2. systems is strongly limited by the intermittent nature of the
wind [4,5]. To overcome this problem, they can be associated
to energy storage systems in order to continuously supply the
load [6,7]. One of the major aspects of this configuration is the
reliable supply of power at a reduced cost. Hydrogen subsys-
tem can handle production fluctuation over long periods [8,9].
In addition, on-site hydrogen generation and storage is
beneficial for complete energy independence and continuous
service [10e13]. In such a context, hydrogen could provide an
excellent mean for storing excess renewable energy [14] for
use during low wind speed period. However, due to the slow
dynamics of fuel cells and electrolyzers, it is interesting to
associate them with battery and supercapacitors storage
systems, for higher dynamic requirements. Therefore, it ari-
ses problems of configuration, energetic reliability and system
cost.
Several researches with the aim of providing a viable so-
lution to these problems were undertaken. In Ref. [15], T
egani
and al have applied to a hybrid stand-alone photovoltaic (PV)
and wind generator (WG) systems, a methodology for optimal
sizing and strategy control based on differential flatness
approach. The purpose was to find the optimal number of
units ensuring that the system cost is minimized subject to
the constraint that the load requirements are completely
covered. The system cost is the sum of capital and mainte-
nance cost. The energy management strategy is presented to
control the energy flows between the PV-WG, load and bat-
teries as hybrid sources to supply a residential household.
Karim and al [16] developed an optimal design for a hybrid
solar-wind energy plant taking into account the number of PV
modules, the number of wind turbines, the wind turbine
height and the turbine rotor diameter as variables to minimize
the cost. The result shows the complementary relationship
between PV and wind generator over the different season of
the year. In Ref. [17], power management strategies for a
stand-alone power system using renewable energy sources
and hydrogen storage are presented. Three power manage-
ment strategies that comprise energy generation from
renewable energy sources (RES) and hydrogen production
have been developed by the author. Each power management
strategy is assessed on its capacity to meet the power load
requirements through effective utilization of the electrolyzer
and fuel cell under variable energy generation from RES. In
Ref. [18], a system that couples several renewable energy
sources and storage mean is used to supply a small commu-
nity in remote area. A genetic algorithm optimization has
shown that it’s possible to obtain a system supplying energy
with a minimum cost. The design depends on the meteoro-
logical characteristics of the site as well as the consumption
profile. In Ref. [19], GA (Genetic Algorithm) and PSO (Particle
Swarm Optimization) algorithms are used to find the opti-
mum sizes of the hybrid energy systems among numerous
configurations, obtained by considering LPSP constraint, to
reach the expected reliability and the lowest LCOE (Levelized
Cost of Energy). The hybrid system is composed of wind, PV,
FC (fuel cell) and battery. In Ref. [20], an optimal sizing method
of a stand-alone hybrid power system based on PV/WG/bat-
tery/hydrogen with improved Ant Colony Optimization (ACO),
for reliable and economic energy supply, is proposed. Two
objectives that take the minimum annual system cost and
maximum system reliability described as the LPSP have been
addressed for sizing. Authors in Ref. [21], deals with the opti-
mization of the design of a PV/WG/FC system based on the
minimization of the overall 20-year cost energy using a
modified PSO algorithm. The result of the modified PSO algo-
rithm is compared with those of the common PSO. The pro-
posed hybrid solution procedure (modified PSO) has better
results than common PSO with respect to capital investment
cost minimization and system reliability level. In Ref. [22], a
techno-economic study of a PV-hydrogen-battery hybrid sys-
tem for off-grid power taking into account impact of perfor-
mances ‘ageing on optimal system sizing is presented. The
results show that hybridizing battery with hydrogen is more
cost beneficial than photovoltaic-battery solution. Moreover,
it show that taking into account the degradation of hydrogen
chain does not impact the optimal results.
In this paper, the optimization of a wind, fuel cell, elec-
trolyzer, battery and supercapacitors system for off-grid ap-
plications regarding the system cost and energetic reliability is
presented. The optimization process is performed using
NSGAII algorithm on the bases of total annualized cost mini-
mization and reliability enhancement. The reliability index
considered is this work is the LPSP.
In order to show the dependency of the results with the
wind profile, sensitivity analysis versus changes in wind
profile and subsystems cost are carried out.
In section System operating strategy, the system operating
strategy is introduced, in section System sizing methodology
and problem formulation the sizing methodology and the
problem formulation. Section Hybrid system component
modeling deals with component modeling, section
Simulation and results simulation and results and section
Conclusion conclusion.
System operating strategy
The system topology is depicted in Fig. 1. In this topology the
supercapacitors are used to handle the dc bus. The advantage
of this topology is to ensure a better protection of the battery
during fast power request transition. This hybrid system
should be able to supply the energetics needs of a residential
household.
The wind generator is used as the main source while the
supercapacitors, battery, fuel cell and electrolyzer are back-up
Fig. 1 e The system illustration figure.
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3. energy sources. The dotted arrows indicate the possible en-
ergy flows direction during charging mode or when the power
generated by the wind generator is greater than the load
power requirement.
The household energy consumption is related to the
occupant behavior, the climatic season and the electrical ap-
pliances. For our work, a four-room house with 6 inhabitants
will be considered. The power consumption profile is evalu-
ated according to the electrical appliances available:
A fridge Aþþþ 300 L (400 kW h/year), two air conditioners,
one in the living room and one in the principal bedroom
(960 kW h/year), a washing machine AAA 5 kg category
(135 kW h/year), a dishwasher AAA (252 kW h/year), a com-
puter (107 kW h/year), 12 economic lamp (240 kW h/year) and
a microwave oven (90 kW h/year). For more details on elec-
trical appliance consumption refer to Refs. [23,24]. It is
assumed that the load power profile is the same for all the
days of the week. The average daily energetic need of this
residential household is about 15 kWh. On Fig. 2 below the
deriving household power profile for a week day is given.
According to the amount of power generated by the main
source, we can determine two main operation modes:
If the power generated by the wind turbine generator is less
than the load power requirement, the secondary source
will work to bridge the energetic gap according to storage
system States Of Charge (SOC) evaluation. SOCSC (t),
SOCSCMIN, SOCSCMAX are respectively the supercapacitor
SOC at time t, minimum and maximum SOC. SOCB (t),
SOCBMIN, SOCBMAX are respectively the battery SOC at time
t, minimum and maximum SOC. If SOCSC (t) SOCSCMIN,
then the deficit power will be supplied by the super-
capacitors till the SOCSC (t) equals SOCSCMIN. If the load is
not totally supplied and SOCB (t) SOCBMIN, the battery will
start to supply until SOCB (t) reaches its minimum value.
Then the fuel cell will be started in order to supply the load.
If the deficit power exceeds the fuel cell rated power or the
stored hydrogen cannot afford it, some percentage of the
load demand is unmet.
If the power generated by the wind generator is higher than
the load power requirements, then the extra power will be
stored in the storage system according to SOC evaluation. If
SOCSC (t) SOCSCMAX, then the extra power will be trans-
ferred to the supercapacitors till the SOCSC (t) equals
SOCSCMAX. If the surplus is not exhausted and SOCB
(t) SOCBMAX, power will be transferred to the battery until
SOCB (t) reaches its maximum value. Then the electrolyzer
will be turned on to produce hydrogen if the power is
within its operating range and if the hydrogen tank is not
full. If there are remaining extra power, it will be sent to a
dump load.
The characteristics of the considered components for the
hybrid system are given in the following Table 1.
The system operating strategy is detailed in the diagram
below (Fig. 3).
System sizing methodology and problem
formulation
Sizing methodology
Using the average hourly wind data and the load power de-
mand the difference between the total generated and
consumed power is calculated at each time step for different
combinations of each component of the hybrid system.
Moreover, for each combination, the total cost is also evalu-
ated. The combination with the lowest cost and the lowest
power difference is chosen. The diagram of the methodology
is given on Fig. 4:
Problem formulation
The problem consists in minimizing objectives functions
under certain conditions. The decision variables that will be
considered here are the number of supercapacitor cell (Nscap),
the number of battery cell (Nbat), the number of fuel cell
module (Nfc), the number of electrolyzer (Nel), the mass of
hydrogen stored (mH), the number of wind generator (Nw) and
the height of the wind tower (Hw).
At the end of the operation time, it is important to keep the
energy in the battery, the supercapacitors and hydrogen
storage tank around their initial levels, in order to be able to
provide a fair evaluation. This condition will be expressed by
(1):
SOCi
tf
SOCiðt0Þ
0:1 (1)
where SOCi(tf) and SOCi(t0) are respectively the final and initial
SOC of storage system i.
The main objective of this hybrid system is the reliable
supply of power at the lowest possible cost. The system
Fig. 2 e The household load power demand.
Table 1 e The characteristics of the system components.
Component Power/capacity/
capacitance
Nominal
voltage
Life
span
Wind turbine [25] 1 kW 20 years
Fuel cell [26] 1.2 kW 26 V 5 years
Electrolyzer [27] 1 kW 5 years
Li-ion Battery [28] 45 A h 3.6 V 10 years
Supercapacitor [29] 2600 F 2.7 V 10 years
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4. reliability is based on the LPSP, which is the ability of the
system to meet the load power demand. It is evaluated as the
ratio of unmet energy and the total energy required by the
load. IfPdeficitðtÞ is the unmet load power demand, at each time
step the power balance in the system imposes:
Pdc Load ¼ Pdc WðtÞ þ Pdc BATTðtÞ þ PSCðtÞ þ Pdc FCðtÞ þ PdeficitðtÞ (2)
The LPSP is given by Refs. [30e32]:
f1 ¼ LPSP ¼
P
T
t¼1
PdeficitðtÞ:Dt
P
T
t¼1
Pdc loadðtÞ:Dt
(3)
where T and Dt are respectively the simulation time and step
of time. In this work, the LPSP is assumed being less or equal
to 5%.
Fig. 3 e Block diagram of the system operating strategy.
Fig. 4 e Diagram of the optimal sizing methodology.
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5. The system financial analysis that is used here is based on
the Total Annualized Cost (TAC). The TAC consists of the total
annual capital costðCCAPÞ, the total annual maintenance and
operation cost ðCOMÞ and the total annual replacement
costðCREPÞ[33e35]. The cost function is then given by:
f2 ¼ CCAP þ COM þ CREP (4)
Cost function modeling
The annual capital cost is obtained from the initial cost of
each component. The wind turbine installation cost is
considered as 25% [36] of its initial cost. The other component
installation costs are neglected. Then, the total initial cost of
the system is given by Ref. [34]:
Cinit ¼ Enom:CBATT þ
X
j
Nj:Cj (5)
Where Nj and Cj are respectively the number of elements
and the initial cost of the component j. This initial cost can be
converted into annual cost by considering the Capital Recov-
ery Factor (CRF), which is given below [33e35]:
CRF ¼
i:ði þ 1Þ
a
ði þ 1Þ
a
1
(6)
where i is the annual interest rate. It consists on the rate at
which a loan can be obtained (iloan) and the inflation rate f. It is
calculated as follow [36]:
i ¼
iloan f
1 þ f
(7)
iloan and f will be taken equal respectively to 5% and 2%. The
annual capital cost is then [37]:
CCAP ¼ Cinit:CRF (8)
The annual maintenance cost is estimated 8% of the wind
tower cost, inverter cost, supercapacitors and battery cost.
The annual maintenance and operating cost is given as follow
[34]:
COM ¼
X
k
Nk:COM k
:ð1 þ fÞ
a
(9)
where Nk and COM k are the number of element and the first
year maintenance cost of the component k.
The annual replacement cost is the sum of the annualized
value of all the replacement cost occurring during the
component lifespan. Here according to the system lifespan,
the supercapacitors, the battery, the fuel cell, the electrolyzer,
the hydrogen tank and the inverter will be replaced. To define
the annual replacement cost, the Sinking Fund Factor (SFF) of
each component should be considered. It is a ratio used to
calculate the future value of a series of equal annual cash
flows. It is given by Refs. [38,39]:
SFFði; componentlifeÞ ¼
i
ð1 þ iÞ
componentlife
1
(10)
CREP ¼
X
j
Nj:Cj REP:SFFðiÞ (11)
where Nj and Cj_REP are respectively the number of element
and the replacement cost of component j.
Non-dominated sorting genetic algorithm (NSGAII)
To solve this optimization problem, the genetic algorithm will
be used. In fact, genetic algorithms are appropriate to solve
multi-objectives nonlinear and linear functions precisely and
efficiently. This algorithm has been used in many sizing works
[34e47]. The method is to randomly generate an initial popu-
lation with a uniform distribution [48]. Then a fast non-
dominated sorted is used to rank the population front and the
crowded distance is calculated in the same front. Then two
individuals randomly selected are subjected to a tournament
selection. If the two individuals come from different front, the
one with the lower front number is selected. In the contrary the
individual with higher crowding distance is selected. And then
throughout crossover and mutation operators an offspring
generation is generated. Finally, the parents and offspring
generation are combined and ranked by using a fast non-
dominated sorting and crowding distance assignment proced-
ure. The best individuals are selected as the new parent popu-
lation. The diagram of the algorithm operation is given below:
This algorithm has been modified to solve our problem.
According to the hybrid storage SOC value, the objectives
functions are penalized in order to select the individual with
lowest cost and LPSP value that satisfied the SOC constraints:
If │SOCj(tf) e SOCj(t0)│ 0.1, the objectives functions are
evaluated according to the expression given in (4) and (5);
If │SOCj(tf) e SOCj(t0)│ 0.1, the objectives functions are
multiplied by a penalty factor. To eliminate all the unde-
sirable solutions, the penalty factor must be taken as great
as possible. Here it is set to 109
.
Hybrid system component modeling
The wind turbine
The wind turbine used in this work is the BWC XL.1 [49].
Considering that the turbine operates at its maximum power
point, a simple model can simulate the output power:
PW ¼
8
:
a1:V3
þ b1:V2
þ c1:V þ d1; VC in V VR
a2:V3
þ b2:V2
þ c2:V þ d2; VR V Vfurl
a3:V3
þ b3:V2
þ c3:V þ d3; Vfurl V VC out
0; V VC out or V VC in
(12)
The triplet (ai, bi, ci) has been determined by the polyfit
function of MATLAB and:
V ¼ Vref :
HW
Href
b
(13)
where VR, VC_in, VC_out and Href are respectively the rated wind
speed, the cut-in and cut-out wind speed, and the reference
height. The cut in speed is the minimum wind speed at which
the turbine blades overcome friction and begin to rotate. The
cut out speed, is the speed at which the turbine blades are
brought to rest to avoid damage from high wind and the
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6. reference height is the height at which the wind speed is
measured (see Fig. 5).
The supercapacitors
A simple Zubieta's model (Fig. 6) [50] will be considered here to
model the supercapacitors bank.
The state equation is given by:
SOC
SCðtÞ ¼
Q
SCðtÞ
QSC MAX
(14)
where QSC (t) is the supercapacitors electrical charge at time t.
from (22) the state of charge at each time step is deduced as
follow:
SOCSCðtÞ ¼ SOCSCðt DtÞ
ISCðtÞ:Dt
CSC:VSC MAX
(15)
With:
SOCSCMIN SOCSCðtÞ SOCSCMAX (16)
To determine the maximum and minimum number of cells
in the supercapacitors bank, the voltage drop expression will
be considered [45,51]:
DVSC ¼ ISC AV:
0
B
B
@
t
NP
NS
CSC cel
þ
NS
NP
RSC cel
1
C
C
A (17)
Where t, NP, DVSC and NS are respectively the discharge
time, the number of parallel branches, the voltage drop and
the number of cell in series, ISC_AV is the average current. If
PSCMAX is the maximal, power delivered by the supercapacitors
and VSCMAX, VSCMIN respectively the maximum and minimum
voltages,
ISC AVMIN ¼
PSCMAX
VSCMAX
: (18)
ISC AVMAX ¼
PSCMAX
VSCMIN
: (19)
From (27) and (28) the maximum and minimum values of
parallel branches can be deduced using the following
expression:
NP ¼
ISC:NS
DVSC
:
t
CSC cel
þ RSC cel
(20)
The number of cells in series is determined according to the
DC bus voltage. In this work, a DC-bus voltage of 48 V with a
limited variation of±10% is considered. This means 52.8 V for
the DC-bus maximum voltage and 43.2 V for the DC-bus min-
imum voltage. As the supercapacitors are directly connected to
the dc bus, the number of cell in series and the range of SOC
variation should be selected so to satisfy the dc bus require-
ment. For the dc bus given characteristics and the voltage and
the admissible voltage fluctuation, the number of cell in series
is set to 20, with a SOC varying between 0.8 and 0.98. If
PSCMAX ¼ 2200W for a discharge time t ¼ 1 min, then NP є [1,5].
The battery
If EBAT (t) is the energy available in the battery and PBAT (t) is the
power exchanged at step time t [33,52]:
EBATðtÞ ¼ EBATðt DtÞ PBATðtÞ:Dt (21)
The state of charge is the given by:
Fig. 5 e Diagram of NSGAII algorithm.
Fig. 6 e Supercapacitor model (model of Zubieta and
Bonert).
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7. SOCBðtÞ ¼ SOCBðt DtÞ
PBATðtÞ:Dt
Enom
(22)
where Enom, the battery nominal energy is given by:
Enom ¼ Nbat:VBAT nom:QBAT nom (23)
where Nbat, VBAT_nom and QBAT_nom are respectively the number
of battery cells, the battery nominal voltage and nominal
capacity.
The state of charge is constrained by:
SOCBMIN SOCBðtÞ SOCBMAX (24)
The battery autonomy A is an important parameter that
must be taken into account in the optimal sizing process,
because it is among the decisive parameters of the system
ability to handle the load demand during low wind speed
period. So if the average power demand by the load is
Pdc_Load_av, the nominal energy of the battery is calculated as
follow [45]:
Enom ¼
A:Pdc Load av
ðSOCBMAX SOCBMINÞ:hbatt:h2
inv
(25)
NBATT ¼
A:Pdc Load av
ðSOCBMAX SOCBMINÞ:hbatt:h2
inv:Enom cell
(26)
where Enom_cell is the battery cell nominal energy. The battery
is the middle term storage unit. Its maximum autonomy is
assumed to be a day. The number of battery cells in series is
determined according to the dc bus voltage. Here it can be set
to 7. ThenNBATT2½7; 154.
The fuel cell
The fuel cell is supplied from the chemical energy available. If
hFC is the fuel cell system overall efficiency, the relationship
between the electrical power produced and the chemical
power received is given by:
hFC:n:F:E:N
H2 R
¼ PFCðtÞ (27)
where n is the number of electrons released per mole of
hydrogen. The hydrogen reacted molar flow is then deduced
[53]:
N
H2 R
¼
PFCðtÞ
hFC:n:F:E
(28)
The constraints on the produced power are as follow:
PFC min PFCðtÞ PFC max (29)
PFC_min is a fraction of PFC_max, 10% in this work.
PFC max ¼ NFC:PFC nom (30)
Where PFC_nom is the fuel cell module, nominal power and
NFC the number of fuel cell module. In case of low wind speed,
the fuel cell must be able to provide the whole energy needed
by the load. According to the maximum hourly power de-
mand, and the nominal power of the fuel cell,
NFC
PLoad max
PFC nom
(31)
The electrolyzer
With the current technologies, the electrolyzer has a mini-
mum operating point between 10% and 50% of its nominal
power. The operating power is then constrained by a
maximum and minimum value.
PELEC min PELECðtÞ PELEC max (32)
PELEC max ¼ NELEC:PELEC nom (33)
PELEC_nom is the electrolyzer module nominal power and
NELEC the number of electrolyzer module.
PELEC min ¼ 10%:PELEC max (34)
By analogy with (36), the hydrogen molar flow produced is
expressed as [48]:
N
H2 P
¼
hELEC:PELECðtÞ
n:F:E
(35)
where hELEC is the electrolyser system overall efficiency.
The hydrogen tank
To reduce the system cost, the maximum pressure of the
hydrogen tank is assumed equal to the electrolyzer operating
pressure. The minimum pressure is equaled to the fuel cell
minimum operating pressure. The amount of hydrogen stored
is given by Ref. [54]:
NH2
ðtÞ ¼ NH2
ðt DtÞ þ
N
H2 P
N
H2 R
:Dt (36)
The hydrogen state of charge can be deduced from the
ideal gas law as follow:
HSOCðtÞ ¼ NH2
ðtÞ:
R:Ttan k
PH2 max:Vtan k
(37)
where, Ttank, Vtank and PH2_max are respectively the hydrogen
tank temperature, volume and maximum pressure. The con-
straints on the state of charge are given in (38):
HSOC MIN HSOCðtÞ HSOC MAX (38)
The amount of hydrogen stored is responsible for the
system autonomy and constitutes the long-term storage unit.
For a desired autonomy of 4 days, with a daily energy de-
mand Edem ¼ 15 kWh, the mass of hydrogen needed consid-
ering the global (fuel cell and hydrogen destocking) efficiency
hFC ¼ 0.5 [55,56], the amount of hydrogen needed must be so
that:
mH ¼
4:Edem
EH:hFC:h2
inv
(39)
where EH is the chemical energy contained in 1 kg of
hydrogen. The mass maximum mass hydrogen needed
here is about 4.5 kg. Due to low wind speed values, mH (kg) є
[1,9].
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8. Simulation and results
Optimal sizing results
The different costs (see Table 2) and the decision variables
bounds (see Table 3) are given is the following tables.
The simulations are based on two months wind and load
profiles. The wind speed data for the period from January, 1st
to December 31st, 2017 for Tanda (Ivory Coast) at a height of
10 m are available on [61]. The wind speed profile that will be
considered for simulation is given below (Fig. 7).
In this work, the solutions to be considered are those with a
LPSP less or equal to 5%. The table below gives the results
obtained for the specified load power profile (Fig. 8).
The best results of the simulations are given in the
following table (Table 4).
The results show a large amount of excess power (dump
load). In fact we have a low average wind speed of 3.84 m s1
while the maximum and minimum wind speed are respec-
tively 11.8 m s1
and 0.11 m s1
, which induces large wind
speed variation around the average value, resulting in high or
low wind energy production. Therefore, backup sources must
have enough capacity to meet the power requirement. More-
over, the reliability and the cost evolve in the same direction.
Indeed, when the reliability increases the TAC increases too
and vice versa. Therefore, the most reliable configuration will
be the most expensive. If the reliability is the most important
parameter, then the results to be considered is S2, but if the
cost is most important then the S6 shall be considered. The
retained solution is S3, WHICH gives about 96.5% of satisfaction
in the load power requirement for about 24% of unutilized
excess power. The battery and supercapacitor state of charge,
the energy stored in the hydrogen tank and the DC bus voltage
are given below (Fig. 9).
In the following figure the contribution of each source in
the load requirement is depicted. It is notice that the load is
satisfied with about 60% of wind energy, 28% of fuel cell en-
ergy, 10% of battery energy and about 0.4% of supercapacitor
energy (see Fig. 10).
For better view of each source contribution the following
figure, give the contribution during 2 weeks operation. B if for
battery, FC for fuel cell and SC for supercapacitor (see Fig. 11).
Sensitivity analysis
Sensitivity analysis is important to determine the effect of
uncertainty or changes in the variables, which do not
depend of the designer such as average wind speed, sub-
system cost. In this section, the effect of changes wind
profile and component cost variation on the overall system
cost is evaluated. It will help determining where the un-
certainties lay, identify the worst influential parameters
and testify the robustness of the optimal solution.
Sensitivity versus changes in wind profile
The wind speed of Tanda varies from 0 m s1
to 11.8 m s1
with an average of 3.84 m s1
. The analysis of TAC versus wind
profile will be made for wind average values between
3.84 m s1
and 11.8 m s1
. The characteristics of wind profile,
Fig. 7 e Wind speed profile for Tanda (year 2017).
Table 2 e The cost of the system component.
Component Initial
cost (V)
Maintenance
cost (V/year)
Replacement
cost (V)
Wind tower 55/m [43] 4.4
Wind turbine 5808/kW [54] 21/kW
Battery 496/kW.h [58] 40/kW.h 496/kW.h
Supercapacitor 23 [59] 2 23
Fuel cell 8270 [60] 205 7088
Electrolyzer 1524 [60] 1143 76
Hydrogen tank 990/kg [60] 11
Power converters 283/kW [54] 8 283/kW
Table 3 e Decisions variables and constraints limits.
Component D
ecisions
variables
Range State of
charge limits
Wind turbine Nw [1,10]
Wind tower Hw(m) [10,30]
Battery Nbat [7; 149] [0.2; 0.9]
Supercapacitor Nscap [40; 100] [0.8; 1]
Fuel cell Nfc [1,5]
Electrolyzer Nelec [1,10]
Hydrogen tank .mH(kg) [1,9] [0.1; 1]
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9. the TAC and the percentage variation in TAC are given in the
table below (Table 5). It is noticed that the TAC decreases
rapidly with increase in average wind speed. The TAC versus
average wind speed curves slope decreases and becomes
practically zero for TAC around 4860 V/year and average wind
speed above 7 m.s1
(Fig. 12). For values of average wind speed
between 3.84 m s1
and 7.1 m s1
, the percentage of decrease
in TAC, considering SOL3, is about 65.52%.
The average wind speed is then a parameter that
strongly influences the TAC. For regions with high wind
Fig. 8 e Pareto front obtained.
Fig. 9 e Energy stored in hydrogen tank (a), state of charge of battery (b), the DC bus voltage (c.) Supercapacitors state of
charge (d.) versus time.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5
5520
10. potential, this system will be very beneficial but for region
with middle wind potential, it will be interesting for cost
effective system to couple the wind generator with photo-
voltaic power system or use photovoltaic power system
alone.
Sensitivity versus changes in subsystems cost
In this section, the effect of changes in subsystem cost on the
TAC is analyzed. In the prospect of mass production due to the
increase in green energy sources requirement, the prices of
fuel cell, supercapacitor, battery and inverter will fall drasti-
cally. The sensitivity analysis will be done according to a
maximum cost variation of 60%.
It is noticed a small change in TAC for supercapacitors cost
variation. For wind generator, fuel cell, electrolyzer, hydrogen
tank and battery cost variations, the TAC varies from about
14448 V/year to respectively 11477V/year, 11817 V/year, 13417
V/year and 13960 V/year and 14019 V/year (Fig. 13). The overall
Fig. 10 e Contribution of each source in the load requirement; a. wind generator, b. supercapacitor, c. Battery, d. fuel cell.
Fig. 11 e Percentage of each source contribution for two weeks operation.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5 5521
11. Table 4 e Simulation results.
S1 S2 S3 S4 S5 S6
WG (kW) 8 7 8 8 7 8
Battery (kW.h) 5.67 12.47 5.67 5.67 11.34 5.67
supercapacitor 100 60 60 40 80 80
Tower height (m) 30 30 30 30 29 29
Fuel cell (kW) 2.4 2.4 2.4 2.4 1.2 1.2
Electrolyzer (kW) 4 7 4 4 5 3
Hydrogen mass (kg) 9 9 9 8.94 9 9
dump Load (%) 24 25 24 24 24 24.5
Less load (%) 3.4 3.4 3.5 3.5 4.4 4.4
LPSP (%) 3.4 3.4 3.5 3.5 4.4 4.4
TAC (V/year) 14592 16888 14448 14374 13152 11508
Pw, is the wind turbine power in kW and the TAC is in V/year. The highlighted solution is the one that will be considered hereafter.
Table 5 e Wind profile characteristics and the associated TAC at a LPSP of 4%.
Average speed a b Vmin Vmax TAC (V/year) Reduction (%)
3.84 4.35 2.23 0.11 11.8 14096 0
4.66 5.28 2.23 0.05 13.5 7932 43.72
5.32 6 2.2 0.07 16.44 6382 54.72
6.21 7 2.2 0.15 19.3 5283 62.52
7.1 8 2.2 0.15 22.7 4860 65.52
Fig. 12 e Total Annualized Cost versus average wind speed.
Fig. 13 e TAC versus changes in sub-systems cost for a LPSP of 3.5%.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5
5522
13. photovoltaı̈ques avec batteries pour l’habitat r
esidentiel
autonome. Th
ese G
enie
electrique. Poitiers. Universit
e de
Poitiers; 2012.
[24] www.curbain.be; Jan. 2018.
[25] Seitzler M. The electrical and mechanical performance
evaluation of a roof-mounted, one-kilowatt wind turbine.
CWEC: California Wind Energy Collaborative, University of
California; March 2009.
[26] Nexa™ (310-0027) power module user's manual. June 16,
2003.
[27] Busquet S. Etude d'un syst
eme autonome de production
d'
energie couplant un champ photovoltaı̈que, un
electrolyseur et une pile
a combustible : r
ealisation d'un banc
d'essai et mod
elisation. Sciences de l'ing
enieur [physics].
Ecole Nationale Sup
erieure des Mines de Paris; 2003.
Français. NNT: 2003ENMP1195. pastel-0000133816.
[28] Saft Communication Department, DOC N
54041-2-0305,
March 2005.
[29] H. Gualous, R. Gallay, A. Berthon. Utilization des
supercondensateurs pour le stockage de l’
energie
embarqu
ee : application transport. In REE2004.
[30] Abbes D, Martinez A, Champenois G. Life cycle
cost,embodied energy loss of power supply probability for
the optimal design of hybrid power systems. Math Comput
Simul April 2014;98:46e62.
[31] Rajkumar RK, Ramachandaramurthy VK, Yong BL, Chia DB.
Techno-economical optimization of hybrid pv/wind/battery
system using Neuro-Fuzzy. Energy August
2011;36(8):5148e53.
[32] Ramoj SK, Jagadish Kumar B. Optimal economical sizing of a
PV-wind hybrid energy system using genetic algorithm and
teaching learning based optimization. Int J Adv Res Elect
Electron Instrum Eng February 2014;3(Issue 2). An ISO 3297:
2007 Certified Organization).
[33] Bouharchouche A, Bouabdallah A, Berkouk EM, Diaf S,
Belmili H. Conception et r
ealisation d’un logiciel de
dimensionnement d’un syst
eme d’
energie hybride
eolien-
photovoltaı̈que. Revue des Energies Renouvelables
2014;17(3):359e76.
[34] Cho J-H, Chun M-G, Hong W-P. Structure optimization of
stand-alone renewable power systems based on multi object
function. Energies 2016;9:649.
[35] Chen P-J, Wang F-C. Design optimization for the hybrid
power system of a green building. Int J Hydrogen Energy
2018;13:2381e93.
[36] Kalinci Y, HEPBASLI A, Dincer I. Techno-economic analysis
of a stand-alone hybrid renewable energy system with
hydrogen production and storage options. Int J Hydrogen
Energy 2015;40:7652e64.
[37] Diaf S, Notton G, Belhamel M, Haddadi M, Louche A. Design
and techno-economical optimization for hybrid PV/wind
system under various meteorological conditions. Appl
Energy 2008;85:968e87.
[38] Hernandez-Torres D, Turpin C, Roboam X, Sareni B.
Mod
elisation en flux d'
energie d'une batterie Li-Ion en vue
d'une optimisation technico-
economique d'un micro-r
eseau
intelligent. In: Symposium de Genie Electrique; Jun 2016.
Grenoble, France.
[39] Sanchez VM, Chavez-Ramirez AU, Duron-Torres SM,
Hernandez J, Arriaga LG, Ramirez JM. Techno-economical
optimization based onswarm intelligence algorithm for a
stand-alonewind-photovoltaic-hydrogen power systemat
south-east region of Mexico. Int J Hydrogen Energy
2014;39:16616e55.
[40] Deep K, Singh KP, Kansal ML, Mohan C. A real coded genetic
algorithm for solving integer and mixed integer optimization
problems. Appl Math Comput 2009;212:505e18.
[41] Wang W, Zmeureanu R, Rivard H. Applying multi-objective
genetic algorithmsin green building design optimization.
Build Environ 2005;40:1512e25.
[42] Sandeep, V Karemore, MrSubhash, Y Kamdi. Optimal sizing
of autonomous wind-PV hybrid system by genetic algorithm
with LPSP technology. Int Refereed J Eng Sci (IRJES) e- ISSN:
2319-183X, 29-35.
[43] Koutroulis E, Kolokotsa D, Potirakis A, Kalaitzakis K.
Methodology for optimal sizing of stand-alone photovoltaic/
wind-generator systems using genetic algorithms. Sol Energy
2006;80:1072e88.
[44] Katsigiannis YA, Georgilakis PS, Karapidakis ES.
Multiobjective genetic algorithm solution to the optimum
economic and environmental performance problem of small
autonomous hybrid power systems with renewables. The
Institution of Engineering and Technology (IET). Renew
Power Gener 2010;4(5):404e19.
[45] C. Y. Yee. reportIntegrating supercapacitors into a hybrid
energy system to reduce overall costs using the genetic
algorithm (GA) and support vector machine (SVM). PhD
thesis, University of Nottingham.
[46] Daniel UB, Lanzerath NF, Bardow A. Multi-objective
optimization of dynamic systems combining genetic
algorithms and Modelica: application to adsorption air-
conditioning systems. In: Proceedings of the11th
International Modelica Conference September; 2015. p. 21e3
[Versailles, France].
[47] Sharifi M, P Guilani P, Shahriari M. Using NSGA II algorithm
for a three-objective redundancy allocation problem with k-
out-of-n sub-systems. J Opt Ind Eng 2016;19:87e95.
[48] K. Deb, U. Bhaskara Rao N., and S. Karthik. Dynamic multi-
objective optimization and decision-making using modified
NSGA-II: a case study on hydrothermal power scheduling.
Kanpur Genetic Algorithms Laboratory (KanGAL) Indian
Institute of Technology Kanpur, PIN 208016, India.
[49] Avril, http://physics.oregonstate.edu; 2018.
[50] Camara MBC. Supercondensateurs pour
echange
dynamiques d’
energie
a bord du v
ehicule
electrique hybride :
mod
elisation,
etude des convertisseurs et commande, vol.
99. Universit
e de Franche-Comt
e; 2007.
[51] J.P. Trov~
ao, P.G. Pereirinha, H.M. Jorge. Design methodology
of energy storage systems for a small electric vehicle.
EsVS24, International battery hybrid and fuel cell electric
vehicle symposium, Stavanger, Norway, May 13-16, 2009.
[52] Hernandez-Torres Da, Turpin C, Roboam X, Sareni B.
Mod
elisation en flux d'
energie d'une batterie Li-Ion en vue
d'une optimisation technico-
economique d'un micro-r
eseau
intelligent. In: Symposium de Genie Electrique; Jun 2016.
Grenoble, France.
[53] Rouhani A, Kord H, Mehrabi M. A comprehensive method for
optimum sizing of hybrid energy systems using intelligence
evolutionary algorithms. Indian J Sci Technol June 2013;6(6).
[54] Olatomiwa L, Mekhilef S, N Huda AS, Sanusi KA. Techno-
economic analysis of hybrid PV-diesel-battery and PV-wind-
diesel-battery power systems for mobile BTS:the way. Energy
Sci Eng April 2015.
[55] Hord
e Th
eophile.
Etude de syst
emes pile
a combustible
hybrid
es embarqu
es pour l’a
eronautique. Autre. Ecole
Nationale Sup
erieure des Mines de Paris; 2012.
[56] O Jensen J, P VestbØ A, Li Q, Bjerrum NJ. The energy efficiency
of onboard hydrogen storage. J Alloy Comp 2007:723e8.
[58] Kairies K-P. Battery storage technology improvements and
cost reductions to 2030: a Deep Dive. International Renewable
Energy Agency Workshop Dusseldorf; Mar 17, 2017.
[59] Gualous H, Gallay R, Berthon A. Utilization des
supercondensateur pour le stockage de l’
energie embarqu
ee
: application transport. 2004. REE.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5
5524
14. [60] Brka A. Optimization of stand-alone hydrogen-based
renewable energy systems using intelligent techniques.
2015. Retrieved from, http://ro.ecu.edu.au/theses/1756.
[61] Global modeling and assimilation office (GMAO). MERRA-2
tavg1_2d_slv_Nx : 2d, 1-hourly, time-averaged, single-level,
assimilation. Single-Level Diagnostics V5.12.4, Greenbelt,
MD, USA, Goddard Earth Sciences Data and Information
Services Center (GES DISC); 2015. Accessed [Data Access 22/
05/2019].
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5 5525
![Optimal sizing of a wind, fuel cell, electrolyzer,
battery and supercapacitor system for off-grid
applications
N'guessan S. Attemene a,b,*
, Krehi S. Agbli c
, Siaka Fofana b
, Daniel Hissel d
a
FEMTO-ST, Univ. Bourgogne Franche-Comte, France
b
University Felix Houphou€
et Boigny of Abidjan-Cocody, Ivory Coast, West Africa
c
Clean Horizon Consulting, Paris, France
d
Univ. Bourgogne Franche Comt
e, FEMTO-ST, FCLAB, CNRS, France
h i g h l i g h t s
The sizing study of a hybrid micro-grid.
The sizing is based on system total annualized cost minimization and loss of power supply probability enhancement.
The algorithm find the smallest component capability to ensure load requirement and system security criteria.
a r t i c l e i n f o
Article history:
Received 12 December 2018
Received in revised form
24 May 2019
Accepted 25 May 2019
Available online 21 June 2019
Keywords:
Optimal sizing
Total annualized cost
Fuel cell
Supercapacitor
Battery
Sensitivity analysis
a b s t r a c t
This paper is focused on the determination of an optimal configuration of a system con-
sisting of a wind turbine, a PEM fuel cell, an alkaline electrolyzer, a battery and a super-
capacitor bank in an off-grid application. The wind generator is used as the main source
while the supercapacitor, battery, fuel cell and electrolyzer are back-up energy sources.
This hybrid system should be able to supply the energetics needs of a residential household
while keeping the system costs as low as possible. The aim of this paper is determining an
optimal configuration set regarding the system total annual cost and its energetic reli-
ability. The total annual cost consists of the annualized capital cost, the annual mainte-
nance cost and the annual replacement cost. The energy reliability is based on Loss of
Power Supply Probability (LPSP). The Non-dominated Sorted Genetic Algorithm (NSGAII) is
used to find the best configuration of the whole set of subsystems. The total annual cost
sensitivity with the changes of wind speed profile, subsystem prices, is also discussed.
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction
Given the consequences generated by the release of green-
house gases in the atmosphere, the general trend in the world
today is to promote environmentally friendly energy systems.
Therefore, initiatives and researches for developing more
economical and reliable green energy sources are undertaken.
Renewable energy sources such as solar (photovoltaic and/or
thermal) and wind are thriving [1e3]. However, they remain
hardly competitive. Indeed, the generation of energy in wind
* Corresponding author. FEMTO-ST, Univ. Bourgogne Franche-Comte, France.
E-mail addresses: nguessan.attemene@femto-st.fr (N.S. Attemene), aks@cleanhorizon.com (K.S. Agbli), fsiaka@hotmail.com (S. Fofana),
daniel.hissel@univ-fcomte.fr (D. Hissel).
Available online at www.sciencedirect.com
ScienceDirect
journal homepage: www.elsevier.com/locate/he
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5
https://doi.org/10.1016/j.ijhydene.2019.05.212
0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.](https://image.slidesharecdn.com/1-s2-211110163503/85/1-s2-0-s0360319919321275-main-1-320.jpg)
![systems is strongly limited by the intermittent nature of the
wind [4,5]. To overcome this problem, they can be associated
to energy storage systems in order to continuously supply the
load [6,7]. One of the major aspects of this configuration is the
reliable supply of power at a reduced cost. Hydrogen subsys-
tem can handle production fluctuation over long periods [8,9].
In addition, on-site hydrogen generation and storage is
beneficial for complete energy independence and continuous
service [10e13]. In such a context, hydrogen could provide an
excellent mean for storing excess renewable energy [14] for
use during low wind speed period. However, due to the slow
dynamics of fuel cells and electrolyzers, it is interesting to
associate them with battery and supercapacitors storage
systems, for higher dynamic requirements. Therefore, it ari-
ses problems of configuration, energetic reliability and system
cost.
Several researches with the aim of providing a viable so-
lution to these problems were undertaken. In Ref. [15], T
egani
and al have applied to a hybrid stand-alone photovoltaic (PV)
and wind generator (WG) systems, a methodology for optimal
sizing and strategy control based on differential flatness
approach. The purpose was to find the optimal number of
units ensuring that the system cost is minimized subject to
the constraint that the load requirements are completely
covered. The system cost is the sum of capital and mainte-
nance cost. The energy management strategy is presented to
control the energy flows between the PV-WG, load and bat-
teries as hybrid sources to supply a residential household.
Karim and al [16] developed an optimal design for a hybrid
solar-wind energy plant taking into account the number of PV
modules, the number of wind turbines, the wind turbine
height and the turbine rotor diameter as variables to minimize
the cost. The result shows the complementary relationship
between PV and wind generator over the different season of
the year. In Ref. [17], power management strategies for a
stand-alone power system using renewable energy sources
and hydrogen storage are presented. Three power manage-
ment strategies that comprise energy generation from
renewable energy sources (RES) and hydrogen production
have been developed by the author. Each power management
strategy is assessed on its capacity to meet the power load
requirements through effective utilization of the electrolyzer
and fuel cell under variable energy generation from RES. In
Ref. [18], a system that couples several renewable energy
sources and storage mean is used to supply a small commu-
nity in remote area. A genetic algorithm optimization has
shown that it’s possible to obtain a system supplying energy
with a minimum cost. The design depends on the meteoro-
logical characteristics of the site as well as the consumption
profile. In Ref. [19], GA (Genetic Algorithm) and PSO (Particle
Swarm Optimization) algorithms are used to find the opti-
mum sizes of the hybrid energy systems among numerous
configurations, obtained by considering LPSP constraint, to
reach the expected reliability and the lowest LCOE (Levelized
Cost of Energy). The hybrid system is composed of wind, PV,
FC (fuel cell) and battery. In Ref. [20], an optimal sizing method
of a stand-alone hybrid power system based on PV/WG/bat-
tery/hydrogen with improved Ant Colony Optimization (ACO),
for reliable and economic energy supply, is proposed. Two
objectives that take the minimum annual system cost and
maximum system reliability described as the LPSP have been
addressed for sizing. Authors in Ref. [21], deals with the opti-
mization of the design of a PV/WG/FC system based on the
minimization of the overall 20-year cost energy using a
modified PSO algorithm. The result of the modified PSO algo-
rithm is compared with those of the common PSO. The pro-
posed hybrid solution procedure (modified PSO) has better
results than common PSO with respect to capital investment
cost minimization and system reliability level. In Ref. [22], a
techno-economic study of a PV-hydrogen-battery hybrid sys-
tem for off-grid power taking into account impact of perfor-
mances ‘ageing on optimal system sizing is presented. The
results show that hybridizing battery with hydrogen is more
cost beneficial than photovoltaic-battery solution. Moreover,
it show that taking into account the degradation of hydrogen
chain does not impact the optimal results.
In this paper, the optimization of a wind, fuel cell, elec-
trolyzer, battery and supercapacitors system for off-grid ap-
plications regarding the system cost and energetic reliability is
presented. The optimization process is performed using
NSGAII algorithm on the bases of total annualized cost mini-
mization and reliability enhancement. The reliability index
considered is this work is the LPSP.
In order to show the dependency of the results with the
wind profile, sensitivity analysis versus changes in wind
profile and subsystems cost are carried out.
In section System operating strategy, the system operating
strategy is introduced, in section System sizing methodology
and problem formulation the sizing methodology and the
problem formulation. Section Hybrid system component
modeling deals with component modeling, section
Simulation and results simulation and results and section
Conclusion conclusion.
System operating strategy
The system topology is depicted in Fig. 1. In this topology the
supercapacitors are used to handle the dc bus. The advantage
of this topology is to ensure a better protection of the battery
during fast power request transition. This hybrid system
should be able to supply the energetics needs of a residential
household.
The wind generator is used as the main source while the
supercapacitors, battery, fuel cell and electrolyzer are back-up
Fig. 1 e The system illustration figure.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 5 ( 2 0 2 0 ) 5 5 1 2 e5 5 2 5 5513](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)