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Probabilistic optimal sizing of stand-alone PV systems with
modeling of variable solar radiation and load demand
Ng, SKK; Zhong, J; Cheng, WM
The 2012 IEEE Power and Energy Society General Meeting, San
Diego, CA., 22-26 July 2012. In IEEE Power and Energy Society
General Meeting Proceedings, 2012, p. 1-7
2012
http://hdl.handle.net/10722/153086
IEEE Power and Energy Society General Meeting Proceedings.
Copyright © IEEE.
1
Probabilistic Optimal Sizing of Stand-Alone PV
Systems with Modeling of Variable Solar
Radiation and Load Demand
Simon K. K. Ng, Student Member, IEEE, J. Zhong, Senior Member, IEEE, and John W. M. Cheng,
Member, IEEE
Abstract—This paper presents a comprehensive sizing
methodology which could contain all key elements necessary to
obtain a practical sizing result for a stand-alone photovoltaic
(PV) system. First, a stochastic solar radiation model based on
limited/incomplete local weather data is formulated to synthesis
various chronological solar radiation patterns. This enables us to
evaluate a long-term system performance and characterize any
extreme weather conditions. Second, a stochastic load simulator
is developed to simulate realistic load patterns. Third, two
reliability indices, Expected-Energy-Not-Supplied (EENS) and
Expected-Excessive-Energy-Supplied (EEES), are incorporated
with an Annualized Cost of System (ACS) to form a new
objective function called an Annualized Reliability and Cost of
System (ARCS) for optimization. We then apply a particle swarm
optimization (PSO) algorithm to obtain the optimum system
configuration for a given acceptable risk level. An actual case
study is conducted to demonstrate the feasibility and
applicability of the proposed methodology.
Index Terms—Stand-alone PV system, sizing optimization,
Expected-Energy-Not-Supplied (EENS), load signatures, particle
swarm optimization (PSO).
W
I. INTRODUCTION
ith increasing emphasis on climate change and
sustainable development, renewable resources are more
widely used in power generation to reduce carbon emissions.
Among all renewable resources, solar energy is one of the
most abundant ones and photovoltaic (PV) technologies have
seen significant improvement in cost and performance in
recent years. Although PV technology is still costly, it has
become feasible and cost competitive in small-scale standalone system. Since solar energy is intermittent with diurnal
characteristics, energy storage such as a battery bank is
essential to act as a backup to ensure a reliable supply [1].
For sizing evaluation, there are two main types of
simulation scenario [2], namely chronological and analytical.
The former requires a time series data while the latter uses a
probability density function (pdf) to simulate the stochastic
characteristic of the renewable resources. The chronological
This work was supported by the HKU seed funding program for basic
research (project no. 200911159128) and CLP Power Hong Kong.
S. K. K. Ng and J. Zhong are with the Department of Electrical and
Electronic Engineering, The University of Hong Kong, Hong Kong (e-mail:
kkng@eee.hku.hk; jzhong@eee.hku.hk).
J. W. M. Cheng is with the CLP Research Institute Ltd., Hong Kong,
China (e-mail: john.cheng@clp.com.hk)
978-1-4673-2729-9/12/$31.00 ©2012 IEEE
simulation is used in this paper because it emulates system
conditions in a continuous time-line to enable detailed
evaluation of the batteries [3].
Accurate solar radiation data is one of the most important
parameters for the feasibility study of a PV project because it
is the main cause of failure/inadequacy in a stand-alone
system if all energies (generated and stored) are depleted [4].
Industrial PV sizing practice requires historical and measured
solar data on site. However, typical durations of measured data
are from a few months to a year which can only offer a limited
view to project its long-term performance. To enhance the
accuracy, modeling solar radiation using artificial neural
network (ANN) [5]-[7] and regressive model [8]-[10] has been
proposed but share different degree of limitations. In this
paper, we propose to use two commonly accessible weather
data, namely solar radiation and total rainfall, to synthesis
variable chronological solar radiation patterns.
On the demand side of the power balance equation, load is
also varying with time and common practices just use a
constant value (e.g. maximum). However, assuming a constant
load pattern may oversimplify the stochastic load nature. We
therefore propose a load simulator based on load signatures as
described in [11], [12] to generate a more realistic and
chronologically-based consumption pattern for our studies.
The optimum design of the system is mainly evaluated by
two objectives: reliability and cost. For reliability, a
commonly used index is Loss-of-Load-Probability (LOLP)
[2], [3], [13]. However, this index is not able to measure the
severity of the shortage period and neglect the excessive
energy that could not be captured by battery due to its
capacity. In order to incorporate these, the Expected-EnergyNot-Supplied (EENS) [14] and the Expected-ExcessiveEnergy-Supplied (EEES) are bundled with an Annualized Cost
of System (ACS) [3] to form a new objective function called
Annualized Reliability and Cost of System (ARCS) for the
optimization process.
Among various optimization techniques proposed to solve
similar sizing problem (e.g. probabilistic approach [14],
graphical construction method [13] and artificial intelligence
method [3], [7]), we propose to use a particle swarm
optimization (PSO) algorithm to obtain the optimum
configuration of PV modules and batteries because it is
generally recognized to be robust in finding global optimal
solutions, especially in multi-model and non-linear
2
optimization problems [15]. This paper is organized as
follows. Section II provides a mathematical formulation of
various system components. The modeling of meteorological
conditions is presented in Section III. Section IV presents a
probabilistic load simulator. Reliability and cost assessment
tools are given in Section V. A stochastic optimal sizing
optimization formulation and the use of PSO algorithm to
solve the problem are described in Section VI. Simulation and
results based on a case study is presented in Section VII and
finally the conclusion.
II. MODELS OF SYSTEM COMPONENTS
A stand-alone PV system mainly includes three
components: 1) PV array, 2) battery bank and 3) inverter. This
paper focuses on the system sizing in which the PV arrays and
the batteries are configured in parallel. When solar energy is
available, surplus PV energy will go into the battery until it is
fully charged. Conversely, the battery will be discharged to
meet the load if solar energy is inadequate or inexistent. This
section describes the mathematical formulations of the system
components.
A. PV Array Power Model
PV array is consisted of modules which are the basic power
conversion units. The number of PV modules is one of the
decision variables in our sizing problem because it determines
the total PV power output as shown in (1):
( )=
( )
; = 1,2, … ,
(1)
where
( ) is the total PV power output at time t in W;
( ) is the power output of PV module at time t in W; and
is the number of PV modules.
To determine the total PV power output, an accurate model
of PV module in terms of received solar radiation is necessary.
In this paper, a regression model is used [16] and formulated
as follows:
( )=
( )+
( ) +
( )
+
( ) ( ); = 1,2, … ,
( )
(2)
where ( ) is the solar radiation at time t in W/m2; ( ) is the
wind speed at time t in m/s;
( ) is the ambient
temperature at time t in oC; and
,
,
and
are
regression coefficients which can be estimated from measured
data.
B. Battery Bank & Inverter Model
A proper sized battery bank requires a detailed formulation
of charging and discharging processes and this can be
characterized by the State-Of-Charge (SOC) of the battery.
SOC at any time, says t, is related to the previous state of SOC
( ) as follows:
and to the battery power
( )=
+
( − 1) ∙ (1 − )
( )
∆
; = 1,2, … ,
(3)
where
( ) and
( − 1) are the SOC at time t and t–1,
respectively; is a self-discharge rate of the battery bank;
is a round-trip efficiency; ∆ is the time step;
is the
energy capacity of a single battery in kWh;
is the number
of batteries; and T is the simulation period. An initial
condition of the SOC, i.e.
(0), is set to be 0.8 in this
paper.
In order to prevent the battery bank from overcharging and
overdischarging, SOC is commonly used as a decision
variable of the bi-directional inverter with the following SOC
constraints:
≤
( )≤
; = 1,2, … ,
(4)
where
and
are the minimum and maximum SOC
values of the battery bank, respectively.
The sign of battery power
( ) can be positive or
negative depending on whether the battery bank is in charging
or in discharging modes as shown by following power balance
equation of the system:
( )=
( )−
( )
; = 1,2, … ,
(5)
where ( ) is the load demand at time t in W;
is the
inverter efficiency. Since there is a power conversion loss in
the bi-directional inverter, this efficiency loss is considered as
part of the load demand.
III. MODELS OF METEOROLOGICAL CONDITIONS
In this section, we provide a statistical method to synthesis
the meteorological conditions in a chronological manner. The
meteorological data include solar radiation, ambient
temperature and wind speed, which are required to determine
the power output of PV arrays.
A. Modeling of Solar Radiation
To generate the chronological solar radiation, we have to
consider two key elements: 1) weather for two consecutive
days and 2) profile of solar radiation for each day.
1) Weather for two consecutive days
The Markov chain model is widely used to simulate
different meteorological conditions such as solar radiation [17]
and wind speed [18]. We apply a first-order Markov chain
model with daily total rainfall as a variable to simulate the
daily weather sequences. The first-order Markov chain model
indicates that the next step only depends on the present state
and not on any earlier states.
In our study, the Hong Kong weather data from 2009 to
2010 are used to model the variations of daily weather
conditions. For simplicity, the daily total rainfall is
categorized into three states:
1) Sunny day (i.e. total rainfall = 0)
2) Light raining day (i.e. 0 < total rainfall ≤ 10 mm)
3) Heavy raining day (i.e. total rainfall > 10 mm)
With above categorization, the 3 × 3 daily transition
3
proobability matrrix
shown as followss:
,
=
,
deriived from the weather dataa is
0.80
= 0.36
0.16
0.19 0.01
0.58 0.06
0.67 0.17
(6)
Matrix in (6) contains the trransition probaabilities
from
ma
staate i at day d to a state j att day d+1. An
ny loss of load
d is
likkely to occur in a system if several heaavy raining days
d
haappen in a contiinuous mannerr.
In order to generate the daily weatherr sequences, the
folllowing proced
dures are propo
osed based on [18]:
[
1) A cumulativ
ve probability transition mattrix is obtain
ned
by summing
g cumulatively along each row
w of , ;
2) An initial staate, says i, is raandomly set;
r
value between 0 an
nd 1 is generaated
3) A uniform random
and comparred with the elements in row i of
to
determine th
he next state. If
I this number is larger than the
cumulative probability off the previous state but smaaller
qual to the cumulative
c
prrobability of the
than or eq
following state, the follow
wing state is dettermined to be the
next state;
mber of days are
4) Step 3 is reepeated until a desired num
generated in
n the simulation
n (e.g. 10,000 days).
d
s
radiation
n for each day
2) Profile of solar
With the daily
y weather statte generated ass above, the next
n
steep is to simulaate the daily prrofile of solar radiation. Table I
sum
mmaries the mean μ and standard deviiation σ of so
olar
ennergy for the three proposed
d weather states based on the
acttual data. In general, we can
n assume that the
t distribution
n of
solar energy for
fo each weaather state fo
ollows a norm
mal
g a
disstribution. Wiith the parameters of Tablee I and using
noormally distribu
uted random number
n
generattor, the stochastic
daaily solar energ
gy can be obtaiined for each state.
s
Then, baased
onn this value, an
n iterative pro
ocedure is used
d to simulate the
daaily profile of solar radiation.
TAB
BLE I
MEAN AND
D STANDARD DEV
VIATION OF WEATH
HER STATES
ndard deviation
Stan
Weather statte
Mean (k
kWh/m2)
(kWh/m2)
1) Sunny day
4.4
40
1.11
2) Light raining day
2.5
56
1.71
3) Heavy raining
0.45
g day
0.9
93
s
day, thee daily profilee of
We know thaat for perfect sunny
solar radiation looks like a Gaussian disttribution and the
hape) is arou
und
ennergy (which is the area under the sh
6.663kWh/m2 as shown
s
in Fig. 2.
2 If the presen
nt state is a sun
nny
daay, and the daily
d
energy is randomly assigned to be
5.553kWh/m2. By
y adding somee random flucctuations, we can
2
iteeratively curtaiil an area of 1.10kWh/m
1
in
n Fig. 2 to obttain
solar irradiancess at different times.
t
Fig. 3 shows
s
a seriess of
mulated solar radiation
r
profile.
sim
Fig. 2 Sollar radiation profilee for perfect sunnyy day
Fig. 3 Sim
mulated chronologiical solar radiationn
B. Moddeling of Ambieent Temperaturre
In thhis paper, wee use a lineear regressionn model to
approxim
mate the ambbient temperatture given thhe simulated
solar irrradiance as shoown in (7):
( )=
( )+
; = 1,2, … ,
(7)
where and
aree regression ccoefficients whhich can be
estimateed from measuured/historical data.
C. Moddeling of Wind Speed
The w
wind speed nnear ground leevel is also ussed as input
parametters for the PV
V power outpuut because it caan affect the
module temperature. The first-ordeer Markov chaain model as
mentionned in modelinng the solar raddiation can also be applied
to modeel the wind speeed [18].
IV. MOD
DELS OF STOCH
HASTIC LOADS
By siimulating diffeerent householld appliances iindividually,
the loadd profile can be emulated. Such a detaileed model is
viable, fflexible and reepresentative [12]. A good eestimation of
consump
mption patterns is necessary iin order to sizee the system
econom
mically and reliiably. The pree-requisite of the accurate
estimatiion of load paatterns is to haave an appliannce database
which contains exppected househhold equipmeent of the
mers. Then, tthe load sim
mulator beginss with the
consum
simulatiion of on-offf operations oof each appliaance in the
databasee. The load prrofile can be ssimulated by ssumming up
individuual appliance’ss operations.
In geeneral, househoold appliances can be classiffied into four
types baased on their nnatures and opeerating charactteristics [12]
and thiss classification is shown in Taable II.
4
TAB
BLE II
TYPE OF APPLIANCE
Type of
aappliance
A
B
C
D
Op
perating
period
p
Fixed
Variable
V
Fixed
Variable
V
Number of
occcurrence per case
Fixed
Fixed
Variable
Variable
Examples
Rice cooker
Induction cook
ker
Toaster
Air conditioneer
With such cllassification, the
t
following load simulattion
proocedures are prresented:
1) In each casee, i.e. 24 hrs, time
t
segmentss are defined (ee.g.
four segmen
nts in this paperr);
ppliance, we assign a prob
bability for itt to
2) For each ap
operate in each time seg
gment, e.g. 0.1 for segmen
nt 1
gment 2 (06:00
0 – 12:00), 0.1 for
(00:00 – 06:00), 0.7 for seg
00 –
segment 3 (12:00 – 18:00)) and 0.1 for seegment 4 (18:0
24:00). Thesse probabilitiess are derived frrom actual usaage;
3) A random number
n
between
n 0 and 1 is drrawn in each tiime
step to deterrmine whether the appliance is switched on
n. If
this number is smaller than
n the assigned probability in the
w be on at th
his time interv
val.
segment, the appliance will
This processs only deterrmines the randomness of an
appliance’s on time and the off time is based on the
expected operating period as shown in Taable II;
4) The numberr of occurrencce of the applliance is coun
nted
during the simulation.
s
Th
he step 3) willl be terminated
d if
the predefined switching frequency
fr
is reaached;
5) Steps 2) – 4)) are repeated for
f other appliaances.
Fig. 4 showss a simulatio
on result by using applian
nces
meentioned in Tab
ble II.
Figg. 4 Simulated resu
ult of load simulato
or
V. SYSTEEM PERFORMAN
NCE ASSESSME
ENT TOOLS
( )≤
=
(8)
( )−
( )|
( )≤
(9)
We ccan obtain thee EENS by ssumming up tthe deficient
energy iin the simulatioon and it can bbe considered toogether with
the systeem cost in our objective funcction
To avvoid oversizinng the system
m, another indeex which is
called E
EEES, is also considered w
with the objective function
and it caan be defined aas:
=
( )−
( )|
( )
(10)
This index aims to evaluate the eexcessive energgy generated
by PV aarrays given thee SOC has reacched the upperr bound.
B. Econnomic Model
The sstand-alone PV
V system consiists of various components
with unneven life exppectancy. The lifetime of P
PV modules
usually is the longest ((e.g. 25 years). For others, thheir lifetimes
are mucch shorter (e.g.. 5 years for batteries). Sincee PV project
is a longg-term investm
ment, a net preesent value (N
NPV) method
with thee concept of A
Annualized Cosst of System (A
ACS) is used
to propeerly benchmarkk the system ccosts. In essennce, the ACS
consistss of three mainn components: 1) annualizedd capital cost
(
)); 2) annualizzed replacemeent cost (
) and 3)
annualizzed maintenannce cost (
). In our stuudy, we only
considerr the costs off two main parrts, namely PV
V array and
battery bank, and the cost of invertter is includedd in the first
one for simplicity.
1) Annnualized capiital cost
The aannualized capital costs of thee PV array andd the battery
bank aree given as folloows:
=
A. Reliability Model
M
The optimum
m design of th
he system is evaluated
e
by two
t
c
These two
t
obbjectives conccurrently: reliaability and cost.
obbjectives are ussually evaluateed separately and
a we proposse a
unnifying objectiv
ve function as follows. The LOLP is a wellw
knnown index to analyze system
m reliability. Mathematically
M
y, it
cann be representeed in terms of SOC
S
as follow
ws:
=
Throuugh simulationn, we can eassily obtain the LOLP by
estimatiing the probaability of thee SOC falls below the
minimum
um value. Sincce this index iis associated w
with the risk
level, w
we have definned it as one of the constrraints in the
optimizaation problem.. In addition too LOLP, we allso proposed
to use ttwo other reliiability indicess. The first onne is EENS
which iss given as folloows:
( ,
)=
(1 + )
(1 + )
−1
(11)
is the initiial capital cost of a componennt in $; CRF
where
is the ccapital recoverry factor which represents the present
value oof a series off equal annuall cash flows;
is the
componnent lifetime inn year; and r is the annual real interest
rate.
2) Annnualized replaacement cost
The rreplacement coost is required ffor a componennt if it gets a
lifetime which is shoorter than thee project lifetiime. In this
paper, oonly the batteryy bank requiress to be replaceed during the
project llifetime (of couurse, one can aalso include thee inverters if
desired)). The annualizzed replacemennt cost of the bbattery bank
5
is given as follow
ws:
=
( ,
)=
(1 + )
−1
(12)
whhere
is the replacement cost of the battery
b
bank in
n $;
is the batteery bank lifetim
me in year; SF
FF is the sink
king
funnd factor obtaiined from the future
f
value off a series of eq
qual
annnual cash flow
ws.
3) Annualized
d maintenancee cost
The annualizeed maintenancee cost is consttant for each year
y
y, it is not considered with an
nnuity.
annd for simplicity
V
VI. SYSTEM OPTIMIZATION
P
MODEL WITH PARTICLE
A
SWAR
RM
OPTIMIIZATION
A. Optimization Formulation
d with the ACS
S to
In this paper, EENS and EEES are bundled
n called Annu
ualized Reliabiility
forrm a new objective function
annd Cost of System
S
(ARCS
S) which can
n simultaneou
usly
opptimize both reeliability and system cost. The
T mathematiical
forrmulation of th
he sizing probleem can be writtten as follows:
min
,
=
∙
+
+
+
+
∙
+
+
(13)
≤
= 0,1
1,2 …
= 0,1
1,2 …
(14)
(15)
(16)
(local) aand gbest (gloobal) [15]. Thee procedures oof Fig. 5 are
summarrized as follow
ws:
1. An initial guess oof the decision parameters is m
made and an
inittial set of partiicles for the PSO algorithm is generated
randdomly.
2. A llocal weather data at the pootential PV sitte is used to
gennerate a time sseries of meteoorological connditions with
the period equal tto the project lifetime. Thosse conditions
are then used to determine thee PV array poower output.
Bassed on the simuulated load proofile and PV poower output,
the SOC can be caalculated in eaach time step.
3. Thee PSO algorithhm is then useed to optimizee the system
connfiguration. It iteratively ssearches for the optimal
connfiguration (i.ee. ∗ and ∗ ) to minimizee the ARCS
as shown in (13). The sizinng constraints which are
assoociated with reeliability indicees as shown inn (14) will be
exaamined for eachh system configuration.
4. Thee optimal confi
figuration is obtained either bby reaching a
maxximum numbeer of iterationss of the PSO aalgorithm, or
by ssatisfying the iimposed consttraints. Otherw
wise, the least
cosst configurationns will be usedd to update the particles for
Carlo simulatioon. It should bbe noted that
the next Monte C
sincce there are onnly two decisionn variables in tthe problem,
the PSO algorithhm can searchh a near optim
mal solution
durring the veryy early iterations (e.g. less than 10
iterrations).
Suubject to
whhere
is th
he value of losst load in $/kW
Wh;
is the
annnualized EEN
NS in kWh/y
year;
is
i the value of
exxcessive energy
y in $/kWh;
is the ann
nualized EEES
S in
kW
Wh/year;
is the upper bound
b
of the
.
The first two terms in (13)) are the reliaability cost wh
hich
quuantifies the seeverity of losss of load poweer with
and
a
thee wastage of excessive
e
solarr energy with
. The th
hird
annd fourth termss are the ACS for
f the PV arraay and the batttery
baank, respectivelly.
Constraint (14
4) is to ensuree the reliability
y of the propo
osed
sizzing should bee lower than an
n acceptable risk level, such
h as
1%
% in the simulation. Constraaints (15) and
d (16) impose the
disscrete natures of
o the decision
n variables.
B. Sizing Frameework
Based on the proposed mo
odels and evalluation indicess, a
floowchart to obttain the optimu
um design parrameters (i.e.
annd
) of th
he PV system by using a PSO
P
algorithm
m is
shown in Fig. 5.
b
on the evolution off a
The PSO algorithm is based
poopulation of particles and th
here are two fitness valuess to
guuide the particcles toward thee best solution
ns, namely pb
best
Fig. 5 Fraamework of optimaal sizing by PSO
6
TABLE VI
COSTS AND LIFETIME OF SYSTTEM COMPONENTSS
Initial capitaal
Replacemennt
Maintenancee
cost
cost
cost (/year))
3000 US$/kW
W
N/A
5 US$/kW
100 US$/kW
Wh
500 US$/kW
Wh
50 US$/kW
W
VII.
V SIMULATIO
ON AND RESUL
LTS
To demonstraate the proposeed sizing meth
hod, a case stu
udy
waas conducted using
u
actual meeteorological data
d obtained frrom
a real stand-alon
ne system insstalled in a reemote island near
n
0 to
Hoong Kong. The meteorologiccal conditions from 05/2010
044/2011 are used
d to derive thee weather modeels. The techniical
paarameters of thee PV module and
a the battery bank are given
n in
Taables III and IV, respectiv
vely. The exp
pected househ
hold
apppliances are given in Table V. Based on the
t proposed lo
oad
mulator, a sam
mple of chronological load sim
mulation is sho
own
sim
in Fig. 6. It can
n be seen that the peak load
d usually occurr at
d 14kW. The average
a
daily lo
oad
nigght with peak power around
coonsumption is about
a
61kWh.
b1
4.73
00.20/day
ID
1
2
3
4
5
6
7
8
9
10
TAB
BLE III
SPECIFICATIONSS OF PV MODULE
b2
b3
b4
-0.01
0..24
0.11
(W)
200
TABLE IV
SPECIFICATIONS OF
O BATTERY BANK
K
(kWh)
0.90
0
0.97
10
0.20
TAB
BLE V
ESTIMATED APPL
LIANCE DATABASE
E
Applian
nce
Power (kW)
Air con
nditioner
1.50
Water pump
p
4.00
1.80
Inductiion cooker
0.50
Lightin
ng
1.00
Microw
wave oven
0.20
Refrigeerator
0.50
Rice Co
ooker
0.70
Water Boiler
B
0.07
TV
0.06
PC
0.95
Quantity
2
1
2
4
2
1
1
2
2
2
PV arrayy
Batteryy
m
60
TABLE VII
PARA
AMETERS OF PSO ALGORITHM
ω
c1
c2
0.7
0.7
1.2
Lifetime
(year)
20
5
g
100
method, the opptimal sizing
Basedd on the propposed sizing m
results ffor LOLP achieeving 1%, 2% and 5% are givven in Table
VIII, givving a minimuum ACS of US$65,441, US$$60,324 and
US$51,8883, respectiveely.
A sennsitively analyysis is also connducted to proovide an indepth sttudy on the sizzing results by varying the nuumber of PV
moduless given the fixxed number oof batteries (i.ee.
= 23)
and the correspondingg result is givenn in Table IX. The optimal
% LOLP is givven by bold
system configuration based on 2%
m Table IX, it is observed thaat increasing
letter in the table. From
mber of PV moddules causes a conflicting ressult between
the num
the EEN
NS and the E
EEES. On one hand, it is reeasonable to
observe that the EE
ENS drop signnificantly withh increasing
EEES is also
number of PV modulees. On the othher hand, the E
modules.
increasinng with the nuumber of PV m
TABLE VIIII
OPTTIMAL SIZING RESU
ULTS OF DIFFEREN
NT RISK LEVELS USING PSO
ALGORITHM
M
Ac ceptable LOLP
1%
2%
5%
∗
∗
125
120
112
26
23
18
A
ACS(US$)
65,441
60,324
51,883
TABLE IX
SEENSITIVITY ANALY
YSIS OF VARYING NUMBER OF PV MODULES
Number oof PV modules
130
100
110
140
120
EENS/y
/year
235
2,557
1,142
122
493
(kWhh)
EEES/yyear
3,753
635
5667
62
11,992
(kWhh)
ACS (U
US$)
62,9088
57,741
65,491
55,157
660,324
ARCS(U
US$)
115,4644
101,905
137,399
137,725
1000,004
V
VIII. CONCLU
USION
Figg. 6 Simulated load
d profile for case study
s
ws a typical initial
i
capital cost,
c
replacem
ment
Table VI show
coost, maintenancce cost and lifeetime of each component in the
system based on generic cost reeference [3]. The
T value of
annd
are assumed to be $32/kWh
h and $12/kW
Wh,
resspectively. Theere are several parameters inv
volved in the PSO
P
alggorithm such as
a the number of
o particles m, weighting facttors
c1 and c2, the in
nertia factor ω and the max
ximum numberr of
t
values aree given in Table VII.
iteerations g and their
In thhis paper, we presented a sizing methodoology which
includess stochastic moodels of solar rradiation and lload patterns
for a sttand-alone PV
V system usinng a chronologgical Monte
Carlo siimulation methhod. A Markovv chain methodd to synthesis
a time sseries weather data was propposed which iss essential to
describee the intermiittent solar ppower outputss. We also
presenteed a stochasticc load model too produce a m
more realistic
consump
mption pattern for sizing stuudies. The optimal sizing
objectivve was also deeveloped such that reliabilityy and system
cost cann be considereed simultaneouusly. The propposed sizing
framewoork was solvedd by a PSO alggorithm. We finnally applied
the propposed framew
work to a case study to dem
monstrate the
feasibiliity of the methhod.
7
IX. ACKNOWLEDGEMENT
The authors would like to acknowledge the financial
supports and valuable technical advices given by CLP Power
HK and CLP Research Institute, particularly Messrs.
Raymond Ho, C. C. Ngan and Dr. Jian Liang.
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Simon K. K. Ng received the B.Eng. (Hons.) and M.Phil. degrees in electrical
engineering from The University of Hong Kong, Hong Kong, China, in 2005
and 2007, respectively. He is currently pursuing the Ph.D. degree of power
systems in the same institution. He was a Modeling Specialist with the CLP
Research Institute Ltd. from 2008 to 2009. His main research activities
include load signature analysis and load modeling.
Jin Zhong (M’05, SM’10) received the B.Sc. degree from Tsinghua
University, Beijing, China, the M.Sc. degree from China Electric Power
Research Institute, Beijing, and the Ph.D degree from Chalmers University of
Technology, Gothenburg, Sweden, in 2003. At present, she is an Associate
Professor in the Department of Electrical and Electronic Engineering of the
University of Hong Kong. Her areas of interest are power system operation,
electricity sector deregulation, ancillary service pricing, and smart grid.
John W M Cheng (M’99) received the B. Eng. from the University of
Saskatchewan, M.Eng. and Ph.D. from McGill University. He is currently the
Manager of Technology Research & Deployment of CLP Holdings based in
Hong Kong. His research interests include load signature studies, Monte Carlo
simulations, renewable energy technologies and smart grid applications. He is
a P.Eng registered in Ontario and a member of HKIE, CIGRE and IERE.