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Design and modeling of an equalizer for fuel cell energy
management systems
Milad Bahrami, Jean-Philippe Martin, Gaël Maranzana, Serge Pierfederici,
Mathieu Weber, Farid Meibody-Tabar, Majid Zandi
To cite this version:
Milad Bahrami, Jean-Philippe Martin, Gaël Maranzana, Serge Pierfederici, Mathieu Weber, et al..
Design and modeling of an equalizer for fuel cell energy management systems. IEEE Transac-
tions on Power Electronics, Institute of Electrical and Electronics Engineers, 2019, 158, pp.1-1.
�10.1109/TPEL.2019.2899150�. �hal-02178404�
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2019.2899150, IEEE
Transactions on Power Electronics
IEEE TRANSACTIONS ON POWER ELECTRONICS
Abstract—During the lifespan of a Polymer Electrolyte
Membrane Fuel Cell (PEMFC) system, some
heterogeneities between the cells constituting the stack
can appear. The voltage of one particular cell in a stack may
decrease because of specific aging or local malfunctioning
such as drying. As a result, more heat is generated in this
cell leading to an increase in its temperature and thus an
additional voltage loss. This snowball effect can result in
the failure of the cell. Therefore, the lifetime of a PEMFC
stack can be increased by applying energy management to
its cells. Notable that the output voltage of a cell is lower
than a stack. Hence, a high conversion ratio converter is
necessary to implement such energy management. An
efficient way to increase the output voltage is to connect
the output capacitors of the converters such as the boosts
in series. Ensuring the converters’ controllability is a key
point to implement energy management. In this paper, an
equalizer system is proposed to ensure the controllability
of the boost converters. The balancing speed and the low
number of switches are the main advantages of this system.
The validity of the proposed system is verified through
simulation and experiments.
Index Terms—Controllability, converter, energy
management, equalizer, Polymer Electrolyte Membrane
Fuel Cell (PEMFC).
I. INTRODUCTION
URABILITY enhancement of Polymer Electrolyte
Membrane Fuel Cells (PEMFCs) is one of the major
challenges to enable the diffusion of this technology in the
mass market. In a stack, different cells are electrically
connected in series to increase the output voltage, whereas they
are supplied with gas in parallel. The whole system lifetime
strongly depends on each cell in such a connection. Therefore,
energy management can have a key role to compensate for the
faults that occurred in each cell. As an example, if the current
production by one particular cell could be decreased to mitigate
local flooding or could be increased to mitigate a local drying,
the electrochemical stability of the stack would be improved. In
the same way, if a faulty cell could be short-circuited, the stack
may continue to operate in degraded mode and ensure the
network reliability. Based on the new patent [1], the current of
any number of cells in a single stack is accessible. As a result,
the behavior of the cells in a stack can be checked and their fault
can be compensated. However, a high voltage conversion ratio
DC-DC converter is required in this case, because the number
of cells in series is decreased. Isolated or high voltage ratio step-
up DC-DC converters can be used but the basic challenge is
efficiency improvement [2], [3].
An efficient way to solve these issues is the series connection
of the DC-DC converters’ output capacitors. This solution leads
to an increase the freedom degree in management and control
of the PEMFCs. The basic drawback of this structure is the
possibility of the controllability loss. For instance, if the input
power of one cell becomes lower than the required amount, the
voltage of the corresponding capacitor will decrease. In this
case and assuming that the DC-DC converter is a boost
converter, the controllability will be lost if the output voltage
becomes lower than the input voltage. In such conditions, a
voltage equalizer or a balancing system can ensure the
controllability.
The equalizer in the literature can be categorized into two
basic groups: with an auxiliary source and without auxiliary
source [4]. The equalizers with auxiliary source use another
source to compensate the lower voltage cells. These equalizers
are not efficient, especially for embedded applications. As seen
in Fig. 1, the equalizers without auxiliary sources, are
categorized into two basic groups: dissipative and non-
dissipative equalizers [4]. Dissipative equalizers use resistance
to decrease the voltage of the higher voltage cells. These
equalizers waste much energy. Therefore, the efficiency is very
low. However, the low cost, simple implementation, and small
size are their advantages [5], [6]. The non-dissipative equalizers
can be divided into three groups: capacitor based [6]–[12],
converter based [4], [13]–[26] and other type equalizers [27],
[28]. A control approach is usually adopted for switches of a
specific structure to balance the voltages in the third group of
equalizers.
A number of capacitors are connected to cells by a number of
switches in the capacitor-based topologies. The cells are
periodically connected to these capacitors, and this operation
continues to the point where all the cells and capacitors reach
the same voltage. These equalizers require a numerous amount
of switches and they are not cost-effective for a large number
of cells or high power applications. In addition, these equalizers
can balance the voltages through several repeated operations.
As a result, they need much time to balance the voltages. The
maximum of the balancing current can be controlled by sizing
the capacitor capacitances. Therefore, the high efficiency in
balancing can be obtained independently of imbalance states
Design and modeling of an equalizer for
fuel cell energy management systems
Milad Bahrami, Jean-Philippe Martin, Gaël Maranzana, Serge Pierfederici, Mathieu Weber, Farid
Meibody-Tabar, Majid Zandi
D
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2019.2899150, IEEE
Transactions on Power Electronics
IEEE TRANSACTIONS ON POWER ELECTRONICS
[6]–[11]. The capacitors of each level of a multi-level converter
were frequently connected to next or previous level capacitors
by using the numerous amount of switch in [11]. In this
topology, the switches and capacitors in the multi-level
converter were used to balance the voltage of capacitors in each
level without adding another device. To overcome the problem
of the balancing time, the resonance phenomenon can be used.
Using the resonance in such topologies, the balancing speed can
be increased simultaneously with achieving the benefits of soft
switching [12].
The converter based equalizer can be categorized into three
groups: cell to stack equalizers [4], stack to cell equalizers [13],
[19]–[25], stack to stack equalizers[26], and cell to cell
equalizers [14]–[18].
A stack to cell equalizer with a flyback converter was used to
equalize the voltage of series lithium-Ion batteries in [23]. A
stack to stack equalizer was used in this topology to realize the
modular approach.
A forward-flyback resonant inverter was used to send energy
from the series cell to cells in [13]. A voltage multiplier circuit
was connected to cells. This circuit is used two diodes for each
cell to automatically select the lower voltage cells and send
energy to them. The required amount of switches was
minimized in this topology at a cost of lower efficiency due to
the use of two diodes for each cell. In this topology, the number
of switches is independent of the number of cells. Similar
topology with a buck converter on the primary side of the
transformer was used in [20] for photovoltaic application. The
forward-flyback converter in [13] the proposed was divided by
a bidirectional converter in [21]. Therefore, the design became
more flexible and circuit implementation was simplified. In
[24], a half-bridge converter was used on the primary side of a
transformer to send energy from the series connected cell to
lower voltage cells. A multi-stacked current doubler was
connected to the secondary side of the transformer in
connecting with cells. The number of diodes and inductances
must be increased by increasing the number of cells. Since this
topology can be implemented with two switches independent of
cells number without a multi-winding transformer, the circuit
design and implementation can be simplified. In [19], [22], an
improved push-pull converter with clamping capacitor was
used to send energy from the series cells to lower voltage cells.
A multi-winding transformer was used in this topology and H-
bridge inverters were used in the secondary windings of the
transformer. This topology needs to measure the voltage to
drive the required H-bridge inverters. The balancing current can
be very high in this topology and as a result, the balancing time
can be reduced.
For the battery applications, it is not necessary to have a large
balancing current, because the voltage difference among cells
slowly increases. Therefore, there is much time to balance the
cells with the lower current to decrease the losses [6]. However,
in such application of which the voltage balancing between
output capacitors of DC-DC converters is required to ensure the
controllability of the converters, the balancing time is the most
important parameter. On the other hand, when the difference
between cell voltages is very high, using the resonance can be
dangerous for power electronic devices due to the high current
peak. Regarding the possible inability of a cell or a set of cells
in injecting the nominal power in a stack, a large difference
between the output capacitor voltages is possible in the fuel cell
applications. As a result, a new equalizer is proposed in this
paper. The proposed equalizer can send energy to the lower
voltage cells. This topology can quickly reach the steady-state
condition by using a small number of switches and ensure the
controllability in the worst conditions. The number of
controlled switches in some converter-based equalizers
depends on the cell numbers [4], [17]–[19], [22], [23], [26].
These equalizers are not effective in term of cost and volume.
In the proposed equalizer, the number of controlled switches is
independent of the cells number. In this paper, the performance
of this equalizer is validated by the simulation and experimental
results. A state space based model is also proposed that can be
used for design purposes.
The rest of this paper is organized as follows: The principals
of the proposed equalizer and the operation modes are described
in Section II. The most important design considerations are also
summarized in this section. In Section III, the simulation results
are presented and compared with the theoretical results. The
experimental results are provided in Section IV to validate the
simulation results. Finally, conclusions are listed in Section V.
II. PROPOSED EQUALIZER
As Mentioned before, a power electronic structure is required
to manage the current of cells separately to increase the lifetime
of the stack. Since the voltage of one cell or a small number of
cells is very low, using a step-up converter is inevitable. In this
case, the conventional boost converter is used for the purpose
of simplicity. To further increase the output voltage, the output
capacitors of boost converters are connected in series. Loss of
controllability is possible in this case. To prevent this
possibility, an equalizer is proposed. The proposed power
electronic structure with the equalizer is shown in Fig. 2 where
the classic boost converters are used to connect the cells to the
DC bus. As seen in this figure, the energy can be transferred
from the series capacitors to the lower voltage capacitors. The
H-bridge inverter can send the energy to even or odd numbered
cells through the transformer. C
H
is a film capacitor at the input
of the H-bridge inverter to stabilize the input voltage of this
converter. The DC link voltage (V
dc
) is determined by the load
requirements. Regarding the embedded application, the
standard voltage of 48 v is adopted for DC link voltage. It is
assumed that the cells inside one stack are broken down into
some group of cells with an identical number of cells.
Furthermore, it is assumed that only one group of cells has a
problem in one moment. In the worst condition, one group of
Fig. 1. Different types of equalizers.
Equalizers
With auxiliary source
Without auxiliary
source
Dissipative
Non-dissipative
Capacitor based
[6]–[12]
Converter based
[4], [13]–[26]
Other
[27], [28]
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2019.2899150, IEEE
Transactions on Power Electronics
IEEE TRANSACTIONS ON POWER ELECTRONICS
cells can inject no power. As a result, the output capacitor
voltage can be changed from zero to 16 v in serial connection
of four output capacitors. The DC link voltage is converted to
the AC voltage on the primary side of the high-frequency
transformer by the H-bridge inverter. This AC voltage is shown
by V
in
.
A. Operation Modes
In this section, the following assumptions are considered in
the operation analysis for the purpose of simplicity:
1. All the switches and diodes are considered as the ideal
devices.
2. Turn ratio for all secondary windings are the same and
equal to
and k is the coupling coefficient.
3. The coupling coefficient between the secondary
windings is perfect.
4. The DC bus voltage is controlled to have a constant
voltage of V
dc
.
The theoretic waveforms of the proposed equalizer are shown
in Fig. 3 in steady state when C
1
and C
2
are the lower voltage
capacitors between the even and odd-numbered cells
respectively. Other cells have the same voltage. The switching
commands of the H-bridge inverter are generated in such a way
that a symmetrical square wave is imposed to the primary side
of the transformer with variable duty cycle. Due to the windings
polarity and the direction of the diodes in the circuit, the odd
and even-numbered diodes can be naturally turned on in the
positive and negative sections of the square wave, respectively.
All the even-numbered/odd-numbered diodes are biased
negatively when the input voltage of the transformer V
in
is
positive/negative. The diode corresponding to the capacitor,
which has the lower voltage between even/odd-numbered
capacitors, conducts the current when the negative/positive
voltage appears on the primary side of the transformer. All the
secondary windings will have the same voltage equal to the
lower voltage capacitor when one diode starts to conduct. As a
result, all the other diodes are reverse biased. The different
operation modes of the proposed equalizer are shown in Fig. 4
when C
1
and C
2
are the lower voltage capacitors. This
assumption is considered in order to investigate all the modes.
1) Mode 1 [t
0
-t
1
: Fig. 4 (a)]: before t
0
two switches S
1
and S
2
were on. At t
0
, S
2
is turned off and S
4
is turned on. Therefore,
the positive voltage is imposed on the primary side of the
transformer. This voltage is induced in the secondary
windings. This voltage leads to the reverse biased of the
even-numbered diodes. Based on the reason mentioned
above, only diode D
1
, which connects to the lower voltage
capacitor between odd-numbered capacitors, conducts
current. As a result, the energy through the leakage
inductance of the transformer is transferred to the capacitor
C
1
. Therefore, the leakage current and voltage of C
1
is
increased. The derivative equations of different state
variables are shown in (1).
(1)
where L is the inductance, r is the resistance, i is the current,
m and f subscripts are used to indicate the magnetizing and
leakage inductance or resistance, V
d
is the diode drop
voltages, V
in
is the input voltage at the primary side of the
transformer,
is the voltage of C
j
,
is the injected
power of FC
j
, and i
load
is the load current.
2) Mode 2 [t
1
-t
2
: Fig. 4 (b)]: S
4
is turned off and S
2
is turned
on as a synchronous rectifier in this mode. Therefore, the
primary side of the transformer is short-circuited. The diode
D
1
continues to conduct but the current passing through it,
which is proportional to the leakage current, is linearly
decreased. The derivative equations in this mode are as
follows:
(2)
The switching frequency is chosen in such a way that the
diode D
1
turns off and the leakage current is reached to the
magnetizing current before the t
2
. The differential equations
are changed when the diode D
1
is turned off (after t
f
) as
follows:
(3)
Fig. 2. Proposed equalizer topology.
0885-8993 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2019.2899150, IEEE
Transactions on Power Electronics
IEEE TRANSACTIONS ON POWER ELECTRONICS
3) Mode 3 [t
2
-t
3
: Fig. 4 (c)]: S
1
is turned off and S
3
is turned
on in this mode. The negative voltage appears on the
primary side of the transformer. In other words,
has a
negative value. This mode like mode 1 has the same effect
on the even numbered capacitors. The voltage of C
2
is the
lowest voltage between the even-numbered capacitors.
Therefore, the diode D
2
is turned on and the leakage current
and the voltage of C
2
starts to increase. The leakage current
negatively increases. The derivative equations in this mode
are as follows:
(4)
4) Mode 4 [t
3
-t
4
: Fig. 4 (d)]: This mode is similar to mode 2
with this difference that S
3
is turned off and S
1
is turned on.
Before the diode D
2
is turned off, the differential equations
of the system are as follows:
(5)
Then, the diode D
2
is turned off and the differential equations
of the system change as (4).
The power is transferred through the transformer to increase
the voltage of lower voltage capacitors. Any losses in the
transformer reduce the power that is received by lower voltage
cells. The transformer leakage inductance can also affect its
transmitting power by affecting its input current. Therefore, the
transformer design has a key role in this topology.
B. Design considerations
The magnetizing inductance of the transformer must be
maximized in order to reduce the magnetizing current. For
instance, L
m
and L
f
of a core with two windings can be
calculated by the following equation:
(6)
Where k is the coupling coefficient and L
1
can be calculated
by:
(7)
N is the number of turns and is the reluctance of the core.
As seen in this equation, increasing the number of turns and
decreasing the reluctance lead to increase the magnetizing
inductance. Increasing the number of turns increases the
volume of the transformer and, therefore, increase the
hysteresis losses. Furthermore, increasing the number of turns
also increases the wire length that leads to an increase of the
wire resistance and, consequently, the copper losses. The
reluctance is inversely proportional to the permeability. Hence,
selecting a core with high permeability can make it possible to
increase the magnetizing inductance with a lower volume. This
also increases the leakage inductance. However, the leakage
inductance affects the maximum transmitting power through
the transformer in each cycle. This power is also the most
important parameter in reducing the equalizing time. To obtain
this power in steady state by considering the first group of cells
as the faulty cells, the diode current can be used to calculate the
transferred energy. Therefore, the transferred energy can be
calculated as follows:
Fig. 3. Theoretical waveforms in steady-state operation of the
proposed equalizer.
Fig. 4. Different operation modes of the proposed equalizer. (a)
Mode 1: t0<t<t1. (b) Mode 2: t1<t<t2. (c) Mode3: t2<t<t3. (d) Mode
4: t3<t<t4.
