A Fast Equalization Method for Series Batteries based on Cuk
Converters
Qinghai Meng and Zhou Zhang
North China University of Technology, Shijingshan, Beijing, China
Keywords: Cuk converters, SOC, Series batteries, Equalization
Abstract: In series battery packs, the accumulated differences among every single battery could significantly decrease
the performances of the packs. Consequently, equalization circuits are very necessary for series batteries.
Based on Cuk converters, this paper introduces a fast equalization method considering SOC (State of
Charge) differences of series batteries. The method increases equalization current as large as possible, and
simultaneously, achieves fast equalization and low consumption. The experimental platform is constructed,
and the results verify the validity of the proposed fast equalization method.
1 INTRODUCTION
With the development of technology, the energy
storage system composed of batteries is widely
applied in the fields of microgrids and new energy
vehicles(Zhang and Wang, 2019). The production
and working environment may lead to the
differences among serial batteries, which could
significantly decrease the performance of the whole
pack(Liu and Zou, 2018). It is of great significance
to apply equalization methods to eliminate the
differences, so as to ensure the high-efficiency of
utilization of energy in the battery pack(Zhiliang and
Xiang, 2018).
The Cuk converter topology is widely used to
perform equalization function(Rui and Lizhi, 2015).
Literature(Yan and Cheng, 2015) surveys the battery
equalization using a fuzzy controller.
Literature(Ouyang and Chen, 2018) researches
quasi-sliding mode control based on Cuk converters
to balance the batteries. Literature (Samadi and Saif,
2014) discusses the predictive control for cell
balancing in Li-ion battery packs. Unfortunately, the
control methods mentioned above are too
complicated to perform an equalization function, and
the balancing speed may not be so fast. This paper
introduces a fast equalization method considering
SOC (State of Charge) differences of series batteries
based on Cuk converters, and simultaneously,
achieves fast equalization and low consumption. The
experimental platform is constructed, and the results
verify the validity of the proposed fast equalization
method.
2 TOPOLOGY ANALYSIS
This paper adopts the bidirectional DC/DC circuit
based on the Cuk converters, as shown in figure 1.
The equalization circuit is divided into two parts, the
left part is a double-layer bridge, mainly used for
selecting the single cell needed to be balanced, and
the right half performs an equalization function,
controlling energy flowing in both directions.
Figure 1. Topology based on the Cuk converter.
3 EQUALIZATION BASIS AND
ITS ESTIMATION
The battery’s state of charge (SOC) is selected as the
equalization basis, which is of more significant
18
Meng, Q. and Zhang, Z.
A Fast Equalization Method for Series Batteries based on Cuk Converters.
DOI: 10.5220/0011104800003355
In Proceedings of the 1st International Joint Conference on Energy and Environmental Engineering (CoEEE 2021), pages 18-21
ISBN: 978-989-758-599-9
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

advantages than the terminal voltage of batteries.
Because the relationship between SOC and the
terminal voltage is nonlinear. SOC can directly
reflect a battery’s state, which can help to obtain a
more accurate result.
After the selection of the equalization basis, the
more important part is to estimate SOC in a proper
way. This paper is based on extended Kalman filter
(EKF) to complete this. The core of EKF is the use
of Taylor expansion for partial linearization. This
paper builds an equation of second-order RC battery
model, as shown in figure 2. The state variables are
the SOC、electrochemical polarization voltage U
1
and concentration polarization voltage U
2
,
controlling variable I. Hence the equation can be
derived as formula (1).
Figure 2. The second-core RC battery model.
() kWI
R
R
Q
ηT
U
U
SOC
U
U
SOC
τ
T
-
τ
T
-
τ
T
-
τ
T
-
+×




























−×








−×+










×










=










+
+
+
2
1
k
k
k
2
1
1k
1k
1k
e12
e11
2
1
e00
0e0
001
2
1
(1)
where η is the Cullen Coefficient, which can be
obtained from battery discharging experiment.
Generally, when the battery is charging, η equals to
1, and less than 1 when discharging.
The observation equation is expressed as:
()
k0kkOCVk
21 VIRUUSOCUU ++++=
(2)
The Kalman Filter is initialized as:
()() []



×=
×=
=
=
=
++
+
）（
）（
T
T
T
vvEv
wwEw
x-xx-xEx
xEx
k
00000
00
ˆˆ
)(
ˆ
0
(3)
and recursived as:
()
()
[]
()


 
−
+
−−+
−
−−
−
+
−
−
−
+
−
−
−=
−+=
+=
+=
=
kkkk
kkkkkk
T
kkk
T
kkk
T
kkkk
kkk
xCLEx
vxgyLxx
vCxCCxL
wAxAx
uxfx
,
ˆˆˆ
),
ˆ
(
ˆ
1
11
11
(4)
According to the Hybrid Pulse Power
Characteristic (HPPC) test presented in the Freedom
Car manual(FreedomCar, 2003) and existing data
obtained before, the time constant
1
τ
、
2
τ
and
polarization resistance R
1
、R
2
can be received from
the MATLAB curve fitting toolbox using the
parameter identification means.
4 CONTROL STRATEGY
In this paper, constant current method is used for
equalization, and the loss can be expressed as
RtIQ
2
1
1
=
(5)
where I
1
is the equalizing current, R is the equivalent
resistance during the process, and t is the time
needed for equalizing. Another equalization method
is to use a rectangular wave with a duty cycle α. If
the two types of equalizing currents start in the same
time, the amplitude of the rectangular wave current
needs to be increased. Therefore, the loss of the
rectangular wave current balanced in one switching
cycle can be derived as
Rt
α
I
tRIQ
2
1
2
22
== α
(6)
where I
2
is the rectangular wave current. The duty
cycle varies from 0 to 100%, so the conclusion is
12
QQ >
(7)
Only when the SOC imbalance degree of the battery
group reaches a certain degree, the equilibrium
control begins, and the balance is judged by the
variance of the SOC to open the equilibrium.The
control policy flowchart is shown in figure 3.
A Fast Equalization Method for Series Batteries based on Cuk Converters
19

SOC variance
>threshold
Turn on
equalization
control
Decide the
number of the
battery with
the largest
deviation
Turn on the
Correspondin
g MOSFETs
Closed-loop
control the
equalization
current
SOC－SOC median
＜threshold
YES
NO
YES
NO
Figure 3. The control strategy flow chart.
5 SIMULATION AND
EXPERIMENT
5.1 Simulation Verification
First, the rated capacity of each single battery in the
simulation is 60Ah, and the rated voltage is 3.3V. In
order to get the results faster, the initial SOCs are set
to 65.502%, 65.503%, and 65.500% respectively.
Figure 4 shows the simulation result using the
proposed control strategy to equalize three batteries.
The SOC of the first battery was set as the median.
The initial SOC deviation of the third battery was
bigger than that of the second one. Hence the third
battery needs to be charging equalized first, where
sets the charging current as 5A. Then the second
battery needs to be completed discharging
equalization, where sets the discharging current as
10A. Figure 5 shows the current of serial battery
packs and the assisting battery respectively.
Figure 4. Simulation result of the equalization process.
Figure 5. The current wave of both sides.
5.2 Experimental Verification
An experimental platform is built for the battery
equalization, as shown in figure 6. Firstly, the
battery pack is discharging equalized, and the
reference values of the discharging currents are 2A,
4A, 6A, 8A, and 10A, respectively. The wave when
the current value is 10A are shown in figure 7. Then
the battery pack is charging equalized, and the
reference values of the charging currents are 2A, 3A,
4A, and 5A, respectively. All the experiments are
successfully realized quantitative control of the
currents. The waves when current value is 5A are
shown in figure 7. And the results verify that method
could achieve fast equalization and low assumption.
Figure 6. The experimental platform.
Figure 7. Discharging and charging current wave.
CoEEE 2021 - International Joint Conference on Energy and Environmental Engineering
20

6 CONCLUSION
This paper introduces a fast equalization method
considering SOC (State of Charge) differences of
series batteries based on Cuk converters. The
method increases equalization current as large as
possible, and simultaneously, achieves fast
equalization and low consumption. The
experimental platform is constructed, and the results
verify the validity of the proposed fast equalization
method.
ACKNOWLEDGMENTS
I’d like to thank all the teachers and students who
helped me to finish this paper. Without their help,
the work can not be completed successfully.
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A Fast Equalization Method for Series Batteries based on Cuk Converters
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