lecture 2 Photovoltaic Systems Engineering Ali Karimpour Assistant Professor Assistant Professor Ferdowsi University of Mashhad Reference for this lecture: Photovoltaic Systems Engineering Third Edition CRC Roger Messenger, Jerry Ventre Ali Karimpour May 2012 Engineering Economy Tenth Edition Prentice Hall, E. Paul DeGarmo, William G. Sullivan, James A. Bontadelli, and Elin M. Wicks.
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lecture 2
Photovoltaic Systems Engineering
Ali KarimpourAssistant ProfessorAssistant Professor
Ferdowsi University of Mashhad
Reference for this lecture:Photovoltaic Systems Engineering Third Edition CRC Roger Messenger, Jerry Ventre
Ali Karimpour May 2012
Engineering Economy Tenth Edition Prentice Hall, E. Paul DeGarmo, William G. Sullivan, James A. Bontadelli, and Elin M. Wicks.
lecture 2
Lecture 10Lecture 10
Economic ConsiderationsIntroduction
* Consumer price index * Inflation and deflation ratep
* Discount or Interest rate * Cash flow
Life Cycle Costing (LCC)
Annual Life Cycle Costing (ALCC)Annual Life Cycle Costing (ALCC)
Capital Cost
Unit Electricity Cost(Levelized Cost)
Ali Karimpour May 2012
2Payback period and rate of return
lecture 2
IntroductionIntroduction
Consumer Price Index(CPI)
Consumer Price Index: CPI is a composite price index thatp pmeasures price changes in food, shelter, medical care, transportation, apparel, andtransportation, apparel, and other selected goods andservices used by individuals and familiesand families.
Ali Karimpour May 2012
3http://www.cbi.ir/category/1624.aspx
lecture 2
IntroductionIntroduction
Inflation and deflation rate
General price inflation: General price inflation is defined as anpincrease in the price paid forgoods and services bringing about a reduction power ofabout a reduction power of purchasing power of the monetary unit.
100)(
)()(
1
1 ×−
=−
−
k
kk
CPICPICPIi
100)(
)()(
1387
13871388 ×−
=CPI
CPICPIi
Ali Karimpour May 2012
47.10%1003.183
3.183203=×
−=
lecture 2
IntroductionIntroduction
Example 1: Suppose one want to change a battery after 5 p pp g yyears and the present price is100$. Find the price ofbattery, if the inflation rate be 15%.
Discount or Interest rateThe amount charged, expressed as a percentage of principal, by a lender to a borrower for the use of assets. Interest rates are typically noted on an annual basis known as the annual percentagetypically noted on an annual basis, known as the annual percentage rate (APR).
)1(1 dCC kk += )1(1 dCC kk ++
d is discount or interest rate.
Ck is the real value of an asset in the kth period.
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lecture 2
IntroductionIntroduction
Example 2: Suppose one diposit1000$ for a period of 4 p pp p pyears with a discount rate 17%, what is the value of his money after 4 years?
40
31
2234 )1()1()1()1( dCdCdCdCC +=+=+=+=
$1874)17.01(1000 44 =+=C
Example 3: Suppose one diposit10,000,000 Rials for a HajExample 3: Suppose one diposit10,000,000 Rials for a Hajprogram in a discount rate of 16%, what is the value of his money after 80 months?
RialsC 690,852,28)1217.01(000,000,10 80
80 =+=
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12
lecture 2
IntroductionIntroduction
Cash flow
Cash flow is the movement of money into or out of a business, project, or financial product. It is usually measured during a specified, finite
IntroductionExample 4: Suppose we borrow 70 000 000 Rials in 14% interest rate
d i 5 i d
Introduction
and in a 5 years period. a) Determine the monthly payment.
liChln
86281)1( +
01167.0%167.11214%,000,000,700 ==== iRialsC
Rialsi
iiCPMTMonthly n 778,628,11)1(
)1(0 =
−++
=
b) Determine the settlement payment after 2.5 years.
?)...( 30210 =++− AAAC1)1(01 −+
= niiCA
1)1()1()1(1)1(
1)1())1(...)1(1(
30
0
30
0029
10 −++−+
=−+
−+−=+++++− n
n
n iiiC
ii
iiCCiiAC
Ali Karimpour May 2012
10835,028,411)1(
)1()1(paymentSettlement 60
3060
0 =−++−+
=i
iiC
lecture 2
Lecture 10Lecture 10
Economic ConsiderationsIntroduction
* Consumer price index * Inflation and deflation ratep
* Discount or Interest rate * Cash flow
Life Cycle Costing (LCC)
Annual Life Cycle Costing (ALCC)Annual Life Cycle Costing (ALCC)
Levelized Cost of Electricity
Capital Cost(Levelized Cost)
Ali Karimpour May 2012
11Payback period and rate of return
lecture 2
Life Cycle Costing (LCC)y g
LCC is a sensible means of evaluating any purchase
Acquisition costs
LCC is a sensible means of evaluating any purchase option when a decision has been made to purchase.
q
Maintenance costsAt the start andduring operation
Replacement costs
during operation
p
At the endSalvage value
At the endDecommissioning cost
d i i hi d hiAli Karimpour May 2012
12And… Loan, incentives, third party ownership, externalities, …
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Life Cycle Costing (LCC)y g
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13
lecture 2
Life Cycle Costing (LCC)y g
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14
lecture 2
Life Cycle Costing (LCC)y g
The time value of money
let Inflation rate (i ) and Discount or interest rate of (d):niCnC )1()( += iCnC )1()( 0 +=
ndNN )1()(
C0 is the present value of an asset, C(n) is the value of asset after n years. ndNnN )1()( 0 +=
N0 is the present money at hand, N(n) is the money after n years.
001 CPCiPW r
n
=⎠⎞
⎜⎝⎛ +
=Present worth
001 d r⎠
⎜⎝ +
Present money needed to buy and asset n years later in
Ali Karimpour May 2012
15Inflation rate of i and discount or interest rate of d
lecture 2
Life Cycle Costing (LCC)Life Cycle Costing (LCC)
Example 5: Suppose one want to change a battery after 5 p pp g yyears and the present price is100$. a) Find the price of battery, if the inflation rate be 15%.b) Fi d h l f h d d b hb) Find the present value of the money needed to bye the
battery.(i=15% and d=20%)
$201)1501(100 5+C $201)15.01(100 55 =+=C
5
$83.801002.0115.01 5
0 =⎟⎠⎞
⎜⎝⎛
++
== CPPW r
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⎠⎝
lecture 2
Life Cycle Costing (LCC)y g
Cumulative Present Worth
0
1
0
2
00 11...
11
11 C
diC
diC
diCPW
n−
⎟⎠⎞
⎜⎝⎛++
++⎟⎠⎞
⎜⎝⎛++
+⎟⎠⎞
⎜⎝⎛++
+=111 ddd ⎠⎝ +⎠⎝ +⎠⎝ +
( ) 012
0 11...1 CxxxxCPW
nn −
=++++= −( ) 00 1 x−
P
PW
aP
Cumulative Present Worth FactorPW
( ) 02
01... CxxxxxCPW
nn −=+++=
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17
( ) 00 1 x−
aa xPP =1
lecture 2
Lecture 10Lecture 10
Economic ConsiderationsIntroduction
* Consumer price index * Inflation and deflation ratep
* Discount or Interest rate * Cash flow
Life Cycle Costing (LCC)
Annual Life Cycle Costing (ALCC)Annual Life Cycle Costing (ALCC)
Levelized Cost of Electricity
Capital Cost(Levelized Cost)
Ali Karimpour May 2012
18Payback period and rate of return
lecture 2
Annual Life Cycle Costing (ALCC)y g
LCC (Life Cycle Costing):
ALCC (Annual Life Cycle Costing):ALCC (Annual Life Cycle Costing):
Ali Karimpour May 2012
19
lecture 2
Levelized Cost of Electricity (LCOE)y
ALCC (Annual Life Cycle Costing):
Unit Electricity Cost (Levelized Cost of Energy (LCOE) )Unit Electricity Cost (Levelized Cost of Energy (LCOE) )
The LCOE is the minimum price at which energy must be ld f j h l f
)/$/($ALCCLCOE KWhorMWh=
sold for an energy project to have present value of zero.
Example 8: PV or gasoline generator to power a warning sign
We need a 24 hours/day warning sign with 2 kWh/day and 20 year lifetime20-year lifetime.
981.011 15.7% of rateinflation and 18% of ratediscount Suppose =++
=dix
2 kWh/day 83 W system
Option #1 Option #2
500 W array 4 $/watty
900 $ storage battery. 500 W gasoline generator 250$
2 kWh/gal 365 gal/yearCh i b tt i h 5
300 $ Charge controller.
2 kWh/gal 365 gal/year
2 $/gal
Changing batteries each 5 years.
100 $/year maintenance. 400 $/year maintenance.
Ali Karimpour May 2012
27Changing generator each 5 years.
lecture 2
Example 8: PV or gasoline generator to power a warning sign
4516177161Pr981011 =
−==
−===
+=
xxPxPxixnn
n 45.161
,77.161
,Pr,981.01
1 =−
==−
===+
=x
xPx
Pxd
x aa
2000 2502000 2502000300900900
250
250250
2000300900818
250
2272065x
5x10x900
900900100
250250730400
7436751645
06187
122426708
x
1aP
10x15x
15xaP
aP
198207081
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lecture 2
Example 8: PV or gasoline generator to power a warning sign
Determine LCC, Capital Cost, NCC, ALCC and LCOE
198207081
2503200
250/0.5=5003200/0.5=6400
1182422
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1182422
1182/730=1.61422/730=0.58
lecture 2
Lecture 10Lecture 10
Economic ConsiderationsIntroduction
* Consumer price index * Inflation and deflation ratep
* Discount or Interest rate * Cash flow
Life Cycle Costing (LCC)
Annual Life Cycle Costing (ALCC)Annual Life Cycle Costing (ALCC)
Levelized Cost of Electricity
Capital Cost(Levelized Cost)
Ali Karimpour May 2012
30Payback period
lecture 2
Payback Period and Rate of Return
Payback Periody)costCapital(0C
nAAAA 321
0min 0 ≥⎠
⎞⎜⎝
⎛−∑
θ
θ k CA1
0⎠⎝
∑=
θ kk
Discounted Payback Period ?
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31
y
lecture 2
Payback Period
Example 9: A capital investment of 1500 MT can be made on a biomass l t S 10 lif ti f th l t d 10 MT (fi d)plant. Suppose a 10 years life time for the plant and 10 MT (fixed)
expense as annual O&M and 50 MT as a annual revenue(fixed revenue) . Suppose the expense of overhaul after 5 years is 300 MT(fixed). Let i=15% and d=20%.
a) Draw the cash flow of project. b) Find LCC of project.
c) Is the project financially profitable? d) Calculate payback period?
1500
300
10
Ali Karimpour May 2012
32550
lecture 2
Payback Period
a) Draw the cash flow of project. b) Find LCC of project.
c) Is the project financially profitable? d) Calculate payback period?
15001500
30010
55010
MTPxLCC a 1662103001500 15 =++=19.4
11,833.0
2.011
10
1 =−−
==+
=x
xxPx a
5642550Revenue × LCCP 78201500540min =→≥⎞
⎜⎛∑ θ
θ
Ali Karimpour May 2012
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5.642550Revenue 1 =−×= LCCPa 78.201500540min1
=→≥⎠
⎜⎝
−∑=
θθ k
k
What about repair price?
lecture 2
Payback Period
Example 10: Consider the biggest solar plant of Mashhad.
Detail of project(25 years life time):216 panel (200 W) each 630 KT totally 136 MT.18 T k h 6 5 MT t t l 117MT18 Tracker each 6.5 MT total 117MT6 inverter each 7KW each 7MT totally 42 MTFoundation 25 MT------------------------320 MT in 43.2 KW no maintenance and let i=15% and d=20%.
Suppose yearly average PSH is 5 hours/day and each kWh is 150 TSuppose yearly average PSH is 5 hours/day and each kWh is 150 Ta) Find LCC of the project. b) Draw the cash flow of project.
) I h j fi i ll fi bl ? d) C l l b k i d?c) Is the project financially profitable? d) Calculate payback period?
LCC=Capital cost is 320 MT Yearly energy=43.2×5×365=78840 kWh
Ali Karimpour May 2012
34Yearly income=150×78840=11.8 MT
lecture 2
Payback Period
Example 10: Consider the biggest solar plant of Mashhad.
a) Find LCC of the project. b) Draw the cash flow of project.
) I th j t fi i ll fit bl ? d) Calc late pa back period?c) Is the project financially profitable? d) Calculate payback period?
LCC=Capital cost is 320 MT Yearly energy=43.2×5×365=78840 kWh