8.0), ('valveA', 4.0), ('valveB', 4.0), ('valveC', 4.0)]
%% Cell type:code id: tags:
```
python
import
networkx
as
nx
Mtrx
=
nx
.
incidence_matrix
(
graph
,
nodes
,
oriented
=
True
)
```
%% Cell type:code id: tags:
```
python
import
networkx
as
nx
def
create_dict
(
GR
:
nx
.
multidigraph
):
data
=
{
None
:{
'
nodes
'
:{},
'
pumps
'
:{},
'
valves
'
:{},
}
}
for
node
in
GR
.
nodes
:
data
[
None
][
'
nodes
'
][
node
]
=
None
data
[
None
][
'
Q
'
][
node
]
=
GR
.
nodes
[
node
][
'
flow
'
]
if
'
pump
'
in
node
:
data
[
None
][
'
pumps
'
][
node
]
=
None
data
[
None
][
'
n
'
][
node
]
=
0.
if
'
valve
'
in
node
:
data
[
None
][
'
valves
'
][
node
]
=
None
return
data
```
%% Cell type:markdown id: tags:
Durchfluss aus Incidenzmatrix beerechnen
Zeilen = knoten
Spalten = kanten
Summe pro knoten = 0
Q pump muss größer gleich sein als alle nachfolgenden durchflüsse
%% Cell type:code id: tags:
```
python
#defining abstract modell for given Network
import
pyomo.environ
as
pyo
from
pyomo.dataportal
import
DataPortal
import
numpy
as
np
from
sklearn.linear_model
import
LinearRegression
modell
=
pyo
.
AbstractModel
()
#notwendige Mengen zur Berechnung der Constraints
modell
.
nodes
=
pyo
.
Set
()
modell
.
pumps
=
pyo
.
Set
()
modell
.
valves
=
pyo
.
Set
()
modell
.
Q_valve
=
pyo
.
Param
(
modell
.
valves
)
#Optimierungsvariable
modell
.
n
=
pyo
.
Var
(
modell
.
pumps
,
bounds
=
(
750
/
3600
,
1
))
modell
.
Q
=
pyo
.
Var
(
modell
.
nodes
)
#Objective
def
PumpPower
(
modell
):
return
sum
(
np
.
dot
(
np
.
array
(
[
modell
.
Q
[
i
]
**
3
,(
modell
.
Q
[
i
]
**
2
)
*
modell
.
n
[
i
],
modell
.
Q
[
i
]
*
modell
.
n
[
i
]
**
2
,
modell
.
n
[
i
]
**
3
]
),
LR_P
.
coef_
)
for
i
in
modell
.
pumps
)
modell
.
Power_Objective
=
pyo
.
Objective
(
rule
=
PumpPower
,
sense
=
pyo
.
minimize
)
def
PumpFlow
(
modell
,
pump
):
pump
=
np
.
dot
(
np
.
array
([
modell
.
Q
[
pump
]
**
2
,
modell
.
n
[
pump
]
*
modell
.
Q
[
pump
],
modell
.
n
[
pump
]
**
2
]),
LR_H
.
coef_
)
return
pump
>=
sum
(
modell
.
Q_valve
[
node
]
for
node
in
graph
.
successors
(
pump
)
if
node
in
modell
.
valves
)
+
sum
(
modell
.
Q
[
n
]
for
n
in
graph
.
successors
(
node
)
if
node
in
modell
.
pumps
)
#modell.Flow_Objective = pyo.Objective(rule=PumpFlow,sense=pyo.as_boolean)
return
np
.
dot
(
np
.
array
([
modell
.
Q
[
pump
]
**
2
,
modell
.
n
[
pump
]
*
modell
.
Q
[
pump
],
modell
.
n
[
pump
]
**
2
]),
LR_H
.
coef_
)
def
Flow_req
(
modell
,
p
):
return
PumpFlow
(
modell
,
p
)
-
pyo
.
summation
(
modell
.
Q
,
index
=
graph
.
successors
(
p
))
modell
.
Flow_Objective
=
pyo
.
Objective
(
modell
.
pumps
,
rule
=
Flow_req
,
sense
=
pyo
.
minimize
)
#Constaints
def
continuityRule
(
modell
,
node
):
return
sum
(
modell
.
Q
[
i
]
for
i
in
graph
.
predecessors
(
node
))
==
sum
(
modell
.
Q
[
j
]
for
j
in
graph
.
successors
(
node
))
return
pyo
.
summation
(
modell
.
Q
,
index
=
graph
.
predecessors
(
node
))
==
pyo
.
summation
(
modell
.
Q
,
index
=
graph
.
successors
(
node
))
#alternative
def
continuityRule2
(
modell
,
node
):
return
0.
==
sum
(
graph
[
node
][
i
][
0
][
'
weight
'
]
for
i
in
graph
[
node
])
#continuity adjustment for change in hight needed
#construction of test Data dictionairy missing
TestData
=
{
None
:{
'
nodes
'
:[
key
for
key
in
graph
.
nodes
.
keys
()],
'
pumps
'
:[
key
for
key
in
graph
.
nodes
.
keys
()
if
'
pump
'
in
key
],
'
valves
'
:[
key
for
key
in
graph
.
nodes
.
keys
()
if
'
valve
'
in
key
],
'
Q_valve
'
:{
'
valveA
'
:
4.
,
'
valveB
'
:
4.
,
'
valveC
'
:
4.
},
}
}
print
(
TestData
)
#data=DataPortal(data_dict=TestData)
#Optimierungsgleichung
#modell.pump_constraint = pyo.Constraint(expr=sum(modell.nodes[k] for k in modell.nodes)==0,rule=continuityRule)
#instance=modell.create_instance(graph,LR_H)
#instance.obj = pyo.Objective(expr=sum(PumpPower(modell.Q[i],modell.n[i],LR_P) for i in modell.pumps),sense=min)
```
%% Output
{None: {'nodes': ['source', 'pump1', 'pump2', 'valveA', 'valveB', 'valveC'], 'pumps': ['pump1', 'pump2'], 'valves': ['valveA', 'valveB', 'valveC'], 'Q_valve': {'valveA': 4.0, 'valveB': 4.0, 'valveC': 4.0}}}
%% Cell type:markdown id: tags:
Frage: gibt es nur eine Lösung für Drehzahl?
Bsp. Optimierung nach Dezentraler Pumpe um modell zu prüfen
%% Cell type:code id: tags:
```
python
from
pyomo.opt
import
SolverFactory
#opt = pyo.SolverFactory('scipampl', executable=r'C:\Program Files\SCIPOptSuite 9.2.0\bin\scip.exe')
instance
=
modell
.
create_instance
(
TestData
)
instance
.
Continuity_constaint
=
pyo
.
Constraint
(
instance
.
nodes
,
rule
=
continuityRule
)
#result=opt.solve(instance, tee=True)
```
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