J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
timization in system model, a nd the va riat ions o f the sig-
nificant design variables is needed to investigate the
usefulness of these simulation and optimization tools
applied to specific applica tions.
The paper proposes a procedure based on genetic al-
gorithms (GA) to get global optimum capacity of PV
array and battery in a SPV system under compromise
between the reliability and to tal installed c ost. Compared
with t he co n ve nt io na l Lagrangian relaxatio n op ti mization,
GA approach finds the global optimum more efficiently.
The sensitivity analysis for the component cost and load
profiles were also discussed to show the impacts of the
optimal results of planning. The optimal sizing of a SPV
system incorporating solar resources uncertainty is also
considered in the aspects of long-ter m pla nning. The real
solar radiation/temperature data from four weather sta-
tions have been tested to simulate the practicability of
planning resul ts for a SPV system.
2. The Optimal Design Method
In the design and planning of stand-alone renewable en-
ergy systems, the optimal sizing is an important and
challenging task as the coordination among renewable
energy resources, generators, storage capacity and it’s
complicated load.
2.1. System Modeling
A SPV system consists of solar array, battery bank, con-
trol and power converting components. The PV-array
convert’s s un light into DC electricity. PV array is made
up of several interconnected PV modules. The batteries
store the electrical energy for use when needed. The
block diagram of the proposed system is shown in Fig-
ure 1.
2.2. The Reliability Analysis of a SPV
Generation
To access the available solar generation of a PV system
in candidate regio n is one of the most impor tant parame-
ters before installation. Because of the intermittent solar
radiation characteristics, which highly influence the re-
sulting energy production, reliability analysis has been
Solar ArrayDC/DC
Converter DC/AC
Inverter
Control of Charge
and discharge
Battery AC
Load
PV
current
Load current
(AC)
Battery current
Figure 1. Block diagram of the SPV system.
considered as an important step in any planning and de-
sign process. In the paper, the reliability index evaluated
is the total loss of load hours (LOLH) which is the sum-
mation of loss of load expectation events expressed in
hours over a specified time (usually one year). At these
time, a SPV system is unable to meet the load require-
ments due to lack of power at an in stant.
LOLH is a feasible measure to sys tem pe r fo r manc e fo r
assumed or known load distribution. Zero LOLH means
that the load will always be satisfied. Larger LOLH im-
plies the customer will be suffered from a higher proba-
bility of losing power. It is a popular demand side index
in the syste m pla nning. LOLH can be de fined b y the fol-
lowing equatio n:
24
11(, )
n
ij
LOLHf i j
= =
=∑∑ (1)
min
min min min
min min
0( (, )(, ))
(,)
(, )1(, )(,1)
(,)
1( (, )(, ))(,1)
ifSij LijS
Sij S
fijifSijS andSijS
Li j
if SijLijSorSijS
−≥
−
= −>−>
− <−<
where
S(i,j): the capacity state of BTY in the ith day- jth
hour,
L(i,j) : the consumed load in the ith day- jth hour ,
f(i,j) : system shor tage in the ith day- jth hour s,
Smin : Minimum battery discharge capacity.
The amount of solar radiation determines the current
output of a PV generation. After considering load profile,
the out put po wer of a PV generation can be conducted to
evaluate the charge/discharge current Ib of BTY. Two
main directio ns of Ib lead to different operation modes of
SPV: positive Ib is the mode of PV generation greater
than load consumption, while negative Ib induced by the
shortage of a SPV generation. At this mode, the state of
charge and minimum battery discharge capacity of BTY
should be integrated to calculate the LOLH. The Sum-
mary of a LOLH table over a specified time (one year)
associated with different combinations of PV/BTY ca-
pacity allocations, i.e. specific reliability constrain, can
be constructed to form the constrained optimization.
2.3. The Cons t r ai n ed Optimization Formulation
The optimal size problem of a SPV system belongs to a
constrained optimization. The optimum achieves at the
best compromise betwe en system power reliability and
cost. The objective function of the proposed system can
be expressed as the installed cost:
(2)
where
C : the total cost for installed a SPV system,
Ci : the initial cost fo r system i ns tallation,