Energy and Power E ngineering, 2013, 5, 356-362
doi:10.4236/epe.2013.54B069 Published Online July 2013 (http://www.scirp .o rg/journal/epe)
Copyright © 2013 SciRes. EPE
Economic and Feasibility Analysis for Stand–alone Solar
Photovoltaic Generation System
Jeeng-Min Ling, Ping-Hsun Liu
Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiw an, China
Email: jmling@mail.stust.edu.tw, liushen@mail.njtc.edu.tw
Received April, 2013
ABSTRACT
The paper presents a feasibility computing approach to solve the optimal planning problem applied to Stand-alone Pho-
tovoltaic (SPV) system by considering the reliability requirement and economical performance. Evaluation technique
based on genetic algorithm to get global optimum capacity o f solar array and battery in a SP V syste m is more efficient-
ly. Explicit strategy selects proper values of systems' parameters improving local exploration and avoiding trapped in
local optimum. Different requirements of system reliability are investigated to achieve the optimal planning of a SPV
syste m. Sensit ivity analysis of components' cost and load pr o files are conducted to demonstrate the impacts of system
uncertainty. The solar radiation and temperature data from the Central Weather Bureau of Taiwan at fou r different loca-
tions were used.
Keywords: Genetic Algorithms; Reliability; Opti mizatio n; Photo voltaic Systems
1. Introduction
Taiwan is located in the subtropical area and possesses
excellent solar radiation for photovoltaic applications.
Some new demonstration photovoltaic systems were in-
stalled on public buildings, such as the World Games
2009 Kaohsiung (1 MWp) and the National Museum of
T aiwa n Hi story (195 KWp) etc. The government contin-
ues to promote the installation of solar photovoltaic sys-
tems through several projects, such as “Solar Top pro-
ject”, “Solar community Project” and “Solar Campus
Project”. It is believed that the installation capacity of
solar photovoltaic systems will be boosted by the “Re-
newable Energy Development Bill” for future comer-
cial applic a tions [1].
SPV systems are becoming increasingly viable and
cost-effective candidates for providing electricity to re-
mote and offshore islands areas which operate at low
capacity factors and where the gird extension is difficult
and not economical. Issues concerning the security of
supply and volta ge rising in the micro-grid underline the
need of storage system, like a stand-alone system, are
becoming increasingly viable recently [2]. The planning
of such an electrification unit requires an estimation of
the capacities of photovoltaic (PV) module and battery
(BTY) to satisfy a given load demand.
Some studies on sizing of the SPV system were stud-
ied [3-6]. The sizing method based on energy generation
simulation for various numbers of PV and BTY capacity
(18 configurations) was presented using suitable models
for the system devices [4]. The selection of the alloca-
tion of PV and BTY under corresponding reliability in-
dices, the loss of load hours (LOLH) and the loss energy,
should be considered the stochastic nature of both the
radiation and the load demand. Based on the Borowy’s
and Salameh method [5], the system operation is simu-
lated for various combination of PV and BTY sizes and
the loss of power supply (LPSP) is calculated for each
combination. For the desired LPSP, the PV versus BTY
size are plotted to get the optimal solution, which mini-
mizes the total system cost from the point on the sizing
curve.
Several software tools are available for the design of
stand-alone renewable energy systems [6-9]. The RET
Screen International Clean Energy Decision Support
Centre in Canada developed a decision making tool, RET
Screen, to help planners to implement renewable energy
and analyze the technical a nd financial viability of po ssi-
ble projects [7]. Hybr id 2 developed by the National Re-
newable Energy Laboratory in USA performs the de-
tailed time series simulat ion of hybrid renewable systems
[8]. The most popular simulation tool, Hybrid Optimiza -
tion Model for Electric Renewable (HOME R) [9], uses
hourly simulation to achieve optimal sizing of isolated
renewable system. Most of the available software tools
only identify and si mulate a single design option; a range
of possible design option is unavailable [6]. F urther-
mor e, the impacts on the effects of non-linearity and op-
J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
357
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:
wb i
CCPV CBTY C= ×+×+
(2)
where
C : the total cost for installed a SPV system,
Ci : the initial cost fo r system i ns tallation,
J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
358
PV, BTY: the capacity of solar array and battery,
CW,Cb : the unit cost of PV ($/Wp) and BTY ($/Wh).
Constraint function ha s be en p ro duce d for eight values
of LOLH, 0, 10, 20, 50, 100, 150, 200 and 400 hours, in
terms of the given load consumption. Different require-
ment of s ystems' reliabilit y can be evaluated by selecting
the suitable simulation range of PV and BTY capacity. It
is significa nt for a SPV planner to get options under dif-
ferent s ystem shor ta ges .
2.4. Optimization Technique using GA
Genetic algorithm (GA) is an population based search
and optimization technique. It has been developed to
imitate the process of natural evolutionary of genetics
[10,11]. GA takes selection, crossover and mutation to
imi- tate evolution processes. The selection eva luation i s
to d eter mine the cho sen c hro mo some, each chro moso me
consists of two genes. Specific values of LOLH with
allocation of PV and BTY in a LOLH table pass the se-
lection evaluation via the fitness cost function. If the
evaluation of qualified chromosome has a lowest total
cost of a SPV system than the cost obtained at the previ-
ous iterations, the size of PV/BTY allocation was con-
sidered to be the optimal solution for the constrained
optimization in this iteration. The optimal solution will
be replaced by better solution, if any, produced in next
GA generations [12]. The optimal solution will then be
sub- ject to the process of crossover and mutation, it
produces the next generation have been reached. The
iteration will continue when convergence c riterion satify.
The flo wchart of the opti mization pr ocess is illu strated
in Figure 2. If any of the initial population chromosomes
violates the system constraint, it is replaced by a new
chromosome. The PV array current output is calculated
according to the PV system model by using the specifi-
cations of the PV module, ambient temperatures and so-
lar radia tion conditions. T he battery capacit y is permitted
to discharge up to a limit defined by the maximum depth
of di scha r ge , which is speci fied by the s yste m desig ner at
the beginning of the optimal capacit y process.
The GA was implemented by Matlab® and employed
the operators of roulette-wheel selection, single-point
crosso ver , si ngle-bit mutatio n, and elite r eplace ment. The
following par ameters are used in the GA simulatio n,
The populatio n size: 200
Generation: 50
Mutation rate: 0.01
3. Analysis of Reliability Simulation
The optimal size of a SP V system at four selected sites of
weather station in Taiwan were investigated and com-
pared. The combination of different PV/BTY capacity
has 3200 various states to evaluate each degree of LOLH
per year. Using the real meteorolo gical data of year 2008
at Tainan weather station, the possible combination of
PV/BTY size associated with different LOLH values can
be depicted by the three dimensional (3D) curve shown
in the Figure 3(a). Eight specified values of LOLH (0,
10, 20, 50, 100, 150, 200 and 400 hours) are selected and
depicted by eight curves in the two dimensional (2D)
distribution with d ifferent colors in Figure 3(b).
Initial guess
Constraints evaluation
and chromosome repair
Meteorological yearly data
Solar radiation
temperature
Solar array model
Battery model
Optimal
result
Selection
Crossover and Mutation
New Generation of
Configuration
Yes
No
Fitness function evaluation
Global optimum Reached ?
Load profile input
Figure 2. Flowchart of the optimal sizing model using G A.
(a) 3D dis tr ibutio n
20003000 40005000 60007000 8000
0.5
1
1.5
2
2.5
3
x 10
4
BTY (Wh)
PV (W p)
LOLH 0
LOLH 10
LOLH 20
LOLH 50
LOLH 100
LOLH 150
LOLH 200
LOLH 400
(b) 2D distribution
Figure 3. Reliability curves for different combinations of
PV/BTY capacity with diff erent LOLH values at Tainan.
J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
359
Each 2D curve indicates the trend of PV/BTY size
changing with a constant system shortage. The different
combinations of PV/BTY capacity which meet the same
reliability degree of power supply can be expressed by
plotting the 2D trad e -off curve. In these 2D trad e-off
curves, the upper most curve belongs to LOLH = 0,
while the lowest curve occurs when the system shortage
hour i s 400 hours.
The optimal size of a SPV system can be affected the
location because of different solar radiation. In order to
clarity the influence of location, the meteorological data
from four different weather stations in the Central
Weather Bureau of Taiwan were simulated. Figure 4
shows these results.
1000 1500 20002500 3000 3500 4000
2000
4000
6000
8000
10000
12000
14000
16000
BTY (Wh)
PV (W p)
LOLH 0
LOLH 10
LOLH 20
LOLH 50
LOLH 100
LOLH 150
LOLH 200
LOLH 400
(a) Chiayi
(b) Tainan
4000 6000 800010000 12000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
4
BTY (Wh)
PV (W p)
LOLH 0
LOLH 10
LOLH 20
LOLH 50
LOLH 100
LOLH 150
LOLH 200
LOLH 400
(d) Dongj itao
0.4 0.6 0.8 11.2 1.4 1.6
x 10
4
1
2
3
4
5
6
x 10
4
BTY (Wh)
PV (W p)
LOLH 0
LOLH 10
LOLH 20
LOLH 50
LOLH 100
LOLH 150
LOLH 200
LOLH 400
(f) Anpu
Figure 4. PV/BTY curves for different LOLH degree at
four locations for Actu al load.
Using the eight LOLH curves shown in Figure 4, the
influence of LO LH on the planning of PV/BTY capacity
of a SP V s ys te m ca n be ide nti fied. Considerable installed
PV and BTY capacity reductions occur as LOLH varies
from 0 to 400 hour. T he Anpu site which has the poorest
solar radiation among these four tested sites causes the
installed capacity of PV/ BTY to be very large. On the
other side, the sites at C hiayi and Tainan characterize a
much richer solar radiation result implying to a smaller
installed capacity.
The LOLH curve shown in Figure 4 can be roughly
divided into two blocks. In the left/vertical block, in-
creasing of smaller PV installed capacit y lead to a re-
markable BTY capacity reduction, especially at the site
of Anp u. In the right/horizontal block, the BTY capacity
decreases gradually with larger increasing of PV installed
capacity. The optimum occurs at the turning point of a
LOLH curve, i.e. the overlapping part of these two
blocks.
Analysis of the relationship of PV/BTY capacity in
terms o f LOLH can determine the optimal capacity allo-
cation status. Due to the unit cost of a PV component is
much larger than that of BTY, the total installation cost
of PV significantly dominates the final optimal cost. A
system with a large PV size and small BTY size can be
prone to quite fast charging/discharging of the batteries.
For this case, the reliability of system would be largely
dependent on the solar radiation alone. Such design ex-
poses the system to instantaneous variations in the solar
radiation. Even though the LOLH can be reduced by
providing a larger PV size, the degree of LOLH may be
quite high depending upon the radiation characteristics.
On the other side, a system with a small PV size and
large BTY size will result in slo wer charging/discharging
rates in the batteries. Most of the converted energy will
be stored when the instantaneous generation is in excess
of the load. This LO LH in the d esi gn may be large due to
a small solar array size.
4. Analysis of Optimal Sizing Simulation
4.1. Influence of Different Load Profile and
Reliability Requirement
The proposed optimal algorithm was implemented by
Matlab. The real solar radiation/temperature data from
the central weather Bureau of T aiwan on the year 2003 to
2009 have been simulated. The influences of four differ-
ent load profiles, constant, peak, sinusoidal and actual
load, are investigated. It is noted that the actual load is
the power profile of a laboratory located at the A build-
ing of Southern T aiwan Universit y of Science and Tech-
nology shown in Figure 5. Daily average of the actual
load for testing is 10.68 kW. Using this value as the
benchmark, three other load profiles, constant, peak and
J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
360
sinusoidal, can be evaluated to investigate the impacts
result from different load profiles during SPV system
planning. This optimal result of PV/BTY corresponds to
the fol lowing hours o f s yst e m sho rt age , e . g., 0 , 10 , 20, 5 0,
150, 200 and 400 as shown in Table 1.
It can be found that the optimal cost for installation is
sensitive to the desired system reliability. The installed
cost of a SPV system will increase to meet the desired
higher system reliability requirement, i.e., LOLH is in-
versely proportional to system cost. As for the influence
of load profile, we can verify the phenomenon that the
installation cost of a SPV implemented in actual load is
lower than other three load types at four testing sizes
because of the diversity of load profile. The highest cost
often occurs in the sinusoidal load, it concentrates the
load consumption in one half of period time.
Influence of locations to the optimal cost can be con-
cluded by the characteristics of solar radiation. Chiayi
region has the lo west total installation cost with its good
solar radiation and ambient temperature average.
Conversely, Anpu has the highest installed cost com-
pared with other regions for the same reason.
01000 2000 3000 40005000 6000 7000 80009000
0
20
40
60
80
100
120
Hour
Load (kW)
Figure 5. Hourl y profile of testing load.
Table 1. The o ptimal size of a spv at 4 sites under four dif feren t l oad pat t e r ns.
(a) Chiayi
Chiayi Fixed load Peak load S i nu s o idal load A c t ua l load
LOLH
(hours ) PV (Wp) BT Y (Wh) C ost (USD) PV (Wp) BTY ( Wh) Cos t (U SD) PV (Wp) BTY ( Wh) Cost (USD) PV (Wp) BTY (W h)
Cost (U SD)
0 3913.7 12612.4 21505.2 3909.5 15114.2 21971.9 3910.0 13778.2 21714.1 2871.5 11397.0 16195.7
10 3896.4 11702.7 21243.6 3893.0 14864.1 21842.6 3884.5 13380.2 21512.5 2824.1 10788.8 15846.7
20 3945.1 9107.1 20975.3 3865.5 14934.8 21722.6 3875.9 12791.9 21356.1 2748.2 10320.1 15386.0
50 3783.6 8767.5 20123.2 3735.6 14996.6 21102.6 3782.1 9367.0 20232.5 2495.4 9982.8 14089.6
100 3462.9 10170.2 18835.1 3753.0 8606.3 19942.7 3243.2 11375.0 18000.6 2240.5 8413.8 12543.7
150 3145.3 10998.3 17450.6 3442.0 9359.4 18575.7 2916.8 8865.8 15923.1 2145.9 6488.5 11708.3
200 2900.0 10225.6 16106.3 3369.9 7420.5 17847.3 2647.5 8786.2 14597.1 2065.2 3364.7 10707.0
400 2427.1 4377.9 12665.7 2580.6 2625.2 13072.0 2016.1 3423.9 10479.9 1602.7 2501.0 8287.8
(b) Tainan
Tainan Fixed load Peak load Si nus oidal load Ac t ual load
LOLH
(hours ) PV (Wp) BTY (Wh) C ost (USD) PV (Wp) BTY (W h) Cos t (U SD) PV (Wp) BTY (W h) Cos t (U SD) PV (Wp) BTY ( Wh) Cos t (U SD)
0 3558.5 18036.9 20832.3 3655.0 21556.7 21987.3 3606.2 18716.9 21196.9 3515.0 21456.0 21286.1
10 3587.0 16118.5 20597.4 3715.6 16879.3 21371.3 3600.4 18103.3 21049.2 3409.3 20956.6 20674.3
20 3618.5 15421.0 20615.2 3622.7 15629.5 20676.1 3657.9 14596.0 20646.4 3298.9 20789.3 20104.6
50 3528.6 13967.3 19894.3 3663.4 15284.7 20806.8 3568.9 14185.0 20133.0 3247.2 19599.6 19621.3
100 3454.4 13122.1 19368.5 3620.8 16108.7 20760.2 3481.0 13112.4 19496.1 3290.9 15090.1 18955.8
150 3375.4 12404.8 18844.5 3612.0 14715.7 20446.0 3386.1 12291.3 18874.3 3165.1 15155.8 18356.3
200 3281.8 12314.1 18371.3 3455.8 17170.2 20163.7 3280.0 11758.9 18254.6 3027.5 15792.7 17810.7
400 3060.4 10631.6 16966.2 3262.9 14874.9 18777.7 3014.3 10708.7 16756.8 2946.3 10736.0 16431.2
(c) Anpu
A npu Fixed load Peak load S inu s oidal load A ctual load
LOLH
(hours ) PV (Wp) BTY ( Wh) Cos t (U SD) PV (Wp) BTY (Wh) Cost (USD) PV (Wp) BTY ( Wh) Cost (US D) PV (W p) BT Y (Wh) Cos t (US D)
0 15589.1 71962.0 89888.9 15589.1 71962.0 89888.9 15602.5 74994.8 90544.3 7777.5 31230.7 43936.6
10 15416.4 70954.2 88851.8 15416.4 70954.2 88851.8 14921.4 70978.2 86447.4 7473.5 29880.6 42194.1
20 15164.4 71332.6 87699.1 15164.4 71332.6 87699.1 14806.9 70079.7 85714.7 7210.6 29149.6 40771.9
50 13538.2 63854.2 78327.6 13538.2 63854.2 78327.6 13600.8 64959.3 78847.5 6697.7 38271.3 40051.4
100 12301.0 56919.5 70955.4 12301.0 56919.5 70955.4 12290.6 56019.9 70730.0 6395.1 35393.9 38018.4
150 11729.7 42473.4 65362.0 11729.7 42473.4 65362.0 11284.0 46565.0 63989.4 5923.7 40131.1 36646.0
200 11053.5 35342.3 60682.3 11053.5 35342.3 60682.3 10485.3 35775.6 58001.1 6152.1 33338.1 36435.4
400 7552.1 43976.5 45321.1 7552.1 43976.5 45321.1 6849.1 40783.1 41277.6 5594.9 31115.5 33290.4
J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
361
0.5 11.5 2
x 10
4
2500
3000
3500
4000
0
1
2
3
4
x 10
4
55
50
60
45
40
30
35
25
20
BTY (Wh)
15
10
PV (Wp)
5
Total cost (US$)
1.8 1.9 22.1 2.2
x 104
3400
3600
3800
4000
0
1
2
3
4
5
x 104
60
50
45
55
40
35
30
25
20
15
BTY (Wh)
10
PV (Wp)
5
Total cost (US$)
1.851.9 1.95 2
x 10
4
4850
4900
4950
5000
0
2
4
6
8
x 10
4
60
55
45
40
50
35
30
25
BTY (Wh)
20
15
10
PV (Wp)
5
Total cost (US$)
22.2 2.4 2.6
x 10
4
6200
6400
6600
6800
0
2
4
6
8
x 10
4
60
50
55
45
40
35
30
25
20
15
BTY (Wh)
10
PV (Wp)
5
Total cost (US$)
2.8 2.9 33.1
x 10
4
7900
8000
8100
8200
0
2
4
6
8
10
x 10
4
55
60
50
45
40
35
30
25
20
15
BTY (Wh)
PV (Wp)
10
5
Total cost (US$)
(a) Chiayi (b) Tainan (c) Tawu (d) Lanyu (e) Anpu
Figure 6. The optimal sizing curve with different ratio of to PV/BTY cost ( LOLH=0, the actual load).
Table 2. T he optimal sizing res ults with different ratio of pv/bty cost under actual load.
Cost
ra tio
Chiayi Tainan Tawu Lanyu Anp u
PV
(Wp) BTY
(W h) Cost
(US$) PV
(Wp) BTY
(W h) Cost
(US$) PV
(Wp) BTY
(W h) Cost
(US$) PV
(Wp) BTY
(W h) Cost
(US$) PV
(Wp) BTY
(W h) Cost
(US$)
5 3517.6
6449.5 4680.0 3838.9 18422.0
7323.7 4968.3 18767.0 8490.4 6622.6 20479.9 10434.3 8161.1 28403.0 13474.5
10 2984.2
10286.6 7812.9 3793.9 18724.6
11032.2 4911.9 19164.4 13294.5 6309.2 22826.6 16727.9 8161.1 28403.1 21419.2
15 2940.5
10811.2 10692.3 3558.2 21411.6
14560.3 4897.9 19337.0 18068.8 6266.4 23335.2 22843.8 7968.7 30737.6 29256.4
20 2668.9
15830.1 13474.3 3556.3 21446.6
18023.3 4892.2 19436.4 22833.7 6253.6 23552.2 28936.5 7967.7 30755.3 37013.3
25 2667.9
15850.9 16071.9 3556.0 21453.5
21485.2 4888.8 19510.5 27594.3 6246.3 23714.7 35020.2 7967.3 30764.4 44769.4
30 2666.6
15884.1 18668.1 3555.5 21465.9
24946.5 4887.4 19548.5 32352.6 6243.2 23800.8 41099.3 7966.8 30777.5 52524.9
35 2666.7
15881.7 21264.1 3555.3 21473.4
28407.5 4885.6 19606.5 37109.4 6240.8 23878.9 47175.7 7966.6 30784.3 60280.3
40 2665.8
15911.3 23858.7 3555.2 21475.3
31868.4 4884.9 19635.0 41865.2 6239.2 23938.3 53250.3 7966.5 30786.8 68035.5
45 2665.3
15934.8 26453.5 3554.9 21488.1
35329.0 4884.4 19656.2 46620.3 6237.6 24008.3 59324.0 7966.3 30792.8 75790.6
50 2665.1
15945.1 29048.2 3554.8 21493.7
38789.6 4885.1 19627.2 51376.1 6237.2 24030.6 65396.4 7966.3 30795.5 83545.6
55 2664.6
15981.7 31645.0 3555.0 21484.2
42250.3 4884.0 19675.0 56129.4 6237.6 24010.2 71468.4 7966.3 30797.7 91300.6
60 2665.1
15944.2 34237.0 3554.7 21497.3
45710.7 4883.3 19713.2 60883.2 6236.6 24065.2 77539.5 7966.3 30797.5 99055.5
4.2. Influence of Component Cost Variations
The variations of component cost for a PV system is un-
cer tain. In this st ud y, the unit cost of a PV is set to be the
range of 4.67~5.61 (USD/Wp) , and a BTY is 0.093~
0.280 (USD/Wh). The base cost of BTY capacity is set to
0.1947 (USD/Wh) for demonstration. A feasible range of
cost ratio will be tested b y 5~60, it ca n be represented as
the ratio of Cw to Cb shown in equation 2.
12 discrete values of cost ratio changing from 5 to 60
with increment 5 were used to show its effects. The fol-
lowing simulation is derived from LOLH equals to 0.
The optimal size in terms of different component cost
ratios are depicted in Figure 6 and Table 2. As sh o wn i n
Figure 6, the optimal size of PV and BTY is insensitive
to the changing of cost ratio when its value greater than
10 to 15. It is believed that the value of cost ratio to be
smaller than 2 0 is unreasonable. I n so me sen ses, it mea n s
explicitly the robust of the optimal results regardless of
price fluctuation. On the other side, a installed cost in-
crease proportionally when the cost ratio grows.
Results show the optimal result regional dependence.
Different pattern of optimal size appears in different re-
gion. The highly regional feature for the planning of a
renewable system should be identified. Challenge from
volatility and spatia l d iversit y o f solar re source is anot her
issue. The optimal size of a SPV system is obviously
reduced when the quality of the solar resources increas-
ing.
5. Conclusions
At different regions with various meteorological condi-
tions and solar energy reserves, the electric power pro-
duction from renewable energy is highly unreliable and
unpredictable. Well-designed system is a basic require-
ment for any system planner. In the paper, Different re-
quirements of system reliability are conducted statistic-
cally to achieve the optimal capacity allocation for a SPV
system. Var iations resulted from the cost of SPV com-
ponent and load amount are investigated to satisfy the
specific reliability requirement to demonstrate the im-
pacts of system uncertainty in the long-term plannin g.
The optimal size of a SPV system is found eff iciently
by a GA optimization technique. Global optimum with
relative computation simplicity has been attained. The
simulation resul ts of this paper is believed to be a worthy
reference for decision-making can be considered as im-
J.-M. LING, P.-H. LIU
Copyright © 2013 SciRes. EPE
362
portant references of the photo voltaic generatio n installa-
tion.
6. Acknowled gements
The authors would like to thank the financial support of
National Science Council under grant number NSC-
101-2221-E-218-043.
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