How Adding a Battery to a Grid-Connected Photovoltaic System Can Increase its Economic Performance : A Comparison of Different Scenarios

The current work investigates how adding a battery of optimal capacity to a grid-connected photovoltaic (PV) system can improve its economic feasibility. Also, the effect of different parameters on the feasibility of the PV system was evaluated. The optimal battery capacity (OBC) was determined for different saving targets of the annual electricity consumption of the chosen building. For this aim, real electricity consumption data of a residential building in Landskrona, Sweden, was used as energy consumption profile. A Solar World SW325XL, which is a monocrystalline solar panel, was selected as PV panel. The calculations were performed under the metrological and economic conditions of southern Sweden. Different working parameters (WPs) were considered (prices of the battery, feed-in tariffs, and saving targets). The performed calculations show that the optimal battery capacity (OBC), in which the payback time (PBT) of the system is maximized, strongly depends on the WP. The proper selection of the battery can considerably increase the economic feasibility of the PV system in southern Sweden. However, in some cases, using battery can have a negative impact on the PBT of the system. The results show that the electricity price, the module price, the inverter price, and the inverter lifetime have the highest effect on the PBT.


Introduction
Today, most of the global energy used is fossil fuel-based [1].The high fossil-fuel dependence of our current system has resulted in increased atmospheric CO 2 concertation from 280 ppm before the industrial revolution to 400 ppm in 2015 [2].According to the IPCC, the use of fossil fuels is the primary driver for climate change [3].This manner leads to extreme heat waves, rising sea levels, changes in precipitation resulting in flooding and droughts, intense hurricanes, and degraded air quality, affect directly and indirectly the physical, social, and psychological health of humans.Therefore, a transformation of the global energy systems is needed, and the growth rates of clean-energy deployment need to be increased.Facing those challenges and achieving the EU targets for 2020 (2020 climate & energy package: ec.europa.eu/clima/policies/strategies/2020_en)and 2050 (2050 Energy Strategy: ec.europa.eu/energy/en/topics/energy-strategy-and-energy-union/2050-energy-strategy), a much faster and widespread utilization of the available local renewable energy resources is required.
Although the current efficiency of the photovoltaic systems is still relatively small and the upfront cost is high [4,5], the abundance of solar energy that strikes the Earth continuously makes such systems a viable alternative.Growing demand for renewable energy sources in recent years, mainly triggered by various regulative frameworks, such as the energy feed-in tariffs in Germany or the Energy Performance Building Directive (EPBD) of the European Union, led to significant reductions in PV Energies 2019, 12, 30 2 of 19 costs due to advancing the manufacturing of solar cells [6].Over the past few years, the price of solar systems has dropped considerably, to the point where such a system can compete with other renewable resources, e.g., wind energy.The fast decrease in system prices combined with the increases in its performance make photovoltaic systems (PVs) resulted in an increased amount installed globally [7].Regarding the worldwide installed capacity, solar photovoltaic is now the third largest renewable energy source with global demand reached 78 GW installed new capacity [8][9][10] with a total installed capacity of 303 GW in 2016 [7,11].Because they have no moving parts, PVs are stable over time, with a typical durability of 25 years and low maintenance is required during their operation [9].
In grid-connected PV systems, which are the most common PV systems in Europe, the electric network is used as virtual energy storage.Explicitly, when the power generation of the PV system surpasses the requirements of the building, the system will export the excessive PV generation into the grid.Conversely, when the production of the PV system does not cover the needs of the building, the system will import electricity from the network.Utilizing the electric grid as energy storage in return reduces the up-front cost of the PV system.Conversely, in some countries, the governmental subsidies for PV systems are decreasing, in term of reducing the feed-in tariff compared to the electricity purchase price.Hence, minimizing the PV energy injection into the utility network, i.e., rise self-consumption can increase the feasibility of such systems [12].Fortunately, the battery manufacturing and technologies have been developing quickly, which leads to dramatic reductions in their prices.Thus, the investigation of PV systems combined with batteries has been addressed in numerous studies [6,7,[12][13][14][15][16][17][18][19].Islam et at., for example, showed a possibility to use a battery with a PV system with a minimum power loss [19].Besides improving the economic performance [11], adding a battery to a PV system can contribute to solving the problem associated with the peak energy consumption periods [20].The economic feasibility of PV systems strongly relies on its upfront cost.Hence, using a battery with the system raises the costs of the system, which can reduce its profitability.Consequently, the definition of the optimum capacity of a battery is a crucial challenge to be addressed in order to enhance the viability of the PV system.Based on the available solar energy and energy consumption, Hesse et al. defined a cost-optimal size of a battery [21].
The effect of using the batteries on the self-consumption depends on the electricity demand profile [18].At the same time, increasing the self-consumption of a PV system results in benefits to the community and industry by reducing the investments in the electricity network [22].The study, thus, focuses on three aspects.The first one is to illustrate how using a battery with the PV system can enhance the financial performance, in the term of reducing its payback time and increasing the self-consumption level.The second goal is defining the optimal capacity of the battery as a function of different settings of working conditions.The third goal demonstrates the impact of the uncertainty in some inputs factors on the results obtained from the simulation model.

Methodology
To achieve the objectives of the current work, real energy consumption data of a residential building in Landskrona (55.87 • N, 12.83 • E), in southern Sweden, were used for the analysis.The chosen structure is a multi-story building of the total area of 2972 m 2 .A computer model was developed to mimic the energy and economic performance of the grid-connected rooftop PV system in which the module elements are attached to the roof of the building.The model was built based on the well-known relationships to calculate PV systems, which were tested in some studies [23][24][25][26][27]. Due to the stability of the monocrystalline PV technology in comparatively cold climate [19], the Solar World SW325XL (monocrystalline based), was selected as candidate PV panels.The optimization of the system was determined by using the built-in solver algorithm in Visual Basic for Applications (Excel VBA reference: docs.microsoft.com/en-us/office/vba/api/overview/excel).The calculations were performed for different scenarios including 1) different price of the battery, 2) different feed-in tariff, and 3) different system size (i.e., annual saving target).The sensitivity analysis was carried out to demonstrate the impact of the various parameters on the feasibility of the system.The considered

Determination of Available Solar Energy
The first and most important step before designing a photovoltaic system is the determination of the available solar energy (ASE) on an inclined surface in the considered site.ASE can be either measured or simulated.Solar radiation simulations have advantages over measurements and are more reliable over the years [28].Unlike measured solar radiation, simulated solar radiation can account for universal climate variations over many years, without having the burden of having to process decades of field data.Also, the actual measurements of the ASE are costly due to the high price of the required instruments.Therefore, simulation is a common method to calculate the available solar energy at a particular location.In this work, a computational model was built to estimate the available solar energy, with the resolution of one hour, per square meter of surface considering different slope and azimuth angles.The model can be used to determine the optimal azimuth and slope angles of the PV modules.The optimum angles are defined as the angles that result in maximum annual electricity generation.The metrological working conditions and the clearness index of the city of Landskrona were taken from [29,30].

Design of the system
Because the buildings in Landskrona are connected to the electricity grid, this work considers the grid-connected PV system.In such an arrangement, the utility network is used as virtual energy storage, which can reduce the upfront costs of the PV system.Still, the electricity output of the PV system fluctuates as the sun passages through the sky during the day.Consequently, there may be times when the energy generation of the PV system exceeds the power needs of the building or conversely.Therefore, in the current study, the electricity demand of the building is met by a

Determination of Available Solar Energy
The first and most important step before designing a photovoltaic system is the determination of the available solar energy (ASE) on an inclined surface in the considered site.ASE can be either measured or simulated.Solar radiation simulations have advantages over measurements and are more reliable over the years [28].Unlike measured solar radiation, simulated solar radiation can account for universal climate variations over many years, without having the burden of having to process decades of field data.Also, the actual measurements of the ASE are costly due to the high price of the required instruments.Therefore, simulation is a common method to calculate the available solar energy at a particular location.In this work, a computational model was built to estimate the available solar energy, with the resolution of one hour, per square meter of surface considering different slope and azimuth angles.The model can be used to determine the optimal azimuth and slope angles of the PV modules.The optimum angles are defined as the angles that result in maximum annual electricity generation.The metrological working conditions and the clearness index of the city of Landskrona were taken from [29,30].

Design of the System
Because the buildings in Landskrona are connected to the electricity grid, this work considers the grid-connected PV system.In such an arrangement, the utility network is used as virtual energy storage, which can reduce the upfront costs of the PV system.Still, the electricity output of the PV system fluctuates as the sun passages through the sky during the day.Consequently, there may be times when the energy generation of the PV system exceeds the power needs of the building or conversely.Therefore, in the current study, the electricity demand of the building is met by a combination of solar energy and grid electricity.In other words, when the generation of PV system exceeds energy requirement, the system will inject the excessive PV generation into the grid.Conversely, when the production of the PV system does not cover the request of the building, the system will import electricity from the network.However, since there is a difference in electricity purchase price and feed-in tariff, there might be an advantage in using a battery with the system.Therefore, the design of the system was assessed with and without the use of a battery and for different saving targets in the annual energy consumption of the case study.This way the benefit of using a battery with a grid-connected PV system was demonstrated.Figure 2 shows the scheme of the proposed grid-connected PV system.combination of solar energy and grid electricity.In other words, when the generation of PV system exceeds energy requirement, the system will inject the excessive PV generation into the grid.Conversely, when the production of the PV system does not cover the request of the building, the system will import electricity from the network.However, since there is a difference in electricity purchase price and feed-in tariff, there might be an advantage in using a battery with the system.Therefore, the design of the system was assessed with and without the use of a battery and for different saving targets in the annual energy consumption of the case study.This way the benefit of using a battery with a grid-connected PV system was demonstrated.Figure 2 shows the scheme of the proposed grid-connected PV system.In this work, a computer model was built to simulate the energy and economic performance of grid-connected rooftop PV system with the resolution of one hour.The model was built on wellestablished equations of designing PV systems that have reported in many published papers [23][24][25][26].The elasticity output per a single PV panel per hour 'i' over a year, Pm,i, is calculated as: Where FF is the fill factor and obtained from the technical sheet of the PV module; DF is derating factor which accounts for all losses throughout the system including module mismatch, module production tolerance, dust/soiling, and wiring, see Table 1.DF is especially crucial in working conditions of Doha where large amounts of dust and sand can be deposited; Isc-act is the actual short circuit current; Voc-act is actual open circuit voltage.Isc-act and Voc-act were approximated will by Ref. [27] and given as: Here Gs,i is the available solar energy per square meter (kW/m 2 ) per hour 'i' over a year; Isc, Voc, and VTC are manufacturer's specification of the selected PV (Table 1); GSCT = 1000 W solar irradiance at standard test conditions; TC,i is the corresponding temperature of the PV panel.The power generation of a PV panel is strongly related to the module temperature [31], which is a function of the ambient temperature and given by [27]: V oc-act =V oc -VTC 1000 In this work, a computer model was built to simulate the energy and economic performance of grid-connected rooftop PV system with the resolution of one hour.The model was built on well-established equations of designing PV systems that have reported in many published papers [23][24][25][26].The elasticity output per a single PV panel per hour 'i' over a year, P m,i , is calculated as: Where FF is the fill factor and obtained from the technical sheet of the PV module; DF is derating factor which accounts for all losses throughout the system including module mismatch, module production tolerance, dust/soiling, and wiring, see Table 1.DF is especially crucial in working conditions of Doha where large amounts of dust and sand can be deposited; I sc-act is the actual short circuit current; V oc-act is actual open circuit voltage.I sc-act and V oc-act were approximated will by Ref. [27] and given as: Here G s,i is the available solar energy per square meter (kW/m 2 ) per hour 'i' over a year; I sc , V oc , and VTC are manufacturer's specification of the selected PV (   of a PV panel is strongly related to the module temperature [31], which is a function of the ambient temperature and given by [27]: Where NOCT is the nominal operating cell temperature, Table 1; G s,i represents the hourly available solar radiation on the inclined surface, (kW).
To be able to use the electricity generation of the PV system, an inverter is required to convert the DC (direct current) voltage into grid appropriate AC voltage.Usually, the performance of the inverters depends on the ratio of the real output capacity to the nominal capacity of the inverter.Keep in mind that the electricity output of the PV system fluctuates daily and seasonally, the performance of the inverters varies during the time.In this study, SMA Sunny SB 6000US-10(270), were used as an inverter and Figure 3 [32] shows its efficiency curve.This way, the annual electricity output per a panel of PV, E m (kWh), can be calculated: Where η inverter is the efficiency of the inverter (%), Figure 3, η w is the wire efficiency (%), Table 2. Keep in mind that the PV system will be designed so that the annual electrical energy output of the system equals the required driving energy of the air conditioning system.Thus, the required number of a chosen PV panel (N) is: where E d is required annual electricity (kWh), σ is the annual saving target (%).Finally, the selfconsumption aspect is usually used to indicate the benefit of integrating the PV system in the utility grid from reduced the stress on the power grid perspective [14].The self-consumption means the electricity output of the PV that is consumed on site.In this study, the self-consumption, ϕ, is calculated as: where E fed (kWh)is the amount of generated electricity that is fed into the utility grid and depends on the size of the PV system, the electricity consumption profile, and battery capacity.
As mentioned above, Solar World SW325XL, which is a monocrystalline module, was selected as candidate PV panels.The specifications of the considered PV panel under standard test conditions (STC) are listed in Table 1.These specifications were collected from technical brochures provided by the producer.These specifications were used as the input data and fed to the computer model.To be able to use the electricity generation of the PV system, an inverter is required to convert the DC (direct current) voltage into grid appropriate alternating current (AC) voltage.Usually, the performance of the inverters depends on the ratio of the real output capacity to the nominal function of the inverter.Keep in mind that the electricity output of PV system fluctuates daily and seasonally, the performance of the inverters varies during the time.In this study, SMA Sunny SB 6000US-10(270), were used as an inverter.The efficiency curve of the selected inverter is shown in Figure 3 [32].Indeed, electricity savings due to the installation of PV systems can be converted into a monetary value by multiplying the annual energy savings by the price electricity [21].Hence, the net income of year 'j' after putting the PV system in service (in USD), i.e., the net cash (Cnet,j) due to installing a PV system is: where Pe and Pe,fed is the current electricity price and feed-in tariff respectively ($/kWh), CO&M,j is the annual cost in year 'j' which covers operation and maintenance including the replacement of the inverter and the battery ($/year), see Table 2; er is the annual escalation rate of electricity price.Here it was assumed that the changes in electricity price and feed-in tariff are following the same pattern [11].Hence, the PV system can be seen as an investment that generates cash.In this study, to aggregate several cash flows, taking into consideration inflows and outflows, cumulative cash flow (CCF) was used [11].The payback time of the investment is defined as the time required to make the CCF equals zero.The CCF ($/year) in the year 'j' after the system began operating becomes: where Cinv is the total front cost of PV system ($); d is the nominal discount rate and given by: where g is the inflation rate; ir is the interest rate, Table 2.While the total up-front cost of PV system was calculated as follows.The price of a PV panel was based on the price given by different suppliers.According to the component prices collected from the literature review, the replacement cost of the inverter (with ten years lifetime) and the labor costs are assumed to be 322 US$/kW and 18 US$/kW, respectively [33][34][35], as listed in Table 2. Mathematically, the upfront cost of a PV system is: where Cpanel and Pnominal are the cost and the nominal capacity of a single PV panel, respectively, see Table 1.
Operation and maintenance (O&M) represent expenses on a system which occur the installation afterward.In this study, the O&M costs during the first 25 years (which was selected as the project economic life) will be only for the surface cleaning of the PV panels.In the USA in 2013, the cost of supervision and twice a year cleaning of a PV system was reported to be 8.3 US$/kW per year [37].Indeed, electricity savings due to the installation of PV systems can be converted into a monetary value by multiplying the annual energy savings by the price electricity [21].Hence, the net income of year 'j' after putting the PV system in service (in USD), i.e., the net cash (C net,j ) due to installing a PV system is: where P e and P e,fed is the current electricity price and feed-in tariff respectively ($/kWh), C O&M,j is the annual cost in year 'j' which covers operation and maintenance including the replacement of the inverter and the battery ($/year), see Table 2; er is the annual escalation rate of electricity price.Here it was assumed that the changes in electricity price and feed-in tariff are following the same pattern [11].
Hence, the PV system can be seen as an investment that generates cash.In this study, to aggregate several cash flows, taking into consideration inflows and outflows, cumulative cash flow (CCF) was used [11].The payback time of the investment is defined as the time required to make the CCF equals zero.The CCF ($/year) in the year 'j' after the system began operating becomes: where C inv is the total front cost of PV system ($); d is the nominal discount rate and given by: where g is the inflation rate; ir is the interest rate, Table 2.While the total up-front cost of PV system was calculated as follows.The price of a PV panel was based on the price given by different suppliers.
According to the component prices collected from the literature review, the replacement cost of the inverter (with ten years lifetime) and the labor costs are assumed to be 322 US$/kW and 18 US$/kW, respectively [33][34][35], as listed in Table 2. Mathematically, the upfront cost of a PV system is: where C panel and P nominal are the cost and the nominal capacity of a single PV panel, respectively, see Table 1.
Operation and maintenance (O&M) represent expenses on a system which occur the installation afterward.In this study, the O&M costs during the first 25 years (which was selected as the project economic life) will be only for the surface cleaning of the PV panels.In the USA in 2013, the cost of supervision and twice a year cleaning of a PV system was reported to be 8.3 US$/kW per year [37].Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.
T c is the cell temperature, T a is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 • and 188 • , respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found G annual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.Using the computer model, which was built based on the most well-known relationships, the generation per unit area of Solar World SW325XL panel can be determined for each hour in the year.Figure 5 shows the hourly electrical production, as well as the monthly energy generation per a square meter of the selected PV panel.The simulation indicates that the annual energy output per a unit area of Solar World SW325XL is 160 kWh.Taking into consideration the results of the existing solar power in Figure 4 and the power generation of the PV panel in Figure 5, the annual effectiveness of the Solar World SW325XL is 13.4%.Figure 6 shows the hour-by-hour average air temperature system of some selected months in the year and the corresponding cell temperature of Solar World SW325XL PV panel.As shown, the higher outdoor air temperate results in higher cell temperature and, consequently, lower efficiency.Using the computer model, which was built based on the most well-known relationships, the generation per unit area of Solar World SW325XL panel can be determined for each hour in the year.Figure 5 shows the hourly electrical production, as well as the monthly energy generation per a square meter of the selected PV panel.The simulation indicates that the annual energy output per a unit area of Solar World SW325XL is 160 kWh.Taking into consideration the results of the existing solar power in Figure 4 and the power generation of the PV panel in Figure 5, the annual effectiveness of the Solar World SW325XL is 13.4%.Using the computer model, which was built based on the most well-known relationships, the generation per unit area of Solar World SW325XL panel can be determined for each hour in the year.Figure 5 shows the hourly electrical production, as well as the monthly energy generation per a square meter of the selected PV panel.The simulation indicates that the annual energy output per a unit area of Solar World SW325XL is 160 kWh.Taking into consideration the results of the existing solar power in Figure 4 and the power generation of the PV panel in Figure 5, the annual effectiveness of the Solar World SW325XL is 13.4%.Figure 6 shows the hour-by-hour average air temperature system of some selected months in the year and the corresponding cell temperature of Solar World SW325XL PV panel.As shown, the higher outdoor air temperate results in higher cell temperature and, consequently, lower efficiency.Figure 6 shows the hour-by-hour average air temperature system of some selected months in the year and the corresponding cell temperature of Solar World SW325XL PV panel.As shown, the higher outdoor air temperate results in higher cell temperature and, consequently, lower efficiency.As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8.As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8.As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8.As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8.
) the matching PV panel efficiency.
As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8. ) energy needs of the buildings and, ( ) the power output of the PV system of 50% saving target (left), and 100% saving target (right).
Given that, the electric network acts as an energy storage device, which in turn can reduce the upfront expenses of a PV system.However, since the feed-in tariff is smaller than the electricity price, there might be an economic advantage of using a battery with the PV system.Also, adding the battery increases self-consumption of the PV electricity generation and, consequently, reduces the need to purchase electricity from the grid.Increased self-consumption can help to lessen the strain on the distribution grid, which presents another advantage of enhancing the self-consumption.Explicitly, once the generation of the PV system surpasses the needs of the building, the system will use the excessive PV generation to charge the battery and export the excess energy to the grid.Conversely, when the production of the PVs does not cover the immediate requirements of the building, the system will import electricity from the battery firstly and from the grid secondly.With the results illustrated in Figure 8, one can see that use a battery will store the excessive electricity generation of the PV system between 7 to 18 o'clock, vary from month to another month, to be used during the peak power, i.e., after 19 o'clock.More details can be seen in the following figures.
Indeed, the amount of energy that can be stored in the battery and injected into the utility grid depending on many factors including the electricity consumption profile, the power generation profile, the size of the PV system (i.e., the saving target in the annual electricity consumption), and the capacity of the battery.Thus, the advantage of using a battery with the PVs strongly depends on these factors.It is worth pointing out that adding a battery to the scheme rises the advantage of the PV system as mentioned above, but also results in an increased initial cost of the system and increased the electricity losses in due to the losses in the battery itself (i.e., the battery efficiency in Table 2).These disadvantages of using the battery can negatively affect the economic performance of the system.Therefore, there is an optimal capacity of the battery that trade-off the advantages and the disadvantages of using a battery with a grid-connected PV system.In this work, therefore, the calculations were performed for different: (1) price of the battery, (2) feed-in tariff, and (3) system size (i.e., annual saving target).With the results illustrated in Figures 9-12, it can be seen that in some cases using a battery with the PV system improves the financial performance of the system, while in other cases adding a battery can have an adverse impact on the financial performance in term of increasing the payback time of the investment.However, under the working conditions in southern Sweden, adding a battery of high price (i.e., >400 $/kWh) to a grid-connected PV system always has a negative impact on its economic performance.It is worth mentioning that the nonlinearities of the results presented in Figures 9-12 are due to the way of calculating the payback time and some critical conditions that appear in some cases.It is worth mentioning that the nonlinearities of the results presented in Figures 9-12 are due to the way of calculating the payback time and some critical conditions that appear in some cases.For example, Figure 13 shows the cumulative cash flow (CCF) As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8.
) energy needs of the buildings and, ( As follows, the number of PV nodule required to meet different saving targets in the annual electricity consumption of the building, 356 MWh, can be calculated.Figure 7 shows the required area and number of PV panels to cover different saving targets in the annual energy consumption of the chosen building.Hence, the minimum area required to reach 50% and 100%, for instance, of the yearly energy needs of the building was found in 1134 and 2310 m 2 , respectively.Recall that the total roof area of the building is 2972 m 2 , one can say only 38% and 78% of the ceiling area is enough to generate 50% and 100%, respectively, of the annual energy consumption of case study.With the electricity consumption profiles illustrated in Figure 1 and the power generation of the panel in Figure 5, there are times when the production of the PV system beats the energy requirements of the building or the vice versa, see Figure 8. ) the power output of the PV system of 50% saving target (left), and 100% saving target (right).
Given that, the electric network acts as an energy storage device, which in turn can reduce the upfront expenses of a PV system.However, since the feed-in tariff is smaller than the electricity price, there might be an economic advantage of using a battery with the PV system.Also, adding the battery increases self-consumption of the PV electricity generation and, consequently, reduces the need to purchase electricity from the grid.Increased self-consumption can help to lessen the strain on the distribution grid, which presents another advantage of enhancing the self-consumption.Explicitly, once the generation of the PV system surpasses the needs of the building, the system will use the excessive PV generation to charge the battery and export the excess energy to the grid.Conversely, when the production of the PVs does not cover the immediate requirements of the building, the system will import electricity from the battery firstly and from the grid secondly.With the results illustrated in Figure 8, one can see that use a battery will store the excessive electricity generation of the PV system between 7 to 18 o'clock, vary from month to another month, to be used during the peak power, i.e., after 19 o'clock.More details can be seen in the following figures.
Indeed, the amount of energy that can be stored in the battery and injected into the utility grid depending on many factors including the electricity consumption profile, the power generation profile, the size of the PV system (i.e., the saving target in the annual electricity consumption), and the capacity of the battery.Thus, the advantage of using a battery with the PVs strongly depends on these factors.It is worth pointing out that adding a battery to the scheme rises the advantage of the PV system as mentioned above, but also results in an increased initial cost of the system and increased the electricity losses in due to the losses in the battery itself (i.e., the battery efficiency in Table 2).These disadvantages of using the battery can negatively affect the economic performance of the system.Therefore, there is an optimal capacity of the battery that trade-off the advantages and the disadvantages of using a battery with a grid-connected PV system.In this work, therefore, the calculations were performed for different: (1) price of the battery, (2) feed-in tariff, and (3) system size (i.e., annual saving target).With the results illustrated in Figures 9-12, it can be seen that in some cases using a battery with the PV system improves the financial performance of the system, while in other cases adding a battery can have an adverse impact on the financial performance in term of increasing the payback time of the investment.However, under the working conditions in southern Sweden, adding a battery of high price (i.e., >400 $/kWh) to a grid-connected PV system always has a negative impact on its economic performance.It is worth mentioning that the nonlinearities of the results presented in Figures 9-12 are due to the way of calculating the payback time and some critical conditions that appear in some cases.It is worth mentioning that the nonlinearities of the results presented in Figures 9-12 are due to the way of calculating the payback time and some critical conditions that appear in some cases.For example, Figure 13 shows the cumulative cash flow (CCF) of a PV with 50% saving target and feed-in tariff = 3.35 Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.(1 ± 25%) x each single data point in Figure 3 Inverter lifetime 7.5-12.5

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.
/kWh for two different battery size (175 and 250 kWh).As can be seen in the case of using a battery of capacity = 175 kWh the CCF becomes positing after 15.4 years, which is the PBT of the system.efore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], able 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating erature, and Gs is the available solar radiation (W/m 2 ).

ensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 s the nominal value of assumed factors.However, these factors are subject to sources of rtainty that may affect the accuracy of the results obtained from the simulation model.Therefore, sitivity analysis was carried out to show the uncertainty and robustness of the obtained results e presence of changes in the assumed factors [46].Table 3 indicates that the considered factors their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity calculated as the changes in the payback time due to variations in the considered factors.

sults and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum ricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a putational model was built to calculate available solar energy on an hourly basis and the optimal uth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in skrona, which are defined as the angles in which the available solar energy is maximized, are d to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from th to month and it is maximized during summertime.Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.(1 ± 25%) x each single data point in Figure 3 Inverter lifetime 7.5-12.5

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.efore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], able 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating erature, and Gs is the available solar radiation (W/m 2 ).
ensitivity Analysis As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 s the nominal value of assumed factors.However, these factors are subject to sources of rtainty that may affect the accuracy of the results obtained from the simulation model.Therefore, sitivity analysis was carried out to show the uncertainty and robustness of the obtained results e presence of changes in the assumed factors [46].Table 3 indicates that the considered factors their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity calculated as the changes in the payback time due to variations in the considered factors.Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors. of a PV with 50% saving target and feed-in tariff = 3.35 ₵/kWh for two different battery size (175 and 250 kWh).As can be seen in the case of using a battery of capacity = 175 kWh the CCF becomes positing after 15.4 years, which is the PBT of the system.efore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], able 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating erature, and Gs is the available solar radiation (W/m 2 ).
ensitivity Analysis As mentioned, some assumptions were made to simulate the grid-connected PV system.Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 /kWh (right).Annual saving target 75%.Also, there are two drops in the CCF immediately after the PBT due to the replacement of the battery and the inverter.However, these drops kept the CCF above zero.While in the other case, using a battery of capacity = 225 kWh led to increasing the investment cost and, consequently, the CCF chart is pull down.Thus, two drops in the CCF sue to the replacement of the battery and the inverter occurred in the negative zone of the CCF, which results in a significant increase in the PBT of the system.
Another important observation can be seen from the results in Figures 9-12 is that the optimal capacity of the battery, which minimizes the payback time of the investment, depends on the working conditions, including the price of the battery, feed-in tariff, and the saving target.Thus, the simulation was performed for different values of the mentioned parameters to determine the optimal capacity of the battery.As illustrated in Figure 14, for every given working conditions there is an optimum capacity of the battery that can improve the financial viability of the system.Increasing the feed-in tariff, for instance, leads to reduce the optimal capacity of the battery.In the case of the high price of the battery, there is no advantage of using a battery with the PV system in southern Sweden.Also, consistent with the results obtained by Hesse et al. [21], Figure 14 shows for a big local electricity consumption, as compared to the size of the PV system, there is no need to use a battery.efore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], able 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating erature, and Gs is the available solar radiation (W/m 2 ).

ensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 s the nominal value of assumed factors.However, these factors are subject to sources of rtainty that may affect the accuracy of the results obtained from the simulation model.Therefore, sitivity analysis was carried out to show the uncertainty and robustness of the obtained results e presence of changes in the assumed factors [46].Table 3 indicates that the considered factors their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity calculated as the changes in the payback time due to variations in the considered factors.

sults and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum ricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a putational model was built to calculate available solar energy on an hourly basis and the optimal uth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in skrona, which are defined as the angles in which the available solar energy is maximized, are d to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from th to month and it is maximized during summertime.Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.Also, there are two drops in the CCF immediately after the PBT due to the replacement of the battery and the inverter.However, these drops kept the CCF above zero.While in the other case, using a battery of capacity = 225 kWh led to increasing the investment cost and, consequently, the CCF chart is pull down.Thus, two drops in the CCF sue to the replacement of the battery and the inverter occurred in the negative zone of the CCF, which results in a significant increase in the PBT of the system.
Another important observation can be seen from the results in Figures 9-12 is that the optimal capacity of the battery, which minimizes the payback time of the investment, depends on the working conditions, including the price of the battery, feed-in tariff, and the saving target.Thus, the simulation was performed for different values of the mentioned parameters to determine the optimal capacity of the battery.As illustrated in Figure 14, for every given working conditions there is an optimum capacity of the battery that can improve the financial viability of the system.Increasing the feed-in tariff, for instance, leads to reduce the optimal capacity of the battery.In the case of the high price of the battery, there is no advantage of using a battery with the PV system in southern Sweden.Also, consistent with the results obtained by Hesse et al. [21], Figure 14 shows for a big local electricity consumption, as compared to the size of the PV system, there is no need to use a battery.refore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating perature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 ws the nominal value of assumed factors.However, these factors are subject to sources of ertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, nsitivity analysis was carried out to show the uncertainty and robustness of the obtained results he presence of changes in the assumed factors [46].Table 3 indicates that the considered factors their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity calculated as the changes in the payback time due to variations in the considered factors.Also, there are two drops in the CCF immediately after the PBT due to the replacement of the battery and the inverter.However, these drops kept the CCF above zero.While in the other case, using a battery of capacity = 225 kWh led to increasing the investment cost and, consequently, the CCF chart is pull down.Thus, two drops in the CCF sue to the replacement of the battery and the inverter occurred in the negative zone of the CCF, which results in a significant increase in the PBT of the system.
Another important observation can be seen from the results in Figures 9-12 is that the optimal capacity of the battery, which minimizes the payback time of the investment, depends on the working conditions, including the price of the battery, feed-in tariff, and the saving target.Thus, the simulation was performed for different values of the mentioned parameters to determine the optimal capacity of the battery.As illustrated in Figure 14, for every given working conditions there is an optimum capacity of the battery that can improve the financial viability of the system.Increasing the feed-in tariff, for instance, leads to reduce the optimal capacity of the battery.In the case of the high price of the battery, there is no advantage of using a battery with the PV system in southern Sweden.Also, consistent with the results obtained by Hesse et al. [21], Figure 14 shows for a big local electricity consumption, as compared to the size of the PV system, there is no need to use a battery.Bearing in mind the electricity consumption profiles and the electricity output from the panels in Figure 8, there are periods when the output from the PV system exceed the electricity demand of the building or vice versa.Figure 15 shows monthly average electricity consumption, the output of PV system, electricity used from PV output, and electricity fed into the grid for a saving target equals 75% of the total electricity consumption of the building and two feed-in tariffs (3.35 and 0.7 ₵/kWh).As shown above (Figure 14), the optimal capacity of the battery depends on the feed-in tariff, which consequently, affects the electricity fed into the grid.In other words, a lower feed-in tariff results in a bigger capacity of the battery and less electricity fed into the grid.Another conclusion can be drawn from Figure 15 is that in the case of adding a battery to the system, there is a difference between the electricity output of the system and the electricity used (net useful electricity).The difference is due to the loose in the battery during the storing time.This loss depends on the capacity of the battery and its efficiency (see Table 2).To demonstrate the benefit of using the battery, the calculations were performed with and without using a battery of the optimal capacity for different annual saving targets and the results are shown in Figures 16 and 17.As shown in Figure 16 the reduction in the payback time due to using a battery of the optimal capacity can be up to 7.3 years.Regarding the self-consumption level, the results in Figure 17 show that combining a battery of the optimal size with the PV system can increase the self-consumption up to 40% percentage points, which consists with the results obtained by Cucchiella et al. [11].Increasing the self-consumption has a positive impact on the environment and the utility network when it cannot absorb all production surpluses [11].Another essential observation from the results is that at the working conditions of southern Sweden using a battery with the PV system improve the economic feasibility of a large system, while for the smaller system there is no efore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], able 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating erature, and Gs is the available solar radiation (W/m 2 ).

ensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 s the nominal value of assumed factors.However, these factors are subject to sources of rtainty that may affect the accuracy of the results obtained from the simulation model.Therefore, sitivity analysis was carried out to show the uncertainty and robustness of the obtained results e presence of changes in the assumed factors [46].Table 3 indicates that the considered factors their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity calculated as the changes in the payback time due to variations in the considered factors.

sults and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum ricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a putational model was built to calculate available solar energy on an hourly basis and the optimal uth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in skrona, which are defined as the angles in which the available solar energy is maximized, are d to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from th to month and it is maximized during summertime.
/kWh (left), and 3.35 Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.(1 ± 25%) x each single data point in Figure 3 Inverter lifetime 7.5-12.5

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from month to month and it is maximized during summertime.

/kWh (right).
Bearing in mind the electricity consumption profiles and the electricity output from the panels in Figure 8, there are periods when the output from the PV system exceed the electricity demand of the building or vice versa.Figure 15 shows monthly average electricity consumption, the output of PV system, electricity used from PV output, and electricity fed into the grid for a saving target equals 75% of the total electricity consumption of the building and two feed-in tariffs (3.35 and 0.7 Energies 2018, 11, x FOR PEER REVIEW Therefore, in the current work, the annual O&M cost for see Table 2. Tc is the cell temperature, Ta is the ambient air te temperature, and Gs is the available solar radiation (W/

Sensitivity Analysis
As mentioned, some assumptions were made to sim shows the nominal value of assumed factors.Howe uncertainty that may affect the accuracy of the results ob a sensitivity analysis was carried out to show the uncer in the presence of changes in the assumed factors [46].and their ranges (i.e., 25% higher and lower than the nom was calculated as the changes in the payback time due t

Results and Discussion
The annual energy consumption of the case stud electricity consumption capacity occurs between 17 computational model was built to calculate available so azimuth and slope angles of the PV panels.The ide Landskrona, which are defined as the angles in which found to be 47 ° and 188 °, respectively.The hourly and listed in Figure 4, while the annual available solar ener 1197 kWh/m 2 .As expected, the results in Figure 4 show month to month and it is maximized during summertim /kWh).As shown above (Figure 14), the optimal capacity of the battery depends on the feed-in tariff, which consequently, affects the electricity fed into the grid.In other words, a lower feed-in tariff results in a bigger capacity of the battery and less electricity fed into the grid.Another conclusion can be drawn from Figure 15 is that in the case of adding a battery to the system, there is a difference between the electricity output of the system and the electricity used (net useful electricity).The difference is due to the loose in the battery during the storing time.This loss depends on the capacity of the battery and its efficiency (see Table 2).Bearing in mind the electricity consumption profiles and the electricity output from the panels in Figure 8, there are periods when the output from the PV system exceed the electricity demand of the building or vice versa.Figure 15 shows monthly average electricity consumption, the output of PV system, electricity used from PV output, and electricity fed into the grid for a saving target equals 75% of the total electricity consumption of the building and two feed-in tariffs (3.35 and 0.7 ₵/kWh).As shown above (Figure 14), the optimal capacity of the battery depends on the feed-in tariff, which consequently, affects the electricity fed into the grid.In other words, a lower feed-in tariff results in a bigger capacity of the battery and less electricity fed into the grid.Another conclusion can be drawn from Figure 15 is that in the case of adding a battery to the system, there is a difference between the electricity output of the system and the electricity used (net useful electricity).The difference is due to the loose in the battery during the storing time.This loss depends on the capacity of the battery and its efficiency (see Table 2).To demonstrate the benefit of using the battery, the calculations were performed with and without using a battery of the optimal capacity for different annual saving targets and the results are shown in Figures 16 and 17.As shown in Figure 16 the reduction in the payback time due to using a battery of the optimal capacity can be up to 7.3 years.Regarding the self-consumption level, the results in Figure 17 show that combining a battery of the optimal size with the PV system can increase the self-consumption up to 40% percentage points, which consists with the results obtained by Cucchiella et al. [11].Increasing the self-consumption has a positive impact on the environment and the utility network when it cannot absorb all production surpluses [11].Another essential observation from the results is that at the working conditions of southern Sweden using a battery with the PV system improve the economic feasibility of a large system, while for the smaller system there is no Therefore, in the current work, the annual O&M cost for the project is assumed to be 1 see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nom temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV s shows the nominal value of assumed factors.However, these factors are subject uncertainty that may affect the accuracy of the results obtained from the simulation mo a sensitivity analysis was carried out to show the uncertainty and robustness of the o in the presence of changes in the assumed factors [46].Table 3 indicates that the con and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors To demonstrate the benefit of using the battery, the calculations were performed with and without using a battery of the optimal capacity for different annual saving targets and the results are shown in Figures 16 and 17.As shown in Figure 16 the reduction in the payback time due to using a battery of the optimal capacity can be up to 7.3 years.Regarding the self-consumption level, the results in Figure 17 show that combining a battery of the optimal size with the PV system can increase the self-consumption up to 40% percentage points, which consists with the results obtained by Cucchiella et al. [11].Increasing the self-consumption has a positive impact on the environment and the utility network when it cannot absorb all production surpluses [11].Another essential observation from the results is that at the working conditions of southern Sweden using a battery with the PV system improve the economic feasibility of a large system, while for the smaller system there is no benefit of using a battery.Also, the advantage of adding a battery to the scheme is more significant when the gap between feed-in tariff the electricity price is more significant.It is worth mentioning that the reductions in the payback time and the increases in the self-consumption level depending on the load profile of the buildings.Individually, for a given location the benefits of using a battery with a grid-connected PV system vary from building to building as the energy consumption profile be different.
Energies 2018, 11, x FOR PEER REVIEW 14 of 19 benefit of using a battery.Also, the advantage of adding a battery to the scheme is more significant when the gap between feed-in tariff the electricity price is more significant.It is worth mentioning that the reductions in the payback time and the increases in the self-consumption level depending on the load profile of the buildings.Individually, for a given location the benefits of using a battery with a grid-connected PV system vary from building to building as the energy consumption profile be different.As mentioned above, some assumptions were made to carry out the simulation of gridconnected PVs, which are listed in Table 2. Indeed, these inputs factors are subject to sources of uncertainty that might affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was performed with the aim to show the uncertainty and the robustness of the obtained results in the presence of changes in the factors assumed.For this objective, the considered factors in this study were thought to vary 25% higher and lower than the nominal values shown in Table 2.The simulations were carried out for different saving targets, different battery prices, and various feed-in tariffs, the results are illustrated in Figures 18 and 19.As shown, the impact of uncertainty of the inputs factors on the economic feasibility of the grid-connected PV system in southern Sweden is influenced by the size of the system (i.e., the saving targets), the feedin tariff, and the price of the battery.However, the electricity price, the module price, the inverter price, and the inverter lifetime seem to be the most critical factors in all cases.The significance of these factors is because the initial cost of the system depends on the components price, while the saving of the system in money term (i.e., cash flow of the system) depends on the electricity price.If the future electricity price, for instance, is 25% higher/lower than the current rate, the calculated payback time of the PV system will 33-52% shorter/longer than the calculated ones under the conditions in Table 2.It can also be seen that the effect of the electricity price on the payback time is more significant for a significant annual saving target and low initial cost of the battery.However, Therefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 shows the nominal value of assumed factors.However, these factors are subject to sources of uncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results in the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity was calculated as the changes in the payback time due to variations in the considered factors.

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1, and the maximum electricity consumption capacity occurs between 17 and 19 o'clock.As mentioned above, a computational model was built to calculate available solar energy on an hourly basis and the optimal azimuth and slope angles of the PV panels.The ideal inclination angle and azimuth angles in Landskrona, which are defined as the angles in which the available solar energy is maximized, are found to be 47 ° and 188 °, respectively.The hourly and monthly average available solar energy are listed in Figure 4, while the annual available solar energy of the inclined surface and found Gannual = 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available solar energy varies from /kWh (left), and 3.35 Energies 2018, 11, x FOR PEER REVIEW Therefore, in the current work, the annual O&M cost for the project is assumed t see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is th temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connecte shows the nominal value of assumed factors.However, these factors are s uncertainty that may affect the accuracy of the results obtained from the simulati a sensitivity analysis was carried out to show the uncertainty and robustness of in the presence of changes in the assumed factors [46].Table 3 indicates that th and their ranges (i.e., 25% higher and lower than the nominal values listed in Ta was calculated as the changes in the payback time due to variations in the consi (1 ± 25%) x each single data point in Figure 3 Inverter lifet

Results and Discussion
The annual energy consumption of the case study is 356 MWh, Figure 1 electricity consumption capacity occurs between 17 and 19 o'clock.As m computational model was built to calculate available solar energy on an hourly b azimuth and slope angles of the PV panels.The ideal inclination angle and Landskrona, which are defined as the angles in which the available solar energ found to be 47 ° and 188 °, respectively.The hourly and monthly average availa listed in Figure 4, while the annual available solar energy of the inclined surfac 1197 kWh/m 2 .As expected, the results in Figure 4 show that the available sola /kWh (right).
Energies 2018, 11, x FOR PEER REVIEW 14 of 19 benefit of using a battery.Also, the advantage of adding a battery to the scheme is more significant when the gap between feed-in tariff the electricity price is more significant.It is worth mentioning that the reductions in the payback time and the increases in the self-consumption level depending on the load profile of the buildings.Individually, for a given location the benefits of using a battery with a grid-connected PV system vary from building to building as the energy consumption profile be different.As mentioned above, some assumptions were made to carry out the simulation of gridconnected PVs, which are listed in Table 2. Indeed, these inputs factors are subject to sources of uncertainty that might affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was performed with the aim to show the uncertainty and the robustness of the obtained results in the presence of changes in the factors assumed.For this objective, the considered factors in this study were thought to vary 25% higher and lower than the nominal values shown in Table 2.The simulations were carried out for different saving targets, different battery prices, and various feed-in tariffs, the results are illustrated in Figures 18 and 19.As shown, the impact of uncertainty of the inputs factors on the economic feasibility of the grid-connected PV system in southern Sweden is influenced by the size of the system (i.e., the saving targets), the feedin tariff, and the price of the battery.However, the electricity price, the module price, the inverter price, and the inverter lifetime seem to be the most critical factors in all cases.The significance of these factors is because the initial cost of the system depends on the components price, while the saving of the system in money term (i.e., cash flow of the system) depends on the electricity price.If the future electricity price, for instance, is 25% higher/lower than the current rate, the calculated payback time of the PV system will 33-52% shorter/longer than the calculated ones under the conditions in Table 2.It can also be seen that the effect of the electricity price on the payback time is more significant for a significant annual saving target and low initial cost of the battery.However, Figure 17.Increased the self-consumption percentage points of the PV system due to use a battery of the optimal capacity versus the saving targets, for feed-in tariff = 6.7 Energies 2018, 11, x FOR PEER REVIEW Therefore, in the current work, the annual O&M cost for the project is assumed to be 1 see Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nom temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV s shows the nominal value of assumed factors.However, these factors are subject uncertainty that may affect the accuracy of the results obtained from the simulation mo a sensitivity analysis was carried out to show the uncertainty and robustness of the o in the presence of changes in the assumed factors [46].Table 3 indicates that the con and their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).
was calculated as the changes in the payback time due to variations in the considered Therefore, in the current work, the annual O&M cost for the proje see Table 2. Tc is the cell temperature, Ta is the ambient air temperatur temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the shows the nominal value of assumed factors.However, these uncertainty that may affect the accuracy of the results obtained fro a sensitivity analysis was carried out to show the uncertainty and in the presence of changes in the assumed factors [46].Table 3 in and their ranges (i.e., 25% higher and lower than the nominal valu was calculated as the changes in the payback time due to variatio As mentioned above, some assumptions were made to carry out the simulation of grid-connected PVs, which are listed in Table 2. Indeed, these inputs factors are subject to sources of uncertainty that might affect the accuracy of the results obtained from the simulation model.Therefore, a sensitivity analysis was performed with the aim to show the uncertainty and the robustness of the obtained results in the presence of changes in the factors assumed.For this objective, the considered factors in this study were thought to vary 25% higher and lower than the nominal values shown in Table 2.The simulations were carried out for different saving targets, different battery prices, and various feed-in tariffs, the results are illustrated in Figures 18 and 19.As shown, the impact of uncertainty of the inputs factors on the economic feasibility of the grid-connected PV system in southern Sweden is influenced by the size of the system (i.e., the saving targets), the feed-in tariff, and the price of the battery.However, the electricity price, the module price, the inverter price, and the inverter lifetime seem to be the most critical factors in all cases.The significance of these factors is because the initial cost of the system depends on the components price, while the saving of the system in money term (i.e., cash flow of the system) depends on the electricity price.If the future electricity price, for instance, is 25% higher/lower than the current rate, the calculated payback time of the PV system will 33-52% shorter/longer than the calculated ones under the conditions in Table 2.It can also be seen that the effect of the electricity price on the payback time is more significant for a significant annual saving target and low initial cost of the battery.However, the impact of the electricity price is weaker when Energies 2019, 12, 30 15 of 19 the feed-in tariff is higher.Another important conclusion can be drawn from the sensitivity analysis is that the influence of the assumed battery price on the feasibility of the PV system is <4% in the worst scenario (big saving target, the low assumed cost of the battery and small feed-in tariff).In other words, the influence of the battery cost on the estimated payback time of PV system in southern Sweden can be neglected especially for small PV system and high feed-in tariff.On another side, the impact of module price is more significant for a minor system and independent from other parameters (i.e., the feed-in tariff and battery price).
In a nutshell, one can say that the sensitivity analysis shows that the impact of the uncertainty in some assumptions, such as battery efficiency and inflation rate, on the feasibility of the PV system can be neglected.While it is essential to pay more attention to the electricity price and close consideration must be given to select some components such as inverter and module before carrying out the financial investigation.
Energies 2018, 11, x FOR PEER REVIEW 15 of 19 the impact of the electricity price is weaker when the feed-in tariff is higher.Another important conclusion can be drawn from the sensitivity analysis is that the influence of the assumed battery price on the feasibility of the PV system is <4% in the worst scenario (big saving target, the low assumed cost of the battery and small feed-in tariff).In other words, the influence of the battery cost on the estimated payback time of PV system in southern Sweden can be neglected especially for small PV system and high feed-in tariff.On another side, the impact of module price is more significant for a minor system and independent from other parameters (i.e., the feed-in tariff and battery price).
In a nutshell, one can say that the sensitivity analysis shows that the impact of the uncertainty in some assumptions, such as battery efficiency and inflation rate, on the feasibility of the PV system can be neglected.While it is essential to pay more attention to the electricity price and close consideration must be given to select some components such as inverter and module before carrying out the financial investigation.2. Tc is the cell temperature, Ta is the ambient air temperatu temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate th shows the nominal value of assumed factors.However, thes uncertainty that may affect the accuracy of the results obtained fr a sensitivity analysis was carried out to show the uncertainty an in the presence of changes in the assumed factors [46].Table 3 and their ranges (i.e., 25% higher and lower than the nominal val herefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], ee Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating emperature, and Gs is the available solar radiation (W/m 2 ). .

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 hows the nominal value of assumed factors.However, these factors are subject to sources of ncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results n the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors /kWh (bottom).Annual saving target 50%.

Conclusions
The primary objective of this work was to investigate the possibility of improving the viability of a grid-connected PV system in a residential building at the working conditions of southern Sweden.The real energy consumption data of a multi-story residential building, in southern Sweden, of the total area of 2972 m 2 was used to generate the electricity consumption profile.A computational model was developed to simulate hour-by-hour the performance of the PV system.The simulation showed that adding a battery to the PV system can significantly improve its performance, in term of reducing the payback time and increasing the self-consumption.While in some cases, it was shown that using a battery with the PV system has a negative impact on the economic feasibility of the system.These mean that the optimal capacity of the batter, in which the payback time of the investment is minimized, strongly depends on the working parameters (WP).Therefore, the calculations were performed for different WPs: (1) different price of the battery, (2) different feed-in tariff, and (3) different system size (i.e., annual saving target).
Compared to not using a battery, the reduction in the payback time and the increase in the selfconsumption of the PV system can be >7 years up to 40% percentage points, respectively.It is important to mention that increasing the self-consumption results in reduced strain on energy supplies and network.
Sensitivity analysis was performed to show the uncertainty and the robustness of the obtained results in the presence of changes in the different parameters.The simulation showed that the influence of the changes on the results depends on the WP.In General, the results show that the electricity price, the module price, the inverter price, and the inverter lifetime have the most significant effect on the accuracy of predicted payback time of the PV system.For example, increase the electricity price by 25% results in reducing the payback time of the PV system will 33%.While the  2. Tc is the cell temperature, Ta is the ambient air temperatu temperature, and Gs is the available solar radiation (W/m 2 ).

Sensitivity Analysis
As mentioned, some assumptions were made to simulate th shows the nominal value of assumed factors.However, thes uncertainty that may affect the accuracy of the results obtained fr a sensitivity analysis was carried out to show the uncertainty an in the presence of changes in the assumed factors [46].Table 3 and their ranges (i.e., 25% higher and lower than the nominal val was calculated as the changes in the payback time due to variati

Results and Discussion
The annual energy consumption of the case study is 356 herefore, in the current work, the annual O&M cost for the project is assumed to be 10 US$/kW [36], ee Table 2. Tc is the cell temperature, Ta is the ambient air temperature, NOCT is the nominal operating emperature, and Gs is the available solar radiation (W/m 2 ). .

Sensitivity Analysis
As mentioned, some assumptions were made to simulate the grid-connected PV system.Table 2 hows the nominal value of assumed factors.However, these factors are subject to sources of ncertainty that may affect the accuracy of the results obtained from the simulation model.Therefore, sensitivity analysis was carried out to show the uncertainty and robustness of the obtained results n the presence of changes in the assumed factors [46].Table 3 indicates that the considered factors nd their ranges (i.e., 25% higher and lower than the nominal values listed in Table 2).The sensitivity as calculated as the changes in the payback time due to variations in the considered factors.

Figure 1 .
Figure 1.Hourly and monthly average electricity demand of the selected building.

Figure 1 .
Figure 1.Hourly and monthly average electricity demand of the selected building.

Figure 2 .
Figure 2. A scheme of the proposed grid-connected PV system.

Figure 2 .
Figure 2. A scheme of the proposed grid-connected PV system.

Energies 2018 , 19 Figure 3 .
Figure 3.The efficiency of the SMA Sunny SB 6000 inverter along with the capacity ratio.

Figure 3 .
Figure 3.The efficiency of the SMA Sunny SB 6000 inverter along with the capacity ratio.

Figure 4 .
Figure 4. Hourly and monthly available solar energy per square meter on the inclined surface (47 inclination angle and 188 azimuth angle).

Figure 5 .
Figure 5. Hour-by-hour power output and monthly energy production per a unit area of Solar World SW325XL on the inclined surface (47 slope angle and 188 azimuth angle).

Figure 4 .
Figure 4. Hourly and monthly available solar energy per square meter on the inclined surface (47 inclination angle and 188 azimuth angle).

Figure 4 .
Figure 4. Hourly and monthly available solar energy per square meter on the inclined surface (47 inclination angle and 188 azimuth angle).

Figure 5 .
Figure 5. Hour-by-hour power output and monthly energy production per a unit area of Solar World SW325XL on the inclined surface (47 slope angle and 188 azimuth angle).

Figure 5 .
Figure 5. Hour-by-hour power output and monthly energy production per a unit area of Solar World SW325XL on the inclined surface (47 slope angle and 188 azimuth angle).

Figure 6 .
Figure 6.Hour-by-hour average of ( ) outdoor air temperature, ( ) the corresponding cell temperature of the PV module, along with ( ) the matching PV panel efficiency.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

) 19 Figure 6 .
Figure 6.Hour-by-hour average of ( ) outdoor air temperature, ( ) the corresponding cell temperature of the PV module, along with ( ) the matching PV panel efficiency.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

19 Figure 6 .
Figure 6.Hour-by-hour average of ( ) outdoor air temperature, ( ) the corresponding cell temperature of the PV module, along with ( ) the matching PV panel efficiency.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

Energies 2018 , 19 Figure 6 .
Figure 6.Hour-by-hour average of ( ) outdoor air temperature, ( ) the corresponding cell temperature of the PV module, along with ( ) the matching PV panel efficiency.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

Figure 8 .
Figure 8. Hour-by-hour daily average of () energy needs of the buildings and, ( ) the power output of the PV system of 50% saving target (left), and 100% saving target (right).

Figure 8 .Figure 6 .
Figure 8. Hour-by-hour daily average of ( Figure 6.Hour-by-hour average of ( ) outdoor air temperature, ( ) the corresponding cell temperature of the PV module, along with ( ) the matching PV panel efficiency.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

Figure 6 .
Figure 6.Hour-by-hour average of ( ) outdoor air temperature, ( ) the corresponding cell temperature of the PV module, along with ( ) the matching PV panel efficiency.

Figure 7 .
Figure 7.The required area vs. the saving target in the annual electricity consumptions of the case study.

Energies 2018 ,
11, x FOR PEER REVIEW 11 of 19of a PV with 50% saving target and feed-in tariff = 3.35 ₵/kWh for two different battery size (175 and 250 kWh).As can be seen in the case of using a battery of capacity = 175 kWh the CCF becomes positing after 15.4 years, which is the PBT of the system.

Figure 9 .
Figure 9.The effect of the battery capacity on the payback time of the PV system for: Feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 25%.

Figure 10 .
Figure 10.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 50%.

Figure 11 .
Figure 11.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 75%.

Figure 9 .
Figure 9.The effect of the battery capacity on the payback time of the PV system for: Feed-in tariff = 6.7 /kWh (left), and 3.35 Energies 2018, 11, x FOR PEER REVIEW 7 of 19 /kWh (right).Annual saving target 25%.Energies 2018, 11, x FOR PEER REVIEW 11 of 19of a PV with 50% saving target and feed-in tariff = 3.35 ₵/kWh for two different battery size (175 and 250 kWh).As can be seen in the case of using a battery of capacity = 175 kWh the CCF becomes positing after 15.4 years, which is the PBT of the system.

Figure 9 .
Figure 9.The effect of the battery capacity on the payback time of the PV system for: Feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 25%.

Figure 10 .
Figure 10.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 50%.

Figure 11 .
Figure 11.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 75%.

Figure 10 .
Figure 10.The effect of the battery capacity on the payback time of the PV system for feed-in tariff = 6.7

Figure 9 .
Figure 9.The effect of the battery capacity on the payback time of the PV system for: Feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 25%.

Figure 10 .
Figure 10.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 50%.

Figure 11 .
Figure 11.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 75%.

Figure 11 .
Figure 11.The effect of the battery capacity on the payback time of the PV system for feed-in tariff = 6.7

Figure 12 .
Figure 12.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 100%.

Figure 12 .
Figure 12.The effect of the battery capacity on the payback time of the PV system for feed-in tariff = 6.7

/ 19 Figure 12 .
Figure 12.The effect of the battery capacity on the payback time of the PV system for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).Annual saving target 100%.

Figure 13 .
Figure 13.Cumulative cash flow for the PV system with saving target = 50% and feed-in tariff = 3.34

Figure 14 .
Figure 14.The optimum capacity of the battery along with the saving targets for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).

Figure 15 .
Figure 15.Monthly electricity consumption, the output of the PV system, electricity used from PV output, and electricity fed into the grid.Fore: feed-in tariff =6.7 ₵/kWh and battery capacity = 0 (left), and feed-in tariff =3.35 ₵/kWh and battery capacity = 183 kWh (right).Annual saving target 75%.

Figure 14 .
Figure 14.The optimum capacity of the battery along with the saving targets for feed-in tariff = 6.7

Energies 2018 , 19 Figure 14 .
Figure 14.The optimum capacity of the battery along with the saving targets for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).

Figure 15 .
Figure 15.Monthly electricity consumption, the output of the PV system, electricity used from PV output, and electricity fed into the grid.Fore: feed-in tariff =6.7 ₵/kWh and battery capacity = 0 (left), and feed-in tariff =3.35 ₵/kWh and battery capacity = 183 kWh (right).Annual saving target 75%.

Figure 15 .
Figure 15.Monthly electricity consumption, the output of the PV system, electricity used from PV output, and electricity fed into the grid.Fore: feed-in tariff = 6.7

/
kWh and battery capacity = 0 (left), and feed-in tariff = 3.35 Energies 11, x FOR PEER REVIEW 7 of 19

Figure 16 .
Figure 16.The payback time of the system with and without using a battery of the optimum capacity versus the saving targets for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).

Figure 17 .
Figure 17.Increased the self-consumption percentage points of the PV system due to use a battery of the optimal capacity versus the saving targets, for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).

Figure 16 .
Figure 16.The payback time of the system with and without using a battery of the optimum capacity versus the saving targets for feed-in tariff = 6.7

Figure 16 .
Figure 16.The payback time of the system with and without using a battery of the optimum capacity versus the saving targets for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).

Figure 17 .
Figure 17.Increased the self-consumption percentage points of the PV system due to use a battery of the optimal capacity versus the saving targets, for feed-in tariff =6.7 ₵/kWh (left), and 3.35 ₵/kWh (right).

Figure 18 .Figure 18 .
Figure 18.The impact of different factors in term of relative changes in the Payback time of the PV system for battery price 128 $/kWh (left) and 250 $/kWh (right).Feed-in tariff: 3.55 ₵/kWh (top), and 6.7 ₵/kWh (bottom).Annual saving target 50%.

Figure 19 .
Figure 19.The impact of different factors in term of relative changes in the Payback time of the PV system for battery price 128 $/kWh (left) and 250 $/kWh (right).Feed-in tariff: 3.55 ₵/kWh (top), and 6.7 ₵/kWh (bottom).Annual saving target 75%.

Figure 19 .
Figure 19.The impact of different factors in term of relative changes in the Payback time of the PV system for battery price 128 $/kWh (left) and 250 $/kWh (right).Feed-in tariff: 3.55

Table
); G SCT = 1000 W solar irradiance at standard test conditions; T C,i is the corresponding temperature of the PV panel.The power generation

Table 1 .
Specifications SW325XL panel at standard test conditions.

Table 2 .
Assumptions made in the present work.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 2 .
Assumptions made in the present work.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in

Table 3 .
The considered parameter i

Table 2 .
Assumptions made in the present work.

Table 2 .
Assumptions made in the present work.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the present work.

Table 3 .
The considered parameter in the sensitivity analysis.

Table 2 .
Assumptions made in the presen

Table 3 .
The considered parameter in the sensit /kWh (right).

Table 2 .
Assumptions made in the prese

Table 2 .
Assumptions made in the present work.

Table 2 .
Assumptions made in the prese

Table 3 .
The considered parameter in the sens (1 ± 25%) x each single data point in Figure

Table 2 .
Assumptions made in the present work.