3. Results and Discussions
In this section, the results obtained in an attempt to optimize a citrus farm located in Bandar-Abbas in terms of LCOE, CAPEX, and WSP for three different LPSPs are presented.
The first concern is to determine the most suitable fixed tilt angle for the PV array (oriented due South). Despite simple rules of thumb considerations for the best PV tilt angle, the problem of panel slope for yielding the maximum solar energy collection can be complex and it is a function of various parameters such as local latitude, surface azimuth, and clearness index [
36]. The variation of the yearly average daily irradiation with respect to the slope of the array was calculated for 0
90°. The optimal tilt angle that leads to the maximum power generation of PV panels for one year is about
= 17° for this city. These results for the optimum tilt angle were confirmed with respect to the cumulative electricity production in a year (not explicitly presented). It is worth mentioning that, although the maximum value of average daily irradiation occurs at 17°, limited reductions were found in the range of 10 to 28 degrees. Therefore, construction of the structures (not considered herein) could be much easier at 20°, for instance, without substantial losses in performance.
In
Figure 11,
Figure 12,
Figure 13 and
Figure 14 the results of the study in terms of the variations of WSP, LCOE, and CAPEX with respect to the number of PV panels are presented for three different thresholds for LPSP. It is assumed that the residents need different reliabilities for their electricity demand leading to LPSP values of 0, 1%, and 3% in
Figure 11,
Figure 12 and
Figure 13, respectively. One should note that despite similar shapes, the y-axes of these figures involve different scales. The lower the value of LPSP, ceteris paribus, the higher the corresponding values of all three other parameters.
In
Figure 11, LPSP = 0 simply means 100% reliability of the system in providing electricity for the residence, 365 days per year. Therefore, based on the algorithm used in the study, LPSP is fixed to the desired value (or tolerance of a customer, or community), and the minimum PV panel and battery capacity are obtained accordingly. In
Figure 11, the capital cost of a 4 panel system (left in
Figure 11) reaches 66,000
$, while the WSP peaks at more than 28% and the LCOE exceeds 7
$/kWh as there is a major requirement for batteries. However, a slight increase in the number of panels produces a rapid decline in both the WSP and LCOE. Nevertheless, the symbolic threshold of 1
$/kWh reaches around 10 panels and further increases do not change the LCOE significantly while the CAPEX increases.
It is obvious that as the number of PV panels increases, the water shortage probability will decrease since the system is capable of producing more electricity. This is mostly at the expense of an increment in the capital cost of the project (CAPEX). Moreover, this is true for the three values of LPSP.
In
Figure 12, similar trends are observed. However, 10 panels with LPSP = 1% will lead to an LCOE of about 33% less than that calculated in
Figure 11. Logically, a higher LPSP has an important effect on the capital cost. CAPEX drops from about 23,000
$ (
Figure 11) to 15,000
$ (
Figure 12) for a 10 panels system.
As the LPSP has such an influence, simulations were also carried out for a 3% LPSP and the results are reported in
Figure 13. Here again, similar trends are observed. However, 10 panels with LPSP = 3% will lead to an LCOE drop of about 40% while the CAPEX reaches as low as 14,000
$ for the 10 panels system.
From
Figure 11,
Figure 12 and
Figure 13, it can be seen that there is a minimum value for the capital cost of the system at different LPSP values. This minimum value happens for 6, 6, and 5 PV panels and for LPSPs of 0, 1%, and 3%, respectively. This is due to the fact that generally, increasing PV panels means making the system bigger, and hence more investment is needed. However, as mentioned earlier, at the extremely low number of PV panels, considerable amounts of battery bank capacity are required for the system to guarantee the threshold values for LPSPs, and consequently, in this case, the battery price dictates the high values of the CAPEX.
The variation of the systems capital cost at PV panel numbers of 4 to 5 or 6 is considerable in all cases of LPSPs. For LCOE trends, the same as the explanations provided in the previous section, i.e., validation section, LCOE decreases by increasing the number of PV panels, since the production of electricity is much higher than the increment in investment cost of the system.
At a fixed LPSP value, the selection of the best sizing of the system in terms of the number of PV panels and battery bank capacity depends on the tolerance of WSP and the capability of the user to pay the investment cost of the system. In fact, this is the end user who decides which system size is compatible with their needs. Here, it is worth noting that WSP = 1% means that there is a yearly average of about 3.6 days for which there could be a water shortage, not a guaranteed shortage. In these periods, the requirement for irrigation could also be less, thus modifying the water demand, as the WSP is correlated to irradiation. Nevertheless, several strategies could be considered to solve this problem, such as personal water storage by individuals during sunny days, prior to critical periods of the year, or variable prices of water per liter with weather predictions. Yet these strategies are not reviewed here.
For instance,
Figure 14 shows that at LPSP = 0, for a PV panel number of five, the LCOE is about 2
$/kWh and reduces to about half at 10 PV panels and to 0.75
$ per kWh at 15 PV panels. This suggests that there should not be much gain in terms of LCOE to increase the number of panels above 10. Furthermore, at LPSP = 0, WSP values for these panel numbers are 9.5%, 2.4%, and 1.5%, respectively (
Figure 15). This reinforces the previous conclusion. Accordingly, still at LPSP = 0, CAPEX equals 22.8 k
$ for 5 PV panels, 23.0 k
$ at 10 PV panels, and 25.5 k
$ at 15 PV panels (
Figure 16). Additionally, this also confirms that 10 panels would be enough.
As another example, at LPSP of 3%, for 5 PV panels, the LCOE is 0.85
$/kWh and reduces to 0.60
$/kWh for 10 PV panels and to 0.56
$/kWh at 15 PV panels (
Figure 14). Furthermore, WSP values for these panel numbers are 6.0%, 2.3%, and 1.0%, respectively (
Figure 15). Additionally, finally, CAPEX (
Figure 16) equals 9.6 k
$, 13.6 k
$, and 18.9 k
$ for 5, 10, and 15 PV panels, respectively. Here, we see that a higher tolerance to a loss of power could lead to substantial savings: the LCOE could be reduced by more than 50% when LPSP increases from 0 to 3%, especially for small systems, and the WSP would also drop. This could sound counter-intuitive, but when people accept several potential periods without electricity (higher LPSP), this provides energy to fill the water tank and thus reduces the WSP. Finally, the CAPEX also drops with higher LPSP.
These graphs (
Figure 14,
Figure 15 and
Figure 16) provide a clear picture of the effect of LPSP and WSP tolerances on sizing and the cost of system. For instance, if investment cost is a concern of the user of the system, selecting a system with PV panels of 6 to 9 would be reasonable since, in these sizes, CAPEX does not increase considerably, but WSP reduces from 5.5% up to 2.9% at LPSP of 0. Additionally, similarly, from 4.6% up to 2.6% at LPSP of 1%, and from 3.5% up to 2.6% at LPSP of 3%.
4. Conclusions
In this study, photovoltaic electrification and water pumping based on a PV-battery system were investigated for a city located in southern Iran, i.e., Bandar-Abbas. Two specific concepts that influence the size and cost of the system were used herein: (1) the water shortage probability (WSP) for the evaluation of drought tolerance in the context of irrigation; and (2) the loss of power supply probability (LPSP) as a tolerance threshold for lack of access to electricity of a rural home. Moreover, a simplified expression for the levelized cost of energy (LCOE) was also implemented to evaluate the financial viability of systems with more than the sole capital expenditure (CAPEX). A MATLAB genuine implementation of a particular electrification/pumping algorithm was carried out. Then, the correct formulation and implementation were validated against a benchmark solution. Additionally, finally, a case study involving parametric variations was undertaken.
The investigations were carried out to determine the appropriate size of the system (in terms of the number of PV panels and the battery capacity required) for selected values of LPSP and to find the corresponding values of WSP, LCOE, and CAPEX.
The results, not surprisingly, revealed that increasing the number of PV panels leads to more energy production and consequently lower WSP. This, however, is at the expense of more investment in the system (CAPEX). However, the effect of increasing energy production may increase the capital cost but leads to the reduction of the LCOE.
Several preponderantly interesting results were found here:
A comparison of different LPSPs shows that a small increase in tolerance for power loss can considerably lower the size, cost, and the LCOE of the system with limited change in water shortage probabilities. This suggests that communities and/or dwellings with limited financial capabilities should consider complementary strategies to avoid running out of water for irrigation.
The WSP could go lower with higher LPSP because more water could be pumped into the tank when people can tolerate power shortages.
There is a minimum in the curve that plots the CAPEX with respect to the number of PV panels in the system where limited variations of WSP and LCOE happen with further increases in the number of PV panels and that for any LPSP. This is due to the battery bank requirement rapid increase below the minimal number of panels which are less expensive. For the current study, this is about 5 to 6 panels.