**7.1 Scenario I: Wind/PV/battery hybrid system**

In this case, a stand-alone hybrid system is considered that is including of wind and PV energy sources and storage batteries. Convergence curves of the PSO algorithm, for five independent runs, are shown in Fig. 9. It is observed that the algorithm converges almost to the same optimal value.

Hourly generated power of PV arrays, WGs is shown in Fig. 10 that could be comparing with load. The hourly expected amount of stored energy in the battery is shown in Fig. 10, too. It is significant that reliable supply of the load at each time step, strongly, depends on the amount of the stored energy. When stored energy in battery reaches its minimum allowable limit, if renewable system cannot satisfy the load, the load will not be supplied. On the other hand, if renewable system can satisfy the load, the extra generated energy will be saved in the battery (and battery is in the state of charge). It is worth pointing out that when the battery has the maximum charge its energy will not increase anymore.

In Fig. 11, the hourly reliability indices in the year are plotted. The amount of hourly demand and load pattern is another important factor in reliability assessment of the system. The size of each component is also calculated and is shown in table 2.

As shown in the above figures, each time step could be analyzed. For example, at around of 6500th time step, the power that is generated by PV arrays and wind turbines is decreased (Fig. 10) and it is not enough to satisfy the load. Also, the energy that saved in the batteries in this step is around the minimum allowable level. So, some of the demand is lost and ELF index is equal to 0.5 (Fig. 11).

Fig. 9. Convergence of the optimization algorithm


Table 2. Optimal combination for hybrid system


Table 3. Reliability indices of PV-wind-battery system

0 20 40 60 80 100 120

Number of iteration

*NWG NPV NBat Pinv (kW) θPV Hhub(m)* 

1 89 12 44 52.61 15.85

*ELF LOEE (kWh/yr) EENS LOLE(h/yr)* 

0.0036 759.49 0.0034 64.57

0.6

Fig. 9. Convergence of the optimization algorithm

Table 2. Optimal combination for hybrid system

Table 3. Reliability indices of PV-wind-battery system

0.8

1 1.2

1.4 1.6 1.8

Total cost (US\$)

2 2.2

2.4 2.6 x 10 6

Fig. 10. Hourly generated power of PV arrays, WGs and hourly expected amount of stored energy in the battery during a year.

Fig. 11. Hourly reliability indices during a year

In this scenario, the mean of ELF index in the year is 0.002 which is less than the maximum ELF tconstraint (0.01). So, this system would not pay for penalty cost. The NPC, which is calculated for this case, would be equal to 1.29769 MUSD that 31272.02 USD of this cost would be for costumer's dissatisfaction.

### **7.2 Scenario II: Wind/battery system**

This system is including of wind source energy and storage batteries. The optimal size of system components is presented in table 4. In this case, the reliability constraint is activated, so it is fixed on maximum allowable value. Because of this, the NPC of system is increased and is reached up to 2.25009 MUS\$. The generated power by wind turbines and amount of energy in storage system is shown in Fig. 12.

As mentioned, in this system, the ELF index is reached to 0.0063 which satisfy the inequality constraint of reliability constraint. Thus, it must not pay the penalty cost and the costumer's dissatisfaction cost would be 0.032424 MUS\$.

0 1000 2000 3000 4000 5000 6000 7000 8000

0 1000 2000 3000 4000 5000 6000 7000 8000

0 1000 2000 3000 4000 5000 6000 7000 8000

In this scenario, the mean of ELF index in the year is 0.002 which is less than the maximum ELF tconstraint (0.01). So, this system would not pay for penalty cost. The NPC, which is calculated for this case, would be equal to 1.29769 MUSD that 31272.02 USD of this cost

This system is including of wind source energy and storage batteries. The optimal size of system components is presented in table 4. In this case, the reliability constraint is activated, so it is fixed on maximum allowable value. Because of this, the NPC of system is increased and is reached up to 2.25009 MUS\$. The generated power by wind turbines and amount of

As mentioned, in this system, the ELF index is reached to 0.0063 which satisfy the inequality constraint of reliability constraint. Thus, it must not pay the penalty cost and the costumer's

Time (hour)

0

1

0

0

Fig. 11. Hourly reliability indices during a year

would be for costumer's dissatisfaction.

**7.2 Scenario II: Wind/battery system** 

energy in storage system is shown in Fig. 12.

dissatisfaction cost would be 0.032424 MUS\$.

10

20

LOEE (kWh)

30

0.5

LOLE

0.5

ELF

1

Fig. 12. Hourly generated power of WGs and hourly expected amount of stored energy in the battery during a year.


Table 4. Optimal combination in wind-Battery system


Table 5. Reliability indices of wind-battery system

### **7.3 Scenario III: PV/Battery systems**

The last scenario is a system including of PV source energy and storage batteries. The size of system components is shown in table 6. Total cost and ELF index corresponding to this case are 0.803237 MUS\$ and 0.0022 respectively that, 0.032423 MUS\$ would be paid as costumer's dissatisfaction cost. The output power of PV arrays and battery energy is shown in Fig. 13.

Fig. 13. Hourly generated power of PV arrays and hourly expected amount of stored energy in the battery during a year.


Table 6. Optimal combination in PV-battery system


Table 7. Reliability indices of PV-battery system

With compare of these scenarios together, it could be seen, the number of batteries in windbattery system is more than the hybrid system and PV-battery system. That's reasonable because in this region (and almost all of regions) fluctuations of wind are more than the fluctuations in radiation, so, when the wind turbine is used, we needed to add more storage system to be sure that the load would be met in all steps. Also, in this region, the peak load is nearer to the peak of PV generation compared with the peak of wind generation. On the other hand, Because of this, the reliability index in the system with wind turbine is less than the system with PV array and subsequently, because of increase in costumer's dissatisfaction cost, the cost of the system with wind turbine is more than the system with PV array.

In any of the scenarios, the reliability constraint is not activated and each scenario will be able to satisfy the inequality constraints without penalty cost. As mentioned before, it is possible to analyze each point of the results to investigate the relation between changes of wind, solar radiation and load with ELF index and charging and discharging states of batteries.
