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Outline Narcisse Ngada DESY, MKK 1) What is simulation ? - - PowerPoint PPT Presentation

Simulation Outline Narcisse Ngada DESY, MKK 1) What is simulation ? 14.05.2014 2) Why simulation ? 3) Principles of simulation 4) Types of simulation Analog simulation Numerical simulation 5) Conclusion 1. What is simulation ? 2.


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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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2

What is simulation?

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion
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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
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4

What is simulation ?

  • Simulation is an imitation of real-world activities
  • Simulation is a procedure to analyse physical

systems

  • 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
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5

What is simulation ?

Physical system Experiments with the physical system Experiments with models

  • f the physical system

Physical model Mathematical model Analytical method (accurate) Simulation (approximate)

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion
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6

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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  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion

Why simulation?

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8

  • A study on the real system could be too dangerous,

too complicated, too expensive

  • The real system doesn’t exist yet, isn’t understood
  • r 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
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9

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

Power accelerators Power converters

Simulation Fields of application

Why simulation ?

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion
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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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11

  • 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
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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
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14

  • 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

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15

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 and Boundary 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
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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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18

  • 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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19

  • 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

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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

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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 were limited 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

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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

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  • 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 section

Groundwater

Glacial till RB Ri

th

Rs1 CL

th

CB

th

RL d1 Rs2 d2 Cs1 Cs2

Example1: temperature simulation for European XFEL at DESY

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24

  • 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 > 16u T1>=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 _Grundw asser := 283.15 T _Luft := 296.15 T _Beton:=273.15 T w r_10:=313.15 T w r_21:=293.15 T w r_22:=303.15

Analog simulation: Simplorer

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

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25

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion
TausR TausL TausH TeinL TeinR TausH TausL TausR TeinH MGrundwasser TeinL TeinR TausH TausL TausR TeinH MGrundwasser1 TeinL TeinR TausH TausL TausR TeinH MGrundwasser2 TeinL TeinR TausH TausL TausR TeinH MGrundwasser3 TeinL TeinR TausH TausL TausR TeinH MGrundwasser4 TeinL TeinR TausH TausL TausR TeinH MGrundwasser5 TeinL TeinR TausH TausL TausR TeinH MGrundwasser6 TeinL TeinR TausH TausL TausR TeinH MGrundwasser7 TeinL TeinR TausH TausL TausR TeinH MGrundwasser8 TeinL TeinR TausH TausL TausR TeinH MGrundwasser9 TeinL TeinR TausH TausL TausR TeinH MGrundwasser10 TeinL TeinR TausH TausL TausR TeinH MGrundwasser11 TeinL TeinR TausH TausL TausR TeinH MGrundwasser12 TeinL TeinR TausH TausL TausR TeinH MGrundwasser13 TeinL TeinR TausH TausL TausR TeinH MGrundwasser14 TeinL TeinR TausH TausL TausR TeinH MGrundwasser15 TeinL TeinR TausH TausL TausR TeinH MGrundwasser16 TeinL TeinR TausH TausL TausR TeinH MGrundwasser17 TeinL TeinR TausH TausL TausR TeinH MGrundwasser18 TeinL TeinR TausH TausL TausR TeinH MGrundwasser19 TeinL TeinR TausH TausL TausR TeinH MGrundwasser20 TeinL TeinR TausH TausL TausR TeinH MGrundwasser21 TeinL TeinR TausH TausL TausR TeinH MGrundwasser22 TeinL TeinR TausH TausL TausR TeinH MGrundwasser23 TeinL TeinR TausH TausL TausR TeinH MGrundwasser24 TeinL TeinR TausH TausL TausR TeinH MGrundwasser25 TeinL TeinR TausH TausL TausR TeinH MGrundwasser26 TeinL TeinR TausH TausL TausR TeinH MGrundwasser27 TeinL TeinR TausH TausL TausR TeinH MGrundwasser28 TeinL TeinR TausH TausL TausR TeinH MGrundwasser29 TeinL TeinR TausH TausL TausR TeinH MGrundwasser30 TeinL TeinR TausH TausL TausR TeinH MGrundwasser31 TeinL TeinR TausH TausL TausR TeinH MGrundwasser32 TeinL TeinR TausH TausL TausR TeinH MGrundwasser33 TeinL TeinR TausH TausL TausR TeinH MGrundwasser34 TeinL TeinR TausH TausL TausR TeinH MGrundwasser35 TeinL TeinR TausH TausL TausR TeinH MGrundwasser36 TeinL TeinR TausH TausL TausR TeinH MGrundwasser37 TeinL TeinR TausH TausL TausR TeinH MGrundwasser38 TeinL TeinR TausH TausL TausR TeinH MGrundwasser39 TeinL TeinR TausH TausL TausR TeinH MGrundwasser40 TeinL TeinR TausH TausL TausR TeinH MGrundwasser41

Θ

TLuft TeinL TeinR TausH TausL TausR TeinH MGrundwasser42 THM1 THM2 THM3

Analog simulation: Simplorer

2100m Outlet: 50 m Inlet

Tunnel length: 2100 m 43 submodels

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

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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 fit measurements only after A good understanding of the real system Measurements on the real system Readjustments of your simulation model

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

Tunnel length [m] Temperature [°C]

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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(1): temperature simulation for European XFEL at DESY

Heat sources in the XTL tunnel Tunnel section In

  • peratation

Service day Pulse cables left LK ON OFF Pulse cables right RK ON OFF MV power cables HT ON ON LV Power cables LK ON ON DC power cables LK ON OFF Pulse Transformators HT ON OFF Impedance matching network HT ON OFF Magnets HT ON OFF 30° C water pipe 1 (VL) RL ON ON 40° C water pipe 1 (RL) HT ON ON 20° C water pipe 2 (VL) HT ON ON 25° C water pipe 2 (RL) HT ON ON 20° C water pipe 3 (VL) HT ON ON 20° C water pipe 4 (VL) RKG ON ON 20° C water pipe 5 (VL) LK ON ON Elektronic racks HT ON ON Waveguides HT ON OFF Lighting HT OFF ON

Two operating modes of the XFEL Inlet temperature: 23°C Temperature after 50m along the tunnel? Temperature after 2100m at the end of the tunnel ? Temperatur behavior in the XTL tunnel after 10 days of machine operating and a service day(~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 14.00 Time [day] 14.00 16.00 18.00 20.00 22.00 24.00 26.00 Y1 [cel] Simplorer1

Rectangular Plot1_1_1_1_1

ANSOFT m1 m2 m3 Curve Info THM1.T TR THM2.T TR THM3.T TR 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

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

Temperature [°C] Time [days]

Temperature after 50 m in the XTL Tunnel (from the end of tunnel)

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29

  • 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 14.00 Time [day] 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 Y1 [cel] Simplorer1

Rectangular Plot1_1_1_1

ANSOFT m1 m2 m3 Curve Info TausR.T TR TausH.T TR TausL.T TR 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

Time [days] Temperature [°C]

Temperature at the beginning of XTL Tunnel (2100 m)

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30

  • 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 capable of 10MW RF station each in a central modulator hall (XHM) RF stations(klytrons & pulstransformers) in the accelerator tunnel (XTL) Up to 1.5 km long triaxial cables between RF stations and modulators

Motivation / Goal

Analyses of EMI behavior with pulse cables and modulators

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31

  • 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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32

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion

Analog simulation: Simplorer

AM 5.I [A] Ra.I [A] t [s] 218.59

  • 183.29
  • 150.00
  • 100.00
  • 50.00

50.00 100.00 150.00 1.63m 2.03m 1.70m 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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33

Roundup

  • Basic understanding of the

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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34

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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35

Meshing and Boundary 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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36

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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37

  • 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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38

  • 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

− Simulations and measurements to confirm the suspicions − Optimization of the grounding system of modulators

Goal Example: grounding of XFEL modulators for RF stations at DESY

− Insulation fault − Inducted current from power cables

Numerical simulation

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39

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion

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

Numerical simulation

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40

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion
  • 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

Numerical simulation

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41

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion

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

Numerical simulation

TNS-system

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42

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

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)

Numerical simulation: Quickfield

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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

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

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44

  • 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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45

  • 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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46

  • 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 ~ 12App Power cables ~ 1,2App

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47

  • 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 ~ 5.6App Power cables ~ 1,2App

Example: grounding of XFEL modulators for RF stations at DESY

Measurement with PE conductor at ~25cm from power cables

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48

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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49

  • 1. What is simulation ?
  • 2. Why simulation ?
  • 3. Principle of simulation
  • 4. Types of simulation
  • 5. Conclusion

Conclusion

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50

  • 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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51

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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52

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?

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53

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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54

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