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Modeling and operation optimization of a proton exchange membrane

fuel cell system for maximum efficiency

In-Su Han a, Sang-Kyun Park b,⇑, Chang-Bock Chung c

a R&D Center, GS Caltex Corp., 359 Expo-ro, Yusung-gu, Daejeon 341222, Republic of Koreab Division of Marine Information Technology, Korea Maritime and Ocean University, Busan 49112, Republic of Koreac School of Applied Chemical Engineering, Chonnam National University, Gwangju 61186, Republic of Korea

a r t i c l e i n f o

Article history:

Received 26 November 2015

Accepted 17 January 2016

Keywords:

Proton exchange membrane fuel cell

Modeling

Simulation

Operation optimization

Artificial neural network

a b s t r a c t

This paper presents an operation optimization method and demonstrates its application to a proton

exchange membrane fuel cell system. A constrained optimization problem was formulated to maximize

the efficiency of a fuel cell system by incorporating practical models derived from actual operations of the

system. Empirical and semi-empirical models for most of the system components were developed based

on artificial neural networks and semi-empirical equations. Prior to system optimizations, the developed

models were validated by comparing simulation results with the measured ones. Moreover, sensitivity

analyses were performed to elucidate the effects of major operating variables on the system efficiency

under practical operating constraints. Then, the optimal operating conditions were sought at various sys-

tem power loads. The optimization results revealed that the efficiency gaps between the worst and best

operation conditions of the system could reach 1.2–5.5% depending on the power output range. To verify

the optimization results, the optimal operating conditions were applied to the fuel cell system, and the

measured results were compared with the expected optimal values. The discrepancies between the mea-

sured and expected values were found to be trivial, indicating that the proposed operation optimization

method was quite successful for a substantial increase in the efficiency of the fuel cell system.

2016 Elsevier Ltd. All rights reserved.

1. Introduction

Fuel cells have been actively studied for the last several decades

because they have been regarded as the most promising alterna-

tives to conventional power generation systems such as internal

combustion engines and gas turbines [1,2]. Several types of fuel

cells, including solid oxide fuel cells (SOFCs), phosphoric acid fuel

cells (PAFCs), molten carbonate fuel cells (MCFCs), direct methanol

fuel cells (DMFCs), alkaline fuel cells (AFCs), and proton exchange

membrane (PEM) fuel cells, have been commercialized for various

applications [3]. Their working principles, advantages and disad-

vantages have been well explained in various references including

a textbook [4]. Among these, PEM fuel cells are suitable for both

stationary and transportation applications such as residential

power generators, cars, buses, forklifts, bicycles, and watercraft

because they offer many advantages, including high efficiencies,

high power densities, short startup times, and low emissions of

pollutants [5].

As fuel cell systems have spread, the need for their operational

optimization to heighten performance or reduce operating costs

has gained increased attention. To maximize the efficiency of a fuel

cell system, and thereby minimize its operating cost, it is essential

that it operates near its optimal operating conditions. This can be

usually achieved by performing operation optimization techniques

based on mathematical models [6]. However, the model-based

optimization of a fuel cell system is a challenging task because

accurate models for all its components must be available in order

to find real optimal operating conditions that will deliver a sub-

stantial improvement in performance. A number of papers dealing

with the operation optimizations of fuel cells have been published

in the open literature. However, most have focused on the opti-

mization of single components [7–12] or sub-systems [13–15]

rather than complete systems [16–22].

A considerable number of papers on the operation optimization

of single fuel cells or sub-systems have been published. Mawardi

et al. [7] proposed a model-based optimization to maximize the

power density of a single PEM fuel cell. Meidanshahi and Karimi

[8] performed an optimization study using a one-dimensional

dynamic model for a singlePEMfuel cell. Zhanget al.[9] determined

the optimal operating temperature of a high-temperature PEM fuel

http://dx.doi.org/10.1016/j.enconman.2016.01.045

0196-8904/ 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +82 514104579; fax: +82 514043985.

E-mail addresses: [email protected] (I.-S. Han), [email protected]

(S.-K. Park), [email protected] (C.-B. Chung).

Energy Conversion and Management 113 (2016) 52–65

Contents lists available at ScienceDirect

Energy Conversion and Management

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n c o n m a n

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cell by considering its performance, CO tolerance, and durability.

Kanani et al. [10] used a response surface method to maximize the

power output of a single PEM fuel cell. Ni et al. [11] carried out aparametric study using an electrochemical model to elucidate the

effects of operating variables on the performance of a single SOFC.

Tafaoli-Masoule et al. [12] employed a genetic algorithmand a quasi

two-dimensional, isothermal model to determine the optimal oper-

ating temperature and pressure of a single DMFC. Subramanyan

et al. [13] performed a multi-objective optimization for a hypothet-

ical SOFC–PEM hybrid sub-system both to minimize the CO2 emis-

sion and to maximize the performance. Caliandro et al. [14]

presented a multi-objective optimization for a SOFC–GT (gas tur-

bine) hybrid sub-system both to maximize the efficiency and to

minimize the capital costs. Ranjbar et al. [15] analyzed the effects

of operating variables on the energy and exergy efficiencies of a

hybrid SOFC sub-system, using a zero-dimensional mathematical

model.Several papers on system-level operation optimizations of PEM

fuel cells have appeared in the open literature. Godat and Marechal

[16] performed a simulation study to find the optimal process

structure and operating conditions for a stationary fuel cell system

consisting of a PEM fuel cell stack and fuel processing units. They

analyzed the sensitivity of the major decision parameters (the

steam-to-carbon ratio, reforming and cell temperatures, and fuel

utilization) on the overall efficiency of the fuel cell system. Bao

et al. [17] carried out an optimization study for a hypothetical

PEM fuel cell system, using a hybrid model that combined a

neural-network model with a first-principles model, to find the

optimal operating conditions that maximized net power genera-

tion. The optimal values of two operating variables (the air stoi-

chiometry and cathode outlet pressure) were sought using agenetic algorithm under three different configurations of the

air-supply system. Wu et al. [18] presented an optimization

approach to find the optimal operating conditions for a 25-cm2 sin-

gle PEM fuel cell coupled with a hypothetical compressor and ahumidifier. They employed a meta-modeling approach in which

the input-output relations were approximated with radial basis

functions (RBFs) using the data obtained from a simulator, to

reduce the computational burden in locating an optimal solution.

Four decision variables—the cell temperature, cathode stoichiome-

try, cathode gas pressure, and cathode relative humidity—were

sought under ideal and realistic system assumptions after accom-

plishing a model validation for the fuel cell. Hasikos et al. [19]

adopted a dynamic first-principles model, which was originally

proposed by Pukrushpan et al. [23], as a hypothetical PEM fuel cell

system composed of a stack and auxiliary units to generate opera-

tional data for optimizations. A meta-modeling approach was

employed to build the optimization models from the operational

data using an RBF neural network. They formulated an optimiza-tion problem to minimize the stack current at a given power

demand, and then the optimal operating conditions were used as

set-points for the dynamic matrix controls (DMCs) of the hypothet-

ical system. Wishart et al. [20] performed a system-level optimiza-

tion for an experimental system comprising a Ballard Mark IV fuel

cell stack, a compressor, and pumps. They demonstrated two dif-

ferent optimization cases to find the optimal operating conditions

for vehicular and stationary applications. Mert et al. [21] presented

an optimization of a PEM fuel cell system for vehicular applica-

tions. They carried out a multi-objective optimization of the vehic-

ular fuel cell system both to maximize the power output, energy,

and exergy efficiencies and to minimize the cost of the produced

work. A simple electrochemical model for a Ballard Xcellsis TM HY-

80 fuel cell engine was employed for the optimization. Fran-gopoulos and Nakos [22] performed optimization simulations for

Nomenclature

b bias vector in an artificial neural network modelC pw heat capacity of the cooling water (4.186 kJ kg

1 K1).F flow rate (SLPM)F stoicH2 stoichiometric flow rate of hydrogen entering the stack

(SLPM)

F purge purge gas flow rate from the stack (SLPM) f transfer function of an artificial neural network modeleF Faraday constant (96,485 C mol1) g transfer function of an artificial neural network modelI current (A) J objective function (%)MWa molecular weight of air (28.97 kg kg-mol

1)N s number of cells in the stackP pressure (gauge pressure in kPa)P a discharge pressure of the air from the air blower (gauge

pressure in kPa)P e ambient pressure (gauge pressure in kPa)R universal gas constant (8.314 J mol1 K1)

RMSE root mean squared error defined by

ffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiPni¼1 ^ yi yið Þ

2=n

q where n is the number of measurements, yi the mea-sured variable, and ^ yi the predicted variable

R2 coefficient of determinationT temperature (C)V cell average cell voltage of the stack (V)W power (kW)W demand power demand of the electricity users (kW)

Greek lettersca mean adiabatic exponent of air (1.402)DT temperature difference (C)

DT g–wa temperature difference between the exhaust gas andthe humidified air (C)

g efficiency (%)gfuel fuel utilization efficiency of the stack (%)h vector of the decision variablesqw density of the cooling water (0.981 kg L 1)x weight matrix in an artificial neural network model

SubscriptsA air blowera airB pump and other balance of plantsc cooling waterg exhaust gas exiting the cathode of the stackP power converterS stackT fuel cell systemwa humidified (wet) air to the stack

SuperscriptsHL hidden layer of an artificial neural network modelin power inputlb lower boundmax maximummin minimum powerOL output layer of an artificial neural network modelout power outputub upper bound

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a PEM fuel cell system designed for a marine application. They

used a simplified semi-empirical model to investigate the effects

of the operating temperature and current density on the perfor-

mance and capital cost of the fuel cell system.

However, most of the papers mentioned above considered

hypothetical systems [16,17,19,22] based on simulation models

rather than actual fuel cell systems, and omitted validation steps

[16,17,19–22] for the modeling and optimization. In this work,

an operation optimization method is proposed and applied to an

actual PEM fuel cell system. For the practical application of the

operation optimization method to an actual fuel cell system, this

paper deals with all the necessary steps for the optimization,

including model development based on empirical and semi-

empirical modeling for most of the fuel cell components, the for-

mulation of an optimization problem, and the verification of the

models and optimization results.

2. System description

Fig. 1 shows the PEM fuel cell system for which the operating

conditions are optimized in this study. This system was originally

designed as a stationary power supplier for various electricityusers. As shown in Fig. 1, the fuel cell system consists of two cab-

inets containing the main module and the power converter. The

main module contains most of the fuel cell components, including

the stack, humidifier, air blower, pump, heat exchanger, control

and cell voltage monitoring (CVM) boards, and other balance of

plants (BOPs). The power converter, which elevates the voltage of

the direct current (DC) power to a desired level, is configured in

a separate cabinet.

Fig. 2 illustrates a schematic process diagram of the PEM fuel

cell system. Pure hydrogen is supplied as a fuel to the stack from

high-pressure hydrogen storage, and air is supplied as an oxidant

from an air blower to the stack. The air blower has a single-stage

centrifugal configuration, and its pressure ratio can reach as high

as 1.42 at a flow rate of 2000 SLPM (standard liter per minute).The supplied air is humidified using a membrane-type gas-to-gas

humidifier attached to the cathode side of the stack. In the humid-

ifier, both the humidity and temperature of the dry air from the air

blower are elevated by absorbing both moisture and heat from the

damp, hot exhaust gas exiting the cathode outlet of the stack. A

stack comprising 146 cells was fabricated for the fuel cell system;

it is capable of generating as much as25.5 kW electric power. The

stack has a unique design on the anode side; the cells are divided

into four stages (or blocks) by inserting barriers between the cells,

to maximize the fuel utilization efficiency without a hydrogen

recirculation pump. The hydrogen travels the four stages in a

cascaded manner, whereas the air passes through the undivided

cathode side, as in a conventional PEM fuel cell stack. Han et al.

[24] proposed this stack design and demonstrated a fuel utilization

efficiency as high as 99.6%. The pressure of the hydrogen entering

the stack is regulated at a specified value using a pressure regula-

tor. Since the anode side of the stack operates in dead-end mode, a

purge valve at the anode outlet must be periodically and briefly

opened to prevent the cell voltage from dropping below a certain

limit. Cooling water is used to remove the heat generated from

the stack using the heat exchanger through which the heat is trans-

ferred from the cooling water to the chilling water supplied from a

utility facility. The cooling water temperature at the stack inlet is

controlled by adjusting the flow rate of the chilling water, and that

at the stack outlet is regulated by adjusting the circulation rate of

the cooling water through the stack. The power converter increases

the voltage of the power generated fromthe stack to a desired level

before being supplied to various electricity users. An electronic

load (Model PLW36K-400-1200, manufactured by AMREL Power)

simulates the power consumption of the electricity users. A small

amount of the power from the stack is supplied via the BOP power

inverter, which lowers the voltage of the stack to around 24 V, for

the operation of the BOPs, including the water pump, sensors, and

control boards. The air flow rate is measured using a mass flow

meter (MFM), and the purge gas flow rate is measured using an

MFM (Model M-20SLPM, manufactured by Alicat Scientific) tem-

porarily installed at the anode outlet of the stack. This flow meter

automatically integrates the purge-gas flow rate for a certain per-

iod of time. The flow rate of the cooling water is measured using a

rotary flow meter. In Fig. 2, T and P indicate temperature and pres-

sure measurements, respectively.

3. Formulation of the optimization problem

The fuel cell system was designed to deliver electric power to

various users with variable demands. The objective of the opti-

mization is to maximize the efficiency of the fuel cell system at a

given power demand. Therefore, the objective function of the opti-

mization problem can be described as follows:

max J ðhÞ ¼ gT ¼W T gSW S

¼W TV cellgfuel

1:482W Sð1Þ

where h is the vector of the decision variables and gT is the system

(electrical) efficiency. In this study, the following four operating

variables are the decision variables to be determined by solving

the optimization problem: (1) the stack current (I S), (2) the air flow

rate to the stack (F a), (3) the cooling water temperature (T c), and (4)

the temperature rise of the cooling water through the stack (DT c).

Main module Power converter

Control boards

Air blower

Humidifier Stack Water pump

CVM boards

Fig. 1. Photo of the PEM fuel cell system for which the operating conditions are optimized.

54 I.-S. Han et al. / Energy Conversion and Management 113 (2016) 52–65

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Fig. 3 presents the power generation and supply diagram of the

system components and electricity users. The stack is the onlypower generation source and all others are consumers. In Fig. 3,

the points captioned with (I , V ) denote the measurements of cur-

rent and voltage, which enable us to directly measure or calculate

the electric power at the required points for modeling and opti-

mization. Based on the diagram, the objective function (1) must

be subject to the following power balances among the system com-

ponents and electricity users:

W T W demand ¼ 0 ð2Þ

W T W outP þ W A ¼ 0 ð3Þ

W S W inP W B ¼ 0 ð4Þ

W S V cellI SN S=1000 ¼ 0 ð5Þ

In the equations above, the power output of the fuel cell system

(W T) must be equal to the power delivered to the electricity users

(W demand), as described in Eq. (2). A portion of the total power from

the power converter (W outP ) is consumed by the air blower (W A)

andthe remainingpower is delivered to the electricity users, satisfy-

ing the power balance described in Eq. (3). The power generated

from the stack (W S) is delivered to both the power converter (W inP )

and the BOP power inverter (W B), satisfying the power balancedescribed in Eq. (4). DC power of 24 V is supplied through the BOP

power inverter to the water pump and other BOPs. The stack is the

only power generator in the fuel cell system and its power genera-

tion can be calculated according to Eq. (5).

The optimal values for all the decision variables and two other

operating variables must be found within the following bounds:

I lbS 6 I S 6 I

ubS ð6Þ

F lba 6 F a 6 F

uba ð7Þ

T lbc 6 T c 6 T

ubc ð8Þ

DT lbc 6 DT c 6 DT

ubc ð9Þ

F lbc 6 F c 6 F

ubc ð10Þ

T g T wa 6 DT g—wa ð11Þ

The lower and upper bounds are imposed on the decision vari-

ables as described in Eqs. (6)–(9). The flow rate of the cooling water

to the stack (F c) has upper and lower bounds because the cooling

water must flow rapidly enough to fill the cooling channels of

the stack and the cooling water pump has a limited capacity, which

is defined by Eq. (10). As described in Eq. (11), the temperature dif-

ference between the stack exhaust gas (T g) and the wet (humidi-

fied) air from the humidifier (T wa) should be less than a specifiedvalue (DT g–wa) to prevent the humidified air from condensing.

Pressureregulator

PC

Air blower

Hydrogen

TC

P

Powerconverter

HX

Humidifier

Stack

Water vessel

Electricity users(Electronic load)

BOP powerinverter

OtherBOPs

MFM

Purge valve control

VC

Chillingwater

Purge gas

Chillingwater return

Air

T

PT

T

Flow meter

Water pump

P

T

T

T

P

TCCooling water

Air exhaust

MFM(for temporary use)

Fig. 2. Schematic process diagram of the PEM fuel cell system. T and P indicate temperature and pressure measurements, respectively.

Air blower

Power

converter

Stack

Electricity users(Electronic load)

BOP power

inverter

OtherBOPs

Water pump

(I, V)

(I, V)

(I, V)

(I, V)

Fig. 3. Power generation and supply diagram for the PEM fuel cell system.


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The optimization problem defined in Eqs. (1)–(11) is a nonlinear

programming (NLP) problem with equality and inequality con-

straints. A sequential quadratic programming (SQP) method is suit-

able for solving this NLP problem [25] efficiently, and therefore,

was employed in this study. The function, fmincon, implementing

an SQP algorithm included in the MATLAB optimization toolbox

[26] was used to solve the optimization problem and perform sen-

sitivity analyses. Because the SQP algorithm does not always guar-

antee a global optimum, a number of starting points for the

decision variables, which were randomly generated, were tested

to locate near-global optimum points. The partial derivatives of

the objective function and nonlinear constraints were approxi-

mated using finite-difference gradients.

4. Experimental and data collection

Mathematical models for the fuel cell system are necessary to

solve the optimization problem. The first step is to collect experi-

mental data to build the models. In this study, test operations of

the fuel cell system were performed to collect operational data

for modeling. The operational data were divided into a modeling

data set and a testing data set for model building and validation,respectively. To collect the modeling data set, the four decision

variables were changed in turn according to the combination of

the decision variables as described in Table 1 during a test opera-

tion. Then, to collect the testing data set, an additional test opera-

tion was carried out by altering the decision variables arbitrarily.

As described in Table 1, three different testing cases that adjusted

the air flow rate to the stack were applied in the test operations.

For each testing case, the flow rate was regulated as a function of

the stack current. As a result, the stoichiometry of air was set to

decrease with increasing stack current, and ranged from 1.59 to

3.66 depending on the stack current and testing case. The cooling

water temperature was controlled at two different temperatures

(54 and 65 C), and the maximum temperature rise of the cooling

water through the stack was also regulated at two different tem-perature gaps (7 and 10 C). Note that the cooling water tempera-

ture rise may not reach its set-point in the lower current range

because the amount of heat generated is insufficient to maintain

the temperature in this range. The stack current was raised from

0 to 250 A in 10- or 20-A steps, and was then reduced to 0 A while

fixing the other three decision variables at a given combination, as

listed in Table 1. The fuel cell system logged the operational data in

a database at 2 s intervals. The first test operation was performed

for about 180 min to collect the modeling data set, and then an

additional test operation was carried out for about 55 min to col-

lect the testing data set. The raw data stored in the database were

averaged every 30 s after removing the data gathered during the

startup and shutdown, to finally afford 311 and 104 data points

for the modeling and testing data sets, respectively.

5. Model development

Empirical and semi-empirical models for most of the system

components, including the stack, humidifier, air blower, power

converter, pump, and other BOPs as shown in Figs. 1 and 2, are pre-

sented in this section.

5.1. Stack–humidifier

The stack and humidifier are treated as a single unit for model-

ing. The unknown variables in modeling the stack–humidifier are

the average cell voltage of the stack (V cell), the temperature of the

stack exhaust gas (T g), the temperature of the humidified air from

the humidifier (T wa), and the fuel utilization efficiency of the stack

(gfuel). To predict the three output variables (V cell, T g, and T wa)

among these unknown variables, an empirical model for the

stack–humidifier was developed by employing artificial neural net-

works (ANNs) [27]. The remaining variable, the fuel utilization effi-

ciency of the stack, was predicted using a semi-empirical model.

Fig. 4 depicts the structure of the neural network, which con-

sists of the five input variables (I S, F a, T c, DT c, and T a), a single

hidden-layer, and the three output variables. ANNs have been

widely used for nonlinear modeling in various fields and also been

applied to the field of fuel cells because they allow greater flexibil-

ity in determining model structures and typically give good predic-

tive performance [28,29]. The basic structure of an ANN consists of

a number of interconnected computing processors, called neurons

or nodes, grouped into input, hidden, and output layers. The

Table 1

Combination of the decision variables altered during the test operations for obtaining the modeling data set.

Decision variables F a T c (C) DT c (C) I S

Combination of the decision variables 358–1054SLPM (corresponding to the stack current 0–250 A) 54 Max 7 0–250 A (10–20A step)

Max 10 ”

65 Max 7 ”

Max 10 ”

421–1240 SLPM (corresponding to the stack current 0–250 A) 54 Max 7 ”

Max 10 ”

65 Max 7 ”

Max 10 ”

484–1426 SLPM (corresponding to the stack current 0–250 A) 54 Max 7 ”

Max 10 ”

65 Max 7 ”

Max 10 ”

Fig. 4. Neural network structure used for modeling of the stack–humidifier.


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strengths of the connections, called weights, among the nodes are

adjusted to obtain a desired output behavior using given informa-

tion and a learning algorithm. Various types of ANNs have been

proposed according to their structures and learning algorithms

for determining the weights [27]. In this study, a feed-forward net-

work with one hidden layer was employed to model the stack–hu-

midifier. It has been shown that this kind of network can

approximate virtually any function of interest to any degree of

accuracy, as long as enough hidden units are available [30]. In pre-

dicting the unknown variables, the final form of the neural net-

work model can be expressed by a function of weight matrices

(xHL and xOL ) and bias vectors (bHL and bOL ):

^ y ¼ bV cell ; bT g ; bT wah i ¼ g OL xOL f HL xHL x þ bHL þ bOL ð12Þwhere x stands for the vector of the input variables and ^ y for the

vector of the predicted output variables. The log-sigmoid transfer

function ( f HL ( x ) = 1/(1 + exp ( x )) and the pure linear transfer

function ( g OL ( x ) = x ) were used for the hidden and output nodes,

respectively. The weight matrix (xHL ) and bias vector (bHL ) for the

hidden layer and those (xOL and bOL ) for the output layer are the

major model training parameters. These parameters were deter-mined using a back-propagation training algorithm [27].

The fuel utilization of the stack was predicted using Eqs. (13)–

(15). The stack operates in dead-end mode and vents purge gas

periodically to avoid flooding. If the flow rate of the purge gas

from the stack is zero, the amount of hydrogen fed into the stack

will be the same as the stoichiometric flow rate of hydrogen

required for the electrochemical reactions. Then, the fuel utiliza-

tion efficiency of the stack will be 100% according to the follow-

ing equation:

gfuel ¼ 1 F purge

F stoicH2

! 100% ð13Þ

In this equation, the flow rate of the purge gas is linearly pro-

portional to the stack output current [24]. A linear regressionwas carried out using the modeling data set to obtain the following

relationship between the purge gas flow rate and the stack current:

F purge ¼ 0:00341 I S þ 0:00534 ð14Þ

The above regression equation explains 99.1% (R2 (coefficient of

determination) = 0.9908) of the total variability of the measured

data for the purge gas flow rate. In Eq. (13), the stoichiometric flow

rate of hydrogen entering the stack can be calculated by

F stoicH2 ¼N SI S

2eF 60Rð298:15Þ101:33 ð15Þwhere N s is the number of cells in the stack, R is the universal gas

constant (8.314 J mol1 K1), and eF denotes the Faraday constant

(96,485 C mol1).

5.2. Air blower

The air blower consumes a considerable amount of power in a

fuel cell systemand is identical to air compressors in terms of ther-

modynamics. Han and Han [31] proposed a hybrid model for an

air-compression system that combined a thermodynamic com-

pression equation with empirical equations. In this study, the air

blower was modeled by employing the same approach as proposed

by Han and Han [31]. The power consumption of the air blower can

be estimated from the following equation which divides the mini-

mum power consumption ðW minA Þ of the air blower by its overall

efficiency (gA).

W A ¼ 100W minA =gA ð16Þ

The minimum power required for the air blower in an adiabatic

and reversible compression process can be calculated by

W minA ¼ F aRðT a þ 273:15Þca50; 680ðca 1ÞMWa

P a þ 101:33

P e þ 101:33

ca 1ca

ð Þ 1

" # ð17Þ

The overall efficiency of the air blower is a function of both the

air flow rate (F a) and the discharge pressure of the air (P a). A mul-

tivariable linear regression analysis was performed using the per-

formance measurement data gathered from the initial testing of

the air blower to finally obtain the following correlation:

gA ¼ 0:0688 F a 1:1740 Pa þ 1:2199 ð18Þ

The discharge pressure of the air is an unknown state variable

and must be predicted to compute the overall efficiency of the

air blower. A simple linear regression using the modeling data

set was satisfactory to obtain the following relationship between

the discharge pressure and the air flow rate:

P a ¼ 0:03057 F a 5:2792 ð19Þ

The R2 for the above regression is as high as 0.9947, and Eqs.

(18) and (19) are valid only when F a ranges from 358 to 1430 SLPM.

5.3. Power converter

The power converter elevates the voltage of the DC power from

the stack to the desired voltage level [32,33]. The following equa-

tion obtained by a linear regression analysis of the modeling data

set (R2 = 0.9997) was used to predict the power output from the

power converter as a function of the power input:

W outP ¼ 0:9428 W

inP 0:1202 ð20Þ

5.4. Pump and other balance of plants

The cooling water pump is one of the major power consuming

components in the fuel cell system. Power consumption by the

other BOPs, including control boards, cell voltage monitoring

board, sensors, and valves, should be taken into account in model-

ing the fuel cell system. The cooling water pump and other BOPs

were considered as a single unit in the model. The following non-

linear equation was used to predict the power consumption of the

pump and other BOPs:

W B ¼ 0:00152 F 3c 0:00093 F

2c þ 0:57 F c þ 386:4

10

3 ð21Þ

The equation above was obtained from a polynomial curve fit-

ting using the modeling data set in which the measured values of

the cooling water flow rate varied between 12 and 53 LPM. The

cooling water flow rate is manipulated to control the temperaturerise of the cooling water through the stack, and therefore, must be

predicted to calculate the power consumption of the pump and

other BOPs. The following equation obtained from a simple heat

balance on the stack was used to calculate the cooling water flow

rate:

F c ¼ 60W S1:482

V cell 1

qwC pwDT c

ð22Þ

6. Results and discussion

6.1. Model validation

The stack–humidifier model predicts the following fourunknownvariables:the averagecell voltageof thestack, the temper-


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ature of thestack exhaust gas, thetemperature of thehumidified air

from the humidifier, and the fuel utilization efficiency. The neural

network model described in Section 5.1 was used to predict these

unknown variables, except for the fuel utilization efficiency. Before

training the neural network, the modeling and testing data were

scaled and mean-centered. The number of hidden nodes in the hid-

den layer is the only tuningparameter in the neural networkmodel.

To determine the tuning parameter, the neural network was trained

using the modeling data set while increasing the number of hidden

nodes over the range from 1 to 20 at intervals of one node. The root

mean squared error (RMSE) between the predicted and measured

outputs, obtainedfrom the neural network model andfrom the test-

ing data set, respectively, was used as the criterionto determine the

optimum number of hidden nodes. Finally, the model structure of

the neural network was established with 7 nodes in a single hidden

layer,which resulted in theminimum RMSE amongthe results from

the numbers of hidden nodes examined.

Fig. 5(a)–(c) compare the predicted outputs with the measured

ones (testing data set) that were not used for training the neural

network. In particular, the predicted values of both the average cell

voltage and the temperature of the stack exhaust gas show excel-

lent agreement with the measured values (Fig. 5(a) and (c)). The

excellent predictive performance is confirmed by the low RMSEs,

0.0023 V and 0.2571 C, for the average cell voltage and the tem-

perature of the stack exhaust gas, respectively. For the temperature

of the humidified air, the predicted values exhibit somewhat larger

deviations from the measured values than those of the other two

output variables, as shown in Fig. 5(b), resulting in a low RMSE

of 0.3892 C and a maximum deviation of 1.1 C.

The fuel utilization efficiency was predicted by the semi-

empirical models, Eqs. (13)–(15). The calculated RMSE between

the predicted and measured values is as small as 0.0160%. Fig. 5

(d) compares the measured and predicted values of the fuel utiliza-

tion efficiency. The predicted values of this variable are generally in

accordance with the measured ones, even though small fluctua-

tions of the fuel utilization efficiency are not predicted well. The

prediction errors arising from these small fluctuations are trivial

if one considers that the fuel utilization efficiency varies within a

maximum range of about 0.06%, which is negligibly small and con-

tributes a maximum prediction error of only about 0.03% in the

system efficiency.

The models for the air blower, the power converter, and the

pump and other BOPs were verified by comparing the predicted

and measured results. Fig. 6(a)–(d) shows the prediction results

for the power consumption of the air blower, the power output

of the converter, the power consumption of the pump and other

BOPs, and the power output of the fuel cell system, respectively.

The power output of the system was calculated from the power

balance equations (Eqs. (3)–(5)). As can be seen in Fig. 6(a)–(d),

all the predicted values match the measured values quite well,

even though there are some small deviations in certain regions.

All the RMSEs for the predicted variables are less than 0.05 kW

(which corresponds to only 0.23% of the maximum power output

of the system): 0.0319, 0.0482, 0.0292, and 0.0489 kW for the

Fig. 5. Prediction results fromthe model for the stack–humidifier:(a) average cell voltage of the stack, (b) temperature of humidified air fromthe humidifier, (c) temperatureof stack exhaust gas, and (d) fuel utilization efficiency of the stack.


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power consumption of the air blower, the power output of the con-

verter, the power consumption of the pump and other BOPs, and

the power output of the system, respectively. The results from

the model validations indicate that the empirical and semi-

empirical models developed for the fuel cell system demonstrate

satisfactory predictive performance and can be used for the

optimization.

6.2. Sensitivity analysis

Prior to conducting the optimization of the operating conditions

of the fuel cell system, it was worth analyzing the extent of the

effect exerted by a decision variable on the objective function

(i.e., the system efficiency). Sensitivity analyses were performed

to elucidate the effects of the decision variables on the objective

function under the constraints given by Eqs. (2)–(11). Among the

four decision variables, the stack current cannot be freely changed

for the sensitivity analyses because it must meet the equality con-

straints (Eqs. (2)–(5)). Thus, the remaining three decision variables

(F a, T c, and DT c) were varied within their operating bounds shown

in Table 2. Each of the three decision variables was gradually

increased from the lower to the upper bound while the other

two decision variables were fixed at constant values, as given in

Table 3, to identify variations in the objective function.

Fig. 7 illustrates the effects of the air flow rate on both the sys-

tem efficiency and the stack power when the power output of the

system is fixed at the following power loads applied to the system

in sequence: 10%, 50%, 75%, and 100%. In general, the power output

Fig. 6. Prediction results from the models for the air blower, power converter, and the pump and other BOPs: (a) power consumption of the air blower, (b) power output of

the power converter, (c) power consumption of the pump and other BOPs, and (d) power output of the system.

Table 2

Constraints imposed on the decision variables and the other two operating variables.

Variable Lower bound Upper bound Remark

I S 0 A 250 A

F a 358 SLPM 1426 SLPM – The lower and upper bounds

vary depending on the stack

current

– The lower and upper bounds

are at stack currents of 0 and

250 A, respectively.

T c 54 C 65 C

DT c 0 C 10 C

F c 12 LPM 53 LPM

DT g–wa N/A 8 C

Table 3

Base operating conditions of the decision variables given for each power load for the

sensitivity analyses.

Power load (%) Decision variablesa

F a (SLPM) T c (C) DT c (C)

10 420 60 1.8

50 805 60 7.0

75 1100 60 8.0

100 1240 60 10.0

a

The stack current is automatically determined by solving the optimizationproblem.


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of a PEM fuel cell stack is known to increase as the air flow rate

entering the stack rises, within a certain limit (i.e., increasing the

stoichiometry of the air) [34,35]. As expected, the stack power

increases almost linearly as the air flow rate increases for all the

power loads considered. Changes in the stack power owing to

the increases in the air flow rate from the lower to the upper

bounds are quite large, ranging from 0.15 to 0.47 kW depending

on the power load applied to the system. For power loads of 10%,

50%, and 75%, the system efficiency shows a tendency to decrease

with an increasing air flow rate. However, for the maximum power

load (100%), the tendency is reversed and decreases with an

increasing air flow rate, as can be observed in Fig. 7(d). When the

air flow rate is changed from the lower to the upper bounds, the

system efficiency reveals substantial changes: 1.8%, 0.9%,

0.4%, and 0.8% for power loads of 10%, 50%, 75%, and 100%,

respectively. From these results, therefore, it can be concluded that

a change in the air flow rate has a considerable effect on the systemefficiency, which can be either positive or negative depending on

the power load applied.

Fig. 8 depicts the effects of the cooling water temperature on

both the system efficiency and the stack power when the power

output of the system is fixed at the same power loads as those

applied in Fig. 7. As can be seen in Fig. 8, the stack power remains

almost constant (about 0 kWfor a 10% load) or is slightly decreased

(0.003, 0.006, and 0.16 kW for 50%, 75%, and 100% loads,

respectively) with increases in the cooling water temperature from

the lower to the upper bounds. On the other hand, the system effi-

ciency shows substantial changes with increases in the cooling

water temperature from the lower to the upper bounds. Fig. 8

shows that the increases in the cooling water temperature result

in some gains in system efficiency. These gains become larger as

the power load is increased, attaining about 0.3%, 0.4%, 0.5%, and

0.7% at loads of 10%, 50%, 75%, and 100%, respectively.

Fig. 9 shows the effects of the rise in the cooling water temper-

ature on both the stack power and the system efficiency when the

power output of the system is fixed at the following loads: 10%,

50%, 75%, and 100%. For all the power loads investigated, the stack

power decreases as the temperature rise of the cooling water

increases within its operating bounds. However, the changes in

the stack power are small when the temperature rise of the cooling

water is altered from the lower to the upper bound, ranging from

0.117 to 0.160 kWdepending on the power load applied to the sys-

tem. The system efficiency increases with the increasing cooling

water temperature rise for all the power loads investigated. The

gains in the system efficiency are not trivially small (2.0%, 0.7%,

0.5%, and 0.3% for power loads of 10%, 50%, 75%, and 100%, respec-

tively) when the temperature rise of the cooling water is elevated

from the lower to the upper bound.The sensitivity analyses suggest that the system efficiency is

somewhat more sensitive to both the air flow rate and the cooling

water temperature rise than to the cooling water temperature. The

system efficiency is proportional to both the cooling water temper-

ature and its temperature rise for all the power loads investigated.

On the other hand, the system efficiency can be increased or

decreased as the air flow rate increases: it is proportional to the air

flow rate when the power load is less than or equal to 75%, and is

inversely proportional to the air flow rate when the power load is

100%. That is, an increase in the air flow rate exerts either a positive

or a negative effect on the system efficiency depending on the

applied power load. It was found that a change in one of the three

decision variables within its operating bounds could produce a sub-

stantial change in the system efficiency (e.g., the 2% increase in

Fig. 7. Effects of the air flow rate on the system efficiency and the stack power: (a) 10% load, (b) 50% load, (c) 75% load, and (d) 100% load.


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Fig. 8. Effects of the cooling water temperature on the system efficiency and the stack power: (a) 10% load, (b) 50% load, (c) 75% load, and (d) 100% load.

Fig. 9. Effects of the temperature rise of the cooling water through the stack on the system efficiency and the stack power: (a) 10% load, (b) 50% load, (c) 75% load, and (d)100% load.


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system efficiency with an increasing cooling water temperature

rise). Therefore, if all three decision variables are simultaneously

changed in a positive manner, it is expected that the system effi-

ciency can be increased by as much as several percent.

6.3. Optimization and verification

The operating conditions for the fuel cell system described inFigs. 1–3 were optimized using the described optimization method.

The optimal operating conditions were sought for a total of 11

power loads which ranged from the minimum (10%) to the maxi-

mum (100%) at intervals of 5–15%. The minimum and maximum

loadscorrespond to systempower outputs of 2.2 and22 kW, respec-

tively. Fig. 10 displays a plot of the maximum system efficiency

against thepower output of thesystem. As shown in Fig. 10, the sys-

tem efficiency rises sharply as the power output increases, until

reaching its maximum, and then gradually declines. Typically, the

system efficiency of a PEM fuel cell system is influenced by both

the stack efficiency and the BOP power consumption. Without the

BOP power consumption, the system efficiency would gradually

diminish as thepower output increases, from its maximum at a zero

load to its minimum at a maximum load. For an actual fuel cell sys-tem, however, the system efficiency displays a unimodal curve

against the power output owing tothe effect of the BOPson the sys-

tem efficiency. The lower system efficiencies in the lower power

output range (2.2 kW < the power output < 6 kW) are due to the

high base-power consumption of the BOPs. The maximum system

efficiency is found to reach the least value of 40.9% at the minimum

power output (2.2 kW) and the greatest value of 45.6% at a power

output of 6.6 kW. As shown in Fig. 10, the maximum system effi-

ciencyis quite variable dependingon the power output, andthe lar-

gest efficiency gap reaches about 4.5% from the differences of the

power load.

The optimal decision variables, illustrated in Fig. 11, were deter-

mined to obtain the maximum system efficiencies shown in

Fig. 10. The stack current is the most effective variable for adjusting

the power output of the system, and thus, its optimal values are

obtained at the points where the stack power generation meets

the power requirements of both the system components and the

electricity users. As can be seen in Fig. 11(b), the optimal values

of the air flow rate are equal to the lower bound until the power

output reaches 13.2 kW, and then rise between the lower and

upper bounds. This indicates that, as expected from Fig. 7, the ten-

dency of the system efficiency to decrease with the increasing air

flow rate begins to reverse at power outputs greater than

13.2 kW. For all the power outputs investigated, the optimal values

of the cooling water temperature are obtained at the upper bound,

as expected from the sensitivity analysis results shown in Fig. 8.

The optimal values of the cooling water temperature rise are

obtained between the lower and upper bounds until the power

output approaches 8.8 kW, after which they stay at the upper

bound. In the lower range of the power output, the heat generated

from the stack is not large, so that the optimal values of the tem-

perature rise of the cooling water are sought below the upper

bound.

Fig. 12 plots the proportions of the power consumption by the

BOPs (the blower, the pump and other BOPs, and the power con-

verter) to the power generation by the stack at the optimal operat-

ing conditions when the power output of the system is varied from

2.2 to 22 kW. The proportion of the total power consumption by

the BOPs to the power generation sharply drops with the power

output, from the largest value (27.6%) at the minimum power out-

put (2.2 kW) to about 16% at a power output of around 6 kW, and

then gradually decreases to 13.5% until the maximum power out-

put is reached. This confirms that the lower system efficiencies

in the lower power output range are mainly due to the relatively

large proportion of the total power consumption by the BOPs to

the power generation in this range. Especially, the pump and other

BOPs show the largest contribution to such large proportions of the

total power consumption in the lower power output range. This

means that, to raise the system efficiency in this lower power out-

put range, the power consumption of the pump and other BOPs

should be reduced. When the power output is greater than about

4.4 kW, the power converter consumes the largest portion of the

total power among the BOPs. This result emphasizes that an

improvement in the efficiency of the power converter will be a

more effective way to increase the system efficiency across the

power output range.It is possible to estimate achievable improvements in the sys-

tem efficiency by calculating the differences between the mini-

mum and maximum system efficiencies obtained from the worst

and best operating conditions, respectively, in the adjustable

ranges of the operating variables. An additional optimization was

carried out to find the minimum system efficiencies owing to the

worst operating conditions by placing a minus sign before the

objective function with the same constraints as those used for

the maximization of the system efficiency. Fig. 13 illustrates the

minimum and maximum system efficiencies along with the effi-

ciency gap between the two against the power output of the sys-

tem. The minimum system efficiency ranges from a low of 35.4%

to a high of 42.3% over the power output range. The efficiency

gap attains the largest value (5.5%) at the minimum power outputand then diminishes with increasing power output until it reaches

the smallest value (1.2%) at 19.8 kW. In the lower power output

range, the efficiency gap is quite large, ranging from 3.6% to 5.5%,

while in the higher power output range (power output > 13.2 kW),

it is smaller, ranging from 1.2% to about 2%. Therefore, the opti-

mizations and operations of the fuel cell system in the lower power

output range should be given a higher priority in handling than

those in the higher power output range to obtain a substantial

increase in the system efficiency.

To verify the operation optimization method proposed in this

study, the operating conditions obtained from the maximizations

of the system efficiency were applied to the fuel cell system. The

decision variables of the system were adjusted to their optimal val-

ues while regulating the power output at each of the followingpower loads in sequence: 10%, 50%, and 100%. After the system

38

40

42

44

46

48

0 5 10 15 20 25

M a x i m u m s

y s t e m e f f

i c i e n c y / %

Power output of the system / kW

Fig. 10. Maximum system efficiency obtained from the optimization across thepower output of the system.


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reached a steady state under each optimal set of operating condi-

tions, the data for the operating variables were collected for

10 min and then averaged. Table 4 compares the measured

optimization results with the expected optimal values. Overall,

the discrepancies between the measured and expected values are

trivially small. The maximum deviation of the system efficiency

is as small as 0.6% when a power load of 10% was applied to the

system. These results indicate that the operation optimization

method is quite successful for a substantial increase in the

efficiency of the fuel cell system.

Fig. 11. Optimal decision variables obtained from the maximization of system efficiency: (a) stack current, (b) air flow rate; (c) cooling water temperature, and (d)

temperature rise of the cooling water through the stack.

0

5

10

15

20

25

30

0 5 10 15 20 25

P r o p o r t i o n o f t h e p o w e r c o n s u m p t i o n

t o t h e p o w e r g e n e r a t i o n / %


Blower

Pump & other BOPs

Converter

Total power consumption

Fig. 12. Proportion of the power consumption by the BOPs (the blower, the pump

and other BOPs, and the power converter) to the power generation by the stack

under the optimal operation conditions when the power output of the system

varies from 2.2 to 22 kW.

0

1

2

3

4

5

6

34

36

38

40

42

44

46

0 5 10 15 20 25

E f f i c i e n c y g a p / %

S y s t e m e

f f i c i e n c y / %


Maximum efficiencyMinimum efficiencyEfficiency gap

Fig. 13. Minimum and maximum system efficiencies against the power output of

the system, obtained from the optimizations under the constraints.


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7. Conclusions

An operation optimization method and its application to an

actual PEM fuel cell system were demonstrated to maximize the

system efficiency. The empirical and semi-empirical models used

in this study covered most of the system components including

the stack, humidifier, blower, power converter, and a pump andother balance of plants. The models are based on neural networks

and semi-empirical equations. Model validations results showed

that the developed models had satisfactory predictive performance

for the optimizations. Sensitivity analyses were carried out to elu-

cidate the effects on the system efficiency of the major operating

variables, including the air flow rate, the cooling water tempera-

ture, and the temperature rise of the cooling water through the

stack. Optimizations of the fuel cell system were performed to seek

the best operating conditions and were verified by comparing the

expected optimal values with the measured ones. The optimization

results showed that the efficiency gaps between the best and worst

performance of the system can reach 1.2–5.5%, depending on the

power load.

The proposed operation optimization method can be easilyextended to similar PEM fuel cell systems for stationary power

generators or vehicular applications, by incorporating an appropri-

ate data set for the targeted components, although the optimiza-

tion model is based on empirical and semi-empirical modeling

for a specific fuel cell system. The optimization method may

require a model update for a specific fuel cell system or a new

operating region. However, this model can be more easily updated

with higher accuracy than first-principles models if a sufficient

amount of operational data is obtained.

Acknowledgement

This work was funded by the Ministry of Trade, Industry &

Energy (MOTIE) through the Korea Institute for the Advancementof Technology (KIAT) under grant number R0001668.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in

the online version, at http://dx.doi.org/10.1016/j.enconman.2016.

01.045.

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Table 4

Implementation results of the optimal operating conditions at various power loads.

Load (%) Values System efficiency (%) System power output (kW) Stack power (kW) Decision variables

I S (A) F a (SLPM) T c (C) DT c (C)

10 Expected 40.9 2.20 3.04 24.8 358 65.0 2.8

Measured 40.3 2.27 3.17 25.9 357 64.9 2.8

Deviation 0.6 0.07 0.13 1.1 1 0.1 0.0

50 Expected 44.6 11.00 12.76 113.5 658 65.0 10.0Measured 44.7 11.11 12.83 114.6 657 64.9 10.3

Deviation 0.1 0.11 0.07 1.1 1 0.1 0.3

100 Expected 41.1 22.00 25.44 246.8 1334 65.0 10.0

Measured 41.0 22.09 25.62 248.0 1326 65.0 10.3

Deviation 0.1 0.09 0.18 1.2 8 0.0 0.3


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