Energy and Power Engineering, 2010, 25-30
doi:10.4236/epe.2010.21005 Published Online February 2010 (http://www.scirp.org/journal/epe)
Research of Supercapacitor Voltage Equalization
Strategy on Rubber-Tyred Gantry Crane Energy
Saving System
Chunhe CHANG1, Jiangping YANG1, Yu LI2, Zho ngni ZHU1
1Air Force Radar Academy, AFRA, Wuhan, China
2South-central University for Nationalities, SCUN, Wuhan, China
Abstract: A model for supercapacitor voltage equalization strategy is analyzed, and on this basis a
supercapacitor voltage equalization method for Rubber Tyred Gantry Crane (RTG) energy saving system is
proposed, namely active voltage equalization method based on Buck-Boost converter. The equalizing speed
of the proposed method is fast. Firstly, the working principle and process of the voltage equalization circuit is
analyzed in detail. In addition, design of active voltage equalization circuit parameters and control strategy
are given. Finally, simulation analysis of the series connection of supercapacitors module is performed.
Results show that this method for equalizing voltage can avoid over-voltage of each cell and possess
practicable and high value for supercapacitor RTG energy saving system.
Keywords: supercapacitor, energy saving, rubber tyred gantry crane (RTG), voltage sharing, sesign of active
equalization circuit
1. Introduction
Supercapacitor is a novel energy storage device based on
the principle of the double layer-electrolyte capacity,
which has many merits such as long lifetime, high
efficiency, fast dynamic response, etc. So it is a power
storage technology that has a bright future in power
storage development. The power driver system in energy
-saving RTG is composed of the diesel generator set,
power balance system (made by supercapacitors), con-
troller and the rising electromotor. Supercapacitors are
used for storing energy from which electromotor gene r a te s
and brakes energy when the load is fallen down, the
superc apacitors rele ase the energy wh ich has been stored
when the load is raising. Thus the original energy which
is consumed by the braking resistance is recycled totally,
then the purpose of energy saving and environment
protection is realized.
Due to the lower voltage of a single supercapacitor,
generally speaking, the series and parallel connection of
supercapacitors form the energy storage module to meet
the energy storage capacity and higher voltage require-
ments. However, the operational voltage of supercapa-
citors is different, and a local over-voltage can appear
over one or several supercapacitors, which would affect
the lifetime and reliability of the system. Therefore, it is
essential and critical to research and realize supercar-
pacitors voltage equalization technology for improving
the supercapacitors power storage technology.
The present supercapacitors voltage equalization
technology mainly includes zener diode type, switch
resistor type, switch capacitor type, inductor type,
forward converter type and flyback converter type
voltage equalization circuits, etc. The switching resistor
type and voltage-regulator diode type voltage equali-
zation circuits consume amount of energy because of
utilizing energy-consuming devices, so the system has
lower efficiency and poorer reliability [1]. Th e switching
capacitor type and inductor type voltage equalization
circuits have ineffective energy flowing, especially when
the two adjacent supercapacitors voltage difference is
very closer or when much more supercapacitors are in
series connection, balancing speed will be slower [2].
Forward converter type and flyback converter type
voltage equalization circuit have a higher efficiency, but
they are not attractive, because they also have many
demerits such as complicated magnetic circuit, big
volume, difficult extended winding and large voltage
equalization error, etc [3]. In view of the existing
problems of the above voltage equalization methods, the
paper proposes an active voltage equalization method
based on the principle of Buck-Boost converter, this
method can transfer energy from the high-voltage
supercapacitors to the low-voltage ones through the
converter rapidly, and it has the character of the low

C. H. CHANG ET AL.
26
energy loss and the high equalizing speed in the process
of charging and discharging.
2. Analysis of Voltage E q ua l ization Model
The supercapacitor charging equalizing model is shown
in Figure 1. On the basis of the paper [4], the model is
further analyzed in detail. Assuming the value of two
optional supercapacitors are 1C and 2C, 1d and 2d
are capacity deviation values of the supercapacitors 1C
and 2C respectively, we define the values of 1C and
2C as below:
11(1 )CC d, 22(1 )CC d (1)
where C is the reference value for capacitors.
If two supercapacitors are connected in series, both of
the initial voltage values are zero, a constant current
I
charges supercapacitors, the voltage difference during
the same time t is defined as following:
12
12
CC C
UUU It
CC

  (2)
where C is the capacity difference between 1C and
2C.
If two supercapacitors are connected in series, both of
the initial voltage values are zero, when different
constant currents 1c
I
and 2c
I
charge supercapacitors,
the voltage difference during the same time t can be
expressed as in (3):
12
12
ccII
Ut
CC

 


(3)
Substituting (1) into (3) when the voltage d ifference is
zero, the relation between charging current and the
supercapacitor capacity deviation can be obtained as
follows:
12 1
21 2
1
1
c
c
I
Cd
I
Cd


 (4)
If two supercapacitors are connected in series, both of
the initial voltage values are zero, the supercapacitors
voltage rise from zero to the upper voltageuUwhen
eq I
eq I
1CI
2C I
1C U
2C U
C U I
1 C
2 C
Figure 1. The supercapacitor charging equalizing mode l
constant current charges supercapacitors, the two cells
voltages can be, respectively, calculated as:
12
1
12
1
2
cc
dd
UU
dd

 , 2
12
1
2
ccUU
dd
 (5)
where 1cU and 2cU are the voltages across the super-
capacitors 1C and 2C at the end of charging and cU
is the total voltage. Obviously, the two supercapacitors
capabilities are same when 1d=2d=0, thus, the
capacitors voltages can be described as: 1cU=2cU=
/2cU=uU.
As Figure 1 is shown, assuming a current of equalizing
current supply eq j
I
kI

(both the two current supplies
are reverse direction) is parallel connected with each
capacitor side,
j
k is equalizing coefficient. Then, the
charging current across 1C and 2C can be, respect-
tively, described as:
1(1 )C
j
I
IK

,2(1 )C
j
I
IK (6)
Substituting (6) into (4), the ration between constant
current source I and the charging current eqI can be
expressed as follows:
21
12 2
jdd
kdd



 (7)
Then, the two supercapacitors charging current can be,
respectively, calculated as:
1
1
12
22
2
cd
I
I
dd

 , 2 2
12
22
2
cd
I
I
dd

 (8)
Usually the supercapacitor capacity deviationd is not
zero, but it is a random value, which variable range is
10%

～20%

. The relation between the equalizing
current eqIand the charging current
I
can be calculated
from d and (7) when the supercapacitors are in voltage
equalization state.
0.143eq
I
I (9)
From (3), it can be concluded that if the superca-
pacitors initial voltage is not zero, the voltage difference
U

will decrease gradually, and
j
k value continues to
increase, the voltage difference across the supercap-
acitors reduces more quickly.
3. Active Voltage Equalization Circuit
In view of the energy of the high-voltage supercapacitors
is directly transferred to the low-voltage supercapacitors,
this paper proposes an effective voltage equalization
method-Active Circuit of Voltages Balance for the
Series Supercapacitors. This method compares with the
methods of “INDUCTION”, and it is characterized by
the low energy loss and the high equalizing speed in the
process of charging and discharging.

C. H. CHANG ET AL.
27
Figure 2. Active circuit of voltages equalization for two
series supercapacitors
Figure 3. The principle circuit of active voltages balance
3.1 The Basic Operational Principle
As shown in Figure 6, switches 1 T, 2 T are MOSFET;
diodes 1 D, 2 D are continued flow diodes; eqL is the
energy storage inductor; 1C, 2C are two adjacent
series cells, respectively. A Buck-Boost converter can be
connected with two adjacent cells of supercapacitors.
The basic operational principle is shown in Figure 7.
As is shown in Figure 3(a) below, when 12ccUU, a
PWM drive signal is given to the switches, and switch
2T is turned off and 1T is turned on. While 1T is on,
supercapacitor 1C, switch 1T and inductor eqL forms
a loop circuit, whose current is 1c
I
. The part of energy
of supercapacitor 1C transfers to inductor eqL. While
1T is off, supercapacitor 2C, inductor eqL and the
diode 2D forms a loop circuit, whose current is 2c
I
.
The energy of inductor eqL transfers to supercapacitor
2C. Similarly, as is shown in Figure 3(b) below, when
1cU＜2cU, switch 1T is turned off and 2T is turned on.
The energy transfers from 2C to 1C until the voltages
of the two supercapacitors are same.
3.2 Analysis of Operation Process of Voltage
Equalization
According to the above principle of voltage equalization,
and in order to analyze the operation process of the
circuit, assume that the following items are satisfied:
1) It is assumed that the voltage of diode, the internal
resistance of inductor, the on-resistance of the switch and
the resistance of the circuit are all ignored, and super-
capacitors are assumed to be ideal capacitors;
2) The circuit works in discontinuous conduction mode
(DCM);
3) The capacity of the supercapacitor mC is less than
that of 1mC

, that it is to say, the supercapacitor mC
voltage is higher than 1mC

, where m is positive integer;
4) Because of the large capacity of supercapacitors and
high swtiching frequency, the supercapacitor can be seen
as a voltage supply during a switching period.
Equivalent circuit of active voltage equalization sys-
tem of two supercapacitors is shown in Figure 4. Refer-
ring to the above equivalent circuit, the operating process
of the voltage equalization can be analyzed in detail as
follows:
3.2.1 Operation Mode 1 (0t1DT)
At t=0, the switchmT is turned on, the diode mD is
turned off. According to the above assumption, the
Figure 4 can be equivalent to Figure 5. During this
operation mode, the supercapacitor mCcharges inductor
m U
m C
m L
1m U

1m C 
mT
m
D
L
i
Figure 4. The equivalent circuit of active voltage equali-
zation system
m U
L
i
m L
Figure 5. Equivalent circuit at mode 1
1m U 
L
i
m
L
Figure 6. Equivalent circuit at mode 2

C. H. CHANG ET AL.
28
mL, and energy is stored in inductor mL, the inductor
current keeps rising linearly. Thus,
1
Lm
i
LU
DT

 (10)
3.2.2 Operation Mode 2 (1DT t12()DDT)
At t=1DT, the switch mT is turned off, the diode mD
is turned on. The Figure 4 can be equivalent to Figure 6.
During this opera tion mode, th e inductor mL discharges
supercapacitor mC, energy is transferred to superca-
pacitor mC, the inductor current keeps falling linearly
from peak value to zero. Thus,
1
2
Lm
i
LU
DT 
 (11)
3.2.3 Operation Mode 3 (12()DDTtT

 )
In this operation mode, the switch mT and the diode
mD are all turned off.
4. Design and Simulation of Active Voltage
Equalization Circuit
4.1 Design of the Active Voltage Equalization
Circuit Parameters and Control Strategy
4.1.1 Operation Range of Duty Ratio
The following conclusion can be obtained from the (10)
and (11).
112mmUD UD  (12)
When the voltage equalization system works at steady
state, the difference between mU and 1mU is very
little. Thus, we can think 1=mmUU U, in addition,
because the circuit works in discontinuous conduction
mode(DCM).
Then, 121DD, 12DD. thus,
12DDD＜50% (13)
From the above inequation, we can obtain D＜50%.
4.1.2 Inductor Selection
In a switching period, the working curve of inductor(L)
current is shown in the Figure 7. The average current
releases from Supercapacitor to the inductor L is:
2
L
avg
DI
I

 (14)
where
L
I
is the peak current of inductor, and it can be
expressed as below:
L
DT U
IL

 (15)
Substituting (14) into (15), thus, the average current
can be calculated as follows:
Figure 7. Working curve of inductor current
2
2
avg
DTU
IL




(16)
From what has been analyzed, it is considered that the
average current of the inductor is also the equalizing
current of active voltage equalization circuit. According
to the principle of voltage equalization of supercapacitors,
if the high-voltage supercapacitors release the average
current avg
I
more than the equalizing current eq
I
, the
voltage equalization can be realized. In order to increase
the voltage equalizing speed, select the coefficient
0.2jk, then 0.2avg
I
I, and substituting this in
Equation into (16), the inductor L can be obtained as
follows:
2
0.4
DTU
L
I


 (17)
In the circuit design, once the energy storage induc-
tor Lis selected, there are two ways to adjust the swi-
tching period:
1) Selecting the fixed switching period T, the
equalizing current will be restrained by the limited cell
voltage U in the process of charging and discharging,
which makes it as a function of the v oltage U;
2) The switching period T changes with the voltage
U, which makes balancing current become a fixed value.
4.1.3 Volta ge E qual i zation Control Strat e gy
Measuring two supercapacitors voltage mU and 1mU

,
the voltage difference can be calculated by the Equation
mU

=mU－1mU

, and comparing the difference with
the reference voltage refU, if mUrefU, then the
voltage Equalization circuit begins to work; if mU


refU, then the voltage equalization circuit stops working.
In fact, if make all the supercapacitors reach the voltage
equalization, every adjacent two supercapacitors will be
parallel connected with a Buck-Boost converter, the
voltage equalization controller generates different diving
signals by analyzing all the measured supercapacitors

C. H. CHANG ET AL.
29
Figure 8. Active circuit of voltages balance for five superca-pacitors series
Figure 9. Active circuit of voltages balance for ten supercapacitors
Figure 10. Simulation results of voltages balance for super-
capacitors
voltage to drive MOSFET, in this way, equalization
among all supercapacitors will be achieved at last.
4.2 The Extension Circuit of Voltage Equalization
Extending the above circuit, we can make it suitable for
more series supercapacitor cells to meet the requirement
of the RTG energy saving system. As is shown in Figure
8, we can see every two adjacent supercapacitors
constitute a group which is controlled to balance voltage
by a Buck-Boost converter. For example, the converter,
which is composed of 1T, 1D, 2T and 2D, balances
the voltages between 1C and 2C, and another one is
composed of 2T, 2D, 3'Tand 3'D, balances the volt-
ages between 2C and 3C.Th e principle of equalization
among 3C, 4C and 5C is the same as the above [5].
Consider ing the demand of hu ndreds of super capacitor
cells in RTG energy saving system, the series structure,
as shown in Figure 8, makes the control components
increase markedly and the control circuit become
complicated. So the series and parallel structure in Figure
9, can be adopted in practical application.
4.3 Saber Simulation Analysis
In order to verify the character of the active voltage
balance circuit in the energy recycling RTG system, we
research the circuit composed of two supercapacitor cells
in series module by the simulation study of Saber.
Assume that the capacitance of one supercapacitor is

C. H. CHANG ET AL.
30
800F and the other one is 1000F, the constant charging
current is 100A, the rate voltage of the supercapacitor is
2.7 V, the energy storage inductor is 1.36uH and the
switching frequency is 10 kHz.
Figure 10 describes the process of charging two super-
capacitors. It can be seen, at the end of the process, that
the voltages of two supercapacitors become the same, no
over-voltage. The result of Saber simulation indicates
that active voltage balance circuit amends the inconsis-
tency of the supercapacitor voltage greatly.
5. Conclusions
The active voltage equalization circuit based on the
reversible Buck-Boost converter has been discussed in
this paper. Theoretical analysis and simulation result
show that the active control circuit can better solve the
problem of the partial over-voltage over the super-
capacitor groups. This method can be applied in the
situation of higher charging or discharging current.
Therefore, it has a high value to be used in the RTG
energy saving system.
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