1. Dipole circuit & diode functioning
Risk analysis of single and double short-to-ground
Arjan Verweij, TE-MPE-PE
RB circuit and diode functioning
Voltage in the circuit
Single short
Double short

2. RB circuit L=15.2 H I (6.5 TeV)=11 kA I (7 TeV)=11.85 kA
Even
point
Odd
point
L=15.2 H
I (6.5 TeV)=11 kA
I (7 TeV)=11.85 kA
Earth current measurement system (H. Thiesen, 2008)

3. RB circuit & diode functioning
Even
point
Odd
point
Normal operation (ramp-up/down, plateau): the diodes are not conducting.
Quench: - the power converter is switched off,
- the quench heaters of the quenching magnet(s) are fired,
→ voltage over the quenching magnet(s) rapidly increases,
→ bypass diodes of the quenching magnets open when VQ>6 V,
→ current in the quenching magnet quickly transfers into its bypass diode, typically with a characteristic time of a few 100 ms.
- the EE switches are opened (with 0.34 & 0.6 s delay in odd & even points.

4. RB circuit & diode functioning
The diode voltage reduces quickly (<1 s) from about 6 V to about 1 V due to the warming-up of the silicon wafer.
The current in the circuit then decays with a time constant of about 100 s (t=L/REE).
The diodes of the quenching magnets, including the busbars towards these diodes, have to support this current.
The energy dissipated in the diode, Q=∫VIdt, is mainly absorbed by the heat sink, and finally transferred to the helium.

5. Some numbers Helium volume in diode box About 5.2 liter
Helium enthalpy from 1.9 to 4.3 K
6 kJ
Latent heat helium
13 kJ
Helium enthalpy from 4.3 K to 100 K
20 kJ
Volume heat sink
2x1.6 liter
Cross-section diode lead
285 mm2
I [kA]
Qstored [MJ]
MIIT’s [MA2s]
Qdiode [kJ]
Tdiode-lead [K]
Theat-sink [K] 6
274
1800
600 42
138 11
920
6050
1100 97
191 13
1284
8450
1300
158
211
Assumptions: adiabatic conditions, Vforward=1 V, t=100 s, RRRCu=100, no additional contact resistances

6. Voltage in the circuit (at 10 kA)
After Fast Power Abort (FPA), the voltage distribution in the circuit changes significantly.

7. Voltage in the circuit after a quench (at 10 kA)
The voltage distribution in the circuit does not depend much on the number and location of the quenched magnets.

8. Single short in the RB circuit
A single short with sufficiently low impedance causes the 1 A fuse to blow, hence moving the 0 V of the circuit to the location of the short.
The associated strong voltage transients very likely triggers the Quench Detection Systems of one or more magnets.
Example for a short at z=2000 m

9. Probability for a single short
LHC statistics: 2 shorts occurred for about 250 quench events, corresponding to about 1000 magnet quenches (with I>1.5 kA)
Line A kA
Short
P1=0.002
Line B
2 secondary 9 kA
Short
P2=2*0.002=0.004
2 secondary 3 kA
Short
P3=2*0.002=0.004
Probability of one short for a high-current quench event is SPi=0.01
A single short should not give collateral damage, but might require warm-up and repair if the fault cannot be removed by the “Earth Fault Burner”.

10. Possible scenario for a double short-to-ground1 4 2 10 11 3 89 3 6 5 7 10 11
1. Magnet quench
2. Converter
switch-off
3. EE1 and EE2 switched in, giving high V
4. Short 1
6. Trips/quenches in other magnets due to voltage transients
5. Fuse blows
7. Short 2
8. RB circuit divided in 2 sub-circuits
9. Inductance imbalance generates current through the shorts
10. Energy dissipated in the short causes melting of the debris
11. Arcs are generated, probably remaining during most of the discharge

11. Simulation of a double short-to-ground
The RB circuits are modelled in detail using PSpice-STEAM (6500 components per circuit!!)
The simulations showed very good agreement with measured transient phenomena:
Power converter switch-off,
EE switch opening,
Appearance of a short-to-ground,
Fuse blowing in the earth measurement system.
Short 1
Short 2
Unknown parameters in the simulation are:
Resistances of the shorts (we assume about 1 W)
The heat needed to melt the debris (we assume 3 kJ)
Voltage needed to generate an arc (we assume 15 V)
Voltage during the arcing process (we assume 15 V)

12. Simulation of a double short-to-ground
I=11 kA (Qstored=920 MJ)
Simulations by M. Prioli
Edebris 1,2 = 3 kJ
Eshort 1,2 = 22 MJ
E EE2 = 80 MJ
E EE1 = 800 MJ
The energy dissipated in the arcs depends mainly on the position of the two arcs, the voltage of the arc, and the current(s) at which the shorts occur.

13. Remarks
The build-up of the current in the shorts is slow, typically A/s.
So most likely the debris melts, contrary to the Earth Fault Burner, where the debris might blow away.
The heat needed to melt the debris has no impact on the occurrence of arcs and on the energy dissipated in the arcs.
For info:
=1 mm, length=40 mm
2 𝐾 1500 𝐾 𝐶𝑝𝑉𝑑𝑇 =200 J
=10 mm, thickness=2 mm
2 𝐾 1500 𝐾 𝐶𝑝𝑉𝑑𝑇 =1000 J

14. Probability for a double short
Line A
8 11 kA
Short 2
P1=8*0.0022
Line B
Short 1
8 11 kA
Short 2
P2=8*0.0022
2 secondary 9 kA
Short 2
P3=2*0.0022
2 secondary 3 kA kA
Short 2
P4=2*0.0022
4 quenches
@ 9 kA
Short 2
P5=2*4*0.0022
2 secondary 9 kA
Short 1
4 quenches
@ 9 kA
Short 2
P6=2*4*0.0022
2 quenches
@3 kA
2 secondary 3 kA
Short 2
P7=2*2*0.0022
Short 1
2 3 kA
Short 2
P8=2*2*0.0022

15. Probability and consequences of a double short
Lines
I [kA]
Qst [MJ]
Earcs [MJ] P1
8*(0.002)2=0.0032%
A-A 11
908
Small P2
A-B
0 to 46 MJ P3
2*(0.002)2=0.0008% 9
608
0 to 30 MJ P4 3 68 P5
2*4*(0.002)2=0.0032%
B-A P6
B-B P7
2*2*(0.002)2=0.0016% P8
0 to 3.4 MJ
So about 0.01% (P2+P3+P5+P8) probability of dissipating an amount of energy in the arcs which is >100x the energy needed to melt a hole in the diode tube.

16. Final remarks
Assuming a training campaign with 500 quench events gives:
on average 500*0.01=5 shorts-to-ground in the diode tube.
→ delay of several days (per short) or possibly warm-up
a 5% probability of a double short without puncture of the diode tube.
→ delay of several days or possibly warm-up
a 5% probability of a double short with puncture of the diode tube.
→ severe damage and warm-up
(all analysis based on very low statistics)
Ongoing or foreseen studies:
Further development of the PSpice-STEAM model
Study if/how we can reduce the voltage transients in the circuit (change the 100 W bypass resistors, add capacitors)
Study if it is beneficial to increase the rating of the earth fuse
Study on an improved earth measurement & monitoring system