Journal Preproof Series hybrid fuel cell/supercapacitor power source A. Siangsanoh, M. Bahrami, W. Kaewmanee, R. Gavagsazghoachani, M. Phattanasak, J.P. Martin, B. NahidMobarakeh, M. Weber, S. Pierfederici, G. Maranzana, S. Didierjean
PII: DOI: Reference:
S03784754(20)300276 https://doi.org/10.1016/j.matcom.2020.02.001 MATCOM 4944
To appear in:
Mathematics and Computers in Simulation
Received date : 15 October 2019 Revised date : 14 January 2020 Accepted date : 1 February 2020 Please cite this article as: A. Siangsanoh, M. Bahrami, W. Kaewmanee et al., Series hybrid fuel cell/supercapacitor power source, Mathematics and Computers in Simulation (2020), doi: https://doi.org/10.1016/j.matcom.2020.02.001. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. c 2020 International Association for Mathematics and Computers in Simulation (IMACS). ⃝ Published by Elsevier B.V. All rights reserved.
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Series hybrid Fuel cell/Supercapacitor Power source
repro of
A. Siangsanoha,b, M. Bahrami b, W. Kaewmanee b, R. Gavagsazghoachani d, M. Phattanasak b, J.P. Martin c, B. NahidMobarakeh c, M. Weber c, S. Pierfederici c, G. Maranzana c, S. Didierjean c
a
LEMTAUniversité de Lorraine, VandoeuvrelèsNancy 54505, France TE King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand c GREENUniversité de Lorraine, VandoeuvrelèsNancy 54505, France d Renewable Energies Engineering Department, Shahid Beheshti University, Tehran 1983969411, Iran b
Abstract
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Hybridization systems working with electric generators and energy storage devices lead to optimal technologies for recent power sources. They are become more popular due to their advantages such as high efficiency, saved energy and low pollution. There are many types of architecture of hybridization. This article proposes a novel converter structure for a hybrid fuel cell/supercapacitor application that the fuel cell is hybridized with a bank of supercapacitors. Its benefits include high efficiency and maximum use of supercapacitor energy. The mathematical model is developed. The operation and modeling of the converter are presented. Closed loop controls by using an indirect sliding mode technique for the inner current loop and the energy control in the outer loop including a disturbance estimator are provided. Finally, simulation and experimental results obtained from the 150 W testbench are given to validate the proposed converter and system. The obtained results have shown that the proposed converter structure offers the right candidate for a hybridization fuel cell/supercapacitor power source.
Keywords: Series Converter, Fuel Cell, Supercapacitor, Power Source
1. Introduction
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Hybridization between an energy source such as fuel cell ( FC) and other sources, e. g. , battery or supercapacitor (SC) has been proposed twenty years ago [1,6]. It combines two or more sources, not only to highlight the benefits but also to mitigate the disadvantages inherited from each source. It has been used in several applications, for example, vehicular [3,4][6,7], and electric aircraft [8], and standalone microgrid [9]. The advantages and disadvantages of these sources can be found as follows. For FC, which is an electrochemical device that produces electricity without any pollution from an electrochemical reaction of hydrogen and oxygen from air [ 10] . Both of them need pipes; especially the air supply system needs a pump [ 6] . Accordingly, the dynamics of FC would be slow. Fuel starvation phenomenon may happen if the supplied gazes’ pressures are not sufficient. This might force FC getting a low lifespan [10]. To avoid such a problem, the power dynamics of FC needs to be controlled. Since FC provides high energy density, it usually used as the main energy source. In contrast, SC has a low energy density, but it has a high power density. It can supply and absorb energy rapidly. Therefore, SC is used as an auxiliary source to deliver the different powers of the main source and the load. Moreover, SC has a long life cycle [9].
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voltage of fuel cell voltage of supercapacitor voltage of point A and B transformer input voltage of the proposed model primary voltage secondary voltage magnetizing inductance Inductance inductive reactance primary current current magnetizing inductance inductor current secondary current switch duty cycle control input delta transformer ratio
repro of
Nomenclature 𝑉 𝑉 𝑉 𝑇𝐹 𝑉 𝑣 𝑣 𝐿 𝐿 𝑟 𝑖 𝑖 𝑖 𝑖 K d u 𝛿 m
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There are several architectures for FC system hybridized with SC [11,12] as shown in Fig. 1. The architecture used only one DC/DC converter is shown in Fig.1(a) where FC and SC are connected directly before entering the converter and load. For this architecture, the output voltage can be regulated but the FC and SC are not controlled. Moreover, the voltage level of the FC and DC are varying equally corresponding to the load power. In this case, it is presented the architecture corresponding to the direct connection of the FC and the SC with controlled DC bus voltage [ 13,14]. In Fig.1(b), the converter is directly connected to FC and it allows to control the dynamics of FC to meet its constraint but the SC is not controlled. And another aspect, Fig. 1(c) resembles the architecture presented in Fig.1(a). However, a converter is placed for the SC to allow controlling its dynamics. In fact, for this architecture, the constraints of FC can be taken into account by indirectly control thanks to the SC converter [ 15,16] . Finally, adding the converter for both FC and SC is presented in Fig. 1(d). One DC/DC converter at the output allows controlling the DC bus voltage to the desired value. The two others allow controlling the instantaneous power of the SC and the FC. In this case, the constraints of the fuel cell, like the maximum value of the power and the dynamic of the current, and the constraints of SC such as maximum value of voltage and power can easily be taken into account. However, the large number of DC/DC converters increase the losses and the weight and reduce the reliability of the system. Therefore, the reduction of DC/DC converter number allows to reduce the losses of the system and also, the weight and volume are reduced. In order to increase the use of electrostatic energy stored in SC, its voltage could decrease to half of its rated voltage value. In this case, SC provides almost 75% of the maximum stored energy. For this reason, DCDC converters with stepup or stepdown function have to be inserted between FC and SC devices. In Fig. 1(e), a novel power electronic architecture u s i n g a series converter is placed between FC and SC. Therefore, all dynamics of the system can be controlled with the proposed converter structure. Theoretically, its efficiency is unity when FC and SC voltages are the same. This condition is obtained in a steady state. In this article, a topology inspired by a partial power converter (PPC), shown in Fig. 2, is presented. This topology is presented in [17,19] for applications of photovoltaic systems. In another way, in [19], a bidirectional PPC is used as a voltage source to control the current between the input and the output for two batteries hybrid electric vehicles. In literature [1718], the output of the converter is placed either the filter capacitor or LC filter to make the output voltage
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constant. But for the proposed topology, the voltage 𝑉 is in a pulse form. Therefore, the filter is not necessary. During operation, if the load changes, the proposed converter cannot keep the output voltage constant.
Converter
DC Bus
Super capacitor
Converter
DC Bus
Super capacitor
(b)
(a) Fuel Cell
Super capacitor
Fuel Cell
repro of
Fuel Cell
Converter
Converter
Fuel Cell
Converter
Super capacitor
Converter
DC Bus
Converter
DC Bus
(d)
(c)
Converter
Super capacitor
DC Bus
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Fuel Cell
(e)
Fig. 1 State of art of FC/SC hybrid system.
VAB
I
VFC
VSC
Direct Power Flow
Jou
Fig. 2 PPC topology.
Anyway, the output voltage can be regulated by using another DCDC converter. The literature firmly concluded that PPC architecture can be applied to a hybrid system. Nowadays, partialpower DCDC converters do not apply to any FC/SC hybridization applications. 2. Proposed Hybrid System and Proposed Power Converter The proposed architecture is detailed in Fig. 3 where the current 𝐼 can be controlled concerning to the constraint of FC either to increase or to decrease. For this application, there is only positive current flows from FC to SC and to the load. There are two switches K2 and K3 that operate the circuit by converting the voltage, which is fed through a
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I L
A
VAB
B
D2 K2 iS2
repro of
transformer from a fullbridge inverter to the voltage 𝑉 . And then, it is connected directly with SC and the load. When the system is in a steadystate, the equation can be defined. 𝑉𝑆𝐶 𝑉𝐴𝐵 𝑉𝐹𝐶 (1)
TF i p
T1
vs2
T3
SC
vp
V FC
VSC
vs3
iS3 D3 K3
R
T2
T4
Fig. 3 Proposed concept of FC/SC hybrid using a series DCDC converter.
There are two operation modes defining by the polarity of 𝑉 , which are a negative value (𝑉 0) and positive value (𝑉 0). To study the behavior of the converter when the system is in a steadystate, 𝑉 and 𝑉 are equal. 2.1 Modeling
ip
i f1
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im
vp
Lm
Lf1
rf1
if2 Lf2
rf2
vp2
Lf3
if3
m
K2 is2
I
rf3
vp3
A
vs2 B
vs3 i s3 K3
Jou
Fig. 4 Modeling of the converter considering parasitic parameters of the transformer.
Fig. 4 shows the model of the proposed converter including the transformer. The magnetizing and leakage inductances, as well as parasitic resistances, are presented in the primary side, which are 𝐿 , 𝐿 , 𝐿 , 𝐿 , 𝑟 , 𝑟 and 𝑟 respectively. The transformer ratio is 𝑚. Where 𝑖 , 𝑖 , 𝑖 are currents flown through the leakage inductances and 𝑖 , 𝑖 are currents on the secondary side. According to the model in Fig.4, the following relations can be defined: 𝑖 𝑖
𝑚𝑖
(2)
𝑚𝑖
The current 𝐼 is the sum of the current on the secondary winding. 𝐼 𝑖 𝑖
(3)
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𝑖 𝑖 𝑟 and 𝐿
𝑟
with 𝑟
𝑖
𝑖 𝐿
𝑖 ;𝑖
𝑖
𝑖
and it leads to:
𝑚𝐼 2𝑖 𝑚 𝐼 2𝑖 𝑚 2𝑖 𝐿 for the sake of simplicity.
From (4), since the current 𝐼 is constant, the time derivative of 𝑖
𝑚𝐼
𝐼
2𝑖
𝑚𝐼,
(4)
repro of
We can observe in Fig. 4 that 𝑖
2𝑖
can be found as
2
2𝑖
𝑚𝐼
2
(5)
Considering the voltage of FC and SC, according to Fig. 3, the voltage 𝑉 can be negative or positive in order to increase or decrease the current 𝑖. So, for the dynamic model, these two cases have to be considered.
2.2 Operation sequence and modeling
vp
VSC
VSC
0 T/2
δT/2 dT/2
0
t
δT/2
0
T/2
T
t
dT/2
t
K2 0
t
K3
t
VAB
t
1
1
K3
T
vp
1
1
K2
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The control of the input current 𝑖 increase or decrease can be done by controlling the voltage 𝑉 to be negative or positive. If one needs the current 𝑖 constant, the averaged voltage of 𝑉 must be zero. In Fig. 5, the control signals and the key waveforms of the converter are defined. The case 𝑉 0 is presented on the left side of Fig. 5. When the voltage 𝑉 fed by the inverter is positive, switch K3 always turned on while switch K2 must be turned off. On the other hand, when 𝑉 is negative, switch K2 is always turn on while switch K3 must be turned off. On the right side is for the case that 𝑉 is positive by controlling switch K2 turns on and K3 switch turns off when the voltage 𝑉 fed by the inverter is positive. In contrast, switch K2 turns off and switch K3 turns on when the voltage 𝑉 fed by the inverter is positive. When 𝑉 is zero, the switches K2 and K3 must turn on to let the current 𝐼 flow and make the voltage 𝑉 zero. For the case 𝑉 0 is shown on the right side of Fig. 5. To taken into account the highvoltage spike caused by a highcurrent rate in leakage inductances, special waveforms (blue square in Fig. 5) are proposed to reduce the leakage inductor current to be zero before switching.
0
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VAB 0
0 and 𝑉
t
0
Fig .5 Key waveforms of the series converter. Left side for 𝑉
For both cases 𝑉
t
0
0 and right side for 𝑉
0
0 will be detailed as follows.
A. Case 𝑽𝑨𝑩 𝟎 In this case, all sequences are shown in Fig.6 while the waveforms are given in Fig.7. The details are as follows. Sequence 1n: in this sequence, the control signal of the Hbridge inverter allows to have 𝑉 positive. The magnetizing current 𝑖 increases. K2 and K3 conduct while 𝑖 decreases and 𝑖 increases. The current 𝑖 increases. The variations of these currents are expressed as:
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𝐿
𝑉
(6)
Subtracting the first two equations of (7), with 𝐿f
𝐿f and 𝑟 𝑣
𝑣 Replacing (8) into (10), one can find the voltages:
In this sequence, 𝑉
is: 𝑚𝑣
𝑉 This sequence ends when 𝑖
(13)
𝑚𝑣
0
reaches zero then 𝐷 and K2 turns off with ZCS while 𝑖
Sequence 2n: 𝑣 is still positive voltage. K3 still conducts while K2 is off. 𝑖 is zero in this sequence. It can be summarized as: 𝑖
𝑉
This mode terminates with 𝑉
𝑚𝑣
𝐼→𝑖
𝑚 𝑉
𝑚𝐼, 𝐿
𝑚𝐼 𝑟
(8)
(9)
𝑟 the voltage relation can be obtained:
𝑣
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𝑖
reaches 𝐼 and 𝑖
𝑟
verifies:
𝑚𝐼𝑟 .
𝑚𝐼𝑟
𝑣
(7)
repro of
𝐿 𝑟 𝑖 𝐿 𝑟 𝑖 𝑣 0 ⎧ 𝑣 ⎪ 𝑣 𝐿 𝑟 𝑖 𝐿 𝑟 𝑖 𝑣 0 ⎨ ⎪𝑣 𝐿 𝑟 𝑖 𝐿 𝑟 𝑖 𝑣 0 ⎩ Since K2 and K3 conduct, the secondary side sees a short circuit and thus the voltages 𝑣 and 𝑣 𝑣 0. 𝑣 Using (5), the current relations can be defined:
and 𝑖
(11)
(12)
equals 𝑚𝐼.
follow the current I whereas
𝑉, 𝑟
(10)
0 𝑚𝑉
(14)
0 and K2 conducts.
Sequence 3n: 𝑉 is zero. K2 and K3 conduct. It can be summarized as: 0
Jou
𝐿
(15)
𝑣
𝐿
𝑟 𝑖
(16)
𝑣
𝐿
𝑟 𝑖
(17)
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ip
ip Lm
vp
im
i f1
sequence 1n
Lf1 rf1
if2 Lf2
rf2
m
vp2 if3
Lf3
K2 is2
I
A
vs2
rf3
B
vp3
sequence 4n
Lf1 rf1
if2 Lf2
rf2
m
K2 is2
vp2
if3
Lf3
A
rf3
B
vs3 i s3 K3
ip
ip
im Lm
i f1
im
Lf1
sequence 2n
rf1
Lf2
rf2
m
Lm
vp
I
K2
A
i f1
Lf1
rf1
sequence 5n
if2 Lf2
rf2
m
K2 is2
vp2
if3
Lf3
rf3
B
vp3
vs3 i s3
Lm
Lf1 rf1
Lf3
sequence 3n
if2 Lf2
rf2
m
vp2
if3
Lf3
Lm
vp
A
vs2
rf3
K2 is2
I
Lf1
B
rf1
A
sequence 6n if2 Lf2
rf3
rf2
m
K2 is2
vp2
vs2
if3
B
vp3
I
K3
rna lP
K3
vp
I
vs2
vp3
vs3 i s3 K3
vp
Lm
vp
i f1
repro of
im
Lf3
rf3
vp3
vs3 i s3
I
A
vs2 B
vs3 i s3 K3
K3
Fig. 6 Sequence of case 𝑉
0.
Subtracting (16) from (17), one gets:
𝑣
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Then with (8), it leads to
𝑣
𝑣 𝑣
𝑚𝐼𝑟 .
(18)
𝐼𝑟 (19)
𝐼𝑟
In the same manner as in sequence 1n detailed in (12): 𝑉
Replacing 𝑣
and 𝑣
𝑣
𝑣
𝐼𝑟
0
(20)
detailed in (19) into (16) and (17) respectively, one can deduce the current 𝑖 : 𝐿
𝑟
𝑖
0
(21)
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This mode terminates with 𝑉
0.
Sequence 4n : 𝑣 is negative, K2 and K3 are switched on. The differential equations for this sequence are: 𝐿
𝑟 𝑖
𝐿
𝑣
𝐿
𝑟 𝑖
𝐿
𝑟 𝑖
𝑣
0
(22)
𝑟 𝑖
𝑣
0
(23)
repro of
𝑣
and 𝑣
Finally, subtracting (22) from (23) and with (24), the voltages 𝑣 𝑣
𝐼𝑟
The voltage between A and B is 𝑉 This mode terminates when 𝑖
reaches 𝐼 and 𝑖
𝑚𝑣
become:
𝑣
𝑚𝑣
(24)
0
(25)
reaches zero and then K3 turns off.
Sequence 5n: the input voltage is still negative, switch K2 is on and K3 is turned off. 𝑖𝑆 and 𝑖𝑓 follow the current I whereas 𝑖𝑠 is zero. Since the current 𝐼 is constant (see fig.7), its time derivative is zero. Therefore, and
𝑑𝑖𝑓 𝑑𝑡
0.
(26)
𝐼→𝑖
𝑚𝐼, 𝐿
𝑣 ,
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𝑖
𝑑𝑖𝑓 𝑑𝑡
0
0
One can find the differential equation for this sequence as 𝑣
𝐿
𝑟 𝑖
𝐿
𝑟 𝑖
𝑣
0.
(27)
𝑣
𝐿
𝑟 𝑖
𝐿
𝑟 𝑖
𝑣
0.
(28)
Like in Sequence 2n, subtracting (26) from (27) and using the relationship in (7), the voltages 𝑣
and 𝑣
can be found
and then, 𝑉𝐴𝐵 for this sequence can be determined as: 𝑉
This mode terminates when 𝑉
𝑚𝑣
𝑚 𝑉
𝑚𝐼 𝑟
𝑟
𝑚𝑉
(29)
0 and K3 turns on.
Jou
Sequence 6n: In this sequence, 𝑉 is zero, both switches are turned on. The behavior of the system is the same as that of sequence 3n. The voltage 𝑉 and the currents 𝑖 , 𝑖 , 𝑖 can be found as follows:
𝐿
This mode terminates when 𝑉
0.
𝑉𝐴𝐵
𝑣𝑠
𝑣𝑠 𝑟
0 𝑖
(30)
0. .
(31) (32)
repro of
K2 K3
rna lP
VAB (V)
Mode of switches
vp (V)
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S1n
(A)
iS2 iS3
I
Jou
Current(A)
if1 im ip
S1n
S2n
Fig. 7 Simulation of key waveforms of the case V
S4n
S3n
Time(s) 0.
S5n
S6n
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B. Case 𝑽𝑨𝑩 𝟎 This case is similar to the case that 𝑉 0 that of Sequence 1n – Sequence 6n. The sequences for this case are provided in Fig. 8 while the waveforms are given in Fig.9.
repro of
Sequence 1p: this sequence detailed in Fig. 8, the control signal of the Hbridge provides the negative 𝑉 . The variations of these currents are expressed as: 𝐿
𝐿 𝑟 ⎧𝑣 ⎪ 𝑣 𝐿 𝑟 ⎨ ⎪ 𝐿 𝑟 ⎩𝑣 In the same manner in Sequence 1n, in this sequence, 𝑉 𝑉 This sequence ends when 𝑖
𝑚𝑣
reaches 𝐼 and 𝑖
𝑣
𝑖
𝐿
𝑟 𝑖
𝑣
0
𝑖
𝐿
𝑟 𝑖
𝑣
0
𝑖
𝐿
𝑟 𝑖
𝑣
0
(33)
(34)
is:
𝑚𝑣
0
reaches zero then K3 turns off with ZCS while 𝑖
(35)
equals 𝑚𝐼.
Sequence 2p : 𝑣 is positive. K2 conducts while K3 is still off. The equations can be derived:
When 𝐿
𝑣 ,
𝐿
𝑟 𝑖
𝐿
𝑟 𝑖
𝑣
0
𝐿
𝑟 𝑖
𝐿
𝑟 𝑖
𝑣
0
𝑟 𝑖
𝐿
𝑟 𝑖
𝑣
0
𝑟
𝑚𝑉
𝐿
rna lP
⎧ 𝑣 ⎪ 𝑣 ⎨ ⎪ ⎩𝑣 0,
0,
For this sequence can be the value of 𝑉
𝑉
This mode terminates with 𝑉
(36)
0.
as:
𝑚𝑣
𝑚 𝑉
𝑚𝐼 𝑟
(37)
0 and K3 conducts.
Sequence 3p : 𝑣 is zero. K2 and K3 conduct. This sequence is the same as the third sequence of case 𝑉 (Sequence 3n). It can be summarized as: 𝐿
0
0 (38)
𝐿
𝐿
𝑟 𝑖
𝑟 𝑖
(39)
𝑣
𝐿
𝐿
𝑟 𝑖
𝑟 𝑖 .
(40)
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𝑣
In the same manner as in sequence 3n:
𝑉
𝑚𝑣
𝑚𝑣
0
(41)
In the same manner as in Sequence 3n, one can find the differential equations for the currents 𝑖 , 𝑖 , and 𝑖
(42)
2 (43)
This mode terminates with 𝑣
0.
𝑖
𝑟
𝐿
2
0
as:
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ip
ip Lm
vp
if1
im
rf1
Lm
sequence 1p
Lf1 rf2
m
vp2 if3 Lf3
K2 is2
I
A
vs2 B
vs3 i s3
if2 Lf2
rf2
m
if3
Lf3
I
A
rf3
B
vs3 i s3 K3
ip
ip
im Lm
if1
im
Lf1 rf1
sequence 2p
Lm
vp
if2 Lf2
rf2
m
vp2 Lf3
K2 is2
I
A
vs2
rf3
B
if1
Lf1
sequence 5p
rf1
Lf2
if3 Lf3
rf2
m
Lm
Lf1 rf1
sequence 3p
if2 Lf2
rf2
m
vp2
if3
Lf3
K2 is2
Lm
vp
I
Lf1 rf1
if2 Lf2
A
rf2
vp2 if3 Lf3
B
vp3
A
B
vs3 i s3
sequence 6p
vs2
rf3
I
K3
rna lP
K3
K2
rf3
vp3
vp
K2 is2
vs2
vp3
K3
vp
rf1
vp2
rf3
vp3
sequence 4p
Lf1
vp
if2 Lf2
i f1
repro of
im
K2 is2
I
A
vs2
rf3
vp3
vs3 i s3
m
B
vs3 i s3 K3
K3
Fig. 8 Sequence of case 𝑉
0
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Sequence 4p : 𝑣 is positive, K2 and K3 are switched on. 𝑣𝑝
𝐿𝑓
𝑣𝑝
𝐿𝑓
𝑑𝑖𝑓
𝑑𝑡
𝑑𝑖𝑓
𝑑𝑡
𝑟 𝑖
𝐿𝑓
𝑟 𝑖
𝐿𝑓
𝑑𝑖𝑓 𝑑𝑡 𝑑𝑖𝑓 𝑑𝑡
𝑟 𝑖
𝑣𝑝
0
(44)
𝑟 𝑖
𝑣𝑝
0
(45)
Finally, subtracting (44) from (45) and with (8), the voltages 𝑣 𝑣
𝐼𝑟
and 𝑣
become:
𝑣
(46)
The voltage between A and B is 𝑉
𝑚𝑣
𝑚𝑣
0
(47)
repro of
K2 K3
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VAB (V)
Mode of switches
vp (V)
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S1p
iS2 iS3
I (A)
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Current(A)
if1 im ip
S1p
S2p
Fig. 9 Simulation of key waveforms of the case V
S4p
S3p
Time(s) 0.
S5p
S6p
Journal Preproof
This mode terminates when 𝑖
reaches 𝐼 and 𝑖
reaches zero and then K3 turns off with 𝑉 𝑚𝑣
𝑉
𝑚 𝑣
𝑚𝐼 𝑟
𝑟
0.
𝑚𝑉
(48)
𝑖
𝐼→𝑖
𝑣𝑝
𝐿𝑓
𝑣𝑝
𝐿𝑓
𝑚𝐼, 𝐿
𝑉,
(49) 𝑑𝑖𝑓
𝐿𝑓
𝑟 𝑖
𝑑𝑡 𝑑𝑖𝑓
𝐿𝑓
𝑟 𝑖
𝑑𝑡
repro of
Sequence 5p : the input voltage 𝑣 is negative, switch K2 is on and K3 is turned off. It can be summarized as:
𝑑𝑖𝑓
𝑑𝑡 𝑑𝑖𝑓 𝑑𝑡
0,
0,
0.
𝑟 𝑖
𝑣𝑝
0
(50)
𝑟 𝑖
𝑣𝑝
0
(51)
𝑉𝐴𝐵 for this sequence can be determined in the same manner as detailed in Sequence 5n as: 𝑉𝐴𝐵 This mode terminates when 𝑉
𝑚𝑣𝑝
𝑚 𝑣𝑝
0 and K2 turns on.
𝑚𝐼 𝑟𝑓
𝑟𝑓
𝑚𝑉𝑠𝑐
(52)
Sequence 6p : 𝑉 is zero, both switches are turned on that same the Sequence 3p. It can be summarized as: 𝐿 𝐿
𝑣
𝐿
𝑉𝐴𝐵
𝑚𝑣𝑠
the differential equations for the currents 𝑖 , 𝑖 , and 𝑖 𝑟
𝐿
2
This mode terminates when 𝑉 3. Control method
2
(53)
𝐿
𝑟 𝑖
𝑟 𝑖
(54)
𝐿
𝑟 𝑖
𝑟 𝑖 .
(55)
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𝑣
0
𝑚𝑣𝑠
0
(56)
are as follows: 𝑖
0
(57) (58)
0.
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To control this system, in steadystate, the SC voltage have to track the FC voltage while respects the FC’ s constraints, which are the changing rate of the fuel current 𝑑𝑖/𝑑𝑡 𝑚𝑎𝑥 [16] and the maximum value of the fuel cell power 𝑃 𝑚𝑎𝑥. The voltage loop is used to define the current reference 𝐼 from the definition of the reference of the SC voltage. The current loop is used to regulate the FC current from the definition mode of VAB. The control block diagram is given in Fig. 10 (top). 3.1 VTDisturbance observer In steadystate, the SC voltage must equal to the FC voltage. But realistically, the supercapacitor voltage does not equal the fuel voltage due to the voltage drop across the diode and the parasitic resistances of the system. This voltage drop, in this paper, is represented by 𝑉 as shown in Fig. 10 (bottom). It can be found using a disturbance observer. 𝑉 is used later to calculate the SC reference voltage. 𝑉 is a veryslow dynamics fictive voltage source, which is placed between FC and the inductor L. The nonlinear observer detailed in [ 20] is applied. The system contained the state x and the estimator are presented in (59) and (60), respectively.
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𝑥
VT Iref Imeasured
VABsel
Disturbance Estimator
VSCm
VT
I
d
δ
B
D2 K2
Iref
Rate Limit
uK2 uK3 uT1 uT2 uT3 uT4
TF i p
iS2
V FC
ₓ ÷
VFCm
FPGAbased PWM GERNERATION
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L
VAB
PFC Saturation
VAB
Calculation of duty cycle VT
A
+
PLoad
Im VFCm
+
0 for VAB < 0 1 for VAB> 0
mode Sliding mode controller
Controller

Voltage to Energy
VSCm
(59)
0
+
Voltage to Energy
Trajectory
𝑔 𝑥, 𝑢
repro of
VSCref VFC + 
𝑓 𝑥, 𝑢 𝑉
T1
vs2
vp
vs3
iS3
T3
SC
R
VSC T2
T4
D3 K3
Fig. 10 (Top) block diagram of the closedloop control, including disturbance observer, (bottom) presentation of 𝑉 .
𝑥
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𝑉
(60)
where 𝑥 is the estimated variable, 𝑒
𝑥
𝑥. 𝑒
𝑉
and 𝐾
𝐾
𝐾 𝑒
𝑔 𝑥, 𝑢 𝐾 𝑒
𝑆∙𝑒 𝑔 𝑥, 𝑢 𝑒
𝑉𝑇 . 𝐾 , 𝐾 and 𝑆 are the parameters needed to be chosen. 𝑒 𝑒𝑝 ∙ 𝑥 . If parameters are chosen as 𝑃 𝐾 ∙ 𝑔 𝑥, 𝑢 𝑒𝑝
𝑒𝑥
With the chosen Lyapunov candidate function 𝑉
𝑓 𝑥, 𝑢
∙ 𝑆, the time derivative of 𝑉 is 𝑉
𝑒
𝑒
∙
𝑆 0
𝑒 0 ∙ 𝑒 𝑃
(61)
And if 𝑃 and 𝑆 are positivedefinite matrices, the system is exponentially stable. Then the values of 𝑆 and 𝑃 can be chosen to make the dynamics of 𝑒 is higher than that of 𝑒 . It means that 𝑆 𝑃.
repro of
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3.2 Voltage and current regulation
In normal operating mode, the control law allows, by the modification of the voltage 𝑉 , to follow the SC voltage. In steadystate, the SC voltage have to track the FC voltage while respects the FC’s constraints, which are
𝑚𝑎𝑥 and
𝑃 𝑚𝑎𝑥 as mentioned earlier. The outer loop is used to define the current reference 𝐼 from the definition of the reference of the SC voltage. The inner loop is used to regulate the FC current from the definition of 𝑉 . Considering Fig. 3, one can express the relationship between the voltages including the voltage across the parasitic resistance of the inductor 𝑟 and the variation over time of the input current 𝐼 as 𝐿
𝑉
𝑟𝐼
𝑉
𝑉
(61)
For the inner loop, indirectsliding mode controller [15, 2223] is utilized as shown in (62) and (63) where the parameters K and λ are related to the controlled bandwidth, which will be chosen. 𝑠
𝐼
𝐼
𝐾
𝑠
To ensure that the current 𝐼 will reach its reference 𝐼
𝐼
𝑑𝑡
𝐼
𝜆𝑠
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𝜆∙𝑠
It can be seen that the current 𝐼 will reach its reference 𝐼
𝑑𝐼𝑟𝑒𝑓
(64)
, if 𝜆 is positive.
Selection mode of 𝑉𝐴𝐵 depends on the value of 𝑉𝐴𝐵 . If it is less than 0, it is mode 𝑉𝐴𝐵 greater than 0, it is mode 𝑉𝐴𝐵 0. 𝑉𝐴𝐵 can be define; 𝜆∗𝑠
(63)
, the product of 𝑠 ∙ 𝑠 must be negative.
𝑠∙𝑠
𝑉
(62)
𝐾𝑖 ∗ 𝑖
𝐼𝑟𝑒𝑓
∗𝐿
𝑟𝑖
𝑉
𝑉
0 and when 𝑉𝐴𝐵
is
(65)
. The sign of Using (61) with (62) and (63), the control voltage 𝑉 is obtained. This voltage is now called 𝑉 𝑉 is utilized for generated the 𝑉 of the converter. The duty cycle is calculated regarding the supercapacitor voltage and the transformer’s turn ratio 𝑚 as 𝑑
𝐶
𝑉
𝑉
(67)
𝐶 𝑉 . The controller for the outer loop is given with
as:
0
K
(66)
𝐼
where y is the variation of energy stored in SC, 𝑦 𝑦

∙
can be found using the power balance when losses are neglected:
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The current reference 𝐼

𝑦
𝑦
𝐾 𝑦
𝑦
𝐾
𝑦
𝑦 𝑑𝜏
(68)
The parameter K and K can be chosen to make the error dynamics as the secondorder system’s response such as 2ξω and K ω with a desired damping factor ξ and a chosen angular frequency ω .
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4. Simulation and Experimental Result
repro of
A MATLAB/Simulink model was developed using parameters detailed in Table 1 and Table 2 to investigate the converter’s behaviors. The proposed model was compared with the one using Simscape power systems blockset in MATLAB/Simulink. The currents such as 𝑖 , 𝑖 , 𝑖 , 𝑖 and voltages such as 𝑉 , 𝑣 , 𝑣 , 𝑣 , 𝑉 of the converter’s model are needed to be used to confirm the validation of the proposed model. However, for the current, only 𝑖 , 𝑖 and 𝑖 can be shown experimentally. Therefore, only 𝑖 , 𝑖 and 𝑖 are shown. Fig. 11 presents the voltage of 𝑉 . In Fig. 12, the current of both switches K2 and K3, which are 𝑖 and 𝑖 in the system are presented and in Fig.13 the current 𝑖 at the output of the Hbridge inverter is presented. The currents 𝑖 , 𝑖 , 𝑖 , voltages 𝑉 are similar. Those results validate the proposed model of the converter. A test bench was built as shown in Fig. 14 (top). There are the fullbridge inverter which the SIC MOSFET inverter module CCS050M12CM2 was used. The switches K  K and diode D  D was realized with IPT004N03L and diode MBRB4030. A planar transformer was used magnetic core ELP64/10/50 for realizing the transformer. The switching command signals were generated using DS5203 FPGA Base Board in dSPACE system. A programmable DC power supply TDK GEN 6085 was used to emulate an FC thanks to the polarization curve as shown in Fig.14 (bottom). A bank of MAXWELL supercapacitor BMOD0083P048 was utilized. All control algorithms were done under MATLAB/Simulink linking between dSPACE hardware and the realtime interface. The waveforms of the primary 0 currents and voltages in steadystate are shown in Fig. 14 for a value of duty cycle and for both cases where 𝑉 and 𝑉 0. The experimental results allow validating the proposed model.
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TABLE 1. SYSTEM PARAMETER
Parameter
Value
Maximum FC voltage
15 V
Maximum FC current
15 A
Maximum SC voltage
15 V
Transformer turn ratio 𝒏𝒑 : 𝒏𝒔𝟏 : 𝒏𝒔𝟐
1:2:2
𝑳𝒎
14 μH
𝑳𝒇𝟏
0.317 μH
𝑳𝒇𝟐
𝑳𝒇𝟑
𝒓𝒇𝟏 𝒓𝒇𝟐
𝒓𝒇𝟑
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Switching frequency
0.144 μH 0.002 Ω 0.47 Ω 40 kHz
TABLE 2. CONTROL AND ESTIMATOR PARAMETERS
𝑲𝒊
Parameter
𝝀
Maximum FC current slope 𝒅𝒊
𝒅𝒕
Value 1000 10 A/s
max
Maximum FC power 𝑷𝑭𝑪 max 𝑲𝒑𝒆
120 W
S
10000
500
Journal Preproof
𝐾 𝑆
repro of
𝑲𝒆𝒊
VAB
Simscape Power System Proposed model
Time(s)
Fig. 11 Simulation results obtained using the model using Simscape power systems blockset and the proposed model: 𝑉
0.
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is2, is3
Simscape Power System Proposed model
Time(s)
𝑉
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Fig. 12 Simulation results obtained using the model using Simscape power systems block set and the proposed model: the currents 𝑖
and 𝑖 .
The voltage 𝑉 determines the dynamics of the current 𝐼, which is related to the voltage of the supercapacitor. If is in a negative mode. It means that the voltage 𝑉 is less than 0 shown in Fig.11. The current of both switches (𝐾
and 𝐾 ) are presented in Fig.12. They start with the half of maximum current . Both switches K2, K3 are turned on in sequences 1, 3, 4, and 6. Especially, they will not operate in the same mode (turn onturn off) in sequences 2 and 5 at the same time. The primary current is presented in Fig. 13. It is the sum of magnetizing current and inductor current 𝑖
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ip
repro of
Simscape Power System Proposed model
Time(s)
Fig. 13 Simulation results obtained using the model using Simscape power systems block set and the proposed model: the current 𝑖 when V
Voltage Probe
Supercapacitor
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dSPACE card
Current Probe
Planar transformer
Inductor
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Fullbridge Inverter
Fig. 14 (Top) test bench, (bottom) characteristic VI curve of fuel cell.
0
Journal Preproof
repro of
Vp =40V/div
VAB =40V/div
i s2 =5A/div
i s3 =5A/div
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time(s)
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Vp =40V/div
VAB =40V/div
i s2 =5A/div
0.1
0.2
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0
0.3
0.4
0.5
i s3 =5A/div
0.6
0.7
0.8
0.9
0 with d
0.2, δ
1
Time(s)
Fig. 15 Experimental results: 𝑉 , primary current, and current of both switches: (Top) V 0.3, δ 0.2.
0.1, (Bottom) V
0 with d
The experimental result of 𝑣 , 𝑉 , 𝑖 , 𝑖 have been presented in Fig. 15. Fig. 15 (Top) shows the case when 𝑉 0. It can be seen that the results of the experiment are slightly 0 and Fig.15 (bottom) shows another one case when 𝑉 different from simulations. It may occur from parasitic resistance, inductance and capacitance of the wires used in the circuit are long, switches, diodes including the effect from dead time.
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repro of
Vp =20V/div
ip =10A/div
VAB =40V/div
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time(s)
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Vp =20V/div
ip =10A/div
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VAB =40V/div
0
0.1
0.2
0.3
0.4
Fig. 16 Experimental results: 𝑣 , 𝑖 , 𝑉
0.5
0.6
0.7
0.8
0.9
1
Time(s) 0 shown in the top and 𝑉
0 shown in the bottom.
The voltage 𝑣 and current 𝑖 are presented in Fig.16. Fig. 16 (top) shows the case that 𝑉 is negative and Fig. 16 (bottom) shows the case that 𝑉 is positive. The voltage and current fluctuate while switches turn off due to the nonideal switches.
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IFC =2A/div
VSC =5V/div
repro of
VFC =5V/div
Pload =50W/div
Time(s)
Fig.17 Hybrid systems shown the interoperability of fuel cell and supercapacitor while supply energy to the load.
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𝑉 and 𝑉 are equal in the steadystate as shown in the yellow line and purple line in Fig.17. In the beginning, there is no load. After that, the load is changed from 0 to 200 W. Since, the response of the supercapacitor is faster than that of the fuel cell, so the SC supplies the power to the load at first. The SC voltage can be low to half of the rated voltage value to supply 75% of the maximum stored energy to load. At t = 400 s, the load is zero. The fuel cell charges the supercapacitor. Therefore, the voltage 𝑉 and 𝑉 will return to the same value as at the beginning. In this test, the current fuel cell is limited at 7 A illustrated in the blue line. 5. Conclusions and Future work
The new power architecture of FC/SC series hybrid has been proposed. The converter modeling including parasitic parameters of the converter such as leakage inductance and resistance of the transformer is provided and validated. The definition of the control signal of the Hbridge inverter strongly reduces the overshoot voltage without using any clamp circuit. The switching frequency is increased but zero current switching (ZCS) in some devices allows to obtain high efficiency. The control algorithms, with the help of the disturbance observer, allows managing the power provided by the fuel cell, and taking into account its constraints.
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6. Acknowledgements
This work was funded by King Mongkut’s University of Technology North Bangkok [grant number KMUTNB63KNOW035] and by the Université de Lorraine. Reference [1]
T. Le, Fuel cells: the epidemic of the future, Proceedings: Electrical Insulation Conference and Electrical Manufacturing and Coil Winding Technology Conference (Cat. No.03CH37480), Indianapolis, Indiana, USA, (2003) 505510.
[2]
A. TRaissi, Current technology of fuel cell systems, IECEC97 Proceedings of the ThirtySecond Intersociety Energy Conversion Engineering Conference (Cat. No.97CH6203), Honolulu, HI, USA, (1997) 19531957.
[3]
M. Zandi, A. Payman, J. Martin, S. Pierfederici, B. Davat and F. MeibodyTabar, Energy Management of a Fuel Cell/Supercapacitor/Battery Power Source for Electric Vehicular Applications, IEEE T. Veh. Technol. 60 (2011) 433443.
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L. Xian, G. Wang, and Y. Wang, Subproportion control of double input buck converter for fuel cell/battery hybrid power supply system, Iet. Power. Electron. 7 (2014) 21412150.
[5]
M. Phattanasak et al., Hybrid Power Source FC/SC with SingleLoop Control Approach: Reference Trajectories Generation, 2017 IEEE Vehicle Power and Propulsion Conference (VPPC), Belfort, (2017) 15.
[6]
Andrew Dicks and David A. J. Rand, Fuel Cell Systems Explained, 3rd Edition, John Wiley and sons, 2018.
[7]
J. Chen and Q. Song, A Decentralized Energy Management Strategy for a Fuel Cell/SupercapacitorBased Auxiliary Power Unit of a More Electric Aircraft, IEEE T. Ind. Electron. 66 (2019) 57365747.
[8]
J. Chen and Q. Song, A Decentralized Dynamic Load Power Allocation Strategy for Fuel Cell/SupercapacitorBased APU of Large More Electric Vehicles, IEEE T. Ind. Electron. 66 (2019) 865875.
[9]
Amin, R. T. Bambang, A. S. Rohman, C. J. Dronkers, R. Ortega and A. Sasongko, Energy Management of Fuel Cell/Battery/Supercapacitor Hybrid Power Sources Using Model Predictive Control, IEEE T. Ind. Inform. 10 (2014) 19922002.
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[4]
[10] S. Abbou, J. Dillet, G. Maranzana, S. Didierjean, O. Lottin, Local potential evolutions during proton exchange membrane fuel cell operation with deadended anodee Part I: impact of water diffusion and nitrogen crossover, J. Power Sources, 340 (2017) 337346. [11] C. Turpin, D. Van Laethem, B. Morin, O. Rallières, X. Roboam, O. Verdu, V. Chaudron, Modelling and analysis of an original direct hybridization of fuel cells and ultracapacitors, Math. comput. Simulat. 131 (2017) 7687. [12] M. GarciaArregui, C. Turpin and S. Astier, Direct connection between a fuel cell and ultracapacitors, 2007 International Conference on Clean Electrical Power, ( 2007) 474479. [13] K. H. Loo, G. R. Zhu, Y. M. Lai and C. K. Tse, Development of a maximumpowerpoint tracking algorithm for direct methanol fuel cell and its realization in a fuel cell/supercapacitor hybrid energy system, 8th International Conference on Power Electronics  ECCE Asia, Jeju, (2011) 17531760. [14] G. Zhu, K. H. Loo, Y. M. Lai and C. K. Tse, QuasiMaximum Efficiency Point Tracking for Direct Methanol Fuel Cell in DMFC/Supercapacitor Hybrid Energy System, IEEE T. Energy Conver. 27 (2012) 561571. [15] Payman, S. Pierfederici and F. MeibodyTabar, Energy Management in a Fuel Cell/Supercapacitor Multisource/Multiload Electrical Hybrid System, IEEE T. Power Electr. 24 (2009) 26812691. [16] A. Payman, S. Pierfederici, F. MeibodyTabar and B. Davat, An Adapted Control Strategy to Minimize DCBus Capacitors of a Parallel Fuel Cell/Ultracapacitor Hybrid System, IEEE T. Power Electr. 26 (2011) 38433852. [17] J. R. R. Zientarski, M. L. d. S. Martins, J. R. Pinheiro and H. L. Hey, Evaluation of Power Processing in Seriesconnected Partialpower Converters, IEEE J. Em. Seo. Top. P. 7 (2019) 343352
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[18] J. R. R. Zientarski, M. L. d. S. Martins, J. R. Pinheiro and H. L. Hey, SeriesConnected PartialPower Converters Applied to PV Systems: A Design Approach Based on StepUp/Down Voltage Regulation Range, IEEE T. Power Electr. 33 (2018) 76227633. [19] Nicolas Allali, Convertisseur haut rendement à dimensionnement réduit pour batterie hybridée puissance/énergie de véhicule électrique : Principe de source de courant controle, Dissertation, Ecole centrale de Lille, 2016. [20] H. Renaudineau, J. P. Martin, B. NahidMobarakeh and S. Pierfederici, DC–DC Converters Dynamic Modeling With State ObserverBased Parameter Estimation, IEEE T. Power Electr. 30 (2015) 33563363.
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[21] Eric Monmasson, Power Electronic Converters: PWM Strategies and Current Control Techniques, ISTE, 2011. [22] R. GavagsazGhoachani, L. Saublet, J. Martin, B. NahidMobarakeh and S. Pierfederici, "Stability Analysis and Active Stabilization of DC Power Systems for Electrified Transportation Systems, Taking into Account the Load Dynamics," in IEEE Transactions on Transportation Electrification, vol. 3, no. 1, pp. 312, March 2017. [23] Pierre Magne, Contribution to the stability analysis and stabilization of DC microgrid with energy storage capability, dissertation, University of Lorraine, 2012.
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repro of
Highlights Series hybrid architecture for fuel cell and supercapacitor was presented A new series converter was prepared The operation of the series converter was detailed The converter’s model was developed and compared the results with that obtained using Simscape power systems blockset in MATLAB/Simulink