Economic analysis and optimization of a renewable energy based.pdf

Economic analysis and optimization of a renewable energy based
power supply system with different energy storages for a remote
island
Muhammad Shahzad Javed a
, Tao Ma a, *
, Jakub Jurasz b
, Fausto A. Canales c
,
Shaoquan Lin a
, Salman Ahmed a
, Yijie Zhang a
a
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
b
Faculty of Management, AGH University, Cracow, Poland
c
Department of Civil and Environmental, Universidad de La Costa, Barranquilla, Colombia
a r t i c l e i n f o
Article history:
Received 22 June 2020
Received in revised form
16 September 2020
Accepted 15 October 2020
Available online 4 November 2020
Keywords:
Off-grid renewable energy system
Hybrid pumped battery storage
Particle swarm optimization
Cost of energy
Energy balance analysis
Sensitivity analysis
a b s t r a c t
This study investigates and compares the various combinations of renewable energies (solar, wind) and
storage technologies (battery, pumped hydro storage, hybrid storage) for an off-grid power supply sys-
tem. Four configurations (i.e., single RE source system, double RE source system, single storage, and
double storage system) based on two scenarios (self-discharge equal to 0% and 1%) are considered, and
their operational performance is compared and analyzed. The energy management strategy created for
the hybrid pumped battery storage (HPBS) considers that batteries cover low energy surplus/shortages
while pumped hydro storage (PHS) is the primary energy storage device for serving high-energy gen-
erations/deficits. The developed mathematical model is optimized using Particle Swarm Optimization
and the performance and results of the optimizer are discussed in particular detail. The results evidence
that self-discharge has a significant impact on the cost of energy (13%e50%) for all configurations due to
the substantial increase in renewable energy (RE) generators size compared to the energy storage ca-
pacity. Even though solar-wind-PHS is the cost-optimal arrangement, it exhibits lower reliability when
compared to solar-wind-HPBS. The study reveals the significance of HPBS in the off-grid RE environment,
allowing more flexible energy management, enabling to guarantee a 100% power supply with minimum
cost and reducing energy curtailment. Additionally, this study presents and discuss the results of a
sensitivity analysis conducted by varying load demand and energy balance of all considered configu-
rations is performed, which reveals the effectiveness of the supplementary functionality of both storages
in hybrid mode. Overall, the role of energy storage in hybrid mode improved, and the total energy
covered by hybrid storage increased (48%), which reduced the direct dependency on variable RE
generation.
© 2020 Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/
licenses/by/4.0/).
1. Introduction
The world is experiencing a transition from fossil-fuel domi-
nated power systems to renewable energy (RE) based power sys-
tems. Adverse environmental impacts of diesel generators, high
fuel cost fluctuations, and the risks associated with fuel trans-
portation and storage make RE resources an alternative solution for
power system design, especially for off-grid power supply.
Additionally, the cost of RE technologies has substantially
decreased over recent years, as the cost of electricity generated
from wind, PV, concentrated solar power, and hydropower declined
considerably between 2010 and 2018 (Fig. 1). According to the In-
ternational Renewable Energy Agency (IRENA) report, over 80% of
solar photovoltaic (PV) and 75% of wind projects to be commis-
sioned in 2020 will produce electricity cheaper than any oil, coal, or
natural gas option [1].
Among the available RE technologies, solar PV, and wind tur-
bines (WT) are the most mature and attractive options of green
energy, especially for the low power and remote areas [3]. However,
volatility, randomness and inherent intermittency of these RE
* Corresponding author.
E-mail addresses: shahzad.sjtu@yahoo.com (M.S. Javed), tao.ma@connect.polyu.
hk (T. Ma).
Contents lists available at ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
https://doi.org/10.1016/j.renene.2020.10.063
0960-1481/© 2020 Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Renewable Energy 164 (2021) 1376e1394

resources usually make them unsuitable for direct integration to
the grid, a claim under debate as illustrated by a recent paper of
Fasihi and Breyer [4]. At the same time, the hybridization of
different RE sources coupled with an energy storage system (ESS)
can significantly improve the system’s reliability [5]. Jacobson et al.
[6] listed the possible approaches/solutions to harmonize the RE
output with demand. Amongst them, they highlight the application
of ESS and the use of the complementary characteristic of RE
generators as the most viable approach, a claim supported by many
recent studies [7]. Technical aspects and performance evaluations
of ESS have been widely discussed in the literature [8], such as the
study by Chen et al. [9], presenting a comprehensive critical review
of all the relevant ESS characteristics. The ESS performance is
mostly affected by power rating, discharge/recharge time, self-
discharge rate, round trip efficiency, operating temperature, and
lifetime. Among all ESS performance parameters, the self-discharge
rate is a significant design and performance parameter, mostly
when storage is the base source for continuous power supply.
Table 1 presents the technical characteristics of the ESS employed
in this study, and it shows that each energy storage has a different
self-discharge rate, depending on the operational environment and
their corresponding size. Since each ESS exhibits a range of storage
self-discharge values (Table 1), this study assesses two cases: 0% (no
self-discharge) and 1% (per day self-discharge), to comprehensively
analyze its effect on the optimal sizing of RES, a feature often
ignored in the literature. The literature about off-grid energy sys-
tems based on RE usually concentrates on developing an econom-
ically optimized system with single energy storage like pumped
hydro [10], battery [11], fuel cell [12], or flywheel [13]. However,
recent literature has assessed renewable energy systems (RES) with
two different energy storage technologies such as the combination
of battery-super capacitor [14], battery-hydrogen [15], capacitor-
Nomenclature table
Parameters/Variables
Cc capital cost ($)
Ck replacement cost ($)
Cm maintenance cost ($)
Crs residual value of system components ($)
Eb energy stored in the battery bank (kWh)
Ed deficit energy (kWh)
Eg energy generated by the hydro turbine (kWh)
Eload load demand (kWh)
Enet net energy (kWh)
Ep energy pumped to UR (kWh)
EPV energy produced by solar arrays (kWh)
ERES energy generated by RES (kWh)
Es available surplus energy (kWh)
Eserved total energy served (kWh)
EUR energy stored in UR (kWh)
EWT energy produced by wind turbines (kWh)
n total system lifetime (years)
Prat rated power of pump/turbine machine (kW)
r discount rate/present worth factor (%)
SOCbatt battery storage state of charge (%)
SOCUR UR state of charge (%)
Tc total system cost ($)
t PHS self-discharge rate (%)
s battery storage self-discharge rate (%)
hPHS PHS overall efficiency (%)
hinv inverter efficiency (%)
hb battery efficiency (%)
Abbreviations
BS battery storage
COE cost of energy
EMS energy management strategy
ESS energy storage system
HPBS hybrid pumped battery storage
PHS pumped hydro storage
PSO particle swarm optimization
PV photovoltaic
RE renewable energy
RES renewable energy system
UR upper reservoir
WT wind turbine
Fig. 1. Costs of different RE sources from 2010 to 2018 (a) Installation cost (b) Levelized cost of energy [1,2].
M.S. Javed, T. Ma, J. Jurasz et al. Renewable Energy 164 (2021) 1376e1394
1377

hydrogen [16], battery/flywheel [17], battery-superconducting
magnetic storage [18] and battery-pumped hydro [19]. The scope
of this study comprises a comparison between the operational
performance of single ESS (battery/pumped hydro) and a hybrid
pumped battery storage (HPBS) in an off-grid RES, using solar/wind
as the base RE sources, aiming at ensuring the smooth and reliable
operation of the system.
The current state of the art suggests a renewed interest in
studies related to off-grid RES, especially for remote areas [21]. For
instance, Liu et al. [22] evaluated the PHS significance for remote
areas and they found that PHS, coupled with RES, can significantly
promote off-grid electricity generation. Elghali et al. [23] investi-
gated the optimal sizing strategy for hybrid storage based RES,
developing a frequency-based energy management strategy,
simplified sizing method, and a procedure for selecting the suitable
energy storage technology. Destro et al. [24] tested the perfor-
mance of RES for a tourist resort using battery and PHS as energy
storage. Their system also included a heat pump, a boiler, and a
diesel engine, with their results indicating that both storages
considerably cover the load demand. Oskouei et al. [25] evaluated a
two-stage operating strategy for reducing the power generation
uncertainties of RES through PHS. Their optimization results
revealed an increase in the overall system benefits, by a simulta-
neous reduction in surplus and blackouts. Previous work of the
authors have evidenced the feasibility of powering a remote island
by using PHS and batteries as a single storage option [26], with a
follow-up study conducting a techno-economic analysis of different
power supply options for an isolated community [27]. Çelik et al.
developed a novel control strategy for balanced power sharing
between RES and grid, revealing that power delivery capability of
grid connected distributed system is improved [28].
RES planning requires the optimum sizing of each component of
the system that would allow meeting the load demand while
satisfying the constraints at the lowest possible costs [29]. The
uncertainties associated with the variable nature of RE sources,
load demand, the performance of generation technologies, and
their fluctuating prices increase the complexity of such optimiza-
tion problems [30]. In the literature, several studies have dealt with
the optimization of an off-grid RES using different approaches,
providing evidence that results are highly dependent on system
parameters [31], geographical and climatic conditions [32], load
data [33], and the algorithm used [34]. The various heuristic and
metaheuristic algorithms employed for the optimal sizing of off-
grid RES include the non-dominated sorting genetic algorithm
[35], grey wolf optimizer [36], honey bee mating optimization [37],
harmony search [38], simulated annealing [39] and particle swarm
optimization (PSO) [40]. However, the majority of the studies
directly describe their optimization models without a detailed
explanation of the working principle of the optimizers employed in
the context of the formulated objective function. Numerous RES
configurations are considered in literature for optimization like PV-
PHS [31], PV-BS [41], WT-BS [42], WT-PHS [43], PV-WT-BS [29], PV-
WT-PHS [5] and PV-WT-HPBS [19]. Previous studies have pre-
dominantly focused on optimal sizing, techno-economic analysis,
and reliability estimation of only one configuration. This study
utilizes the PSO algorithm to determine the optimal configuration
(in terms of minimizing the total cost) of nine RES that use solar/
wind as base RE sources and different ESS, followed by an assess-
ment of the operational results of each cost-optimal configuration
to appraise the benefits. Besides, this research discuss the energy
management strategy (EMS), reliability of supply and coordination
of HPBS coupled with PV/WT system.
Based on the conducted literature review, the authors found the
following research scientific gaps:
1) Most of the studies considered only one type of RES and did not
compare the feasibility of different systems configurations for
the proposed off-grid region, which is fundamental when the
only purpose is to meet energy demand [29,43,44].
2) In off-grid RES, the ESS is a core component that requires an
accurate sizing. However, most of the studies ignored the self-
discharge effect in ESS modeling for the sake of simplicity,
jeopardizing the reliability of whole system (especially when
batteries provide the energy storage capability) [5,41,42].
3) There is a scarcity of studies that assess and compare the per-
formance of off-grid RES using battery and PHS as single ESS and
hybrid storage (i.e., HPBS) in terms of life cycle cost, reliability,
and energy balance.
Within this context, the main objective of this study is to eval-
uate the optimal configuration of different power supply options
using batteries, PHS, and HPBS for energy storage, followed by a
comparative analysis of all optimized supply options in terms of
cost, reliability, and power balance. Additional contributions of this
research are:
1) Mathematical modeling of HPBS and flexible EMS, focusing on
reliability and economy for off-grid RES, prioritizing PHS under
given constraints.
2) The application of the PSO technique for determining the
optimal sizing of nine different off-grid RES configurations
comprising PV, WT, BS, and PHS, while also considering energy
storage self-discharge, a feature neglected in previous studies
for simplification.
3) The study compares the operational performance of four sce-
narios, with systems based on a single or double RE sources, or
single or a hybrid storage system and a hybrid storage system.
Table 1
PHS and batteries technical characteristics [9,20].
Parameter Unit PHS Lead-acid Lithium-ion
Energy density W h/L 0.5e2 50e90 200e400
Power density W/L 0.5e1.5 10e400 1500-10,000
Power rating MW 10e3000a
0e40 0e100
Self-discharge % very small 0.1e0.3 0.1e0.3
Roundtrip efficiency % 60e80% 80e90% 90e98%
Cycling times cycles 10,000e30,000 500-1800 1000-20,000
Response time e minutes/not rapid milliseconds milliseconds
Storage duration e long-term minutes-days (short term) minutes-days (short term)
Maturity e mature mature demonstration
Lifetime Years 40e60 5e15 5e15
a
Based on authors best knowledge: A) Smallest PHS in operation is “Fu
zine 6.5 MW” located in Croatia B) Biggest is planned in China (not more than 4000 MW).
1378

The rest of the paper is structured as follows: Section 2 contains
the proposed RES description, input data used, involved cases for
analysis, and energy management strategy. Section 3 describes the
optimization process, objective function and the working principle
of the proposed algorithm. Section 4 presents the discussion on the
major findings, energy balance analysis, and sensitivity analysis.
Finally, section 5 includes the concluding remarks and future
research directions.
2. System description
2.1. Proposed off-grid hybrid energy system
The schematic diagram shown in Fig. 2 presents the proposed
off-grid RES coupled with hybrid pumped hydro battery storage.
The different RES configurations considered in this study consist of
various combinations of PV arrays, wind turbines, converter/
inverter, controller, BS, PHS, and dump load. Due to the intermit-
tency of RE generators, there are energy deficient and energy excess
periods. During the excess generation periods, the demand is
initially met through wind turbine output (for hybrid RES scenario),
efficiently utilizing the surplus energy for energy storage (i.e.,
pumping the water to the upper reservoir (UR) and BS charging).
On the other hand, during energy-deficient periods, water is
released from UR for producing hydroelectricity. In the case of
hybrid storage, generation from PHS has and minor energy short-
ages are covered by BS, working as supplementary ESS when PHS is
unable to generate electricity due to the low state of charge. A
comprehensive discussion of the proposed EMS of HPBS is available
in the following section.
Even though Due to the inherent intermittency of RE sources
and the mismatching between supply-demand, the off-grid RES
requires an energy balance for the stable operation, which could be
accomplished by employing hybrid storage. The benefits of hybrid
storage are power supply flexibility, increased system reliability
(self-energy dependence), enhanced operational life of storages,
lessened dump load, reduction of RE generators size and energy
storage capacity. Finally, hybrid storage guarantees the availability
of sufficient stored energy each time to meet the dynamic load
demand, hence maximizing benefits from the renewables.
2.2. Input data and involved system configurations
This study evaluates nine different off-grid RES configurations,
as shown in Table 2, and compares their operational performance.
In the first case, solar PV is the only renewable source of the RES,
and its assessment considers single BS/PHS storage and HPBS.
Similarly, in case two, wind power is employed as the only base
source, and then the third case evaluates both (solar/wind) sources
for energy generation.
A remote island named Jiuduansha (3140 N, 121450 E) located
near Shanghai is the case study of this paper. This island currently
has no access to electricity (as it is located very far from the national
grid), and it has a small population. Based on this, a design load for
ten houses is anticipated as 255.6 kW h per day. A 5% hourly and
daily randomness, as well as seasonal variations, are added for a
more practical simulation of the real conditions, as shown in Fig. 3.
The solar and wind meteorological data used in this study cor-
responds to the records from the small meteorological station of
Shanghai Jiao Tong University [3]. The data maps shown in Fig. 4
presents the average one-year solar irradiance and wind data
with an hourly time step. The yearly average wind speed is 5.65 m/
s, while the average solar potential is 4.13 kW h/m2
/day. The pro-
posed yearly data is used in the process of optimization to include
Fig. 2. Energy flow schematic of typical off-grid RES coupled with HPBS.
Table 2
Configurations considered in this study.
Battery PHS PHS þ Battery
Case#01 PV only PV only PV only
Case#02 Wind only Wind only Wind only
Case#03 PV þ Wind PV þ Wind PV þ Wind
1379

the seasonal variations of solar radiation, wind speed, and load
demand. This annual data is repeatedly used over the whole project
lifetime.
2.3. Solar and wind energy modeling
The essential technical and cost information of the selected solar
PV modules and wind turbines is given in the appendix (Table A1).
The energy output of the PV module can be calculated using the
following equation [45]:
PPV ðtÞ ¼ fPV :YPV :
IT ðtÞ
IS
(1)
where fPV is the derating factor (80% for this study [45]); YPV is the
PV module rated capacity (kW); IT ðtÞis the incident solar radiation
on PV surface area (kWh/m2
) and ISis the standard solar radiation
(1000 w/m2
).
This study considers a 5 kW wind turbine, whose main technical
and cost details are available in the appendix (Table A1). Ref. [3]
details the technical information of the selected WT (including
power curve). The output energy of a WT at the time (t) can be
calculated as:
PWTðtÞ ¼
8

:
0 jvðtÞ vcin or vðtÞ vcout
pr*
vðtÞ vcin
vr vcout
jvcin vðtÞ vr
pr jvr vðtÞ vcout
9

=

;
(2)
where pris the rated power of WT; vðtÞis the wind velocity at the
time (t); vr,vcin,vcout are the rated, cut-in and cut-off wind velocities
of selected WT.
2.4. Proposed energy management strategy
The operating strategy of RES with single energy storage rather
straightforward, due to only one dispatchable source, i.e., PHS/BS.
Whenever the difference between RE generators output and load
(net energy) is positive, meaning that power generated by renew-
ables is sufficient to meet the load demand, surplus energy is
employed to charge single energy storage (in this study, it could be
PHS or BS). Any further surplus energy can be dumped or sent to
the grid (in grid-connected case). On the other hand, whenever net
energy is negative, the only supplementary energy source (PHS/BS)
releases energy to meet the deficit. If there is still an energy outage,
it is considered as loss of load. The charging and discharging models
of PHS and BS are described in the following subsection, while the
operating strategy adopted in this study for single energy storage
(PHS/BS) based off-grid RES configurations are in detail in previous
studies from authors [3,5,31]. This section outlines a rule-based
EMS for off-grid HPBS based RES (Fig. 5), proposed to make sure
each storage functions appropriately, i.e., charging/discharging and
the supply/demand balance. Additionally, the proposed EMS en-
sures an efficient system operation with less operating cost and
maximum system reliability. The proposed EMS controls the flow of
energy between RES, load, and HPBS, where it is divided into two
modes based on the available net energyEnetðtÞ, and it can be
calculated by using the following formula:
Fig. 3. Load demand (a) hourly demand of a typical day (b) month-wise whole year load demand.
1380

Fig. 4. RE resources contour (a) solar irradiance (b) wind velocity.
Fig. 5. Energy management strategy of off-grid RES coupled with HPBS.
1381

EnetðtÞ ¼ EPVðtÞ þ EWTðtÞ EloadðtÞ (3)
2.4.1. Charging mode ðEnetðtÞ 0Þ
In this scenario, RE generators are producing enough energy,
and the net power is positive; therefore, the surplus energy serves
to charge HPBS. Since PHS is a large-capacity energy storage system
and it is uneconomical to run PHS for smaller energy inputs, a
technical limitation for PHS is introduced to reduce the energy spill
due to the start/stop of PHS [19,46]. Besides, reducing the number
of start/stop times of PHS consequently increases the turboma-
chinery lifetime, which is the main fraction of the PHS cost. A 20% of
pump/turbine machine rated power constraint is applied for PHS
operation [19], and energy lower than this constraint will be used
to charge BS. This setting reduces the energy curtailment and im-
proves the exploitation of RE sources. Surplus energy sent to the UR
can be expressed as [47]:
EpðtÞ ¼ min½qðtÞrghhPHS; Es (4)
qðtÞis the water flow from pump (m3
/sec); ris the density of water
(kg/m3
); gis the gravity acceleration (m/s2
); his head of UR (m);
hPHSis the overall PHS efficiency; EpðtÞis the energy pumped to UR
in time ðtÞand Esis the available surplus energy.
Energy stored EURðtÞin UR at any time ðtÞcan be calculated as [5]:
EURðtÞ ¼ EURðt 1Þ

1
t:Dt
24

þ
ð
t
t1
EpðtÞdt
ð
t
t1
EgðtÞdt (5)
SOCURðtÞ ¼
EURðtÞ
EURðmaxÞ
(6)
SOCmin SOCURðtÞ SOCmax (7)
tis the PHS self-discharge and SOCURðtÞis the state of charge of UR at
the time (t).
If the available surplus energy Escould not be used for PHS
charging due to technical constraints, i.e., excess energy is less than
20% of PHS rated power or SOCURis 100%, then it will be used for BS
charging. BS charging using surplus energy can be expressed as
[3,21]:
EbðtÞ ¼ Ebðt 1Þ:

1
s:Dt
24

þ

ERESðtÞ EpðtÞ EloadðtÞ=hinv

hb
(8)
SOCbattðtÞ ¼
EbðtÞ
Emax
b
(9)
SOCmin SOCbattðtÞ SOCmax (10)
EbðtÞis the energy stored in BS at the time ðtÞ; sis the self-discharge
rate; ERESðtÞis energy generated by RES; hinv,hb are the inverter and
battery efficiencies respectively, and Emax
b
is the maximum BS ca-
pacity. The technical and economic details of all RES components
are available in the appendix (Table A1).
2.4.2. Discharging mode ðEnetðtÞ 0Þ
If the RE generators fail to meet the load demand (net energy is
negative), HPBS will work in discharging mode. At first, the esti-
mation of the energy deficit Edserves to calculate which storage can
cover this deficit, or if both ESS will be simultaneously employed.
Secondly, the algorithm will check theSOCURand minimum tech-
nical PHS operational constraint to trigger the PHS discharge pro-
cess according to the following expression [19,48]:
EgðtÞ ¼ min½qðtÞrghhPHS; Ed (11)
If PHS is unable to cover the energy deficit due to the minimum
state of charge limit, or can only partially cover it, the remaining
amount will be served by BS. The BS discharging can be expressed
as [29,49]:
EbðtÞ ¼ Ebðt 1Þ:

1
s:Dt
24

loadðtÞ=hinv
ERESðtÞ EgðtÞ

hb
(12)
However, if PHS is unable to cover any part of load demand, BS
will ensure to cover the whole energy deficit as a last case. If both
storages fail to meet load demand, then it will be considered as loss
of power supply probability (LPSP). It is a widely used reliability
index and could be defined as the total hours of energy not served
ðENSÞdivided by the number of total hours. LPSP can be expressed
as [31,33]:
LPSP ¼
P
8760
i¼1
hours½ENS
8760
(13)
If the state of charge of ESS is 100% and there is surplus energy
after meeting the load demand, it is considered as excess energy. It
can be expressed in terms of percentage like LPSP and can be
written as:
Excess energy ð%Þ ¼
sumðsurplus energy generatedÞ
sumðenergy servedÞ
(14)
3. Optimization process
The capabilities of meta-heuristic optimization algorithms in
the field of RES have been extensively demonstrated and well-
proved [50]. Many researchers have comparatively examined the
performance of these meta-heuristics. This study employs the
particle swarm optimization algorithm, which is described in the
following subsection.
3.1. Optimization objective and fitness function
The objective function of all considered configurations is to
minimize the system’s total cost (objective fitness value) by sizing
each component of RES while satisfying all the operational con-
straints. The realization of the objective mainly depends on the
installed capacities of solar, wind, inverter, and ESS. The mathe-
matical formulation of the PV-WT-BS-PHS system is presented in
this section as it involves all components. Therefore, it allows
modeling other configurations by merely omitting any element
1382

unnecessary for that system. The summary of the proposed opti-
mization model is presented in Table 3. RES total cost ðTcÞinvolves
capital, maintenance, and replacement costs of each configuration
component.
Min Tc
¼
X
i
Ni

Cc
i þ Cm
i þ Ck
i

Crs
(15)
Niis the capacity of each component and decision variable in opti-
mization formulation; Cc
i ; Cm
i ; Ck
i represents the capital, mainte-
nance, and replacement cost ($) of each component, respectively;
Crsis the residual value and Tcis the system’s total cost ($).
Various costs occur during the system’s lifetime, such as oper-
ational and maintenance cost, replacement cost, and residual/
salvage value. The discount rate approach could be used to convert
all future cash flows to present, allowing to make comparisons of
different cost optimum configurations at net present value
ðNPVÞ[26]. In the life cycle cost analysis, the following equation
could be used to NPV of all recurring and capital costs of the system.
NPV½r; n; c ¼
C1
ð1 þ rÞ1
þ
C2
ð1 þ rÞ2
þ ::: þ
Cn
ð1 þ rÞn ¼
X
n
j¼1
Cj
ð1 þ rÞj
(16)
For instance, the BS lifetime is assumed five years in this study,
and the present value of all incurred cost on the BS replacement
during the whole system lifetime will be:
NPVbatt ¼ Pbatt

1 þ
1
ð1 þ rÞ5
þ
1
ð1 þ rÞ10
þ
1
ð1 þ rÞ15

(17)
Total system cost during the study period could be expressed as:
Tc
¼ Cc
þ Cm
þ Ck
Crs
(18)
¼ Cc
þ NPV

r; n; Cm
þ NPV
h
r; n; Ck
i
NPV

r; n; Crs
(19)
¼ Cc
þ
X
n
j¼1
Cm
j
ð1 þ rÞj
þ
X
n
j¼1
Ck
j
ð1 þ rÞj

Crs
n
ð1 þ rÞn (20)
¼
X
n
j¼0
Ck
j
ð1 þ rÞj
þ
X
n1
j¼1
Cm
j
ð1 þ rÞj
þ
Cm
j Crs
n
ð1 þ rÞj
(21)
Crs
¼ Ci
Nremi
lifei
(22)
where ris the discount rate/present worth factor (6% considered for
this study); nis the total system lifetime (20 years); Crepresents any
cost type ($); Pbattis the present value of battery; NPVis the net
present value; Nremiis the remaining life of the ith component and
lifeiis the total life of the ith component.
Finally, the cost of energy (COE), i.e., cost per kWh can be
calculated as:
COE ¼
Tc
Eserved
(23)
Eservedis the energy served by RES during the total study period.
3.2. Particle swarm optimization
Particle swarm optimizer is a meta-heuristic optimization al-
gorithm, attempting to solve non-linear and non-convex problems
based on the social behavior of a flock of birds or swarm of insects.
The exploration and exploitation behavior of swarm particles
mainly depends on the continuous exchange of information based
on swarm group intelligence and particles’ intelligence. The ad-
vantages of the proposed algorithm over other techniques are:
minimum dependency on the particles’ initialization points, rapid
and high convergence rate, ease of use, simplicity, and least storage
requirement. Javed et al. compared the performance of different
nature-inspired optimization algorithms for developed RES prob-
lems and inferred that PSO outperforms other optimizers in terms
of minimizing the objective function value with the least relative
error [51].
Each feasible solution in PSO is called a particle with a number of
decision variables and searches for a global solution in ndimension
search space [40]. Each particle is defined by a velocity vector
vi2ℝn
0and position vectorxi2ℝn
0 while the swarm’s search space
is constrained byxmin xi xmax. In this study, the capacity opti-
mization of each RES component refers to the particle position
vector.
In every generation, the next particle’s next position is always
defined by its location in the previous iteration and its current
velocity.
xiðg þ 1Þ ¼ xiðgÞ þ viðg þ 1Þ (24)
At each time step, the algorithm verifies the current position of
each particle to make sure that exploration is occurring within the
search space. If a particle moves out from the search space, the
algorithm reiterates its previous position based on the particle’s
previous history [52]. For integer solution, the new location of each
particle is rounded off to the nearest number such thatxi2ℤn
0:
xiðgÞ ¼ floorðxiðgÞ þ 0:5Þ (25)
Table 3
Proposed optimization model summary.
Objective function Minimize the system’s total cost MinðTcÞ
Decision variables PV capacity ðNPVÞ
WT capacity ðNWTÞ
Battery storage capacity ðNbattÞ
UR reservoir capacity ðNURÞ
Scenario parameter Self-discharge rate [0, 1]
Constraints Minimum and maximum number of decision variables NminðPV; WT; batt; URÞ
NmaxðPV; WT; batt; URÞ
ESS constraints SOCmin SOCbattðtÞ SOCmax
SOCmin SOCURðtÞ SOCmax
PHS technical constraint 20% of PHS rated power
1383

The particle velocity calculation at ðg þ 1Þiteration can be scaled
down in three subparts: (I) velocity of the ithparticle in the
gthiteration; (II) distance to personal best ðpbestÞ, i.e., the cognitive
component; (III) distance to global best ðgbestÞ,i.e., the social
component.
viðg þ 1Þ ¼ fiw:viðgÞ þ f1:rand1:ðpbest xiðgÞÞ
þf2:rand2:ðgbest xiðgÞÞ i ¼ 1; 2; :::; np
(26)
irepresents the number of particles and gdenotes the number of
iterations. The exploration and exploitation behavior of the PSO
algorithm can be controlled through inertia weight ðfiwÞ, which
linearly decreases from the maximum value (0.9) to the minimum
value (0.4 or 0.2), depending on the number of decision variables
and problem complexity [40]. Inertia weight of ithparticle at
gthiteration can be expressed as:
fiw ¼ fmax g

fmax fmin
gmax

(27)
The cognition weight f1and social weight f2can be adjusted to
improve the behavior of particles and the overall performance of
the swarm. However, these weights are generally selected under
the criteria f1 þ f2 4to prevent any type of explosion [52]. The
graphical representation in Fig. 6 illustrates the particles’ move-
ment in search space. A Flowchart of the PSO pseudocode imple-
mentation in MATLAB is available in the appendix (Fig. A1). The
execution of PSO comprises four evaluation criteria: the first cri-
terion is the swarm initialization to check whether particles initial
points are within search space or not; the second criterion is to
verify that the position of each swarm particle satisfies the problem
constraint; the third criterion is to update the particle best position
if the fitness value of the particle is better (smaller) than its his-
torical best value, and the fourth criterion is to check whether the
particle best value is better (smaller) than swarm’s global best, and
if so, update the global best position of the swarm. The PSO pa-
rameters employed for this study are presented in Table 4.
Fig. 7 shows the PSO exploration and exploitation behavior for
the optimization of HPBS based RES. An Intel® Core™ i7-7700 CPU
@ 3.6 GHz, RAM 16.0 GB computer is used for simulations. This
figure allows observing that the algorithm converges to the global
solution in 80th iteration, while the average fitness of all particles
represents the deviation in the fitness value of each particle, which
becomes narrower as the number of iteration advances. The search
history presents the exploration and exploitation behavior of the
proposed algorithm. It can be observed that particles firstly explore
the entire search space and then exploit a specific area based on
their exchange of information and their own intelligence. Red dots
represent the particle at their final iteration and the small white
box denotes a global solution.
4. Results and discussions
The proposed PSO optimization algorithm is applied to all cases,
as discussed in section 2.2. Off-grid RES simulation programing and
PSO functions are developed and implemented in MATLAB. All
configurations are simulated for one-year period and repeated
three times to ensure that the proposed decision variables are
optimum. For the sake of fair comparison between the different
configurations, the assumptions made are listed in the appendix
(Table A2).
4.1. Optimal system configurations
The simulation of all the different configurations evaluate two
scenarios: with and without considering self-discharge, and Table 5
Fig. 6. Visual representation of the swarm particles in PSO.
Table 4
PSO parameters employed for this study.
Parameter Symbol Value
Variables (Dimensions) var 2 to 5 (problem dependent)
Search space xmin Lower bound (0)
xmax Upper bound (variable dependent)
Repetitions rep 3
Population pop 100
Generations gen 100
Inertia weight fiw 0.9 to 0.2 (linearly decrease)
Cognition weight f1 2.0
Social weight f2 2.0
1384

Fig. 7. Exploration and exploitation performance of PSO for HPBS based RES.
Table 5
Results of optimal sizing of each conﬁguration with self-discharge 0% and 1%.
Self-discharge ESS RE source PV Wind Battery capacity PHS capacity COE LPSP Excess energy
kW kW kWh kWh $/kWh (%) (%)
0% Batt PV only 214 e 646 e 0.601 0 1.36
WT only e 300 932 e 0.865 0 3.26
PV þ WT 96 75 364 e 0.383 0 1.17
PHS PV only 221 e e 594 0.302 1.28 1.04
WT only e 280 e 821 0.399 2.1 2.38
PV þ WT 84 75 e 320 0.196 2.3 0.62
HPBS PV only 219 e 8 567 0.307 0 0.92
WT only e 278 13 800 0.409 0 2.8
PV þ WT 83 71 17 310 0.215 0 0.48
1% Batt PV only 800 e 292 e 0.823 0 7.5
WT only e 535 1333 e 1.32 0 5.35
PV þ WT 107 80 472 e 0.467 0 1.02
PHS PV only 290 e e 688 0.373 1.1 1.12
WT only e 350 e 1448 0.576 1.9 2.01
PV þ WT 105 85 e 340 0.222 2 0.65
HPBS PV only 282 e 7 680 0.378 0 0.88
WT only e 497 10 943 0.610 0 3.55
PV þ WT 103 80 19 330 0.243 0 0.45
Fig. 8. Global best COE value vs. swarm generations of optimal systems.
1385

shows the results for both of them. The results indicate that the PV-
WT-PHS system is cost-optimum, while HPBS based PV-WT system
is optimum concerning reliability for both scenarios. Fig. 8 shows
the convergence curve of both optimum systems. PV-WT-PHS
configuration converges rapidly (50 iterations) compared to the
HPBS system (80 iterations) since the later problem has more de-
cision variables, thus increasing its complexity. The results evi-
dence that considering self-discharge has a significant influence on
the cost of systems, as observed for all cases. For instance, the
optimal COE increased from 0.196 $/kWh to 0.222 $/kWh with
storage self-discharge as 1%, a consideration generally ignored in
similar research. When the self-discharge effect is taken into ac-
count, the results indicate that BS size considerably reduces in PV
only case, while BS size significantly increased in the case with only
WT. This contrary trend is probably due to the higher intermittency
of wind energy compared to solar energy, and most of the load is
directly meet from PV produced energy, causing the algorithm to
decrease the BS size in PV only case. It is also observed that there is
a trade-off between system excess energy and BS size, which is
evident from Table 5, as the algorithm decreases the BS size in PV
only case (with self-discharge), the percent of excess energy
increased from 1.36 to 7.5. The same trend repeats in other
considered configurations in Table 5. In the case of hybrid-source
arrangements, the algorithm identifies the maximum capacity of
RE generators in the BS case (in both scenarios), since BS has
continuous replacement and high maintenance cost compared to
PHS only and HPBS. The highest excess energy across all the
considered cases is observed in wind power only configurations,
which reflects the high variability linked to wind energy and un-
derlines the importance of energy storage for wind only arrange-
ments to ensure the system’s reliability. The least excess energy
with least energy storage size can be seen only in HPBS cases, which
highlights the hybrid storage relevance in the RE environment,
especially battery and PHS, due to their supplementary function-
ality in both energy surplus and deficit modes.
Among the solar/wind only energy systems, the PV-PHS system
is the cost-wise optimal configuration, but it has an unmet load of
1.1% and 1.28% for both scenarios. On the other hand, the HPBS
coupled PV system has the least cost with 0% loss of load. It is clear
from the results that all configurations that include PHS have a loss
of load because PHS could only be derived when available power or
deficit power is more than or equal to 20% of rated pump/turbine
power. Although designed PHS based systems could meet 100%
load demand if the minimum technical-operational constraint
were omitted, it is not economical to turn on a PHS for small loads
because of the low-efficiency output of pump/turbine at low loads
[46]. Using PHS for serving small loads would also increase the
number of start/stop cycles of the turbomachinery, which can
significantly affect its operational life. On the other hand, configu-
rations that include HPBS have 100% reliability for off-grid power
supply with minimum cost. For both scenarios under consideration,
the PV-WT-HPBS system is cost-optimum just after PV-WT-PHS
systems, which highlights the relevance of hybrid storage. The
function of BS in hybrid storage is to cover the small energy deficits,
and therefore, it has smaller storage capacity in all HPBS configu-
rations ranging from 7 kW h to 19 kW h. Due to the small battery
storage capacity in HPBS, the effect of self-discharge on the total
storage capacity of hybrid storage systems is very small compared
to their RE generators size.
Configurations based on a single RE source require a higher
capital cost, and consequently, they present higher COE values.
Additionally, they also exhibit considerable energy curtailment
rates, especially when the self-discharge effect is taken into account
for a simulation closer to the real-world conditions. For instance,
among all configurations, the WT-BS system (with self-discharge) is
the configuration with the highest rated RE generator (535 kW) and
storage capacity (1333 kW h), but it also presents the highest excess
energy (5.35%). It can be seen that PV-WT systems, regardless of
storage type, have the lowest excess energy, highlighting the rele-
vance of the combined generation from different RE sources,
especially for off-grid RES. From the results, it is possible to argue
that the PV-WT-HPBS system is the most suitable configuration for
the proposed off-grid area in terms of cost and reliability, while PHS
could also be a promising option at the expense of small loss of
load. Also, energy storage self-discharge has an impact on system
component sizing and eventually affects overall system cost, mostly
when the battery serves as ESS.
As mentioned in the literature review, several studies deal on
the subject of optimizing off-grid RES with energy storage for
achieving the minimum levelized COE and high reliability; yet, a
few have performed comparative analysis between the objective
values of systems with different ESS in one study [53,54]. Javed
et al. performed the comprehensive review of ESS based PV/WT
systems concerning techno-economic and reliability criteria, and
their findings revealed that the COE value of RES varies from 0.099
$/kWh to 0.286 $/kWh, depending on several factors like network
mode, storage type, taxation, optimization algorithm and RE
availability [2]. Ma et al. optimized a PV/WT/BS system and re-
ported a COE value is 0.595 $/kWh with 0% LPSP and 48.6% dump
load [45]. In another study, Ma et al. optimized a PV/WT/PHS sys-
tem using a genetic algorithm, and the optimized scenario pre-
sented a COE value of 0.286 $/kWh, with LPSP value 0% and 19.7%
excess energy [5]. Guezgouz et al. optimized the sizing of a PV/WT/
HPBS system with 97.5% reliability and reported a COE value is 0.190
$/kWh, with a total curtailment of 190 MWH [19]. All these studies
mentioned above ignored the ESS self-discharge rate for the sake of
simplicity. Based on these previous studies, there is clear that the
optimization results of the proposed model are well-matched with
literature findings, and this suggests that the proposed operating
strategy and optimization method are suitable for adequate sizing,
improving RES reliability evaluation, and for reducing energy
curtailment.
4.2. Economic analysis
The bar plot in Fig. 9 shows the cost breakdown of all configu-
rations. The results indicate that energy storage is the major
component of cost in a single-source RES, while BS has the highest
impact due to its continuous replacement and high maintenance
expenses. Also, the cost of RE generators for single-source RES is
higher when compared to hybrid-source systems. For instance, the
cost of RE generators for PV-WT-BS is lower when compared to RES
only considering solar PV or wind power. It is noticeable that, for
the same type of configuration, the capital cost for is higher than
that of PHS/HPBS. For example, the capital cost associated with
energy storage in the PV-WT system with BS accounts for more
than 50% of entire system, while for PHS and HPBS, the storage cost
is similar to the initial cost of the RE generator. Salvage value is
shown with dark grey color, and it is worth mentioning that energy
systems containing PV would present salvage value at the end of
the project horizon since the whole system’s life is set at 20 years in
this study while the useful life for PV equipment is set at 25 years. It
1386

Fig. 9. Cost break down of each optimal conﬁguration.
Fig. 10. One year energy balance analysis of all optimal conﬁgurations.
1387

can be seen from Fig. 9 that optimal configurations, i.e., PV-WT-PHS
and PV-WT-HPBS, exhibit a cost fraction to installation, operation,
and maintenance smaller than for all the other arrangements.
Hence, this suggests that energy storage capital cost is a significant
driver for COE, along with RE generators’ capital cost and operation
and maintenance expenses.
4.3. Energy balance analysis
The monthly energy balance analysis of all considered cases in
Fig. 10 shows that the majority of the load demand is directly met
from RE generators in single-source based energy systems, while
ESS plays a vital role in RES with two sources, by handling more
than 40% of the produced energy. This feature considerably in-
creases the size of RE generators and the capital cost in single-
source based energy system. Additionally, when that single RE
source is not available for more extended periods, it may affect the
system’s reliability. Alternatively, PV-WT based systems also have
lower installed RE generator capacities and energy storage size. For
instance, wind-only based RES has the highest energy storage
capacity but the role of energy storage during system operation is
trivial (i.e., the amount of energy charging/discharging is meager).
The same phenomenon occurs for PV-only configurations. For PV-
WT arrangements, WT contributes more to energy production
compared to solar energy, mainly because the proposed remote
location has high wind energy density. Minimal charging and dis-
charging amounts of BS for HPBS are visible, as battery frequently
only covers a small energy surplus and deficit amounts, while PHS
provides the majority of energy required to cover higher energy
shortages.
The role of ESS in the PV-WT system is shown in Fig. 11. In single
storage cases, the contribution of storage in the demand satisfac-
tion is minimum when compared to HPBS. It is noticeable that
42.8% of the total energy served is covered by battery only, while
PHS covered 45.2% of load demand. In the HPBS case, PHS is
considered as the primary ESS and covered 44% of the load demand
while battery frequently covers the small disparities between
supply and demand (2.8%). Overall, the amount of energy covered
in HPBS scenario increased (48%), which improves the system
reliability when compared to single storage systems, especially for
Fig. 11. Role off ESS in covering load demand (a) PV-WT-HPBS (b) PV-WT-PHS (c) PV-WT-BS.
Fig. 12. Storage operational time of each configuration during a whole year.
1388

Fig. 13. Sensitivity analysis of varying load of all considered cases on (a) RE generators (b) storage capacity.
1389

off-grid RES. On the other hand, it reduces the direct dependency
on RE generation; therefore, RE variability can be managed more
conveniently compared to single storage systems.
Fig. 12 shows the operational time for each ESS of each config-
uration during a whole year. The results indicate that ESS remains
operational for more than 6500 h when solar is the only energy
source. This behavior relates to the fact that solar is only available
during the day-time, but the storage has to cover the remaining
load demand. The opposite trend is visible when the wind is the
only source of energy generation, as most of the time, the load
requirements are directly met from wind power, and storage re-
mains operational for less than 4000 h.
On the other hand, the ESS operational time for PV-WT based
energy systems is around 5000 h. It is noticeable that PHS in HPBS
is active for 5042 h, while this figure is 5367 h when only PHS is
considered. This similar amount of operational hours of PHS in
HPBS is because sometimes both ESS come into operation to meet
load demand (i.e., when the state of charge is minimum or one
storage is unable to meet the whole energy deficit/surplus). The
operational time of BS for all configurations in HPBS is slightly more
than 2000 h, which ensures the systems 100% reliability and
highlights hybrid storage significance, especially for off-grid
systems.
4.4. Sensitivity analysis on load consumption, energy storage
capacity, and renewable energy sources
This section presents and discuss the results of a thorough
sensitivity analysis conducted on all considered configurations by
varying the load demand to corroborate the validity of the pro-
posed model. As mentioned above, the load demand considered for
this study is 255.6 kW h. The effect of load demand variation on RE
generators size and ESS size is shown in Fig. 13. The load is varied
from 179 kW h to 333 kW h with the step of 26 kW h. It is clear from
Fig. 13 (a) that configurations that considers only WT (shown with
blue bars) as RE source require higher installed generating capacity
when compared to other energy systems. Additionally, Fig. 13 in-
dicates that PV-WT based arrangements present the lowest
installed RE capacity, which simultaneously increases with load
demands. The effect of varying the load demand on the ESS capacity
is evident from Fig. 13 (b). It is noticeable that WT based energy
systems have the highest ESS capacity regardless. Green color
represents the PHS capacity, while BS size is shown in purple. The
size of battery storage in HPBS based configurations is minimal
since BS is only used to cover small energy deficits/surplus. It can be
concluded that using two (PV-WT) energy generation sources
simultaneously reduces the storage capacity size and enhances the
system’s reliability and overall cost, especially for off-grid RES.
Fig. 14 shows the cumulative cash flows for savings/losses of
hybrid PV-WT RES, comparing each ESS with diesel generation cost
over the entire system lifetime, set at twenty years. Payback time
calculation requires the annualized cost of each considered system
and a reference system (diesel generator only). The annualized
costs are subtracted for each consecutive year giving the loss/profit
of each year. It can be seen that the positive cash flow of PHS and
HPBS starts from the fifth-year while BS needs a more extended
period (7 years) to profit since BS has replacement after each five
years. Overall, PHS has slightly more cash savings after twenty
years lifespan compared to HPBS as the later includes batteries that
require constant replacement.
5. Conclusions
Energy storage has become an integral component of renewable
energy systems to align supply and demand. At the same time,
selection of the appropriate energy storage technology, adequate
energy management strategy, and optimal sizing does not only
strengthen the system’s reliability but also considerably minimize
Fig. 14. Cumulative cash flow savings of optimal configuration of each considered case during whole RES lifetime.
1390

the system capital cost. This study explored the provision of
different renewable energy systems for a remote island. This
research begins by describing the mathematical formulation, the
operating strategy, and the objective function of an optimization
model of a hybrid pumped battery storage based RES, which is
solved using particle swarm optimization. A total of nine different
configurations of solar/wind/battery/PHS were considered, and two
scenarios were examined based on ESS self-discharge (0% and 1%).
The COE value of all configurations was higher (13%e50%) when
the ESS self-discharge effect is considered as a design parameter, a
feature ignored in most studies for simplicity. Moreover, the
installed RE capacity of all optimal configurations has a significant
increase compared to ESS capacity when self-discharge is taken
into account, mainly because of the high capital and maintenance
cost of ESS. Even though PV-WT-PHS is a cost-optimal system in
both scenarios and provides the highest cost reduction, it cannot
support low load values due to the minimum operational constraint
set on the turbomachinery. Meanwhile, the hybrid pumped battery
storage, coupled with solar and wind sources, does not only pro-
vides a high level of supply reliability, but it also accomplishes it
with minimum COE compared to all other configurations. The least
excess energy with least energy storage size is observed for HPBS
cases, which highlights the importance of hybrid storage in the RE
environment, especially battery and PHS, due to their supplemen-
tary functionality in both energy surplus and deficit modes. The
payback period of PHS and HPBS based configurations is not more
than five years, while the payback time of RES configurations with
battery storage is more than seven years.
The sensitivity analysis reveals that configurations comprising
more than one RE source require lower energy storage and installed
RE capacity, providing higher reliability and, eventually, a better
economic performance, especially for off-grid areas. Overall, the
results of this study suggests that hybrid storage based RES is a
suitable option for remote places as it considerably reduces the COE
and energy curtailment, especially systems like the HPBS that
benefit from the supplementary characteristics of each other.
Finally, considering the proposed study’s shortcomings, some
future research directions and limitations can be summarized as
follows:
Since the focus of this study was to conduct a comparative
analysis of different off-grid RE configurations, the reference
value for PHS operation (20% of rated PHS power) employed in
this study for switching between two energy storages needs to
be tested further by varying the proposed parameter.
ESS self-discharge is a temperature-dependent parameter,
especially for battery storage. It was considered constant in this
study (i.e., 0% and 1%) for the sake of fair comparison between
considered configurations. Future studies admit a comprehen-
sive analysis of evaluating self-discharge as a parameter varying
with temperature.
Global warming is a major concern at present; however, the
affect of environmental parameters on the design of the
considered configurations was ignored in this paper (i.e. battery
emissions, PHS land requirement). These parameters could be
added as optimization objectives in future studies.
CRediT authorship contribution statement
Muhammad Shahzad Javed: Conceptualization, Methodology,
Investigation, Software, Data curation, Writing - original draft. Tao
Ma: Conceptualization, Supervision, Funding acquisition. Jakub
Jurasz: Conceptualization, Investigation. Fausto A. Canales: Data
curation, Writing - review editing. Shaoquan Lin: Software, Data
curation. Salman Ahmed: Methodology, Investigation. Yijie Zhang:
Writing - review editing.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgments
The authors appreciate the financial supports provided by Na-
tional Natural Science Foundation of China (NSFC) through the
Grant No. 51976124 and Science, Technology Innovation Committee
(STIC) of Shenzhen Municipality through the Grant No.
JSGG20180504165907910.
Appendix
Table A1
Technical and cost figures for RES components [19,55e58].
Component Parameter Value
PV module Unit cost 896 $/kW
Operation maintenance cost 15 $/kW-year
Life time 25 years
Wind turbine Unit cost 998 $/kW
Operation maintenance cost 20 $/kW-year
Life time 20 years
Battery storage Type Lead-acid
Unit cost 274 $/kWh
Operation maintenance cost 2 $/kW
Round trip efficiency 86%
Life time 5 years
PHS Civil work cost 253 $/kWh
Machinery cost 370 $/kW
Round trip efficiency 80%
Life time 60 years
Converter Unit cost 336 $/kW
Efficiency 95%
Table A2
Assumptions made for fair comparison.
Parameter Value
ESS initial charge 50% of rated capacity [59]
Pump/turbine machine rated capacity 10 kW, 11 kW
SOCmin BS ¼ 20%, PHS ¼ 5% [60]
PHS head 60 m
ESS Self-discharge rate 0% 1%
Inverter size 31 kW (Peak load dependent) [3]
Days of autonomy BS ¼ 10 h, PHS ¼ 3 days [61]
1391

Fig. A1. Flow chart of PSO pseudocode implementation for RES.
1392

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