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Renewable Energy Resources (RER)
Rui Castro
rcastro@tecnico.ulisboa.pt
https://sites.google.com/site/ruigameirocastro/
Economic assessment of renewable energy projects
Chapter 2
2
Profitability of a project
• Capital costs (€/MW)
• Minimum rate of return (%)
• Price paid for the electricity (€/MWh)
• Annual utilisation factor (h)
DISCOUNT RATE
• Cash inflows and outflows are spread over a period of time and time has a monetary value
• For instance, if possible, the natural choice is to pay in the future.
• Why?– The amount to be paid in the future may be invested.
– The actual accumulated amount may be much higher.
– The money invested over time will give a real income.
Discount Rate
nn rFF
rFrrFrrFrFF
rFrFFF
F
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200002
0001
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r: Discount Rate
1)1(
10 t
t
r
FF
• Discount rate or effective interest rate (r)
– Allows to convert a value referred to a date to an equivalent amount referred to another date (usually the present time)
– Appreciation of the investment
– Minimum profitability that the investor requires to invest in a given project
– Capital recovery at a certain remuneration + risk reward
6
Discount Rate
LEVELIZED COST OF ENERGY (LCOE)
Production cost
aVFT cWCPCCC CT is the total annual cost (€)
1)1(
10 t
t
r
FF
r is the rate of return or discount rate
n
jjTn
TTT
rA
r
A
r
A
r
AI
1201
)1(
1
)1(...
)1()1(
I01 is the investment per MW
(€/MW)
AT is the investment annuity
1)1(
)1(1
)1(
1)1(
)1(
1
1
n
n
a
n
nn
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r
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1)1(01
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Production cost
PICPCF 01)( The fixed O&M costs must be added to the annuity.
They are assumed to be proportional to the
investment per MW, the proportionality factor being .
aT cWPIC 01)( The variable cost c includes the fuel cost and the cost
of CO2 emissions, when applicable.
aT
T chIP
CC 0101 )( Annual total production cost per installed MW
I01 is the overnight cost
LCOE and marginal cost
ch
Ic
h
Cc
W
CP
W
CCLCOE
aaaa
Tavg
01)(
cW
Cc
a
Tmrg
To ensure the economic sustainability of the power station in the short-term, the
marginal cost must be recovered through the sale of electricity (price p).
This condition imposes: p>=cmrg
To ensure the economic sustainability of the power station in the long run, the
average cost must be recovered through the sale of electricity (price p).
This condition imposes: p>=LCOE
Marginal cost - Cost of the last unit produced
LCOE – Levelized Cost Of Energy
LCOE(USD/MWh)
Technology $USD/MWh (2013)
Wave 500
Tidal 450
CSP-Fresnel 280
CSP-Tower 240
CSP-Trough+storage 260
Fuel cells 230
Wind offshore 220
CSP-Trough 280
CSP-Tower+storage 190
PV-Thin Films 125
PV-c-Si tracking 125
Biomass-gasification 130
PV-c-Si 140
Geothermal-binary 100
Wind onshore 80
Solid waste 110
Biomass-incineration 125
Geothermal-flash 70
Landfill gas 60
Biomass-Anaerobic digestion 150
Large Hydro 70
Small Hydro 70
Nuclear 90
CHP 70
CCGT 70
Coal 80
Example
SHP Wind PV
n years 30 20 20
ha h 2300 2300 1750
r 5% 5% 5%
beta 1.0% 1.0% 0.5%
I01 €/MW 1.7 1.2 1.2
Compute the LCOE (€/MWh)
SmallHydro
Wind PV
LCOE (€/MWh)
55.47 47.08 58.45
ECONOMIC ASSESSMENT INDEXES
Net Present Value (NPV)
14
Simplified model
Criteria for Profitability
n
jj
j
t
n
jj
j
n
Sn
jj
j
r
MOI
r
I
r
V
r
RNPV
1
1
01 )1(
&
)1()1()1(
ta IkDRNPV
NPV analysis
• NPV > 0; Feasible project– the investment is recovered, the minimum rate of
return of capital is achieved and a surplus is accomplished
• NPV = 0; Uncertain project– the investment is recovered and the minimum rate of
return of capital is achieved; the profitability of the project is doubtful
• NPV < 0; Project is not feasible
• The greater the discount rate the lower the NPV
15
Criteria for Profitability
Internal Rate of Return (IRR)
Discount rate that makes NPV=0
16
Simplified model
Criteria for Profitability
n
jj
j
t
n
jj
j
n
Sn
jj
j
IRR
MOI
IRR
I
IRR
V
IRR
R
1
1
01 )1(
&
)1()1()1(
tn
n
N IIRRIRR
IRRR
1
11
DRRN
IRR computation
17
Gauss
Criteria for Profitability
Simplified model
nk
nk
t
Nk
IRR
IRR
I
RIRR
)(
)(
)1(
1
11
IRR approximate computation
18
Linear interpolation (aprox.)
Criteria for Profitability
r
NPV
(r1,NPV1)
(r2,NPV2)
12
1121 )(
NPVNPV
NPVrrrIRR
IRR analysis
• IRR > r → NPV > 0 Project feasible
• IRR < r → NPV < 0 Project unfeasible
19
Criteria for Profitability
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