Content uploaded by M. Trifkovic

Author content

All content in this area was uploaded by M. Trifkovic on Mar 07, 2016

Content may be subject to copyright.

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014 169

Modeling and Control of a Renewable Hybrid

Energy System With Hydrogen Storage

Milana Trifkovic, Mehdi Sheikhzadeh, Khaled Nigim, Senior Member, IEEE, and Prodromos Daoutidis

Abstract— This paper deals with system integration and

controller design for power management of a stand-alone renew-

able energy (RE) hybrid system, which is at the construction stage

in Lambton College (Sarnia, ON, Canada). The system consists

of ﬁve main components: photovoltaic arrays, wind turbine,

electrolyzer, hydrogen storage tanks, and fuel cell. The model for

each process component is developed, and all the components

are integrated in a MATLAB/Simulink environment. A two-

level control system is implemented, comprising a supervisory

controller, which ensures the power balance between intermittent

RE generation, energy storage, and dynamic load demand, as well

as local controllers for the photovoltaic, wind, electrolyzer, and

fuel cell unit. Simulations are performed to document the efﬁcacy

of the proposed power management strategy.

Index Terms—Hybrid system, hydrogen storage, model

predictive control (MPC), power management, renewable energy

(RE).

I. INTRODUCTION

RENEWABLE energy (RE) sources will become an

increasingly important part of power generation as the

reserves of fossil fuels get closer to depletion. Among avail-

able RE technologies, wind and solar energy sources are

the most promising options, as they are omnipresent, freely

available, and environmentally friendly. Although these tech-

nologies are improving in various aspects, the drawbacks

associated with them, such as their intermittent nature and

high capital cost, remain the main obstacles to their utilization.

Consequently, only 3% of total global electricity is generated

from nonhydro renewable sources [1].

Because of their intermittent nature, wind and solar energy

resources in a given area can be complementary on a daily

and/or seasonal basis. It has been shown that hybrid combina-

tions of two or more renewable power generation technologies

in stand-alone applications are economically viable and can

improve the system’s performance [2]–[6]. Additionally, in

order to ensure grid-like power for autonomous systems, a

storage medium or energy carrier is needed. The energy

Manuscript received May 2, 2012; revised November 19, 2012; accepted

January 20, 2013. Manuscript received in ﬁnal form February 18, 2013. Date

of publication March 11, 2013; date of current version December 17, 2013.

Recommended by Associate Editor S. Varigonda.

M. Trifkovic and P. Daoutidis are with the Department of Chemical

Engineering and Materials Science, University of Minnesota, Minneapolis,

MN 550455 USA (e-mail: trifk001@umn.edu; daout001@umn.edu).

M. Sheikhzadeh and K. Nigim are with the Department of Instrumentation

and Control, Lambton College, Sarnia, ON N7S 6K4, Canada (e-mail:

Mehdi.Sheikhzadeh@lambton.on.ca; c0548578@lambton.on.ca).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TCST.2013.2248156

storage technologies can be classiﬁed into capacity-oriented

(pumped hydroelectric systems, compressed air, hydrogen) and

access-oriented storage devices (batteries, ﬂywheels, superca-

pacitors, and superconducting magnetic energy storage) [7].

Each one of them has several advantages and disadvantages,

and one has to consider factors such as the operating cost,

power response time, efﬁciency and calendar life when select-

ing a suitable storage technology. For example, conventional

battery storage is energy efﬁcient, but the cost of energy

storage is very high [8]. Pumped hydro is suitable for large-

scale applications but it is applicable only in certain locations.

Hydrogen is an attractive energy carrier since it is one of

the cleanest, lightest, and most efﬁcient fuels, but it has a

slow power response time. The disadvantage of the slow

dynamics can be compensated by implementing a suitable

power management tool.

Proper sizing of each component in a hybrid energy system

is a key factor for its technoeconomic feasibility [9]–[11].

Unit sizing and technology selection can be based on meeting

requirements such as using the available generation technology

and not exceeding the equipment power rating, or on satisfying

constraints and achieving multiple objectives such as mini-

mizing environmental impact, installation and operating costs,

payback periods on investment, and maximizing reliability.

The optimization problem can sometimes have conﬂicting

objectives and thus be complex. A comprehensive survey

of studies that addressed the complexities involved in the

design of hybrid RE power generation technologies has been

reported [12].

Signiﬁcant research effort has been devoted to the modeling

and control of individual process components as well as

integrated RE systems. Most of the studies that have dealt

with hybrid energy systems have been performed in the

simulation mode [5], [11], [13]–[17], with only a few dealing

with real-time application [18]–[21] due to the high capital

cost associated with design and implementation. The optimal

integration of hydrogen storage with RE sources and the power

management of such systems have also received considerable

attention [8]–[10], [18], [22]–[25].

The importance of a control strategy for the optimal oper-

ation of the photovoltaic (PV)/hydrogen/battery systems has

been shown previously [23]. The outputs from the various

generation sources of a hybrid energy system need to be

coordinated and controlled to realize its full beneﬁt. Thus,

development of suitable power management that ensures meet-

ing the customer load demand despite the intermittent nature

of RE sources is an integral part of ensuring the system’s

1063-6536 © 2013 IEEE

170 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014

reliability and achieving operational efﬁciency [26]. The aim

of this paper is to present a comprehensive study of the

automation system design for a stand-alone power system

located in Sarnia, ON, Canada. In a preliminary version of this

study, we introduced a simpliﬁed model and control strategy

for this system [27]. Here, we describe the comprehensive

model for the wind/PV/electrolyzer/fuel cell system and a

power management tool that utilizes decentralized adaptive

model predictive control (MPC) at the local control level and

decision-based control at the supervisory level. Speciﬁcally,

power generated from wind and PV is stored in the form

of hydrogen. Maximum power point tracking (MPPT) on

the PV system and the pitch angle and power controllers

on the wind turbine ensure optimal power generation by the

RE sources. The supervisory controller computes the power

references for the fuel cell and electrolyzer subsystems at

each sampling time. The power references are sent to the

local decentralized MPC system, which brings the fuel cell

and electrolyzer subsystems to the desired power reference

values while minimizing a suitable cost function. The perfor-

mance and effectiveness of the proposed control architecture

is evaluated through simulations.

II. PROCE SS MODEL

Dynamic, ﬁrst-principles models of the individual units

along with their system integration are described in the fol-

lowing subsections. It is assumed that the electrochemical

reactions in the electrolyzer and fuel cell are instantaneous.

Although the model does not include phenomena with a very

slow response (i.e., catalyst and membrane degradation in the

fuel cell and electrolyzer), it captures the essential dynamics

of the system and allows the implementation and evaluation

of the proposed control strategy.

A. Wind Energy Conversion System

The wind energy conversion system (WECS) consists of a

turbine to capture the energy in the wind, a drive train to speed

up the rotational speed of the shaft, and a generator to convert

the mechanical energy into electrical energy (see Fig. 1). In

this paper, a variable-speed wind turbine with the capability

of continuous adaptation (acceleration or deceleration) of the

rotational speed ωof the wind turbine to the wind speed vis

used. The main classiﬁcation of variable-speed wind turbines

is according to their generator, among which WECS equipped

with doubly fed inductance generators (DFIGs) are the most

common type. The possibility of pitch control with an efﬁcient

transmission of the power to the grid through active and

reactive power control has made them very attractive due to

the rising issue of the wind power impact on the electrical

network. In these types of generators, the stator of the machine

is directly connected to the grid and the rotor power is handled

by converters [28].

The WECS model consists of three main parts: wind tur-

bine rotor, drive train, and generator. The wind turbine rotor

converts the kinetic energy of the wind into mechanical energy

by producing torque. Since the energy contained in the wind

is in the form of kinetic energy, its magnitude depends on the

Fig. 1. Wind energy conversion block diagram.

air density and wind velocity. The wind power obtained by

the turbine rotor is given by [15], [25], and [29]

Pw=1

2ρAv3cp(λ, β ) (1)

where Pwis the power extracted from the wind, ρis the air

density, Ais the swept area by the wind, and cpis the power

coefﬁcient which is a function of the tip speed ratio λand

the pitch angle of the rotor blades β. The tip speed ratio is

described as [29]

λ=ωmR

v(2)

where ωmis the rotational speed and Ris the radius of the

wind turbine rotor.

The drive train transfers the power from the turbine rotor

to the generator. It includes the input rotating shaft connected

to the gear box and the output shaft connecting the drive train

to the generator. The main model equations for the drive train

are as follows [29], [30]:

dωm

dt =1

2HmTm−Kθmg −Dmωm(3)

dωg

dt =1

2HgKθmg −Te−Dgωg(4)

dθmg

dt =ω0ωm−ωg(5)

where Tmis the accelerating torque, Teis the decelerating

torque, Kis the effective shaft stiffness, θmg is the twist in the

shaft system, ωgis the generator speed, ω0is speed constant of

the system, Dmωmis the damping torque in the wind turbine,

and Dgωgis the damping torque in the generator. It is assumed

that the shaft stiffness is constant.

A model that is commonly used for the induction generator

is the Park model [31]. The stator is directly connected

to the grid and the stator voltage (vs) is imposed by the

grid. The rotor voltage (vr) is controlled by a converter and

this voltage is used to control the captured power from the

wind generator [29]. A set of converters on the rotor side

provides an opportunity to manipulate the rotor side voltage

and consequently the captured power. The main generator

model equations are as follows [31]:

vs=RS

is+d

ψs

dt (6)

vr=Rr

ir+dψr

dt −jωr

ψr.(7)

TRIFKOVIC et al.: MODELING AND CONTROL OF A HYBRID RE SYSTEM WITH HYDROGEN STORAGE 171

Fig. 2. Equivalent circuit model for a PV cell.

The stator and rotor ﬂuxes are given by

ψs=Ls

is+Lm

ir(8)

ψr=Lr

ir+Lm

is(9)

where

isis the current space vector, vsand vrare the

rotor and stator voltage space vectors, respectively, Lmis the

magnetizing inductance, Lsand Lrare the rotor and inductor

self-inductances, respectively, Rsand Rrare the rotor and

stator resistance, respectively, and ψsand ψrare the rotor

and stator ﬂux space vectors, respectively.

B. Solar Energy Conversion System

The solar energy conversion system or PV process is a

physical process through which solar energy is converted

directly into electrical energy. A solar cell is usually repre-

sented by an electrical equivalent one-diode model as shown in

Fig. 2.

The model contains a short-circuit current Isc , a diode, and a

series resistance RSand the resistance RPinside each cell and

in the connection between the cells. The correlation between

the output PV voltage and the current of a PV cell or a module

can be expressed as [32]

Ipv =Isc −ID−VD

RP(10)

Vpv =VD−RSIpv (11)

ID=I0e(VD/VT)−1(12)

where I0is the saturation current, VDis the diode voltage,

IDis the diode current, and VTis the diode voltage. Standard

PV characteristics are needed to solve the model, including

the short-circuit current Isc, the open-circuit voltage Voc,the

rated current IR, and the voltage VRat the maximum power

point (MPP) under standard test conditions (25 °C). The effect

of temperature on the PV panel is not considered. Cells are

normally grouped into modules, which are then connected in

arrays with MPparallel branches, each with MSmodules in

series. Under the assumption that the modules are identical

and are all exposed to the same ambient irradiation, the

solar cell arrays current and voltage (Iaand Va) can be

calculated as

Ia=MPIpv (13)

Va=MSVpv.(14)

Fig. 3. Electrolyzer modeling block diagram.

C. Hydrogen Generation (PEM Electrolyzer) System

The electrolysis of water using cells with a polymer elec-

trolyte membrane (PEM) is a very efﬁcient method of produc-

ing hydrogen. PEM electrolyzers are very simple and compact

and have demonstrated higher current density capability than

conventional alkaline water electrolyzers [33]. The reactions

that take place at the anode and the cathode of a PEM

electrolyzer are described below

Anode Reaction :H2O→2H++1

2O2+2e(15)

Cathode Reaction :2H++2e→H2.(16)

The supplied water to the anode side is decomposed into

oxygen gas, hydrogen protons, and electrons. The hydrogen

protons are transported through the proton conductive mem-

brane to the cathode side. At the same time, the electrons

exit the PEM electrolyzer cell via the external circuit, which

supplies the driving force (i.e., cell potential) for the reaction,

whereas at the cathode side the hydrogen protons and the

external circuit electrons recombine to form hydrogen gas.

The dynamic model for a PEM electrolyzer is composed of

four ancillaries: the anode, the cathode, the membrane, and

the voltage ancillary (Fig. 3). The anode ancillary calculates

oxygen and water ﬂows and their partial pressures. The

cathode system calculates hydrogen and water partial pres-

sures and their ﬂows. The membrane ancillary computes the

water content, electro-osmotic drag, water diffusion, and the

conductivity of the membrane. The voltage ancillary calculates

the electrolyzer’s voltage by incorporating the Nernst equation,

ohmic polarization, and activation polarization.

The material balance equations for the anode ancillary are

given by

Anode :dN

O2

dt =Nin

O2−Nout

O2+Ngen

O2

dN

H2O

dt =Nin

H2O−Nout

H2O−Nmem

H2O.(17)

The number of moles of water NH2Oand oxygen NO2,the

electrolyzer temperature, and the water and oxygen partial

pressures pH2Oand pO2are used to calculate the anode total

pressure pAnode =pH2O+pO2and the oxygen mole fraction

yO2inside the anode channel using the ideal gas law and

thermodynamic properties [34]. Electrochemistry principles

are used to calculate the rates of oxygen generation Ngen

O2

during the water splitting reaction. The rate of generated

172 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014

oxygen is obtained from Faraday’s law as

Ngen

O2=nele IeleηF

nst F(18)

where nele is the number of electrolyzer cells, Iele is the

electrolyzer applied current, nst is the reaction stoichiometry

coefﬁcient, ηFis the Faraday efﬁciency, and Fis the Faraday

constant. The detailed calculations are given in [34].

Similar to the anode ancillary, the cathode molar ﬂows of

water and hydrogen are obtained by calculating the partial

pressures pH2Oand pH2, respectively, cathode total pressure

pC, and the hydrogen mole fraction

Cathode :dN

H2

dt =Nin

H2−Nout

H2+Ngen

H2

dN

H2O

dt =Nin

H2O−Nout

H2O+Nmem

H2O.(19)

The rate of hydrogen generated in the water-splitting reac-

tion, Ngen

H2, is a function of the stack current

Ngen

H2=nele IeleηF

nst F.(20)

The water transport through the membrane is achieved by

electro-osmotic drag and diffusion phenomena [35], [36]. Note

that the membrane molar rate is needed to calculate the molar

rates in the anode and cathode ancillaries [see (17) and (19)].

The amount of water transported is dependent on the electro-

osmotic drag coefﬁcient nd, which is deﬁned as the number

of water molecules carried by each proton. Water diffusion

through the membrane is calculated by Fick’s law, and the

combination of these two phenomena is shown in the following

equation:

Nmem

H2O=MH2OAele nd¯

Iele

F+Dw

cw,c−cw,a

tm(21)

where MH2Ois molecular weight of water, Ais the area

of the electrolyzer cell, ¯

Iele is the current density, Dwis

the water diffusion coefﬁcient, cw,cand cw,aare the water

concentration at the cathode and anode surface, respectively,

and tmis the thickness of the membrane. The electro-osmotic

drag and diffusion coefﬁcient vary with the water content in

the membrane, i.e., λm, and empirical relationships describing

these correlations are given in [36].

The total electrolyzer voltage can be represented as

Vele =Eele +Vact

ele +Vohm

ele (22)

where Eele is the open-circuit voltage, Vact

ele is the activation

polarization, and Vohm

ele is the ohmic polarization. The open-

circuit voltage (Eele), deﬁned by the Nernst equation and the

activation and ohmic overpotentials are modeled according to

[34] and [37]

⎧

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎩

Eele =1

2FGele +RTele ln pele

H2pele

O2

αele

H2O

Vact

ele =RTele

2βFln ¯

Iele

¯

Iele0

Vohm

ele =¯

Iele Rohm

ele

(23)

where Ris the universal gas constant, Gele is the Gibbs free

energy of formation, Tele is the absolute temperature, αele

H2O

is the water activity between the anode and the electrolyte,

Fig. 4. Fuel cell modeling block diagram.

and pele

H2and pele

O2are the partial pressures of hydrogen, and

oxygen, respectively. The activation polarization is a function

of the current density ¯

Iele, the exchange current density ¯

Iele0,

and the charge transfer coefﬁcient β. The ohmic polarization

is a function of the membrane resistance Rohm

ele , which can

be calculated by using the membrane conductivity and its

thickness [34].

Assuming a lumped thermal capacitance model, the overall

thermal energy balance can be expressed as [22] and [25]

Cele dT

ele

dt =˙

Qgen −˙

Qloss −˙

Qcool (24)

where Cele is the overall heat capacity of the electrolyzer, ˙

Qgen

is the heat power generated inside the electrolyzer stack, ˙

Qloss

is the heat power loss, and ˙

Qcool is the heat power loss due

to cooling. Each term in the thermal energy balance equation

is calculated as follows:

⎧

⎪

⎨

⎪

⎩

˙

Qgen =nele Iele (Vele −Vth)

˙

Qloss =Tele−T0

Rth

ele

˙

Qcool =Cm

ele Tout

m−Tin

m

(25)

where Vth is the thermal voltage, T0is the ambient tem-

perature, Rth

ele is the thermal resistance, Cm

ele is the cooling

medium overall heat capacity, and Tmis the cooling medium

temperature.

D. Hydrogen Consumption (Fuel Cell) System

The reverse equivalent of a PEM electrolyzer is a PEM fuel

cell, which is thus modeled similar to the PEM electrolyzer

described in the previous section. Chemical energy of the

hydrogen fuel is converted into electricity through a chemical

reaction with oxygen. The byproducts of this reaction are

water and heat. The dynamic fuel cell model used here was

developed in [38] and it is divided into four main ancillaries:

the anode, the cathode, the membrane, and the voltage (Fig. 4).

The mole balance equations for oxygen, nitrogen, hydrogen,

and water mass on the anode and cathode side of the PEM

TRIFKOVIC et al.: MODELING AND CONTROL OF A HYBRID RE SYSTEM WITH HYDROGEN STORAGE 173

fuel cell can be written as follows:

Anode :dN

H2

dt =Nin

H2−Nout

H2+Nreac

H2

dN

H2O

dt =Nin

H2O−Nout

H2O−Nmem

H2O

(26)

Cathode :⎧

⎪

⎪

⎨

⎪

⎪

⎩

dN

O2

dt =Nin

O2−Nout

O2+Nreac

O2

dN

H2O

dt =Nin

H2O−Nout

H2O+Ngen

H2O+Nmem

H2O

dNN2

dt =Nin

N2−Nout

N2.

(27)

The molar rate of water inside the cathode, NH2O, depends

on the summation of vapor ﬂows, because it is assumed that

the liquid water does not leave the stack and evaporates into

the cathode gas if cathode humidity drops below 100%. Water

is in vapor form until the relative humidity of the gas exceeds

saturation (100%), at which point the vapor condenses into

liquid water [39]. Similar to the electrolyzer, the ideal gas law,

thermodynamic properties, and electrochemistry principles can

be used to calculate the components’ partial pressures, total

pressure at the anode and cathode, moles of reacted hydrogen

and oxygen, as well as the generated water [38].

The fuel cell voltage is calculated based on voltage drops

associated with all the losses as follows:

Vfc =Efc −Vact

fc −Vohm

fc −Vconc

fc (28)

where Vfc is the fuel cell voltage, Efc is the open-circuit

voltage, Vact

fc is the activation polarization, Vohm

fc is the ohmic

polarization, and Vconc

fc is the concentration overpotential. The

open-circuit voltage and ohmic polarization are calculated as

in 23. The activation and concentration overpotentials are

obtained by the following equations:

⎧

⎨

⎩

Vact

fc =Vact

0+cact,11−ecact,2¯

Ifc

Vconc

fc =¯

Ifc cconc,1¯

Ifc

¯

Imax

fc cconc,2(29)

where ¯

Ifc is the fuel cell current density, Vact

0is the voltage

drop at zero current density, and a cact and cconc and ¯

Imax

fc are

constants that depend on the temperature and reactant partial

pressure and are obtained empirically [38].

The heat generated by the fuel cell chemical reaction can

be written as

Cfc dT

fc

dt =˙

Qgen −˙

Qelec −˙

Qs.+l.−˙

Qloss (30)

where ˙

Qgen is the heat generated from chemical reaction, ˙

Qelec

is the generated electrical energy, ˙

Qs.+l.is the absorbed latent

and sensible heat, and ˙

Qloss is the heat loss. These terms are

given by the following relations:

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

˙

Qgen =Nreac

H2Hreac

fc

˙

Qelec =Vfc Ifc

˙

Qs.+l.=

i=H2,O2,H2O

Ci

×Nout

iTfc −Nin

iTin+Ngen

H2OHv

˙

Qloss =hfc Afc (Tfc −Tamb)

(31)

where Hreac

fc is the enthalpy of reaction, Ciis the speciﬁc

heat capacity, Hvis the heat of evaporation, hfc is the fuel

cell heat transfer coefﬁcient, Afc is the fuel cell surface area,

and Tamb is the ambient temperature. The detailed model

for all the fuel cell ancillaries can be found in [25], [38],

and [40].

E. Hydrogen Storage System

Hydrogen storage consists of a compressor and a hydrogen

tank. The required compression work can be estimated as

follows [25]:

Pcomp =Nout

H2|ele 2ncRTin

ηc(n−1)

×Pout

√PinPout nc−1

nc−1(32)

where Pcomp is the compressors consumed power, Tin is

the hydrogen temperature from the electolyzer (assumed to

be equal to Tele), and ηcis the compressor efﬁciency. The

hydrogen mole balance in the tank is obtained as

dN

H2

dt tank =Nin

H2

dt fc −Nout

H2

dt ele

.(33)

Accumulated hydrogen in the tank calculated by 33 is used

to estimate the hydrogen pressure in the tank under the

assumption that the tank temperature Ttank is constant, using

the Beattie–Bridgeman equation [25]

Ptank =Ntank

H2

2RTtank

V2

tank 1−a1Ntank

H2

VtankT3

tank

×Vtank

Ntank

H2+a21−a3Ntank

H2

Vtank

−

a41−a5Ntank

H2

Vtank Ntank

H2

2

V2

tank

(34)

where Ptank is the tank pressure, Vtank is the tank volume, and

a1–a5are empirical parameters [25].

III. CONTROL ARCHITECTURE

A multilevel control scheme has been reported as a more

practical and efﬁcient hierarchy for controlling hybrid energy

systems [41]. The applied control structure for the system

studied here consists of two layers: the supervisory controller

and low-level local controllers. The supervisory control layer

monitors and controls the power ﬂow from the RE sources to

the storage components and power consumption centers. It also

computes the operating trajectories for the fuel cell and elec-

trolyzer subsystems. The local controller layer is responsible

for regulating each process component to improve efﬁciency

and optimize its performance. All process subsystems and their

controllers are connected to the supervisory controller.

The applied control scheme aims to fulﬁll the following

objectives.

1) Optimally using the energy resources.

2) Meeting the load demand.

3) Operating the system efﬁciently.

In the following subsections, these two control layers are

described in detail.

174 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014

A. Supervisory Power Control

The hybrid energy system consists of the power generation

(wind, PV, and fuel cell) and the power consumption com-

ponents (electrolyzer, auxillary equipment, and the main load

demand). Power ﬂow in the hybrid system is shown in Fig. 5.

The net power (Pnet), which is the difference between the

generation sources and the load demand, is calculated as

Pnet =Pwind +Ppv−(Pload +Pae)(35)

where Pwind and Ppv are the power generated by the wind

and solar energy conversion systems, respectively, Pload is the

load demand, and Pae is the power consumed by auxiliary

equipment in the system.

The generated power from the renewable sources can be

either used directly to meet the load demand or transferred to

the hydrogen production process. Because of the intermittent

nature of RE as well as the dynamic load demand, Pnet can

have a positive, zero, or negative value at any instant. In

the case of Pnet =0, there is sufﬁcient power generated

from the renewable sources to meet the load and auxiliary

equipment demand with neither excess nor deﬁcit of energy.

The electrolyzer and fuel cell activation and deactivation are

basedonthePnet value which is calculated in each sampling

interval. When there is excess power generated (Pnet >0), the

electrolyzer is activated. On the other hand, when there is a

deﬁcit in power generation (Pnet <0), the fuel cell stack is

activated to consume previously stored hydrogen and convert it

to electricity. The fuel cell activation will occur only if there is

a sufﬁcient supply of hydrogen in the storage tank. Otherwise,

the hybrid system enters a “hydrogen starvation” mode. This

can occur as a consequence of either extreme operational

conditions, such as low availability of renewable sources and

very high load demand, or inappropriate unit sizing. The power

management logic is shown below

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

If (Pnet >0)

→ζele =1,ζ

fc =0,ζ

comp =1

If Pnet >0&Ptank ≥Pub

tank

→ζele =0,ζ

fc =0,ζ

comp =0

If Pnet <0&Ptank ≥Plb

tank

→ζele =0,ζ

fc =1,ζ

comp =0

If Pnet <0&Ptank <Plb

tank

→ζele =0,ζ

fc =0,ζ

comp =0

If (Pnet =0)

→ζele =0,ζ

fc =0,ζ

comp =0.

(36)

In the above, Plb

tank and Pub

tank are the low hydrogen pressure

tanks lower and higher limits, respectively, and ζele,ζfc,and

ζcomp are the operational modes (ON/OFF) for the electrolyzer,

fuel cell, and compressor, respectively. According to (36), the

electrolyzer becomes activated as soon as there is positive Pnet.

However, if the excess power is less than the electrolyzers

rated power, the generated power will be completely used to

keep the electrolyzer running while not satisfying the load

demand. Equation (36) can be modiﬁed as follows to prevent

Fig. 5. Supervisory power management block diagram.

this problem

If Pnet >Prated

ele

→ζele =1,ζ

fc =0,ζ

comp =1(37)

where Prated

ele is the electrolyzers rated power.

B. Local Controllers

Each component in the studied hybrid energy system has

its own local controller which enforces optimal operation of

the corresponding unit based on the available information with

respect to power generated from the WECS and PV, and power

demand.

1) Wind System Controllers: The wind turbine power output

varies with the wind speed, and this dependency is represented

by a wind turbine characteristic curve. The characteristic curve

has three distinct zones according to the corresponding wind

speeds: cut-in, rated, and cut-out. Below the cut-in wind speed

and above the cut-out wind speed, the output power is zero.

When the wind velocity is between the cut-in and rated

wind speeds, the local controller is responsible to extract the

maximum power according to the wind turbine characteristic

curve. This is achieved by controlling the active and reactive

power of the rotor. The control scheme consists of two series

of two proportional integral (PI) controllers. The actual turbine

speed (ωm)and wind turbine characteristic are used to estimate

the maximum possible power as a reference. The active and

reactive power is compared to its reference, and the offset

for both are sent to two stage controllers to adjust the current

and voltage of the rotor converter side in order to obtain the

maximum possible power. The switching dynamics, the power

losses in the converter, and delays caused by the intermediate

dc converter are assumed to be negligible [42], [43].

Between the rated and cut-out wind speeds, the DFIG

wind turbine activates a blade pitch angle controller to reduce

the power coefﬁcient and, consequently, the extracted power

from the wind. This controller prevents high generator speed,

and hence prevents mechanical damage of the turbine. The

control action is based on comparing the generator speed to

its reference and sending the error signal to PID controller,

which estimates the reference value for the pitch angle.

TRIFKOVIC et al.: MODELING AND CONTROL OF A HYBRID RE SYSTEM WITH HYDROGEN STORAGE 175

The offset between reference and actual pitch angle is mini-

mized by a second P controller.

2) Solar System Controllers: Despite all improvements, PV

modules still have a relatively low conversion efﬁciency. The

voltage–current–Power (V–I–P) characteristic curves for a

PV array speciﬁes a unique operating point at which the

maximum possible power is delivered. The MPPT algorithm

is used for extracting the maximum available power from the

PV module under certain voltage and current conditions. There

are several MPPT techniques reported in the literature [44],

[45]. The perturbation and observation method (P&O) is one

of the most common and effective ways of power tracking

for PV arrays [45]. In this paper, the current perturbation

and observation method (CP&O) is applied [45]. The MPP

tracker operates by periodically incrementing or decrementing

the solar array current (Ipv). If a given perturbation leads to an

increase (decrease) of the output power of the PV (Ppv), then

the subsequent perturbation is generated in the same (opposite)

direction. The perturbation magnitude was set to 0.02 A.

3) Model Predictive Control of Electrolyzer and Fuel Cell:

Implementation of power control over the electrolyzer and

the fuel cell can improve their efﬁciency and consequently

the hydrogen generation and storage. The constraints and

dynamics of the electrolyzer and fuel cell are decoupled as

they operate in a sequential mode; i.e., when the fuel cell is

ON (OFF), the electrolyzer is OFF (ON). A decentralized MPC

scheme was employed to regulate the power of the electrolyzer

and fuel cell. A key advantage of MPC is its ability to deal

with constraints in a systematic and straightforward manner.

This is of particular importance for the PEM electrolyzer

and fuel cell operation, where abrupt changes in the current

load produce more uneven water/current distribution and

promote degradation of the membrane, which in turn

decreases the overall efﬁciency and the working life of these

units. A decentralized approach is the most appropriate one

because of the limited exchange of information between the

subsystems [46]. Moreover, a decentralized implementation of

MPC has the advantage of reducing the optimization problem

into a number of smaller and easily tractable ones. Each

controller determines the constraint-admissible and optimum

value of the current that can be applied on the electrolyzer/fuel

cell at each sampling time. For control design purposes,

the nonlinear models of the electrolyzer and fuel cell were

linearized and discretized using the ﬁrst-order hold conversion

method. The resulting state space model has the form

x(k+1)=Ax(k)+Bu(k)+Dd(k)

y(k)=Cx(k)(38)

where kis the sampling time, and A,B,D,andCare matrices

of appropriate dimensions. x,u,d,andyare the model

states, manipulated variables, disturbances, and model outputs,

respectively. The electrolyzer state space model variables are

⎧

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎩

xele =δNa

O2,δNa

H2O,δNc

H2,δNc

H2OT

yele =δPele,δVele,δNH2,δpH2T

uele =[δIele],

dele =δTa

ele

(39)

where the operator δindicates the deviation from the

operating point, and the aand csuperscripts stand for anode

and cathode, respectively. Pele is the controlled variable,

while the rest of the outputs are measured ones.

The fuel cell state space model variables are

⎧

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎩

xfc =δpfc,δNa

H2,δNa

H2OδNc

N2,δNc

O2T

yfc =[δPfc,δVfc]T

ufc =[δIfc]

dfc =δTc

fc

(40)

where Pfc is the fuel cell generated power chosen as the

controlled variable, Tc

fc is the input air temperature, and Vfc is

the fuel cell voltage (the measured output). For both systems,

the control objective is imposed at any instant by the Pnet

value from the power management controller [(35)–(37)].

The model predictive controller is designed to mini-

mize the following ﬁnite horizon control and performance

index:

min

uJ(x(t), u(t), t)=⎧

⎪

⎨

⎪

⎩

HP

k=1Wy[y(k)−y(k)ref ]2

+HC

k=1Wu[u(k)−u(k)ref ]2

+HC

k=1Wu[u(k|k+1)]2

(41)

subject to :⎧

⎪

⎨

⎪

⎩

y(k)lb <y(k)<y(k)up

u(k)lb <u(k)<u(k)up

u(k)lb <u(k)<u(k)up

(42)

where Wyand Wuare input and output weight factors for

each variable, and HPand HCare the prediction and control

horizons, respectively. The objective function was subjected to

a set of constraints, consisting of the fuel cell and electrolyzer

output power upper and lower limits (yub,ylb), current upper

and lower limits (uub,ulb), and the rate of change in the

electrolyzer and fuel cell current (u). The output power

upper and lower limits (yub,ylb)are deﬁned by the fuel cell

and electrolyzer power operating range.

Two sets of operating conditions, which correspond to 10%

and 90% of the rated power for the fuel cell and electrolyzer,

were used for model linearization. The resulting linear mod-

els are provided in Supporting Information. Based on these

linearized models, two MPC controllers were designed for

each unit. In each control period, a suitable controller is

chosen to enforce the remote power set point calculated by the

supervisory controller. If the signal value was <50% of the

rated power, the low operating range controller was selected.

Otherwise, the high operating range controller was chosen.

This strategy is advantageous, as it minimizes the model

mismatch by having multiple models while signiﬁcantly sim-

plifying its implementation, which is of particular importance

for real-time studies.

Aside from the power control, the fuel cell has two addi-

tional PI controllers which minimize the pressure difference

between the cathode and anode by manipulating the hydrogen

ﬂow and keep the desired air humidity by injecting the

appropriate amount of water vapor into the air stream entering

the cathode side, respectively.

176 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014

TAB L E I

SUMMARIZED SYSTEM COMPONENT SIZING USED IN SIMULATION

Wind system

Rated power 4kW

Cut-in speed 3m/s

Cut-out speed 12 m/s

Rated speed 7m/s

PV system

Rated power 120 W/panel

Total rated power 2.4 kW

PV array 20 ×2

Temperature 25 °C

Electrolyzer

Rated power 2.8 kW

H2Flow rate 8slpm

Output pressure 14 atm

H2Storage

Tank vo lum e 50 m3

Tank pressure 150–200 atm

Compressor pressure 200 atm

Fuel cell Rated power 1.9 kW

H2Flow rate 15 slpm

Load Power 1–2 kW

IV. RESULTS AND DISCUSSION

The proposed hybrid stand-alone system model consisting

of the previously described components was implemented

using the MATLAB and Simulink software. Model testing

was performed under various conditions using historical wind

data, irradiance, ambient temperature, as well as dynamic load

demand data. The sizing of the process components in the

existing stand-alone system is shown in Table I.

The sizing of the various process components was per-

formed according to the electricity energy balance for small

loads typical of residential demand. This load demand is

intermittent in nature, and it was assumed that its minimum,

maximum, and average alues are 0.5, 1.9, and 1 kW, respec-

tively. The sizing was performed according to the net power,

which is estimated based on the difference of the power

generated by wind and PV and the power demand at all times.

Assuming a capacity factor (combination of the overall unit

efﬁciency and the effect of geographical location) of 15% and

10% for the wind turbine and PV array, respectively, 4-kW

ratedwindpowerand2.4-kWPVrated power were estimated.

The fuel cell needs to supply the maximum load demand when

there is no sufﬁcient power generated by the PV and wind.

Therefore, the estimated size of the fuel cell stack is 1.9 kW.

The electrolyzer capacity should be adequate to use the surplus

power from the RE sources. The maximum excess power will

occur when there is minimum load and maximum power from

the RE sources, which corresponds to 6.4 kW of electrolyzer

capacity. However, the situation when both wind and solar

power reach their maximum points while the load demand is

at its lowest is very unlikely, and thus a 2.8 kW capacity for

the electrolyzer was used.

The presented simulation results are based on the average

weather data for a winter day in the Sarnia, Ontario region, and

the load demand for the installed stand-alone system. Table II

presents the PID tuning parameters for the various low-level

(c)

(b)

(a)

Fig. 6. RE conversion systems. (a) Wind speed and solar data. (b) Generated

power. (c) Pitch angle controller output for wind turbine.

controllers applied on the wind and fuel cell subsystems. In

this table, kc,τi,andτdare the proportional, integral, and

derivative constants, respectively.

The wind and irradiance data along with the corresponding

generated power is shown in Fig. 6(a) and (b). As was

mentioned previously, between the cut-in and rated speeds

(3 and 7 m/s) the WECS power control is regulating the

generator converter to generate the maximum possible power

by manipulating the turbine speed. Above the wind speed of 7

m/s, the pitch controller is maintaining the power at the rated

wind turbine power, as is shown in 6(c).

Fig. 7(a) shows the total generated power, the load

demand, and their difference (Pnet). The Pnet trend shown in

Fig. 7(a) is used to activate or deactivate the hydrogen system

components. Fig. 7(b) presents the electrolyzer and fuel cell

status throughout the simulation period. When Pnet >Pele,

TRIFKOVIC et al.: MODELING AND CONTROL OF A HYBRID RE SYSTEM WITH HYDROGEN STORAGE 177

TAB L E I I

CONTROLLER TUNING PARAMETERS

Wind pitch controller Reference pitch estimator PD controller: kc=35,τ

d=0.2

Pitch angle controller P controller: kc=500

Wind power controller

Rotor side current controller PI controller: kc=0.3,τ

i=0.037

Grid side current controller PI controller: kc=1,τ

i=0.01

Voltage controller PI controller: kc=0.02,τ

i=0.4

Fuel cell controller Hydrogen ﬂow controller PI controller: kc=1.2,τ

i=0.01

Air humidity controller P controller: kc=1

(a)

(b)

Fig. 7. Power balance and hydrogen system components activation. (a) Power

trends including net power, total generated RE and load demand with auxiliary

equipment consumption. (b) Electrolyzer and fuel cell activation/deactivation.

there is excess power available for hydrogen generation, which

will result in the activation of the electrolyzer at its rated

capacity. In the case of Pnet <0, the fuel cell is activated

to supply the power deﬁcit [see Fig. 7(b)].

As mentioned previously, the objective of the power man-

agement supervisory controller is not only to enable and

disable the hydrogen system components but also to send the

remote set point to the fuel cell and electrolyzer via Pnet.The

model predictive controller was designed for the electrolyzer

and fuel cell and then integrated with the nonlinear model of

the plant. The length of the prediction horizon affects both the

computational time and the performance of the system. The

prediction horizon (Wy) and control horizon (Wu)wassetto

15 and 8 intervals for the electrolyzer, and 10 and 4 intervals

for the fuel cell. The operational range for the electrolyzer and

fuel cell is 200–2800 and 100–1900 W, respectively. A variable

(b)

(a)

Fig. 8. Electrolyzer MPC. (a) Performance in terms of tracking net power.

(b) Generated hydrogen.

(b)

(a)

Fig. 9. Fuel cell MPC. (a) Performance in terms of power generated.

(b) Consumed hydrogen.

sampling time with maximum size of 1 s was used for data

measurement. The remote set point for the MPC controllers

was Pnet for the electrolyzer and |Pnet|for the fuel cell.

Figs. 8 and 9 show the performance of the MPC controllers

implemented for the electrolyzer and fuel cell, respectively.

The controllers show robust set-point tracking despite the

variation in the set points. It is important to note that the

hydrogen generation by the electrolyzer and its consumption

by the fuel cell are signiﬁcantly more efﬁcient. Also, note that

the ability to run the electrolyzer at lower capacity enables

its activation below its rated power (Prated

ele ). This in turn

results in using the RE more efﬁciently and, consequently,

in higher hydrogen generation. More importantly, MPC elim-

inates frequent turning on and off of the electrolyzer, which

can decrease the lifespan of the unit drastically. For the fuel

178 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 1, JANUARY 2014

cell, we demonstrate two criteria for the fuel cell activation

without the power controller (Fig. 9). In the ﬁrst criterion

(without MPC1), Pnet <0and|Pnet|>Pfc, which results in

the more conservativehydrogen usage but also fails to meet the

load demand. On the other hand, the second criterion (without

MPC2), Pnet <0and|Pnet|<Pfc, resulting in overgeneration

of electricity as the fuel cell is always operated at its rated

capacity with previously stored hydrogen depleting rapidly.

The implementation of the MPC eliminates these problems

and results in the successful demand tracking and adequate

hydrogen usage, as shown in Fig. 9.

V. CONCLUSION

A comprehensive detailed model for a stand-alone hybrid

energy system with wind turbine and solar energy conversion,

electrolyzer, fuel cell, and hydrogen storage components was

developed. A supervisory controller for proper power man-

agement and a set of local controllers for efﬁcient hydrogen

generation and consumption were implemented. A model

predictive controller was designed for optimal operation of the

electrolyzer and fuel cell. The controller performance showed

signiﬁcant improvement in the utilization of both components,

and consequently better power management of the hybrid

energy system could be achieved in comparison to the case

when there was no model predictive controller. Future work

will focus on the model validation and implementation of the

power management tool in real time on the hybrid system built

in Lambton College. We also plan to implement a dynamic

optimization formulation at the supervisory level which would

account for the weather and demand prediction to ensure

smooth operation and minimization of the operational cost.

ACKNOWLEDGMENT

The authors would like to thank F. Hernandez for his help

with data collection and S. Karimi for useful discussions.

REFERENCES

[1] “Annual energy outlook 2011,” U.S. Energy Inf. Administration, Wash-

ington, DC, USA, 2011.

[2] S. S. Dihrab and K. Sopian, “Electricity generation of hybrid PV/wind

systems in Iraq,” Renew. Energy, vol. 35, no. 6, pp. 1303–1307, 2010.

[3] R. Dufo-López and J. L. Bernal-Agustín, “Multi-objective design of

PV–wind–diesel–hydrogen–battery systems,” Renew. Energy, vol. 33,

no. 12, pp. 2559–2572, Dec. 2008.

[4] M. A. Elhadidy and S. M. Shaahid, “Promoting applications of hybrid

(Wind +Photovoltaic +Diesel +Battery)power systems in hot regions,”

Renew. Energy, vol. 29, no. 4, pp. 517–528, Apr. 2004.

[5] G. Giannakoudis, A. I. Papadopoulos, P. Seferlis, and S. Voutetakis,

“Optimum design and operation under uncertainty of power systems

using renewable energy sources and hydrogen storage,” Int. J. Hydrogen

Energy, vol. 35, no. 3, pp. 872–891, 2010.

[6] M. Soroush and D. Chmielewski, “Process systems opportunities in

power generation, storage and distribution,” Comput. Chem. Eng.,to

be published.

[7] M. H. Nehrir, C. Wang, K. Strunz, H. Aki, R. Ramakumar, J. Bing,

Z. Miao, and Z. Salameh, “A review of hybrid Renewable/Alternative

energy systems for electric power generation: Conﬁgurations, con-

trol, and applications,” IEEE Trans. Sustain. Energy, vol. 2, no. 4,

pp. 392–403, Oct. 2011.

[8] S. R. Vosen and J. O. Keller, “Hybrid energy storage systems for stand-

alone electric power systems: Optimization of system performance and

cost through control strategies,” Int. J. Hydrogen Energy, vol. 24, no. 12,

pp. 1139–1156, Dec. 1999.

[9] M. Santarelli, M. Cali, and S. Macagno, “Design and analysis of stand-

alone hydrogen energy systems with different renewable sources,” Int.

J. Hydrogen Energy, vol. 29, no. 15, pp. 1571–1586, Dec. 2004.

[10] D. Nelson, M. Nehrir, and C. Wang, “Unit sizing and cost analysis of

stand-alone hybrid wind/PV/fuel cell power generation systems,” Renew.

Energy, vol. 31, no. 10, pp. 1641–1656, 2006.

[11] H. Yang, L. Lu, and W. Zhou, “A novel optimization sizing model

for hybrid solar-wind power generation system,” Solar Energy, vol. 81,

no. 1, pp. 76–84, Jan. 2007.

[12] J. L. Bernal-Agustín and R. Dufo-López, “Simulation and optimiza-

tion of stand-alone hybrid renewable energy systems,” Renew. Sustain.

Energy Rev., vol. 13, no. 8, pp. 2111–2118, Oct. 2009.

[13] R. Karki and R. Billinton, “Reliability/cost implications of PV and wind

energy utilization in small isolated power systems,” IEEE Trans. Energy

Convers., vol. 16, no. 4, pp. 368–373, Dec. 2001.

[14] F. Valenciaga and P. F. Puleston, “Supervisor control for a stand-alone

hybrid generation system using wind and photovoltaic energy,” IEEE

Trans. Energy Convers., vol. 20, no. 2, pp. 398–405, Jun. 2005.

[15] W. Qi, J. Liu, X. Chen, and P. D. Christoﬁdes, “Supervisory predictive

control of standalone wind/solar energy generation systems,” IEEE

Trans. Control Syst. Technol., vol. 19, no. 1, pp. 199–207, Jan. 2011.

[16] C. Wang and M. H. Nehrir, “Power management of a stand-alone

wind/photovoltaic/fuel-cell energy system,” IEEE Trans. Energy Con-

vers., vol. 23, no. 3, pp. 957–967, Sep. 2008.

[17] S. Kim, J. H. Jeon, C. H. Cho, J. B. Ahn, and S. H. Kwon, “Dynamic

modeling and control of a grid-connected hybrid generation system with

versatile power transfer,” IEEE Trans. Ind. Electron., vol. 55, no. 4,

pp. 1677–1688, Apr. 2008.

[18] Ø. Ulleberg, T. Nakken, and A. Eté, “The wind/hydrogen demonstration

system at utsira in norway: Evaluation of system performance using

operational data and updated hydrogen energy system modeling tools,”

Int. J. Hydrogen Energy, vol. 35, no. 5, pp. 1841–1852, Mar. 2010.

[19] P. Hollmuller, J.-M. Joubert, B. Lachal, and K. Yvon, “Evaluation of

a5kW

pphotovoltaic hydrogen production and storage installation for

a residential home in Switzerland,” Int. J. Hydrogen Energy, vol. 25,

no. 2, pp. 97–109, 2000.

[20] D. Ipsakis, S. Voutetakis, P. Seferlis, F. Stergiopoulos, and C. Elmasides,

“Power management strategies for a stand-alone power system using

renewable energy sources and hydrogen storage,” Int. J. Hydrogen

Energy, vol. 34, no. 16, pp. 7081–7095, 2009.

[21] C. Ziogou, D. Ipsakis, C. Elmasides, F. Stergiopoulos, S. Papadopoulou,

P. Seferlis, and S. Voutetakis, “Automation infrastructure and operation

control strategy in a stand-alone power system based on renewable

energy sources,” J. Power Sour., vol. 196, pp. 9488–9499, Nov. 2011.

[22] Ø. Ulleberg, “Modeling of advanced alkaline electrolyzers: A sys-

tem simulation approach,” Int. J. Hydrogen Energy, vol. 28, no. 1,

pp. 21–33, Jan. 2003.

[23] Ø. Ulleberg, “The importance of control strategies in PV-hydrogen

systems,” Solar Energy, vol. 76, nos. 1–3, pp. 323–329, Jan.–Feb. 2004.

[24] C. Wang, M. H. Nehrir, and S. R. Shaw, “Dynamic models and model

validation for PEM fuel cells using electrical circuits,” IEEE Trans.

Energy Convers., vol. 20, no. 2, pp. 442–451, Jun. 2005.

[25] C. Wang, “Modeling and control of hybrid wind/photovoltaic/fuel cell

distributed generation systems,” Ph.D. dissertation, Monatana Univ.,

Missoula, MT, USA, 2006.

[26] A. L. Dimeas and N. D. Hatziargyriou, “Operation of a multiagent

system for microgrid control,” IEEE Trans. Power Syst., vol. 20, no. 3,

pp. 1447–1455, Aug. 2005.

[27] M. Trifkovic, M. Sheikhzadeh, K. Nigim, and P. Daoutidis, “Hierarchical

control of a renewable hybrid energy system,” in Proc. 51st IEEE Annu.

Conf. Decision Control, Dec. 2012, pp. 6376–6381.

[28] B. C. Babu and K. B. Mohanty, “Doubly-fed induction generator for

variable speed wind energy conversion systems-modeling & simulation,”

Int. J. Comput. Electr. Eng., vol. 2, no. 1, pp. 141–147, Feb. 2010.

[29] J. López, P. Sanchis, X. Roboam, and L. Marroyo, “Dynamic behavior

of the doubly fed induction generator during three-phase voltage dips,”

IEEE Trans. Energy Convers., vol. 22, no. 3, pp. 709–717, Sep. 2007.

[30] W. Qi, J. Liu, and P. D. Christoﬁdes, “A distributed control framework

for smart grid development: Energy/water system optimal operation

and electric grid integration,” J. Process. Control, vol. 21, no. 10,

pp. 1504–1516, Dec. 2011.

[31] W. Leonhard, Control of Electrical Drives. New York, USA: Springer-

Verlag, 2001.

[32] H. Bourdoucen and A. Gastli, “Tuning of PV array layout conﬁgurations

for maximum power delivery,” Int. J. Electr. Inf. Eng., vol. 2, no. 4,

pp. 211–217, 2008.

TRIFKOVIC et al.: MODELING AND CONTROL OF A HYBRID RE SYSTEM WITH HYDROGEN STORAGE 179

[33] A. Marshall, B. Borresen, G. Hagen, M. Tsypkin, and R. Tunold,

“Hydrogen production by advanced proton exchange membrane (PEM)

water electrolysers-reduced energy consumption by improved electro-

catalysis,” Energy, vol. 32, no. 4, pp. 431–436, 2007.

[34] H. Görgün, “Dynamic modeling of a proton exchange membrane (PEM)

electrolyzer,” Int. J. Hydrogen Energy, vol. 31, no. 1, pp. 29–38, 2006.

[35] T. V. Nguyen and R. E. White, “A water and heat management model for

proton-exchange-membrane fuel cells,” J. Electrochem. Soc., vol. 140,

no. 8, pp. 2178–2186, 1993.

[36] S. Dutta, S. Shimpalee, and J. Van Zee, “Numerical prediction of mass-

exchange between cathode and anode channels in a PEM fuel cell,” Int.

J. Heat Mass Transfer, vol. 44, no. 11, pp. 2029–2042, 2001.

[37] N. Dale, M. Mann, and H. Salehfar, “Semiempirical model based

on thermodynamic principles for determining 6 kW proton exchange

membrane electrolyzer stack characteristics,” J. Power Sour., vol. 185,

no. 2, pp. 1348–1353, 2008.

[38] J. T. Pukrushpan, A. G. Stefanopoulou, and H. Peng, Control of Fuel Cell

Power Systems: Principles, Modeling, Analysis, and Feedback Design.

New York, USA: Springer-Verlag, 2004.

[39] B. J. T. Pukrushpan, A. G. Stefanopoulou, and H. Peng, “Avoid fuel cell

oxygen starvation with air ﬂow controllers,” IEEE Control Syst. Mag.,

vol. 24, no. 2, pp. 30–46, Apr. 2004.

[40] M. Arcak, H. Görgün, L. M. Pedersen, and S. Varigonda, “A nonlinear

observer design for fuel cell hydrogen estimation,” IEEE Trans. Control

Syst. Technol., vol. 12, no. 1, pp. 101–110, Jan. 2004.

[41] Z. Jiang and R. A. Dougal, “Hierarchical microgrid paradigm for

integration of distributed energy resources,” in Proc. IEEE Power Energy

Soc. General Meeting—Convers. Del. Electr. Energy 21st Century,Jul.

2008, pp. 1–8.

[42] V. Akhmatov, “Variable-speed wind turbines with doubly-fed induction

generators, part I: Modelling in dynamic simulation tools,” Wind Eng. ,

vol. 26, no. 2, pp. 85–108, 2002.

[43] R. Pena, J. Clare, and G. Asher, “A doubly fed induction generator

using back-to-back PWM converters supplying an isolated load from a

variable speed wind turbine,” IEEE Proc. Electr. Power Appl., vol. 143,

no. 5, pp. 380–387, Sep. 1996.

[44] M. A. S. Masoum, H. Dehbonei, and E. F. Fuchs, “Theoretical and

experimental analyses of photovoltaic systems with voltage- and current-

based maximum power-point tracking,” IEEE Trans. Energy Convers.,

vol. 17, no. 4, pp. 514–522, Dec. 2002.

[45] T. Esram and P. L. Chapman, “Comparison of photovoltaic array max-

imum power point tracking techniques,” IEEE Trans. Energy Convers.,

vol. 22, no. 2, pp. 439–449, Jun. 2007.

[46] D. M. Raimondo, L. Magni, and R. Scattolini, “Decentralized MPC of

nonlinear systems: An input-to-state stability approach,” Int. J. Robust

Nonlinear Control, vol. 17, no. 17, pp. 1651–1667, 2007.

Milana Trifkovic received the B.S.E. and Ph.D.

degrees in chemical engineering from the University

of Western Ontario, London, ON, Canada, in 2006

and 2010, respectively.

She is a Post-Doctoral Fellow with the Department

of Chemical Engineering and Materials Science,

University of Minnesota, Minneapolis, MN, USA.

Her current research interests include polymer mate-

rial processing, RT control systems, microgrids, and

distributed generation.

Mehdi Sheikhzadeh received the B.S.E. degree

from Ferdowsi University, Mashhad, Iran, the M.S.E.

degree from the Sharif University of Technology,

Tehran, Iran, in 1997 and 1999, respectively, and

the Ph.D. degree from the University of Western

Ontario, London, ON, Canada, all in chemical engi-

neering.

He is currently an Industrial Research Chair at

Colleges granted by the Natural Sciences and Engi-

neering Research Council of Canada and is a Profes-

sor of the Instrumentation and Control Program with

Lambton College. His current research interests include modeling, advanced

process control and optimization of energy systems.

Khaled Nigim (M’85–SM’00) received the Ph.D.

degree in electrical engineering from the University

of Leicester, Leicester, U.K., in 1983.

He is currently the Research Lead in develop-

ing power management controller in the renew-

able energy conversion and storage research project

funded by NSERC, and is a registered Professional

Engineer in Ontario, Canada. His current research

interests include renewable energy resources integra-

tion, islanding strategy, challenging and opportuni-

ties of distributed generation fuelled by alternative

energy sources, the development of AC and DC micro-grid concepts as well as

reactive power compensation for wind farms and photovoltaic energy parks.

Prodromos Daoutidis received the Diploma degree

in chemical engineering from the Aristotle Univer-

sity of Thessaloniki, Thessaloniki, Greece, and the

M.S.E. degrees in chemical engineering and elec-

trical engineering systems and the Ph.D. degree in

chemical engineering from the University of Michi-

gan, Ann Arbor, MI, USA, in 1987, 1988, and 1991,

respectively.

He is a Professor with the Department of Chemical

Engineering and Materials Science, University of

Minnesota, Minneapolis, MN, USA. His current

research interests include control of nonlinear and distributed parameter

systems, control of differential algebraic systems, model reduction, chemical

and biological reaction systems, control of advanced materials processing, and

design and control of energy systems.