Renewable and Sustainable Energy Reviews 183 (2023) 113476
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Renewable and Sustainable Energy Reviews
journal homepage: www.elsevier.com/locate/rser
A state-of-the-art review and bibliometric analysis on the sizing
optimization of off-grid hybrid renewable energy systems
Yi He a, Su Guo b, *, Peixin Dong c, Yi Zhang b, Jing Huang b, Jianxu Zhou a
a
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210024, China
College of Energy and Electrical Engineering, Hohai University, Nanjing, 211000, China
c
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
b
A R T I C L E I N F O
A B S T R A C T
Keywords:
Hybrid renewable energy system
Hybrid energy storage system
Rural electrification
Sizing optimization
Energy management strategy
Bibliometric analysis
The development of off-grid hybrid renewable energy systems (HRESs) is essential to rural electrification and
global decarbonization. Based on 299 journal papers in the recent five years, this work conducts a state-of-the-art
qualitative review and quantitative bibliometric analysis on the sizing optimization of off-grid HRESs. An
overview of system configurations, energy management strategies, performance evaluation indicators, and sizing
methodologies are presented, and bibliometric analysis is conducted to reveal the overall scope and mainstream
of this research field. Finally, promising future works are summarized on the basis of current research gaps. The
results of bibliometric analysis indicate that: (1) solar photovoltaic and batteries are the most common energy
source and energy storage respectively, and wind-photovoltaic-battery-diesel is the most popular system
configuration; (2) most researchers apply rule-based energy management strategies rather than optimized
strategies, owing to their advantages of simple implementation and fast computation; (3) 97.99% of articles
considers economic indicators in the sizing optimization model, and techno-economic feasibility is the essential
research foundation at the planning stage; (4) meta-heuristic algorithms and the HOMER software tool are the
two most popular sizing methodologies for off-grid HRESs. In future works, hybrid energy storage systems, deep
reinforcement learning-based energy management strategy, sustainability and resilience indicators, as well as
distributionally robust optimization-based sizing methodologies are promising research directions. Overall, the
presented overviews and outlooks can provide holistic theoretical knowledge about sizing optimization research
for practitioners, thus promoting the academic progress and practical implementation of off-grid HRESs.
1. Introduction
Electrification has a significant impact on social development and
people’s living quality, especially in remote rural areas. However, mil­
lions of residents living in the islands or village areas currently have no
access to electricity due to the long distance from the utility grid [1]. The
grid extension to remote areas is not cost-effective and difficult with
engineering construction, so it is essential to develop local off-grid en­
ergy systems. Fossil fuel-based diesel generator (DG) is a technically
feasible option for rural electrification, but it is environmentally infea­
sible owing to the considerable carbon and sulfur dioxide emissions
during the process of operation and fuel transportation, which is con­
trary to the carbon neutrality commitment [2]. In addition to grid
extension and fossil fuel-based generators, the utilization of indigenous
renewable energy such as wind and solar resources for power generation
is another viable solution for rural electrification. Renewable energy
resources hold several favorable characteristics, such as wide distribu­
tion, local abundance, and no carbon emission during operation [3],
which are suitable for distributed power supply. On the other hand, the
intermittency, volatility, and uncertainty of renewable energy resources
will severely limit their power supply reliability and stability, so
standalone wind or solar photovoltaic (PV) power plants cannot guar­
antee continuous load satisfaction [4].
To address the drawbacks of renewable energy, the concept of hybrid
renewable energy system (HRES) is proposed, which integrates two or
more complementary renewable energy sources, energy storages, and
backup sources [5]. Although renewable energy is the primary supplier,
the application of energy storage plays a pivotal role in ensuring a
reliable power supply. The renewable energy output inevitably mis­
matches with the residential load profile, so energy storage can function
as a load via charging process in the case of surplus renewable power
* Corresponding author.
E-mail address: guosu81@126.com (S. Guo).
https://doi.org/10.1016/j.rser.2023.113476
Received 31 October 2022; Received in revised form 14 June 2023; Accepted 16 June 2023
Available online 28 June 2023
1364-0321/© 2023 Elsevier Ltd. All rights reserved.
Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
DE
DP
DRL
DRO
EMPC
ESCEA
FA
FPA
GA
GAMS
GOA
GWO
HOMER
HOGA
HSO
LINGO
MCDM
MILP
MOEA
MOPSO
MPC
NSGA-II
PDF
PSO
RHO
SA
SAM
SPEA-II
SQP
TOPSIS
Abbreviations
Systems
CAES
CSP
DG
DSM
EMS
EV
GES
HESS
HKT
HRES
HES
PHS
PV
SC
TES
compressed air energy storage
concentrated solar power
diesel generator
demand side management
energy management strategy
electric vehicle
gravity energy storage
hybrid energy storage system
hydrokinetic turbine
hybrid renewable energy system
hydrogen energy storage
pumped hydro storage
photovoltaic
supercapacitor
thermal energy storage
Indicators
ACS
ECR
HDI
JC
LCOE
LCCF
LEOE
LPSP
NPC
annualized cost of system
energy curtailment rate
human development index
job creation
levelized cost of energy
life cycle carbon footprint
levelized emission of energy
loss of power supply probability
net present cost
Methods
ABC
artificial bee colony
ACO
ant colony optimization
differential evolution
dynamic programming
deep reinforcement learning
distributionally robust optimization
economic model predictive control
electric system cascade extended analysis
firefly algorithm
flower pollination algorithm
genetic algorithm
general algebraic modeling system
grasshopper optimization algorithm
grey wolf optimizer
hybrid optimization of multiple energy resources
hybrid optimization of genetic algorithm
harmony search optimization
linear interactive and general optimizer
multi-criteria decision-making methods
mixed integer linear programming
Multi-objective evolutionary algorithm
multi-objective particle swarm optimization
model predictive control
non-dominated sorting genetic algorithm-II
probability density function
particle swarm optimization
receding horizon optimization
simulated annealing
system advisor model
strength Pareto evolutionary algorithm-II
sequential quadratic programming
technique for order preference by similarity to an ideal
solution
environmental/social indicators were further involved in the perfor­
mance evaluation. However, energy storage technologies were so
generalized that the characteristics of different energy storages were
neglected. Mazzeo et al. [12] carried out a comprehensive statistical
analysis of wind-PV HRESs, including the occurrence frequency of sys­
tem configuration options, performance indicators, and optimization
algorithms. However, this review article was devoted to quantitative
statistical analysis, but the theoretical knowledge related to system
modeling and sizing methodologies was just briefly introduced. Pan­
diyan et al. [13] introduced the research protocol of implementing
standalone HRESs for rural electrification, where hydropower and
biomass energy were included in the system configurations, but the
overview of system modeling and various sizing methodologies was not
presented. Zebra et al. [14] provided a review on off-grid HRESs in
developing countries, while this work focused on the techno-economic
feasibility in practical applications rather than the overview of sizing
optimization investigations. Both Memon et al. [15] and Thir­
unavukkarasu et al. [16] presented a specialized overview of sizing
optimization methodologies of off-grid HRESs, where recently devel­
oped meta-heuristic algorithms were included. However, critical infor­
mation including system configurations and energy management
strategies was not presented.
A summary of previous literature reviews on the sizing optimization
of off-grid HRESs is shown in the Appendix (Table A1). It indicates that
all previous review articles did not present a comprehensive overview
covering system modeling, topologies, energy management strategies,
sizing methodologies, and quantitative bibliometric analysis. Moreover,
publications about sizing optimization have dramatically increased in
recent years, in which various emerging system components (renewable
generation, or a power source via discharging process in the case of
unmet load demand, thus achieving the supply-demand power balance
[6]. However, how to optimally determine the capacity configuration of
each component in HRES is worthy of investigation at the planning stage
since undersized configuration may lead to insufficient power supply
while oversized configuration may result in high investment cost and
considerable energy curtailment. Hence, the sizing optimization of
off-grid HRESs has attracted extensive academic and industrial
attentions.
Reviews on the sizing optimization of off-grid HRESs were conducted
in previous literature, mainly including system configurations, compo­
nents modeling, performance evaluation indicators, and optimization
methodologies. For instance, Dawoud et al. [7] reviewed the system
components in off-grid HRESs along with corresponding mathematical
models, design criteria, and various sizing optimization techniques.
However, system components were limited to wind/PV/battery/DG,
and design criteria only considered techno-economic indicators. Khan
et al. [8] presented an overview focusing on system modeling and
optimization techniques for off-grid wind-PV HRESs, while other
promising renewable energy technologies such as biomass, hydropower,
etc., were not considered. Anoune et al. [9] conducted a detailed review
on the sizing optimization of off-grid wind-PV HRESs, in which different
topologies of HRESs were included. Nevertheless, emerging renewable
technologies were still neglected. Sawle et al. [10] reviewed the
modeling and reliability-cost sizing optimization of off-grid HRESs, and
case studies were conducted to compare the performance of different
system configurations. However, various sizing optimization method­
ologies were not introduced. Lian et al. [11] considered hydropower
components in the system configuration of off-grid HRESs, and
2
Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
energy and energy storage technologies) and novel advanced sizing
methodologies were adopted. Therefore, previous review articles based
on the literature published several years ago cannot exactly reveal the
current research status, and it is necessary to conduct an up-to-date and
more comprehensive review on this hotspot. To this end, this paper in­
vestigates a state-of-the-art qualitative review and quantitative biblio­
metric analysis on the sizing optimization of off-grid HRESs, and the
main contributions are summarized as follows.
(4) Based on 299 journal papers in the recent five years, the biblio­
metric analyses for yearly publications, country and journal dis­
tributions, system configurations, energy management strategies,
performance evaluation indicators, and sizing methodologies are
conducted to present a quantitative overview of the sizing opti­
mization of off-grid HRESs, revealing both the overall scope and
mainstream of this research field.
(5) Based on the qualitative and quantitative overview of the current
research status on the sizing optimization of off-grid HRESs, the
prospects of future works are holistically discussed from the
perspective of four separate sections, providing promising
research directions for relevant researchers and promoting aca­
demic progress in energy system planning fields.
(1) The review framework follows the standard protocol of the sizing
optimization of off-grid HRESs, including a comprehensive
overview of system configurations, energy management strate­
gies, performance evaluation indicators, and sizing methodolo­
gies. In this way, potential readers can clearly understand the
regular research roadmap.
(2) This review not only introduces the operating principles of con­
ventional and emerging energy sources and energy storage
technologies in system configurations, but also presents the
widely-used mathematical models for each component, which
provides instructive references for potential practitioners to
conduct relevant research works.
(3) The energy management strategy for operation simulation and
performance evaluation is seldom considered by previous review
articles, which will have a significant impact on the optimal
sizing results. To fill up this research gap, this review innova­
tively presents the overview of energy management strategies
applied in sizing optimization research.
The remainder of this paper is organized as follows: Section 2 pre­
sents the bibliometric overviews of published journal papers. Section 3
introduces system configurations, including different energy sources,
energy storages, and topologies. Section 4 introduces energy manage­
ment strategies for sizing optimization. Section 5 introduces various
performance evaluation indicators. Section 6 introduces representative
sizing methodologies. Finally, the overall findings and outlooks are
discussed in Section 7, and conclusions are introduced in Section 8.
2. Bibliometric overviews
In order to provide a holistic bibliometric overview of the state-ofthe-art research status of off-grid HRESs, Fig. 1 visualizes the biblio­
graphic network map for the co-occurrence of relevant keywords with
Fig. 1. Bibliographic network visualization map of the co-occurrence for “hybrid renewable energy system” keyword (the circle size represents the occurrence
frequency of keywords, and the line thickness represents the co-occurrence strength of two keywords).
3
Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
the assistance of the VOSviewer software tool, including 5774 documents
retrieved from the Web of Science database during the period
2018.01–2022.06. As shown in the network map, “renewable energy”,
“optimization”, and “design” are the most frequent keywords, thus
highlighting the popularity and significance of the subject of “the sizing
optimization of off-grid hybrid renewable energy systems".
Subsequently, 299 journal papers concerning the topic of “the sizing
optimization of off-grid HRESs” in the recent five years
(2018.01–2022.06) are screened out for further bibliometric analysis,
including yearly trend, country distribution, and journal distribution.
The bibliometric overviews of the sizing optimization of off-grid HRESs
are shown in Fig. 2.
Fig. 2(a) shows the trend of the yearly number of relevant published
journal papers. It can be seen that the number of published papers
gradually increases in recent years. It should be noted that if all-year
published papers in 2022 are included in the bibliometric analysis, the
publication number for 2022 will probably exceed the figure for 2021.
This increasing trend reveals that the concerning topic attracts more
academic attention.
Fig. 2(b) indicates the top 10 countries with the largest number of
relevant published papers. China leads in published papers, followed by
India and Iran. It reflects that these countries hold abundant renewable
resources and promising actual implementation of off-grid HRESs, thus
promoting their academic and industrial research. Moreover, this topic
has aroused global attention as the published papers are spread over 50
countries.
Fig. 2(c) presents the top 10 journals with the largest number of
relevant published papers. ENERGY published the largest number of
research papers on this topic, followed by Energy Conversion and
Management and Renewable Energy. This information can provide
guidelines for researchers to decide which journals can potentially
publish their research works.
3. System configurations
The system configurations of HRESs are composed of energy sources,
energy storages, and the linking topology, which are comprehensively
introduced in this section.
3.1. Energy sources
Energy sources adopted in off-grid HRESs mainly consist of wind
power, solar PV, concentrated solar power (CSP), micro hydropower,
hydrokinetic power, biomass power, and backup DG. The power gen­
eration principles and mathematical models of different energy sources
are introduced in this subsection, along with the relevant research
highlights.
3.1.1. Wind power
Wind resources can be utilized to generate electricity by wind tur­
bines, which convert the wind kinetic energy into mechanical energy via
blades, and then into electrical energy via generators. The type of wind
turbine is characterized by a wind power curve, which defines its power
output at a specific wind speed. The theoretical power output of wind
turbines depends on the wind speed at the hub height and its wind
power curve. The widely-used mathematical model of wind turbines in
the sizing optimization of HRESs is shown as below [17].
⎧
0 v(t) < vci
⎪
⎪
⎪
⎪
3
⎪
3
⎪
⎪
⎨ v(t) − vci × PWT vci ≤ v(t) < vR
3
3
vR − vci
PWT (t) =
(1)
⎪
⎪
⎪
⎪
P
v
≤
v(t)
<
v
WT
R
co
⎪
⎪
⎪
⎩
0 vco ≤ v(t)
where, PWT (t) is the power output of wind turbine at time t. PWT is the
nominal power of wind turbine. v(t) is the wind speed at time t. vci , vco
and vR are the cut-in, cut-off, and rated wind speed of wind turbine
Fig. 2. Bibliometric overviews of the sizing optimization of off-grid HRESs. (a) The trend of the yearly number of relevant published journal papers. (b) The top 10
countries with the largest number of relevant published papers. (c) The top 10 journals with the largest number of relevant published papers. (d) Journal
abbreviations.
4
Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
respectively, which can be retrieved from the wind power curve.
The wind power curve has a direct impact on the technical perfor­
mance of wind turbines. The optimal selection of wind turbines in offgrid HRESs was investigated by researchers via the techno-economic
assessment of different types of wind turbines. Firtina-Ertis et al. [18]
compared the technical performance of seven types of wind turbines in a
standalone wind-hydrogen net-zero house. The results indicated that the
wind turbine with higher power output at low wind speed generated
higher yearly total power production. Mehrjerdi et al. [19] considered
the optimal selection of 35 wind turbines in the wind-PV HRES design.
The results showed that boundary conditions including wind speed
patterns and load profiles significantly affected the optimal selection of
wind turbine type. Rakhshani et al. [20] explored the mixed installation
of multiple different wind turbines in off-grid HRESs. The simulation
results demonstrated that the multi-turbine model led to 4.6% cost
reduction, higher renewable energy penetration, and less environmental
effect compared to the mono-turbine model, owing to the higher level of
wind energy extraction from the optimal combination of multiple types
of wind turbines.
concentrate the radiation to generate thermal energy, which is subse­
quently converted into electricity via power cycles. According to the
concentrating principle and receiver type, CSP plants are classified as
parabolic trough, central power tower, linear Fresnel, and parabolic dish
types. The theoretical power output of CSP depends basically on the
direct normal irradiance and the solar-to-thermal-to-power conversion
efficiency. The mathematical model of CSP is shown as below [25].
PCSP (t) = DNI(t) × ASF × ηREC × ηPC
where, PCSP (t) is the power output of CSP at time t. DNI(t) is the direct
normal irradiance at time t. ASF is the area of solar field. ηREC is the solarto-thermal conversion efficiency of solar receiver. ηPC is the thermal-topower conversion efficiency of power cycles, such as organic Rankine
cycle, supercritical CO2 Brayton cycle, etc.
In terms of the techno-economic feasibility and performance com­
parison of different CSP plants, Starke et al. [26] investigated the
multi-objective capacity optimization of PV-CSP hybrid plants consid­
ering two types of CSP technologies (parabolic trough collector and
central receiver system). The simulation results indicated that the
parabolic trough collector presented lower cost while the central
receiver system could achieve higher capacity factor for baseload sup­
ply. Li et al. [27] studied the optimal sizing of wind-CSP HRES with an
electric heater, which converted the surplus wind power into thermal
energy for storage. The simulation results showed that the introduction
of electric heater could achieve the deep interaction between wind and
CSP subsystem, thus mitigating wind power curtailment and reducing
the overall cost. However, the techno-economic performance compari­
son of four types of CSP technologies in HRESs is a knowledge gap that
can be filled in future works.
3.1.2. Solar photovoltaic
Solar PV uses semiconductor materials to directly generate elec­
tricity from solar energy via the photoelectric effect. The theoretical
power output of PV is mainly decided by the global solar radiation on
the inclined PV surface and its operating temperature. The mathematical
model of PV power generation is shown as below [13].
PPV (t) = PPV ×
I(t)
× [1 − β × (TPV (t) − TSTC )]
ISTC
TPV (t) = Tamb (t) + (TNOM − TREF ) ×
I(t)
IREF
(4)
(2)
(3)
3.1.4. Micro hydropower
Hydropower turbines harness the potential energy of water flow to
generate electricity in river basin areas. The theoretical power output of
micro hydropower depends on the head height and flow rate. The
mathematical model of hydropower is shown as below [28].
where, PPV (t) is the power output of PV at time t. PPV is the nominal
power of PV. I(t) is the tilted irradiance at time t. TPV (t) and Tamb (t) are
the operating temperature of PV and ambient temperature at time t. ISTC
and TSTC are the irradiance and temperature on standard test condition.
IREF and TREF are the reference irradiance and temperature. TNOM is the
nominal operating cell temperature. β is the temperature coefficient.
The solar tracking technologies, including fixed axis, adjusted hori­
zontal axis, adjusted vertical axis, and adjusted dual axis, will signifi­
cantly influence the received solar radiation on the inclined surface of
PV panels. Meanwhile, the installation cost for different solar tracking
technologies varies with structural complexity. Therefore, the optimal
selection of solar tracking technology affects the overall technoeconomic performance of solar PV systems. Shabani et al. [21]
assessed the techno-economic role of solar tracking technology in a
standalone PV-based HRES. The results revealed that the fixed-tilt
tracking technology led to the lowest total cost, and the optimal selec­
tion of solar tracking technology could possibly achieve 18.2% cost
savings. Babatunde et al. [22] also studied the effect of solar tracking
technology on the optimal design of off-grid PV-based HRESs. The
monthly/weekly/daily/hourly adjustment periods were considered in
the solar tracking technologies, and the results showed that the daily
adjusted horizontal axis tracking system was the optimal selection for
Nigerian resource condition, while the dual axis tracking system was
more suitable for South Africa. Salameh et al. [23] revealed that
PV-based HRES with dual-axis solar trackers performed higher renew­
able energy fraction and lower cost than single-axis (horizontal or ver­
tical) solar trackers in the United Arab Emirates. Contrarily, Makhdoomi
et al. [24] discovered that using solar trackers was not as cost-effective
as fixed PV panels in off-grid PV-based HRESs of Iran.
PMH (t) = ηHT (t) × ρ × g × h × f (t)
(5)
where, PMH (t) is the power output of micro hydropower at time t. ηHT (t)
is the water-to-power conversion efficiency of hydraulic turbine at time
t, which depends on the volumetric flow rate. ρ is the water density. g is
the gravitational acceleration. h is the elevating head height. f(t) is the
volumetric flow rate at time t.
The techno-economic feasibility of micro hydropower in off-grid
HRESs has been validated in previous research works. Hermann et al.
[28] analyzed the techno-economic-environmental feasibility of a micro
hydropower-assisted HRES in Sub-Saharan Africa. The results presented
that the micro hydropower-assisted HRES was cost-efficient for rural
household electrification and could effectively decrease carbon emis­
sions. Odou et al. [29] analyzed the techno-economic feasibility of micro
hydropower-assisted HRESs for sustainable rural electrification in
Benin. The results revealed that micro hydropower was a vital compo­
nent to achieving the lowest cost and ensuring a reliable power supply.
3.1.5. Hydrokinetic power
Hydrokinetic power is also a category of hydropower technology,
while it harnesses the kinetic energy of natural streamflow in ocean
currents or tides rather than potential energy from waterfall. The
theoretical power output of hydrokinetic turbines (HKT) is mainly
determined by the streamflow velocity. The mathematical model of HKT
is shown as below [30].
3.1.3. Concentrated solar power
CSP is another efficient technology for solar energy utilization. CSP
plants collect solar radiation using reflective optical elements that
5
PHKT (t) = Eflow (t) × AHKT × CP × ηHKT
(6)
1
Eflow (t) = × ρ × vflow (t)3
2
(7)
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
fuel consumption of DG has a linear relationship with its nominal power
and actual power output. The mathematical model of DG is shown as
below [32].
where, PHKT (t) is the power output of HKT at time t. Eflow (t) is the energy
density of stream flow at time t. vflow (t) is the stream flow velocity at
time t. ρ is the water density. AHKT is the rotor area of HKT. CP is the
power coefficient of stream flow dynamic efficiency. ηHKT is the waterto-power conversion efficiency of HKT.
The techno-economic viability of HKT has been verified in some
specific regions. Ibrahim et al. [30] compared the techno-economic
performance of HKT and wind turbines in a standalone HRES for desa­
lination unit, and the results indicated that the HKT-based HRES ach­
ieved the minimum power generation cost. Lata-García et al. [31]
conducted the optimal siting of HKT and the techno-economic analysis
of an isolated HKT-based HRES. The location with the highest waterflow
speed was optimally selected to maximize the technical performance of
HKT, and the HKT-based HRES was techno-economically feasible for
rural power supply.
FDG (t) = Fa × PDG + Fb × PDG (t)
where, FDG (t) is the diesel fuel consumption at time t. PDG is the nominal
power of DG. PDG (t) is the actual power output of DG at time t. Fa and Fb
are the intercept and slope coefficients of fuel consumption curve.
3.2. Energy storages
Energy storage technologies are applied in off-grid HRESs to regulate
the imbalance between intermittent renewables power supply and load
demand. Energy storages are classified as electrochemical, electromag­
netic, chemical, mechanical, and thermal types. Energy storages adop­
ted in off-grid HRES applications consist of various batteries,
supercapacitor (SC), pumped hydro storage (PHS), hydrogen energy
storage (HES), thermal energy storage (TES), compressed air energy
storage (CAES), gravity energy storage (GES), and hybrid energy storage
systems (HESSs). The brief classification of energy storage technologies
is shown in Fig. 3, and their techno-economic characteristics can refer to
Ref. [34]. The operating principle, mathematical models, and research
highlights of different energy storages are presented in this subsection.
Furthermore, the input variables, output variables, and technical pa­
rameters of models for different energy sources and energy storages
technologies are shown in the Appendix (Table A2).
3.1.6. Biomass power
Biomass power plants generally include an anaerobic digestion
reactor where methane fuel is produced from the decomposition of
organic wastes, a methane reformer, and a fuel-fired generator. The
biomass sources include wood waste, agricultural residue, animal waste,
and energy crops. The theoretical power output of biomass generators is
linearly related to methane fuel consumption. The mathematical model
of biomass generators is shown as below [32].
PBG (t) = ηBG × LHVBG × FBG (t)
(9)
(8)
where, PBG (t) is the power output of biomass generator at time t. ηBG is
the biomass-to-power conversion efficiency. LHVBG is the lower heating
value of biomass, depending on the methane content. FBG (t) is the
biomass fuel consumption at time t.
3.2.1. Battery
Battery is categorized as electrochemical energy storage technology,
and its operating principle is based on the exchange of electrons between
oxidation and reduction chemical reactions. Batteries are the most
common energy storage component in off-grid HRES applications,
which mainly include Lithium-ion battery, Lead-acid battery, Nickel
Cadmium battery, Sodium Sulfur battery, and redox flow battery. The
depth of discharge, round-trip efficiency, unit investment power/ca­
pacity cost, and design lifetime are the decisive parameters for battery’s
techno-economic performance. The widely-used mathematical model of
battery is shown as follow [5].
3.1.7. Backup diesel generator
Because of the intermittency and fluctuation of renewable energy
sources such as wind and solar energy, off-grid HRESs based on 100%
renewable energy are difficult to meet the load demand reliably and
cost-effectively [33]. Hence, backup energy sources such as DG with
high flexibility are widely used in off-grid HRESs to improve operational
reliability and economic feasibility. DG generates power based on diesel
fuel and air compression, so it is not affected by meteorological condi­
tions and can reliably supply unmet loads even in extreme scenarios. The
in
out
EBES (t) = EBES (t − 1) × (1 − σ BES ) + EBES
(t) − EBES
(t)
Fig. 3. Classification of energy storage technologies.
6
(10)
Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
in
char
EBES
(t) = ηchar
BES × PBES (t) × Δt
out
EBES
(t) =
Pdisc
BES (t)
disc
BES
η
× Δt
manner [45].
(11)
3.2.2. Supercapacitor
SC belongs to the type of electromagnetic energy storage technology,
which operates via different electrostatic and redox processes between
the positive and negative electrodes. The category of SC mainly consists
of electric double layer capacitor and pseudo-capacitor (faradaic SC). SC
is generally coupled with batteries or HES, since its characteristics of
high power density and fast response can be complementary with other
energy storage technologies to achieve better regulation capability. The
techno-economic performance of SC depends on its self-discharging rate,
depth of discharge, round-trip efficiency, unit investment power/ca­
pacity cost, and design lifetime. The mathematical model of SC is shown
as follow [46].
(12)
where, EBES (t) is the available energy of battery at time t. Ein
BES (t) and
char
Eout
BES (t) are the input and output energy of battery at time t. PBES (t) and
char
Pdisc
BES (t) are the charging and discharging power of battery at time t. ηBES
disc
and ηBES are the charging and discharging efficiency of battery. σ BES is
the self-discharging rate of battery. Δt is the simulation timescale.
The techno-economic comparisons of different types of batteries in
HRES applications have generated widespread research interest. Kaa­
beche et al. [35] investigated the optimal sizing and techno-economic
comparison of off-grid HRESs with three different batteries (Lead-acid,
Lithium-ion and Nickel–Cadmium). The results revealed that Lead-acid
battery had the lowest cost under the same reliability constraints, fol­
lowed by Lithium-ion and Nickel–Cadmium battery. This was because
Lead-acid battery had the lowest unit investment cost despite the rela­
tively low round-trip efficiency and short lifetime. Das et al. [36]
explored the effect of different batteries (Lead-acid, Lithium-ion and
Vanadium redox flow) on the techno-economic-environmental perfor­
mance of standalone HRESs. The results indicated that Lithium-ion and
Lead-acid battery had better economic performance and less operational
emissions than Vanadium redox flow battery. Jiang et al. [37] studied
the optimal configuration of HRESs considering mixed types of batteries
and capacity degradation characteristics. The results showed that
Lead-acid/Lithium-ion hybrid batteries were more cost-effective than
the single type of battery, because different types of batteries could
complementarily operate to achieve better cycling and economic per­
formance. Ridha et al. [38] analyzed the performance of standalone
PV-based HRESs with three types of batteries (Lead-acid, Lithium-ion
and AGM). The results showed that the HRES with Lead-acid battery
had the best techno-economic performance among various configura­
tions. Li et al. [39] analyzed the techno-economic feasibility and emis­
sions indexes of a standalone wind-diesel HRES with different batteries
(Lead-acid, Lithium-ion and Zinc–Bromine). The results revealed that
Zinc–Bromine was the most cost-effective alternative while Lithium-ion
was the most environment-friendly one. Arévalo et al. [40] also
compared the economic performance of three types of batteries (Lea­
d-acid, Lithium-ion and Vanadium redox flow) in HRES applications,
and the results showed that Vanadium redox flow battery presented the
lowest cost. Kumar et al. [41] investigated the techno-economic per­
formance of isolated PV-diesel HRESs with four types of batteries
(Lead-acid, Lithium-ion, Vanadium redox flow and Zinc–Bromine flow).
The results found that Zinc–Bromine flow battery was the most
techno-economic solution for different locations. Overall, although
conclusions on the techno-economic rankings of various types of bat­
teries differed from study to study due to the difference in technical
parameters and cost scenarios, Lead-acid and Lithium-ion battery were
the most popular alternative in all HRES applications.
On the other hand, proliferating electric vehicles (EVs) can be
recognized as mobile battery, which can help balance the supplydemand mismatch for off-grid residential HRESs. Sadeghi et al. [42]
investigated the optimal sizing of HRESs with EVs, and the results found
that EVs increased system reliability via optimal charging and dis­
charging management. Yang et al. [43] presented the optimal design of a
wind-PV-diesel HRES with stationary battery as well as mobile EV,
indicating that the presence of EV could decrease the installation cost of
stationary battery in HRES. Ghazvini et al. [44] considered the
vehicle-to-grid parking lot as a controllable load in the optimal sizing of
an autonomous PV-battery-diesel HRES, and the results indicated that
the parking lot could reduce the total system cost by 5.31%. Moreover,
retired EV batteries (maximum state of charge <80%) were proposed to
be reused in HRESs until the maximum state of charge was degraded to
less than 60%, thus exploiting the residual values in a cost-effective
in
out
ESC (t) = ESC (t − 1) × (1 − σSC ) + ESC
(t) − ESC
(t)
(13)
in
char
ESC
(t) = ηchar
SC × PSC (t) × Δt
(14)
out
ESC
(t) =
Pdisc
SC (t)
ηdisc
SC
× Δt
(15)
out
where, ESC (t) is the available energy of SC at time t. Ein
SC (t) and ESC (t) are
char
disc
the input and output energy of SC at time t. PSC (t) and PSC (t) are the
disc
charging and discharging power of SC at time t. ηchar
SC and ηSC are the
charging and discharging efficiency of SC. σSC is the self-discharging rate
of SC.
Jacob et al. [47] investigated the sizing optimization of PV-based
microgrids equipped with short-term SC, mid-term battery and
long-term HES. Different types of energy storages were employed to
handle the supply-demand variability in various timescales based on
their nominal discharge time. Mohseni et al. [48] applied SC in an iso­
lated hydrogen-based microgrid to improve the system transient sta­
bility, as well as prolong the lifetime of fuel cell by decreasing its start-up
and shut-down cycles. Abdelkader et al. [49] studied the sizing opti­
mization of a standalone HRES with battery-SC. Frequency management
based on discrete Fourier transform was applied to control the coordi­
nated operation strategy, in which fast-frequency dynamics were regu­
lated by SC and slow-frequency dynamics were covered by battery.
Elmorshedy et al. [50] investigated the optimal design and energy
management of SC-battery in an isolated HRES. The results indicated
that the integration of SC could efficiently enhance the dynamic per­
formance of HRES, including maintaining the active power balance and
regulating the voltage and frequency under different meteorological
disturbances. Xu et al. [51] applied SC-battery to jointly mitigate the
fluctuations of standalone wind power, in which SC was used to regulate
the drastic power surges and battery was for slow fluctuations. Luta et al.
[52] conducted the optimal sizing of HES-SC in off-grid HRES applica­
tions, where SC covered the transient peak loads and fast fluctuations
while HES was to maintain the energy balance. Salameh et al. [53]
compared the techno-economic-environmental performance of SC and
battery in standalone PV-diesel-fuel cell HRESs, and the results revealed
that the SC-based HRES achieved lower levelized cost, higher renewable
energy fraction, and less environmental effect compared to
battery-based HRES.
3.2.3. Pumped hydro storage
PHS is categorized as mechanical energy storage technology, which
generally consists of hydraulic pumps, hydraulic turbines, and upper/
lower reservoirs. Electrical energy is stored as the potential energy of
water in upper reservoirs via hydraulic pump, and the stored water can
flow back to lower reservoirs for power generation via hydraulic tur­
bine. The hydraulic pump and turbine can also be integrated into a
reversible pump-turbine machine to simplify the pipeline structure and
reduce installation cost. The technical performance of PHS depends on
the conversion efficiency of hydraulic pump and turbine, as well as the
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
design elevating head height. The mathematical model of PHS is shown
as follow [54].
in
out
VUR (t) = VUR (t − 1) × (1 − σ UR ) + VUR
(t) − VUR
(t)
η × PHP (t)
in
VUR
(t) = HP
× Δt
ρ×g×h
out
VUR
(t) =
PHT (t)
ηHT × ρ × g × h
× Δt
in
MHS
(t) =
(16)
out
MHS
(t) =
(17)
HHV
PFC (t)
ηFC × HHV
× Δt
× Δt
(20)
(21)
out
where, MHS (t) is the available mass of HES at time t. Min
HS (t) and MHS (t)
are the input and output mass of HES at time t. PEL (t) is the charging
power of electrolyzer at time t. PFC (t) is the discharging power of fuel cell
at time t. ηEL is the power-to-hydrogen efficiency of electrolyzer. ηFC is
the hydrogen-to-power efficiency of fuel cell. HHV is the higher heat
value of hydrogen. σ HS is the leakage loss rate of HES.
In terms of the feasibility analysis of HES applications, Bartolucci
et al. [65] proposed a fuel cell-based HRES to supply a constant load for
off-grid telecom stations, in which the PV excess energy was utilized to
produce hydrogen via electrolyzer, and the produced and imported
hydrogen ensured the constant load supply via fuel cell. Firtina-Ertis
et al. [18] investigated the technical feasibility and optimal design of
wind-hydrogen HRES for a standalone zero-energy house considering
the part-load hydrogen production/consumption rate. The results
showed that the wind-hydrogen HRES with oversized wind capacity was
capable to continuously supply all-year residential load. Abo-Elyousr
et al. [66] verified the geographical-independent techno-economic
feasibility of HES in wind-PV HRESs in three different regions. The
maturity and risk analysis of hydrogen storage were further investigated
through readiness levels. Izadi et al. [67] investigated the optimal design
of wind-PV-hydrogen HRESs for zero-energy buildings at four different
climate locations. The results revealed that the integration of HES could
increase system reliability and mitigate grid dependency. Rezk et al.
[68] studied the techno-economic feasibility of PV-hydrogen HRESs for
a reverse osmosis desalination plant. The results indicated that
PV-hydrogen was an economically viable option and the standalone
HRES was cheaper than the grid extension. Rad et al. [69] analyzed the
techno-economic performance of wind-PV-biomass-hydrogen HRESs for
rural electrification and the results showed that HES could effectively
improve the system flexibility. Moreover, the performance of natural gas
reformer and electrolyzer was compared to reveal that the reformer had
less cost but created more carbon emissions. Sun et al. [70] conducted
the techno-economic-environmental design of a PV-biowaste-hydrogen
HRES, and the results verified the economic viability of this
HES-based configuration. Jahannoosh et al. [71] optimized the
cost-effective design of wind-PV-hydrogen HRESs, and the results
showed that HES could effectively compensate for the fluctuation of
wind-PV power production to achieve optimal reliability. Samy et al.
[72] explored the possibility of utilizing fuel cell/electrolyzer as energy
storage rather than batteries in wind-PV HRESs for rural electrification,
and the simulated results verified its economic viability. Nguyen et al.
[73] presented the optimal design of sustainable wind-PV-hydrogen
HRESs for the aquaculture sector, in which electrolyzer was mainly
utilized to produce pure oxygen for aquatic creatures and the by-product
hydrogen was used for backup sources via fuel cell. The results showed
that the utilization of electrolyzer/fuel cell could reduce annualized cost
and carbon emissions. Mezzai et al. [74] established the mathematical
model topology and power management strategy of a wind-PV-fuel cell
HRES via Simulink, and its effectiveness was verified by the comparison
of simulated and experimental results.
(18)
in
where, VUR (t) is the available volume of upper reservoir at time t. VUR
(t)
out
and VUR (t) are the input and output volume of upper reservoir at time t.
PHP (t) is the charging power of hydraulic pump at time t. PHT (t) is the
discharging power of hydraulic turbine at time t. ηHP and ηHT are the
efficiency of hydraulic pump and turbine respectively. σ UR is the leakage
and vaporization loss rate of upper reservoir. ρ is the water density. g is
the gravitational acceleration. h is the elevating head height.
Nyeche et al. [55] presented the modeling and optimization of a
wind-PV-PHS HRES in coastal communities, and the results indicated
that the proposed system was technically feasible to achieve the full
satisfaction of load demand. Xu et al. [56] investigated the optimal
design of a wind-solar-hydropower HRES with PHS, in which the
part-load efficiency characteristics of hydraulic pump and turbine were
considered. The results showed that the optimal HRES configuration
could guarantee power supply reliability and reduce capital cost. Mai­
sanam et al. [57] studied the optimal sizing of a sustainable
PV-biomass-PHS HRES. The results showed that PHS and biomass
generator could effectively cover the peak load demand. Nassar et al.
[58] presented the dynamic analysis and sizing optimization of a
wind-PV-PHS HRES in an urban community. The results revealed that
PHS was cost-competitive and reliable for sustainable power supply in
favorable geographical locations. Katsaprakakis et al. [59] aimed to
select the techno-economically optimal energy storage in autonomous
HRESs, including PHS, Lead-acid and Lithium-ion battery. The results
highlighted that PHS could support long-period autonomy and secure
power supply in islanded applications. Islam et al. [60] explored the
techno-economic optimization of a wind-PV-hydropower-PHS HRES
with zero emissions. The results indicated that PHS could reduce the cost
of HRES compared to battery despite a slightly higher supply-demand
deviation. Al-Ghussain et al. [61] investigated the capacity optimiza­
tion of wind-PV HRESs with alternative short-term battery or long-term
PHS at a Mediterranean university campus. The results showed that
wind-PV-PHS achieved the highest renewable energy fraction. Awan
et al. [62] analyzed the techno-economic-environmental performance of
PHS, battery and HES in off-grid HRESs. The results concluded that PHS
was the most environment-friendly option, which had the highest
renewable energy fraction and the lowest CO2 emissions. Contrarily,
Shabani et al. [63] studied the techno-economic comparison of micro
PHS and battery in standalone HRESs. The results revealed that, with the
full satisfaction of load demand, battery achieved higher economic
benefits and lower energy curtailment than micro PHS.
3.2.4. Hydrogen energy storage
HES is categorized as the type of chemical energy storage technol­
ogy, which can be adopted to regulate intermittent renewable energy
output via the reversible power-to-hydrogen conversion cycle. The main
components of HES consist of electrolyzers, compressors, hydrogen
tanks, and fuel cells. The type of electrolyzer and fuel cell is basically
comprised of alkaline, proton exchange membrane, and solid oxide. The
technical performance of HES is determined by the conversion efficiency
of electrolyzer and fuel cell, as well as the higher heating value of
hydrogen. The mathematical model of HES is shown as follow [64].
in
out
MHS (t) = MHS (t − 1) × (1 − σ HS ) + MHS
(t) − MHS
(t)
ηEL × PEL (t)
3.2.5. Thermal energy storage
TES technologies can be classified as sensible heat storage, latent
heat storage or phase change heat storage, and thermo-chemical storage
according to heat storing principles. Sensible heat storage is the simplest
TES technology, which stores heat through the temperature difference of
heat transfer mediums, such as water, molten salt, and solid concrete.
TES based on the molten salt medium has been widely applied in com­
mercial CSP plants due to its technical maturity and cost-effectiveness
(19)
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Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
[75]. Molten salt-based TES consisting of resistant electric heaters,
storage tanks and power cycles can function as a large-scale electrical
energy storage via thermodynamic process. The technical performance
of molten salt-based TES depends on the power-to-heat efficiency of
electric heater, the heat-to-power efficiency curve of power cycle, and
the self-dissipating rate of molten salt tanks. The mathematical model of
TES is shown as follow [17].
out
QTES (t) = QTES (t − 1) × (1 − σTES ) + Qin
TES (t) − QTES (t)
(22)
Qin
TES (t) = ηEH × PEH (t) × Δt
(23)
Qout
TES (t) =
PPB (t)
ηPB
× Δt
[81].
(
MAC (t) = MAC (t − 1) +
VAC (t) =
PCOM (t)
αCOM
−
)
PEX (t)
× Δt
βEX
MAC (t) × R × TAC
pAC
(25)
(26)
where, MAC (t) and VAC (t) are the mass and volume of available highpressure air in the air container at time t. PCOM (t) is the charging
power of compressor at time t. PEX (t) is the discharging power of
expander at time t. R is the gas constant. TAC is the air rated temperature
in air container. pAC is the air rated pressure in air container. αCOM is the
required power of compressing air per unit mass. βEX is the generated
power of expanding air per unit mass.
Xu et al. [81] investigated the optimal design of a standalone
wind-diesel HRES with an adiabatic CAES, which utilized the curtailed
wind power for air compression and then supplied the unmet load via a
reverse process. However, this work ignored the techno-economic
comparisons between CAES and other energy storage alternatives.
Zhao et al. [82] conducted the multi-objective optimization of HRESs
with underwater CAES for seawater desalination, and a real-world case
was implemented to illustrate the techno-economic-environmental
feasibility of the proposed system. The results showed that HRESs
with underwater CAES could flexibly accommodate the electrical load of
reverse osmosis plants and reduce carbon emissions significantly.
(24)
out
where, QTES (t) is the available heat of TES at time t. Qin
TES (t) and QTES (t)
are the input and output heat of TES at time t. PEH (t) is the charging
power of electric heater at time t. PPB (t) is the discharging power of
power block at time t. ηEH is the power-to-heat efficiency of electric
heater. ηPB is the heat-to-power efficiency of power block. σ TES is the selfdissipating rate.
Guo et al. [76] investigated the capacity optimization of a wind-PV
HRES with molten salt-based TES. The results indicated that the
molten salt-based TES could effectively improve the utilization rate of
transmission channels and decrease the lifecycle total cost compared to
battery. He et al. [77] proposed a wind-PV-TES cogeneration system, in
which electric heater-molten salt storage-power block was employed to
balance the power load while an additional heat exchanger was applied
to supply the heating load. The simulated results indicated that the
TES-based
cogeneration
system
achieved
better
techno-economic-environmental performance than the power supply
system. He et al. [17] further investigated the quantitative
techno-economic comparison of different energy storage technologies in
HRES applications, and the results showed that molten salt-based TES
was the most cost-effective alternative in various resource and load level
conditions. Kiptoo et al. [78] proposed a pumped TES for isolated
renewable energy microgrids, in which the pumped TES using crushed
rock as heat storage medium consisted of compressor, expander, and
hot/cold storage tanks. The results revealed that wind-PV-TES config­
uration was more techno-economically efficient than battery-based
configuration. Yang et al. [79] studied the optimal capacity and oper­
ation strategy of a wind-PV-CSP HRES with molten salt-based TES. The
results validated that CSP with TES was a cost-effective subsystem to
improve system reliability. Starke et al. [26] proposed the hybridization
of CSP-PV solar power system, in which the cheap PV subsystem could
reduce the total investment cost and the expensive CSP subsystem could
improve the operational flexibility as well as the overall capacity factor.
The simulated results indicated that the PV-CSP hybrid system
techno-economically outperformed either standalone PV or CSP plant.
3.2.7. Gravity energy storage
GES is another type of mechanical energy storage technology, which
shares similar functioning principles with PHS. GES stores energy as the
gravitational potential energy of heavy objects. One type of GES in­
cludes motors, generators, heavy objects, and affiliated traction devices
[83]. In the charging process, the electric motor drives the heavy objects
to a higher height, thus achieving the electrical-to-potential energy
conversion. In the discharging process, the heavy objects descend at a
certain height and drive the generator for power production. Another
type of GES consists of reversible pump turbine, sealed container, heavy
piston, and pipeline system [84]. In the charging mode, the pump con­
verts the electrical energy into the kinetic energy of water, which drives
the piston to move upward in the container. In the discharging mode, the
piston descends and forces the pressurized water flow back to the tur­
bine/generator for power generation. The mathematical model of GES
adopted in the HRES design is shown as follow [84].
3.2.6. Compressed air energy storage
CAES is categorized as mechanical energy storage, which stores en­
ergy as the potential energy of compressed air. The main components of
CAES consist of compressor, expander, heat exchanger, and air
container. CAES uses electricity to compress air via compressor, and
then the high-pressure air stored in the air container can be released to
generate power via expander, thus achieving the cycle process of energy
storing and discharging. CAES can be classified as diabatic CAES,
adiabatic CAES, and iso-thermal CAES according to the idealized process
of energy conversion [80]. In diabatic CAES, the heat produced in the
compression process is wasted and external heat sources are required in
the expansion process. By comparison, the compression heat is recycled
in the adiabatic CAES and utilized in the expansion process. Moreover,
the iso-thermal CAES attempts to reduce energy conversion loss by
maintaining constant temperature operation in the compression and
expansion process. The mathematical model of CAES is shown as follow
)
(
1
EGES (t) = ηGES × g × × π × D2 × Hpiston (t) × ρpiston − ρwater
4
(
)
× Hcontainer − Hpiston (t)
(27)
)
(
Pchar
GES (t) = ηpump × ρpiston − ρwater × g × h × Qchar (t)
(28)
)
(
Pdisc
GES (t) = ηturbine × ρpiston − ρwater × g × h × Qdisc (t)
(29)
where, EGES (t) is the available energy of GES at time t. Pchar
GES (t) and
Pdisc
GES (t) are the charging power and discharging power of GES at time t.
ηpump and ηturbine are the pump and turbine efficiency of reversible pump
turbine. ρpiston and ρwater are the piston density and water density. Qchar (t)
and Qdisc (t) are the charging and discharging flow rate of GES at time t.
Hcontainer is the height of container. Hpiston (t) is the height of piston at time
t. g is the gravitational acceleration. h is the height of water. ηGES is the
overall efficiency of GES. D is the diameter of piston.
Hou et al. [83] investigated the optimal capacity configuration of a
wind-PV-GES system, and compared the technical-economic perfor­
mance of GES, battery and CAES. The simulation results indicated that
GES was economically feasible and had better economic performance
than battery and CAES. Meanwhile, GES was identified to have natural
advantages in remote mountainous regions, as the significant altitude
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
difference could be directly utilized for its installation. Emrani et al. [84]
proposed a methodology to optimize the sizing and deployment of GES
in wind-PV HRESs. Especially, the structural design parameters
including the height and diameter of container, piston, container wall
and base thickness, as well as the area of steel reinforcement were
considered together with sizing variables in the optimization problem,
and the technical feasibility of GES was verified via operation simula­
tion. Emrani et al. [85] further carried out the capacity optimization of
off-grid wind-PV-GES systems based on techno-economic performance
indicators. The optimal results revealed that the wind-PV-GES could
achieve full satisfaction of the load demand, and GES was more
cost-effective for high reliability requirement compared to battery.
curtailment and extend the battery lifetime. Marocco et al. [88] studied
the techno-economic feasibility of off-grid HRESs with battery-HES in
four remote areas. The simulated results based on financial analysis
revealed that the application of battery-HES could effectively mitigate
the consumption of external fossil fuels in off-grid power systems. Mah
et al. [89] utilized battery-HES to tackle the supply-demand imbalance
for renewable energy microgrids. The optimization results showed that
battery-HES produced significantly less carbon footprint, which was
more environment-friendly than single battery. Guezgouz et al. [90]
investigated the operation strategy and optimal sizing of off-grid HRESs
with battery-PHS. The results indicated that battery-PHS achieved
higher reliability at lower cost and reduced the renewable energy
curtailment compared to either single energy storage. Javed et al. [91]
proposed a novel operating strategy for battery-PHS in off-grid HRESs
based on the operation range of reversible pump-turbine machine. The
simulated results concluded that battery-PHS could effectively manage
the energy mismatch owing to their complementary characteristics.
However, the economic performance of battery-PHS was not analyzed.
He et al. [5,6] proposed a novel HESS configuration based on battery
and molten salt-based TES, in which the flexibility of battery and the
cost-effectiveness of TES were utilized to achieve better
techno-economic performance. The results revealed that battery-TES
performed higher reliability than single TES and better
cost-effectiveness than single battery. Yang et al. [79] investigated the
optimal capacity and operation strategy of a wind-solar HRES with
battery-TES, and the results indicated that TES-battery was essential to
achieve higher reliability without sacrificing economic performance. Liu
et al. [92] investigated the techno-economic feasibility of battery-TES in
PV-CSP hybrid solar plants considering the current and future scenarios.
The results found that the integration of battery-TES could improve
reliability more economically in the current scenarios, while the
techno-economic performance of battery might dominate that of TES in
future cost reduction scenarios. Khiareddine et al. [93] investigated the
sizing optimization of a standalone wind-PV-hydrogen-battery HRES, in
which the operation strategies considering the operating priority of
battery/hydrogen was optimized to allocate the energy curtailment. The
results highlighted the superiority of HESS with respect to individual
energy storage.
3.2.8. Hybrid energy storage system
Except for individual energy storage technologies, HESS configura­
tions including two or more heterogenous and supplementary types of
energy storages were applied in off-grid HRESs. Different energy stor­
ages are mainly characterized by power density, energy density, storage
duration, response time, round-trip efficiency, cycle lifetime, and
operating flexibility [34]. In off-grid HRES applications, high-level
power supply reliability requires energy storage to fully balance the
supply-demand mismatch in multiple power scales and time scales. To
be specific, short-term energy regulation requires energy storage with
fast response, while long-term energy regulation requires energy storage
with long storage duration and high energy density. Meanwhile,
small-scale energy regulation requires energy storage with high oper­
ating flexibility, whereas large-scale energy regulation requires energy
storage with high power density. Moreover, the economic feasibility of
energy storage is a vital and non-negligible factor in practical applica­
tions, which highly depends on the unit investment cost and cycle life­
time. However, any existing energy storage technology cannot satisfy
the abovementioned technical and cost-effective requirements simulta­
neously, so two or more energy storages with supplementary charac­
teristics can operate coordinately to achieve higher reliability and
cost-effectiveness.
Firstly, energy storages can be hybridized for different timescale
operations, such as battery-SC and battery-HES. In battery-SC, the
combination of long-term battery with high energy density and shortterm SC with high power density can improve the overall efficiency
and extend the energy storage lifetime. In battery-HES, battery with
high power density is used as the short-term energy storage while HES
with high energy density is used as the long-term backup source.
Moreover, HES without self-discharging loss is a promising seasonal
energy storage owing to its long storage duration [86]. On the other
hand, energy storages can be hybridized to obtain the optimal trade-off
between technical reliability and cost-effectiveness, such as battery-PHS
and battery-TES. PHS and molten salt-based TES are inefficient to
operate in low part-load conditions because of the part-load efficiency
characteristics of hydraulic pump/turbine (the charging and discharging
units of PHS), and power block (the discharging unit of TES). Therefore,
battery with high operating flexibility can coordinate with PHS/TES to
undertake small-scale energy regulation and avoid the inefficient
part-load operation of PHS/TES, so the combination of battery and
PHS/TES is more technically reliable than single PHS/TES. By com­
parison, battery has high investment cost and short cycle lifetime, while
PHS and TES have relatively lower investment cost and longer cycle
lifetime, so the hybridization of battery and PHS/TES is more econom­
ically feasible than single battery.
Regarding the techno-economic feasibility analysis of HESSs, Jing
et al. [87] proposed to integrate battery-SC with standalone PV power
systems. Theoretical analysis and numerical simulation for different
HESSs were conducted to quantitatively validate the effectiveness of
HESSs in mitigating battery stress. Xu et al. [51] applied battery-SC to
reduce wind curtailment for off-grid wind power plants, and a
multi-objective optimization model for HESS sizing was proposed. The
results indicated that battery-SC could significantly reduce wind
3.3. Size classifications
Based on the sizing results of all considered literature, Fig. 4 shows
the size classifications of different energy sources and energy storages
technologies in off-grid HRESs. Due to the lack of an explicit classifi­
cation standard for the size of HRESs, this paper regards technologies
with a rated power of <100 kW as small-scale, technologies with a rated
power of 100 kW-10 MW as medium-scale, and technologies with a
rated power of >10 MW as large-scale applications.
In terms of energy sources, wind power and solar PV can be imple­
mented in small-scale, medium-scale, and large-scale applications owing
to their wide range of nominal power and modular characteristics.
Biomass power and DG are generally implemented in small-scale and
medium-scale applications due to their role as backup sources rather
than primary energy suppliers. Moreover, HKT which is limited to
coastal areas has not yet been implemented in large-scale applications.
Finally, micro hydropower is only available for medium-scale applica­
tions, and CSP is only available for large-scale applications owing to its
low energy density.
Regarding energy storages, batteries and HES can be implemented in
all-scale applications owing to their highly modular characteristics,
which are also the most common storage options in off-grid HRESs. SC
with high power density and the highest unit investment cost is basically
adopted in small-scale applications to undertake short-term and fast
regulations. Furthermore, PHS is available for medium-scale and largescale applications based on the volume of reservoirs, while molten saltbased TES, CAES, and GES are only available for large-scale applications
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Fig. 4. Size classifications of energy sources and energy storages in off-grid HRESs.
due to their bulk engineering structures.
should be connected to the AC bus via AC/DC-DC/AC converters to
stabilize the frequency of power output [94]. Hybrid AC/DC-coupled
topology is the most popular one in off-grid HRESs, in which all en­
ergy sources and storage technologies are separately connected to their
corresponding AC or DC bus, and an interface converter is adopted for
interconnections.
The advantages and disadvantages of different topologies are pre­
sented in the Appendix (Table A3). Based on the topology of off-grid
HRESs, several control strategies can be applied to ensure an uninter­
rupted power supply for critical loads and stabilize the voltage and
frequency [95]. Conventional control strategies include droop control,
virtual impedance loop-based droop control, master-slave control,
multi-agent based control, and maximum power point tracking, etc. By
3.4. Topologies
The implementation of off-grid HRESs generally follows three types
of topologies, namely DC-coupled topology, AC-coupled topology, and
hybrid AC/DC-coupled topology [9]. The schematic diagrams of
different topologies are shown in Fig. 5(a) and 5(c). The basic difference
between these topologies is the application of converters. In DC-coupled
topology, solar PV, batteries, SC, and HES are connected to the DC bus
via DC/DC converters, while all remaining components are connected
via AC/DC converters. In AC-coupled topology, although the rotating
technologies such as wind power and HKT are AC energy sources, they
Fig. 5(A). Schematic diagram of DC-coupled topology for off-grid HRESs.
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Fig. 5(B). Schematic diagram of AC-coupled topology for off-grid HRESs.
Fig. 5(C). Schematic diagram of hybrid AC/DC-coupled topology for off-grid HRESs.
comparison, advanced control strategies consist of supervisory control
(centralized, decentralized, hierarchical), intelligent control (fuzzy
logic, artificial neural network, meta-heuristic algorithms, etc.), and
adaptive control (model predictive control, reinforcement learning, etc.)
[96]. Sahoo et al. [95] presented a systematic review of the hierarchical
control strategies for AC-coupled, DC-coupled, and hybrid
AC/DC-coupled topology. Particularly, the advantages and disadvan­
tages of different control strategies for each topology are comparatively
analyzed. Unamuno et al. [94] reviewed the topologies and corre­
sponding control strategies for hybrid AC/DC-coupled HRESs, with the
focus on hierarchical control strategies including primary, secondary,
and tertiary control levels. Gupta et al. [97] also reviewed the control
strategies for hybrid AC/DC-coupled HRESs from the perspectives of
interlinking converters, power management, coordinated control, sta­
bility analysis, power quality, and protection.
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following and cycle charging depends on whether DG will charge the
battery to maintain its preset state of charge level. DG in load following
strategy only supplies enough power to cover the instantaneous load,
while it will operate at 100% rated power to charge the battery in the
cycle charging strategy. Concerning the load following strategy, when
the wind-PV output is higher than the load demand, the surplus energy
will be stored in the battery. If the surplus energy exceeds the available
maximum capacity of battery, there will be energy curtailment.
Contrarily, when the wind-PV output is lower than the load demand, the
battery will discharge electricity to supply the remaining load. If the
remaining load cannot be covered by the battery owing to its minimum
capacity constraint, DG will operate in part-load condition to reach an
instantaneous supply-demand balance.
The impact of different rule-based EMSs on the sizing results was
studied by some researchers. Quitoras et al. [98] applied both load
following and cycle charging strategy in the optimal design of a remote
community HRES. The results found that load following strategy was
more suitable for co-generation system, while cycle charging strategy
was favorable for electricity-only system. Nesamalar et al. [99] analyzed
the techno-economic performance of HRESs for an educational institu­
tion considering both load following and cycle charging strategy. The
results revealed that HRESs with load following dispatch achieved
optimal performance. Udeh et al. [100] explored the difference of load
following and cycle charging dispatch modes in HRESs with Stirling
engine and organic Rankine cycle as backup sources. The results indi­
cated that cycle charging strategy led to lower carbon emissions, but
higher cost compared to load following strategy.
The EMS of HESSs in off-grid applications is more complicated due to
the coordinated operation between different energy storages. Guezgouz
et al. [90] studied the optimal design of battery-PHS based on a novel
coordinated rule-based EMS, in which the PHS was responsible for
large-scale energy regulation, while the flexible battery covered the
small-scale energy imbalance which could not be regulated by PHS due
to the operating characteristics of hydraulic pump/turbine. Yang et al.
[79] considered two different output priorities in the rule-based EMS of
3.5. Bibliometric analysis of system configurations
Fig. 6 shows the bibliometric analysis of energy sources and energy
storages respectively, including the occurrence frequency and percent­
age of each component. In terms of energy sources, solar PV is employed
in 96.99% of literature, followed by wind power (54.52%) and DG
(45.15%). Solar PV dominates the occurrence frequency because solar
energy is the most ubiquitous and distributed renewable resource
around the world. Concerning energy storages, batteries are the most
popular option owing to their mature technology and installed flexi­
bility, accounting for 83.95% of all relevant literature. Meanwhile, the
application of HESSs attracts increasing academic interest, accounting
for 15.05% of literature. Moreover, the most popular and representative
system configuration for off-grid HRESs is the wind-PV-battery-DG,
which is capable to meet the required reliability in off-grid applica­
tions at a reasonable cost.
4. Energy management strategies
An energy management strategy (EMS) is used to coordinately con­
trol the energy flow of components in HRESs. In off-grid applications,
the basic objective of EMS is to satisfy the load demand as reliably as
possible. EMS adopted in off-grid HRESs can be classified as predefined
rule-based EMS and real-time optimized EMS. Moreover, demand side
management (DSM) can be integrated with supply-side energy man­
agement to achieve a higher supply-demand matching degree, thus
further improving system reliability and reducing required storage ca­
pacity. An overview of different EMSs is introduced in this section.
4.1. Rule-based energy management strategy
Rule-based EMS is to determine the operation status of system
components by following a predefined flow chart. Taking the wind-PVbattery-DG HRES for example, the rule-based EMS generally includes
load following and cycle charging. The difference between load
Fig. 6. Bibliometric analysis of system configurations including energy sources and energy storages.
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
electrical-thermal HESS. The results discovered that system with power
block output priority achieved better techno-economic performance
than system with battery output priority. In the coordinated rule-based
EMS of battery-HES, battery with high power density takes priority to
undertake the short-term energy regulation, while HES with high energy
density and low self-discharging rate is served as a backup source for
long-term regulation when battery is unable to cover the mismatch.
Furthermore, some control parameters in the rule-based EMS of
HESSs can be optimized to improve the system reliability. For instance,
Yi He et al. [6] considered the operating threshold of power block as an
operation decision variable to coordinate the EMS of electrical-thermal
HESS. Only when the supply-demand mismatch exceeds the operating
threshold will the power block take priority for power output, otherwise
the power block will be in the standby state. The operating threshold
optimization could achieve a balance between low-efficiency operation
and shut-down, thus maintaining the highest reliability. Abdelshafy
et al. [101] proposed an allocation factor to be optimized in the coor­
dinated rule-based EMS of battery-PHS, in which the allocation factor
ensured that a part of excess energy was always stored in battery to
maintain its sufficient regulation capability and operational flexibility.
The results indicated that the optimal allocation factor could reduce the
energy exchange with the grid.
and other passive hours were controlled by rule-based EMS. The simu­
lated results showed that the combined EMS could effectively reduce the
computational burden. Xu et al. [81] investigated the optimal design of a
standalone HRES based on a bi-level stochastic programming frame­
work, in which the inner-layer EMS optimization was modeled via
scenario-based analysis and solved by mathematical programming. The
results indicated that the stochastic optimized EMS performed higher
operational flexibility. Forough et al. [105] applied a real-time RHO-­
based operation in the lifecycle sizing optimization framework of
HRESs, and the mixed integer convex programming method was adop­
ted to achieve the optimal EMS. The advantage of RHO was the ability to
globally consider the impact of future conditions on the present opera­
tional variables. The results showed that the implemented RHO reduced
the operation cost by 6% and increased the renewable energy level by
34% compared to conventional EMS optimization. Fioriti et al. [106]
compared the economic performance of load following EMS and
RHO-based EMS in the optimal design of off-grid HRESs. The results
revealed that the RHO-based sizing results performed better perfor­
mances in terms of net present value, internal rate of return, and
payback period. Swaminathan et al. [107] applied MPC method in the
optimal sizing and dispatch of an islanded HRES, where MPC took the
predictive future states into account to repeatedly optimize the current
variable until the ending time horizon. The comparisons of optimal
sizing between rule-based EMS and MPC showed that MPC led to 13%
decrease in battery storage capacity and achieved 6% lower investment
cost compared to rule-based EMS. Rullo et al. [108] presented a novel
sizing optimization method for standalone HRESs with economic model
predictive control (EMPC) method. The difference between EMPC and
MPC was that EMPC optimized economic objectives instead of penal­
izing the deviations of constraints. The results indicated that EMPC
could effectively reduce investment cost and operating cost in compar­
ison to a heuristic-based EMS. Moreover, Serir et al. [109] applied three
energy management strategies to control a wind-PV-battery HRES for
supplying pumping systems, and the simulation results revealed that the
adaptive fuzzy logic controller was more efficient and robust to reach
the maximum power point. Roumila et al. [110] further adopted fuzzy
logic controller to manage the generation-load balance of a
wind-PV-battery-diesel HRES. The results indicated that the adopted
control strategies can efficiently maintain the system reliability in
different meteorological conditions.
Furthermore, Kotb et al. [111] considered the optimal control
strategy of an autonomous HRES to achieve the maximum available
power of wind-PV via maximum power point tracking and improve the
power quality via converter controller. The simulation results showed
that the optimized control strategy could effectively maintain the
voltage and frequency stability of the whole system under various
generation and load disturbances. However, the optimal control strategy
was separately investigated as a posterior evaluation after the sizing
optimization, and the feedback of control strategies on the sizing results
was not considered. Elmorshedy et al. [112] also investigated the sizing
optimization of an isolated HRES along with the optimal control strat­
egy, which analyzed the dynamic response, power balance, and volta­
ge/frequency control of HRES in different meteorological and load
conditions. Similarly, control strategies and sizing are separately opti­
mized and the impact of control strategies on the sizing is neglected.
Therefore, the bi-level coordinated optimization of sizing and
second-scale control strategies for off-grid HRESs is an interesting and
challenging research gap to be bridged in future works.
4.2. Optimized energy management strategy
The optimized EMS for off-grid HRESs considers the operation status
of each component as decision variables to establish an operation opti­
mization model based on specific objectives. Compared to rule-based
EMS, the optimized EMS can ensure optimality towards different ob­
jectives, but it requires higher computational complexity and longer
computational time because the operational variables should be ob­
tained by real-time optimization.
The optimized EMS can be integrated with the sizing optimization to
develop a multi-layer co-optimization framework, in which the real-time
operation strategy is optimized in the inner-layer and the sizing
configuration is optimized in the outer-layer. The multi-layer co-opti­
mization framework is deeply coupled via data interaction between
different layers, as the out-layer sizing decision variables provide
boundary conditions for the inner-layer operation optimization model,
while the inner-layer optimal objective value provides feedback for the
outer-layer objective function. The objectives of the optimized EMS are
generally to minimize the operating cost or maximize the power supply
reliability, and the energy balance constraint and operating constraints
of each component are considered in the operation optimization model.
Based on the collected literature, mathematical programming, dy­
namic programming (DP), finite automata, stochastic programming,
receding horizon optimization (RHO), model predictive control (MPC),
etc., have been applied to optimize EMS in the sizing optimization of offgrid HRESs. To be specific, He et al. [5] applied mathematical pro­
gramming to optimize the EMS of electrical-thermal HESS based on the
minimization of the power deviation between charging/discharging
power of energy storages and the net load. The results showed that the
optimized EMS obtained better sizing solutions with lower investment
cost than the rule-based EMS. Khawaja et al. [102] innovatively applied
finite automata to generate multiple EMSs for off-grid HRESs, and the
EMSs were iteratively renovated according to a tailored evaluation
model until the optimal EMS was found. The simulated results indicated
that the proposed finite automata-based framework yielded better sizing
results with lower levelized cost. Lee et al. [103] compared the impact of
optimized EMS and rule-based EMS on the optimal design of isolated
HRESs. The results discovered that the DP-based optimized EMS ob­
tained lower lifecycle cost and shorter payback period compared to
simple rule-based EMS, indicating that the application of rule-based
EMS suffered from an optimality loss. Chedid et al. [104] proposed a
combined optimized and rule-based EMS to ensure the optimal power
flow of HRESs, in which only certain active hours were optimized via DP
4.3. Demand side management
Demand side management (DSM) is a portfolio of measures to
improve the energy system at the consumption side, which can be
categorized as energy efficiency improvement, time-of-use tariff, de­
mand response and spinning reserve [113]. Demand response can in­
crease the supply-demand matching degree by altering the load pattern,
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
because some deferrable load demands such as air conditioner and
heating systems can be regulated similarly to the management of power
generation. Therefore, demand response can be integrated with the EMS
of HRESs to achieve higher power supply reliability.
He et al. [5] investigated the impact of demand response on the
optimal sizing of electrical-thermal HESS. The results showed that the
demand response strategy could shift the load pattern to effectively
mitigate the net difference between renewable power supply and load
demand, thus reducing the required storage capacity and investment
cost. Kiptoo et al. [78] proposed a novel renewable generation-based
dynamic pricing demand response strategy for optimal planning of an
isolated HRES. The results indicated that the proposed demand response
strategy could minimize the mismatch between renewable generation
and load demand profile, thereby achieving a significant reduction of
the total operating cost compared to traditional time-of-use and direct
load control strategies. Hermann et al. [28] applied an energy conser­
vation DSM strategy in the techno-economic-environmental optimal
configuration of off-grid HRESs. The results revealed that the DSM
strategy could significantly reduce the hourly load demand, thus
achieving considerable cost savings for rural communities. Ghazvini
et al. [44] considered the electric vehicle-to-grid parking lot as a
controllable load for demand response, in which the electric vehicle
charged and discharged power according to electric price variations.
The simulation results showed that the demand response of parking lot
could reduce the total cost by 5.21%. Tu et al. [114] considered
multi-layer demand scheduling in the sizing optimization of standalone
HRESs. The obtained results showed that load deferring was a
cost-effective measure to match the renewable generation profiles, and
it could greatly reduce the required battery capacity.
Fig. 8. The classification of performance evaluation indicators.
5.1. Technical reliability indicators
Technical reliability indicators are considered to evaluate the ability
of off-grid HRESs to satisfy the load demand, which is the basic premise
of sizing configuration. Technical reliability indicators can be consid­
ered as objective or constraint according to the decision-maker’s pref­
erence. The most popular technical reliability indicator is the loss of
power supply probability (LPSP), which is defined as the unmet load
divided by the total load over the simulation period or the frequency of
the power supply that is unable to meet the load demand. Likewise,
other technical reliability indicators such as loss of load probability,
deficiency of power supply probability, loss of load expected, and loss of
energy expected, refer to the same situation that power supply cannot
meet the load demand. The formulation of LPSP is shown as below [11].
⃒
∑T ⃒⃒
Pload (t) − Psupply (t)⃒
LPSP = t=1 ∑T
(30)
, if Psupply (t) < Pload (t)
t=1 Pload (t)
4.4. Bibliometric analysis of energy management strategy
Fig. 7 displays the bibliometric analysis of EMSs adopted in the sizing
optimization of off-grid HRESs. Rule-based EMS accounts for the largest
proportion at 86.29%, while the remaining 12.71% of literature adopted
the optimized EMS. This is because the rule-based EMS holds simple
implementation and fast computation in sizing optimization problems
compared to the optimized EMS. Moreover, only 2.68% of literature
considers the impact of DSM strategy on the supply-demand energy
balance and optimal sizing results.
∑T
LPSP =
t=1 sign(t)
T
{
, sign(t) =
1, if Psupply (t) < Pload (t)
0, if Psupply (t) ≥ Pload (t)
(31)
where, Pload (t) is the load demand at time t. Psupply (t) is the power supply
of HRESs at time t. sign(t) is a symbol variable indicating if power supply
can meet the load demand at time t. T is the simulation period.
5. Performance evaluation indicators
5.2. Economic indicators
The sizing optimization model of HRESs is based on several perfor­
mance evaluation indicators, mainly including technical, economic,
environmental, social-political, and energy-efficiency categories. The
classification of performance evaluation indicators is shown in Fig. 8,
and detailed descriptions of each indicator are presented in this section.
The sizing optimization of off-grid HRESs generally aims to meet the
load demand at an acceptable cost, so economic indicators are essential
to evaluate the system feasibility. Economic indicators and the above­
mentioned technical reliability indicators are jointly applied in the vast
Fig. 7. Bibliometric analysis of EMSs adopted in the sizing optimization of off-grid HRESs.
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
majority of sizing optimization problems. The frequently-used economic
indicators consist of lifecycle net present cost (NPC), annualized cost of
system (ACS), and levelized cost of energy (LCOE). NPC is defined as the
total discounted cost throughout the life cycle, including initial invest­
ment cost, annual operation & maintenance cost, replacement cost, and
salvage value at the end of lifetime. ACS refers to the sum of annualized
investment cost, annualized replacement cost, and operation & main­
tenance cost. LCOE is defined as the lifecycle total cost divided by the
lifecycle total energy generation, which is used to evaluate the average
power generation cost per kilowatt-hour. The formulations of these
economic indicators are presented as below [11].
NPC = Cinitial +
∑NS Cannual
Creplace
Vsalvage
+
−
n=1 (1 + r)n
(1 + r)NR (1 + r)NS
(
ACS = Cinitial + Creplace
LCOE =
Cinitial +
)
r⋅(1 + r)NS
×
+ Cannual
(1 + r)NS − 1
∑NS
Cannual
n=1 (1+r)n
∑ NS
n=1
C
replace
+ (1+r)
NR −
Vsalvage
(1+r)NS
n
Efirst (1− d)
(1+r)n
assessed the life cycle environmental sustainability of off-grid small-­
scale HRESs. Eight environmental indicators including climate change,
air pollution, water and soil pollution, ecotoxicity, resource depletion,
land use, and human health were considered. The results indicated that
batteries were a major environmental hotspot while PV and large-scale
wind turbines were environmentally more sustainable. Nagapurkar et al.
[116] conducted an environmental life cycle assessment of
renewable-based microgrids. The results showed that the LCCF of
renewable-based microgrids was extremely lower than that of equiva­
lent conventional electric grids.
5.4. Social-political indicators
(32)
The development of HRESs should be in accordance with the na­
tional policies and the objectives of sustainable social development.
Social-political indicators evaluate the impacts of HRES installation on
humans, relevant industries and society. Hence, social-political in­
dicators are meaningful to be considered in the sizing optimization of
off-grid HRESs. The quantitative social-political indicators at the plan­
ning stage of HRESs mainly include human development index (HDI)
and job creation (JC). HDI is a statistic index to measure the social and
economic development level of a country, which can be reflected in the
annual electricity consumption per capita. JC occurs in the process of
production, transportation, installation, operation and maintenance of
energy systems, which can be evaluated according to the generated
electricity or installed capacity of different energy sources. The formu­
lations of social-political indicators are shown as below [11].
)
(
∑8760
Eload (t) − 0.0319
(38)
HDI = 0.0978 × ln
t=1
(33)
(34)
where, Cinitial is the initial investment cost. Cannual is the annual opera­
tion & maintenance cost. Creplace is the replacement cost. Vsalvage is the
salvage value at the end of lifetime. NR is the year of component
replacement. NS is the design lifetime. r is the discount rate. Efirst is the
first-year energy production. d is the degradation rate.
5.3. Environmental indicators
The development of renewable energy generation is aimed to
decrease the proportion of traditional fossil fuel-based power genera­
tion, reduce carbon emissions and alleviate the environmental pollution
induced by the power sector. Furthermore, many countries have
implemented carbon neutrality commitments to slow down the process
of global warming [2]. Hence, environmental indicators should be taken
into full consideration in the sizing optimization of off-grid HRESs.
Environmental indicators mainly consist of direct carbon emission, life
cycle carbon footprint (LCCF), and levelized emission of energy (LEOE).
Direct carbon emission is produced in the operating process of
non-renewable power generation technologies, such as biomass power
and fossil fuel-based generators. LCCF refers to all carbon emissions of
energy systems throughout the lifetime, including not only the direct
carbon emissions during the operation, but also the indirect carbon
emissions during the production, transportation, installation, and
end-of-life disposal of each component. LEOE applies the same principle
as the economic indicator LCOE, which quantifies the carbon emissions
per kilowatt-hour of energy generated over the lifetime. The formula­
tions of environmental indicators are shown as below [11].
∑T ∑N
Ecarbon =
θn ⋅Pfossil.n (t)
(35)
t=1
n=1
LCCF = Ecarbon +
LEOE =
Ecarbon +
∑N
n=1
δn ⋅Cfossil.n +
∑M
m=1
δm ⋅Crenew.m
∑N
∑M
n=1 δn ⋅Cfossil.n +
m=1 δm ⋅Crenew.m
∑NS
n
E
(1
−
d)
first
n=1
JC =
∑M
m=1
jcm ⋅Crenew.m +
∑T ∑N
t=1
n=1
jcn ⋅Pfossil.n (t)
(39)
where, Eload (t) is the load demand at time t. jcm is the job creation factor
of renewable installed capacity. jcn is the job creation coefficient of
electricity generated by fossil-based technologies. Cfossil.n is the rated
capacity of the n-th fossil-based technology. Crenew.m is the rated capacity
of the m-th renewable energy technology.
The social-political indicators have been considered in the sizing
optimization. Sawle et al. [117] regarded HDI, JC and particle matter as
social-political indicators to investigate the social-techno-economic
optimal design of HRESs. Khan et al. [118] considered HDI, JC and so­
cial acceptance as social-political indicators, and the sizing optimization
of HRESs was conducted from a techno-economic and social perspective.
Eriksson et al. [119] proposed a semi-quantitative composite
social-political indicator via the subjective weight assignment method,
and the design optimization was investigated by compromising tech­
nical, economic, environmental and social-political objectives.
Lopez-Gonzalez et al. [120] evaluated the environmental, technical,
socio-economic and institutional sustainability of multiple microgrid
projects, in which socio-economic indexes included the concepts of
community empowerment, inclusion and governance. Petrelli et al.
[121] proposed a multi-objective sizing methodology for rural micro­
grids, considering socio-economic (NPC, JC) and social security (public
lighting coverage) indicators.
(36)
(37)
5.5. Energy-efficiency indicators
where, Ecarbon is the direct carbon emissions produced by non-renewable
energy technologies. θn is the direct carbon emission coefficient of fossilbased technologies per kilowatt-hour. Pfossil.n (t) is the power output of
the n-th fossil-based technology at time t. δm and δn are the indirect
carbon emission coefficients of renewable and fossil-based technologies
per kilowatt-hour. Cfossil.n is the rated capacity of the n-th fossil-based
technology. Crenew.m is the rated capacity of the m-th renewable energy
technology.
In terms of the environmental impact of HRESs, Aberilla et al. [115]
The oversized configuration of renewable energy technologies may
lead to considerable energy curtailment because of limited transmission
capacity and load demand. The issue of high-proportion energy
curtailment has aroused extensive concern in academia and govern­
ments. Hence, energy-efficiency indicators like energy curtailment rate
(ECR) have been considered in the sizing optimization of off-grid HRESs.
ECR refers to the proportion of renewable energy generation that cannot
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
be consumed by the load demand, reflecting the utilization efficiency of
renewable energy. The formulation of energy-efficiency indicators is
shown as below [77].
∑T
|Prenew (t) − Pload (t)|
ECR = t=1 ∑T
, if Prenew (t) > Pload (t)
(40)
t=1 Prenew (t)
where, Prenew (t) is the renewable energy generation at time t. Pload (t) is
the load demand at time t.
He et al. [77] considered ECR as the energy-efficiency indicator and
proposed a many-objective sizing optimization model based on tech­
nical, economic, environmental and energy-efficiency objectives. Guo
et al. [76] regarded the utilization rate of transmission channel capacity
as the energy-efficiency indicator and investigated the multi-objective
sizing optimization based on economic and energy-efficiency objec­
tives. Xu et al. [51] considered the minimization of wind curtailment
rate in the sizing optimization of off-grid wind-based HRESs. Das et al.
[122] evaluated the prospect of the minimization of excess energy from
power and freshwater cogeneration systems. Javed et al. [123]
employed excess energy as a boundary constraint as well as a posterior
evaluation indicator for the techno-economic sizing optimization.
5.6. Bibliometric analysis of performance indicators
Fig. 9 presents the bibliometric analysis of performance evaluation
indicators. 97.99% of literature considers the economic indicators in the
sizing optimization, and the technical reliability indicators are regarded
as objective or constraints in 49.5% of literature. The primary aim of
HRES installation is to meet the load demand at the lowest cost, so the
techno-economic feasibility analysis is the essential research foundation
for sizing optimization, which is also the most frequent subject among
relevant literature. Moreover, with the growing concern about global
warming and air pollution issues, many researchers consider the envi­
ronmental indicators in the sizing optimization problems, accounting for
18.06% of literature. However, social-political indicators are rarely
considered in the sizing optimization problems as it is rather compli­
cated to accurately quantify the socio-political impact of HRES
installation.
Fig. 10. Classification of sizing methodologies for off-grid HRESs.
disadvantages of various sizing optimization methodologies is shown in
the Appendix (Table A4). The specific introductions for each sizing
methodology are presented in this section.
6.1. Software tools
The most representative and frequently-used software tool for sizing
optimization of off-grid HRESs is HOMER (Hybrid Optimization of
Multiple Energy Resources), which was developed by the U.S. National
Renewable Energy Laboratory. The objective of sizing optimization in
HOMER is to minimize NPC and cover the load demand reliably, and the
built-in optimizer is genetic algorithm (GA). The sizing optimization
procedures of HOMER consist of simulation, optimization, and sensi­
tivity analysis. Users can customize the system configuration according
to their preference, and the data input including wind speed, solar
irradiance, and load profile can be obtained from the built-in database or
exterior sources. The benefits of HOMER include easy and efficient an­
alytics, simplified optimization, insightful customer-facing proposals,
and customizable design. Nevertheless, the sizing objective and opti­
mizer of HOMER are fixed, so it may be inapplicable for diversified
design requirements, such as techno-economic-environmental multiobjective sizing optimization. Moreover, other software tools for sizing
6. Sizing methodologies
After developing sizing optimization model based on the aforemen­
tioned performance evaluation indicators, appropriate methodologies
should be applied to explore the optimal solution. The sizing method­
ologies for off-grid HRESs mainly include software tools, meta-heuristic
algorithms, multi-objective evolutionary algorithms, mathematical
programming, iterative method, analytical methods, and uncertaintyhandling methods. The classification of sizing methodologies for offgrid HRESs is shown in Fig. 10, and a summary of the advantages and
Fig. 9. Bibliometric analysis of performance evaluation indicators.
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
optimization such as HOGA (Hybrid Optimization of Genetic Algo­
rithm), HYBRID2, and EnergyPLAN are rarely applied in academic
research according to our literature investigation.
Elkadeem et al. [124] applied HOMER in the siting and sizing opti­
mization of HRESs, in which HOMER provided the feasible system
design with the optimal sizes for different potential locations, and then
the optimal site was selected via a multi-criteria decision-making
approach. Yang et al. [125] applied HOMER for initial sizing optimi­
zation, and other performance indicators were included in the second
optimization layer to improve the accuracy of the optimal solution.
Ibrahim et al. [30] applied HOMER to investigate the optimal design and
performance analysis of a standalone HRES with desalination units in
Egypt. Kotb et al. [111] studied the coordinated energy management
and design of a standalone HRES with the assistance of HOMER.
Moreover, HOMER was applied as a benchmark in several references
[32,81,126–128] to validate the accuracy of sizing optimization results
obtained by other methodologies.
et al. [132] compared the performance of four meta-heuristics (FA, FPA,
HSO, ABC) in the sizing optimization of HRESs, and the results revealed
that FA had the shortest execution time and the best convergence
performance.
Moreover, some researchers investigated the performance improve­
ment of hybrid meta-heuristic algorithms in HRES sizing optimization.
Abo-Elyousr et al. [66] investigated the optimal sizing of
hydrogen-based HRESs via two modified versions of ACO-PSO hybrid
method, and the results showed that the ACO updated PSO hybrid al­
gorithm achieved the best performance for economic sizing optimiza­
tion. Zhang et al. [133] proposed a novel HSO-SA hybrid method with
chaotic search for HRES sizing optimization. The simulation results
indicated that the performance of HS-SA hybrid method was superior to
that of HSO or SA. Mellouk et al. [134] developed an efficient hybrid
method named parallel-GA-PSO for sizing optimization. The results
proved that the proposed parallel-GA-PSO was better than ordinary GA
or PSO in terms of computational efficiency and convergence perfor­
mance. Abdelshafy et al. [135] utilized a PSO-GWO hybrid approach for
HRES optimal design, and the results showed that the PSO-GWO hybrid
approach achieved faster convergence speed and better convergence
optimality compared to isolated PSO or GWO. Elnozahy et al. [136]
compared two PSO-GOA hybrid methods (GOA initialized PSO, GOA
updated PSO) in the sizing optimization of renewable energy-based
microgrids. The results indicated that the GOA initialized PSO hybrid
method had better solving performance. Jahannoosh et al. [71] pro­
posed a hybrid GWO-sine cosine algorithm for economic-reliable mul­
ti-objective design. The simulated results proved the superiority of the
proposed hybrid method in terms of convergence speed and accuracy.
6.2. Meta-heuristic algorithms
Meta-heuristic algorithms are generative and searching procedures
that determine the nearly-optimal solution of an optimization problem.
The overall performance of meta-heuristic algorithms depends on the
balance of exploration and exploitation processes. Meta-heuristic algo­
rithms are capable to solve non-linear and non-differential optimization
problems with acceptable accuracy and high computational efficiency.
With regard to the sizing optimization of off-grid HRESs, the relation­
ship between the objective function and decision variables is non-linear
and complex, so meta-heuristic algorithms have been widely used in
energy system planning. The most classical meta-heuristic algorithms
consist of GA, particle swarm optimization (PSO), differential evolution
(DE), and simulated annealing (SA). There are also some nature-inspired
meta-heuristic algorithms applied in the sizing optimization of HRESs,
such as ant colony optimization (ACO), artificial bee colony algorithm
(ABC), cuckoo search, firefly algorithm (FA), grey wolf optimizer
(GWO), teaching-and-learning-based optimization, harmony search
optimization (HSO), flower pollination algorithm (FPA), grasshopper
optimization algorithm (GOA), etc. Furthermore, improved algorithms
such as quantum particle swarm particle optimization and adaptive
differential evolution, as well as hybrid meta-heuristic algorithms such
as GA-PSO and HS-SA, have been proposed to further enhance the
computational performance.
Some researchers specifically investigated the performance com­
parisons of multiple meta-heuristic algorithms in the applications of
HRES sizing optimization. Fares et al. [129] presented a comprehensive
performance comparison of ten meta-heuristic algorithms considering
different technical reliability constraints. The results indicated that FA
had the shortest execution time, while SA achieved the best compromise
of convergence, robustness and computational efficiency, which was the
best option for sizing optimization. Mohseni et al. [48] also compared
the holistic performance of eight meta-heuristics, including both the
classical and novel nature-inspired algorithms. The results showed that
the moth-flame optimization algorithm could obtain the optimal solu­
tion with lower system cost compared to other algorithms. Kaabeche
et al. [35] compared the performance of the four most recent
meta-heuristic algorithms considering different battery technologies.
The results indicated that Jaya algorithm achieved superior convergence
and robustness performance. Javed et al. [130] presented a performance
comparison of four classical meta-heuristic algorithms (GA, PSO, ACO,
FA), and the formulations of respective working principles were
described in detail. The comparative results revealed that GA and PSO
hold better exploration behavior while ACO and FA behaved better
exploitation. El-Sattar et al. [131] investigated the optimal design of a
standalone HRES via the five most recent meta-heuristics. The results
demonstrated that the slime mould algorithm achieved the best per­
formance shown in the convergence curve and statistical analysis. Eteiba
6.3. Multi-objective evolutionary algorithms
Multi-objective evolutionary algorithm (MOEA) is an exploration
and exploitation method to obtain the approximately optimal solutions
set (Pareto front) for multiple conflicting objectives. The generative
operators of MOEAs such as crossover and mutation originate from
meta-heuristic algorithms, while the representative working principle of
MOEA is the introduction of “Pareto dominance” concept into the fitness
evaluation process. Pareto dominance means that solution-A dominates
solution-B if all objectives of solution-A are not inferior to those of
solution-B and at least one objective of solution-A is better than that of
solution-B [137]. Since there are several performance evaluation in­
dicators in the HRES optimal design, MOEAs have been applied to
efficiently optimize the multi-objective sizing problems considering
technical, economic, and environmental objectives simultaneously. The
most straightforward MOEA is to convert the multi-objective problem to
a mono-objective problem via weighted summation approach, which is
then solved by meta-heuristic algorithms. However, the weighted sum­
mation approach can only obtain an individual solution, rather than an
evenly-distributed feasible solution set. The representative MOEAs
include non-dominated sorting genetic algorithm-II (NSGA-II),
multi-objective particle swarm optimization (MOPSO), multi-objective
evolutionary algorithm based on decomposition (MOEA/D), strength
Pareto evolutionary algorithm-II (SPEA-II), etc. Furthermore,
multi-criteria decision-making methods (MCDM) such as technique for
order preference by similarity to an ideal solution (TOPSIS), VIKOR, and
fuzzy decision-making, are commonly coordinated with MOEAs to
determine the optimal compromise solution from the Pareto front set.
He et al. [17] studied the techno-economic multi-objective HRES
sizing optimization and compared the overall performance of four
representative MOEAs (NSGA-II, MOPSO, MOEA/D, SPEA-II) in terms of
convergence optimality, diversity, robustness and computational effi­
ciency. The results showed that NSGA-II yielded the best convergence
optimality, while MOPSO and SPEA-II achieved the best comprehensive
performance. Xu et al. [138] employed a reinforcement learning-based
NSGA-II in the multi-objective configuration optimization of off-grid
HRESs, in which the control parameters of NSGA-II were adaptively
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set by reinforcement learning. The results indicated that the modified
NSGA-II was superior to the ordinary NSGA-II in terms of diversity.
Huang et al. [45] compared the performance of NSGA-II and MOEA/D in
the context of HRES multi-objective sizing optimization, and the results
revealed that NSGA-II outperformed MOEA/D with respect to uniform
distribution and convergence optimality. Ghiasi [139] considered the
performance comparison of MOPSO and NSGA-II in the multi-objective
HRES design optimization. The results demonstrated that MOPSO yiel­
ded better optimal solutions than NSGA-II. He et al. [77] considered
technical, economic, environmental and energy-efficiency indicators
simultaneously to investigate the many-objective (the number of ob­
jectives is larger than 3) optimal design of a cogeneration system.
NSGA-III, principal component analysis and TOPSIS coupled method
was employed to solve the many-objective optimization problem. The
case study verified the effectiveness of the proposed coupled method,
and revealed that NSGA-III performed better convergence and diversity
than MOEA/D. He et al. [6] also proposed a novel MOEA based on
decision-making, which involves decision-making operator in the se­
lection process of MOEA. The simulated results indicated that the pro­
posed algorithm achieved better convergence and diversity in the
targeted region compared to NSGA-II.
index and DSM strategy. Alberizzi et al. [145] proposed a novel MILP
algorithm for assessing the optimal design of HRESs, and the significant
impact of resources data selection on the optimal configuration was
emphasized. Forough et al. [146] proposed a lifecycle sizing and oper­
ation optimization framework for HRESs based on convex programming
and RHO. Jiang et al. [37] proposed a GAMS-based mathematical model
to optimize the type, capacity and scheduling scheme of battery energy
storage in HRES. DICOPT in GAMS was selected as the global solver for
the main problem, while CPLEX and NOCOPT in GAMS were deployed
as the local solvers for sub-problems. Tu et al. [114] developed a
two-stage MILP model for optimal sizing and scheduling of
renewable-based microgrids, in which all non-linear components were
handled by piecewise linearization.
6.5. Iterative method
The iterative method generally follows a recursive traversal process
to evaluate the techno-economic performance of all potential HRES
sizing configurations. Iterative method is a classical and easy-toimplement approach for sizing optimization, but it may encounter
computational burden in many-variable complex problems due to the
enumeration characteristics. The simple procedures of iterative method
for HRES sizing optimization are presented as follow.
6.4. Mathematical programming
(1) The initial sizing configurations such as the rated power/capacity
of components, and the iterative steps for each decision variable
are determined.
(2) Operation simulation of the sizing configuration is conducted to
evaluate the technical reliability performance. If the system can
cover the load demand in acceptable reliability, this sizing
configuration is identified as a feasible solution and its economic
performance will be assessed for further selection.
(3) Sizing configurations are enumerated according to the iterative
steps, and operation simulation and techno-economic assessment
are repeated for all sizing configurations.
(4) The sizing configuration with the best economic performance
among all technically feasible solutions is chosen as the optimal
sizing configuration.
Mathematical programming tackles real-life optimization or
decision-making problems via establishing mathematical models,
including objective functions, constraints and decision variables, which
are then solved by traditional mathematical methods, such as simplex,
branch and bound, branch and cut, row and column generation [140].
Mathematical programming consists of mixed integer linear program­
ming (MILP), mixed integer non-linear programming, sequential
quadratic programming (SQP), convex programming, etc. Mathematical
programming problems are normally solved by optimizer tools, such as
IBM CPLEX, GAMS (general algebraic modeling system), LINGO (linear
interactive and general optimizer), Gurobi, Yalmip, etc. The planning
design of energy systems is essentially a mathematical optimization
problem, in which the capacity configurations of components are deci­
sion variables, operating boundary conditions of each component are
constraints, and the abovementioned performance evaluation indicators
are employed as objective functions, so mathematical programming has
been widely used in the sizing optimization of HRESs. The advantage of
mathematical programming is to yield accurate and robust optimal so­
lutions, rather than approximately optimal solutions obtained by
meta-heuristic algorithms. However, the computational efficiency of
mathematical programming is unacceptable in large-scale complex
optimization problems.
Song et al. [141] formulated the optimal design of remote HRESs as
an economic-oriented MILP problem, considering the constraints of
renewable energy penetration and energy curtailment, which was
solved by Gurobi tool in MATLAB environment. Gioutsos et al. [142]
considered levelized cost of storage as objective function, and the
cost-optimal sizing was formulated as a SQP problem, which was solved
by gradient descent method. Adefarati et al. [143] considered technical,
economic and environmental indicators to investigate the optimal
design of renewable-based microgrids. The objective function was
formulated
via
weighted
summation
of
the
techno-economic-environmental indicators, and the optimization prob­
lem was solved by fmincon function of MATLAB toolbox. Moretti et al.
[144] proposed an integrated design and operation optimization algo­
rithm for rural electrification based on the MILP formulation. The results
indicated that the MILP-based method led to higher reliability as well as
lower cost of electricity compared to the considered heuristic algorithm.
Mehrjerdi et al. [19] utilized MILP formulation to investigate the
modeling and design of autonomous HRESs considering the selection of
wind turbine technology. Kiptoo et al. [78] deployed MILP algorithm in
the techno-economic design of isolated HRESs considering the economic
Katsaprakakis et al. [59] investigated the optimal design of insular
microgrids with different energy storage technologies via iterative
method, in which the rated power of wind/PV was set as the iterative
step, renewable energy penetration was the technically feasible condi­
tion, and overall economic indicators were employed to select the
optimal design. Al-Buraiki et al. [147] utilized iterative method to
conduct the techno-economic analysis and optimization of standalone
HRESs. The number of batteries was set as the iterative step, and the
optimal system was identified when the required LPSP was guaranteed
and the lowest LCOE was achieved. Martín et al. [148] proposed a
two-stage methodology for HRES optimal sizing based on iterative
method. The sizes of renewable components were directly determined
according to the production and consumption patterns in the first stage,
and the battery size was iteratively evaluated by electrical and aging
models. Balaji et al. [149] explored the optimal renewable fraction for
off-grid
HRESs,
and
the
operation
simulation
and
economic-environmental analysis were conducted via iterative method.
6.6. Analytical methods
Analytical methods generally establish mathematical models to
formulate the direct relationship between system feasibility and
component capacity configurations. The optimal HRES configuration is
determined by comparing multi-dimensional performance indicators of
all feasible system configurations. Analytical methods also refer to a
generalization of approaches that apply specific standards to select the
optimal configuration, such as pinch analysis, design space approach,
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
electric system cascade extended analysis (ESCEA), etc. The working
principle of analytical methods is similar to the iterative method, since
both have simple implementation and overall consideration for the
whole design space, but the comprehensive performance evaluation and
operation simulation will lead to long computational time.
Jacob et al. [47] applied pinch analysis and design space approach to
investigate the optimal design of HESS in PV-based microgrids. The
pinch analysis determined the minimum energy storage capacity by
ensuring that the cumulative production always exceeded the cumula­
tive consumption. Chennaif et al. [150] developed an extended ESCEA
to determine the optimal capacities of HRESs considering LPSP and
LCOE as the techno-economic indicators. The comparative results with
reference System Advisor Model (SAM) validated that the proposed
ESCEA method could successfully identify the optimal configuration
within minor differences. John et al. [151,152] proposed a method for
the optimal sizing of different HRESs based on pinch analysis. All
technically feasible solutions formed the design space and sizing curves,
which were utilized to determine the optimum configuration based on
economic criteria evaluation.
uncertainties of electric vehicles including the arrival/departure time
and the arriving state of charge were modeled via Monte Carlo simula­
tion. Yang et al. [43] studied the robust multi-objective design of iso­
lated HRESs with stationary/mobile batteries, in which the uncertainties
of load demand, renewable energy and mobile electric vehicles were
fully considered via probability distributions. An adaptive robust opti­
mization technique based on hybrid meta-heuristic algorithm was
adopted to search for the optimal system configuration. Cho et al. [157]
proposed a scenario-based optimization model for the optimal design of
PV-battery HRESs considering the uncertainties of solar irradiance and
load patterns. The results found that the number of scenarios could have
a significant impact on the sizing results. He et al. [6] employed a
data-driven artificial neural network model to capture the uncertainty of
wind power in actual operation, and the simulated results validated the
accuracy of the uncertainty-handling model. Guo et al. [76] introduced
the concept of exceeding probability to simulate the uncertainties of
wind and solar PV power output, and the yearly energy production and
power curves at different probability levels were adopted in the HRES
sizing optimization.
6.7. Uncertainty-handling methods
6.8. Bibliometric analysis of sizing methodologies
All the aforementioned sizing optimization methods can be catego­
rized as deterministic methods since the uncertainties of renewable
energy resources and load demand are not considered. To this end,
several probabilistic and possibilistic methods are proposed to tackle the
uncertainties in the HRES sizing optimization problems, mainly
including stochastic optimization, robust optimization, chanceconstrained programming, Monte Carlo simulation, scenario-based
analysis, fuzzy membership function [153]. Stochastic optimization
applies the expectance value of all possible scenarios to tackle the un­
certainties, while robust optimization ensures that the solution is
feasible for all cases, especially in the worst case. Chance-constrained
programming handles optimization problems with uncertain con­
straints, which allows the uncertain constraints to be violated within a
specific confidence level. Monte Carlo simulation utilizes continuous
probability density function (PDF) sampling to represent the un­
certainties, while scenario-based analysis is based on discrete PDF.
Fuzzy membership function is applied for uncertainty representation
when the PDF of uncertain parameters is unknown, and then dealt with
fuzzy arithmetic. The uncertainty-handling methods can yield more
accurate and realistic sizing results than deterministic methods, while
their modeling and calculation processes are more complicated.
Roberts et al. [154] proposed a robust multi-objective optimization
method for HRES sizing. The uncertainties of renewable resources
availability, components failure and load demand were simulated via
Latin hypercubic sampling method and Monte Carlo simulation. The
supremum of NPC and LPSP indicators in the worst case was considered
as objective function to ensure robustness. The results indicated that the
proposed method could yield feasible robust solutions and guarantee
reliable power generation. Li et al. [27] utilized two-stage stochastic
programming to investigate the HRES optimal sizing, in which the un­
certainties of wind speed and solar irradiance were considered via
scenario-based analysis. Lee et al. [155] studied the multi-objective
capacity optimization of HRESs considering the multiple uncertainties
of renewable energy resources and load demand. Chance-constrained
programming was applied to determine the optimal system configura­
tions with the acceptable reliability level, and then fuzzy
decision-making was adopted to find the economic-environmental
trade-off solution. Zhu et al. [156] adopted a rough interval-Copula
stochastic planning programming model to handle multiple uncertain
parameters in the design optimization of isolated HRESs. The feasibility
of the proposed model was proved by case studies, and the results
revealed that uncertainties had a significant impact on the system
configuration and total cost. Sadeghi et al. [42] investigated the
multi-objective optimization of HRESs with electric vehicles. The
Fig. 11 shows the bibliometric analysis of sizing methodologies for
off-grid HRESs. The occurrence frequency of meta-heuristic algorithms
and software tools is the highest, accounting for 33.78% and 32.44% of
the relevant literature respectively. HOMER software is quite popular
for the feasibility analysis of rural electrification in remote areas because
of its straightforward procedures, abundant functions, and reliable
sizing results. By comparison, the popularity of meta-heuristic algo­
rithms originates from the abundant diversity of the algorithm itself,
since there are millions of meta-heuristic algorithms based on various
working principles and improved strategies that can be innovatively
applied in the sizing optimization. Furthermore, quite a few researchers
utilize MOEAs and mathematical programming for optimal sizing, ac­
counting for 17.06% and 11.71% of all literature respectively. Never­
theless, uncertainty-handling methods are seldom applied in the sizing
optimization of off-grid HRESs, taking up only 3.01% of all literature.
7. Findings and outlooks
An extensive overview of the sizing optimization of off-grid HRESs is
conducted in this study, including system configurations, energy man­
agement strategies, performance evaluation indicators, and sizing
methodologies. The bibliometric analysis based on 299 journal papers
(2018.01–2022.06) reveals that wind-PV-battery-DG system configura­
tion, rule-based energy management strategy, techno-economic in­
dicators, and meta-heuristic algorithms are the most frequently-used
modules in the sizing optimization of off-grid HRESs. Based on the
current research status and research gaps, the scope of potential future
works consists of the following directions.
(1) System configurations: In terms of energy sources, wind turbine
and solar PV technologies are widely applied in the off-grid
HRESs around the world. There are also some promising energy
sources such as geothermal energy, which can be utilized in the
off-grid HRESs, and the techno-economic feasibility of emerging
power generation technologies can be investigated. Concerning
the option of energy storages, various battery technologies are
frequently adopted in off-grid HRESs. However, the investment
cost of large-scale batteries will impose a considerable financial
burden on the system investors. Molten salt TES with electric
heater and power cycle was found to be more cost-effective than
battery [17], and the TES-battery configuration could achieve
higher reliability and economic performance [6]. Hence, HESS
with multiple complementary energy storages should be regarded
as the mainstream of future academic and industrial research,
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
Fig. 11. Bibliometric analysis of sizing methodologies for off-grid HRESs.
rather than individual energy storage. Regarding the load de­
mands, most off-grid HRESs were proposed to supply only elec­
tricity load, which is limited to meet the growing diversified
energy demand. The possibility of heating load supply via heat
generation devices, hydrogen and oxygen supply via electrolyzer,
as well as purified water supply via reverse osmosis plant can be
integrated to develop a multi-generation system. Moreover, in
terms of the topology of off-grid HRESs, there is currently no
literature investigating the impact of different topologies on the
sizing results. AC-coupled, DC-coupled, and hybrid topologies
have distinct converters and auxiliary devices, which may influ­
ence the techno-economic performance of different system con­
figurations, so it deserves to conduct a comparative analysis on
different topologies of HRESs.
(2) Energy management strategies: The most frequently-used rulebased EMS determines the actual operating conditions based on
the predefined simple flow chart, so the optimality cannot be
guaranteed. By comparison, optimized EMS can ensure optimal
operation via real-time optimization, but it must re-optimize for
each different data input, which is time-consuming and also a
waste of computing resources. However, an emerging technology
called deep reinforcement learning (DRL) can possibly be applied
in the EMS for off-grid HRESs [158]. DRL can obtain an optimal
EMS policy via large amount of model training in the early stage
of planning. The function of the obtained policy is similar to the
predefined rules in rule-based EMS, which determines the action
(operating condition) according to the state (data input), while
the trained policy can guarantee operational optimality owing to
the deep learning process. Furthermore, the optimal policy of
DRL is trained once and for all, and it can significantly avoid
re-optimization, which is more computationally efficient than the
real-time optimized EMS. Therefore, the application of DRL in the
sizing optimization and the performance comparison of different
EMS methods are promising research interests. In terms of
second-scale control strategies, some advanced control tech­
niques such as hierarchical control, intelligence control, adaptive
control etc., have been successfully implemented to maintain
dynamic generation-demand balance and the stability of volta­
ge/frequency in various meteorological and load conditions.
However, although the coordinated optimization of hour-scale or
minute-scale EMS and sizing has already been a popular research
protocol, the optimal second-scale control strategies and optimal
sizing are separately investigated. Therefore, it is worthwhile to
conduct the co-optimization of sizing and second-scale control
and investigate the impact of various advanced control tech­
niques on the optimal sizing results.
(3) Performance evaluation indicators: The technical, economic,
environmental, socio-political, and energy-efficiency indicators
have been considered as objectives or constraints, whereas the
operational safety indicators including frequency fluctuation and
voltage fluctuation are seldom considered in the sizing optimi­
zation problems. Moreover, some emerging composite indicators
such as sustainability and resilience can also be regarded as sizing
objectives. Sustainability is defined as the long-term balance
between environmental health, social equity, and economic vi­
tality [115]. Resilience normally refers to the capability of power
systems to withstand natural disasters and human-made attacks,
which may cause large blackouts [159]. The sustainability and
resilience performances of energy systems throughout the life
cycle depend basically on the construction of subsystems, in­
frastructures, and transmission lines at the planning stage.
Therefore, the sizing optimization of off-grid HRESs considering
operational safety, sustainability, and resilience indicators is a
potential research direction.
(4) Sizing methodologies: A large variety of meta-heuristic algo­
rithms have been applied to energy system planning problems,
but the comparison results of algorithm performance concluded
from different literature are quite inconsistent. Hence, it is
necessary to propose an acknowledged benchmark for algorithm
performance testing. Moreover, few references applied the
uncertainty-handling methods in sizing optimization, but the
uncertainties of renewable resources and load demand are inev­
itable and non-negligible, so deterministic methods may yield
unreasonable oversized or undersized results. An emerging
uncertainty-handling method called distributionally robust opti­
mization (DRO) is promising to refine the shortcomings of sto­
chastic optimization (too sensitive or low robustness) and robust
optimization (too conservative). DRO establishes an ambiguity
uncertainty set including all possible probability distributions
based on historical data, and the optimal robust solution is ob­
tained in the case where the prediction error of uncertainty fac­
tors follows the worst probability distribution [160]. DRO has
been successfully applied in the optimal scheduling problems of
multi-energy systems, while rarely in planning problems. There­
fore, the introduction of DRO in the sizing optimization for
off-grid HRESs and the superiority of DRO over other
uncertainty-handling methods are worthy of further
investigation.
8. Conclusions
This study carries out an up-to-date review and bibliometric analysis
on the sizing optimization of off-grid HRESs based on 299 journal papers
in the recent five years. The system configurations, energy management
strategies, performance evaluation indicators, and sizing methodologies
for off-grid HRESs are reviewed, and the corresponding bibliometric
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Renewable and Sustainable Energy Reviews 183 (2023) 113476
analysis is further conducted. The following conclusions and projected
future works can be drawn from the qualitative overview and quanti­
tative bibliometric analysis.
emerging uncertainty-handling methods such as distributionally
robust optimization can be attempted in the sizing optimization
problems.
(1) The system configuration of off-grid HRESs depends on the option
of energy sources, energy storages, and topology. 96.99% of ar­
ticles select solar photovoltaic as an energy source, 83.95% of
articles choose battery as the energy storage, and windphotovoltaic-battery-diesel is the most frequently-applied sys­
tem configuration. Moreover, hybrid energy storage systems and
multi-generation systems are promising research directions in
future works.
(2) Rule-based and optimized energy management strategy, as well
as demand side management, are applied to achieve supplydemand energy balance. 86.29% of articles apply rule-based en­
ergy management strategy, significantly higher than the
remaining proportion of optimized strategy. In future works,
deep reinforcement learning techniques with excellent optimality
and computational efficiency can be employed for energy
management.
(3) Technical, economic, environmental, social-political, and energyefficiency indicators are applied in the sizing optimization
models, in which economic and technical indicators are consid­
ered in 97.99% and 49.50% of articles respectively. Furthermore,
operational safety, sustainability, and resilience indicators can be
considered in sizing planning.
(4) Meta-heuristic algorithms and HOMER software tool are the most
popular methodologies for the sizing optimization of off-grid
HRESs, accounting for 33.78% and 32.44% of all literature
respectively. However, uncertainties of renewable energy re­
sources and load demand are inevitable at the planning stage, so
To summarize, the presented state-of-the-art review and bibliometric
analysis can provide practitioners in energy system planning with
comprehensive theoretical knowledge about the sizing optimization
research of off-grid HRESs. Moreover, the provided mathematical
models of system components along with corresponding instructions,
and various sizing methodologies can facilitate practitioners to imple­
ment HRESs in real-life applications.
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.
Data availability
Data will be made available on request.
Acknowledgements
This work was supported by the Postgraduate Research & Practice
Innovation Program of Jiangsu Province [grant number KYCX23_0718];
the Hong Kong, Macao and Taiwan Science and Technology Cooperation
Program of Jiangsu Province of China [grant number BZ2021057]; the
National Natural Science Foundation of China [grant number
62004060]; the Fundamental Research Funds for the Central Univer­
sities [grant number B230205033].
Appendix
See Table A1-A4.
Table A1
Summary of review papers focusing on the sizing optimization of off-grid hybrid renewable energy systems.
Sources
System
components
Mathematical
models
Topologies
Energy management
strategies
Performance
indicators
Sizing
methodologies
Bibliometric
analysis
Outlooks
Dawoud et al. [7]
Khan et al. [8]
Anoune et al. [9]
Sawle et al. [10]
Lian et al. [11]
Mazzeo et al. [12]
Pandiyan et al. [13]
Zebra et al. [14]
Memon et al. [15]
Thirunavukkarasu
et al. [16]
This work
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Notes: ☑ represents included, and ☒ represents not included.
Table A2
The input variables, output variables, and technical parameters of models for different energy sources and energy storages technologies.
Technologies
Input variables
Output variables
Technical parameters
Source
Wind power
wind speed
wind power output
[17]
Solar PV
tilted irradiance
ambient temperature
PV power output
cut-in wind speed
cut-out wind speed
rated wind speed
rated power of wind turbine
temperature coefficient
nominal operating cell temperature
rated power of PV panel
[17]
(continued on next page)
22
Renewable and Sustainable Energy Reviews 183 (2023) 113476
Y. He et al.
Table A2 (continued )
Technologies
Input variables
Output variables
Technical parameters
Source
Concentrated solar power
direct normal irradiance
CSP power output
[25]
Micro-hydropower
volumetric flow rate
micro-hydropower power output
Hydrokinetic power
stream flow velocity
HKT power output
Biomass power
biomass fuel consumption
biomass generator power output
Diesel generator
diesel fuel consumption
DG power output
Battery
charging and discharging power of battery
available energy of battery
Supercapacitor
charging and discharging power of SC
available energy of SC
Pumped hydro storage
charging power of hydraulic pump
discharging power of hydraulic turbine
available volume of upper reservoir
Hydrogen storage
charging power of electrolyzer discharging power
of fuel cell
available mass of HES
Thermal Energy storage
charging power of electric heater
discharging power of power block
available heat of TES
Compressed air energy
storage
charging power of compressor
discharging power of expander
available mass and volume of highpressure air
Gravity energy storage
charging and discharging flow rate of GES
available energy of GES
area of solar field
solar-to-thermal efficiency of solar receiver
thermal-to-power efficiency of power cycles
conversion efficiency of hydraulic turbine
elevating head height
rotor area of HKT
conversion efficiency of HKT
power coefficient of streamflow dynamic
efficiency
conversion efficiency of biomass generator
lower heating value of biomass
nominal power of DG
intercept and slope coefficients of
consumption curve
charging and discharging efficiency of
battery
self-discharging rate of battery
charging and discharging efficiency of SC
self-discharging rate of SC
efficiency of hydraulic pump and turbine
leakage and vaporization loss rate of upper
reservoir
elevating head height
power-to-hydrogen efficiency of
electrolyzer
hydrogen-to-power efficiency of fuel cell
higher heat value of hydrogen
leakage loss rate of HES
power-to-heat efficiency of electric heater
heat-to-power efficiency of power block
self-dissipating rate of TES
air rated temperature in air container
air rated pressure in air container
required power of compressing air per unit
mass
generated power of expanding air per unit
mass
overall efficiency of GES
efficiency of reversible pump turbine
geometric parameters of GES
[28]
[30]
[32]
[32]
[5]
[46]
[56]
[64]
[17]
[81]
[84]
Table A3
The advantages and disadvantages of different topologies in off-grid HRESs [9,96].
Topology
Advantages
Disadvantages
DC-coupled
Synchronism not required
Direct interconnection reduces multiple power conversions
Easy interconnection with DC energy sources, storages, and loads
Minimized power converter loss
AC-coupled
The use of transformer with high efficiency
Stable voltage by controlling reactive power independently
Good reliability - easily detecting and repairing failed services
Standard interfacing and modular structure
Easy multi-voltage and multi-terminal matching
Minimizing the multiple conversions and conversion losses
Enhancing the reliability and economy of the entire system
Managing different loads and generator units independently uninterruptable power supply and
enhancement in power quality
Less systematized voltage transformation in DC
system
Concerns about the voltage compatibility
Corrosion concerns with the DC electrodes
Expensive cost for installing and maintenance
Synchronism required
The need for power factor and harmonic distortion
correction
Reduced efficiency when connected to DC sources
and loads
Complex system and more operational problems
Difficult assimilation of sub-grids with distinct
characteristics
Hybrid AC/DCcoupled
Table A4
Summary of advantages and disadvantages of sizing optimization methodologies [16].
Sizing methodologies
Advantages
Disadvantages
Software tools - HOMER
User friendly
Easy and efficient analytics
No requirement for coding
Insightful customer-facing proposals
Fixed sizing optimization model and optimizer
Limited options for system components
(continued on next page)
23
Y. He et al.
Renewable and Sustainable Energy Reviews 183 (2023) 113476
Table A4 (continued )
Sizing methodologies
Advantages
Disadvantages
Meta-heuristic algorithms
Non-linear and discrete optimization
High computational efficiency
Numerous options of optimization models and optimizers
Non-linear and discrete optimization
Numerous options of optimization models and optimizers
Tackling conflicting objectives simultaneously
A comprehensive set of optimal solutions
The exact optimum
Mathematical interpretability
Easy to implement
Capability to trace the threats at early phases
Easy to implement
Premature convergence
Approximate optimum rather than the exact optimum
Control parameters tuning
Curse of dimensionality
Premature convergence
Approximate optimum rather than the exact optimum
Control parameters tuning
Difficulty in solving non-linear problems
Moderate computational efficiency
Long computational time
Multi-objective evolutionary algorithms
Mathematical programming
Iterative method
Analytical methods
Uncertainty-handling methods
Ability to tackling uncertainties
Suitability for real-life applications
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