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Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers...

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Narcisse Ngada DESY, MKK 14.05.2014 Outline 1) What is simulation ? 2) Why simulation ? 3) Principles of simulation 4) Types of simulation 5) Conclusion Simulation Analog simulation Numerical simulation
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Page 1: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

Narcisse Ngada

DESY, MKK

14.05.2014

Outline

1) What is simulation ?

2) Why simulation ?

3) Principles of simulation

4) Types of simulation

5) Conclusion

Simulation

� Analog simulation� Numerical simulation

Page 2: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

2

What is simulation?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 3: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

3

Those who can, do. Those who can't, simulate. -- anonymous writer

What is simulation ?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 4: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

4

What is simulation ?

� Simulation is a procedure to analyse physicalsystems

� Simulation is an imitation of real-world activities

� Simulation is performed by developing a model

� A model builds a conceptual framing to describe a physical system

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 5: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

5

What is simulation ?

Physical system

Experiments withphysical system

Experimenta with modelsof physical system

Physical modelMathematical

model

Analytical method(accurate)

Simulation(approximate)

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 6: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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Physical system Simulation model

But please never forget!

What is simulation ?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Simulations are gross simplifications of the reality and are only as good as their underlying assumptions

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7

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Why simulation?

Page 8: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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� A study on the real system could be too dangerous, too complicated, too expensive

� The real system doesn’t exist yet, isn’t understood or is very complex

� The real system is working too fast / too slow or can’t be observed directly

� Nowadays the complexity of physical systems in the power converters world makes the use of simulation unavoidable

Why simulation ?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 9: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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� Physics� Astrophysics� Chemistry� Biology� ecomomics� Engineering� Social science� Training� Education� Video games� And more…

� Power accelerators� Power convertersSimulation

Fields of application

Why simulation ?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 10: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

10

� Saving time and money

� Repeatable and optimizable

� Studying the behavior of a system without building it

� Helps to find un-expected behavior of the physical system

Advantages of simulation

Why simulation ?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

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� Simulation errors

� Can’t provide easy answers to complex problems

� Can’t solve problems by itself

� Time consuming and expensive

Disadvantages of simulation

Why simulation ?

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 12: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

12

Principle of simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

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13

(1) Analog simulation

Simulation

� Input data (Modeling)� Boundary conditions� Solution of differential / integral equations

� Time precisely controllable

� Space less controllable

� Mainly for circuit simulation

(2) Numerical simulation

� Space precisely controllable

� Time less controllable

� Mainly for field simulation

Principle of simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 14: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

(1) Analog simulation (2) Numerical simulation

Surface current distribution of the coil and magnetic field strength along a vertical cut plane

The current and voltage waveforms for a pure inductance circuit

time

Page 15: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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Kirchhoff's circuit laws

System of DE / IE

Modeling(Schematic)

+ +

Current law

Voltage law

(1) Analog simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Principle of simulation

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16

Meshing andBoundary conditions

System of DE / IE

Modeling (Geometric)

+ +

(2) Numerical simulation

Principle of simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Page 17: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

17

Types of simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog simulation

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� Pspice

� Psim

� Matlab / Simulink / SimPowerSystems / PLECS

� LTSpice

� CASPOC

� ANSYS Simplorer

Analog simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Some simulation tools

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Tunnel design

Example(1): temperature simulation for European XFEL at DESY

Analog simulation

Page 20: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

− Overview of temperature profile along the XTL-tunnel

− Stable temperature profile (max. ∆T of +/- 0.5 K) during operation modes

Example(1): temperature simulation for European XFEL at DESY

� Motivation

� Input parameters

− Heat sources / Heat sinks (dependent on a position)

− Geology of the ground

− Experience and temperature measurement in HERA

− Analyze the transient thermal processes in the XTL tunnel

� Goal

Analog simulation

Page 21: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

1) Analyses with Matlab werelimited to steady state calculation

2) Analyses with ANSYS CFD would have cost too much computing time & capacity

Example(1): temperature simulation for European XFEL at DESY

Analog simulation

Page 22: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

� Complex multiphysics circuit analysis:

� AC, DC and TR analysis

� Based on numerical methods of mathematics

� Non linear Multidomain-System simulation

� Very stable simulation algorithm

� Enough user licenses in our department

ANSYS Simplorer als simulation tool

Analog Simulation: Simplorer

electrical, power electronic, electromagnetic, thermal, electromechanical and hydraulic

Example(1): temperature simulation for European XFEL at DESY

Page 23: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

23

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

� Duality principle

� 50 m XTL tunnel sectionGroundwater

Glacial till

RB RithRs1

CLth

CBth

RL

d1

Rs2

d2

Cs1Cs2

Example1: temperature simulation for European XFEL at DESY

Page 24: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Start values

- Ground water: 10oC

- Concrete: 10oC

- Inlet temperature: 23oC

T3>=1.8u

SET: Sw1:=1

SET: Sw2:=0

SET: Sw3:=0

DEL: T3##7200

T2 > 16uT1>=1500u

SET: Sw1:=1

SET: Sw2:=0

SET: Sw3:=0

DEL: T2##3600

SET: Sw1:=1

SET: Sw2:=0

SET: Sw3:=0

SET: Sw1:=1

SET: Sw2:=0

SET: Sw3:=0

DEL: T1##7200

ICA:

T_Grundwasser := 283.15

T_Luft := 296.15

T_Beton:=273.15

Twr_10:=313.15

Twr_21:=293.15

Twr_22:=303.15

Analog Simulation: Simplorer

Example(1): temperature simulation for European XFEL at DESY

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

TausR

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Θ

TLuft TeinL

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THM1

THM2

THM3

Analog Simulation: Simplorer

50m

Outlet: 2150 m

1050 m

Inlet

� Tunnel length: 2100 m� 43 submodels

Example(1): temperature simulation for European XFEL at DESY

Page 26: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

26

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

12.03.2013: Temperature in the empty main tunnel

Analog Simulation: Simplorer

Simulation could fitting measurements only after� Good understanding of real system� Measurements on real system� Readjustments of your simulation model

Example(1): temperature simulation for European XFEL at DESY

Tunnel length [m]

Tem

pera

ture

[°C

]

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27

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

Example(1): temperature simulation for European XFEL at DESY

Heat

sourcesin

theX

TL

tunnel

Tunnel section

In operatation

Service

day

Pulse cables left LK ON OFFPulse cables right RK ON OFFMV power cables HT ON ONLV Power cables LK ON ONDC power cables LK ON OFFPulse Transformators HT ON OFFImpedance matching network HT ON OFFMagnets HT ON OFF30°C water pipe 1 (VL) RL ON ON40°C water pipe 1 (RL) HT ON ON20°C water pipe 2 (VL) HT ON ON25°C water pipe 2 (RL) HT ON ON20°C water pipe 3 (VL) HT ON ON20°C water pipe 4 (VL) RKG ON ON20°C water pipe 5 (VL) LK ON ONElektronic racks HT ON ONWaveguides HT ON OFFLighting HT OFF ON

Two operating modes of the XFEL

� Inlet temperature: 23°C

� Temperatur after 50m in the tunnel?

� Temperature after 2100m at the end of thetunnel ?

� Temperatur behavior in the XTL tunnel after 10 days of machine operating and a serviceday(~10 h) ?

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00Time [day]

15.00

17.50

20.00

22.50

25.00

27.50

30.00

32.50

Y1

[ce

l]

Simplorer1Rectangular Plot1_1_1_1 ANSOFT

m1m2

m3

Curve Info

TausR.TTR

TausH.TTR

TausL.TTR

Name X Y

m1 1.3000E+001 2.7595E+001

m2 1.3000E+001 2.7470E+001

m3 1.3000E+001 2.5799E+001

Analog Simulation: Simplorer

Example(1): temperature simulation for European XFEL at DESY

Temperature after 50 m in the XTL Tunnel

Time [days]

Tem

pera

ture

[°C

]

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00Time [day]

14.00

16.00

18.00

20.00

22.00

24.00

26.00

Y1

[ce

l]

Simplorer1Rectangular Plot1_1_1_1_1 ANSOFT

m1

m2

m3

Curve Info

THM1.TTR

THM2.TTR

THM3.TTR

Name X Y

m1 1.3000E+001 2.2830E+001

m2 1.3000E+001 2.1804E+001

m3 1.3000E+001 2.0224E+001

Analog Simulation: Simplorer

Temperature at the end of XTL Tunnel (2150 m)

Example(1): temperature simulation for European XFEL at DESY

Tem

pera

ture

[°C

]

Time [days]

Page 30: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

Example(2): EMI behavior of XFEL modulators with pulse cables

� 29 HV pulse power supplies (modulators) of 10MW RF station each in a central modulator hall (XHM)

� RF stations(klytrons & pulstransformers) in theaccelerator tunnel (XTL)

� Up to 1.5 km long triaxial cables between RF stations and modulators

� Analyses of EMI behavior with pulse cables and modulators

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

Example(2): EMI behavior of XFEL modulators with pulse cables

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

AM5.I [A] Ra.I [A]

t [s]

218.59

-183.29

0

-150.00

-100.00

-50.00

50.00

100.00

150.00

1.63m 2.03m1.70m 1.75m 1.80m 1.85m 1.90m 1.95m

Measurement Simulation

Example(2): EMI behavior of XFEL modulators with pulse cables

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Ansys Simplorer vs LTSpice IV

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

ANSYS Simplorer LTSpice IV

� Limited student version / not free

� Analog & digital circuitssimulation

� Idealized / accurate model ofcomponents

� Schematic draw(comfortable)

� Multiphysics simulation

� Free & popular

� Mainly analog circuits simulation

� Accurate model of components

� Schematic draw(not comfortable)

� Electrical circuit simulation

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Roundup

� Basic understanding of physical system for a good simulation model

� Simulation model as simple as possible

� Simulation model as complex as needed

� Measurement of physical model to optimize the simulation model

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Analog Simulation: Simplorer

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Types of simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation

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Meshing andBoundary conditions

System of DE / IE

Models (geometric)

+ +

Numerical simulation

Numerical Simulation splits the problem into smaller pieces, solves those separately with numerical methods, and finally merges the partial results into the solution for the entire problem.

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

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� finite difference method

� method of weighted residuals

� moment method

� finite element method

� transmission-line modeling

� Monte Carlo method

� method of lines

Numerical simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Some numerical methods

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� ANSYS CFD

� ANSYS HFSS

� CST Microwave studio

� ANSYS Maxwell 2D

� FEKO

� CONCEPT-II

� Quickfield

Numerical simulation

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Some simulation tools

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

− EMI during the commissioning of Modulators

− Measurement of high inducted current on PE conductor

− Source of high inducted current not clear (50Hz / up to 50App)

� Motivation

� Suspicion

− Theoretical analysis and measurement to confirm the suspicions− Optimization of the grounding system of modulators

� Goal

Numerical simulation: Quickfield

Example: grounding of XFEL modulators for RF stations at DESY

− Insulation fault− Inducted current from power cables

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� Easy to learn / Easy to use

� Mainly for EM fields simulation

� Coupled multiphysics

� Various analysis types

� Electrical circuit combined with fields simulation

� Only basic components for electrical circuit analysis

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

Quickfield as simulation tool

Example: grounding of XFEL modulators for RF stations at DESY

AC, DC and transient electromagnetics, electrostatics, DC, AC and transient electric analysis, steady-state and transient heat transfer, Stress analysis)

Page 41: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

41

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

Transformer HV racks Power & PE cables Modulator

� 29 HV pulse power supplies (Modulators) capable of 10MW RF station each

� Modulators in a central modulator hall (XHM)

� RF stations in the accelerator tunnel

View of modulators hall

Example: grounding of XFEL modulators for RF stations at DESY

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

Nbr. of modulators

Output Voltage

Output current

Ave. Output power

Max. pulse power

Pulse duration

Pulse repetition rate

29

0 – 12kV

0 – 2 kA

max. 380kW

16,8 MW

0,2 – 1,7 ms

1 – 30 Hz

Technical data of a modulator

Example: grounding of XFEL modulators for RF stations at DESY

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43

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

View of grounding system in the hall: PE conductor near power cables

Measure of 21 Arms / 50Hz Interference current on PE-conductor

Example: grounding of XFEL modulators for RF stations at DESY

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

H-Field

Current density

I = 182,13 A

I = 182,14 A

I = 182,13 A

I = 18,53 Arms

I = 18,53 Arms

I= 0,0094 A

ρ=120°

ρ=240°

ρ=0°

Example: grounding of XFEL modulators for RF stations at DESY

Simulation results of PE conductor near power cables

Page 45: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

6 Arms

6 Arms

H-Field

Current density

Example: grounding of XFEL modulators for RF stations at DESY

Simulation results with PE conductor between power cables

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46

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

2,8 Arms

2,8 Arms

Current density

H-Field

Simulation results of PE conductor at ~25cm from power cables

Example: grounding of XFEL modulators for RF stations at DESY

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

Picture Measurement

Umod =10kV; Pulse repetition =10Hz; Pulse length =1000us

Example: grounding of XFEL modulators for RF stations at DESY

Measurement with PE conductor between power cables

PE conductor ~ 12A pp

Power cables ~ 1,2A pp

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

Picture Measurement

Umod =10kV; Pulse repetition =10Hz; Pulse length =1000us

PE conductor ~ 5.6A pp

Power cables ~ 1,2A pp

Example: grounding of XFEL modulators for RF stations at DESY

Measurement with PE conductor at ~25cm from power cables

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Roundup

� Simulation to investigate a best solution for modulators grounding system

� Simulation for better understanding of real system

� Simulation to reduce the installation time of physical system

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Numerical simulation: Quickfield

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1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Conclusion

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� Comfortable, intuitive input of the circuit model

� Correct error messages

� Robust execution of the simulation

� Output data to be used in other softwares

� Good user support

� Portability of models in software update

Conclusion

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Expectations for a good simulation tool

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� More intuitive usage

� Lower simulation time

� Models & results transfer

� Better user support & extended online help

� Various models of components

Conclusion

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Challenges in world of simulation

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1) Investment in time and money

2) Clearly state the problem to solve

3) Determine the general type of simulation tool

4) Check the functional requirements

5) Select the most appropriate Tool

Conclusion

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Checklist to opt for a simulation tool?

Page 54: Cern Accelerator School Talk [Kompatibilitätsmodus] · 2017-07-08 · Can’t provide easy answers to complex problems Can’t solve problems by itself Time consuming and expensive

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1) Basic understanding of your real system

2) Simulation model as simple as possible

3) Simulation model as complex as necessary

4) Interaction between simulation and physical system

Conclusion

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion

Important points to perform a good simulation

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Those who can, do. Those who can't, simulate. -- anonymous writer

Thank you for attention!

Conclusion

Those who can, simulate. Those who can't, don’t simulate.

1. What is simulation ?

2. Why simulation ?

3. Principle of simulation

4. Types of simulation

5. Conclusion


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