Download Frequency Transfer Function*of a dipole

Frequency Transfer Function
of a dipole
What is it
Why is it important
How to calculate it
How to model it
How to measure it
Emmanuele Ravaioli
LHC-CM
Thanks to Hugues Thiesen, Guy Deferne, Christian Giloux,
Bernard Dubois, Emmanuel Garde, Miguel Cerqueira Bastos
11-11-2011
Frequency Transfer Function of a dipole
• Simulation of the electrical behavior of the LHC dipole circuits
• Model of a dipole
• Frequency Transfer Function
• Measurements in SM18: Set-up and results
• Comments on the results…
• Conclusions & Further Work
Emmanuele Ravaioli
LHC-CM
11-11-2011
2
Simulation of the electrical behavior of the LHC dipole circuits
For more info:
• TE-Magnet-Seminary - Circuit simulations of the main LHC dipoles and the case of the 'unbalanced' dipoles – Ravaioli
• 5JO-3_Ravaioli_20110916
• Modeling of the voltage waves in the LHC main dipole circuits
Emmanuele Ravaioli
LHC-CM
11-11-2011
3
Model of a dipole
L = Laperture = 49 mH
C = Cground = 150 nF
Rp = Rparallel = 100 Ω
Cp = 1 pF (for the moment)
k = 0.75
7 Ω < R1,2 < 10 Ω
Eddy Currents in the coils
Inhomogeneous AC
behavior of the two
apertures of the dipole
Magnetization Effects
Different frequency
response
Parasitic Coil-to-Ground
Capacitance
Phase-velocity of the
wave changing along
the dipole chain
Parasitic Turn-to-Turn
Capacitance
Each aperture shifts the
wave of a different
angle
For more info:
• 5JO-3_Ravaioli_20110916
• Modeling of the voltage waves in the LHC main dipole circuits
Emmanuele Ravaioli
LHC-CM
11-11-2011
4
Frequency Transfer Function
Example:
L = 2*Laperture = 98 mH
C = 2*Cground = 300 nF
R = Rparallel = 100 Ω
Matlab application
for the study of the parameters
of the proposed model
of a dipole aperture
Impedance of a stand-alone aperture model: (C/2) // [ (1-k)*L + (k*L // R) ] (second Z/2 bypassed by a short-circuit)
Impedance of a series of aperture models:
(Cp, Rp ignored here for simplicity)
(C/2) // ∑Nmodules { [ (1-k)*L + (k*L // R) ] + C // [ (1-k)*L + (k*L // R) ] }
Emmanuele Ravaioli
LHC-CM
11-11-2011
5
Measurements in SM18: Set-up
• Two power converters in parallel, one providing the current level I_max and the other one providing a
sinusoidal oscillation of ±4 V at a frequency sweeping between 30 and 2 kHz.
• The gain-phase analyzer measures two differential voltages: one coming directly from the voltage taps of
the dipole (Umag) and one proportional to the current flowing through the DCCT, ie through the dipole
(Imag); this latter signal is acquired through an AC coupled differential amplifier with a gain of 1000.
•
•
•
•
•
•
Test without current (only Gain-Phase Analyzer and dipole, no PCs; frequency range: 1-20 kHz)
Tests at different I_max: 0 A ; 50 A ; 1 kA ; 2 kA ; 3 kA ; 4 kA ; 5 kA ; 6 kA .
Tests at different dI/dt (varying current): 0 A/s ; ±10 A/s ; 20 A/s ; 30 A/s ; 40 A/s ; ±50 A/s .
Tests measuring two separate apertures.
Tests measuring four separate poles.
Test after disconnecting Rparallel .
Emmanuele Ravaioli
LHC-CM
11-11-2011
6
Measurements in SM18: Results
No PCs – Impedance
Imax = 0*
* Without Power Converters
dI/dt = 0 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Magnet
7
Measurements in SM18: Results
Different Imax – Phase
Imax = 0*
* Without Power Converters
dI/dt = 0 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Magnet
8
Different Imax – Impedance
Measurements in SM18: Results
Imax = 0*, 50, 1000, 2000, 3000, 4000, 5000, 6000 A
* Without Power Converters
Emmanuele Ravaioli
LHC-CM
dI/dt = 0 A/s
11-11-2011
Magnet
9
Different Imax – Phase
Measurements in SM18: Results
Imax = 0*, 50, 1000, 2000, 3000, 4000, 5000, 6000 A
* Without Power Converters
Emmanuele Ravaioli
LHC-CM
dI/dt = 0 A/s
11-11-2011
Magnet
10
Measurements in SM18: Results
Different Imax – Impedance
Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A
Emmanuele Ravaioli
dI/dt = 10 A/s
LHC-CM
11-11-2011
Magnet
11
Measurements in SM18: Results
Different Imax – Phase
Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A
dI/dt = 10 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Magnet
12
Measurements in SM18: Results
Different Imax – Impedance
Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A
Emmanuele Ravaioli
dI/dt = -10 A/s
LHC-CM
11-11-2011
Magnet
13
Measurements in SM18: Results
Different Imax – Phase
Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A
dI/dt = -10 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Magnet
14
Measurements in SM18: Results
Different Imax – Impedance
dI/dt = 0, ±10, 20, 30, 40, ±50 A/s
Emmanuele Ravaioli
Imax > 50
LHC-CM
11-11-2011
Magnet
15
Measurements in SM18: Results
Different Imax – Phase
dI/dt = 0, ±10, 20, 30, 40, ±50 A/s
Emmanuele Ravaioli
Imax > 50
LHC-CM
11-11-2011
Magnet
16
Measurements in SM18: Results
Different Imax – Impedance
Imax = 0*, 50 A
* Without Power Converters
dI/dt = 0 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Apertures
17
Measurements in SM18: Results
Different Imax – Phase
Imax = 0*, 50 A
* Without Power Converters
dI/dt = 0 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Apertures
18
Measurements in SM18: Results
Different Imax – Impedance
Imax = 0*, 0 A
* Without Power Converters
dI/dt = 0 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Poles
19
Measurements in SM18: Results
Different Imax – Phase
Imax = 0*, 0 A
* Without Power Converters
dI/dt = 0 A/s
Emmanuele Ravaioli
LHC-CM
11-11-2011
Poles
20
Measurements in SM18: Results
Different Imax – Impedance
Imax = 0*, 50**, 1000, 2000 A
* Without Power Converters, With Rparallel
dI/dt = 0 A/s
** With Rparallel
Emmanuele Ravaioli
LHC-CM
11-11-2011
Magnet, No Rparallel
21
Measurements in SM18: Results
Different Imax – Phase
Imax = 0*, 50**, 1000, 2000 A
* Without Power Converters, With Rparallel
dI/dt = 0 A/s
** With Rparallel
Emmanuele Ravaioli
LHC-CM
11-11-2011
Magnet, No Rparallel
22
Measurements in SM18: Results
Different Imax – Impedance
Imax = 0*, 50**, 1000 A
* Without Power Converters, With Rparallel
dI/dt = 0 A/s
** With Rparallel
Emmanuele Ravaioli
LHC-CM
11-11-2011
Apertures, No Rparallel
23
Measurements in SM18: Results
Different Imax – Phase
Imax = 0*, 50**, 1000 A
* Without Power Converters, With Rparallel
dI/dt = 0 A/s
** With Rparallel
Emmanuele Ravaioli
LHC-CM
11-11-2011
Apertures, No Rparallel
24
Comments on the results...
1.
-1
The measured Frequency Transfer Function (FTF) is not fitting with the expected one, and
corresponds to parameters different from the nominal ones:
•
•
L
Rparallel
49 mH
100 Ω
→ 35 mH
→ 80 Ω
• k
• R
0.75
10 Ω
→
→
0.45-0.55
30 Ω
• The shape of the measured Frequency Transfer Function does not correspond to the expected curve
calculated with the adopted electrical model.
Possible explanation: The model has been tailored on the measurements during Fast Power Aborts, when
the main excitation frequency is ~28.5 Hz. Therefore it is possible that the model fits well the behavior
of the dipoles, but only around 30 Hz. (see the qualitative example below: measurement, old model,
new model)
Emmanuele Ravaioli
LHC-CM
11-11-2011
25
Comments on the results...
-1b
• Development of a new electrical model of the dipole apertures, fitting their behavior in a wider range
of frequency, and test of its capability to simulate the actual behavior of the dipole circuit. Such a
model could be developed by fitting the curve of the impedance of an aperture without Rparallel , and
may include the splitting of the inductance in 3 parts (4 free parameters: k1, k2, R1, R2). Fitting already
started with Matlab.
Emmanuele Ravaioli
LHC-CM
11-11-2011
26
Comments on the results...
2.
-2
The AC inductance of the dipole even at low frequency (0.1 Hz) is about 35-40 mH, whereas the
measured DC value is close to the nominal ~100 mH. This phenomenon has been observed in the past.
The AC inductance was measured with two independent systems (without PCs between 0.1 Hz and 20
kHz; with PCs between 30 Hz and 2 kHz) with similar outcome. It would be interesting to perform this
measurement also for the new configuration between 0.1 Hz and 30 Hz. (first attempt on Wednesday,
still problems; Hugues is taking care of it).
→ At which frequency is the dipole changing its inductance?
3.
FTF almost independent on the current level (!)
→ Why do the dipoles exhibit a different behavior at different current?
3.
FTF almost independent on the current ramp-rate (!)
4.
FTF of the two apertures is very similar
→ Did we spot a perfectly balanced dipole?
Emmanuele Ravaioli
LHC-CM
11-11-2011
27
Conclusions & Further Work
• The measurement system seems to work fine, and the results have physical significance.
• The initial problems related to the poor quality of the measurement of the DCCT current have been
solved (Miguel).
• Thanks to the SM18 team for the kind support!
Further Work
• Measurements of the FTF with the current configuration (parallel PCs) between 0.1 Hz and 30 Hz. To
be done modulating a sinusoidal signal with the large PC, and measuring the impedance corresponding
to different frequencies (manually).
• Repeat the same measurements on another available spare dipole, hoping to spot an unbalanced dipole.
• Development of a new electrical model of the dipole apertures, fitting their behavior in a wider range
of frequency, and test of its capability to simulate the actual behavior of the dipole circuit. Such a model
could be developed by fitting the curve of the impedance of an aperture without Rparallel , and may
include the splitting of the inductance in 3 parts (4 free parameters: k1, k2, R1, R2). Fitting already
started with Matlab.
• Enlightened by the new results and model, check that the expected change of FTF is theoretically
visible (With the old model, changing R1,2 between 7 and 10 Ω leads to a difference of ~1 dB of the
impedance of two unbalanced apertures... With the new?).
• Analysis of the past FTF measurements (at cold, no PCs, 0 current).
• Analysis of the measurements of the FTF of the whole chain of 154 dipoles (Report Interpretation of
the TFM tests of dipole circuits, PJK (?), 5 March 2008), and comparison with the calculated FTF of the
series of 308 aperture models.
Emmanuele Ravaioli
LHC-CM
11-11-2011
28