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

)1(

)1()1)(1()1()1(

)1(

0

200002

0001

0

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

jja

r

rr

k

rr

r

rk

aTn

n

T kArr

rAI

)1(

1)1(01

01011)1(

)1(II

r

rrA

n

n

T

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