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
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 .
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 –. 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: email@example.com; firstname.lastname@example.org).
M. Sheikhzadeh and K. Nigim are with the Department of Instrumentation
and Control, Lambton College, Sarnia, ON N7S 6K4, Canada (e-mail:
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) .
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 . 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 –.
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
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 , , –, with only a few dealing
with real-time application – 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 –, , –.
The importance of a control strategy for the optimal oper-
ation of the photovoltaic (PV)/hydrogen/battery systems has
been shown previously . 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 . 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 . 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 .
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 , , and 
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 
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 , :
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 . 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 . 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 :
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
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
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 
Ipv =Isc −ID−VD
Vpv =VD−RSIpv (11)
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
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 . The reactions
that take place at the anode and the cathode of a PEM
electrolyzer are described below
Anode Reaction :H2O→2H++1
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
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 . Electrochemistry principles
are used to calculate the rates of oxygen generation Ngen
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
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 .
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
The rate of hydrogen generated in the water-splitting reac-
H2, is a function of the stack current
The water transport through the membrane is achieved by
electro-osmotic drag and diffusion phenomena , . 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
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 .
The total electrolyzer voltage can be represented as
Vele =Eele +Vact
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
 and 
2FGele +RTele ln pele
where Ris the universal gas constant, Gele is the Gibbs free
energy of formation, Tele is the absolute temperature, αele
is the water activity between the anode and the electrolyte,
Fig. 4. Fuel cell modeling block diagram.
O2are the partial pressures of hydrogen, and
oxygen, respectively. The activation polarization is a function
of the current density ¯
Iele, the exchange current density ¯
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
Assuming a lumped thermal capacitance model, the overall
thermal energy balance can be expressed as  and 
where Cele is the overall heat capacity of the electrolyzer, ˙
is the heat power generated inside the electrolyzer stack, ˙
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)
where Vth is the thermal voltage, T0is the ambient tem-
ele is the thermal resistance, Cm
ele is the cooling
medium overall heat capacity, and Tmis the cooling medium
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  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:
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 . 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 .
The fuel cell voltage is calculated based on voltage drops
associated with all the losses as follows:
Vfc =Efc −Vact
where Vfc is the fuel cell voltage, Efc is the open-circuit
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:
Ifc is the fuel cell current density, Vact
0is the voltage
drop at zero current density, and a cact and cconc and ¯
constants that depend on the temperature and reactant partial
pressure and are obtained empirically .
The heat generated by the fuel cell chemical reaction can
be written as
Qgen is the heat generated from chemical reaction, ˙
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:
Qelec =Vfc Ifc
Qloss =hfc Afc (Tfc −Tamb)
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 , ,
E. Hydrogen Storage System
Hydrogen storage consists of a compressor and a hydrogen
tank. The required compression work can be estimated as
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
dt tank =Nin
dt fc −Nout
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 
where Ptank is the tank pressure, Vtank is the tank volume, and
a1–a5are empirical parameters .
III. CONTROL ARCHITECTURE
A multilevel control scheme has been reported as a more
practical and efﬁcient hierarchy for controlling hybrid energy
systems . 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
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)
If Pnet >0&Ptank ≥Pub
If Pnet <0&Ptank ≥Plb
If Pnet <0&Ptank <Plb
If (Pnet =0)
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.
If Pnet >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
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 , .
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 ,
. The perturbation and observation method (P&O) is one
of the most common and effective ways of power tracking
for PV arrays . In this paper, the current perturbation
and observation method (CP&O) is applied . 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 . 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
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
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
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
uJ(x(t), u(t), t)=⎧
subject to :⎧
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
Rated power 4kW
Cut-in speed 3m/s
Cut-out speed 12 m/s
Rated speed 7m/s
Rated power 120 W/panel
Total rated power 2.4 kW
PV array 20 ×2
Temperature 25 °C
Rated power 2.8 kW
H2Flow rate 8slpm
Output pressure 14 atm
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
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
Pitch angle controller P controller: kc=500
Wind power controller
Rotor side current controller PI controller: kc=0.3,τ
Grid side current controller PI controller: kc=1,τ
Voltage controller PI controller: kc=0.02,τ
Fuel cell controller Hydrogen ﬂow controller PI controller: kc=1.2,τ
Air humidity controller P controller: kc=1
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
Fig. 8. Electrolyzer MPC. (a) Performance in terms of tracking net power.
(b) Generated hydrogen.
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.
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.
The authors would like to thank F. Hernandez for his help
with data collection and S. Karimi for useful discussions.
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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
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-
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,
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.