IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010 519
Start-Up and Dynamic Modeling of the Multilevel
Modular Capacitor-Clamped Converter
Faisal H. Khan, Member, IEEE, Leon M. Tolbert, Senior Member, IEEE, and William E. Webb
the capacitors of the MMCCC explains the start-up and steady-
state voltage balancing. Once these capacitor voltages are found
for different time intervals, the start-up and steady-state voltages
at various nodes of the MMCCC can be obtained. This analysis
provides the necessary proof that explains the stable operation of
circuit. In addition, the analysis also shows how the LV side of the
ratio of the circuit is N. In addition to the analytical and simulation
results, experimental results are included to support the analytical
proof of concept.
Index Terms—DC–DC power conversion, power capacitors,
power conversion, power electronics, power semiconductor
can be designed to operate at very high efficiency. The mul-
tilevel modular capacitor-clamped dc–dc converter (MMCCC)
presented in  had a capacitor-clamped modular architecture
or charge-pump technology –. The MMCCC topology
has a bidirectional power management feature, and multiple
loads and sources can be simultaneously connected to this con-
verter. MMCCC’s various features and applications in hybrid
electric and fuel cell automobiles were demonstrated in 
and . The originality and proof of concept of this topol-
ogy was verified by several simulation and experimental results
in these literatures. As the MMCCC topology is a capacitor-
clamped circuit, the proper operation and the capability to pro-
duce a certain conversion ratio (CR) can be proven by knowing
the various capacitor voltages during the start-up and steady-
state operation of the converter.
APACITOR-clamped or switched-capacitor converters
are based on capacitive energy transfer mechanisms, and
by Oak Ridge National Laboratory under UT-Battelle Contract 4000007596.
Recommended for publication by Associate Editor A. Rufer.
versity of Utah, Salt Lake City, UT 84112 USA (e-mail: email@example.com).
W. E. Webb is with the Electric Power Research Institute (EPRI), Knoxville,
TN 37932 USA (e-mail: firstname.lastname@example.org).
L. M. Tolbert is with the Department of Electrical and Computer Engi-
neering, University of Tennessee, Knoxville, TN 37996-2100 USA, and also
with Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA (e-mail:
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/TPEL.2009.2025273
The MMCCC is inherently a bidirectional dc–dc converter.
side experiences a voltage of VLV. On the other hand, a voltage
source VLVconnected at the LV side produces a load voltage of
VHVat the HV side. In both cases, VHV/VLV= N, where N is
the CR of the circuit. The schematic of a five-level MMCCC is
shown in Fig. 1.
This paper will provide the analytical derivation of the MM-
CCC voltage transfer mechanisms. The mathematical expres-
sions rely on the MMCCC circuit’s inherent nature to produce
a specific CR. In addition, several simulation and experimental
voltage expressions derived in this paper.
II. BASIC CONSTRUCTION AND OPERATION OF THE MMCCC
The basic operation of the MMCCC has some similarities
with the flying capacitor multilevel dc–dc converter (FCMDC)
shown in –. It was presented in  that the MMCCC
exhibits some of the favorable properties of the FCMDC and
the series–parallel converter , . The property that achieves
equal voltage stress across the transistors was adopted from the
FCMDC topology, and the modular construction was adopted
is a five-level MMCCC, and the circuit has a CR equal to 5. The
terminology of voltage levels present in the circuit has been
used slightly differently in this paper. Usually, a multilevel dc–
dc converter with a CR equal to N is defined as an (N + 1)-
level converter. This convention was adopted from multilevel
inverters where zero voltage is a working voltage level in the
level for the MMCCC in this paper.
An N-level MMCCC circuit requires (3N − 2) transistors,
and the method of charge transfer requires two subintervals
 shown in Fig. 2. Compared to the FCMDC topology, the
requirement of only two subintervals, regardless of the CR of
Eachtransistorwillbe ONinoneofthetwosubintervalsand OFF
in the other, which means that the transistors can be separated
into two groups that have complementary operations. In the
MMCCC shown in Fig. 1, transistors SR1–SR7 are activated in
subinterval 1 and SB1–SB6 are activated in subinterval 2.
For ease of understanding, the working principle of the MM-
CCC is discussed in the down conversion or buck mode in
this paper. In a five-level FCMDC, it takes five subintervals
to complete the power transfer operation from the input to
the output of the circuit. However, in the MMCCC, multiple
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520IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010
Fig. 1.Schematic of a five-level MMCCC circuit with four modules.
(a) Schematic of state 1 or the first subinterval. (b) Schematic of state 2 or
the second subinterval.
Steady-state operational diagrams of a five-level MMCCC.
mutually exclusive charge–discharge operations are executed in
only two subintervals. In the first subinterval, C5 and C1 are
being charged from VHV, and C4is discharged through C3and
tions are executed simultaneously. Inthe second subinterval,C5
is discharged to C4and C1, and C3is discharged to C2and C1.
the next subinterval. Although, it seems that C1is always being
expression shows otherwise. It will be shown later how in each
subinterval, C1is being charged for some time, and discharged
for the remaining time in the subinterval. The charge–discharge
mechanism of various capacitors inside the MMCCC is shown
in Table I. In this table, the charge–discharge operation of the
MMCCC is also compared with a five-level FCMDC. The de-
tailed operating principle of the MMCCC can be found in 
CHARGE–DISCHARGE OPERATION IN VARIOUS SUBINTERVALS OF AN FCMDC
AND MMCCC CONVERTER
The MMCCC circuit uses a hybrid architecture that com-
bines the favorable features of series–parallel converter and
FCMDC converter . The modeling technique of various
published literatures , , , , –. The MMCCC
modeling technique discussed in the following sections was not
adopted from any particular previous derivation; rather, it was
influenced by the previous works. The MMCCC circuit has two
modes of operations: dynamic state or start-up and the steady
state. Two different sets of boundary conditions are applied to
deduce the equivalent models of the operational circuit in these
two modes. Section III explains how the various capacitors at-
tain steady voltages once the converter is energized. Section IV
discusses the voltage variations of the capacitors once a load is
connected to the converter.
III. START-UP ANALYSIS OF MMCCC
The MMCCC produces a CR based on the stored and trans-
ferred charges among the capacitors. It is required to find the
capacitor voltages at different time intervals to prove the con-
cept of the MMCCC topology. The following assumptions were
made prior to the actual computational steps: 1) capacitors do
voltage stress across the transistors and makes the analysis in
the most conservative manner, and 2) RC ? T/2, where R is the
530 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010
Experimental efficiency for a 5-kW MMCCC at different loading
voltage across a capacitor is comparable for all capacitors.
The impact of a step load change at the LV side was inves-
tigated further, which is shown in Fig. 16. At 229.4 W output,
the LV side voltage was 35.66 V, and it decreased to 34.10 V
immediately after the additional load was connected to the cir-
cuit. The voltage variation is 4.37% of the steady-state value,
and the voltage returned to the previous voltage within 0.4 s.
age variation was 4.45%. Differences were observed between
the steady-state values before and after the step load change
took place. This is expected from the MMCCC circuit with-
out any voltage regulation where the steady-state output voltage
decreases with increased output power.
E. Efficiency of the MMCCC
The charge/discharge operation of the MMCCC has similar-
ities with the FCMDC. Thus, a well-constructed MMCCC with
proper current traces and appropriate components should be as
efficient as an FCMDC. Fig. 17 shows the efficiency profile of
a 5-kW MMCCC. The maximum efficiency obtained from this
circuit is 96.5%, and efficiency decays with increased load. It
was found that the 5-kW MMCCC circuit suffered from volt-
age drops across the current paths used in the circuit, and this
explains why the conduction loss in the circuit starts to domi-
nate at higher output levels. By using fast gate driving circuits,
suitable MOSFETs, and adequate current paths, the efficiency
level could be extended to the 97%–98% level for the MMCCC.
A well-designed FCMDC can achieve efficiency in the range of
96%–98% for various operating conditions .
A detailed analytical approach to calculate the capacitor volt-
Because the circuit is based on capacitor-clamped topology, the
thereby, the CR of the circuit can be determined. The analysis
and the amount of voltage ripplepresent atthe output. The start-
up analysis was simplified by reducing one variable from the
equation, and the final capacitor voltages were obtained using
eigenvalue–eigenvector decomposition. In addition, an average
current/charge model was developed, and all the capacitor volt-
capacitors exhibit charge balancing among themselves through
up and steady-state quantities were verified by experimental
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in electrical engineering from Bangladesh Univer-
sity of Engineering and Technology (BUET), Dhaka,
Bangladesh, in 1999,and theM.S degreein electrical
engineering from Arizona State University, Tempe,
in 2003, and the Ph.D. degree in electrical engineer-
ing from The University of Tennessee, Knoxville, in
Since July 2009, he has been with the Electri-
cal and Computer Engineering (ECE) Department of
University of Utah as an Assistant Professor. Prior to
joining the ECE department, he was a Senior Power Electronics Engineer at
the Electric Power Research Institute (EPRI), Knoxville from 2007–2009. His
current research interests include dc-dc converters, hybrid electric and fuel cell
automobile power management, induction generators, and vehicle battery cell
voltage management system.
Dr. Khan currently holds the Vice Chair position of the IEEE LED Lighting
Standard Committee PAR1789. He is a member of the IEEE Power Electron-
ics Society, the IEEE Industry Applications Society, and the IEEE Industrial
Electronics Society. He has served as a Reviewer and the Session Chair for
several IEEE transactions and conferences. He received the 2007 First Prize
Paper Award of the Industrial Power Converter Committee of the IEEE Industry
Leon M. Tolbert (S’88–M’91–SM’98) received the
Bachelor’s, M.S., and Ph.D. degrees in electrical
engineering from Georgia Institute of Technology,
Atlanta, in 1989, 1991, and 1999, respectively, all in
In 1991, he joined the Engineering Division, Oak
is currently a Research Engineer in the Power Elec-
tronics and Electric Machinery Research Center. In
1999, he was appointed as an Assistant Professor in
ing, The University of Tennessee, Knoxville, where he is currently the Min Kao
Professor in the Min Kao Department of Electrical Engineering and Computer
He is a Registered Professional Engineer in the state of Tennessee. Since
2007, he has been an Associate Editor of the IEEE TRANSACTIONS ON POWER
ELECTRONICS. He was the Chairman of the Education Activities Committee of
for the IEEE POWER ELECTRONICS LETTERS from 2003 to 2006. He received
the National Science Foundation (NSF) CAREER Award in 2001, and was the
recipient of the 2001 IEEE Industry Applications Society Outstanding Young
Member Award. He received two Prize Paper Awards from the IEEE Industry
Applications Society Annual Meeting.
trical engineering and computer engineering from
North Carolina State University, Raleigh, in 2004,
and the M.Sc. degree in electrical and computer
engineering from Georgia Institute of Technology,
Atlanta, in 2006.
He was a Senior Electrical Engineer for CSC Ad-
vanced Marine Enterprises, Washington, DC, where
he was engaged in providing total ship acquisition
support to several branches of the armed forces of
the United States, including the Navy, Marine Corps,
Army, and Coast Guard, and was responsible for the overall design, specifica-
tion,and integration of ships’ electrical systems, many ofwhich utilized electric
propulsion. In 2008, he joined the Electric Power Research Institute (EPRI),
where he is currently a Project Engineer and Scientist. His current research in-
terests include the design of critical power systems, including surge protection
and power conditioning.