mathematical modelling, simulation and optimization using...
TRANSCRIPT
![Page 1: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/1.jpg)
CRC/Transregio 154Mathematical Modelling, Simulation and Optimization
using the Example of Gas Networks
Alexander Martin15.03.2015
![Page 2: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/2.jpg)
CRC/Transregio 154Overview
Alexander Martin
![Page 3: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/3.jpg)
Mathematical modeling, simulation, and optimization
Modeling and numerical simulationexistence, uniqueness, regularityeffizient algorithms, convergence, error control
Nonlinear optimization and controlefficient algorithms, convergence, error controllocal optima and their characterization
Integer programmingglobally optimalanalysis of the solution space c
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 3
![Page 4: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/4.jpg)
Mathematical modeling, simulation, and optimization
Modeling and numerical simulationexistence, uniqueness, regularityeffizient algorithms, convergence, error control
Nonlinear optimization and controlefficient algorithms, convergence, error controllocal optima and their characterization
Integer programmingglobally optimalanalysis of the solution space c
Coupling: integer and continuous
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 3
![Page 5: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/5.jpg)
Mathematical modeling, simulation, and optimization
Modeling and numerical simulationexistence, uniqueness, regularityeffizient algorithms, convergence, error control
Nonlinear optimization and controlefficient algorithms, convergence, error controllocal optima and their characterization
Integer programmingglobally optimalanalysis of the solution space c
Coupling: integer and continuousactive research area
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 3
![Page 6: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/6.jpg)
Mathematical modeling, simulation, and optimization
Modeling and numerical simulationexistence, uniqueness, regularityeffizient algorithms, convergence, error control
Nonlinear optimization and controlefficient algorithms, convergence, error controllocal optima and their characterization
Integer programmingglobally optimalanalysis of the solution space c
Coupling: integer and continuous with uncertaintyactive research areauncertain data
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 3
![Page 7: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/7.jpg)
Mathematical modeling, simulation, and optimization
Modeling and numerical simulationexistence, uniqueness, regularityeffizient algorithms, convergence, error control
Nonlinear optimization and controlefficient algorithms, convergence, error controllocal optima and their characterization
Integer programmingglobally optimalanalysis of the solution space c
Coupling: integer and continuous with uncertaintyactive research areauncertain datageneral methods out-of-reach
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 3
![Page 8: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/8.jpg)
Gas networks
Networks are inherently discreteVentil a with switching variable sa ∈ {0, 1}
sa = 0 ⇒ qa = 0sa = 1 ⇒ pi = pj
Physics are inherently continuous
∂ρ
∂t+
∂(ρv)∂x
= 0
∂(ρv)∂t
+∂(ρv2 + p)
∂x+ gρ
∂h∂x
+λ
2Dρ |v | v = 0
∂E∂t
+∂(Ev + pv)
∂x+ Aρvg
∂h∂x
+ π D cHT (T − Tsoil) = 0.
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 4
![Page 9: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/9.jpg)
Gas networks
Networks are inherently discrete/switchingVentil a with switching variable sa ∈ {0, 1}
sa = 0 ⇒ qa = 0sa = 1 ⇒ pi = pj
Physics are inherently continuous/switching
∂ρ
∂t+
∂(ρv)∂x
= 0
∂(ρv)∂t
+∂(ρv2 + p)
∂x+ gρ
∂h∂x
+λ
2Dρ |v | v = 0
∂E∂t
+∂(Ev + pv)
∂x+ Aρvg
∂h∂x
+ π D cHT (T − Tsoil) = 0.
PORZ_VS-S(11p/s, 12p/s)
PORZ_VS-H(5, 6)
PORZ_VS-H1(5, 6)
VA_193 VA_192 VA_198
VA_
VA_194 VA_195 VA_199
PI_798 VA_198O0003 80060012008
VA_192I
PI_799 VA_199O0004
VA_193O
PI_863
HEROS-H-S-FI
800600120010
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 4
![Page 10: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/10.jpg)
Gas networks
Networks are inherently discrete/switchingVentil a with switching variable sa ∈ {0, 1}
sa = 0 ⇒ qa = 0sa = 1 ⇒ pi = pj
Physics are inherently continuous/switching
∂ρ
∂t+
∂(ρv)∂x
= 0
∂(ρv)∂t
+∂(ρv2 + p)
∂x+ gρ
∂h∂x
+λ
2Dρ |v | v = 0
∂E∂t
+∂(Ev + pv)
∂x+ Aρvg
∂h∂x
+ π D cHT (T − Tsoil) = 0.
PORZ_VS-S(11p/s, 12p/s)
PORZ_VS-H(5, 6)
PORZ_VS-H1(5, 6)
VA_193 VA_192 VA_198
VA_
VA_194 VA_195 VA_199
PI_798 VA_198O0003 80060012008
VA_192I
PI_799 VA_199O0004
VA_193O
PI_863
HEROS-H-S-FI
800600120010
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 4
![Page 11: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/11.jpg)
Gas networks
Networks are inherently discrete/switchingVentil a with switching variable sa ∈ {0, 1}
sa = 0 ⇒ qa = 0sa = 1 ⇒ pi = pj
Physics are inherently continuous/switching
∂ρ
∂t+
∂(ρv)∂x
= 0
∂(ρv)∂t
+∂(ρv2 + p)
∂x+ gρ
∂h∂x
+λ
2Dρ |v | v = 0
∂E∂t
+∂(Ev + pv)
∂x+ Aρvg
∂h∂x
+ π D cHT (T − Tsoil) = 0.
PORZ_VS-S(11p/s, 12p/s)
PORZ_VS-H(5, 6)
PORZ_VS-H1(5, 6)
VA_193 VA_192 VA_198
VA_
VA_194 VA_195 VA_199
PI_798 VA_198O0003 80060012008
VA_192I
PI_799 VA_199O0004
VA_193O
PI_863
HEROS-H-S-FI
800600120010
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 4
![Page 12: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/12.jpg)
Gas networksGas networks are very big
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 5
![Page 13: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/13.jpg)
Gas networksGas networks are very big
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 5
![Page 14: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/14.jpg)
Gas networksGas networks are very big
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 5
![Page 15: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/15.jpg)
Gas networksGas networks are very big
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 5
![Page 16: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/16.jpg)
Gas networks
Gas plays a major role in the tranformation of the energysystem
Gas . . .is sufficiently available (within this time period)is promptly disposableis storableis traded
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 6
![Page 17: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/17.jpg)
Gas networks
Exact methods are necessaryin optimization andin simulation (via error estimators)
Entries
Exits
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 7
![Page 18: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/18.jpg)
Gas networks
Exact methods are necessaryin optimization andin simulation (via error estimators)
Entries
Exitsbooked capacity
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 7
![Page 19: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/19.jpg)
Gas networks
Exact methods are necessaryin optimization andin simulation (via error estimators)
Entries
Exitsbooked capacity
10 5
520
10
Nomination A
5 5
00
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 7
![Page 20: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/20.jpg)
Gas networks
Exact methods are necessaryin optimization andin simulation (via error estimators)
Entries
Exitsbooked capacity
10 5
520
10
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 7
![Page 21: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/21.jpg)
Gas networks
Exact methods are necessaryin optimization andin simulation (via error estimators)
Distinction stationary/instationary is relevantMarket assumes stationary situationsPhysics are instationary
Entries
Exitsbooked capacity
10 5
520
10
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 7
![Page 22: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/22.jpg)
Gas networks
Exact methods are necessaryin optimization andin simulation (via error estimators)
Distinction stationary/instationary is relevantMarket assumes stationary situationsPhysics are instationary
Uncertaintiesat the entry/exit nodesin the model parameters
Entries
Exitsbooked capacity
10 5
520
10
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 7
![Page 23: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/23.jpg)
Mathematical questions and goalsusing the example feasibility/infeasibility
In-/feasibilty of nominations
Consistent hierarchy of models and their coupling
Error estimators and controls
Exact methods and their coupling
We need ...a global mathematical understanding of the input/output behaviour ofoptimally controlled dynamic networks
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 8
![Page 24: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/24.jpg)
Teamwork
• Graduate school
• Integration in excellent existing structuresBMS, CE, ESE, EnCN, . . .
• common data base• Demonstrators
Demo OPT OPT SIM Un- ModelMINLP ODE/PDE certainty Coupling
Nomination A07 A01, A05, B02 C02 B04, B05, C03 B03
Power Plant A04 A02 C02, C04 A03
Storage B07, A05 A02 B01, C04 B06 B01, B03
Berlin, Darmstadt, Erlangen, Duisburg
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 9
![Page 25: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/25.jpg)
Teamwork
• Graduate school• Integration in excellent existing structures
BMS, CE, ESE, EnCN, . . .
• common data base• Demonstrators
Demo OPT OPT SIM Un- ModelMINLP ODE/PDE certainty Coupling
Nomination A07 A01, A05, B02 C02 B04, B05, C03 B03
Power Plant A04 A02 C02, C04 A03
Storage B07, A05 A02 B01, C04 B06 B01, B03
Berlin, Darmstadt, Erlangen, Duisburg
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 9
![Page 26: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/26.jpg)
Teamwork
• Graduate school• Integration in excellent existing structures
BMS, CE, ESE, EnCN, . . .• common data base
• Demonstrators
Demo OPT OPT SIM Un- ModelMINLP ODE/PDE certainty Coupling
Nomination A07 A01, A05, B02 C02 B04, B05, C03 B03
Power Plant A04 A02 C02, C04 A03
Storage B07, A05 A02 B01, C04 B06 B01, B03
Berlin, Darmstadt, Erlangen, Duisburg
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 9
![Page 27: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/27.jpg)
Teamwork
• Graduate school• Integration in excellent existing structures
BMS, CE, ESE, EnCN, . . .• common data base• Demonstrators
Demo OPT OPT SIM Un- ModelMINLP ODE/PDE certainty Coupling
Nomination A07 A01, A05, B02 C02 B04, B05, C03 B03
Power Plant A04 A02 C02, C04 A03
Storage B07, A05 A02 B01, C04 B06 B01, B03
Berlin, Darmstadt, Erlangen, Duisburg
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 9
![Page 28: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/28.jpg)
Teamwork within Demonstrator 1How to get from Nomination A to Nomination B
• •
• • •
Entries
Exits
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 10
![Page 29: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/29.jpg)
Teamwork within Demonstrator 1How to get from Nomination A to Nomination B
stationary/instationary:B07/07 Combinatorial decisions (on large networks)A01/05 Corresponding optimal control
C02 Physical Validation
• •
• • •
Entries
Exits
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 10
![Page 30: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/30.jpg)
Teamwork within Demonstrator 1How to get from Nomination A to Nomination B
stationary/instationary:B07/07 Combinatorial decisions (on large networks)A01/05 Corresponding optimal control
C02 Physical Validation
Complemented byC03 an analysis of reachabilityB03 regulation of the solution interfaces
• •
• • •
Entries
Exits
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 10
![Page 31: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/31.jpg)
Teamwork within Demonstrator 1How to get from Nomination A to Nomination B
stationary/instationary:B07/07 Combinatorial decisions (on large networks)A01/05 Corresponding optimal control
C02 Physical Validation
Complemented byC03 an analysis of reachabilityB03 regulation of the solution interfaces
Impact of uncertaintiesB04/05 Existence of flows with chance constraints
B02 Robust Identification of paramaters at smallscale
• •
• • •
Entries
Exits
Nomination A
5 5
00
10
Nomination B
10 5
520
10
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 10
![Page 32: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/32.jpg)
Topics across projects and sites
Topic Berlin Darmstadt Erlangen Essen
Discretization C02 C04, B01 C02
Uncertainty B04 B06, C03 B05, C03
Switching Systems A03 A02 B02
Infeasibility A07 A01 A05, B07
Error Estimators / Control B03, C02 B01 C02
Model Coupling A04, B03 B01 A03
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 11
![Page 33: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/33.jpg)
TRR 154’s future
Gas networks
• Marketability
• Security of Supply
• Coupling of energycarriers
Mathematics
• Model extentions
• Increase inComplexity
• Multiscales anduncertainties
• MultilevelOptimization
• Coupling networkswith physicaltransport
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 12
![Page 34: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/34.jpg)
TRR 154’s future
Gas networks
• Marketability
• Security of Supply
• Coupling of energycarriers
Mathematics
• Model extentions
• Increase inComplexity
• Multiscales anduncertainties
• MultilevelOptimization
• Coupling networkswith physicaltransport
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 12
![Page 35: Mathematical Modelling, Simulation and Optimization using ...cost-td1207.zib.de/.../meeting-cost-trr514-martin_2.pdfEntries Exits booked capacity 10 5 5 20 10 Nomination A 5 0 0 10](https://reader036.vdocuments.mx/reader036/viewer/2022081620/6116e1409d178d1b9353921a/html5/thumbnails/35.jpg)
TRR 154’s future
Gas networks
• Marketability
• Security of Supply
• Coupling of energycarriers
Mathematics
• Model extentions
• Increase inComplexity
• Multiscales anduncertainties
• MultilevelOptimization
• Coupling networkswith physicaltransport
15.03.2015 | A. Martin | CRC/Transregio 154: Overview 12