First look at the voltages
during a quench
Tiina Salmi and Antti Stenvall
T. Salmi, TUT
1
Outline
• Parameters for the analyzed Block and cosθ designs
• Calculation procedure
• Simulated scenarios
• Results
• Summary
T. Salmi, TUT
2
Input parameters
T. Salmi, TUT
3
Input - Block (v.26b)
• 1 aperture,
• Cable parameters (twist-pitch accounted):
• Field distribution from Roxie
• Number of turns (Nturns_tot) = 608
• 152 turns * 2 sides * 2 coils
• 1 turn is 14-m-long
@Inom
Ains. (mm2)
fCu
FNb3Sn
fG10
RRR
Cable 1 (HF)
32.55
0.363
0.363
0.274
100
Cable 2 (LF)
21.93
0.336
0.336
0.328
100
• Iop = 1.05*Inom = 8862 A, Bp = 17.2 T, L = 42.5 mH/m
• Inital hotspot in the LF cable with highest field
• Quench protection: Nominal tQdelay in each turn is 40 ms
- 15 ms for detection (+val. etc) and 25 ms for ”heaters”
Lmag
Rmag(t)
𝐼𝑚𝑎𝑔 𝑡
T. Salmi, TUT
4
Input - Cosθ (v. 28b-38-opt3)
• 1 aperture
• Cable parameters:
• Field distribution from Roxie
• Number of turns (Nturns_tot) = 456
• 114 turns * 2 sides * 2 coils
@Inom
Ains. (mm2)
fCu
FNb3Sn
fG10
RRR
Cable 1 (HF)
38.035
0.362
0.362
0.276
100
Cable 2 (LF)
22.380
0.455
0.222
0.323
100
• Iop = 1.05*Inom = 11802 A, Bp = 17.0 T, L = 23 mH/m
• Inital hotspot in the LF cable with highest field
• Quench protection: Nominal tQdelay in each turn is 40 ms
- 15 ms for detection (+val. etc) and 25 ms for ”heaters”
Lmag
Rmag(t)
𝐼𝑚𝑎𝑔 𝑡
T. Salmi, TUT
5
Electrical order of the turns (winding order)
IN
OUT
T. Salmi, TUT
6
Calculation procedure
Coodi – Code for current decay calculation based on known protection efficiency
(T. Salmi & A. Stenvall, TAS 26(4), 2016)
T. Salmi, TUT
7
Calculation procedure
Temperature profile at t = 100 ms (hotspot not incl.)
At each time step, ∆𝑡
1. Temperature of each turn (and hotspot)
2. Resistance of each turn, Rturn
3. Total resistance of magnet and current decay, ∆𝐼𝑚𝑎𝑔
2 full turns is 4 turns in the analysis
𝑅𝑖 =
𝜌𝐶𝑢
𝑙
𝐴𝐶𝑢
If t > tQdelay
l = 14 m
R2 R4
R3 R1
T. Salmi, TUT
8
Calculation procedure
Temperature profile at t = 100 ms (hotspot not incl.)
At each time step, ∆𝑡
1. Temperature of each turn (and hotspot)
2. Resistance of each turn, Rturn
3. Total resistance of magnet and current decay, ∆𝐼𝑚𝑎𝑔
NEW
4. Voltages in each turn, Vturn
𝑉𝑖 = 𝑉𝑟𝑒𝑠,𝑖 + 𝑉𝑖𝑛𝑑,𝑖
V2
V3
V1
V𝑟𝑒𝑠,𝑖 = 𝑅𝑖 𝐼𝑚𝑎𝑔 (𝑡 −
V𝑖𝑛𝑑,𝑖
R2 R4
Δ𝑡
)
2
𝐿𝑚𝑎𝑔
∆𝐼𝑚𝑎𝑔
=
𝑁𝑡𝑢𝑟𝑛𝑠_𝑡𝑜𝑡
Δ𝑡
R3 R1
T. Salmi, TUT
9
Calculation procedure
Temperature profile at t = 100 ms (hotspot not incl.)
At each time step, ∆𝑡
1. Temperature of each turn (and hotspot)
2. Resistance of each turn, Rturn
3. Total resistance of magnet and current decay, ∆𝐼𝑚𝑎𝑔
NEW
4. Voltages in each turn, Vturn
5. Potential to ground in each turn, Uturn
U3 = V1+V2+V3
V2
U2 = V1+V2
T. Salmi, TUT
V3
V1
U1 = V1
0 V (gnd)
10
Calculation procedure
Temperature profile at t = 100 ms (hotspot not incl.)
At each time step, ∆𝑡
1. Temperature of each turn (and hotspot)
2. Resistance of each turn, Rturn
3. Total resistance of magnet and current decay, ∆𝐼𝑚𝑎𝑔
NEW
4. Voltages in each turn, Vturn
5. Potential to ground in each turn, Uturn
6. Voltages between neighboring cables, Vlat, Vvert,
Vlat,1 = |U1 – U3|
U3 = V1+V2+V3
V2
U2 = V1+V2
T. Salmi, TUT
V3
V1
U1 = V1
0 V (gnd)
11
IN THIS EXAMPLE TWIST PITCH NOT ACCOUNTED!
Examples of the potential-to-ground
Turn end-to-end voltage at t = 100 ms:
The turns are ordered in the ”winding order”, which is
defined in the input.
100
Turns in winding order
Pot. to gnd (V)
0
-100 0
100
200
300
400
600
-200
-300
-400
-500
t = 100 ms
-600
Max |pot. to gnd| (V)
500
Potential to ground at each turn (at the ”end” of each turn):
2000
Max abs(Ugnd)
1500
(turn#608)
OUT
In the nom. case
max is ~ (-)1.4 kV
1000
500
IN
(turn#1
0
0
T. Salmi, TUT
0.1
0.2
0.3
Time (s)
0.4
0.5
0.6
12
Examples of voltages between neigboring cables
Voltage between lateral neighbors at t = 100 ms. Shows
the voltage to the neighbor towards the pole.
80
70
60
50
40
30
20
10
0
Max
abs(Vlat)
0
0.2
0.4
Time (s)
0.6
Max layer-to-layer voltage (V)
Max turn-to-turn voltage (V)
The nearest neighbor turns are defined from the
coordinates in the field map (.map2d from ROXIE).
• Lateral neighbors face their wide side to each other.
• Vertical neighbors are in different layers and have
the smallest distance between the center points.
1400
1200
Max
abs(Vvert)
1000
Voltage between vertical neighbor. Shows the voltage
to the neighbor on the ”upper” layer.
800
600
400
200
0
0
0.2
0.4
Time (s)
0.6
Maximum btw lat. neighbors is ~ 70 V,
and btw vert, neighbors ~1.2 kV.
T. Salmi, TUT
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Simulation scenarios
T. Salmi, TUT
14
Different scenarios vor voltage calculation
0. Nominal case: All blocks quench at 40 ms
3. Heater failure in 2 blocks (Block) in one layer (costheta)
1. ”Realistic” heater delays in the coil turns
4. Heater failure in 4 blocks
2. All heaters fail in 1 coil-half (75% covered with heaters)
5. Heater failure in 8 blocks
Two cases:
A- The turns with failed heaters quench 40 ms after they’d have otherwise quenched
B - They do not quench at all but stay at 4.5 K
Ap1
Side
B
Side
B
T. Salmi, TUT
Side
A
Coil 1
Side
A
Coil 2
15
”Realistic” heater delays
• Heaters are 25 um thick stainless steel (same as HiLumi)
• Insulation to coil is 75 um polyimide (increased from HiLumi because of larger voltages)
• Heater peak power 100 W/cm2, HFU circuit time constant 50 ms (similar to HiLumi)
• Heaters cover the entire turns length no heating statinos (overly optimistic)
• Heaters can be put between the layers (optimistic, likely to require a different insualtion material)
• Simulations with CoHDA: Quench onset when the cable maximum temperature reaches Tcs (optimistic), BUT
• Delays are associated to the average field in the cable (conservative)
60
BLOCK
40
Cable 1, CoHDA
FIT, cable 1
30
COSTHETA
50
FIT, cable 2
Heater delay (ms)
50
Heater delay (ms)
60
Cable 2, CoHDA
20
Cable 2, CoHDA
FIT, cable 2
40
Cable 1, CoHDA
FIT, cable 1
30
20
10
10
0
0
0
0
T. Salmi, TUT
5
10
Magnetic field (T)
15
20
Detection delay = 15 ms (optimistic)
5
10
Magnetic field (T)
15
20
16
Results
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Ap2
Side
A
Results, block
Ap1
Side
B
Side
B
Coil 1
Side
A
0. Nominal case: All blocks quench at 40 ms
Side
B
3. Heater failure in 2 blocks
Coil 2
1. ”Realistic” heater delays in the coil turns
4. Heater failure in 4 blocks
2. All heaters fail in 1 coil-half (75% covered with heaters)
5. Heater failure in 8 blocks
Side
B
Side
A
Coil 1
Side
A
Coil 2
Case
Non-quenching blocks
Tmax (K)
Max |V to gnd| (V)
|V turn-to-turn| (V) |V layer-to-layer| (V)
0
N/A
310
1400
70
1200
1
N/A
280
1300
100
1300
2 –A
1-8
300
3400
130
2500
2–B
1-8
320
5100
140
3400
3–A
38, 39
290
1200
110
1100
3–B
38, 39
300
1200
120
1400
4–A
5, 29, 30, 31
300
2700
120
2300
4–B
5, 29, 30, 31
310
3700
130
3000
5–A
6, 7, 35, 32, 33, 36, 37
330
2300
150
2300
5–B
6, 7, 35, 32, 33, 36, 37
370
3600
200
4700
T. Salmi, TUT
Across
Midplane
not
computed
yet
18
Results cosTheta
0. Nominal case: All blocks quench at 40 ms,
1. ”Realistic” heater delays in the coil turns
Case
Non-quenching blocks
Tmax (K)
Max |V to gnd| (V)
|V turn-to-turn| (V) |V layer-to-layer| (V)
0
N/A
360
2200
70
2200
1
N/A
310
2200
100
2100
Case 1: Temperature at 100 ms (hotspot not
included):
T. Salmi, TUT
Case 1: Potential to ground at 100 ms:
19
Ap2
Ap1
Side
A
Results cosTheta failure cases
Side
B
Side
A
Coil 1
Side
B
Coil 1
Side
2. All heaters fail in 1 coil-half (75% covered
with heaters)
A
3. Heater failure in 1 layer
Coil 2
Side
B
Side
A
Coil 2
Side
B
4. Heater failure in 4 blocks
5. Heater failure in 8 blocks
Case
Non-quenching blocks
Tmax (K)
Max |V to gnd| (V)
|V turn-to-turn| (V) |V layer-to-layer| (V)
2 –A
1-14 (coil 1, side A)
340
3700
130
3700
2–B
1-14 (coil 1, side A)
360
4800
150
4800
3–A
9-12 (coil 1, side A)
320
2800
110
2800
3–B
9-12 (coil 1, side A)
330
3200
120
3100
4–A
13 in all coils side A &B
330
2400
120
2400
4–B
13 in all coils side A &B
340
2500
130
2500
5–A
5, 9 on all coils side
A&B
350
3100
140
2600
5–B
5, 9 on all coils side
A&B
370
4400
150
3400
T. Salmi, TUT
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Summary
• The very first estimation of the magnitude of expected voltages:
L (mH/m)
I (105% Inom) (A)
• Voltage to ground 1-5 kV
Block
42.5
8862
• Turn-to-turn voltages around 100 V (70-200 V)
CosTheat
22.7
11862
• Layer-to-layer voltages 1-5 kV
• Temperatures do not excape in small failure cases (but voltages rise)
• Block has smaller temperatures, and smaller layer-to-layer, no big difference in potential or turn-to-turn
• The tool is now coded (almost, improvement and cross-check are coming), analysis is fast
• Next month: Analysis continues and deepens for all design options, more realistic cases
• Need to define the realistic / important / worstcase cases
T. Salmi, TUT
21
Appendix
T. Salmi, TUT
22
Block diagram
For tdet < t < tend
For t < tdet
t = 0, initialization
Ti = Tbath, for all i
THotspot = Tcs,HS
LHotspot = LINZ
Imag = Iop
1st time step
ΔMIITS = Δt(Iop)2
Compute ΔTHotspot
Compute LHotspot
Compute RHotspot
Rmag = RHotspot
ΔMIITS = Δt(Iop)2
INITIALIZATION
ONLY HOTSPOT
EVOLVES
Compute ΔTHotspot
Compute LHotspot
Compute RHotspot
For all turns, i:
Compute ΔTi
Compute Ri
Compute Rmag
Update Lmag
Compute current decay
Compute ΔMIITs
Update Bi and BHS
Compute voltages
QP ACTIVATES, MAGNET
RESISTANCE INCREASES AND
CURRENT DECAYS
T. Salmi, TUT
23
Block diagram
For tdet < t < tend
For t < tdet
t = 0, initialization
Ti = Tbath, for all i
THotspot = Tcs,HS
LHotspot = LINZ
Imag = Iop
1st time step
ΔMIITS = Δt(Iop)2
t = Δt
INITIALIZATION
Compute ΔTHotspot
Compute LHotspot
Compute RHotspot
Rmag = RHotspot
ΔMIITS = Δt(Iop)2
t = Δt
ONLY HOTSPOT
EVOLVES
Basis of the temperature calculation:
ΔMIITS is the MIITs increase during the prev. Δt.
How large ΔT it causes in different cables?
T. Salmi, TUT
Compute ΔTHotspot
Compute LHotspot
Compute RHotspot
For all turns, i:
Compute ΔTi
Compute Ri
Compute Rmag
Update Lmag
Compute current decay
Compute ΔMIITs
Update Bi and BHS
Compute voltages
QP ACTIVATES, MAGNET
RESISTANCE INCREASES AND
CURRENT DECAYS
24
IN THE BLOCK EXAMPLE CASE THE TWIST PITCH NOT
ACCOUNTED!!! (it is accouinted in the later analysis)
1. Temperature calculation
HOTSPOT
HEATER QUENCHED TURNS:
Temperature increase:
Temperature increase in each turn:
𝜌𝐶𝑢 (𝑇, 𝐵, 𝑅𝑅𝑅)
∆𝑇(𝑡) = 106 ∆𝑀𝐼𝐼𝑇𝑆(𝑡 − Δ𝑡)
𝐶𝑣(𝑇)𝐴2𝑐𝑎𝑏𝑙𝑒 𝑓𝐶𝑢
However, if t < tQdelay then ΔT = 0.
Hotspot temperature evolution in the nominal case.
Temperature profile at t = 100 ms (hotspot not incl.)
Temperature (K)
Mat. props. using T and B computed at t=t-Δt.
400
Tmax ≈ 320 K
300
200
100
Hotspot
0
0
T. Salmi, TUT
0.1
0.2
Time (s)
0.3
0.4
25
2. Resistance calculation
HOTSPOT
HEATER QUENCHED TURNS:
Length and resistance:
Resistance of each turn, i:
𝐿𝐻𝑜𝑡𝑠𝑝𝑜𝑡 𝑡 = 𝐿𝐼𝑁𝑍 + 2 ∗ 𝑁𝑍𝑃𝑉𝐻𝑜𝑡𝑠𝑝𝑜𝑡 ∗ 𝑡
𝑅𝐻𝑜𝑡𝑠𝑜𝑝𝑡 𝑡 =
𝜌𝐶𝑢 𝑇, 𝐵, 𝑅𝑅𝑅
𝐿𝐻𝑜𝑡𝑠𝑝𝑜𝑡 (𝑡)
𝐴𝐶𝑢
Mat. props. using just computed T(t) but B
computed at t=t-Δt.
𝑅𝑡𝑢𝑟𝑛,𝑖 𝑡 =
𝜌𝐶𝑢,𝑖 𝑇𝑖 , 𝐵𝑖 , 𝑅𝑅𝑅𝑖
𝐿𝑟𝑒𝑠,𝑖
𝐴𝐶𝑢,𝑖
If t < tQdelay,i then
𝑅𝑡𝑢𝑟𝑛,𝑖 𝑡 = 0.
Here heaters quench the entire turn, and Lres is the mag.
length (14 m). For simulations with heating stations see
appendix.
Resistance profile at t = 100 ms (hotspot not incl.)
MAGNET
Total resistance that drives the current decay:
𝑁𝑡𝑢𝑟𝑛𝑠_𝑡𝑜𝑡
𝑅𝑚𝑎𝑔 (𝑡) =
𝑅𝑡𝑢𝑟𝑛,𝑖 𝑡 +𝑅𝐻𝑜𝑡𝑠𝑝𝑜𝑡 (𝑡)
𝑖=1
T. Salmi, TUT
26
3. Current decay
MAGNET
Magnet resistance evolution in the nominal case
Magnet resistance (Ω)
The time constant driving the current decay:
𝐿𝑚𝑎𝑔 𝐼𝑚𝑎𝑔
𝜏(𝑡) =
𝑅𝑚𝑎𝑔 𝑡
Inductance (Lmag) vs Imag is an input (tabulated).
8
6
> 7 Ω !!!
4
2
Rmag
0
0
0.2
The new current:
Current decay
Δ𝑡
−
𝜏(𝑡)
𝑒
10000
ΔMIITs from average current during the timestep:
𝐼𝑚𝑎𝑔 𝑡 + 𝐼𝑚𝑎𝑔 𝑡 − ∆𝑡
−6
∆𝑀𝐼𝐼𝑇𝑆 = 10 ∆𝑡
2
2
Magnetic field decays directly proportionally to the current decay.
T. Salmi, TUT
0.6
Time (s)
Magnet current (A)
𝐼𝑚𝑎𝑔 𝑡 = 𝐼𝑚𝑎𝑔 𝑡 − Δ𝑡
0.4
8000
imag
6000
MIITs ≈ 12 A2s
4000
2000
0
0
0.2
0.4
Time (s)
0.6
27
4. Voltage computation
HOTSPOT
HEATER QUENCHED TURNS:
Only resistive voltage:
Resistive voltage in each turn, i:
V𝐻𝑜𝑡𝑠𝑝𝑜𝑡 (𝑡) = 𝑅𝐻𝑜𝑡𝑠𝑝𝑜𝑡
1
𝑡
𝐼
𝑡 + 𝐼𝑚𝑎𝑔 (𝑡 − Δ𝑡)
2 𝑚𝑎𝑔
V𝑟𝑒𝑠,𝑖 (𝑡) = 𝑅𝑡𝑢𝑟𝑛,𝑖 𝑡
1
𝐼
𝑡 + 𝐼𝑚𝑎𝑔 (𝑡 − Δ𝑡)
2 𝑚𝑎𝑔
Resistive voltages computed for the average Imag of
the time step, because also inductive voltages
computed for the average dImag/dt.
For the turn i = turn_hotspot:
V𝑟𝑒𝑠,𝑖 𝑡 = V𝑟𝑒𝑠,𝑖 𝑡 + V𝐻𝑜𝑡𝑠𝑝𝑜𝑡 (𝑡)
MAGNET
Inductive voltage in each turn, i:
Resistive, inductive and terminal voltage:
1
V𝑟𝑒𝑠,𝑚𝑎𝑔 (𝑡) = 𝑅𝑚𝑎𝑔 𝑡
𝐼
𝑡 + 𝐼𝑚𝑎𝑔 (𝑡 − Δ𝑡)
2 𝑚𝑎𝑔
V𝑖𝑛𝑑,𝑚𝑎𝑔 (𝑡) = 𝐿𝑚𝑎𝑔 𝑡
𝐼𝑚𝑎𝑔 𝑡 − 𝐼𝑚𝑎𝑔 (𝑡 − Δ𝑡)
Δ𝑡
V𝑡𝑜𝑡,𝑚𝑎𝑔 𝑡 = 𝑉𝑟𝑒𝑠,𝑚𝑎𝑔 𝑡 + 𝑉𝑖𝑛𝑑,𝑚𝑎𝑔 𝑡
T. Salmi, TUT
𝐿𝑚𝑎𝑔 𝑡
𝐼𝑚𝑎𝑔 𝑡 − 𝐼𝑚𝑎𝑔 (𝑡 − Δ𝑡)
V𝑖𝑛𝑑,𝑖 (𝑡) =
𝑁𝑡𝑢𝑟𝑛𝑠_𝑡𝑜𝑡
Δ𝑡
Inductance of each turn is the total magnet inductance
divided by the number of turns.
Total voltage in each turn, i:
V𝑡𝑜𝑡,𝑖 𝑡 = 𝑉𝑟𝑒𝑠,𝑖 𝑡 + 𝑉𝑖𝑛𝑑,𝑖 𝑡
28
4. Examples of Vres and Vind in the nominal case (t = 100 ms)
Resistive component in each turn:
Inductive component in each turn:
Temperature in each turn:
Magnetic field in each turn:
T. Salmi, TUT
29
4. Voltage computation: Potential to ground
Turn end-to-end voltage at t = 100 ms:
HEATER QUENCHED TURNS:
The turns are ordered in the ”winding order”, which is
defined in the input.
The potential to gnd is the sum of total voltages in all
previous turns and the total voltage in that turn, i:
100
Turns in winding order
Pot. to gnd (V)
0
-100 0
100
200
300
400
600
-200
Potential to ground at each turn (at the ”end” of each turn):
-300
-400
-500
t = 100 ms
-600
Max |pot. to gnd| (V)
500
2000
Max abs(Ugnd)
1500
(turn#608)
OUT
IN
(turn#1)
In the nom. case
max is ~ (-)1.4 kV
1000
500
0
0
T. Salmi, TUT
0.1
0.2
0.3
Time (s)
0.4
0.5
0.6
30
4. Voltage computation: Voltages between neigboring cables
Voltage between lateral neighbors at t = 100 ms. Shows
the voltage to the neighbor towards the pole.
HEATER QUENCHED TURNS:
The nearest neighbor turns are defined from the
coordinates in the field map (.map2d from ROXIE).
• Lateral neighbors face their wide side to each other.
• Vertical neighbors are in different layers and have
the smallest distance between the center points.
80
70
60
50
40
30
20
10
0
Max
abs(Vlat)
0
T. Salmi, TUT
0.2
0.4
Time (s)
0.6
Max layer-to-layer voltage (V)
Max turn-to-turn voltage (V)
The voltages btw the neighbors are the difference in
their potentials. (The absolute value is taken.)
Voltage between vertical neighbor. Shows the voltage
to the neighbor on the ”upper” layer.
1400
1200
Max
abs(Vvert)
1000
800
600
400
200
0
0
0.2
0.4
Time (s)
Maximum btw lat. neighbors is ~ 70 V,
and btw vert, neighbors ~1.2 kV.
0.6
31
Schematic showing the voltages across turn ends
4 turns:
Vtot
Side B
Side A
VLat
Vtot
VLat
14 m
T. Salmi, TUT
32
Miscallaneous notes
• In the calculation procudure description the heaters quench the entire turn. If heating stations are used, the turn is
divided in two: The heater covered cable and the cable between heating stations where quench propagated with the
input NZPV
• Possible to add also bronze for the cable
• Hotspot voltage now has only resistive component. This could be improved in the future, if it is used for quench
detection.
• Turn numbering from Roxie for the first quarter of Xsect
• Turns electrical order as discussed with Clement
• The inductance is constant. A rough estimation for costheta suggested, that it can impact about 15 K in the nominal
case
T. Salmi, TUT
33
Concept of ΔMIITS
Volumetric heat generation and the associated temperature increase:
All current flows in the copper:
Re-organizing…
𝑓𝐶𝑢
𝐼𝑚𝑎𝑔
𝑓𝐶𝑢 𝐴𝐶𝑎𝑏𝑙𝑒
2
𝐼𝑚𝑎𝑔
Δ𝑡
2
𝜌𝐶𝑢 Δ𝑡 = 𝐶𝑣 Δ𝑇
𝜌𝐶𝑢
𝐴2𝐶𝑎𝑏𝑙𝑒 𝑓𝐶𝑢 𝐶𝑣
ΔIITS
= 106ΔMIITS
𝐽2 𝜌Δ𝑡 = 𝐶𝑣 Δ𝑇
Symbols and units
= Δ𝑇
J
(A/m2)
ρ
(Ωm)
Cv
(J/K/m3)
Δt
s
Time step
ΔT
K
Temperature increase
fCu
Acable
T. Salmi, TUT
Current density
Electrical resistivity
Volum. heat capacity of ins. cable
(Cu + Nb3Sn + G10)
Cu fraction in the ins. cable
m2
Area of the insulated cable Xsection
34