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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE Industry ApplIcAtIons MAgAzInE • July|Aug 2014 • www.IEEE.org/IAs 2 HIS ARTICLE PRESENTS THE ANAL- ysis and design of a hybrid fuel cell bat- tery auxiliary power unit (APU) for remote applications where a fuel cell is the main energy source, operating for slow power dynamics while a battery or a supercapacitor compen- sates the fast transient peak power requirements. A fuzzy logic-based control has been implemented in the energy management performance control to impose that the fuel cell operates most of the time in its best operating point and maintains the battery state of charge in its best oper- ating range, which contributes to a longer lifetime, min- imizes maintenance requirements, and approaches the best fuel-to-electricity system efficiency. 1077-2618/14/$31.00©2014IEEE T By MArcElo godoy sIMõEs, BEnJAMIn BlunIEr, & ABdEllAtIf MIrAouI Digital Object Identifier 10.1109/MIAS.2013.2288375 Date of publication: 18 April 2014 © XXXXX Design of a battery auxiliary power un it for remote applications

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IEEE

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his article presents the anal-

ysis and design of a hybrid fuel cell bat-

tery auxiliary power unit (apU) for

remote applications where a fuel cell is

the main energy source, operating for slow power

dynamics while a battery or a supercapacitor compen-

sates the fast transient peak power requirements. a fuzzy

logic-based control has been implemented in the energy

management performance control to impose that the fuel

cell operates most of the time in its best operating point

and maintains the battery state of charge in its best oper-

ating range, which contributes to a longer lifetime, min-

imizes maintenance requirements, and approaches the

best fuel-to-electricity system efficiency.

1077-2618/14/$31.00©2014IEEE

T

Fuzzy-Based energy

ManageMent Control

By MArcElo godoy s IMõEs , BEnJAMIn BlunIEr , & ABdEllAt I f M IrAouI

Digital Object Identifier 10.1109/MIAS.2013.2288375

Date of publication: 18 April 2014

© XXXXX

Design of a battery auxiliary power unit for remote applications

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Fuel Cell-Powered Hybrid APU apUs are important for decentralized or distributed energy production, such as telecom, remote sites, or even military applications [1], [2]. hybridization is often required, and a main fuel source is supplemented by stor-age. sizing and optimization are usually performed to minimize the weight and volume for a given application. a fuel cell-powered hybrid apU [3] is an interesting solu-tion, as observed in Figure 1. When refueled by hydrogen cartridges, a fuel cell has almost no noise in operation, pro-viding electricity and heat with water as a by-product [4]. this article presents an energy management performance improvement control of a combined structure [a fuel cell and a peaking power source (pps)] where the pps (i.e., a battery or supercapacitors) provides fast variation power and the fuel cell supplies the base average load [5].

a fuzzy logic algorithm maximizes the efficiency of the system and minimizes the cycles of shutdown and the restarting of the fuel cell, eventually contributing to the lon-ger life expectancy of the system. in this article, a topology consisting of a 300-W fuel cell stack connected to a superca-pacitor pack of a nickel–metal hydride battery (ni–Mh) battery through a dc/dc buck converter is presented. the choice between supercapacitors and/or a battery depends on the user’s needs and the load characteristics. Batteries have a good energy density but a low power density. On the other hand, supercapacitors have a better power density but a lower energy density. in addition, unlike batteries, superca-pacitors have almost unlimited charge/discharge cycles. Fuel cells are not bidirectional systems, and they have a slow time transient response for controlling hydrogen and air inlets. therefore, a transient compensation must be accomplished with another reversible power or energy source (supercapaci-tors or battery, respectively) that will handle the power tran-sients [6]. supercapacitors are preferable for loads with high power peaks, short transients, and a high number of charge and discharge cycles. Batteries are preferable for loads with long transients without power peak transient cycles [7].

the mathematical modeling for a proton exchange membrane (peM) fuel cell is very complex and requires knowledge of several electrochemistry parameters that are not easy to obtain for the commercially available fuel cell stacks [8]. the theoretical equations for

expressing the best power operating point, as well as the overall efficiency of the fuel cell, are very difficult to model, and experimental-based solutions are the only possible approach [8]. therefore, the novelty of the pro-posed control is to fine-tune a fuzzy-based control using the heuristics of the system operation, including, for example, the avoidance of very high currents (which impose a lot of hydrogen flow) as well as the avoidance of off cycles that stress the fuel cell during turn-on and make their lifetime shorter.

a rather simple and robust structure has been chosen to validate the relevance of the proposed energy management control approach, where the aim is to have the simplest and least expensive system that can be adapted for several ppss, such as supercapacitors or batteries, with optimized operation as a portable unit.

Fuel Cell Hybrid Systema complete electrical model has been analyzed, developed, and used to develop the control laws and energy manage-ment strategies before they are implemented in the real system. the modeling and simulation results were pre-sented in a previous paper, where a ni–Mh battery sup-plied the peak power [9].

the apU is shown in Figure 2. the fuel cell used is a peM fuel cell. it operates at a low temperature and at a room atmospheric pressure on the cathode side. its rated power is 300 W for a voltage ranging from 30–60 V. a dc/dc buck converter is connected to the stack, and the output dc-voltage is controlled over the dc link.

Other very interesting converter topologies with bet-ter performance and lower costs have been proposed in [10]–[12]. these converters could be used in a new design of such a system. the pps imposes the value of the dc bus voltage (around 24 V), which is dependent on its state of charge (soc). the pps can be changed with-out changing the architecture of the system as long as its voltage remains below the operating voltage of the fuel cell. this system has been designed to accommodate a voltage range of 10–36 V. table 1 shows the fuel cell apU specifications.

the experimental work has been verified with an embed-ded dspace microautobox integrated with the apU. such

A fuel cell battery hybrid APU. 1

The APU system and its components.

300-WAtmospheric

Fuel CellStack

Power Board

Peaking Power Source (dc Bus)Battery or Supercapacitors

Buck Converter

Measurement andSignal Processing

Board

Microautobox (dSPACE)(Rapid Prototyping)

2

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rapid prototyping and real-time implementation allowed the control structure designed in MatlaB/simulink to be fully developed for an industrial application. Using virtual prototyping an implementation methodology validated the whole system, including the control and components design (the inductance and capacitance sizing, battery capacity, power electronics, fuel cell power, and so on, using simula-tion tools). the system model and the multiloop control, including the fuzzy logic-based energy management sys-tems, were implemented in MatlaB–simulink, as shown in Figure 3, and then validated in a simulation by direct compilation and target downloading into the dspace microautobox. For the final industrial version, the control system will be implemented in a compact, low-cost micro-controller-based board.

low-power fuel cells like the one utilized for this apU operate at atmospheric pressure where air is supplied, with three fans at a high-stoichiometric ratio. the fuel cell is air-cooled using the same fans as the air supply. the high stoichiometric ratio ensures that there is almost no oxygen depletion and no electrodes flooding. as the fuel cell sys-tem (energy source) is hybridized with the pps, its dynamic does not need to be high. to increase the lifetime of the fuel cell, the strategy aims at keeping the fuel cell current dynamics as low as possible. ideally, the fuel cell should deliver a constant power matching the average load power corresponding to the power at its best efficiency.

therefore, it can be assumed that the fuel cell is always in steady state and, for this reason, a static model of the fuel cell is used in the simulation-based design. For higher-power applications, the static characteristic cannot be used to describe the fuel cell system; the compressor and the air dynamic (the air pressure inside the channels),

as well as the water content of the membrane, will affect the membrane resistance have to be considered. For power fuel systems readers are referred to the more complex models presented in [13].

Control StrategyOptimization problems can be solved based on a successive approximation solution of the generalized hamilton–Jacobi–Bellman equation, and neural network solutions have been used, where they are tuned a priori in off-line mode, and a closed-loop control, based on recursive least squares or other methods, may bring the updated control laws to converge to the optimal control. Usually, for an optimization-based control strategy, it is required to find a solution for

( ( )) { ( ( )) ( ( ), ( )) },minJ X t J X t g X t X t U1 1( )u t

0= + + + -) ) (1)

where ( ( ), ( ))g X t X t 1+ is the immediate cost incurred by ,u t^ h the control action, at time ,t and U0 is a defined

heuristic term. to adapt ( ( )),J X t the right-hand side of (1) must be known a priori. therefore, to get that, one may have to wait for a time step until the next input becomes available. consequently, ( ( ))J X t 1+ can be cal-culated using a performance index at time .t 1+^ h how-ever, when the problem’s temporal nature does not allow waiting for the subsequent time steps to infer the incre-mental costs, other solutions must be used to calculate

,x t 1+^ h and it has been found that a fuzzy logic-based system would be the simplest and best solution for such an optimization strategy [14].

the battery soc can be considered as a dynamic sys-tem; the system can be written as

x k x k P T1 b b sh+ = +^ ^h h (2)

. if. if ,

PP

0 95 01 0 0

<b

b

b $h = '

where Pb is the battery power level defined by the Ibat of Figure 1, bh is the battery charge acceptance (0.95 for charge and 1 for discharge), and Ts is the sampling time. the chosen criterion for N samples can be written as

, ,J m P k TH FC sk

N

0

1

2D==

-

^ h/ (3)

where ,m P kH FC2 ^ h is the hydrogen mass consumed for the power PFC during the sampling time .Ts the fuel cell power is obviously l imited by P PFCMIN FC#

,PFCMAX# where, in this application, P 0FCMIN = and PFCMAX = W,300 where the hydrogen taken for the output power will be variable in accordance to the mea-sured cell efficiency shown in Figure 4(a).

ravey et al. [14] demonstrated that such a fuzzy controller based on the soc of the pps can give optimal results for a given load profile family. they compared the

TAble 1. THe FUel Cell AUXIlIARY POWeR UNIT SPeCIFICATIONS.

Rated power 300 wfuel cell voltage range 30–60 Vdc output voltage 10–36 VDC output current (max) 30 AEmbedded storage (max)

Battery or supercapacitors

Buck Converter

IStack IToc

IStack

IStack,Ref FuzzyController

BatterySoC

PIa

IBattVBattVStack

Fuel CellStack

VV

dc

B.M.S.

Load

dc +

+-

-+

-

IStackBus

3The APU control structure.

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results (e.g., the fuel cell power, soc profiles, and hydrogen consumption) with the optimal results found with an off-line dynamic programming algorithm, which is able to find the optimal results based on the a priori known load profile. this previous fuzzy logic control study supports the use of this apU as a low-power adaptation of the structure for fuel cell-based hybrid electric vehicles [14]. in such a structure, the load is taken by any ouput circuit and the system should aim to have a long life and to minimize the turn-on and turn-off cycles in addition to avoiding charging the battery with the maximum fuel cell current operation point, which impresses a very low efficiency and high utilization of hydrogen.

Fuzzy Logic Controlthe main motivation and novelty in using a fuzzy logic-based control for the fuel cell apU is that there is no simple model for the soc for batteries, and electrochem-istry-based modeling is heavily dependent on knowledge of the battery’s internal parameters. in addition, this apU can be used with either battery or supercapacitor storage, and the fuzzy logic controller works for both op-tions. a proportional-integral (pi)-based control was used in [9] to generate the reference voltage for a dc-link system to improve the transient response of a fuel cell. however, such a control does not impose the best soc, and the pi design is ad hoc made dependent on the fine-tuning of the fuel cell’s slow dynamic response. the con-troller proposed in this article has been defined heuristically based on experimental work, where initially the fuel cell power is plotted against the output current (Figure 5) and then, using a mass flow meter, the system efficiency is plotted against the fuel cell power. there-fore, there is an inverse mapping of the system efficiency in terms of the impressed output current using those ex-perimental data that can be expressed by rules. the au-thors conducted an extensive state-of-the-art literature survey and firmly believe that a control system has not been proposed like as the one described in this article, which aims to impress the fuel cell output current for achieving the best efficiency and improved soc of a hy-brid storage system (battery or supercapacitor).

Most fuzzy systems are based on rules such as those shown in Figure 5. the rules are defined based on the system heuristics, and, for this controller, the inverse function has been designed so that the set point for the fuel cell current will have a prescribed soc. the input information is fed back from the device as it operates and actuates on the operation, i.e., crisp input information from the device is converted into fuzzy values for each input fuzzy set by the fuzzification block. the universe of discourse of the input variables determines the required scaling for correct per-unit operation. the fol-lowing steps must be conducted to design a fuzzy logic control structure:

1) identify and name the inputs and their ranges.2) identify and name the outputs and their ranges.3) create the fuzzy partitions (degree of fuzzy member-

ship function) for each input and output.4) construct the rule base under which the system will

operate.

5) Decide how the action will be executed by assigning strengths to the rules.

6) combine the rules and defuzzify the output.the normalization and scaling gains are very impor-

tant because the fuzzy system can be retrofitted for other devices or ranges of operation simply by changing the scaling of the input and output. the decision-making logic determines how the fuzzy logic operations are per-formed. in the fuzzy algorithm, the fuzzy rules are con-nected together (using the Or operator) to form the rule base. the fuzzy algorithm that maps p inputs onto q outputs has pq rules with the following form:

:r11 iF ( is )x A1 then ( is )y B1

:r12 iF ( is )x A1 then ( is )y B2

h h h:r q1 iF ( is )x A1 then ( is )y Bq

h h h:r21 iF ( is )x A2 then ( is )y B1

h h h:rpq iF ( is )x A p then ( is )y Bq .

The fuel cell system performances and working zones. The current–power and efficiency characteristics permit the out-put membership function (i.e., the fuel cell current) of the fuzzy controller to be defined. (a) An experimental fuel cell’s current–power characteristic and (b) measured efficiency.

Fuel Cell Power(b)

Avoided (Bad Efficiency)

Should BeAvoided

Best EfficiencyRegion

0 50 100 150 200 250 300 350

0.5

0.45

0.4

0.35

0.3

0.25Fu

el C

ell S

yste

m E

ffici

ency

0.2

0.15

0.1

0.05

0

00

50

100

150

P (

W)

200

250

300

1 2 3 4 5I (A)

(a)

Imax

Pmax

Experimental

6 7 8 9 10

Interpolation

4

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each rule, ,rij maps the thi multivariate fuzzy input set Ai to the thj univariate output set with confidence .cij the degree to which element x is related to element y is repre-sented by the membership function ,x yrijn ^ h defined in the product space A A Bn1 # # #g by

, , , ,x y t x c yr A ij Biji jn n n=^ ^ ^^h h hh (4)

where t is a triangular norm usually chosen to be the min or the product operator. if s and t are the max and min operators, the fuzzy inference becomes

, , .max miny x x yB A Rin n n=^ ^ ^^h h hh6 @ (5)

the fuzzy output set yBn ^ h in (5) must be transformed into a crisp output (with defuzzification computation) to get a real number variable ouput to be used in the system decision-making strategy.

APU Energy Management Strategythe main objective of an energy management strategy (eMs) is to develop a simple and robust energy manage-ment control approach, where the objective for such an eMs is to have the simplest and least expensive system that can be adapted by the user for other ppss and loads depending on the application. such a controller should be implemented in a simple microcontroller to reduce the cost of the system. the control strategy has to consider the following components’ constraints:

1) it should limit the fuel cell dynamics and voltage cycling (especially high voltages) to increase its lifetime.

2) it should make the fuel cell work around the best working points (where its efficiency is the highest).

3) it should maintain the pps (battery or supercapaci-tors) soc in a prescribed window and limit the cycling in the case of a battery.

the time the fuel cell takes to reach the desired power depends on the control strategy. advanced neural network-based control systems have been proposed for implementing approximated optimal control using cere-bellar model articulation controller networks [15], [16], supporting that artificial intelligence-based control is adequate for complex systems such as fuel cells. in this case, the fuel cell current is based on the soc level of the pps. the fuel cell current should be maintained in the best efficiency window, as shown in the green box in Figure 4(b). the operating points at a higher power should be avoided but are authorized if necessary (e.g., when the soc is too low).

the operating points at a lower power are avoided—in this case, the fuel cell is switched off. the parameters of the fuzzy controller are tunable by the user and are repre-sented by trapezoidal functions, as shown in Figure 6(a) and (b) for the soc and the fuel cell current, respectively. the rules were defined by the simulation studies to be very simple:

1) iF (soc is low) then (iFc is high).2) iF (soc is good) then (iFc is optimal).3) iF (soc is high) then (iFc is low).For a given load profile, the membership parameters

can be optimized using an off-line optimization algo-rithm, such as dynamic programming, to obtain the best overall energy efficiency.

experimental evaluation the experimental development was implemented in accordance to Figures 2 and 3, where the pps is a super-capacitor bank composed of two 58 F–15 V packs. the supercapacitor’s soc is calculated as

SoC( )

,UU t

scap,

scap,

max2

02

= (6)

where ( )U tscap,02 is the instantaneous supercapacitor’s

open-circuit voltage and Uscap,max2 is its maximum voltage.

in this case Uscap,max = 30 V as two supercapacitors’ packs of 15 V are in series. the instantaneous supercapacitor bank voltage is computed as

( ) ( ) ( ),U t U t R I t2scap, scap scaps0 $= - (7)

where Rs is the series resistance of a supercapacitor’s pack (given by the manufacturer) and Iscap is its cur-rent. the experimental setup is shown in Figure 7; it is composed by a supervision computer connected to the microautobox with a graphic user interface (con-trolDesk).

the industrial version of the apU is supplied by an external metal hydride tank, as shown in Figure 1. how-ever, for the experiment, it is more convenient to use exter-nal compressed hydrogen tanks as the metal hydride tanks need to be refilled. the electrochemical fuel cell system needs a balance of a plant supervisory layer that manages

A fuzzy-based decision-making strategy.

Input

Output

Fuzzification

ApplyingMembership

Rules

Defuzzification

Making aDecision

Fuzzy RuleApplication

MakingInferences

and Associations

5

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the hydrogen purge, the air for reaction and cooling, and the humidity and temperature management. these are not in the scope of this article, and interested readers should refer to [9].

the model and simulation permit the eMs to be tested under various driving cycles. this allows several strategies and setup parameters to be tuned to optimize the system response and check the system constraints (i.e., the dynamics, currents, voltage, and peaks). the simulations were provided by [7], and, for the sake of applicability, this article focuses only on the experimen-tal approach.

Experimental Results

Test 1, Gaussian Distributionthe load current profile (Figure 8) has been randomly generated (Gaussian distribution) with an average current of 7 a, which corresponds to the nominal fuel cell power, a variance of 6 a, and a sample time of 3 s to produce high dynamic currents with high peaks of currents. Figure 8 shows the currents on the dc bus. it can be seen that the fuel cell current contribution on the dc bus is smooth and almost constant. On the other hand, the supercapacitors handle the peaks and dynamics.

the fuel cell current is maintained in the best effi-ciency region most of the time, as shown in Figure 9. the current is always between 3 and 6 a, which corresponds to the best efficiency power window shown in Figure 5(a). the experimental powers distribution over the load pro-file is shown in Figure 10: when the fuel cell delivers some power, it is always at the best efficiency. the fuel

The fuzzy controller membership functions: (a) the SoC membership functions and (b) the output variable, normal-ized fuel cell current.

Low Good High

Low Optimal

Input Variable SoC

(a)

(b)

00

1

0

1

1

Output Variable IFC (Normalized)0 1

High

6

The experimental setup.

ExternalHydrogen

Supply

300-W Fuel CellSystem

Supercapacitors(2 # 15 V

in Series, 58 F each)

Active Load(Piloted with a PC

and General-PurposeInterface Bus)

Supervision(ControlDesk)

AuxiliaryPower Unit

7

The current on the dc bus. At the beginning, the fuel cell current is zero because the supercapacitor’s SoC is high. The fuel cell current is very slow.

0-10

-5

0

5

10

15

50 100 150

ILoad IScap IStack,dc

200 250 300 350

8

The fuel cell current is always around the current giving the maximum efficiency (between good and high for the fuzzy membership functions).

Time (s)

High

Good

Low

0

Fuel

Cel

l Cur

rent

0

1

2

3

4

5

6

7

50 100 150 200 250 300 350

9

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cell is switched off at the beginning as the supercapaci-tor’s soc is high: the number of fuel cell on/off cycles is equal to one over the load profile. at the beginning of the tests, the supercapacitor’s soc is high (Figure 11). as the good region corresponds to an soc between 0.25 and 0.8 [Figure 6(a)], the fuel cell does not deliver any power at the beginning to let the soc reach a lower soc. then, the soc is maintained over the load profile in the soc win-dow defined by the user.

Test 1, Uniform load Profilethe load current profile (Figure 12) has been randomly generated (uniform distribution) with currents between 0 and 10 a. With this current profile, the load variation is more pronounced and the supercapacitors are more solic-ited. two tests have been carried out with the same load profile: the first one with a high initial soc and the second

The fuel cell power statistical distribution. The fuel cell delivers the power at its maximum efficiency according to Figure 5(b).

00

1

2

3

Num

ber

of P

oint

s

4

5

6# 104

20 40 60 80 100Fuel Cell Power (W)

Fuel Cell Power Working Point Distribution

120 140 160 180 200

10

The supercapacitor’s SoC is maintained in the good region.

High

Good

Low

Sup

erca

paci

tor’s

SoC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

0 50 100 150 200 250 300 350

11

The currents on the dc bus: the SoC at t 0= is high and the fuel cell current is zero at the beginning.

0-15

-10

-5

0

5

10

15

20

25

50 100Time (s)

dc C

urre

nts

150 200

ILoad IScap IStack,dc

12

Several currents flowing in the dc bus: the SoC at t 0= is low and the fuel cell current is high at the beginning to recover a good SoC.

0-20

-15

-10

-5

0

5

10

15

20

25

50 100Time (s)

dc C

urre

nts

150 200

ILoad IScap IStack,dc

13

The fuel cell currents for two different initial SoCs and the same current load profile.

High

Good

Low

0 50 100

Time (s)

VScap,t=0 = 28 V(SoCt=0 = 0.87)

VScap,t=0 = 15 V(SoCt=0 = 0.25)

150 200

Fuel

Cel

l Cur

rent

0

1

2

3

4

5

6

7

14

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one with a low soc. the objective is to demonstrate that the controller works independently of the initial soc even if it is low. the dc bus currents for the high and low initial soc are shown in Figures 12 and 13, respectively.

the fuel cell current and the soc for both tests are superimposed in Figures 14 and 15, respectively. except at the beginning, when the soc is very low, the fuel cell current is maintained in its best operating range. For a high initial soc, the fuel cell is switched off one time dur-ing the experiment. in the two cases, the initial conditions influence the starting of the system, but the control strat-egy permits the system to recover the best operating con-ditions after some minutes (fewer than two minutes in this case). in the two experiments, most of the working points, when the fuel cell system delivers some power, are in the best efficiency region, as shown in Figures 16 and 17.

Conclusiona hybrid fuel cell battery apU has been designed, mod-eled, simulated, and evaluated experimentally. the fuel cell in this system supplies energy for the apU, but, because it has slow dynamics due the electrochemical balance of the plant, a pps must be used to compensate the fast transient load peak power requirements. the overall control system has been approached to optimize the fuel-to-electricity effi-ciency and maintain a rapid recovery of the battery soc. a fuzzy logic-based decision-making strategy advanced the control system, achieving the best performance range. the minimization of the shutdown and overcurrent conditions, which contribute to a longer lifetime and minimal mainte-nance needs, was experimentally observed. such operating conditions at low voltages and fewer shutdown cycles (thermal and voltage cycling) permit the fuel cell to have a longer lifetime and avoid cell degradation. it is then expected that this controller will improve the system reli-ability (i.e., less maintenance) and lifetime. With a simple rule-based system, the system performance was found to recover the soc conditions without the typical control overhead by state machine decision-making procedures. the proposed control strategy is easy to retrofit to any other apU system, and it is expected to improve the industry applicability of traditional apU controllers.

DedicationWe dedicate this article to the memory of our friend and coauthor Dr. Benjamin Blunier, formerly an associate professor at the University of technology of Belfort-Montbéliard.

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The final SoC is well recovered. After a transient, the SoC is maintained in the best operating region defined by the user.

High

Good

Low

0 50 100

Time (s)

VScap,t=0 = 28 V(SoCt=0 = 0.87)

VScap,t=0 = 15 V(SoCt=0 = 0.25)

150 200

Sup

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tor’s

SoC

00.10.20.30.40.50.60.70.80.9

1

Hig

Go

Lo

0 50 100

Time (s)

VScap tVV 0 = 28 V(SoCt 0 = 0.87)

150 2000

0.10.20.30.40.50.60.70.80.9

1

15

The fuel cell power is always maintained in the best efficien-cy region. There are two fuel cell on/off cycles (Figure 14).

00

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120 140 160 180 200

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A low initial SoC. The fuel cell power is maintained at the best efficiency region with fewer stop times than in tests with a high initial SoC (stopped only at the end when the load stopped because the SoC had to be recovered).

00

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s

4# 104

20 40 60 80 100Fuel Cell Power (W)

Fuel Cell Power Working Point Distribution

120 140 160 180 200

17

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Marcelo Godoy Simões ([email protected]) is with the Colorado School of Mines. Benjamin Blunier, deceased, was with the Univer-sity of Technology of Belfort-Montbéliard, France. Abdellatif Miraoui is the president of Cadi Ayyad University, Marrakech, Morocco. Simões and Miraoui are Senior Members of the IEEE. Blunier was a Member of the IEEE. This article first appeared as “Fuzzy Logic Controller Development of a Hybrid Fuel Cell-Bat-tery Auxiliary Power Unit for Remote Applications” at the 2010 IEEE IAS International Conference on Industry Applications.