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Comparative study of artificial intelligencetechniques for sizing of a hydrogen-basedstand-alone photovoltaic/wind hybrid system

Akbar Maleki, Alireza Askarzadeh*

Department of Energy Management and Optimization, Institute of Science and High Technology and Environmental

Sciences, Graduate University of Advanced Technology, Kerman, Iran

a r t i c l e i n f o

Article history:

Received 30 November 2013

Received in revised form

19 April 2014

Accepted 21 April 2014

Available online 20 May 2014

Keywords:

Hybrid systems

PV/wind/fuel cell

Optimal sizing

Artificial intelligence

a b s t r a c t

As non-polluting reliable energy sources, stand-alone photovoltaic/wind/fuel cell (PV/

wind/FC) hybrid systems are being studied from various aspects in recent years. In such

systems, optimum sizing is the main issue for having a cost-effective system. This paper

evaluates the performance of different artificial intelligence (AI) techniques for optimum

sizing of a PV/wind/FC hybrid system to continuously satisfy the load demand with the

minimal total annual cost. For this aim, the sizing problem is formulated and four well-

known heuristic algorithms, namely, particle swarm optimization (PSO), tabu search

(TS), simulated annealing (SA), and harmony search (HS), are applied to the system and the

results are compared in terms of the total annual cost. It can be seen that not only average

results produced by PSO are more promising than those of the other algorithms but also

PSO has the most robustness. As another investigation, the sizing is also performed for a

PV/wind/battery hybrid system and the results are compared with those of the PV/wind/FC

system.

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

reserved.

Introduction

Photovoltaic (PV) systems and wind turbines (WTs) are being

used worldwide to contribute in meeting the electrical power

demand. The most important challenge of the single-

renewable energy systems is their dependency to the envi-

ronmental conditions (solar radiation and wind speed). As a

solution, renewable energy sources are combined with each

other (hybrid system) to provide more continuous electrical

power. Therefore, hybrid systems have more reliability than

single-renewable energy systems.

For a PV/wind hybrid system, it is necessary to provide an

energy storage device. The storage system meets the

remaining demand when the renewable sources have low

energy. The storage device can be a battery bank, super

capacitor bank, superconducting magnetic energy storage

(SMES), or an FC/electrolyzer system. Conventionally, deep-

cycle lead acid batteries are used for energy storage. Never-

theless, the associated environmental concerns limit the

application of PV/wind/battery-based systems. Recent re-

searches have focused on using FC/electrolyzer as the storage

device [1e17]. Using PV/wind/FC system leads to having a

non-polluting reliable energy source. In such system,

* Corresponding author. Tel./fax: þ98 342 6233176.E-mail addresses: [email protected] (A. Maleki), [email protected], [email protected] (A. Askarzadeh).

Available online at www.sciencedirect.com

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electrolyzer produces hydrogen by the excess electrical energy

of the PV and wind sources. The hydrogen can then be used to

supply an FCwhich is considered as a secondary power source

when the demand is high.

For the better understanding of the different aspects of

hydrogen-based hybrid systems, thereby to efficiently utilize

PV/wind/FC systems, various investigations have been

developed. In hybrid systems, appropriate sizing is one of the

most important issues that results in having a cost-effective

energy system. Literature study indicates that there are

many attempts based on probabilistic, analytical and heuristic

methods for optimal sizing of hybrid systems. Diaf et al. [18]

have optimized hybrid system size based on loss of power

supply probability (LPSP) and the levelized cost of energy

(LCE). Borowy and Salameh [19] have introduced loss of load

probability (LLP) concept for finding the optimal size of the PV/

wind hybrid system. Shrestha and Goel [20] have presented a

methodology for optimal sizing based on energy generation

simulation. Maghraby et al. [21] have used the desired system

performance level (SPL) requirement to select the number of

PVs and batteries. Energy balance has been used for design of

hybrid PV/wind systems [22]. Prasad and Natarajan [23] have

presented a methodology for optimization of PV/wind system

based on deficiency of power supply probability (DPSP), rela-

tive excess power generated (REPG), unutilized energy proba-

bility (UEP), life cycle cost (LCC), levelized energy cost (LEC)

and life cycle unit cost (LUC) of power generation with battery

bank. Nonlinear programming [24] and HOMER [25] are other

algorithms used for optimal design of hybrid systems. Heu-

ristic algorithms such as genetic algorithm (GA) [26,27],

(a)Wind Generator

PV Panel

Battery

+

DC/DC

Load

DC bus

DC/DC

AC/DC

DC/AC

(b)Wind Generator

PV Panel

Fuel cell

+

DC/DC

Load

DC bus

DC/DC

AC/DC

DC/AC

H2 Tanks

Electrolyzer

Fig. 1 e Schematic of the hybrid systems. (a) PV/wind/battery-based hybrid system and (b) PV/wind/FC-based hybrid

system.

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simulated annealing [28] and harmony search [29] are other

techniques for sizing of hybrid systems. A detailed review of

these methods can be found in Ref. [30].

In spite of these investigations, an informative model

suitable for sizing of PV/wind/FC system and consequently, an

efficient optimization technique are seldom available. In this

paper, a stand-alone hybrid energy system consisting of PV,

wind, FC, and electrolyzer is considered. PV and wind are pri-

mary power sources of the system and the FC/electrolyzer

combination is used as a backup and a long-term storage sys-

tem.Theperformanceof this system is comparedwith thatof a

system consisting of PV, wind, and battery. At fist, the systems

components aremodeled to define the total annual cost (TAC).

Then, TAC is considered as the fitness (or objective) function

and the optimization techniques are employed to find the

optimal number of the system components. Fig. 1 shows the

schematic of PV/wind/battery and PV/wind/FC systems.

Most electrolyzers produce hydrogen at a pressure around

30 bars [31]. On the other hand, the reactant pressures within

a proton exchangemembrane FC (PEMFC) are around 1.2 bar (a

bit higher than atmosphere pressure) [32]. As a result, in most

studies, electrolyzer’s output is directly injected to a hydrogen

tank [6,32e36]. However, in some cases, for raising the density

of stored energy, a compressor may pressurize electrolyzer’s

output up to 200 bar [31]. In this paper, the electrolyzer is

directly connected to the hydrogen tank.

As a branch of artificial intelligence (AI), heuristic algo-

rithms (inspired by natural processes or phenomena) are high

quality optimization tools which have received considerable

attention to solve complex optimization problems. Study of

the literature reveals that some heuristic algorithms have

been applied to different aspects of hybrid systems [26e29].

This paper evaluates the performance of four well-known

heuristic algorithms on the sizing problem of PV/wind/FC

and PV/wind/battery systems. These algorithms are: particle

swarm optimization (PSO) (inspired by social behavior of an-

imals) [37], tabu search (TS) (inspired by the conclusion of the

cognitive psychology about the human memory) [38], simu-

lated annealing (SA) (inspired by annealing of metals) [39,40],

and harmony search (HS) (inspired by musician’s improvisa-

tion process) [41]. The performance of the algorithms is

compared in terms of accuracy and computational cost.

The rest of this paper is organized as follows: Section Sizing

formulation introduces the equations of the system compo-

nents in detail and formulates the sizing problem; in

Section Artificial intelligence (AI) techniques, the AI tech-

niques are briefly introduced; the performance of the AI

techniques on a case study is discussed in Section Results; and

conclusion is finally given in Section Conclusion.

Sizing formulation

Modeling the system components

PV systemThe output power of each PV system (pPV) at time t can be

obtained from the solar radiation by the following formula:

pPVðtÞ ¼ IðtÞ � A� hPV (1)

where I is the solar radiation, A denotes the PV area and hPV is

the overall efficiency of PV panels and DC/DC converter. It is

assumed that the PV panels have maximum power point

tracking (MPPT) system. Also, temperature effects on the PV

panels are ignored. If the number of PV systems is NPV, the

overall produced power is PPV(t) ¼ NPV � pPV(t).

Wind turbine (WT)For a wind turbine, if the wind speed exceeds the cut-in value,

the wind turbine generator starts generating. If the wind

speed exceeds the rated speed of the wind turbine, it gener-

ates constant output power, and if thewind speed exceeds the

cut-out value, the wind turbine generator stops running to

protect the generator. The produced power of each wind tur-

bine (pWT) at time t is obtained as follows:

pWTðtÞ ¼

8>>><>>>:

0 vðtÞ � vcut�in or vðtÞ � vcut�out

PrvðtÞ � vcut�in

vr � vcut�out

Pr

vcut�in < vðtÞ < vr

vr < vðtÞ < vcut�out

(2)

where v is the wind speed, Pr is the rated power of the wind

turbine, and vcut-in, vcut-out and vr are cut-in, cut-out, and rated

speed of the wind turbine, respectively. If the number of wind

turbines is NWind, the overall produced power is

PWT(t) ¼ NWind � pWT(t).

FC/electrolyzerIn the PV/wind/FC-based hybrid system, the storage system

works as follows:

A charging efficiency for electrolyzer and a discharging

efficiency for FC are used in calculating the efficiency of the

storage system. If the power generated from the wind/PV

system is greater than the load demand at time t, the elec-

trolyzer will be used to fill the hydrogen tanks.

The amount of hydrogen stored in the tanks is obtained by

the following equation.

EStorðtÞ ¼ EStorðt� 1Þ þ�ðEPVðtÞ þ EWTðtÞÞ � ELoadðtÞ

hInv

�� hElect (3)

where EStor(t) and EStor(t � 1) are the energy stored in the

hydrogen tanks at hours t and t � 1, respectively, hInv is the

efficiency of the inverter, and hElect is the efficiency of the

electrolyzer.

When the load demand is greater than the energy gener-

ated by the wind/PV system, the FC is used to supply the load.

In this case, the amount of hydrogen in the tanks at hour t is

obtained by

EStorðtÞ ¼ EStorðt� 1Þ ��ELoadðtÞhInv

� ðEPVðtÞ þ EWTðtÞÞ��

hFC (4)

where hFC is the overall efficiency of the FC and its corre-

sponding DC/DC converter.

BatteryThanks to the random behaviors of PV panels and wind tur-

bines, the battery bank capacity constantly changes corre-

spondingly in PV/wind battery-based hybrid system. In such

system, state of charge (SOC) of the battery is acquired as

follows:

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When the total output of PV panels and wind generators is

greater than the load energy, the battery bank is in charging

state. The charge quantity of the battery bank at time t can be

obtained by

EBattðtÞ ¼ EBattðt� 1Þ � ð1� sÞ þ�ðEPVðtÞ þ EWTðtÞÞ � ELoadðtÞ

hInv

�� hBatt (5)

where EBatt(t) and EBatt(t � 1) are the charge quantities of bat-

tery bank at time t and t� 1, s is the hourly self-discharge rate,

hInv denotes the inverter efficiency, ELoad is the load demand,

and hBatt is the charge efficiency of the battery bank.

When the total output of PV panels and wind generators is

less than the load demand, the battery bank is in discharging

state. In this paper, the discharge efficiency of battery bank is

assumed to be 1. Therefore, the charge quantity of the battery

bank at time t can be obtained by

EBattðtÞ ¼ EBattðt� 1Þ � ð1� sÞ ��ELoadðtÞhInv

� ðEPVðtÞ þ EWTðtÞÞ�

(6)

Cost modeling

Objective functionPV/wind/FC-based hybrid system. The objective function of

the optimum design problem is the minimization of the total

annual cost (CT). The total annual cost consists of the annual

capital cost (CCpt) and the annual maintenance cost (CMtn). To

optimally design the hybrid generation system, the optimi-

zation problem, defined by Eq. (7), should be solved using an

optimization technique.

Minimize CT ¼ CCpt þ CMtn (7)

Maintenance cost occurs during the project life while

capital cost occurs at the beginning of a project.

In order to convert the initial capital cost to the annual

capital cost, capital recovery factor (CRF), defined by Eq. (8) is

used.

CRF ¼ ið1þ iÞnð1þ iÞn � 1

(8)

where i is the interest rate and n denotes the life span of the

system.

Some components of PV/wind/FC system need to be

replaced several times over the project lifetime. In this paper,

the lifetime of FC/electrolyzer is assumed to be 5 years. By

using the single payment present worth factor, we have

CFC=Elect ¼�PFC=Elect þ Pins

FC=Elect

�� 1þ 1

ð1þ iÞ5 þ1

ð1þ iÞ10

þ 1

ð1þ iÞ15!

(9)

where CFC/Elect is the present worth of FC/electrolyzer system,

PFC=Elect is FC/electrolyzer price and PinsFC=Elect denotes FC/elec-

trolyzer installation fee.

In the same way, the lifetime of converter/inverter is

assumed to be 10 years. By using the single payment present

worth factor, we have

CConv=Inv ¼ PConv=Inv � 1þ 1

ð1þ iÞ10!

(10)

where CConv/Inv is the present worth of converter/inverter

components and PConv/Inv is the converter/inverter price.

By breaking up the capital cost of PV/wind/FC system into

the annual costs of wind turbine, PV panel, FC/electrolyzer

and converter/inverter, Eq. (11) is obtained.

CCpt ¼ ið1þ iÞnð1þ iÞn � 1

�NWind � CWind þNPV � CPV þNTank � CTank

þ CFC=Elect þNConv=Inv � CConv=Inv

�(11)

where CWind is unit cost of wind turbine, CPV is unit cost of PV

panel, NTank is the number of storage tanks, CTank is unit cost

of hydrogen storage tank and NConv/Inv is the number of con-

verter/inverter systems.

For obtaining the annual maintenance cost of the system

components, the following equation is used:

CMtn ¼ NPV � CPVMtn þNWind � CWind

Mtn þ CFCMtn þ CElect

Mtn (12)

where CPVMnt, C

WindMnt , CFC

Mnt and CElectMnt are the annual maintenance

costs of PV, wind turbine, fuel cell and electrolyzer systems,

respectively. The maintenance costs of hydrogen tank and

converter/inverter systems are neglected.

PV/wind/battery-based hybrid system. In PV/wind/battery

system, the lifetime of each battery is assumed to be 10 years.

By using the single payment present worth factor, we have

CBatt ¼ PBatt � 1þ 1

ð1þ iÞ10!

(13)

where CBatt is the present worth of battery and P is the battery

price.

For this system, total annual capital and maintenance

costs are obtained by Eqs. (14) and (15), respectively.

CCpt ¼ ið1þ iÞnð1þ iÞn � 1

�NWind � CWind þNPV � CPV þNBatt � CBatt

þNConv=Inv � CConv=Inv

�(14)

where NBatt is the number of batteries.

CMtn ¼ NPV � CPVMtn þNWind � CWind

Mtn (15)

The maintenance cost of battery is neglected.

ConstraintsFor both PV/wind/FC and PV/wind/battery systems, the

following constraints should be satisfied:

NWind ¼ Integer; 0 � NWind � NmaxWind (16)

NPV ¼ Integer; 0 � NPV � NmaxPV (17)

where NmaxWind and Nmax

PV are the maximum available number of

wind turbines and PV panels, respectively.

In PV/wind/FC system, in addition to Eqs. (16) and (17), the

following equations should be satisfied:

NTank ¼ Integer; 0 � NTank � NmaxTank (18)

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EminStor � EStor � Emax

Stor (19)

where NmaxTank is maximum number of hydrogen tanks and Emin

Stor

(assumed to be 0 in this study) and EmaxStor denote the minimum

and maximum storage capacity of the hydrogen tanks,

respectively.

For PV/wind/battery system, in addition to Eqs. (16) and

(17), the number of storage batteries should satisfy

NBatt ¼ Integer; 0 � NBatt � NmaxBatt . Moreover, at any time, the

charge quantity of battery bank should satisfy the constraint

of EminBatt � Et

Batt � EmaxBatt . The maximum charge quantity of bat-

tery bank ðEmaxBatt Þ takes the value of nominal capacity of battery

bank (SBatt) and the minimum charge quantity of the battery

bank ðEminBattÞ is obtained by maximum depth of discharge

(DOD).

EminBatt ¼ ð1�DODÞ � SBatt (20)

Artificial intelligence (AI) techniques

Particle swarm optimization algorithm (PSO)

Originally invented by Kennedy and Eberhart in 1995 [37], PSO

is a population-based metaheuristic algorithm attempting to

discover the global solution of an optimization problem by

simulating the animals social behavior such as fish schooling,

bird flocking, etc. PSO has been one of the most popular

optimization algorithms because it has simple concept, is easy

to implement and can quickly find a reasonably good solution.

In PSO algorithm, each feasible solution of the problem is

called a particle which is specified by a vector containing the

problem variables. At the beginning of the algorithm, a group

of particles is randomly initialized in the search space. Each

particle makes use of its memory and flies through the search

space for obtaining a better position than its current one. In its

memory a particle memorizes the best experience found by

itself (pbest) as well as the group’s best experience (gbest). The

updating pattern of a particle in each iteration (iter) is as

follows:

vkðiterþ 1Þ ¼ wðiterÞ � vkðiterÞ þ c1 � r1ðpbestkðiterÞ � xkðiterÞÞþ c2 � r2ðgbestðiterÞ � xkðiterÞÞ

(21)

xkðiterþ 1Þ ¼ vkðiterþ 1Þ þ xkðiterÞ ðiter ¼ 1;2;.; itermaxÞ (22)

where xk denotes the particle’s position, k ¼ 1,2,.,Np is the

particle’s index, Np is the size of population (number of par-

ticles), vk denotes the particle’s velocity, r1 and r2 are uniform

random numbers between 0 and 1 which are generated

independently for each particle in each update, c1 and c2 are

learning factors which control the importance of the best so-

lution ever found by kth particle and the best solution found

by the swarm, respectively, itermax denotes the maximum

iteration times and w is known as inertia weight which is

started from a positive initial value (w0) and is decreased

during the iterations by w(iter þ 1) ¼ b � w(iter).

The steps of the PSO algorithm can be expressed as follows:

Step 1) A population is randomly generated in the search

space.

Step 2) The initial velocity of each particle is randomly

generated.

Step 3) Objective function value for each particle is

calculated.

Step 4) The initial position of each particle is selected as its

pbest and the best particle among the population is chosen

as gbest.

Step 5) Particles move to new positions based on Eqs. (21)

and (22).

Step 6) If a particle exceeds the allowed range it is replaced

by its previous position.

Step 7) Objective function value for each particle is

calculated.

Step 8) pbest and gbest are updated.

Step 9) The stopping criterion is checked. If it is satisfied

the algorithm is terminated and gbest is selected as the

optimal solution. Otherwise, Steps 5 to 8 are repeated.

Tabu search (TS)

Originally proposed by Glover [38], TS is an iterative procedure

that starts from a random initial solution and tries to find a

better solution. In TS, tabu list and aspiration criterion play

important roles for escaping local optima. TS can be repre-

sented by the following steps [42]:

Step 1: iteration index (iter) is set to 0 and an initial solution

(xinitial) is randomly generated. This solution is set as the

current solution as well as the best solution, xbest (i.e.,

xinitial ¼ xcurrent ¼ xbest).

Step 2: a set of trial solutions (ntrial), at the vicinity of the

current solution are produced. Each trial solution (xtrial) is

put into the objective function and its quality is calculated.

The trial solutions are sorted based on their objective

function values in ascending order. Let us define xjtrial as the

jth trial solution in the sorted setwhere 1� j� ntrial. So, x1trialrepresents the best trial solution in terms of the objective

function value.

Step 3: j is set to 1. If CTðxjtrialÞ > CTðxbestÞ, we go to Step 4,

else we set xbest ¼ xjtrial xbest ¼ xjtrial and go to Step 4.

Step 4: the tabu status of xjtrial is checked. If it is not in the

tabu list, then it is put in the tabu list, we set xcurrent ¼ xjtrialand go to Step 7. If it is in tabu list, we go to Step 5.

Step 5: the aspiration criterion of xjtrial is checked. If it is

satisfied, then the tabu restrictions are overrided, the

aspiration level is updated, xcurrent ¼ xjtrial, andwe go to Step

7. If not, j ¼ j þ 1 and we go to Step 6.

Step 6: If j > ntrial, we go to Step 7, else we go back to Step 4.

Step 7: the stopping criterion is checked.

Simulated annealing algorithm (SA)

The name and inspiration of SA originates from annealing in

metallurgy, a process involving heating and controlled cooling

of a metal to increase the size of its crystals and reduce its

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defects. SA starts its search by a large enough temperature (T)

to search a broad region of the space and terminates it by a

small temperature tomove downhill according to the steepest

descent heuristic. In SA, as the iterations progress, the tem-

perature is gradually reduced.

The SA used in this study is same as that proposed in Ref.

[28] which is a discrete SA (DSA). At any iteration (iter), the

current solution is x(iter) and the corresponding objective

function value is defined by f(x(iter)). The probability of the

next solution, x(iter þ 1), being at xnew (a random solution

near-by x(iter)) depends both on the difference between the

corresponding fitness values, DF ¼ f(xnew) � f(x(iter)), and also

on the temperature. As a result, the position of the next so-

lution is determined as follows:

xðiterþ 1Þ ¼

xnew if expð�DF=TÞ > rxðiterÞ o:w:

(23)

where r is an uniform random number in [0, 1].

As can be seen, if DF� 0, xnew is always accepted. There is a

probability of selecting xnew as x(iter þ 1) even though the

function value at xnew is worse than that at x(iter). This prob-

ability depends on DF and T values. The process of producing

new solutions continues until maximum number of itera-

tions, itermax, is met. In DSA, xnew and T change by the

following formulas during the iterations:

xnew ¼ xðiterÞ þWF (24)

Tðiterþ 1Þ ¼ s� TðiterÞ (25)

where WF is a vector with the elements randomly distributed

between [�wf wf] and s is the step size. The algorithm is

started by an initial temperature (T0).

Harmony search (HS)

HS is a heuristic algorithm which attempts to mimic the

musicians’ improvisation process. The HS used in this study is

same as that proposed in Ref. [29] which is a discrete HS (DHS).

The key parameters which play important role in the

convergence of the HS algorithm are harmony memory

considering rate (HMCR), pitch adjusting rate (PAR), and

bandwidth of generation (bw). These parameters can be

potentially useful in adjusting convergence rate of the algo-

rithm to the optimal solution. The HMCR varying between

0 and 1 is the rate of choosing one value from the HM. PAR and

bw are defined as follows:

PARðtÞ ¼ PARmin þ PARmax � PARmin

itermax� iter (26)

bwðtÞ ¼ bwmax expðc� iterÞ (27)

c ¼ Lnðbwmin=bwmaxÞitermax

(28)

where PARmax and PARmin are the maximum and minimum

pitch adjusting rates, respectively, and bwmax, bwmin are the

maximum and minimum bandwidths, respectively. In HS, a

new harmony is produced by the following pseudocode:

where xnew is the improvised harmony and r1 as well as r2 are

uniformly distributed random numbers between 0 and 1. The

parameter rw is obtained as follows:

rw ¼

1 r3 < 0:5�1 otherwise

(29)

where r3 is a uniformly distributed random number between

0 and 1.

Table 1 e The parameters of the system components.

i 5%

n 20 years

Wind turbine

Pr 1 kW

Vcut-in 2.5 m/s

Vcut-out 13 m/s

Vr 11 m/s

CWind 3200$

CWindMnt 100$

PV panel

Prs 120 W

CPV 614$

CPVMnt 0$

Area 1.07 m2

Efficiency 12%

Fuel cell

Rated power 3 kW

hfuel-cell 50%

Life span 5 years

CFC 20,000$

CFCMnt 1400$

Electrolyzer

Rated power 3 kW

helect 74%

Life span 5 years

Celect 20,000$

CelectMnt 1400$

CT-tanks 2000$

Nominal capacity of hydrogen tank 0.3 kWh

Power converter/inverter

Rated power 3 kW

hInv 95%

Life span 10 years

CInv 2000$

Battery

Voltage 12 V

SBatt 1.35 kWh

hBC 85%

CBatt 130$

Life span 5 years

DOD 0.8

s 0.0002

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Results

In order to evaluate the performance of the heuristic tech-

niques for optimum sizing of a real system, the solar insola-

tion and wind speed information collected from Rafsanjan

(latitude 30.40� N), Iran are used. Table 1 lists the parameters

of the components. The average hourly insolation and wind

speed profiles and the corresponding produced powers (ob-

tained from Eqs. (1) and (2)) are illustrated in Figs. 2 and 3,

respectively. The average hourly load demand considered in

this paper is shown in Fig. 4.

MATLAB software is used to code and execute the heuristic

algorithms. To compare the performance of the algorithms,

fifty independent runs are performed and the results are re-

ported. The parameters of the algorithms are adjusted as

follows:

PSO : Np ¼ 10; c1 ¼ 2; c2 ¼ 2;b ¼ 0:99; w0 ¼ 1; itermax ¼ 100:

TS : ntrial ¼ 10; itermax ¼ 100:

SA : wf ¼ 5; s ¼ 0:97; T0 ¼ 100; itermax ¼ 1000:

HS : HMCR ¼ 0:9; PARmax ¼ 1; PARmin ¼ 0:1; bwmax ¼ 1;

bwmin ¼ 0:01; itermax ¼ 1000:

The algorithms attempt to find the optimum number of PV

panels (NPV), wind turbines (NWind) and hydrogen tanks (NTank)

in PV/wind/FC-based hybrid system and the optimumnumber

of PV panels, wind turbines and batteries (NBatt) in PV/wind/

battery system. In this study, PV/FC, wind/FC, PV/battery, and

wind/battery systems are also considered for investigation.

The minimum and maximum numbers of each component

are set to 0 and 200, respectively. At initial moment, it is

assumed that the charge of each battery and hydrogen tank is

30% of its nominal capacity.

Table 2 summarizes the results of the algorithms on the

sizing problem. In this table, the mean (Mean), standard de-

viation (Std.), worst (Worst) and best (Best) indexes as well as

the rank (Rank) of each algorithm for each case are given. The

indexes have been reported over 50 runs.

As can be seen, for the PV/wind/FC system the total annual

cost is obtained 18,798.05$ which is lower than that of PV/FC

(46,744.79$) and wind/FC (20,364.75$) systems. So, among the

hydrogen-based hybrid system, PV/wind/FC system is

economically a better choice for power generation. On the

other hand, wind/battery systemwith the total annual cost of

4554.98$ is the best choice among the battery-based systems.

Comparison of the hybrid systemswith battery and hydrogen-

based storage systems shows that wind/battery system is

economically the best choice for use because it has the min-

imum total annual cost. From the results, it is clear that

economically battery is a better candidate for energy storage.

Though this investigation indicates that hydrogen energy

storage systems are not economically competitive with bat-

tery storage systems, there are other benefits to hydrogen

storage system worth mentioning. FC/electrolyzer storage

system is environmentally friendly, has small footprint and

hydrogen can be shipped to the site if storage is low.Moreover,

with improvement in the efficiency of both FC andelec-

trolyzer, FC/electrolyzer storage system can be economically

competitive in the future.

Table 2 reveals that the Best index of the algorithms is same

meaning that each algorithm finds the optimum solution at

least one time over 50 runs. When we compare the perfor-

mance of PSO, TS, SA, and HS algorithms on the sizing prob-

lems, it is found that PSO yields better result than the other

algorithms in terms ofMean, Std., andWorst indexes on all the

hybrid systems except PV/wind/battery system. In this case,

Fig. 2 e Average hourly profiles of PV system, insolation

and produced power.

Fig. 3 e Average hourly profiles of wind turbine, wind

speed and produced power.

Fig. 4 e Average hourly load demand.

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the performances of HS and TS are better than PSO perfor-

mance. The small values of PSO’s Std. denote the robustness of

this algorithm. It is important to mention that all the algo-

rithms have been performed over a same number of fitness

evaluations. The last row of Table 2 indicates the final rank of

the algorithms in solving the sizing problems. Based on the

average rank we can order the search power of the algorithms

as PSO > TS > HS > SA.

Table 3 shows the optimal number of each component and

the system costs in detail for the hybrid systems. The optimal

size of the systems are as follows: PV/wind/FC: NPV ¼ 10,

NWind ¼ 9, NTank ¼ 26; PV/FC: NPV ¼ 133, NTank ¼ 184; wind/FC:

Table 2 e The mean, standard deviation, best, worst performances of the algorithms over the hybrid systems.

Hybrid system Index Algorithm

PSO TS SA HS

PV/wind/FC Mean 19,217 20,169.69 20,827.6 23,703.88

Std. 1159.5 1727.43 3885.71 2830.86

Best 18,798.05 18,798.05 18,798.05 18,798.05

Worst 24,182 25,095.26 37,129.66 32,290.95

Rank 1 2 3 4

PV/FC Mean 46,744.79 46,820.21 46,799.78 46,983.54

Std. 3.638e-11 77.44 97.71 183.76

Best 46,744.79 46,744.79 46,744.79 46,744.79

Worst 46,744.79 47,041.85 47,227.69 47,488.16

Rank 1 3 2 4

Wind/FC Mean 20,364.75 24,702.50 27,581.5 22,791.3

Std. 2.1828e-11 4934.46 5281.47 2012.29

Best 20,364.75 20,364.75 20,364.75 20,364.75

Worst 20,364.75 35,378.75 37,144.09 30,760.48

Rank 1 3 4 2

PV/wind/battery Mean 5134.1 5085.84 5311.04 4907.38

Std. 656.13 549.79 461.85 180.95

Best 4623.15 4623.15 4623.15 4623.15

Worst 6216.5 7080.17 6216.48 5385.93

Rank 3 2 4 1

PV/battery Mean 5957.7 6031.18 7219.44 6530.56

Std. 1.51 172.55 292.04 390

Best 5957.47 5957.47 5957.47 5957.47

Worst 5968.3 6914.52 7219.44 7538.73

Rank 1 2 4 3

Wind/battery Mean 4712.5 6053.34 6305.01 5456.91

Std. 345.65 956.57 957.63 988.93

Best 4554.98 4554.98 4554.98 4554.98

Worst 5706.6 7725.51 7395.21 9837.81

Rank 1 3 4 2

Average rank 1.33 2.5 3.5 2.66

Final rank 1 2 4 3

Table 3 e Summary of the results obtained by the algorithms.

NPV NWind NBatt NTank NInv PVcost

Windcost

Batterycost

FCcost

Electrolyzercost

H2 tankcost

Invertercost

Totalcost

PV/wind/FC

Optimal solution 10 9 e 26 4 492.7 3211 e

4942.9

4942.9 4172.6 1036 18,798.05

PV/FC

Optimal solution 133 e e 184 3 6552.8 e e

4942.9

4942.9 29,529.3 777 46,744.79

Wind/FC

Optimal solution e 11 e 36 3 e 3924.5 e

4942.9

4942.9 5777.5 777 20,364.75

PV/wind/battery

Optimal solution 10 8 8 e 4 492.7 2854.2 240.2 e e e 1036 4623.15

PV/battery

Optimal solution 57 e 79 e 3 2808 e 2372.1 e e e 777 5957.47

Wind/battery

Optimal solution e 10 7 e 3 e 3567.8 210.2 e e e 777 4554.98

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NWind ¼ 11, NTank ¼ 36; PV/wind/battery NPV ¼ 10, NWind ¼ 8,

NBatt ¼ 8; PV/battery: NPV ¼ 57, NBatt ¼ 79; wind/battery

NWind ¼ 10, NBatt ¼ 7. Figs. 5 and 6 represent the break down of

the total annual cost for the hybrid systems.

Figs. 7e9 illustrate the convergence process of the algo-

rithms for finding the optimal size of the systems. In these

figures, the best total annual cost is plotted vs. iteration

number. Comparison of the figures shows that PSO and TS

converge to the optimal solution more quickly than HS and

SA. In figures the convergence process of PSO and TS have

been plotted up to 100 iterations, because maximum number

of iterations for these algorithms has set to 100 while for HS

and SA this value is 1000. In order to compare the computa-

tional cost of the algorithms, Table 4 has been shown. From

this table, it can be concluded that the computational cost of

TS is less than that of the other algorithms. Also, the

computing time of PSO is more than that of TS, HS, and SA.

At time t, the difference between the generated and

demanded powers of the systems is obtained by

DPt ¼ ðPtPV þ PtWTÞ � PtLoad. Fig. 10 represents the difference be-

tween the generated and demanded powers (DP) for the six

optimized systems and Fig. 11 shows the storage level of the

batteries and hydrogen tanks. For example, consider the PV/

WT/FC system. In this case, negative sign of DPmeans that the

generated power of PV and WT systems can not satisfy the

Fig. 5 e Break down of the total annual cost. (a) PV/wind/

FC; (b) PV/FC and (c) wind/FC.

Fig. 6 e Break down of the total annual cost. (a) PV/wind/

battery; (b) PV/battery and (c) wind/battery.

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load. So, the FC starts to work and meets the remaining load

demand. For instance, at 9th hour,DP is negative (Fig. 10(a)). At

this time, form Fig. 11(a), it is seen that the storage level of

hydrogen tank is positive meaning that the storage device can

Fig. 7 e Convergence process of the algorithms for finding

the optimum size. (a) PV/wind/FC; (b) PV/wind/battery.

Fig. 8 e Convergence process of the algorithms for finding

the optimum size. (a) PV/FC; (b) PV/battery.

Fig. 9 e Convergence process of the algorithms for finding

the optimum size. (a) wind/FC; (b) wind/battery.

Table 4 e Comparison of the algorithms in terms of thecomputational cost (second).

Hybrid system Index Algorithm

PSO TS SA HS

PV/wind/FC Mean 0.192 0.047 0.082 0.082

Min 0.156 0.031 0.047 0.062

Max 0.250 0.094 0.140 0.109

PV/FC Mean 0.185 0.039 0.07 0.082

Min 0.172 0.016 0.062 0.047

Max 0.218 0.094 0.094 0.125

Wind/FC Mean 0.172 0.027 0.072 0.078

Min 0.156 0.016 0.047 0.062

Max 0.218 0.062 0.094 0.109

PV/wind/battery Mean 0.663 0.051 0.070 0.077

Min 0.546 0.031 0.062 0.062

Max 0.78 0.078 0.094 0.140

PV/battery Mean 0.706 0.047 0.065 0.071

Min 0.515 0.031 0.047 0.062

Max 0.967 0.078 0.094 0.094

Wind/battery Mean 0.698 0.057 0.066 0.074

Min 0.624 0.031 0.062 0.062

Max 0.796 0.12 0.094 0.109

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meet the deficit power. Simulation results show that the

optimized hybrid systems will be able to supply the load

demand.

In practice, most of the remote regions have electrical

power typically generated by diesel generators. This system is

difficult to maintain, very inefficient, and subject to frequent

outages. To protect against power outages due to mechanical

breakdowns, redundant generators are frequently in place,

resulting in higher capital costs. Maintenance work is most

often performed by skilled workers from outside of the re-

gions. Fuel must also be transported to the regions. All of this

leads to having an expensive generation system. For this aim

as well as in response to concerns about climate change, en-

ergy independence and economic stimulus, development of

renewable energy in worldwide has been encouraged by

government policy. As a result, according to the above-

mentioned reasons and the difficulties of transforming the

electrical energy to the remote regions, the renewable sources

can be promising alternatives.

Conclusion

This paper studies the economic aspects of PV/wind/FC and

PV/wind/battery systems and performance of different heu-

ristic optimization techniques to optimally size these sys-

tems. It is found that hybrid systems with battery storage are

economically better choice for producing electrical power

than hybrid systems with hydrogen-based storage systems.

With improvement in the efficiency of both FC and electro-

lyzer, FC/electrolyzer storage system can be economically

competitive in the future.

To optimally size the hybrid systems, different heuristic

techniques are applied to find the optimum number of each

component. From the optimization viewpoint, it is found that

PSO yields more promising results than TS, SA, and HS in

terms of the total annual cost.

Acknowledgment

The financial support of the Graduate University of Advanced

Technology is greatly acknowledged.

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