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3. Sizing of Hybrid PV/Batteries Bank/Diesel Generator System 271

inertia weight is assumed to decrease linearly from w max value to w min value as
described in the following equation:
t
t
w ¼ w min þðw max w min Þ (8.26)
max iter
In [23], a tightening coefficient c is introduced to improve the convergence of the
optimization process. This technique is known as constriction PSO (CPSO). The ve-
locity vector equation becomes:

v tþ1 ¼ c v t i; j þ 4 r t pbest t i; j x t i; j
1 1i; j
i; j
(8.27)

t t t
þ 4 r gbest x ; j˛f1; 2; .ng
2 2i; j i; j i; j
where c is the constriction coefficient defined as:
2
c ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (8.28)
2
4 2 þ 4 44
where 4 ¼ 4 þ 4 , 4 > 4. Typically, 4 ¼ 4:1 and 4 ¼ 4 ,so c ¼ 0.7298844.
2
1
1
2
3.2.5 Simulation Result and Discussion
A standalone hybrid PV/batteries bank/DG renewable energy system has been
designed to supply the load of a house in a remote area in Tunisia, which is off-
grid connected. The structure of the house and its load are assumed similar to
what is described in Section 3. PSO algorithm has been used to optimally size the
hybrid energy system. The PSO algorithm is coded using Matlab software. The
average daily load of the house investigated is shown in Fig. 8.7B, which represents
the maximum daily load. It is assumed that the solar irradiation and the load power
are constant during each hourly time interval. Figs. 8.9 and 8.10 show the sun solar
radiation and ambient temperature in Tunisia in the month of March.

FIGURE 8.9
Sun irradiation in Tunisia for an arbitrary day in March.