**3. Results**

*3.1. Renewable-Energy Hybrid System*

The SMHES sizing was carried out for 0 HD (only PVS) and 1 HD (only MCS). Table 1 shows the parameters for the PVS and MCS.


**Table 1.** SMHES parameters in case study.

The generation profile was analyzed with respect to the home power-demand profile, which allows the hours of the day, when it is possible to cover the energy demand, the range where there is an energy surplus, or where it is necessary to use energy storage to cover the demand to be determined. Figure 10a shows a consumption–generation profile in a representative day in the year (day 355, December) when each renewable system produces 7.5 kWh/day in the seasonal minimums. Under this scenario, the amount of energy extracted from the MCS is higher than that from the PVS due to a higher daily availability; therefore, the MCS requires lower installed capacity, 0.458 kW, while solar requires an installation of 2.1 kW. It is worth mentioning that although the MCS generation profile shows fewer hourly variations, there are fluctuations that are less visible on the scale compared to the PVS generation profile. Figure 10b shows the total generation. The system considers only output power. From this perspective, the intersection of the generation curve with the demand curve allows us to visualize the points where the hybrid system is not able to cover the demand.

**Figure 10.** (**a**) Generation–consumption profile of SMHES supplied by an installed capacity PVS of 2.1 kW or an MCS of 0.458 kW; (**b**) total generation–consumption profile of SMHES indicating the energy supplied by renewable resources, energy supplied by energy storage, and surplus of energy.

#### *3.2. Hybridization Analysis Results*

Applying the algorithm developed in the Matlab® program, the curves of the hybridization process were obtained at different HDs for the 365 days of the year; daily variations during the year are shown in Appendix A in Figure A1 and includes daily variations in energy consumption and supply in the 12 months. Figure 11 shows a representative day (355 day) of generation–consumption profiles with different HDs for comparison. For each case, an energy-balance analysis was carried out for different HDs. Table 2 shows

the power (kW) and energy (kWh/day) generation of the SMHES, RPCESS, percentage reduction in the RPCESS for different HDs, and the average charge–discharge cycles.

**Figure 11.** Generation–consumption profiles with different hybridization degrees: (**a**) 0 HD; (**b**) 0.2 HD; (**c**) 0.5 HD; (**d**) 0.8 HD; (**e**) 1 HD.


**Table 2.** Solar–Marine-Current Hybrid System (average results).

\* In Case 6, PVS and MCS provide the maximum power, double the energy that the system requires, which is included for comparison purposes. \*\* % Reduction in RPESS with respect to Case 1, where there is the largest energy-storage system.

The graphs in Figure 11 show the total generation of the PVS and the MCS for different HDs. The amount of energy that can be covered by the SMHES can be observed by comparing the area under the curve of the consumption profile of the house to the total generation curve. Similarly, the variation in the maximum power with respect to the degree of hybridization can be observed.

The hybridization mainly affects the total amount of energy stored per day. In Case 1 (HD 0), where the energy is totally supplied by the PVS, the energy required to be stored is 5.39 kWh/day, while for Case 5 (HD 1), where the energy is totally supplied by the MCS, the energy required to be stored is lower than in Case 1 at only 0.85 kWh/day. The number of cycles that the RPESS has to perform to achieve this goal is one cycle for Case 1 and three cycles at 0.5 HD. It is worth mentioning that these cycles do not imply full charge or discharge. The RPESS can have important implications in the cycle life as the number of cycles increase, with triple the charge–discharge cycles than with 0.5 HD. However, the capacity of the RPESS can be reduced by 55% for HD = 0.5 and 79% for HD = 1. This capacity reduction is due to the similarity of the demand and MCS profiles during the daytime to the PVS.

#### *3.3. Evaluation System Hybridization in the Year*

The annual analysis allowed us to determine the total number of required charge and discharge cycles according to the HD (Figure 12). The analysis showed that 0 HD requires more daily energy storage, 5.5 kWh/day, than 1 HD requiring 0.85 KWH/day, while the number of cycles per year is higher at 0.2 HD that the other HD.

**Figure 12.** Number of cycles in a year in the different cases of hybridization and the comparison with daily energy storage.

According to the analysis in Section 3.1, the daily consumption (7.5 kWh/day) can be easily covered by the production of the PVS and MCS at different HDs. The estimated amount of energy lost with the full participation of the PVS (HD 0) is 1477 kWh/year (Figure 13a), while for a system with the full participation of the MCS (HD 1), it is 7576 kWh/year (Figure 13b). This surplus energy can be stored for days with a higher consumption than the estimated value (base load) and for days where the amount of energy produced by the SMCHS cannot cover the energy demand.

**Figure 13.** PVS and MCS daily generation: (**a**) 0 HD and (**b**) 1 HD, with respect to the minimum seasonal generation corresponding to the base load (7.5 kWh/day).

These results show that a greater participation of the PVS has advantages in terms of lower seasonal storage (lower seasonal losses). However, seasonal storage also depends on the HD (Figure 14). In the case of 0.2 HD, the energy surplus is 2697 kWh/year; for 0.5 HD, it is 4527 kW/year; and for 0.8 HD, it is 6296 kWh/year.

**Figure 14.** PVS and MCS daily generation: (**a**) 0.2 HD, (**b**) 0.5 HD, and (**c**) 0.8 HD, with respect to the minimum seasonal generation corresponding to the base load (7.5 kWh/day).

It was necessary to evaluate the seasonal variability of the system since it would help to complement the results obtained from the daily analysis. From this analysis, the percentage of days of the year in which the demand can be totally covered was found to be 91% for 0 HD and 92% for 1 HD, while the highest availability was found for 0.3 HD at 98.5% (Figure 15).

**Figure 15.** Minimum generation availability at different HDs.

To cover the deficit of energy, different alternatives can be used, from oversizing the SMCHS to the use of an auxiliary internal combustion system, increasing the PCEES capacity or using a second ESS; for this purpose, a PCESS was used. Figure 15 shows that despite having an adequate coverage of days, most of the ESSs have significant surpluses of energy that are not used, as shown in Figures 13 and 14. Figure 16 shows the amount of seasonal minimum storage required for days, which is unable to cover the base demand. The results indicate that at 0 HD, it is 5.4 kWh/day, while at 1 HD, it is 6.4 kWh/day. The analysis showed that the HD with the lowest seasonal storage for these days is 0.6 HD with 3.86 kWh/day.

**Figure 16.** Seasonal energy storage at different HDs; additional energy storage per day with less generation than base load (7.5kWh/day).

#### *3.4. Energy-Storage Selection*

Renewable-energy hybridization analysis determines the feasibility of the degree of participation of the PVS and MCS based on the daily number of cycles of the storage system. The determination of the best RPCESS and PCESS options for a specific application is an important task, which requires the analysis of several factors (described in Table 3). Many aspects should be considered for the evaluation of a storage system; the most critical factors in this study were power rating (C4), response time (C5), and storage duration (C6), as the objective was to validate the technology.


According to the methodology of Saaty, the weighting carried out is considered reasonable, given that the consistency ratio (CR) was less than 0.1 (Table 4). On the other hand, the evaluations carried out with the TOPSIS method found that the electrochemical classification of EESs was better than the mechanical classification since the criterion power rating was minimized to find an EES with a low power rating. The best options were as follows: (1) li-ion batteries and (2) Pb batteries for the RPCESS (Table 5); (1) hydrogen and (2) small CAES for the PCEES; (1) supercapacitors and (2) li-ion batteries for the REES based on the best response time.


**Table 4.** Weighting of the Multi-Criteria Decision Analysis.

Note: nmax is an eigenvalue of the decision matrix; CI is the consistency index; and CR is the consistency ratio.


**Table 5.** Ranking of EES using the TOPSIS method.

The obtained results consider the fluctuations between generation and demand in time intervals from hours to months (seasonal). The importance of daily storage was found to be able to cover the energy-demand profile, and variations in seasonal energy expedients were shown. Often, in stand-alone systems, the ESS is oversized in order to cover days with a higher consumption or lack of renewable generation. However, this might compromise the cycle life due to the number of daily cycles that the ESS performs. Therefore, a reserve (backup) storage system that exploits seasonal surpluses may be a technically viable alternative. The storage viability for daily and seasonal storage was evaluated through a multi-criteria method.

For energy storage for the RPCESS (daily fluctuations), it was found that the most important criteria are response time followed by the number of cycles and efficiency. In the case of the PCESS (seasonal fluctuations), the most important criteria are the duration of storage, followed by the response time; as it is used for low-power systems, a low-power range is better. The results of the Multi-Criteria Decision Analysis (TOPSIS) for the selection of the best ESS are shown in Table 5, which are listed from one to eight at the feasibility level. The RESS, PCESS, and RPCESS are compared, and a hierarchy is shown: (1) is the best option, and (8) is the worst storage system option. For the REES, supercapacitors were found to be adequate for periods of time shorter than days, while for longer periods, PCESS hydrogen storage is adequate, and RPCEES lithium-ion batteries are the best alternative. This information allows us to validate the importance of developing lithium-ion batteries and hydrogen energy-storage systems.
