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Improving the PEMFC energy efficiency byoptimizing the fueling rates based on extremumseeking algorithm

Nicu Bizon a,b,*aUniversity of Pitesti, 1 Targu din Vale, Arges, 110040 Pitesti, RomaniabUniversity Politehnica of Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania

a r t i c l e i n f o

Article history:

Received 6 March 2014

Received in revised form

24 April 2014

Accepted 26 April 2014

Available online 27 May 2014

Keywords:

Fuel cell system

Energy efficiency

Maximum efficiency point tracking

Extremum seeking algorithm

Air and fuel flow control

* University of Pitesti, 1 Targu din Vale, ArE-mail addresses: nicubizon@yahoo.com

http://dx.doi.org/10.1016/j.ijhydene.2014.04.10360-3199/Copyright ª 2014, Hydrogen Ener

a b s t r a c t

In this paper, the energy efficiency of the Proton Exchange Membrane Fuel Cell (PEMFC)

systems based on the fueling rates is systematically investigated. The PEMFC system under

dynamic load must be operated close to the Maximum Efficiency Point (MEP) to obtain the

highest energy efficiency. This is a difficult task because the MEP is dependent on the

PEMFC parameters and the control PEMFC variables, besides the load profile. Thus, the MEP

must be tracked dynamically with a safe search speed and funded accurately during the

stationary regimes. Consequently, a real-time control is recommended to be used. The

Extremum Seeking (ES) control scheme is proposed here to evaluate the FC net power at

the MEP under different fueling rates and load profiles. Some interesting conclusions are

obtained based on the comparative method proposed using as reference a base control

technique or a PEMFC stack: 1) the MEP is different based on the control of the fuel or air

flow rate; 2) the energy efficiency increases if both fueling flow rates are controlled; 3) the

energy efficiency is less sensitive to power losses if the MEP is tracked by the ES controller

based on air flow rate; 4) the strategy of load following control considering the fuel flow rate

as an input variable is recommended based on the observation that the MEP is more

sensitive to this in comparison to the air flow rate; 5) the design of an appropriate MEP

tracking controller should equally focus on safe operation and the increase of the perfor-

mances such as the search speed and tracking accuracy under dynamic load. All these

remarks are based on an extensive numerical simulation, which are highlighted in this

paper by the main results shown.

Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

Introduction

Hydrogen is a carrier vector of energy being used to the

transport and storage of energy from different sources [1].

ges, 110040 Pitesti, Roma, nicu.bizon@upit.ro.94gy Publications, LLC. Publ

Combinations of hydrogen are found in large quantities in

nature, but obtaining a molecular hydrogen is an energy

consuming process. Thus, the sustainable production of

hydrogen is based on the decomposition of water using

different renewable energy sources, in particular the solar

nia. Tel.: þ40 348 453 201; fax: þ40 348 453 200.

ished by Elsevier Ltd. All rights reserved.

Fig. 1 e The PEMFC system.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 410642

energy [2]. Following the energy generating process, the pure

water is produced, which can be consumed or included to the

industrial water circuit [3]. In this context, the concept of

hydrogen based technology, including the production, storage

and use of hydrogen as energy carrier, will be the center of

attention for researchers in the field of sustainable energy for

coming years [4].

In last decade, a number of topologies hybrid power sour-

ces hydrogen based have been proposed and analyzed in

terms of improving the energy efficiency, optimizing the

control of the DC bus, sizing the energy storage system, and

increasing the life cycle and durability under dynamic load etc

[5,6]. Among the various types of fuel cell, the PEMFC systems

are most used because they are suitable for both automotive

and residential applications due to the high energy density,

low emissions and low temperature operation [7,8].

The PEMFC stack is an electrochemical device in which

chemical energy is converted directly into electrical energy.

The PEMFC stack operates with hydrogen and oxygen to

generate energy with an efficiency of 45e50%, reaching 80%

yield if heat is also recovered [7,8].

The hydrogen is generated by electrolysis or taken from a

hydrogen tank, using different supply modes with hydrogen

[9]: flow-through, dead-end anode, or with recirculation.

Regarding the fuel supply modes, it can be noticed the

following: the continuous-flow mode is not used for normal

applications due to the dangers associated with excess

hydrogen that is eliminated outside of PEMFC system [10]; the

dead-end anode feed mode requires special attention on the

frequency and duration of purging to ensure efficient and

stable operation [11,12]; the recirculation mode is most effi-

cient [9], but can be unpractical to implement it for small

power applications [13]. This paper will analyze the energy

efficiency of the PEMFC system based on the hydrogen flow

rate measured at the input of the PEMFC stack in order to

cover all fuel supply modes. It is obvious that the fuel con-

sumption depends by the fuel supply modes used, but this is

outside the scope of this paper.

Also, it is known that FC net power depends by air flow rate

measured at the input of the PEMFC stack [14,15]. Thus, the

control of thePEMFCsystemto increase theenergyefficiency is

a challenging action if both fueling rates are considered [16,17].

In addition, it is known that other two control systemsmust to

be appropriately designed to maintain the energy efficiency

obtained by optimizing the air/fuel fueling rates of the PEMFC

system [18,19]: the water supply and the heat management.

The analysis presented in this paper is focused on improving

the energy efficiencyby controlling both air and fuel flow rates.

The possibilities to maximize the energy efficiency of the

PEMFC system under different load power levels will be

analyzed in this paper considering the ensemble composed

from the PEMFC stack and the fueling subsystems (Fig. 1).

It is known that the PEMFC system contains other various

auxiliary equipments (including the air compressor, humidifi-

er, pumps, cooling water circulation, and the measurement,

control, signalizing and protection circuits),besides the PEMFC

stack. The power consumption of air compressor is up to 80%

power of the overall auxiliary equipments [20], and this repre-

sents up to 20% of the FC power available [21]. Thus, the PEMFC

systems must operate close to the MEP in order to obtain high

energy efficiency [14,22]. On the other hand, theMEP is difficult

to be tracked because the operating point depends by the

PEMFC system parameters and the load dynamic [23,24].

Consequently, the recent researchwas focused in thisdirection

to maximize the output power of the PEMFC system [25].

To find a better solution for the management of air supply,

different control algorithms were proposed: the dynamic

feed-forwardefeedback control [26], sliding mode control [27],

supper twisting algorithm [15,28], perturb and observe algo-

rithm [29], ES control [30,31], model predictive control [32,33],

and intelligent control based on neural networks [34] and

fuzzy logic [35,36]. Advanced control schemes based on LQR/

LRS strategies [37,38], nonlinear differential flatness-based

control [39,40], time delay control [41], and adaptive control

[42] where proposed in the last years, too. Also, the optimi-

zation strategies have been considered to maximize the effi-

ciency of the whole PEMFC system or the operation of the

compressor [43]. The proposed strategies regulate the air

pressure to the required load power, increasing the FC net

power with about 3%e10% in comparison with the power

obtained in constant pressuremode. It can be noticed that not

all control schemes aforementioned tolerate the uncertainty

on state variables of the PEMFC system [44].

In this paper, the MEP tracking control based on Single-

Input Dual-Output Extremum Seeking (SIDOES) control

scheme proposed in Ref. [45] will be used. This SIDOES control

scheme assures higher search speed and improved tracking

accuracy of the MEP, improving the basic performances of the

classical ES control schemes [46,47].

The static feed-forward (sFF) control technique [21] will be

used as reference to report the improvements on FC net

power. Then the SIDOES control scheme will be used (see

Fig. 2). The improvements on FC net power will be highlighted

by the achievements obtained for the PEMFC system under

test in comparison with the reference.

Themain goal of this paper is to show that energy efficiency

of the PEMFC system can be further improved by controlling

both fueling rates. The SIDOES scheme is used to accurately

determine the unknown MEP of the PEMFC system under

constant and dynamic load. The experiments under dynamic

loadwereperformedbynumerical simulation to showthehigh

search speed of the SIDOES scheme. Also, this paper contrib-

utes to research the fueling flow rates control of the PEMFC

Fig. 2 e The simulation diagram.

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systemsbasedon load followingcontrol scheme, analyzing the

control sensitivities to the air and fuel flow rates.

The paper is organized as follows. Section PEMFC system

modeling and control briefly presents the issues related to

the system modeling and control. The accuracy of the used

model is not so important in this study because the

improvement of the FC net power will be shown through

comparison. The main relations and parameters used in

simulation are shown. Section The energy efficiency of the

PEMFC system deals with the energy efficiency of the PEMFC

system. Themodel of the SIDOES control scheme is detailed in

Section The single-input dual-output ES (SIDOES) control

scheme. Themethodology to evaluate the FC energy efficiency

is highlighted in Section The methodology to evaluate the FC

energy efficiency. First, it is shown the availabilities in maxi-

mizing the FC net power by regulating air flow rate and fuel

flow rate, respectively. The comparative results on FC energy

efficiency are shown using the sFF control as reference. Sec-

ond, the improvement of the FC energy efficiency is shown if

one of the fueling rates is controlled by the ES control scheme

and other is still controlled by the sFF regulator. The

comparative improvements in the FC net power based on

control of both fueling rates are shown in Section The

improvement in the FC net power. The performances of the

SIDOES control schemes under different load are clearly

highlighted here. The comparative dynamic performances

during the MEP searching and tracking phases are highlighted

in Section The MEP searching and tracking process using the

load following control based on the fuel or air flow rate. Last

Section concludes the paper.

PEMFC system modeling and control

The PEMFC system is complex as a structure, having a

nonlinear model developed based on principles of electro-

chemistry, thermodynamics, and fluid andmass flow transfer

[18]. Themain subsystems of the PEMFC systemare the PEMFC

stack, air supply subsystem, hydrogen supply subsystem,

thermal management subsystem, and a power conditioner.

Fig. 3 e The FC parameters and the PeI characteristic for

FuelFr and AirFr of 40.69 lpm and 245.3 lpm.

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The PEMFC stack could be modeled by a nonlinear truth

model [41] or reduced order models obtained by linearization

[21]. Linearization of the PEMFC nonlinear model in an oper-

ating point is usually used to shown the stability of the control

loops designed. The ES control is intrinsic robust based on the

integrator block included [46,47]. Thus, the stability of the ES

control loop used to regulate the AirFr can be shown in the

samemanner as in Ref. [29] based on simplified PEMFCmodel.

Because this paper is mainly focused on the evaluation of

energy efficiency based on MEP tracking control, only a short

description of the PEMFC stack, compressormodel and fueling

regulators is provided here. Moreover, the accuracy of the

PEMFC stack model is not so important in this study because

the improvement of the FC net power will be shown through

comparison using two PEMFC stack (see Fig. 2): one reference

and one under test. Thus, the PEMFC model included in the

Matlab-Simulink� toolboxes will be used in all simulations

performed in this paper.

Since the compressor air flow in the cathode (AirFr) and

hydrogen flow in the anode (FuelFr) affect the power pro-

duced, these flow rates are chosen to be the input variables.

The FC current is amanageable variable to control these input

variables based on sFF control [21]:

FuelFr ¼ 60000$R$ð273þ qÞ$NC$iFC2F$

�101325$PfðH2Þ

�$�Uf ðH2Þ

�100

�$�xH2

�100

� (1)

AirFr ¼ 60000$R$ð273þ qÞ$NC$iFC

4F$�101325$Pf ðO2Þ

�$�UfðO2Þ

�100

�$�yO2

.100

� (2)

where:

R ¼ 8.3145 J/(mol K);

F ¼ 96,485 As/mol;

NC represents the number of cells in series (65);

q e operating temperature (65��C)UfðH2Þ, UfðO2Þ e nominal utilization of the hydrogen (99.56%)

and oxygen (59.3%);

PfðH2Þ, PfðO2Þ e pressure of the fuel (1.5 bar) and air (1 bar);

xH2 , yO2 e composition of fuel (99.95%) and oxidant (21%).

The values for the preset model of the 6 kWe45 V PEMFC

stack are mentioned above (in the brackets) and also in Fig. 3.

The air and fuel partial pressures follow the load profile

with delays in range from few seconds to several of hundreds

of seconds:

pH2¼

1=kH2

1þ tH2$s

�FuelFr$yH2

� 2Nc

4FUH2

IFC

�;

tH2¼ Vanode

R$ð273þ qÞ$kH2

(3)

pO2¼

1=kO2

1þ tO2$s

�AirFr$yO2

� Nc

4FUO2

IFC

�; tO2

¼ Vcathode

R$ð273þqÞ$kO2

(4)

where:

tH2 and tO2 are the hydrogen and oxygen time constants (s);

Vanode, Vcathode e volume of the anode and cathode (m3);

kH2 , kO2 e hydrogen and oxygen valve molar constants

[kmol (atm s)�1];

Because the thermodynamic time constant is of the order

ofminutes, this will be neglected in the simulation performed.

The time constant of the PEMFC stack is set to 2 s if it is not

mentioned otherwise.

The FC power characteristic at fueling conditions of

AirFr¼ 245.3 lpmand FuelFr¼ 40.69 lpm is shown in Fig. 3, too.

The FC net power is directly available:

Pnet ¼ VFC$Inet (5)

where Inet is the FC net current (the current that supply the

load via the power conditioner).

Also, the FC net power is easy to be measured in all FC

applications based on (6):

Pnet ¼ PFC � Paux (6)

The auxiliary power, Paux, is the part of FC power, PFC, that

cover the consumption of the auxiliaries such as air

compressor, water pump, radiators and fans used in a

particular PEMFC system, besides other electrical and elec-

tronics circuits used in control loops, security systems,

signaling operations etc. As it was mentioned above, the

auxiliary power is mainly given by the air compressor [7,43].

Thus, this assumption will be considered below, without

reducing the generality of the findings of this study.

The Pcm power consumed by the air compressor is

computed based on (7) [48]:

Pcm ¼ �a2$AirFr

2 þ a1$AirFþ a0

�$ðb1$IFC þ b0Þ$kcm (7)

where a0 ¼ 0.6, a1 ¼ 0.04, a2 ¼ �0.00003231, b0 ¼ 0.9987, and

b1 ¼ 46.02.

Fig. 4 e The net power surface for the 6 kW PEMFC stack

supplied by compressor 1.

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The parameter kcm changes the level of the Pcm power and

can model the nonlinearities of the compressor based on a

look-up table [43]. This parameter is set to 1 and 2 for

compressor 1 (CM1) and 2 (CM2) used in simulation.

The dynamic of both compressors is considered as a 2nd

order system [48]:

GdðcmÞ ¼ u2cm

s2 þ 2xcmucm$sþ u2cm

(8)

where tcm ¼ 2p/ucm and xcm will set the time constant and the

surge level of the compressor. Usually, this dynamic is

neglected in studies of the PEMFC system behavior [29]. So,

this will also be neglected here in order to highlight the effect

of the PEMFC time constant on the tracking accuracy.

Two different power levels will be used for the air

compressor in order to evaluate the dependence of the PEMFC

energy efficiency by the level of the power losses. The FC net

power and energy efficiency of the PEMFC system will be

computed for the both PEMFC systems based on same PEMFC

stack.

Fig. 5 e The net power surface for the 6 kW PEMFC stack

supplied by compressor 2.

The energy efficiency of the PEMFC system

The energy efficiency of the PEMFC system is one of main

goals related to control techniques analyzed in the literature,

besides the goal to keep optimal oxygen excess ratio trajectory

in order to avoid oxygen starvation [49] or to minimize the

hydrogen consumption [44]. It is known that the PEMFC en-

ergy efficiency is dependent to the dynamic load [50]. So, the

challenging task in designing the fueling controller could be

more difficult if the fueling rates are adaptively changed close

to safety values that depend to load profile [48,51]. This effect

of limiting the fueling rates will be presented here, as well.

The PEMFC energy efficiency is defined as percent of the FC

net power delivered to the load from the FC power available at

the FC terminals [9,43]:

hsys ¼ Pnet=PFC (9)

The overall electric efficiency of the PEMFC system (hel) is

defined in Ref. [43] taking into account the net electric power

used to react one mole of hydrogen and the fuel utilization

coefficient (hf):

hel ¼ hf $hFC$hsys (10)

where the FC stack efficiency (hFC) is the ratio between the

produced energy and the heat produced by burning the

hydrogen fuel.

The analysis performed in this paper will be focused on the

PEMFC system energy efficiency (hsys) that mainly depends on

the load level. An optimum value for the fueling rates must be

determined by the real-time controller (the fuel processor) for

each load level. The optimization problem can be defined if

the objective function is convex. It is know that the FC net

power related to the AirFr (or the oxygen excess ratio) is a

convex function, and a lot of papers use this approach in

solving the MEP tracking control problem [14,29,30].

In this paper, the convex surfaces of the FC net power

related to the AirFr and load level will be used to define the

MEP tracking control problem in next section. Figs. 4 and 5

show the load-level cuts of these surfaces that were drawn

considering the AirFr as linear variable during a load level set

by the FC current. These load-level cuts are shown in Fig. 6 for

both compressors.

The static MEP could be estimated based on static charac-

teristic shown in figures above, but the tracking of dynamic

MEP is a difficult task that could be solved using real-time

optimization algorithms. Different multi-dimensional maps,

which are functions of current density, AirFr, cathode pres-

sure, anode pressure, and cathode inlet humidity, are used in

nonlinear control loops of the PEMFC system. In this paper a

real-time optimization algorithm based on perturbed ES con-

trol scheme is proposed based on 2-D nonlinear map of the FC

net power.

The single-input dual-output ES (SIDOES) controlscheme

Because the FC current, IFC, defines a FuelFr value based on

appropriate controller, it is obvious that the FC net power can

be also represented by a nonlinear convex map, Pnet ¼ J(AirFr,

FuelFr). Also, the dynamics of the FC stack can be represented

by a smooth function, f, based on statesmodel,where the state

vector, x, can be, for example, of a 9th [21] or 6th [15] order.

Thus, in brief, the ES control problem can be mathemati-

cally defined as:

Fig. 6 e The net power characteristics of the 6 kW PEMFC

stack under different load power levels (the air supplied by

the compressor 1 and 2).

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Maximize:

Pnet ¼ Jðx; i1; i2; IFCÞ (11)

Subject to:

_x ¼ fðx; i1; i2; IFCÞ; x˛X (12)

where i1 ¼ AirFr and i2 ¼ FuelFr are the control inputs, and IFCis the disturbance input.

So, considering Pnet ¼ J(i1, i2), the net power in an operating

point (i10, i20) can be approximated by the Taylor series:

Pnet ¼ Jði1; i2Þ ¼XNp2¼0

XNp1¼0

ði1 � i10Þp1 ði2 � i20Þp2p1!p2!

$vp1þp2 J

vxp11 vxp2

2

ði10; i20Þ (13)

The gradients, G1 and G2, can be estimated by:

Gp ¼ vJvip

ði10; i20Þ ¼ dJdt

dipdt

; p ¼ 1; 2 (14)

The dithers used in SIDOES control scheme to extract the

gradients can have different frequency or the same frequency,

but complementary phases in the last case. It is known that

the gradients are frequency dependent [45], so the last variant

has the advantage of obtaining a search speed in both di-

rections that is not dependent by the dither frequency.

Consequently, the orthogonal signals sd1 ¼ sin(udt) and

sd2 ¼ cos(udt) will be used (see Fig. 7).

The gradients will be estimated below considering the

following assumptions:

- three components of the Taylor series will be used;

- the band pass filter (BPF) is ideal, having the cut-off fre-

quencies of ul ¼ alud, 3 < al < 4, and uh ¼ ahud, 0 < ah < 1;

- kN ¼ 1 (in simulation kN ¼ 1/VFC).

Consequently, ipBPF signals (p ¼ 1, 2) at BPF outputs will be:

ipBPFðtÞyD1$ipLFðtÞ þ 12D2$i

2pLFðtÞ þ

16D3$i

3pLFðtÞ (15)

where

D1 ¼ vJvi1

ði10; i20Þþ vjvi2

ði10; i20Þ

D2 ¼ vJ2

vi21ði10; i20Þþ2

vJ2

vi1vi2ði10; i20ÞþvJ2

vi22ði10; i20Þ

D3 ¼ vJ3

vi31ði10; i20Þþ3

vJ3

vi21vi2ði10; i20Þþ3

vJ3

vi1vi22ði10; i20ÞþvJ3

vi32ði10; i20Þ

(16)

The low frequency (LF) harmonics of the iLF signal, which

assures the dither persistence in the ES control loop, will be

given by (17):

i1LFðtÞ ¼X3

p¼1

a1p sin�judtþ 41p

�; i2LFðtÞ ¼

X3

p¼1

b1p sin�judtþ j1p

�

(17)

These ipBPF signals are thenmodulated with the orthogonal

dithers, obtaining the ipDM signals:

ipDMðtÞ ¼ ipBPFðtÞ$sin½udtþ ðp� 1Þp=2�; p ¼ 1;2 (18)

The ipDM signals can be rewritten as:

ipDMðtÞyksgp þ ipDMðLFÞðtÞ; p ¼ 1;2 (19)

where:

ksg1 ¼ 12D1a1RSS1 cos 41

ksg2 ¼ 12D1b1RSS2 sin j1

RSS1y1þ 18D3

D1

�a21 þ 2a2

2 þ 2a23

�

RSS2y1þ 18D3

D1

�b21 þ 2b2

2 þ 2b23

�

(20)

The ipDM signals contain the required gradient, besides the

LF components that assures the dither persistence [52]. Finally

an integral controller with gain k1 drives this estimated

gradient to zero during the searching phase.

Thus, the signals injected in the ES control loops (the

probing signals) will be:

ipðtÞyk1ksgp$tþ k2H1p sin½udtþ ðp� 1Þp=2� þ ipLFðtÞ; p ¼ 1; 2

(21)

where H1p is the magnitude of the fundamental harmonic of

the ipBPF signal, p ¼ 1, 2.

Of course, the magnitude of LF components of the probing

signals is time-dependent [52].

If the ES control loop gain, k1, is set proportional to the

dither frequency in order to improve the dither persistence

[45,52],

k1 ¼ kd$ud (22)

then the gradients can be estimated by

KSSðpÞ ¼ ksgðpÞ$kd$ud; p ¼ 1; 2 (23)

In conclusion, the time-evolution of the G1 gradient can be

obtained based on equations of the ES control scheme 1:

Pnet ¼ Jðx; i1; i2; IFCÞ; inet ¼ pnet

�VFC (24)

ihpf�

¼ �uhihpf þuhiN; if ¼ inet � ihpf ; iBPF�

¼ �uliBPF þulif ; (25)

Fig. 7 e The SIDOES control scheme.

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iDM ¼ iBPF$sinðudtÞ (26)

iint�

¼ iDM (27)

iloop ¼ k1iint (28)

dg ¼ k2H1 sinðudtÞ; dm ¼ Am sinðudtÞ (29)

i1 ¼ iloop þ dg þ dm (30)

where equations (24)e(30) represent the FC net power char-

acteristics, the band pass filter, the modulator, the integrator,

the gained gradient, the dithers, and the current reference.

The HPF state is denoted by ihpf and other notations for the

signals used in above equations are highlighted on Fig. 7. Be-

sides the signals, the following notations have been used:

k1 is the ES loop gain;

k2 e the dither gain;

H1 e the magnitude of first harmonic of the FC net current;

* e the convolution operator.

TheG2 gradient can be estimated based on equations of the

ES control scheme 1 written in the same manner as above.

It was shown that the estimated gradients follow the gra-

dients obtained by simulation [45]. The Rss value is the

improvement in the search speed of the proposed SIDOES

control scheme in comparison with classical perturbed-based

ES control scheme [45]. Besides high search speed, the pro-

posed SIDOES control scheme has up to 99.99 tracking accu-

racy during stationary phase based on variable amplitude of

the dither, which is modulated with the H1 magnitude [52].

The H1 magnitude is self-adaptive during the searching, sta-

tionary, and tracking phases (see Refs. [45,52] and the results

shown in Section The MEP searching and tracking process).

In the classical perturbed-based ESC scheme, the ampli-

tude of the dither signal is kept constant [53] or decays

exponentially [54]. It is necessary to have high amplitude for

the dither during the searching and tracking phases to obtain

a high search speed to find the MEP. It is obvious that the H1

magnitude is high during these phases. So, the dither ampli-

tude must to be limited via the saturation block (AM) to a safe

value of search speed (up to 50 A/s [48]), besides the rate

limiter included in the fuel regulators.

On the other hand, the H1 magnitude decreases to zero

during the stationary phase, thus the minimum dither, dm,

assures the fine tracking of the MEP. It is known that sta-

tionary accuracy is dependent by the dither parameters dur-

ing this phase [55], so the dm amplitude, Am, is set to 0.001 to

reduce the power ripple andud to 2p$10 rad/sec to increase the

stationary accuracy and maintain a sufficient high dynamic

accuracy during the transitory phases. If a lower or higher

value will be set, then the searching process will interfere less

or more with the PEMFC dynamics (see the results section). It

is known that the stationary accuracy can be made arbitrarily

Fig. 8 e The diagram to compute the FC net power under

sFF control.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 410648

small by decreasing the Am amplitude, and the search speed

can bemade arbitrarily fast by increasing the dither frequency

[55].

Based on above discussion, if it is not otherwise stated, the

simulation parameters (for both ES control schemes) are the

following: ud ¼ 2p$10, uh ¼ 0.1ud, ul ¼ 5.5ud, k1 ¼ ud, k2 ¼ 2,

AM ¼ 2, Am ¼ 0.001.

The methodology to evaluate the FC energyefficiency

First, the FC net power under sFF control is evaluated,

mentioned by equations (1) and (2).

The stationary value of FC net power is computed for the

FuelFrsFF and AirFrsFF set by the Fuel and Air flow rate’s reg-

ulators considering the FC current as common input (see

Fig. 8). If the switch is on AirFr position that is linear variable,

then the FC net power characteristics (which are shown in

Fig. 6) where drawn based on same simulation diagram.

The values of FC net power obtained for both compressors,

Pnet1 and Pnet2, are listed on column 4 and 6 of Table 1. The

values of the energy efficiency for the PEMFC systems based

on same the PEMFC stack are listed in column 9 and 10 of

Table 1.

Second, the FC net power under sFF control for the FuelFr is

evaluated (the values mentioned on column 2 of Table 1) and

ES control for the AirFr based on simulation diagram shown in

Table 1 e The FC net power under sFF control for airFR and Fu

IFC [A] FuelFrsFF [lpm] AirFrsFF [lpm] Pnet1 [W] Pcm1 [W

115 43.19 258.8 4730 636.2

120 45 270.1 4870 675

125 46.94 281.3 5004 714.7

130 48.82 300.7 5134 754.7

135 50.7 303.8 5259 795.1

140 52.58 315.1 5380 825.9

145 54.45 326.3 5498 877

Fig. 9. The results obtained are mentioned for both compres-

sors in Tables 2 and 3.

The values of the energy efficiency for the PEMFC systems

based on same the PEMFC stack are listed on column 7 of

Tables 2 and 3.

Third, the FC net power under sFF control for the AirFr is

evaluated (the values mentioned on the column 3 of Table 1)

and ES control for the FuelFr. Note that the simulation dia-

gram is similar with that shown in Fig. 9, excepting the fact

that the inputs for the fueling regulators were switched be-

tween them. The results obtained are mentioned for both

compressors in Tables 4 and 5.

The values of the energy efficiency for the PEMFC systems

based on same the PEMFC stack are listed on column 7 of

Tables 4 and 5.

An improvement in energy efficiency for PEMFC systems

can be noted in the last two cases in comparison with the first

case (the sFF control), but it is difficult to compare the obtained

results between them. This is because different values of the

FC current are obtained based on ES control in comparison

with the sFF control. Thus, if both AirFr and FuelFr inputs are

controlled, then amethod to evaluate the improvement in the

FC net power must be considered by comparison, as was

suggested in Introduction section based on Fig. 2.

The improvement in the FC net power

To compute the improvement in net power during the MEP

search process by both input variables two case are

considered.

First, is the case shown in Fig. 10, where the FuelFr is ES

controlled and the optimum AirFr is searched based on FC

current, which is ES controlled, too.

The two FC systems used are equally supplied with air and

hydrogen via the corresponding regulators. The AirFr regu-

lator is controlled by the current of the FC system that oper-

ates as reference under a given load. The load profile can be

set by the load sequence to be constant, linear variable, or to

follows a given load profile (see Fig. 2).

For the 6 kW FC stack supplied by compressor 1, the

improvement in the FC net power,DPnet(1fa)¼ Pnet(1fa)� Pnet(2fa),

is computed on column 2 of Table 6 and shown in Fig. 11. The

trend line shows that the improvement in the net power in-

creases with a rate of 1.3 W/A. Also, the improvement in the

FC net power, DPnet(2fa), for the 6 kW FC stack supplied by

compressor 2 is computed in column 3 of Table 6. In this case,

the improvement in the FC net power increases with a much

higher rate, which is of about 5.3 W/A. This means that the

elFr of the 6 kW FC stack supplied by CM1 and CM2.

] Pnet2 [W] Pcm2 [W] PFC [W] hsys1 [%] hsys2 [%]

4094 1272 5366 88.1 76.3

4194 1350 5545 87.8 75.6

4289 1429 5719 87.5 75.0

4379 1509 5889 87.2 74.4

4463 1590 6054 86.9 73.7

4544 1672 6216 86.6 73.1

4619 1754 6373 86.3 72.5

Fig. 9 e The diagram to compute the FC net power under

sFF control for the FuelFr and ES control for the AirFr.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 4 10649

PEMFC system must to be mandatory operated close to the

MEP if the power losses are high or the system operates at full

load, otherwise the energy efficiency decreases dramatically.

On the other hand, for the FC stack 6 kW FC stack supplied

by compressor 1 and 2, it can be noted that the relative

improvement in the FC net power, DPnet(2fa)/DPnet(1fa), has

values in range 1.5e1.8. This also means that the PEMFC

Table 3 e The FC net power under aES control for AirFr of the

FuelFrsFF [lpm] IFC2a [A] AirFrM2a [lpm] Pn

43.19 113.1 254.6

45 117.8 266.2

46.94 122.8 276.5

48.82 127.7 287.4

50.7 132.6 298.3

52.58 137.4 309.3

54.45 142.2 320.1

Table 2 e The FC net power under aES control for AirFr of the

FuelFrsFF [lpm] IFC1a [A] AirFrM1a [lpm] Pn

43.19 113.1 254.6

45 117.8 266.2

46.94 122.8 276.5

48.82 127.7 287.4

50.7 132.6 298.3

52.58 137.4 309.3

54.45 142.2 320.1

systemmust to be mandatory operated close to the MEP if the

power losses are high, otherwise the energy efficiency de-

creases dramatically.

Second, is the case shown in Fig. 2, where the AirFr is ES

controlled and the optimum FuelFr is searched based on FC

current, which is ES controlled, too. For the 6 kW FC stack

supplied by compressor 1 and 2, the improvements in the FC

net power, DPnet(paf) ¼ Pnet(paf) � Pnet(paf), p ¼ 1, 2, are shown on

column 4 and 5 of Table 6. The improvement in the FC net

power increases in these cases with a rate of 1.6 W/A, and

1.73 W/A (see Fig. 11). This means that in this case the im-

provements in FC net power are less sensitive to power losses

and load level. Also, the relative improvement in the FC net

power, DPnet(2af)/DPnet(1af), has a value of about 1.09, which is

lower than a value in range 1.5e1.8 (obtained based on

simulation diagram 10). This also sustains that the improve-

ment in the FC net power is less sensitive to power losses if the

optimum AirFr is set by the ES controller.

In this last case (the simulation diagram 2) it is obvious that

small changes in the FuelFr affect in less measure the opti-

mum in FC net power obtained by controlling the AirFr. Thus,

is better to control the compressor power to maximize the FC

net power and set the FuelFr by an appropriate controller,

without losing much FC net power if the FuelFr is not close to

the optimal value.

Furthermore, the comparative improvements in the FC net

power, DPnet(1fa)/DPnet(1af) and DPnet(2fa)/DPnet(2af), are 3e4 times

lower for the simulation diagram 2 in comparison with the

simulation diagram 10. This means that the MEP is more sen-

sitive to FuelFr changes than the changes in AirFr. So, under

dynamic load, it is recommended a load following control of the

FuelFr [56] and an optimal control of the AirFr based on appro-

priate strategy that can maximize the energy efficiency [43].

The I1 and I2 currents and Pnet1 power are saved as vectors

(Iref1, Iref2, and Pnet) to show the MEP searching and tracking

process.

6 kW FC stack supplied by CM2.

et2a [W] Pcm2a [W] PFC2a [W] hsys2a [%]

4245 1243 5487 77.4

4353 1314 5666 76.8

4463 1392 5855 76.2

4564 1470 6034 75.6

4661 1548 6208 75.1

4753 1626 6379 74.5

4840 1706 6546 73.9

6 kW FC stack supplied by CM1.

et1a [W] Pcm1a [W] PFC1a [W] hsys1a [%]

4866 621 5487 88.7

5009 657 5666 88.4

5158 697 5855 88.1

5298 735 6034 87.8

5434 774 6208 87.5

5566 813 6379 87.3

5693 853 6546 87.0

Table 4 e The FC net power under aES control for FuelFr of the 6 kW FC stack supplied by CM1.

AirFrMsFF [lpm] IFC1f [A] FuelFr1f [lpm] Pnet1f [W] Pcm1f [W] PFC1f [W] hsys1f [%]

258.8 128.3 48.18 5214 192 5406 96.4

270.1 132.4 49.74 5376 201 5577 96.4

281.3 136.4 51.25 5533 210 5743 96.3

300.7 143.2 53.79 5797 225 6022 96.3

303.8 144.3 54.19 5838 228 6066 96.2

315.1 148.1 55.62 5986 237 6223 96.2

326.3 151.8 57.01 6129 247 6376 96.1

Table 5 e The FC net power under aES control for FuelFr of the 6 kW FC stack supplied by CM2.

AirFrMsFF [lpm] IFC2f [A] FuelFr2f [lpm] Pnet2f [W] Pcm2f [W] PFC2f [W] hsys2f [%]

258.8 128.3 48.18 5022 384 5406 92.9

270.1 132.4 49.74 5175 402 5577 92.8

281.3 136.4 51.25 5323 420 5743 92.7

300.7 143.2 53.79 5572 450 6022 92.5

303.8 144.3 54.19 5610 456 6066 92.5

315.1 148.1 55.62 5749 474 6223 92.4

326.3 151.8 57.01 5882 494 6376 92.3

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 410650

The MEP searching and tracking process

As it was mentioned, the MEP searching is dependent by the

dither frequency. The time constant of the PEMFC stack was

set to 2 s, and three values of the dither frequency are used in

simulation shown in Figs. 12e14: 1, 10, and 100 Hz.

The MEP searching in 3D and 2D space is shown in Figs. 12

and 13 based on simulation diagram shown in Fig. 10. It can be

observed that different searching dynamics are obtained

(Fig. 12). The gradients could be estimated based on equation

Fig. 10 e The diagram to evaluate the improvement in the FC ne

of the optimum AirFr based on FC current.

(23). If the same parameters are used for both ES control

schemes, then the search speeds will be almost equal based

on equation (20) (see Fig. 13).

Even if different values are obtained for the AirFr and FC

current, the differences in the stationary accuracy are less to

0.1% (see plots a2, b2, and c2 on bottom of Fig. 14 for dither

frequency of 1, 10, and 100 Hz). The results are obtained based

on simulation diagram 10 for an FC current of 145 A. It is

known that the accuracy depends by the dither frequency

with a factor of O(ud2) [17]. Thus, the dither frequency can be

chosen to obtain the transitory time of same order with the

t power considering the ES control for FuelFr and ES search

Table 6 e The improvements in the FC net power usingsimulation diagram from Fig. 10 (DPnet(1fa) and DPnet(2fa))and Fig. 2 (DPnet(1af) and DPnet(2af)) for both compressors(CM1 and CM2).

IFC[A]

DPnet(1fa)[W]

DPnet(2fa)[W]

DPnet(1af)[W]

DPnet(2af)[W]

115 333 516 111 121

120 337 539 118 129

125 342 563 126 137

130 348 589 134 146

135 355 616 142 155

140 363 645 150 164

145 373 675 159 173

Fig. 12 e The 3D searching of FC net power for different

dither frequencies.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 4 10651

PEMFC time constant in order to have the best compromise

between the accuracy and search speed. This conclusion is

also valid for the results obtained based on simulation dia-

gram 2, where the FuelFr is regulated by the ES control scheme

(see plots a1, b1, and c1 on top of Fig. 14).

It can be observed that the H1 magnitude of the FC net

current is high during the search phase and decreases to zero

during the stationary phase. The role of the H1 magnitude

under dynamic load will be shown based on simulation dia-

gram represented in Fig. 10. The dither frequency is set to

50 Hz here to have the best compromise between the accuracy

and search speed. The tracking of the dynamic load is shown

in Figs. 15 and 16, without and with the use of the current rate

limiter, respectively.

The H1 magnitude has high values during the searching

phase in both cases (see plot 2 on Figs. 15 and 16). Thus, the

amplitude of the gained dither must to be limited via a satu-

ration block in order to avoid unsafe gradients. In the first case

(with high search speed), the load profile can be tracked by the

FC net, but the oxygen starvation could appear during sharp

changes in load (see plot 3 on Fig. 15). So, an adaptive rate

limiter for the FC current must to be used [17], even if the

Fig. 11 e The improvement in the FC net power.

dynamic accuracy is reduced by the fueling rates that have a

controlled or limited slope (see plot 4 and 5 on Fig. 16).

Conclusion

In this paper it is performed a systematic approach of the

possibilities to increase the energy efficiency of the PEMFC

system under dynamic load. The dynamic MEP is tracked

using an ES control scheme. The FC net power values are

compared with those obtained using a sFF control scheme. A

mixed control scheme is then used to evaluate the improve-

ment in FC net power if the AirFr or FuelFr variable is used as

controlled input of the PEMFC system in the load following

loop. The improvements in FC net power are different, being

higher if the FuelFr is used as controlled input of the PEMFC

system in the load following loop. This means a lot of

hydrogen economy in standalone or vehicle applications.

Further, if the AirFr is also controlled via an ES controller, then

the MEP could be better tracked dynamically. The stationary

accuracy is about 99.9% for a large range of the dither fre-

quency, but the dynamic accuracy is more dependent on the

chosen value for the dither frequency. Thus, this must to be

set in relation with the principal time constant of the process

controlled. To have the best compromise between the

Fig. 13 e The 2D searching of FC net power for different

dither frequencies.

Fig. 14 e The searching of FC net power for different dither frequencies.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 410652

accuracy and search speed, the dither period can be chosen of

about 100 times the principal time constant. In addition, to

avoid the oxygen starvation, an adaptive rate limiter of the

fueling rates to the FC current must to be used under dynamic

load.

In conclusion, the following remarks could be formulated:

1) the energy efficiencies are different for two proposed stra-

tegies of load following control based on the AirFr or FuelFr

variable; 2) the strategy of load following control based on

FuelFr seems to be more efficient, but this issues must be

Fig. 15 e The MEP searching without the use of the rate

limiter for the FC current.

comparatively analyzed based on hybrid power source topol-

ogies with those strategies implemented; 3) the parameters

designed for an appropriate MEP tracking controller must to

assure a limited search speed up to safe value to avoid oxygen

starvation; 4) the tracking controller design should focus

equally on tracking accuracy during transient and stationary

regimes of the PEMFC system under dynamic load.

Besides the higher tracking accuracy obtained, the SIDOES

control scheme proposed here to control the fueling rates

Fig. 16 e The MEP searching with the use of the rate limiter

for the FC current.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 9 ( 2 0 1 4 ) 1 0 6 4 1e1 0 6 5 4 10653

presents other several advantages in comparison with re-

ported results in the literature: (1) it is faster, (2) it is robust,

and (3) the energy efficiency increases in all cases with a

percent that depend by the nominal power of the compressor.

Apart from these observations and advantages presented

by controlling both fueling rates via an SIDOES control

scheme, a number of issues arise to be further analyzed from

the point of view of the costs of these solutions: 1) the

advanced control solution proposed here must be compared

with the costless solutions that use one or both AirFr and

FuelFr variables with a fixed opening valve with imposed

characteristic pressure-flow; 2) the load following control e

FuelFr based must be compared with the load following con-

trol e AirFr based; 3) the adaptive rate limiter of the fueling

rates to the FC current must be compared with the costless

solutions that use a fixed rate limiter up to a safe value to

avoid oxygen starvation.

A global analysis that will consider the energy efficiency

and implementation costs may be considered to sustain these

advanced implementations suggested here or other from the

literature.

Acknowledgment

The research leading to these results has received funding

from the Romanian e EEA Research Programme operated by

the MEN e PO/UEFISCDI-IA under the Project EEA-JRP-RO-NO-

2013-1-0034 and PN-II-CT-RO-FR-2014-2-0019.

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