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3. Sizing of Hybrid PV/Batteries Bank/Diesel Generator System 269

of 20 years, and initial cost of the DG including used fuel cost. These costs are
implemented in the following set of equations:

(8.17)
cost PV ¼ðcost of investement þ 20 cost of maintenanceÞ N pv
cost battery ¼ðcost of investement þ y cost of investementÞ N bat (8.18)

cost DG ¼ C DE þ C oil þ C fuel (8.19)
where y represents the number of battery replacements during 20 years of system
operation, C DE is the capital cost of the DG, C oil is the cost of lubricating oil
used in the DE, and C fuel is the cost of diesel fuel consumed.

3.2.2 Optimization Constraints
The following set of constraints is used in the sizing optimization process of the
hybrid PV/batteries bank/DG renewable energy system:

7kW P d 15 kW (8.20)
55 N pv 66 (8.21)
6 N bat 10 (8.22)

LLP ¼ 0 (8.23)
These ranges give the best performance in the optimization process. The choice of
each range affects the conversion of the optimization algorithm and the obtained re-
sults. The optimization algorithm was executed many times and the results of each
run were used in determining the ranges of each parameter that gives best hybrid en-
ergy system size.

3.2.3 Methodology
PSO algorithm is used to optimally size the hybrid PV/batteries bank/DG renewable
energy system. The optimization process is achieved for both minimum overall sys-
tem cost and pollution criteria. Typically, PSO algorithms do not always guarantee
optimal solution. In fact, achieving algorithm conversion and optimal solution de-
pends mainly on the chosen range of each part used in the hybrid system. In addition,
the final achieved solution depends on the used optimization strategy for the hybrid
system.
The strategy used in the optimization process consists of three phases. The first
phase is introduced to size both the PV panels array that supplies the load during the
daytime and the batteries bank that supplies the load when produced PV power is not
sufficient to meets the load needs especially during sunset and sunrise. In this step,
the optimal numbers of PV panels and batteries are found. Typically, the number of
PV panels should be maximized, while the number of batteries should be minimized