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UNIVERSITY OFSISTAN AND BALUCHESTAN
A Novel Techno-Economical Optimization Approach Based on Linear
Integer Programing (LIP) for Hybrid Renewable systems
Saeed Reza Nazari Estahbanati Department of Mechanical Engineering, University of Sistan and Baluchestan.
S. Masoud Barakati Department of Power Electronic Engineering, University of Sistan and Baluchestan.
Mehri Mehrjoo Department of Telecommunication, University of Sistan and Baluchestan.
Mohammad Ali Yazdanpanah Jahromi Department of Mechanical Engineering, University of Guilan.
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Wind Turbine Power
( / )ref refH H • Adjusting the measured wind speed
1/7 for open land
• The weibull distribution function ( ( ) )( 1)( ) ( ).( ) .kv
k ck vf v e
c c
0 5 10 15 20-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Wind Speed(m/s)
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. . ( , , )out days hours cE n n P f k c v
• Output energy of wind turbine• Power curve of small wind turbine “Lakota S, SC”
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
1.4
Wind speed (m/s)
Powe
r out
put (
kW)
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5
maxmax max min
max min
. . .( ) . .( ).exp( .ln( ))oci ix cv N
iN iN
V VE EV S T T T S V S V V
E E V V
. . .( )ix sc ci N
iN
EI p I T T T
E
0 1000 2000 3000 4000 5000 6000 7000 8000 90000
200
400
600
800
1000
1200
Time(h)
Sola
ra R
adia
tion(
Wh/
m2 )
0 1000 2000 3000 4000 5000 6000 7000 8000 9000-10
-5
0
5
10
15
20
25
30
35
40
Time(h)
Tem
prat
ure(
C)
PV Array Power
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0 200 400 600 800 1000 12000
1
2
3
4
5
6
voltage (v)
Cur
rent
(A)
0 200 400 600 800 1000 12000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
voltage (v)
pow
er (W
)
. 1( ) .[1 exp( )]
1 .1 exp( )
x
x
V I VP V
bV bb
• b, usually changes from 0.01 to 0.18.
( ).( ).( )PV out xE P E solarwindow TotalDay
1( ) .[1 exp( )]
1 .1 exp( )
X
x
I VI V
bV bb
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Operation of Battery• Capacity of the BT depends on temperature
' '' .(1 .( 298.15))bat bat c batC C T • δC suggested 0.6 % per degree
( ) ( ) ( ( ) / )( )
( )PV WT ACLoad inverter DCLoad
batbat
P t P t P t PI t
V t
• The BT current rate
• ηinverter = 92%
'
( ). ..( 1) ( ).(1 )
24bat bat
bat
I t ttSOC t SOC t
C
SOCmax=1, SOCmin=1-DOD. and DOD is 60%.
• The Battery SOC
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Optimization Problem
ObjectiveFunction minn(npv×UCEEPV+nWT×UCEEWT+nBAT×UCEEBAT)
Constrains
0<LPSP<0.03
SOCmin<SOC<SOCmax
npv ,nWT ,nBAT>0
(npv ,nWT ,nBAT)ϵƵ
Decision Variables Number of PV (nPV),WT(nWT),BAT(nBT)
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Economic Analysis
minacap arep aACS C C C
ACSUCEE
ATED ATED stands the annual total energy demand in (kWh).
. ( , )acap cap projC C CRF i Y
(1 )( , )
(1 ) 1
n
n
i iCRF i n
i
1loani f
if
• Unit Cost of Electricity Energy
0 1000 2000 3000 4000 5000 6000 7000 8000 90000.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time(h)
Lo
ad
(kW
) . ( , )arep rep repC C SFF i Y ( , )(1 ) 1reprep Y
iSFF i Y
i
( ) .(1).(1 )namain amaninC n C f
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Reliability Analysis
0
( ( ) ( ))T
available neededt
Time P t P tLPSP
T
• Loss of Power Supply Probability
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RESUALTS•The proposed methodology has been used to achieve the proper size of off-grid
power system, to supply the load demand of a remote area by using of branch and cut
based on linear integer programing (LIP). The typical meteorological of one year hourly
data collected for solar radiation, temperature and wind speed. The location of
Marvdasht, Fars, Iran (Latitude: 29°50'N, Longitude: 52°40'E) is chosen for case study.
Results displayed as an optimal Pareto front. Each solution of the best Pareto front was
achieved by a combination of hybrid systems in some manner to reach higher reliability.
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optimal solutions of components
NoPV
numberWT number BT number
UCEE ($/kW)
LPSP%
1 2 2 1 257.6142 1.242 1 1 4 191.1375 2.403 2 1 2 211.8478 0.004 2 2 2 196.7711 2.855 3 2 1 187.5020 0.53
The best configurations among the results are shown in below table. The lowest Unit cost of electricity energy (UCEE) achieved in related on the candidate number 5 but the lowest LPSP is given by choice 3.
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The relation between LPSP and UCEE is shown in below figure. With increasing the LPSP the value of the UCEE is decreased and vice versa by decreasing the value of the LPSP the UCEE is increasing. The Branch and cut method is a suitable method to reach the best size. It is needed lower time in comparison of the evolutionary methods to reach the results and it guarantees that the obtain results is really the optimal solution.
0 0.5 1 1.5 2 2.5 3180
190
200
210
220
230
240
250
260
LPSP%
UC
EE
($/k
W)
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I really appreciate for your concern
The End