Economic and Feasibility Analysis for Stand–alone Solar Photovoltaic Generation System

doi:10.4236/epe.2013.54B069

Paper Menu >>

Journal Menu >>

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)

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: [email protected], [email protected]

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

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

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:

11(, )

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

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

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

1.5

2.5

x 10

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

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

2000 3000 4000 5000 6000 70008000

0.5

1.5

2.5

x 10

BTY (Wh)

PV (W p)

LOLH 0

LOLH 10

LOLH 20

LOLH 50

LOLH 100

LOLH 150

LOLH 200

LOLH 400

(b) Tainan

4000 6000 800010000 12000

0.5

1.5

2.5

3.5

4.5

5x 10

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

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

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

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

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

361

0.5 11.5 2

x 10

2500

3000

3500

4000

x 10

BTY (Wh)

PV (Wp)

Total cost (US$)

1.8 1.9 22.1 2.2

x 104

3400

3600

3800

4000

x 104

BTY (Wh)

PV (Wp)

Total cost (US$)

1.851.9 1.95 2

x 10

4850

4900

4950

5000

x 10

BTY (Wh)

PV (Wp)

Total cost (US$)

22.2 2.4 2.6

x 10

6200

6400

6600

6800

x 10

BTY (Wh)

PV (Wp)

Total cost (US$)

2.8 2.9 33.1

x 10

7900

8000

8100

8200

x 10

BTY (Wh)

PV (Wp)

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

(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

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.

REFERENCES

[1] J. J. Hwang, “Promotional Policy for Renewable Energy

Development in Taiwan,” Renewable and Sustainable

Energ y Reviews, Vol. 14, No. 3, 2010, pp. 1079-1087.

doi:10.1016/j.rser.2009.10.029

[2] R. Hara, et al., “Testin g the Technologies: Demonstration

Grid-connected Photovoltaic Projects in Japan,” IEEE

Power and Energy Magazine, Vol. 7, No. 3, May/June

2009, pp . 77-85.

[3] W. X. Shen, “Optimally Sizing of Solar Array and Bat-

tery in Standalone Photovoltaic System in Malaysia,”

Renewable Energy, Vol. 34, No.1, 2009, pp. 348-352.

doi:10.1016/j.renene.2008.03.015

[4] G. B. Shrestha and L. Goel , “A Study on Optimal Sizing

of Stan d-alone Photovoltaic Stations,” IEEE Transactions

on Energy Con ver sion, Vol.13, No. 4, 1998, pp.373-378.

doi:10.1109/60.736323

[5] S. B. Borowy and Z . M. Salameh, “Methodology for Op-

timal Sizing of the Combination of a Battery Bank and

PV Array in a Wind/PV Hybrid System,” IEEE Transac-

tions on Energy Conversion, Vol. 11, No. 2, 1996,

pp.367-375.

[6] Jose L. Bernal-Agustin and R. Dufo-Lopez, “Simulation

and Optimization of Stand-alone Hybrid Renewable

Energy Systems,” Renewable and Sustainable Energy

Reviews, Vol. 13, No. 8, 2009, pp. 2111-2118.

[7] RETS, 2004. Available:

http://www.retscreen.net/ang/t_software.php

[8] RERL, 2007. Available:

http://www.ceere. org/rerl/projects/software/hybrid2/Hy2_

users_manual.pdf.

[9] Homer, The Hybrid Optimization Model for Electric Re-

newable, Available:

http://www.nrel.gov/homer/includes/downloads/HOMER

Brochure_English.pdf.

[10] J. Holland, Adaptation in Natural and Artificial Systems:

The University of Michigan. 1975

[11] P. Arun, R. Banerjee and S. Bandyopadhyay, “Optimal

sizing of Photovoltaic Battery Systems Incorporating

Uncertainty through Design Space Approach,” Solar

Energy, Vol. 83, No.7, 2009, pp.1013-1025.

doi:10.1016/j.solener.2009.01.003

[12] Y. X. Hong, Z. Wei, L. Lin and F. H. Zhao, “Opimal

Sizing Method for Stand-alone Hybrid Solar-wind Sys-

tem with LPSP Technology by using Genetic Algorithm,”

Solar Energy, 2008, pp. 354-367.