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RenewIslands meets optimization:
Efficient synthesis of renewable energy systems
Philipp Petruschke, Philip Voll, André Bardow
*
Institute of Technical Thermodynamics
RWTH Aachen University, Aachen, Germany
Email: andre.bardow@ltt.rwthaachen.de
Goran Gasparovic, Goran Krajačić, Neven Duić
Department of Energy, Power Engineering and Ecology
Faculty of Mechanical Engineering and Naval Architecture
University of Zagreb, Zagreb, Croatia
Email: goran.gasparovic@fsb.hr
ABSTRACT
An efficient synthesis method for renewable energy systems is presented that exploits
synergies between heuristic and optimizationbased approaches. For this purpose, the
RenewIslands method has been integrated into a superstructurebased optimization approach.
The resulting hybrid approach consists of two steps: First, heuristicbased equipment
preselection identifies a set of promising candidate technologies. Next, the preselected
technologies are employed in superstructurebased optimization to determine the optimal
renewable energy system. The heuristic preselection systematically avoids excessively large
superstructures, while the subsequent optimization ensures that the optimal solution is
selected. The proposed method is applied to the case of Mljet Island, Croatia. Concepts for
renewable energy systems are generated that require up to 59 % less investment costs
compared to solutions derived by a classical simulation approach. At the same time, solution
times are less than 2 minutes. The hybrid approach thus provides an efficient route to the
synthesis of renewable energy systems.
1) INTRODUCTION
The synthesis of energy supply systems with renewable resources is a key lever for facing the
challenges of sustainable development and climate protection [1, 2]. However, this is an
intrinsically difficult task: A key challenge in the synthesis of renewable energy systems is to
cope with the inherent complexity stemming from the temporal and spatial interdependencies
associated with renewable resources. Additionally, the variety of available technologies and
possible combinations adds to the complexity. Moreover, three hierarchicallydependant
synthesis levels need to be taken into account [3] (Figure 1): The configuration level where
equipment choices are made, the sizing level that determines (nominal) capacities and the
operational level that specifies the actual load dispatch. Besides, the associated economic and
ecological impacts have to be considered. Therefore, to find the best solution for a given
synthesis problem, complex relationships and tradeoffs between technical, economical and
ecological consequences have to be balanced.
*
Corresponding author
Figure 1. Hierarchicallydependant levels configuration, sizing and
operation to be taken into account for the synthesis of energy supply
systems.
For the solution of such synthesis problems, two types of approaches are widely followed.
Traditionally, heuristicbased approaches are used, but also optimizationbased approaches
have been developed. Heuristicbased approaches typically rely on specific expert knowledge
or physical insights to define possible energy systems and analyze them in simulation studies
[4–9]. On the one hand, this heuristicbased approach is usually robust and generates adequate
solutions with manageable effort. On the other hand, only a limited number of alternatives can
be studied in simulations and the risk to overlook superior solutions is high [3]. In contrast,
optimizationbased synthesis approaches allow for the investigation of a virtually unlimited
number of alternatives and thus generally enable to find the optimal solution among all
possible alternatives [10–16]. However, for large problems modeling effort and solution times
can become prohibitively large [17, 18].
To combine the advantages from both approaches, in other fields so called hybrid approaches
have been successfully developed that combine heuristics and optimization techniques [19].
In this work, a hybrid approach is developed for the efficient synthesis of renewable energy
systems. The proposed method builds upon the RenewIslands method by Duić et al. [20] and
the automated superstructurebased optimization approach developed by Voll et al. [21].
This paper is organized as follows: In section 2, the proposed hybrid approach is presented. In
section 3, a real world case study is considered  the island of Mljet, Croatia. The new method
is applied to synthesize possible renewable energy systems with up to 100 % share of
renewable resources. To evaluate and validate the method, the results are compared to
findings from an earlier publication where the RenewIslands method has been applied to the
same case but without optimization [22]. Finally, the paper is summarized (section 4).
2) A HYBRID APPROACH FOR THE SYNTHESIS OF RENEWABLE ENERGY
SYSTEMS
The proposed hybrid approach combines two wellfounded synthesis methods. The
RenewIslands method has been developed for energy planning of isolated islands [23] and has
been implemented into the H2RES software [9, 24]. Its core concept is to use heuristic rules
to evaluate and structure information on local resources and demands, select promising
renewable technologies and devise possible energy systems. The inputs are qualitative
statements about the energy demand levels and the available resources which are classified as
“low”, “medium” or “high”. A range of ifthenrelations is then used to derive a set of
promising technologies. Based on this set of technologies, the synthesis alternatives to be
considered are heuristically defined by the user and assessed in simulation studies (for details
the reader is referred to [20]). The major strength of the RenewIslands method is that it
significantly narrows down the complexity of the synthesis problem by systematically
eliminating unsuitable technologies from consideration. The major shortcoming of the
RenewIslands method is that it requires the heuristic definition of synthesis alternatives by the
user. In general, the optimal solution is not included within this limited set of alternatives and
the RenewIslands method will thus lead to suboptimal solutions only.
The method developed by Voll et al. [21] has successfully been used for the automated
synthesis of distributed energy supply systems. It is implemented as “eSynthesis” module into
the TOPEnergy framework [25, 26]. The key concept is to apply rigorous, superstructure
based optimization to the configuration, sizing and operation of energy systems. To
circumvent the manual definition of a superstructure containing all possible synthesis
alternatives, a successive optimization approach is realized that automatically generates and
optimizes a set of superstructure models until the optimal solution has been identified. For
this purpose, the method includes an algorithm for the automated superstructure and model
generation based on a set of specified technologies. Controlled by another algorithm, the
(initially) generated superstructure model is successively optimized and expanded until it
yields the optimal solution. However, the technologies considered in the superstructure should
be limited to meaningful options since excessively large superstructures lead to increased
computational effort.
To enable the efficient synthesis of renewable energy systems, the two discussed approaches
have been integrated as follows (Figure 2): In a first step, the RenewIslands method is used to
reduce the complexity of the considered synthesis problem by preselecting promising
candidate technologies. Next, instead of assessing the identified technologies in scenariotype
simulation studies [9, 22], they are fed into the eSynthesis module of TOPEnergy to
determine the optimal synthesis solution by superstructurebased optimization.
Figure 2. Proposed twostep hybrid approach for the synthesis of renewable energy systems.
The candidate technologies identified by heuristic preselection (step 1) are employed in
superstructurebased optimization (step 2) to determine the optimal renewable energy system.
In view of the authors, the proposed hybrid approach has the potential to combine the benefits
of heuristic and optimizationbased synthesis. First of all, RenewIslands provides a
transparent method with clearly defined rules for the selection of candidate technologies. This
avoids the use of subjective assumptions as often required in current practice. Furthermore,
the heuristic preselection of candidate technologies leads in two ways to a significant
complexity reduction and facilitation of the optimizationbased synthesis. On the one hand,
the superstructure is kept small and contains only the essential equipment options.
Correspondingly, the number of discrete degrees of freedom of the mathematical model (i.e.
binary variables) is reduced. Since binary variables exponentially influence the solution time
[27, 28], it is desirable to keep their number as small as possible. On the other hand, the
mathematical modeling of the excluded technologies can also be omitted. Thus, further
benefits in the solution process and a reduced modeling effort are expected. Most importantly
in practice, for excluded technologies, the timeconsuming effort for data collection and
parameterization becomes obsolete.
3) CASE STUDY “MLJET ISLAND”
In the following, a real world case study – the Island of Mljet, Croatia – is considered. This
case study has already been analyzed by Krajačić et al. [22] with the original form of the
RenewIslands method, i.e., using simulation studies instead of rigorous optimization. The
objective was set to identify energy supply systems for Mljet that maximize the use of locally
available renewable resources and to investigate their economic viability. In the present work,
the proposed hybrid approach is applied to the same objective. To evaluate and validate the
method, all results are compared to the original study [22].
The island of Mljet is located on the Eastern part of the Adriatic Sea. Mljet measures 37 km in
length by 3.2 km average width and an area of 100 km². General population of Mljet from the
2001 census was 1111 inhabitants. Local economy mainly relies on viticulture, olive growing
and tourism.
Step 1: Preselection of candidate technologies
Following the proposed hybrid approach, in a first step, candidate technologies for a
renewablebased energy system for Mljet Island are determined by heuristic preselection.
According to the RenewIslands method, starting point for the preselection is a systematic
mapping and assessment of the local needs and available resources (Table 1). Mljet is
connected to the mainland with two undersea electricity grid connections. There is no
electricity generation capacity on the island. Due to a lack of potable water in the summer,
three desalination plants are installed on the island. Together with a 300bed hotel, these
desalination plants present the largest electricity consumers. The demand for heating and
cooling is low because the climate of Mljet is Mediterranean with average yearly temperatures
in the range of 9 °C in January to 24 °C in July. Thus, there is only a low demand for heating
and cooling. Transport fuel is delivered via ship and there is only one fuel station for the
entire island. The results of this mapping have been adopted from the original publication
[22]. They are also described in more detail in [20].
Table 1. Needs and resources of Mljet Island, assessed according to the
RenewIslands method.
Needs
Level
Geographic distribution
Electricity
Medium
Dispersed
Heat
Low
Dispersed
Cold
Low
Dispersed
Resources
Wind
Medium

Solar
Medium

Hydro
Medium

Biomass
High

Geothermal
Low

Grid connection
Strong

Natural gas pipeline
No

LNG terminal
No

Oil terminal /refinery
No

Oil derivatives terminal
No

Based on this evaluation, the RenewIslands method (c.f. section 2) is applied for equipment
preselection. Its application yields that 14 of 17 conversion technologies and 5 of 7 storage
technologies can be eliminated from the general set of technologies defined in the
RenewIslands method (Figure 3). Hence, the preselection reduces the number of equipment
considered from 24 to only 5. In particular, the provision of heat and cold can be excluded
from further consideration due to the low demand for these needs and their dispersed
geographic distribution. Hence, the synthesis task reduces to a renewable electricity supply
system. Apart from the existing mainland grid connection, the remaining candidate
technologies are wind turbines, photovoltaic cells and a hydrogen loop consisting of an
electrolyser, a fuel cell and hydrogen storage. Further details on the preselection are provided
in [20].
Figure 3. Preselection of candidate technologies for the synthesis of a renewable
electricity supply system for Mljet Island. Based on the assessment of local needs and
resources, heuristic “ifthen” rules of the RenewIslands method are used to eliminate
unsuitable options from the general set of technologies.
Electricity
1. Wind turbines
2. Solar PV
3. Solar thermal
4. Hydroelectric
5. Geothermal plant
6. Biomass plant
7. Diesel engine
8. Combined cycle gas turbine
9. Fuel cell
Heating
10. Solar collector
11. Geothermal heating
12. Heat pump
13. Gas boiler
14. Biomass boiler
Cooling
15. Solar absorbers
16. Gas coolers
17. Electricity coolers
Electricity Storage
18. Reversible Hydro
19. Electrolyser
20. Reformer
21. Hydrogen storage
22. Batteries
Heat storage
23. Heat storage
24. Cold bank
Electricity
1. Wind turbines
2. Solar PV
3. Fuel cell
Electricity Storage
4. Electrolyser
5. Hydrogen storage
Candidate technologies
for Mljet Island
General set of technologies [20]
heuristic
“ifthen” rules
[20]
Needs & resources
of Mljet Island
Step 2: Superstructurebased optimization
Setup of the optimization model. The preselection step has lead to five candidate technologies
for a renewable electricity supply system for Mljet Island. Now, in the second step of the
proposed hybrid method, the optimal synthesis of a system considering only these candidate
technologies is determined by superstructurebased optimization.
The method developed by Voll et al. [21] provides an algorithm for automated superstructure
and model generation. This algorithm makes use of the PGraph based maximal structure
generation method [29]. Its application to the candidate technologies yields the initial
superstructure illustrated in Figure 4. The renewable electricity produced by wind turbines
and photovoltaic cells can be used to satisfy the local demand, to operate the electrolyser
loading the hydrogen storage or it can be exported to the mainland. Demand satisfaction is
also possible by operating the fuel cell unloading the hydrogen storage or by importing
electricity from the mainland.
The underlying technology models are kept consistent to the original models [22], i.e., exactly
the same data for demand, operating behavior, costs, etc. is used. This implies the following
assumptions:
 all calculations are based on known annual time series with discrete time steps of 1 hour
for demand and generation data (wind speeds, solar irradiation, etc.);
 for the power output of the wind turbines, partload behavior is modeled with the help of
performance curves;
 for all other technologies, constant efficiencies are assumed and neither partload
behavior, minimum partload restrictions or minimum technology sizes are considered;
 the specific investment costs of the equipment are kept constant, i.e., no economy of scale
effects are modeled;
 the share of renewable electricity in the grid is not limited, i.e., 100 % demand satisfaction
by renewable resources is allowed; however, the export of excess electricity is limited to
30 % of the annual renewable production;
 the hydrogen loop can only be operated by renewable resources.
Figure 4. General superstructure of a renewable electricity supply system for
Mljet Island based on the preselected technologies.
With these assumptions, the optimization model is formulated as MILP with integertype
variables only for the sizing of the wind turbines. All other technologies can be sized
continuously. Hence, the application of the successive superstructure expansion algorithm of
the method by Voll et al. [21] is not required in this example. Thus, the problem can be solved
to the global optimal solution in a single run using CPLEX® 12.5 as solver on a 3.3 GHz
Intel® Core™ i52500 CPU with 3.23 GB RAM.
Scenarios. The superstructure for the electricity supply system presented above (Figure 4) is
the most general superstructure considered. In [22], additional scenarios are studied involving
other subsets of the candidate technologies, cf. Table 2. In the present work, several of these
scenarios are studied as well. This comparison of the results enables the evaluation of the
hybrid method. To model the additional scenarios, constraints to fix decisions on the
structural level are added to the general mathematical problem description. The scenarios are
numbered as in [22]
1
. The general superstructure is represented by scenario 12. In the
following, the superstructure optimization model set up above is solved for each scenario and
the results are presented and discussed.
Table 2. Definition of scenarios for the case study.
Original Scenario Number
Wind
PV
Electrolyser
Fuel Cell
H2 Storage
2
4
6
8
10
12
The optimal renewable energy system. In accordance to the original study [22], the scenarios
are optimized aiming at a maximum share of renewable energies. Hence, minimization of
electricity import is used as objective function. Each scenario is solved to its optimal solution
in less than a minute. The solution comprises all information on the structure of the energy
system, the sizing of the technologies and a schedule for the operation in every hour of the
year. The results are shown in Figure 5 a). As should be expected, optimizationbased results
are always equal or better than the results from the previous simulation study [22]. In
particular, optimizationbased synthesis increases the share of renewable resources for
scenarios 2 and 6 by 8 % and 3 %, respectively. Furthermore, optimization confirms that a
share of 35 % is the maximum value to be reached when only photovoltaic panels are
installed (scenario 4). Naturally, no improvements can be found for scenarios 8, 10 and 12
with a share of renewable resources already at its maximum level of 100 %.
For the sole minimization of electricity import, costs are not taken into account. Hence, at a
share of 100 % renewable resources, solutions are found with highly oversized storage
capacities (variables are set to their upper bounds by optimization). These solutions lead to
immense investment costs. To avoid the economically undesirable oversizing of equipment,
the optimization runs are repeated using the minimization of investment costs as objective
function (Figure 5b).
1
In [22], also scenarios with a grid limit of 30 % renewable penetration and / or hydrogen use for mobility needs
are studied. These scenarios have uneven and / or higher numbers and are not considered in the present work.
Figure 5. Comparison of simulation and optimization results for all scenarios: a) Maximum share of
renewable resources as objective for optimization. b) Minimum investment costs as objective for
optimization, where the share of renewable resources from the simulation results is set as constraint.
In this case, a constraint is added assuring that for each scenario the share of renewable
resources must still be equal or greater than in the original simulation study [22]. Again, for
each scenario, the optimal solution can be found within solution times smaller than 2 minutes.
All solutions require less investment costs at equal or higher shares of renewable resources.
The cost reductions range between 11 % (scenario 10) and 59 % (scenario 12). The largest
reduction of 59 % is achieved in scenario 12 which represents the general superstructure and
thus possesses the highest degree of freedom for optimization. However, even when the
structure is fixed and only sizing and operation decisions are taken into account (scenarios 2
10), the optimization still yields large savings. Note that scenarios 8 and 12 have an identical
optimal solution. This solution represents the cheapest concept to supply Mljet Island with
100 % electricity from locally available renewable resources with the technologies considered
(Figure 6). For a complete overview, the detailed results for all scenarios are summarized in
Table 3.
Figure 6. Minimum investment cost solution of a 100 % renewable electricity supply system
for Mljet Island, identified by optimization of the general superstructure. Units not selected
are shown in light grey.
a) b)
31%
35%
50%
100%
100%
100%
39%
53%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2
4
6
8
10
12
Share of renewable resources
Simulation
Optimization
1
10
8
38
86
63
5
26
77
26
10
20
30
40
50
60
70
80
90
100
2
4
6
8
10
12
Investment costs / Mio. €
Simulation
Optimization
Table 3. Comparison of simulation and optimization results for all scenarios. “sim” = simulation
results, “RES” = optimization results for maximum share of renewables, “INVEST” = optimization
results for minimum investment. Variables at their upper bound are marked with an asterisk (*).
Scenario
Wind
/MW
PV
/MW
Electrolyser
/MW
Fuel cell
/MW
H2 storage
/MWh
Renewable
resources
Investment
/Mio. €
2
sim
0.8
31 %
1.2
RES
0.8
39 %
1.2
INVEST
0.6
31 %
0.8
4
sim
1.9
35 %
10.4
RES
1.9
35 %
10.4
INVEST
1.9
35 %
10.4
6
sim
0.7
1.2
50 %
7.7
RES
0.6
1.3
53 %
8.2
INVEST
0.8
0.7
50 %
5.2
8
sim
6
4.5
1.8
873
100 %
37.7
RES
6
6
1.8
5000*
100 %
95.8
INVEST
5.3
2.5
1.8
487
100 %
26.3
10
sim
12.1
4.4
1.8
210
100 %
86.3
RES
14.3
10.7
1.8
5000*
100 %
177.5
INVEST
10.4
4.6
1.8
217
100 %
77.4
12
sim
1.2
7.8
4
1.8
188
100 %
63.4
RES
2.1
8.5
7.9
1.8
5000*
100 %
141.2
INVEST
5.3
2.5
1.8
487
100 %
26.3
The results show large benefits of the optimizationbased synthesis in terms of investment
costs. Now, it is analyzed where these benefits come from. For this purpose, a detailed
comparison of the simulation and optimization results for scenario 8 is presented.
The major difference in the optimization and simulation results is the sizing of the electrolyser
and the hydrogen storage. While the original simulation study proposes the installation of an
electrolyser with about 4.5 MW nominal capacity, the optimizationbased synthesis yields an
optimal size of 2.5 MW (Table 3). Likewise, the simulation study recommends a size of 873
MWh for the H2 storage whereas the optimal size lies at 487 MWh. In both cases, the
capacities determined in the simulation study are almost twice the size required in the optimal
solution. Accordingly, the investment costs for these oversized components are almost twice
as high (23 Mio. € vs. 13 Mio. €). Regarding the installed capacity of wind power, the
differences are not as significant. In the simulation study 6 MW are installed; the optimal
solution provides 5.3 MW. However, the types of installed wind turbines differ between the
approaches. In the simulation study, wind turbines of the type “Enercon”, “Vestas” and
“Fuhrländer” are installed. The optimal solution in contrast chooses only wind turbines of the
type “Fuhrländer”. Thus, among all available wind turbines the “Fuhrländer” type possesses
the best tradeoffs between (locally dependant) performance characteristics and costs. In total,
the savings achieved by installing less capacity and better suited types of wind turbines
accumulate to about 1 Mio. € in the optimal solution. In summary, the significant reduction of
investment costs found by the superstructurebased optimization is the result of both a better
equipment sizing and a better configuration (i.e. equipment choice) of the renewable
electricity supply system compared to the solution suggested in the original simulation study.
However, equipment configuration and sizing are not independent from its operation.
Correspondingly, also the operation strategy for the presented optimal solution differs from
the original simulation result (Figure 7): A higher share of wind energy is stored via the
hydrogen loop (59 % instead of 53 %) and less wind energy is used for direct demand supply.
The controllable components of the hydrogen loop (electrolyser and fuel cell) can be better
utilized in this strategy. This offers more flexibility for demand satisfaction.
Figure 7. Comparison of wind power utilization in scenario 8: a) Results of the original
simulation study. b) Optimal operation strategy.
Multiobjective analysis. Finally, due to the reduced computational effort of the hybrid
approach, multiobjective optimization [30–32] is possible to provide additional insights. A
Pareto frontier (Figure 8, top) is generated using the εconstraint method [31] to investigate
how much investment is at least necessary for a certain share of renewable resources. The
generation of the Pareto frontier requires nine additional optimization runs and is completed
in 24 minutes.
The slope of the Pareto frontier (Figure 8, top) shows that it becomes progressively expensive
to increase the share of renewable resources towards 100 %, as progressively more equipment
needs to be installed (Figure 8, bottom). Roughly three ranges can be identified: Renewable
resources supplying less than 40 %, 4090 % or up to 100 % of the demand. If renewable
resources supply less than 40 % of the demand, moderate costs of less than 1.5 Mio. € occur
and it is sufficient to install wind turbines. The wind power can be used for synchronous
demand supply and no energy storage is needed. However, if a share of more than 40 % of
renewable resources is desired, it becomes unavoidable to compensate the temporal offset
between generation and demand and to provide energy storage by installing the hydrogen
loop. From that point on, the costs for the electrolyser, the hydrogen storage and the fuel cell
add to the total investment costs and the slope of the Pareto frontier becomes steeper. At a
share of 60 % of renewable resources, investment costs have reached already 5 Mio. € and
further increase up to 15 Mio. € at 90 %. Due to the conversion losses that occur in the
hydrogen loop, considerably more wind energy than required for demand supply needs to be
harvested. Accordingly, the installed equipment size of wind turbines rises from 0.9 MW to
4.3 MW between 40 % and 90 % share of renewable resources. Likewise, the electrolyser size
rises from less than 100 kW to almost 2 MW to convert the harvested (surplus) wind power
into hydrogen. Between 4090 %, both the installed fuel cell size and the storage size can be
kept relatively low. For a share of renewable resources between 90100 %, the slope of the
Pareto frontier rises again. In fact, the last 10 % are almost equally expensive as the first 90 %
with investment costs increasing from 15 Mio. € up to 26 Mio. €. This is mostly due to fact
that the fuel cell and storage capacities now need to be expanded massively (by the factors
three and four, respectively ) to cover the lack of wind in summer when the electricity demand
is at its peak.
11%
59%
30%
demand supply
hydrogen generation
grid export
b)
17%
53%
30%
demand supply
hydrogen generation
grid export
a)
Figure 8. Results of the multicriteria optimization for the case study. Top graph: Pareto frontier
showing minimum invest costs for a given share of renewable resources. Bottom graph:
Corresponding equipment sizes.
4) SUMMARY
This paper presents a hybrid approach for the synthesis of renewable energy systems. The
hybrid approach consists of an initial heuristicbased preselection of candidate technologies
followed by a rigorous optimization and is based on the RenewIslands method [20] and
superstructurebased optimization as developed by Voll et al. [21]. The preselection effects an
important complexity reduction of the synthesis problem facilitating the optimal synthesis by
avoiding large superstructures and reducing the modeling effort.
The application of the hybrid approach to the case study of Mljet Island shows that the
complexity of the synthesis problem can successfully be narrowed down by preselecting five
promising candidate technologies from a comprehensive set of more than 20 options. The
implemented MILP optimization model is solved in less than two minutes to the global
optimal solution using a standard solver. A comparison of the optimization results to the
results originally derived by simulation [22] demonstrates a clear benefit of the hybrid
approach. For the most general scenario, the optimal solution requires only 41 % of the
investment costs determined by simulation at an equal share of 100 % renewable resources in
the energy system.
4.3
0.9
0.17
1.9
0.6
123
100
200
300
400
500
600
1
2
3
4
5
6
Equipment size / MW
Share of renewable resources
Wind
Electrolyser
Fuel Cell
Hydrogen storage
Storage size / MWh
26
15
5
1.4
0.25
5
10
15
20
25
30
Investment costs / Mio. €
The low computational effort achieved by the hybrid approach also enables to provide
additional insights for the case study by performing multicriteria optimization. The
calculated Pareto frontier reveals that it becomes progressively expensive to reach a share of
100 % renewable resources. The last 10 % require equal investments to the first 90 % since
equipment capacities need to be extended immensely.
In light of the short solution times and the excellent optimization results, the proposed hybrid
approach represents an efficient and comprehensive method for the synthesis of renewable
energy systems.
Acknowledgment
It is gratefully acknowledged that this work has been supported by the Croatian Science
Foundation through the “Optimization of Renewable Electricity Generation Systems
Connected in a Microgrid” collaborative research project, grant No. HRZZ 08/40.
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