1
Analysis and Evaluation of DC-Link Capacitors for High Power
Density Electric Vehicle Drive Systems
H. Wen1, W. Xiao1, and Xuhui Wen2, P.R. Armstrong1,3
1
Electrical Power Engineering Program, Masdar Institute of Science and Technology, Abu
Dhabi, United Arab Emirates (Email: hwen@masdar.ac.ae).
2
Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China (e-mail:
wxh@mail.iee.ac.cn)
3
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Abstract - In electric vehicle (EV) inverter systems, dc-link capacitors, which are bulky,
heavy and susceptible to degradation from self heating, can become a critical obstacle to high
power density. This paper presents a comprehensive method for analysis and comparative
evaluation of dc-link capacitor applications to minimize the volume, mass and capacitance.
Models of equivalent series resistance (ESR) that are valid over a range of frequency and
operating temperature are derived and experimentally validated. The RMS values and frequency
spectra of capacitor current are analyzed with respect to three modulation strategies and various
operating conditions over practical ranges of load power factor and modulation index in EV
drive systems. The modeling and analysis also consider the self-heating process and resulting
core temperature of the dc-link capacitors, which impacts their lifetimes. Based on an 80kW
permanent-magnet (PM) motor drive system, the application of electrolytic capacitors and film
capacitors has been evaluated by both simulation and experimental tests. The inverter power
density is improved from 2.99 kW/L to 13.3 kW/L without sacrificing system performance in
terms of power loss, core temperature, and lifetime.
Index Terms - Electric Vehicle (EV); Power Density; Dc-Link Capacitor; Ripple Current
Stress; Equivalent Series Resistance (ESR); Parasitic Inductance.
2
I. INTRODUCTION
Electric Vehicle (EV) research has intensified recently due to the global warming and other
environmental concerns surrounding the existing petroleum-based transportation infrastructure
[1, 2]. In EVs, the most common power interface between batteries and traction motors is the
voltage source inverter (VSI), as shown in Fig. 1. Current EV inverter research is concerned
with aspects of compact design [3-5], low cost [6, 7], high reliability [8-10] and long lifetime
[11]. Several topologies and optimization strategies have been investigated to meet multiple
objectives under the stringent operation requirements of EV inverters [12-15]. For example,
overload conditions of 2-2.5 times rated capacity can last 1-3 minutes and power electronic
components are expected to tolerate inlet coolant temperatures up to 105ºC [16]. Other design
requirements include high efficiency and high power density [17].
ibat
iinv
ic1
ic 3
ic 5
id 1
icap
Vin
S1
Cdc
S3
iq1
ic 4
S4
S5
ic 6
S6
ic 2
ia
ib
ic
Motor
S2
Fig. 1 Schematic of a typical electric vehicle drive system including a battery bank, dc-link
capacitors, VSI, and traction motor from left to right.
Many efforts have been directed toward improving the power density, which may be
quantified as the power density by weight (PDW) and the power density by volume (PDV). For
example, the FreedomCAR and Vehicle Technologies (FCVT) program in the U.S. aims to
develop energy efficient and environmentally friendly highway transportation systems[18, 19].
The FCVT program reports that the PDW and the PDV of EV inverters have been increased
from 4.08 to 10.04 kW/kg and from 2.03 to 8.82 kW/L, respectively [3]. Further improvement
is expected to achieve more than 14.1 kW/L in PDV of EV inverters according to the FCVT
3
technology roadmap [18]. A corresponding technology roadmap has been defined in China in
terms of cost, efficiency, and power density [20]. In an example of high performance
possibilities, the latest SiC JFETs-based inverter shows a potential 51 kW/L PDV while
achieving 97.8% efficiency [21]. Table I summarizes main technical parameters and objectives
corresponding to the road maps and timelines of EV drive system development programs in
U.S. and China.
TABLE I
SUMMARY OF TECHNICAL ROAD MAP TARGETS FOR ELECTRIC VEHICLE DRIVE SYSTEMS
Subsystem
Inverter
Parameters
FreedomCar FreedomCar Chinese Goals
phase I [3] phase II [3]
in 2006 [22]
FreedomCar
FreedomCar
Goals in 2006 [18] Goals in 2020*[19]
Sic JFET-based
Converter
[21, 23]
PDW (kW/kg)
4.08
10.04
2~5
>12
>14.1
>51
PDV (kW/L)
2.03
8.82
~
>12
>13.4
>51
Efficiency
@maximum load
80~88%
80~88%
90~92%
92%
94%
97.8%
Motor types
IM
IM
PM, IM and SRM
PM
PM
PM
PDW (kW/kg)
0.5~1
0.5~1
0.5~1
>1.2
>1.6
>1,3
PDV (kW/L)
1.01~
1.01~
1.01~
>3.7
>5.7
>5
Efficiency
90
90
92~95%
>93%
>94%
>93%
Efficiency
72~84%
76~86%
90~92%
92%
94%
>92%
Cooling mode
Forced air
Liquid
Liquid
Liquid
Liquid or air
Natural air
Ambient Temp.
-25~50 °C
-25~50 °C
~70 °C
~105 °C
105 °C
120 °C
Cost($/kW)
-
-
70
<105
<62.7
-
Total Mileage (km)
-
-
241402 (15 yrs)
241402 (15 yrs)
Motor
System
241402 (15 yrs) 241402 (15 yrs)
* Based on a maximum coolant or air temperature of 105°C
In EV inverter systems, the dc-link capacitors are essential to provide reactive power,
attenuate ripple current, reduce the emission of electro-magnetic interference, and suppress
voltage spikes caused by leakage inductance and switching operations [24]. DC-link capacitors
are bulky, heavy and expensive [25]. One typical design comprises five electrolytic capacitors,
which are connected in parallel with the battery bank to supply a 80 kW motor drive system
[26]. Each capacitor is 9.4 cm in diameter and 14.6 cm in height. Since the five dc-link
capacitors occupy more than 40% of the volume, the achievable PDV is limited to 2.99 kW/L.
Furthermore, the height of dc-link capacitors is higher than most IGBT modules and requires a
crooked busbar to make the connection. The resulting parasitic inductance may exceed 100 nH
4
causing voltage spikes, which are a major factor in the failure of power electronic devices. For
the above-mentioned reasons, an optimum design of dc-link capacitor is critical to achieve the
goals shown in Table I. Some basic requirements for choosing and comparing different
capacitors for EV inverter applications include the following.
 The dc-link capacitors should be able to handle the ripple current under all VSI operating
conditions for EV applications. The AC ripple current should never exceed 10% of the rated
battery current to avoid significant degradation on the lifetime of battery.
 The ripple voltage across the dc bus should be limited to 10% of the rated voltage for all
expected load conditions. Low inductance capacitors are preferred to avoid overvoltage failure
of IGBTs.
 Hot spot temperature should be below 105°C under maximum ambient temperature for
any expected load condition.
Ripple current is one of the main considerations in sizing and selecting dc-link capacitors.
Approaches have been proposed to reduce the capacitor current ripple and minimize the
capacitor size without violating other constraints by coordinating the modulation strategies
between the active rectifier and the PWM inverter stages [27, 28]. The coordinating modulation
method has been shown to cancel most of the dc-link capacitor ripple current in Hybrid EV
DC-DC converters and inverter system applications [29]. However, the implementation of
coordinating control strategies is infeasible for the EV drive system shown in Fig. 1, where the
dc-link capacitors are connected directly in parallel with the battery bank without any power
stages in between [30, 31]. For the EV drive system shown in Fig. 1, research mainly focuses
on the ripple current analysis and current harmonics calculation [31-34]. Most analysis has
been based on an ideal capacitor model, which cannot accurately predict power loss and
capacitor lifetime. The ideal capacitor model does not properly account for the effects of
variation of load power factor and modulation index in a practical EV system. Models that
include equivalent series resistances (ESR) and show the effects of temperature and frequency
are investigated and applied to electrolytic capacitors in [35-37]. Their modeling approach
5
concentrates on only the characteristic analysis for electrolytic capacitors. A systematic
comprehensive evaluation of the benefits and drawbacks of film capacitors for EV inverter
applications has not been reported. The basic requirements, system constraints, and
performance metrics have not been fully and systematically addressed. In EV inverter systems,
the capacitor ripple current consists of various frequency components corresponding to
different pulse width modulation (PWM) strategies. Therefore, the frequency spectrum analysis
of the capacitor current and an accurate model of ESR with consideration of the temperature
and frequency response are important to properly account for the self-heating process of dc-link
capacitors. Further, the electro-thermal coupling dynamics must be evaluated to estimate the
true core temperature of the dc-link capacitors, which is critical to predict capacitor lifetime.
This paper presents a comprehensive analysis and evaluation of dc-link capacitors in EV
inverter systems to improve the power density. The analysis starts with ESR models of both
electrolytic and film capacitors. The derived mathematical models are verified by experiments.
The voltage and current stresses are analyzed with respect to three common modulation
strategies including sinusoidal PWM (SPWM), space vector modulation (SVM) and third
harmonics injection (THI). The frequency spectrum of the capacitor ripple current is also
investigated corresponding to these modulation strategies over the practical ranges of load
power factor and modulation index. Based on the above analysis, the self-heating process and
the resulting core temperature are modeled and analyzed. Two design schemes using
electrolytic and film capacitors are compared through simulation and experiments in terms of
power loss, core temperature, lifetime and battery current harmonics. The proposed design has
been tested in an 80kW permanent-magnet (PM) motor drive system.
II. CAPACITOR CHARACTERISTICS
This section investigates the ESR models of electrolytic and film capacitors and shows the
characteristics of frequency and self heating.
6
A. Electrolytic capacitor
Electrolytic capacitors are commonly used as the dc-link capacitors due to their large
capacitance per unit volume. The ESR model of an electrolytic capacitor is illustrated in Fig. 2
[38], where the resistance R0 accounts for the sum of resistances of foil, tabs, and terminals, R1
represents the electrolyte resistance, C1 represents the terminal capacitance, and the parallel
combination of R2 and C2 represents the dielectric dynamics. The ESR of the capacitor in terms
of the frequency responses is derived accordingly.
ESRe  R1  R0 
R2
1   2 fR2C2 
2
(1)
For electrolytic capacitors, a rise in temperature causes a decrease in ESR because the
resistance R1 is reduced by the increased conductivity of electrolyte. The effect of temperature
on R1 is described by (2) [35, 39].
R1  R1b e
Tbase T
F
(2)
where R1b represents the value of R1 at the base temperature Tbase (27 oC), T is the capacitor core
temperature (oC), and F is a temperature sensitivity factor [40].
C1
C2
R2
R1
R0
Fig. 2 ESR model of an electrolytic capacitor.
B. Film capacitor
A R-L-C series equivalent circuit that includes the equivalent inductance Lc, capacitance Cc
and resistance Rc is used to model film capacitors. When the operating frequency is higher than
1 kHz, the ESR value can be modeled as a function of frequency based on [41].
7
ESR  f    Rs  As   K ( f )  As
(3)
where Rs is the base resistance, f represents the frequency, and As is a given value depending on
the capacitor size. K(f) is the predefined function showing the effect of frequency, which is
usually given by plots in manufacturer datasheets. In this analysis, K(f) is mathematically
expressed as a cubic polynomial function, as shown in (4), in which the coefficients k0-3 can be
established by using least square curve fitting.
K ( f )  k3  f 3  k2  f 2  k1  f  k0
(4)
In contrast with the electrolytic capacitor, the ESR value of film capacitors increases with
the frequency. Its temperature-sensitivity is less than that of electrolytic capacitors [41] because
the ESR of film capacitors results mainly from the tabs and contact resistances, but not from the
electrolyte [42].
C. Ripple current multiplier
Since the ESR values of electrolytic and film capacitors show frequency-dependent
characteristics, a ripple current multiplier Mf is defined in (5) to characterize the ripple current
that capacitors can absorb at a given frequency.
Mf 
If
I100

ESR100
ESR f
(5)
where I100 and ESR100 are defined as the rated ripple current and the ESR value at 100Hz, which
are usually given by manufacturers. If and ESRf represent ripple current and ESR at a specific
frequency. Electrolytic capacitors are characterized as absorbing more high-frequency ripple
current than the low-frequency component. Conversely, the film capacitors usually handle less
high-frequency ripple current because the ripple current multiplier drops with increasing ESRf.
III. CAPACITOR RIPPLE CURRENT AND VOLTAGE
The battery current (ibat) is the sum of capacitor current (icap) and dc-link current (iinv), as
shown in Fig. 1. These current waveforms are greatly affected by the load power factor cos ,
8
which determines the current flowing into IGBT devices or free-wheeling diodes of the VSI. As
a result, the practical EV operating conditions, expressed in terms of load power factor and
modulation index, must be considered in evaluating the capacitor ripple current and voltage.
A. Capacitor ripple current analysis
Based on the synthesis of the inverter input current modulation by SVM [34], the RMS
capacitor ripple current Icap can be expressed by (6).
I cap  I N
M 
4 3  4cos 2  6   9  M   cos 2  1
32 
(6)
where, M is the modulation index, IN is the output phase current amplitude, and  is the phase
delay of inverter output current with respect to the voltage fundamental.
Fig. 3 illustrates the dependence of Icap/IN on modulation index M and load power factor
cos . The modulation index corresponding to the maximum RMS value of capacitor ripple
current is denoted as MIcap(max), and it depends somewhat on modulation strategy. The SPWM
and SVM share the same expression (7) for MIcap(max), and for THI MIcap(max) is given by (8).
 4 3(2cos 2  3) 
M Icap (max)  min 
,1
 9  cos 2  1 
(7)
 4 3(2cos 2  3)

M Icap (max)  min 
,1.15
 9  cos 2  1

(8)
9
0.5
I
/I
cap N
0.4
THI
SPWM & SVM
0.3
0.2
0.1
0
1
0.8
0.6
0.4
cos 
0.2
0
0
0.2
0.4
0.6
0.8
1 1.15
M
Fig. 3 Ratio of Icap/Il is a function of modulation index M and load power factor cos .
Shown in Fig. 3, the blue line illustrates the maximum RMS value of capacitor ripple current
corresponding to the THI modulation strategy, under which the modulation index can range
from 0 to 1.15. The black line indicates the upper bound (M = 1) of MIcap(max) when modulation
is by SPWM or SVM . In order to address typical operation conditions, the distribution of
MIcap(max) in relation to the load power factor is plotted in a two-dimensional space, which is
shown in Fig. 4. When the cos is lower than a certain value of the power factor th , the ratio
increases with M and reaches to the maximum at the upper bound of modulation range. When
cos is larger than th , MIcap(max) is located in the middle of the modulation range, no longer at
the upper bound. It is noticeable that THI shows a different th value from SPWM and SVM
since the modulation index is up to 1.15. In the case of THI, the threshold value of the load
power factor cos th is 0.43, while the corresponding threshold value of load power factor th is
0.49 in the cases of SPWM and SVM. Based on the above analysis, five typical operating
conditions denoted by P1-P5 are defined in Table II.
10
TABLE II
PREDEFINED TYPICAL OPERATING CONDITIONS P1-P5
Operating condition
Modulation index M
Load power factor cos
P1
1.15
0.43
P2
1
0.49
P3
1.15
0.23
P4
1
0.23
P5
0.625
0.954
1.2
P1 (0.43,1.15)
P3 (0.23,1,15)
1.1
P2 (0.49,1)
Icap(max)
1
M
THI
SPWM&SVM
P4 (0.23,1)
0.9
0.8
0.7
P5 (0.954, 0.625)
0.6
0.5
0
0.2
0.4
0.6
0.8
1
cos 
Fig. 4 The distribution of MIcap(max) corresponding to power factor cos .
The maximum current stress on a dc-link capacitor can be estimated by applying (6) over a
wide variety of load conditions for a specific motor, modulation method, and battery. Here we
consider an 80kW permanent-magnet (PM) motor is supplied by a 312V battery pack. The
capacitor maximum current stress is calculated as 105A, which is used as the base value for
capacitor ripple current evaluation.
B. Capacitor voltage ripple analysis
Table III summarizes the expressions for dc-link capacitor RMS ripple voltage (in per unit)
for different modulation strategies [43]. The base value is given by (9), where Cd is the dc-link
capacitance and f1 is the inverter switching frequency.
Vb _ volrip 
IN
Cd f1
(9)
11
TABLE III
DC-LINK CAPACITOR VOLTAGE RIPPLE EXPRESSIONS FOR SPWM, SVM AND THI
Modulation Strategies
Voltage ripple of dc-link capacitor (p.u.) [43]
0.5
SPWM

M 
96 3
9
8 3 
M  M 2  cos 2  
M
 6 
16 
5
2
5


SVM
M 
96 3
108  81 3 2 
8 3 
M
M  cos 2  
M
 6 
16 
5
16
5


M
16
THI

96 3
63 2 
8 3 
M
M  cos 2  
M
 6 
5
16
5



0.5
0.5
Fig. 5 illustrates the characteristic of dc-link ripple voltage in per unit with regard to the
modulation index M, the load power factor cos for the three modulation strategies. When the
load power factor is zero, the ripple voltage levels are the same for all three modulation
strategies SPWM, SVM and THI. When the load power factor is non-zero, the SPWM shows the
largest voltage ripple, the THI gives the lowest voltage ripple and the SVM demonstrates
relatively low voltage ripple.
v
cap
(p.u. %)
8
6
4
2
0
0
0.2
0.4
0.6
0.8
cos 
SPWM
SVM
THI
1
1.151
0
0.4 0.2
0.6
0.8
M
Fig. 5 Characteristics of the voltage ripple across the dc link as a function of modulation index
M and power factor cos for the three modulation strategies SPWM, SVM, and THI.
C. Frequency Spectrum of Capacitor Ripple Current
The frequency spectra of capacitor current icap for the predefined operating conditions, Pi,
and modulation methods are illustrated in Fig. 6 and are summarized in Table IV to
demonstrate the interaction of modulation strategy and operating condition. The current spectra
12
contain significant switching frequency f1 multiples and their sidebands (sbs). At low cos ,
switching frequency sidebands are usually the biggest harmonic components and the current
spectrum is more or less evenly distributed among f1 sbs, 3f1 sbs and 2f1. At high cos (larger
than 0.49 for SVM), 2f1 is the dominant component and its amplitude increases with cos . For
instance, the largest harmonic component is nearly 21% of output current amplitude at cos
=0.49, while the corresponding harmonic component reaches as high as 48.8% at cos =0.954.
Moreover, the impact of modulation strategy on current spectrum distribution is obvious at high
cos and the major harmonics for SVM will extend to higher frequency such as 6f1. One can
see that the ESR characteristic of the dc-link capacitor is highly affected by frequency for both
electrolytic and film capacitors. The FFT results shown in Fig. 6 and Table IV provide
60
60
50
50
40
40
Mag (% of IN)
Mag (% of IN)
information essential to proper sizing of the dc-link capacitors.
30
20
10
20
10
0
2
4
6
Frequency (kHz)
8
0
10
0
2
4
x 10
4
6
Frequency (kHz)
8
10
4
x 10
(a) P5 (M=0.625, cos =0.954), SVM
(b) P5 (M=0.625, cos =0.954), SPWM
60
60
50
50
40
40
Mag (% of IN)
Mag (% of IN)
0
30
30
20
10
0
30
20
10
0
2
4
6
Frequency (kHz)
8
(c) P5 (M=0.625, cos =0.954), THI
10
4
x 10
0
0
2
4
6
Frequency (kHz)
8
(d) P1 (M=1.15, cos =0.43), THI
10
4
x 10
60
60
50
50
40
40
Mag (% of IN)
Mag (% of IN)
13
30
20
10
20
10
0
2
4
6
Frequency (kHz)
8
0
10
0
2
4
6
Frequency (kHz)
4
x 10
8
4
(f) P3 (M=1.15, cos =0.23), THI
60
60
50
50
40
40
30
20
10
0
10
x 10
(e) P2 (M=1, cos =0.49), SVM
Mag (% of IN)
Mag (% of IN)
0
30
30
20
10
0
2
4
6
Frequency (kHz)
8
10
0
0
2
4
6
Frequency (kHz)
4
x 10
(g) P4 (M=1, cos =0.23), SVM
8
10
4
x 10
(h) P4 (M=1, cos =0.23), SPWM
Fig. 6 Frequency spectra of capacitor current based on modulation strategy and predefined
operating condition: load power factor and modulation index.
TABLE IV
COMPARISON OF SPECTRAL DISTRIBUTION FOR THE THREE MODULATION STRATEGIES AND
FIVE OPERATING CONDITIONS
Operating
condition
Modulation
P4
Major three components sorted by magnitude (% of IN)
frequency
magnitude
frequency
magnitude
frequency
magnitude
SPWM
3f1 sbs
19.2
f1 sbs
17.2
2f1
10.2
P4
SVM
f1 sbs
16.6
3f1 sbs
15.9
2f1
11.7
P1
THI
f1 sbs
20.2
3f1 sbs
12.3
2f1
7.3
P1
THI
f1 sbs
19.7
2f1
13.6
3f1 sbs
11.4
P2
SPWM
2f1
21.7
f1 sbs
15.4
3f1 sbs
14.7
P2
SVM
2f1
21.7
3f1 sbs
17.4
f1 sbs
17
P5
SPWM
2f1
49.2
4f1
13.1
3f1 sbs
11.1
P5
SVM
2f1
52
4f1
14
6f1
9.9
P5
THI
2f1
48.8
3f1 sbs
9.9
4f1
8.7
14
IV. PERFORMANCE METRICS
Based on the above analysis, four metrics are proposed to evaluate the performance of dclink capacitors: power loss, core temperature, capacitor life, and battery ripple current.
A. Power Loss and Core Temperature
The power loss of dc-link capacitors is the sum of the power dissipation of ESR from
individual frequency current components that can be calculated by using the ripple current
multiplier Mf. The expression is shown in (10), where ESR fi represents the ESR value
corresponding to the specific frequency fi and I cap is the RMS current absorbed by the capacitor
fi
at a certain frequency fi.

Pcap   ESR fi I cap f
i

2
 I cap fi
 ESR100  
 Mf




2
(10)
The self-heating process of dc-link capacitors can be numerically evaluated by using the
coupled electrothermal method. Fig. 7 depicts the iterative solution process. The computation
starts with a given ambient temperature Ta. The capacitor core temperature Tj_C is initially
calculated by using the capacitor power loss and the equivalent thermal model [41, 44].
Thermal resistances are denoted by Rhc, from hot spot to can, Rca from can to ambient, Rbp, from
can base to mounting plate, and Rha from mounting plate to ambient air. The equivalent thermal
resistance from the core of capacitor to the ambient is given by:

Rca   Rbp  Rpa  

Req _ cap   Rhc 
Rca  Rbp  Rpa 


(11)
The values of ESR and ripple current are updated repeatedly using the previous value of Tc
for each update. The iterative corrections are repeated until the process converges to within a
given tolerance. The core temperature Tj_C and the temperature rise T j _ C are used for
predicting the capacitor lifetime.
15
Start
Initial Temperature Ta=65℃
ESR model of capacitors
Necessary info.
From datasheet
I cap f from circuit simulation
i
On-line power loss calculation
2
 I cap fi
  ESR fi I cap f  ESR100  
i
M
 f

Pcap




2
Thermal model of capacitors
Tj _ C
T j _ c Rhc Tc Rbp R pa
Pcap
Rca
Ta
No
If
T j _ C  T j _ C 1
t
 ?
Yes
Calculated T j _ C , T j _ C
Fig. 7 Flowchart for iterative solving process of core temperature and ESR.
B. Capacitor Lifetime
The capacitor lifetime is influenced by the capacitor core temperature and the ripple current
and is given [17] for both kinds of capacitors by:
Le  Lb  2
T j _ C Ta
10
K
  I 2  T
1    j _ C
  I 0   10


(12)
where Lb is the capacitor lifetime under its maximum temperature and commonly given by
manufacturer datasheets. I0 denotes the allowable maximum ripple current at a given frequency,
also given in data sheets, and I denotes the actual ripple current value. The K is a constant,
which is typically assigned a value of 2 [17].
C. Battery ripple current analysis
Studies show that ripple current affects battery lifetime due to the internal temperature rise
[45]. Therefore, the battery ripple current should be maintained under a certain limit to avoid
the harmful effect. The dc-link capacitor is represented by an equivalent circuit including Rc, Lc
16
and Cc, as shown in Fig. 8. The switching frequency is 20 kHz, and that the ESR of battery
pack and interconnects can be neglected since the impedance of interconnects is dominated by
the inductance component, shown as L1 in Fig. 8. It includes the inductance introduced by the
battery pack and interconnects between the battery pack and the inverter. The battery ripple
current can be obtained as (13) according to the equivalent circuit shown in Fig. 8.
L1
Lc
I cap
I bat ,ac
I inv
Rc
Cc
Fig. 8 Equivalent AC circuit of the EV inverter for the battery ripple current analysis.
I bat , ac  s   I inv  s  
Lc Cc s 2  Rc Cc s  1
( Lc   L1,base )Cc s 2  Rc Cc s  1
(13)
  L1 L1b
(14)
The reference values of inductance (L1b) are assigned to 10 µH considering the practical
component layout and the parameters of interconnects. The RMS battery ripple current in
percentage can be defined by the division of AC RMS value (Ibat, ac) over the DC RMS current
(Ibat, dc), as shown in (15).
I bat 
I
bat , ac  fi 
I bat , dc
 100%
(15)
V. EVALUATION RESULTS AND DISCUSSION
This section includes the validations of the derived capacitor ESR models by experimental
tests and the analysis of dc-link capacitor current. Then two configurations of dc-link capacitors
are comparatively investigated through simulation and experiment for an 80 kW PM motor
drive system in terms of the previously defined performance metrics.
17
The parameters of two dc-link capacitor designs, Scheme I and Scheme II, are listed in
Table V. Scheme I uses five 3300µF electrolytic capacitors (ALS332QP500) and Scheme II
includes two 220µF film capacitors (AVX FFVE6K0227K). The capacitor specifications are
given in the Appendix. Both Schemes meet the base requirements shown in section I and are
comparable considering product availability, effect of ripple frequency, temperature, etc.
TABLE V
MAIN PARAMETERS FOR TWO DESIGN SCHEMES
Parameters
Scheme I
Scheme II
5
2
ALS332QP500
FFVE6K0227K
Total Capacitance(µF)
16500
440
Volume (LWH, cm)
38×7.7×15
16.8×8.2×8
Ripple current limit (A)
132
200
*
566
176
Quantity
Manufacturer Part
Cost($)
*
Source: http://eu.mouser.com, Date: Feb. 20, 2012
A. Validation of Capacitors Model
The ESR values using the derived model are plotted together with the experimental results
as shown in Fig. 9. The ESR values are measured using a HP4263B LCR meter. The
mathematical model shown in (1) matches the experiment evaluation regarding to the
frequency effect. Table VI summarizes the model parameters for the electrolytic capacitor.
50
measurement
math model
ESR (m )
40
30
20
10
0
-1
10
0
10
Frequency (kHz)
1
10
Fig. 9 Comparison of measured and modeled ESR for the electrolytic capacitor ALS332QP500
at 300°K.
18
TABLE VI
MODEL PARAMETERS OF THE ELECTROLYTIC CAPACITOR ALS332QP500
Parameters
Value
Resistance of foil, tabs, and terminals R0 (mΩ)
5.03
Resistance of electrolyte R1b @ 300 K (mΩ)
o
o
6
-1
Temperature sensitivity factor F ( K )
21
Dielectric loss resistance R2 (mΩ)
38.35
Terminal capacitance C1 (µF)
3300
Dielectric loss capacitance C2 (µF)
11.6
The modeling process of the film capacitor is described in Section 2B, which includes the
polynomial expression of the frequency dependent parameter K(f) and the parameter extraction
through the comparison with the measured impedance. Fig. 10 shows that the mathematical
model matches the experimentally measured frequency response for the 500V/220µF film
capacitor AVX FFVE6K0227K. Table VII summarizes the equivalent circuit parameters of
film capacitors.
40
1.5
measured
math model
measured
math model
20
()
Zc (m )
0
1
0.5
-20
-40
-60
-80
0
-2
10
10
-1
0
10
Frequency (kHz)
1
10
2
10
-100
-2
10
-1
10
0
10
Frequency (kHz)
(a)
10
1
2
10
(b)
Fig. 10 Comparison of measured and modeled impedance
for the film capacitor AVX
FFVE6K0227K at 300°K; (a) Amplitude characteristic; (b) Phase characteristic.
TABLE VII
MODEL PARAMETERS OF THE FILM CAPACITOR AVX FFVE6K0227K
Parameters
Value
Equivalent series inductance Lc (nH)
40
Coefficient of K expression f3
0.0000003173
Equivalent series capacitance Cc (µF)
210
Coefficient of K expression f2
-0.000124
1
Coefficient of K expression f1
0.02369
0.24
Coefficient of K expression f0
1.014
Base resistance Rs (mΩ)
Parameter defined by height As (mΩ)
Parameters
Value
19
The ESR characteristics of two schemes are compared in Fig. 11. It shows the ESR of
scheme II is always lower than that of the scheme I through the frequency span. Furthermore,
the ESR of scheme I decreases remarkably when the temperature increases from 27°C to 70°C.
scheme I(T a=27o C)
ESR (m )
4
scheme I(T a=70o C)
3
scheme II(T a=27o C)
2
1
0
0
10
1
2
10
Frequency (kHz)
10
Fig. 11 ESR comparison of the two design schemes for dc-link capacitors with respect to the
operating frequency and temperature.
The capacitor ripple current multiplier Mf was defined in (5) and used to evaluate the
capacitor power loss by using (10). Based on the verified mathematical models, the estimated
Mf values are summarized in Table VIII corresponding to both design schemes.
TABLE VIII
RIPPLE CURRENT MULTIPLIER Mf OF TWO DESIGN SCHEMES FOR DC-LINK CAPACITORS
Frequency
(kHz)
Mf for
Scheme I
Mf for
Scheme II
Frequency
(kHz)
Mf for
Scheme I
Mf for
Scheme II
0.1
0.2
0.5
1
2
1
1.08
1.39
1.74
1.95
1
1
1
1
0.99
5
10
20
50
100
2.04
2.05
2.05
2.06
2.06
0.98
0.97
0.95
0.90
0.86
B. Validation of Ripple Current Analysis
The RMS value of the capacitor ripple current is evaluated by Pspice simulation. The load is
a 0.2Ω resistor connected with a variable inductor, which can be used to effect different load
power factors. The inverter is modulated by the SVM algorithm and the switching frequency is
20 kHz. One test case, which corresponds to the constant power operation mode of motors,
maintains constant output current and the constant input voltage. The test condition is designed
such that IN is constant at 84A and Vin = 312V with a adjusted modulation indexes, M. The
20
simulated capacitor current RMS value is compared with the value estimated from the
mathematical model in (6). Table IX presents the results, which include the simulated capacitor
current RMS value (Icap), the estimated capacitor RMS current (Icap_est), and the estimation error (
 I ) under different operating conditions. The root-mean-square deviation (RMSD) is used to
cap
evaluate the differences between the mathematical modeling results and the simulation results.
This indicates that the RMSD value is 0.36 A, which is small relative to the average capacitor
current RMS value 22.77 A.
TABLE IX
CAPACITOR CURRENT COMPARISON BETWEEN THE SIMULATION AND MODEL ESTIMATION FOR
CONSTANT OUTPUT CURRENT (84A) AND INPUT VOLTAGE (312V)
I
L (mH)
cos
M
Icap (A)
Icap_est (A)
4
0.16
0.729
27.74
26.97
0.77
2.7
0.23
0.497
23.34
23.11
0.23
1
0.54
0.211
19.72
19.78
-0.06
0.5
0.79
0.145
20.97
20.97
0
0.2
0.95
0.119
22.10
22.04
0.06
cap
(A)
TABLE X
CAPACITOR CURRENT COMPARISON BETWEEN THE SIMULATION AND THE MODEL
ESTIMATION FOR CONSTANT OUTPUT CURRENT (84A) AND MODULATION INDEX (0.84)
L (mH) cos Vin (V) Icap (A) Icap_est (A)  I (A)
cap
4
0.16
261.7
26.79
27.44
-0.65
2.7
0.23
184.8
29.52
28.99
0.53
1
0.54
77.5
31.54
30.83
0.71
0.5
0.79
53.1
33.92
33.32
0.60
0.2
0.95
43.4
35.76
35.22
0.54
The second test case keeps the output current and modulation index constant, where IN =
84A and M = 0.84. The input voltage is tuned according to the variation of the load power
factor. Table X presents the comparison between the simulation results and the model
estimation. The RMSD result is 0.61A and the average capacitor ripple current RMS value is
31.51 A. The simulation verified the proposed mathematical models and indicated a 1.85%
relative modeling error based on the two cases. Furthermore, it exhibits the same trends as the
analysis derived in Section 2A and illustrated in Fig. 3.
21
C. Evaluation of Performance Metrics
The power loss and core temperature are calculated and illustrated in Fig. 12. The main
parameters of two design schemes are defined in Table V. As shown in Fig. 12a, the capacitor
power loss of the Scheme II is significantly lower than the scheme I due to the reduction of
ESR value. It shows that the capacitor power loss increases with the load power factor and
decreases with the ambient temperature Ta in Scheme I. The power loss is nearly constant when
Ta varies from 45°C to 85°C in Scheme II due to the insensitive temperature factor of film
capacitors. The estimated core temperature of both schemes is illustrated in Fig. 12b. Scheme II
shows a lightly higher core temperature considering the volume difference of dc-link
capacitors. The thermal resistance is calculated to be 1.02 K/W for both electrolyte and film
capacitors considering the outer diameters and air flow rate.
90
Scheme II
10
0.23
j-C
Scheme I
T
20
cap
30
(oC)
40
(W)
100
P
50
80
70
60
50
0.23
0.49
0.954
cos 
Scheme I
0.49
85
75
65
o
Ta ( C)
(a)
55
Scheme II
45
0.954
cos 
85
75
65
55
45
Ta (oC)
(b)
Fig. 12 Performance comparison between two schemes; (a) Power loss; (b) Core temperature.
The impact of modulation strategy on the capacitor power loss is illustrated in Fig. 13,
where the load power factor is constant ( cos = 0.23). Among three modulation strategies, the
THI modulation shows the highest power loss due to the frequency spectrum distribution of the
capacitor current, which is about 10% higher than that of the SVM. The SVM shows moderate
impact on the power loss of dc-link capacitors, which is roughly 3% higher than the SPWM.
Shown in Fig. 13a, the power loss decreases with the increased temperature, which is the
characteristic of electrolyte capacitors. For scheme II, the power loss of dc-link capacitors is
22
lower as shown in Fig. 13b and the temperature variation shows insignificant impact to the
power loss, which is the characteristic of film capacitors.
36
17
THI
SVM
SPWM
34
16.5
Pcap (W)
Pcap (W)
32
THI
SVM
SPWM
30
16
28
15.5
26
24
45
50
55
60
65
70
T a (o C)
75
80
15
45
85
50
55
60
(a)
65
70
T a (o C)
75
80
85
(b)
Fig. 13 Power loss of dc-link capacitors among three switching modulation strategies. (a)
Scheme I – five 3300µF electrolytic capacitors; (b) Scheme II – two 220µF film capacitors.
The lifetime of the two design schemes can be predicted using the mathematical models of
capacitor ESR and ripple current. The lifetime estimation is based on the expression (12), where
the key parameters are derived from the product datasheet and shown in Appendix. Apparently,
the temperature and its variation significantly affect the lifetime of dc-link capacitors, as shown
in Fig. 14. Moreover, the life expectancy of the film capacitor is about 180 kilo hours and times
longer than that of the electrolytic capacitor when the operating ambient temperature is constant
at 65°C.
800
Lifetime (kilo hours)
Lifetime (kilo hours)
80
60
40
20
0
45
50
55
60
65
70
T a (o C)
75
80
85
(a)
600
400
200
0
45
50
55
60
65
70
T a (o C)
75
80
85
(b)
Fig. 14 Life expectancy of the two design schemes for dc-link capacitors with the ambient
temperature spanning from 45°C to 85°C. (a) Scheme I – five 3300µF electrolytic capacitors;
(b) Scheme II – two 220µF film capacitors.
23
Twenty-six valve-regulated lead-acid (VRLA) batteries are series connected to form the
battery pack, of which the DC bus voltage is rated as 312V. The battery model is 6-DM-150
VRLA, which is specially designed for EV applications and manufactured by FENGFAN Co.
Ltd.. The product specification is shown in Table A-I. The battery internal resistance is a
nonlinear function of the states of charge (SOC). The measured internal resistance of the
battery pack ranges from 46 mΩ to 182 mΩ.
Battery current harmonics are analyzed for the two design schemes. An upper bound on AC
ripple current is defined as 10% of the rated battery current to avoid degradation of battery life.
The main parameters of the two schemes are defined in Table V. The RMS battery ripple
current in percentage is calculated by using the expression in (15) and the equivalent circuit
shown in Fig. 8. Fig. 15 shows the analysis results of battery ripple current, where the symbol α
is predefined in (14) and determined by the equivalent circuit shown in Fig. 8. The battery
ripple current in scheme II is higher than the ripple current in scheme I due to the vast reduction
of capacitance. The capacitance in scheme II is 440µF, which is about 2.6% of the capacitance
in scheme I. Therefore, to meet the 10% upper bound, α must be larger than 0.6 in scheme II
with consideration of various combinations of modulation index and load power factor. In
practical EV system, the cable interconnect provides enough impedance to guarantee α larger
than 0.6 since the inverter and the battery bank are located at some distance.
8
15
 Ibat (%)
Ibat (%)
6
4
2
0
0
0.23
0.2
0.49
0.4
0.6
0.6
1

0.954
5
0
0
0.2
0.2
0.4
0.4
0.625
0.6
0.8
0.8
10
0.8
0.8
cos 
1

(a)
(b)
1
M
24
150
200
150
Ibat (%)
Ibat (%)
100
50
100
50
0
0
0.23
0.2
0.49
0.4
0.6
0.6
1

0.954
0.2
0.2
0.4
0.4
0.625
0.6
0.8
0.8
0
0
0.8
0.8
cos 
1

(c)
1
M
(d)
Fig. 15 Battery ripple current analysis for two design schemes (five 3300µF electrolytic
capacitors and two 220µF film capacitors). (a) ΔIbat with cos and α in scheme I; (b) ΔIbat with
M and α in scheme I; (c) ΔIbat with cos and α in scheme II; (b) ΔIbat with M and α in scheme
II.
D. Experiment with 80kW PM Motor
The EV drive system is now tested with an 80kW permanent magnet AC motor, of which
the parameters of which are summarized in the Appendix. Fig. 16 shows a corner of the
inverter assembly with the two film capacitors.
Fig. 16 Photo of the EV inverter assembly with two film capacitors.
The experimental switching frequency is 20 KHz and the output current frequency is 93 Hz.
Fig. 17 shows the experimentally measured waveforms with respect to the proposed schemes II.
Shown in the oscilloscope screen, the CH1 and CH2 represent the output current (upper
waveform) and capacitor current (lower waveform), respectively. Fig. 17b illustrates a detailed
look of the output current and the capacitor current, of which the overall views are shown in
Fig. 17a. The current signals are sensed by Rogowski coils, which are transducers for
25
measuring alternating current (AC) or high frequency current pulses. The current waveforms
are represented voltage signals and shown in the oscilloscope screen. Considering that the scale
factors are 2 mV/A and 1 mV/A for the CH1 and CH2, respectively, the actual current scales
are 100A/div for both channels.
The experiment shows that the ripple current spectrum contains significant switching
frequency multiples and their sidebands, as predicted by the analysis of Section 3C. Each film
capacitor absorbs 38A ripple current, as shown in Fig. 17a and Fig. 17b. Thus, the test shows
the total ripple current through the film capacitor banks is 76A, when the inverter output
current is 135ARMS. Considering the high load power factor (cosϕ> 0.9) of the PM motor and
the modulation index (M = 0.6), the measured ratio Icap/IN was 0.4 consistent with (6), as
illustrated in Fig. 3.
(a)
26
(b)
Fig. 17 The experimental waveforms of scheme II using two film capacitors. (a) the output
phase current (upper scale factor: 2mV/A) and film capacitor current (upper scale factor:
1mV/A) in scheme II with current scale of 100A/div; (b) Zoom-in detailed look of the output
phase current (upper scale factor: 2mV/A) and film capacitor current (upper scale factor:
1mV/A) in scheme II with current scale of 100A/div.
Fig. 18 shows the experimentally measured waveforms with respect to the schemes I.
Shown in the oscilloscope screen, the CH1 and CH2 represent the high frequency capacitor
current (upper waveform) and output current (lower waveform), respectively. Considering that
the correspondingly scale factors are 5 mV/A and 2 mV/A for the CH1 and CH2, the actual
current scales are 20A/div and 100A/div for CH1 and CH2. The individual electrolytic
capacitor ripple current is 16.2A. Thus, the five electrolytic capacitors share the total 81A
ripple current through the parallel interconnected capacitor bank. It demonstrates that each film
capacitor can handle more ripple current due to the low ESR characteristics.
27
Fig. 18 The experimental dc-link capacitor current (upper scale factor: 5mV/A) and output
phase current (lower scale factor: 2mV/A) waveforms of scheme I using five electrolytic
capacitors for 80kW PM motor.
The DC bus voltage ripple is recorded and shown in Fig. 19 at the rated capacity of 80kW.
In order to analysis the fluctuation of the DC bus voltage, the measured voltage ripple is
zoomed and displayed in the center of in the oscilloscope screen. The zero axes are far from the
trigger level indictor because the ripple voltage is far below the dc bus voltage. The scale of
0.2V/div showing in the Fig. 19 represents the actual voltage scale of 35V/div considering the
voltage division network parameter. The oscilloscope screen shows the measured RMS and the
peak value is 1.81V and 1.925V respectively, which represents the actual 317V RMS DC
voltage and the actual 337V peak voltage. Therefore, the ripple magnitude is recorded as the
6.31% of the dc bus voltage.
28
Fig. 19 Measured DC bus voltage ripple for EV inverter with proposed design scheme with the
scale of 35V/div.
Summary of Experimental Results. Table XI summarizes performance comparison between
the two design schemes. Main parameters of two schemes are defined in Table V. The scheme
II show the significant advantages regarding to the small size, low parasitic inductance, long
lifetime, reduced bus voltage spikes, and improved power density. It is shown that the power
density is increased to 13.3 kW/L by applying scheme II in contrast of 2.99 kW/L by using the
scheme I. For battery ripple current, the constraint of α  0.6 is required for the scheme II. This
is achievable by considering the practical layout of electric vehicles.
TABLE XI
PERFORMANCE COMPARISON OF TWO DESIGN SCHEMES
Parameters
Scheme I
Scheme II
16500
440
Electrolytic
Film
Measured parasitic inductance (nH)
124
34
Measured ripple current (A)
81
76
40.8
20.6
73.3
75.5
Life expectancy (Hours) for Ta=65 C
16092
181530
ΔIbat for α=0.6
1.8%
8.7%
57
35
PDW(kW/kg)
4.67
11
PDV (kW/L)
2.99
13.3
Capacitance (mF)
Capacitor type
Power loss (W)**
o
Core temperature ( C)** =0.954
o
Switching voltage spike across IGBT (V)
*
* With 2µF snubber capacitor; **for Ta = 65 ˚C and cos() = 0.954
VI. CONCLUSION
This paper presents a comprehensive analysis and comparative evaluation of dc-link
capacitors to meet EV system requirements of long lifetime, high reliability, low cost, and high
power density. The main findings and contributions of the research are summarized as follows:
1) Modulation strategy: regarding the dc-link capacitor ripple current, three modulation
strategies of SPWM, SVM and THI show approximately the same RMS values. Considering the
ripple voltage, THI modulation shows the lowest value across the dc-link capacitors followed
29
closely by SVM modulation. However, THI results in the highest capacitor power loss, which is
10% higher than that of SVM. Capacitor power losses correspond to the ripple frequency
spectrum, which is different among modulation strategies. The SVM shows moderate impact on
the capacitor power loss, which is roughly 3% more than that of the SPWM.
2) Influence of operating conditions: operating conditions of EV inverters may be expressed
in terms of the practical ranges of load power factor ( cos ) and modulation index M. When
cos is less than 0.43, the peak ripple current always results from the upper bound of M. After
the threshold (0.43), increasing of load power factor cos causes a decreasing of MIcap(max),
which is the modulation index referring to the maximum RMS value of capacitor ripple.
Furthermore, the power factor has great impact on the frequency spectrum of the dc-link
capacitor ripple current. For low cos , the ripple current spectrum is fairly evenly distributed
along the switching frequency (f1) sidebands (sbs), 3f1 sbs and 2f1. For high cos (larger than
0.49 for SVM), 2f1 is the dominant component and its amplitude increases with cos . The
largest harmonic component is nearly 21% of output current amplitude at low cos , while the
corresponding harmonic component reaches as high as 48.8% at the high cos .
3) Modeling of ESR and self-heating characteristics: the ESR models of electrolytic and film
capacitors are derived and experimentally validated. Two dc-link capacitor designs are used for
the comparative evaluation. The ESR of scheme II (film capacitor) is always lower than that of
scheme I (electrolytic) throughout the frequency spectrum. The ESR value of scheme I
decreases with increasing temperature, which is more significant than that of the scheme II.
Furthermore, the RMS values and frequency spectra of the dc-link capacitor current are
analyzed. The self-heating effect is subsequently considered and numerically evaluated by
using the iterative simultaneous solution for core temperature and ESR by electro-thermal
coupling method to predict the core temperature.
temperature.
Lifetime estimates are based on core
30
Experimental evaluation of two design schemes: The applications and performance of
electrolytic capacitors (scheme I) and film capacitors (scheme II) were tested and compared and
evaluated in terms of power loss, core temperature, lifetime and battery current harmonics
based on a practical 80kW permanent-magnet motor drive system. The comparison verifies that
the film capacitor application shows significant advantages shown by the improved power
density, low power loss, low parasitic inductance, and long lifetime. The capacitor power loss
introduced by the scheme II is roughly half of the value of scheme I due to the lower ESR value.
The analysis shows that the values of capacitor core temperature are close to each other in both
schemes. At the rated ambient temperature of 65 oC, the lifetime of the film capacitors is ten
times longer than that of scheme I. Regarding to the battery ripple current, both schemes meet
the 10% upper bound limit considering the practical EV system layout. Further, the parasitic
inductance is reduced to 34 nH in contrast with the value of 100 nH for scheme I. The power
density of 13.3 kW/L was achieved by applying the proposed scheme II, which is compared to
the PDV of 2.99 kW/L for scheme I.
31
APPENDIX
TABLE A-I
SPECIFICATION OF THE VRLA BATTERY (6-DM-150)
Parameters
C20(Ah)
Cold Cranking Amperes defined by BCI (A)
Rated voltage (V)
Weight (kg)
Value
150
300
12
32.5
TABLE A-II
SPECIFICATION OF EVOX RIFA ALS332QP500AND AVX FFVE6K0227K
Comparison
Items
Max ESR(mΩ)
at 20 oC/ 100hz
Max Impedance
(mΩ) at 20oC /
10 khz
Ripple
current(A) at
85°C & 10 khz
Life time
Lb at 85°C
(hrs)
ALS332QP500
FFVE6K0227K
51
1
32
-
26.4
100
4000
30000
TABLE A-III
MAIN PARAMETERS OF AC INDUCTION MOTOR
Parameters
Stator resistor (mΩ)
Stator leakage inductance (mH)
Rotor resistor (mΩ)
Rotor leakage inductance (mH)
Mutual inductance (mH)
Pairs of poles
Rated speed(rpm)
Value
6.8
0.071789
4.23
0.0921067
2.2857359
3
1860
Expected
ambient
temperature
Ta(oC)
65
65
32
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