Transient Thermal, Electrical and Lifetime Analysis of
Large-Can Aluminum Electrolytic Capacitors
Sam G. Parler, Jr., P.E.
Director of Research and Development
Presented at The Applied Power Electronics Conference (APEC) 2015
1
Outline:
I. Consequences and analysis techniques of transient behavior
peculiar to large aluminum electrolytic capacitors:
1. Time-varying hotspot location
2. Highly anisotropic winding
3. Coaxial microstructure and non-uniformly distributed RC behavior
II. Calculating capacitor lifetime with time-varying stressors:
1. Why arithmetic averaging doesn’t work
2. Development of nonlinear averaging technique
3. Example of application to discrete stressor distribution
4. Example of application to continuous stressor distribution
Presented at The Applied Power Electronics Conference (APEC) 2015
2
Distinguishing feature #1: Time-varying hotspot location
Tab Mass
Winding Mass
<<
Tab R
Winding R
Spatial distribution of transient response to current
pulse will be much different from that of the steady
state response.
Steady state response to 30 amps rms in 45 ºC
ambient shows tabs running no hotter than winding:
Presented at The Applied Power Electronics Conference (APEC) 2015
3
Time-varying hotspot location
Transient Response to 16 kA pulse at 45 ºC
initial temperature and subsequent cool-down
shows <0.1 ºC heat rise in winding but 5 ºC
heat rise in the aluminum tabs:
The tab cool-down curve from initial 10 ºC
step shows a time constant of 7 seconds.
Presented at The Applied Power Electronics Conference (APEC) 2015
4
Time-varying hotspot location
Modeling approaches include FEA as previously shown, or lumpedelement Spice model as shown in the thermal circuit below.
Thermal
→
Electrical
mCP → C
θ→R
P→I
T→V
Presented at The Applied Power Electronics Conference (APEC) 2015
5
Distinguishing feature #2: Highly anisotropic winding
The winding is of cellulosic separators and aluminum foils, and thus exhibits thermal
anisotropicity over two orders of magnitude higher conductivity in the axial than in the radial
direction. This behavior can be captured in FEA using diagonal tensor conductivity matrix,
e.g. {0.6,0.6,100}, or approximated in Spice by using separate axial and radial thermal
resistances. Note: Fixed radial conductivity valid only for large capacitors.
Nota bene:
The can wall
is not
isothermal !
Presented at The Applied Power Electronics Conference (APEC) 2015
6
Highly anisotropic winding
Below is a comparison of a metallized polypropylene film capacitor and
an aluminum electrolytic capacitor, both approx 76x120 mm and
dissipating 5 watts in 45 ºC environment.
Presented at The Applied Power Electronics Conference (APEC) 2015
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Distinguishing feature #3:
Coaxial microstructure and distributed RC behavior
The electrolyte is an ionically conductive fluid; this is not the dielectric.
The dielectric is aluminum oxide Al2O3 which is grown in an anodizing bath upon
the tortuous surface of a highly etched aluminum foil.
In an aluminum
electrolytic
capacitor, the (+)
conductor is the
aluminum anode foil
and the (-) is the
electrolyte.
Note: In the micrographs below, the aluminum surrounding the alumina dielectric tubes has been dissolved away.
Presented at The Applied Power Electronics Conference (APEC) 2015
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Coaxial microstructure and distributed RC behavior
URC Analytic or Spice Element as a first approximat ion :
Units:
Cap vs. Frequency & Temp
1000
r [Ω/m]
c [F/m]
Shortcoming:
Above model predicts R
& C to fall as 1/√f
(Warburg element) while
typical behavior
is usually closer to 1/f.
Cap (µF)
L [m]
100
10
1
0.1
10
100
1000
10000
100000
1000000
Freq (Hz)
85 ºC
65 ºC
25 ºC
0 ºC
‐20 ºC
‐40 ºC
45 ºC
Presented at The Applied Power Electronics Conference (APEC) 2015
1/f Reference
9
Transient modeling of non-uniformly distributed RC behavior
Potential improvements to uniform RC line model: Finite-length tapered RC line
PSpice implementation?
* Non-uniform / tapered lines not directly supported in PSpice
* While exact expressions in s domain exist for some taper profiles, they
generally involve Bessel and Kelvin functions, which make it impossible to
implement directly as ABM “ELAPLACE” component.
* Possible approximation: Use PSpice’s EFREQ source with (freq, mag, phase)
list as shown on next slide.
Other Approaches:
FEA easily accommodates arbitrary taper profiles
FEA shape-optimization tools can find a best-fit taper
Presented at The Applied Power Electronics Conference (APEC) 2015
10
Transient modeling of non-uniformly distributed RC behavior
* Data taken at -40 ºC in chamber with Z bridge controlled with VB.net
* Data stored in spreadsheet automatically using VB.net (see below)
* Spreadsheet data converted to Spice-compatible (f,|Z|,θ) listing
using spreadsheet text functions
* Cut and paste into PSpice .cir file seen at right Æ
* PSpice graphical outputs seen at lower right
* Data and simulate match well
* Next step is to apply to transient excitation
Data and Representative Model Points: R, C, ρ, |Z| vs. Frequency & Temperature
0
1000
‐0.2
100
‐0.4
‐0.8
‐1
ρ (rad)
R,|Z|(Ω); C(µF)
‐0.6
10
1
‐1.2
‐1.4
0.1
‐1.6
0.01
10
100
1000
10000
100000
‐1.8
1000000
Freq (Hz)
‐40 ºC R (Ω) Data
‐40 ºC C (F) Points
‐40 ºC |Z| (Ω) Points
‐40 ºC /θ (rad) Points
‐40 ºC R (Ω) Points
‐40 ºC C (F) Data
‐40 ºC |Z| (Ω) Data
‐40 ºC /θ (rad) Data
Presented at The Applied Power Electronics Conference (APEC) 2015
11
Transient modeling of non-uniformly distributed RC behavior
There is a problem in Spice:
* Warning messages of non-causality
* Message advices to delay excitation by at least 34.5 ms
However:
* Delaying excitation by 100 ms does not fix the problem
* Warning message still occurs
* Response waveform is not correct
Presented at The Applied Power Electronics Conference (APEC) 2015
12
Transient modeling of non-uniformly distributed RC behavior
Alternative Approach using FEA Shape-Optimization Techniques:
* Start with rectangular, electrolyte-filled pore with capacitive walls
* Create a “deformed mesh” that allows the vertical pore wall to move radially by dr(z) where
dr =
N
∑q
k =1
k
d k sin kπ s
* Minimize an objective function representing the impedance error, e.g.:
⎛ R
R
⎜⎜
− TARGET
R
⎝ RTARGET
2
⎞ ⎛ C
C
⎟⎟ + ⎜⎜
− TARGET
C
⎠ ⎝ CTARGET
⎞
⎟⎟
⎠
2
Presented at The Applied Power Electronics Conference (APEC) 2015
13
Transient modeling of non-uniformly distributed RC behavior
Physical Model Assures Causality
Voltage varying with zero
terminal current is typical
of capacitor exhibiting
dielectric relaxation,
dielectric loss and
“soakage”
Presented at The Applied Power Electronics Conference (APEC) 2015
14
Other transient modeling considerations:
Calculating lifetime with time-varying stressors
Typical capacitor lifetime equation is:
where
L = LB M V 2(TB −TC ) /10
LB = Base lifetime with rated DC voltage applied at TB ambient
TC = Core temperature
MV = Voltage multiplier such as (VR/VA)3 where
VR = rated DC voltage and
VA = applied DC voltage (VA ≤ VR )
Obviously lifetime varies with the applied stressors in a highly nonlinear manner.
Thus when the stressors vary with time, arithmetic averaging is not valid.
Actual capacitor lifetime will in general be lower than the arithmetic average.
For example, if the capacitor is operating at 25 ºC for 12 hours per day and
at 85 ºC for the other 12 hours per day, the lifetime will be considerably
less than the lifetime calculated at a constant 55 ºC.
So… How do we calculate the lifetime when the stressors vary with time?
Presented at The Applied Power Electronics Conference (APEC) 2015
15
Calculating lifetime with time-varying stressors
L = LB M V 2(TB −TC ) /10
We calculate the lifetime when the stressors vary with time as follows:
Let us consider a time varying core temperature TC(t).
If L is the lifetime, then the rate at which the lifetime is consumed is 1/L.
Therefore for each elapsed time element dt, the portion of the total lifetime
that is consumed is dt/L. This can be done on an hour-by-hour basis in a
spreadsheet, or it can be calculated analytically as follows:
If the stressor TC(t) is applied for a representative period τ then the lifetime
is:
τ
τ
L=
τ
∫
0
dt
L[ stressors (t )]
=
τ
∫
0
dt
L[TC (t )]
Presented at The Applied Power Electronics Conference (APEC) 2015
16
Calculating lifetime with time-varying stressors
L = LB M V 2(TB −TC ) /10
Assume the above has LB = 5 kh, TB = 105 ºC and MV = 1.5, then
at TC = 55 ºC the lifetime is L = 5 kh × 1.5 × 250/10 = 240 kh.
Revisiting the problem of a capacitor operating at 25 ºC for 12 hours per day and
at 85 ºC for the other 12 hours per day, we have τ = 24 h and
TC (t ) =
L=
τ
τ
∫
0
dt
L[ stressors (t )]
=
τ
τ
∫
0
=
25 0 ≤ t < 12 ⎫
⎬
85 12 ≤ t < 24⎭
dt
L[TC (t )]
=
24h
12
∫
0
24h
12h
12h
+
1920kh 30kh
dt
7.5kh × 2
105 − 25
10
+∫
dt
24
12
7.5kh × 2
105 −85
10
= 59,077 h << 240 kh
Presented at The Applied Power Electronics Conference (APEC) 2015
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Example: Calculating lifetime with daily and seasonally varying stressors
L = LB M V 2(TB −TC ) /10
Again assume the above has LB = 5 kh, TB = 105 ºC and MV = 1.5.
Assume average temperature is 65 ºC and that the daily temperature and
annual variations are sinusoidal, each with 20 ºC peak-to-peak.
In Mathematica we calculate the lifetime as 95 kh:
Presented at The Applied Power Electronics Conference (APEC) 2015
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Summary
There are some properties of large aluminum electrolytic capacitors that differ
from small ones, such as:
Constant radial thermal conductivity
Relative electrothermal tab stress during large pulse currents
Quite a few properties of aluminum electrolytic capacitors differ from those of
metallized film and most other capacitors, including:
Lossy aluminum tabs
High thermal anisotropicity
Large impedance variation with temperature due to electrolyte viscosity
Large dielectric loss and attendant memory effects
Distributed RC impedance behavior
The above characteristics can make transient modeling a challenge.
Lifetime models of large aluminum electrolytic capacitors are similar to those of
other technologies, but special techniques need to be used in order to model the
lifetime under time-varying stressors.
Presented at The Applied Power Electronics Conference (APEC) 2015
19
Biography
Sam G. Parler, Jr., P.E., was born in South Carolina, USA, in
1961 and studied electrical engineering at Clemson University.
After receiving his BSEE degree in 1984, he worked for Union
Switch & Signal as a test engineer and as a product engineer.
From 1988 to 1991 he directed a Strategic Defense Initiative
(also known as Star Wars) contract for Cornell Dubilier,
developing high energy density capacitors for military
applications. In 1994 he co-founded Maven Capacitor Corporation (presently owned
by St. Jude Medical) to develop and produce high energy density aluminum
electrolytic pulse capacitors for implantable defibrillators.
Mr. Parler has served as Director of Research and Development for Cornell Dubilier
since 1996, and is a Senior Member of the IEEE and holds five patents in the area of
capacitors, including two on hermetically sealed aluminum electrolytic capacitors.
His topics of capacitor research include thermal modeling, impedance and SParameter modeling, structural modeling, life and reliability modeling. Mr. Parler is
always seeking ways to model and improve capacitor performance.
Presented at The Applied Power Electronics Conference (APEC) 2015
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