3.3. Modeling of Resource Components
The estimation of the produced energy from a wind turbine is based on its power curve provided by the manufacturer. The power curve shows the correlation between the power output of the WT and the wind speed at hub height, considering the power coefficient. Enercon E-44’s 900 Kw power curve is employed in this study. Wind speed data are obtained at the altitude where the weather station is installed. To determine the wind speed at the hub height of the wind turbine, an equation is used for the representation of the height dependence of the wind speed, which is based on the roughness height parameter of the installation surface [
44].
PVs compared to other RESs are superior due to their ability for direct electricity production, their silent mode operation, and the fact that they can be gradually implemented into an RES system. Also, they produce zero CO
2 emissions, they require minimum maintenance costs, they have a long lifetime, and their installation is more aesthetically acceptable compared to other RESs and especially to WTs. To estimate the output of a PV,
, Formulas (1)–(3) have been used [
45]:
where
is the the peak capacity of the PV array (W/m
2),
is the global solar irradiance on the inclined surface (W/m
2),
is the standard radiation parameter and is equal to 1000 W/m
2,
is the efficiency of a PV system (%),
is inverter efficiency (%),
is the grid-connected efficiency (%),
is the efficiency parameter related to the temperature of the PV cell (%),
is the PV module efficiency temperature coefficient (/°C),
is the temperature of PV cells (°C),
is the reference standard temperature of PV modules, equal to 25 °C,
is the ambient temperature (°C),
refers to the operating temperature of PV modules under the ambient temperature of
, equal to 20 °C, and under the environment of solar irradiance
, equal to 800 W/m
2.
It is assumed that twin-shift tracking stents are coupled with the series-parallel-connected PVs, helping in the rotation of the PVs and ensuring the perpendicular incidence of the solar irradiance. In this way, the utilization of the maximum solar energy is achieved [
46]. The conversion of direct current, produced by the PV, to alternative current (AC), is performed through the connection with an inverter. PVs produce most of their energy at the point where there is the intersection of the load with the current voltage, according to the voltage–current curve (I–V) of the PV. In real-time operations, the load mismatch and the variation in the solar irradiance and the temperature prevent this intersection [
47]. To surmount this and to consistently maximize the PVs’ output in accordance with the temperature and the solar irradiation, it is assumed that PVs are connected to the inverter through the Maximum Power Point Tracking control (MPPT) [
48]. This means that the produced power output of the PVs is supposed to be at every time-step equal to the maximum power [
49].
In order to accommodate the intermittent nature of both renewable energy sources, storage technology must be used to meet the supply and demand, simultaneously. PHS, BT, FC, PHBH and PHFC are employed as storage systems in this research study.
The storage units exploit the surplus energy,
(kWh), from the WTs and the PVs. The PHS uses this energy to pump seawater to a reservoir at a high altitude, through the pumping station. The release of water from the reservoir at a higher altitude when the demand for electricity is higher, in order to flow toward the reservoir at the lower altitude, generates electricity for the island’s electricity grid through the hydroelectric plant. The reservoir’s altitude and the available water both affect how much energy is produced. The stored water in the higher reservoir from time step t-1 is added to the water from the next time step. The benefit of this procedure is the potential to store surplus energy and exploit it when the demand is high or when the RES potential is low, even though more energy is needed for pumping water than is generated through the hydro turbine. The volume of the pumped water
(m
3) and the produced hydro energy,
(kWh), for every time step, are given by Formulas (4) and (5) [
50]:
where
is the pumping efficiency (%),
is the density of the water (kg/m
3),
is the acceleration due to gravity (m/s
2) and
is the net head (m).
is the amount of released water from the upper reservoir (m
3) and
is the turbine efficiency (%). In the simulations, it is assumed, for safety reasons, that the reservoir’s lower limit cannot be less than 10% of its total capacity. The pumped hydro storage system consists of the upper reservoir, the pumping station, and the hydro turbine.
The charging of the battery, in the case of surplus energy, is estimated by Formula (6), while its discharge is estimated using Formula (7):
where
is the state of charge at time t (kWh),
is the state of charge at time
t − 1 (kWh),
is the self-discharge rate (%) and
is the efficiency of the battery (%). Self-discharge rate describes a battery’s decreasing level of charge when it is not in use. The new
SOC for each time step depends not only on the efficiency of the battery and the energy surplus or deficit, but also on the state of charge of the previous time step, which is always affected by the self-discharge rate, even if the battery is on standby. Also, it is assumed that the minimum state of charge of the battery cannot be less than (
) the total capacity of the battery, due to safety reasons, where
is the depth of discharge of the battery (%) and is given by the manufacturer.
Hydrogen can be produced using an electrolyzer, which converts surplus energy to hydrogen through the electrolysis. Electrolysis requires desalinated water. The hydrogen produced by the surplus energy is estimated using Formula (8), while the produced energy from the fuel cell is estimated using Formula (9) [
51]:
where
is the efficiency of the electrolyzer (%) and
is the efficiency of the fuel cell (%).
When there is surplus energy, the amount of hydrogen remaining in the hydrogen tank at the time step
t,
, is estimated by (10), while, when there is an energy deficit it is estimated according to Formula (11):
It is assumed that the lower limit of the hydrogen tank cannot be less than 10% of the total capacity due to safety reasons.
The assumptions for the technical characteristics of all storage technologies are presented in
Table 2.
A desalination unit is coupled in all scenarios for the fulfillment of required water for domestic and agricultural purposes, using water from the sea. Also, the desalination unit is necessary in scenarios where energy is stored through the production of hydrogen. In these cases, the generation of green hydrogen presupposes the electrolysis of pure desalinated water.
3.4. Configurations and Energy Management Strategy
In this section, the configurations that will be examined, based on the combination of the RES and the storage methods that were analyzed in the previous section, are presented. A storage system is coupled in all configurations as the stochastic nature of the RES (wind and solar) potential prevents the simultaneous satisfaction of demand in correspondence with renewable energy production. Based on the configuration examined, a PHS, a BT, and an HT are used for the storage of excess energy. Also, two configurations with hybrid storage technologies are evaluated; a pumped hydro–battery hybrid storage (PHBH), which consists of a PHS and a battery, and a pumped hydro–hydrogen hybrid storage (PHFC), which consists of a PHS, an electrolyzer, and a fuel cell. Also, in all of the configurations a desalination unit is coupled for the satisfaction of domestic and irrigation water supply.
The three RES (wind, solar, and hydro) and the performance of various storage systems (PHS, battery, hydrogen) form the foundations for the suggested energy management scenarios for both single and hybrid storage. These scenarios compare the effectiveness of these storage methods in meeting basic needs of society, i.e., electricity and fresh water. In the first configuration (WT/PV/DU/PHS), the PHS is used for the exploitation of the surplus energy. In Configuration 2 (WT/PV/DU/BT), the storage method involves the use of batteries, instead of the PHS system of Configuration 1. In the third configuration (WT/PV/DU/FC), the battery has been replaced with a hydrogen production and utilization system. In Configuration 4 (WT/PV/DU/PHBH), a hybrid pumped battery storage system, consisting of a PHS and a battery, is used, and in the fifth configuration (WT/PV/DU/ PHFC) the hybrid storage system consists of a PHS, an electrolyzer, and a fuel cell. In
Table 3, the configurations that are examined in this study are presented.
The nominal capacities of the installed WTs and PVs are selected based on the meteorological data (wind and solar potential, temperature, precipitation), on the island’s requirements for energy and freshwater (household consumption, domestic and irrigation water), and according to the methodology described in [
52]. The HRES’s number of autonomous days is used to dimension the storage systems (reservoir [
52], batteries [
53], hydrogen tank [
54]). This number provides the days that the storage unit of the HRES provides the required energy for the demands of the island, even if the RES potential is low and no energy can be produced by the WTs and the PVs. Energy storage systems typically consider two days of autonomy [
55]. Additionally, it is assumed that the hydrogen tank and batteries will be at their lowest capacities at the beginning of the simulation and that the reservoir will be 50% filled. By using the extra energy generated by WTs and PVs, seawater is pumped into the higher reservoir. It must be noted that this reservoir does not provide water to the desalination unit of the island. The DU is supplied with seawater and adds fresh water to the desalination reservoir. The pumps need a surplus of energy to function properly, and if there is not sufficient energy for them to start their operation, then no water is pumped to the upper reservoir. The pumping station must be capable of absorbing the maximum RES output minus the energy that is given to fulfill the demands, and its nominal power is calculated using [
52]. The same applies to determining the hydro turbine’s rated power. It must be ensured that in the case of low wind potential, it can handle the maximum load [
52]. For the sizing of the fuel cell and the electrolyzer, it is considered that the first is capable of handling any electrical demand that cannot be met by other RES or storage systems, according to [
54], depending on the configuration under examination, and the second can convert any surplus energy into hydrogen at each time step [
54]. Data of the installed components of each configuration is presented in
Table 4. Depending on the scenario under consideration, load demand not met by WTs, PVs, PHS, BT, or FC is met by the grid, which necessitates the startup of the nearby power plant. To control the response of the HRES and its reliability in covering the required demand for electricity and drinking and irrigation water supply, the simulations are performed with hourly data inputs, to guarantee the highest possible reliability of the results.
The first three configurations of the HRESs are considered to have simple storage, i.e., a single storage unit for the surplus energy. The storage strategy followed is shown in
Figure 1. The procedure is performed for one year of data (i = 8760). Meteorological data and the island’s demand statistics are provided as inputs. The WTs and PVs’ combined energy output is estimated according to the under-consideration configuration. In every configuration, priority is given to the domestic water, after to the irrigation water and at last to the energy for electricity demand. The renewable energy produced is calculated (RES) for each step and it is determined if the corresponding demand can be met, according to the priority and according to the produced renewable energy. When all demands have been checked it is determined whether there is surplus energy
Esur. If there is excess energy, the available storage space in the storage unit is checked. If there is no space, then, unfortunately, the excess energy is rejected. That means that the produced energy cannot be utilized by the grid or by the storage unit. This happens repeatedly in every installed RES project without the integration of storage technology, where produced RES energy cannot be utilized. An attempt to avoid this is by the incorporation of a storage unit. If there is additional space in the examined storage unit then the storage unit’s new state of charge is determined, always ensuring that the maximum state of charge level of the storage unit is not exceeded and the fulfillment of the demands is estimated for this time step. For every time step (hourly time steps) the met and unmet demands are estimated at first according to the produced renewable energy and afterward according to the stored energy to each of the storage units, based on the scenario examined. That means how many kWh of household consumption and how many cubic meters of desalinated domestic and irrigation water can be satisfied at the end of each time step. Also, it is determined whether there is available stored energy in the storage unit if there is no surplus energy,
Esur < 0, but there is still unmet demand. If stored energy is accessible, the new state of charge is determined and finally, the fulfilled and unmet demands for an hour are once more approximated.
Within the last two configurations, there is hybrid storage, i.e., a combination of two different storage methods. The storage strategy followed is shown in
Figure 2. The step is, again, conducted hourly and the procedure is performed for one year of data (i = 8760). Again, as in the simple storage method, the data are entered, and the process is no different until the control of excess energy
. After this step, the method of controlling and utilizing the excess energy differs. As it is shown in the flowchart, if there is excess energy, the first storage unit is checked for available storage space. If there is available space, then the new state of charge of the first storage unit is calculated. If not, or if there is still excess energy, the second storage unit is checked for available storage space. If there is available space, then the new state of charge of the second storage unit is calculated. If not, or if there is still excess energy after the charging of the second storage unit until its maximum state of charge level, then unfortunately the excess energy is rejected. In both storage units, it is always checked that the maximum state of charge level is not exceeded when they are in charging mode. If there is no excess energy but there is still demand that has not been fulfilled, the first storage unit is checked for available stored energy. If there is available stored energy, then the new state of charge is calculated. If not, or if there is still unmet demand, the second storage unit is checked for available stored energy. If there is available stored energy, then the new state of charge is calculated and, in any case, it is checked if there is still an unmet demand, and both met and unmet demand is estimated for each step.
3.5. Evaluation Analysis
For the evaluation and the comparison of the different configurations of the HRES indices about energy, economic and environmental analysis are estimated. The loss of load (), the loss of load probability (), the cost of energy (), the cost of water (), the payback period () and eliminated amounts of CO2 () are also estimated.
Formulas (12) and (13) estimates
and
respectively, for the evaluation of the reliability of each HRES:
where
indicates the specific demand of energy that is about to be fulfilled or not, between energy for domestic water desalination,
, energy for irrigation water desalination,
, and energy for household consumption,
. The hourly time steps for one year (1–8760) are indicated by index
, and
is the loss of load of each demand
.
Formula (14) estimates the
[
56] as follows:
where
CAPEX is the initial investment cost of the HRES (in EUR),
OPEX is the operating and maintaining costs of each component (in EUR),
is the cost of replacing the component at the end of its lifetime (in EUR),
is the salvage cost (in EUR),
is the lifetime of the HRES (1, 2, …,
= 25), and
is the produced energy by the HRES (in kWh). The salvage cost [
51] is estimated separately for each component, according to Formula (15), where
is the lifetime of each component,
is the lifetime of the HRES, and
is the discount rate (%). The initial costs represent the initial investment, installation, and replacement costs of the system, including the cost of each unit, depending on the configuration examined. The initial cost does not include any subsidies from the national or local government policies. The operation and maintenance costs refer to the corresponding costs for the total life; 25 years of an HRES.
In order to recover the full cost of the investment, the
determines project’s required years of operation. It is based on net annual savings (
) and the overall investment cost. Formula (16) provides a mathematical description of it:
The net annual savings contains the net revenue it is expected to earn each year by using the HRES instead of other energy sources.
PBP is determined using the current kWh pricing and the current cost for desalinated water. According to the PPC, the average tariff, based on different consumptions (daytime or nighttime consumption), determines the cost of a kWh. Today, the price is 0.22833 €. (Public Power Corporation, Athens, Greece, 2023). However, such projects can be more competitive by a reduction in the selling price gap. This can be achieved in the event of an increase in energy prices. Freshwater for the islands costs between 7 and 12 €/m
3 [
26,
57], and in this study, is considered equal to 10 €/m
3. It is important to note that the PBP calculation evaluates the financial viability of a project without considering other factors that may impact the return on investment, such as inflation, tax benefits, or changes in energy prices over time.
Formula (17) is used to calculate the amounts of CO
2 that the HRES system eliminates,
(tn/year), when 1 kWh supplied by the HRES replaces 1 kWh provided by the LPS as follows:
where
and
are the generated energy from the WTs and the PVs, respectively.
and
are the emission factors of the WTs and the PVs and are equal to 13.7 g CO
2/kWh and 50 g CO
2/kWh, respectively [
58].
represents the emission factor of each country’s grid. According to the country datasheet, the GHG intensity of electricity production for Greece in 2021 is about 397 g CO
2/kWh [
59]. One ton of CO
2 is priced according to the market rate for a ton on 10 September 2023 [
60], which is 81.52 EUR/tn. Note that its price displays an average daily increasing trend of 0.6%. In
Table 5, the data used for the economic evaluation are presented.