lable at ScienceDirect

Renewable Energy 34 (2009) 6–13

Contents lists avai

Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Review

Cost determination of the electro-mechanical equipmentof a small hydro-power plant

B. Ogayar*, P.G. VidalGrupo de Investigacion IDEA, Escuela Politecnica Superior, University of Jaen, Campus de Las Lagunillas, s/n. 23071-Jaen, Spain

a r t i c l e i n f o

Article history:Received 15 October 2007Accepted 25 April 2008Available online 17 July 2008

Keywords:Small hydroCostElectro-mechanical equipment

* Corresponding author. Tel.: þ34 953212858; fax:E-mail address: bogayar@ujaen.es (B. Ogayar).

0960-1481/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.renene.2008.04.039

a b s t r a c t

One of the most important elements on the recovery of a small hydro-power plant is the electro-mechanical equipment (turbine–alternator), since the cost of the equipment means a high percentage ofthe total budget of the plant. The present paper intends to develop a series of equations which determineits cost from basic parameters such as power and net head. These calculations are focused at a level ofprevious study, so it will be necessary to carry out the engineering project and request a budget tocompanies specialized on the construction of electro-mechanical equipment to know its cost moreaccurately. Although there is a great diversity in the typology of turbines and alternators, data frommanufacturers which cover all the considered range have been used. The above equations have beendeveloped for the most common of turbines: Pelton, Francis, Kaplan and semiKaplan for a power rangebelow 2 MW.The obtained equations have been validated with data from real installations which have been subject toanalysis by engineering companies working on the assembly and design of small plants.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The cost of the electro-mechanical equipment (turbine, alter-nator and regulator) means a high percentage of a small hydro-power plant budget (around 30% and 40% of the total sum). It stemsfrom this the importance of the determination of that cost, whichcould directly influence the project feasibility (Fig. 1).

For the determination of the cost of the electro-mechanicalequipment, there are graphs which can approximately calculatethose costs. But these graphs refer to a distant time period, sincethey use to be at least 10 years old. Besides, manufacturers ofturbines and alternators do not supply any information about cost,since every installation is different and complex.

An example of these graphs are those developed by theInstitute for Energy Diversification and Saving [Instituto para laDiversificacion y Ahorro de la Energıa, IDAE, Spain], with which itis possible to determinate the cost of a turbine depending on itspower and net head [7].

From an analytical point of view and analyzing the state of artfor the calculation of the cost of electro-mechanical equipment, ithas been checked that a great part of authors use an expressiondepending on the power (P) and net head (H) of the small plant.This expression is

þ34 953212478.

All rights reserved.

COST ¼ a Pb�1HcðV=kWÞ (1)

where a, b and c coefficients depend on the geographical, space ortime field in which they are used.

Among some bibliographical references, it should be remarkedthe contribution made by J.L. Gordon and Penman [3] two of thegreatest specialists on the design of small plants. They werepioneers in using an equation which generally relates the cost ofthe equipment with its power and net head.

Subsequently, several authors have developed different costequations for different countries [1,11,12,15]. One of the most recent byDr. Kaldellis [8,9], in 2007, for plants located in Greece was proposed.

Some functions of costs that have been developed in the liter-ature for various regions are shown in Table 1. This table alsogathers the year in which that functions were proposed.

2. Cost analysis methodology

Given that the different existing equations are more than 20years old, checking large differences between them and havingenough current data of costs depending on power and head, wecarried out the determination of the constants a, b and c ofexpression (1).

For the determination of these parameters a best-fit analysiswill be carried out for diverse costs. The methodology of thisanalysis has been included in the Appendix.

40%

8% 22%

30%CIVIL

WORKS

TURBOGENERATORSET

CONSTRUCTIONENGINEERING AND MANAGEMENT

ELECTRIC, REGULATIONAND CONTROLEQUIPMENTS

Fig 1. Distribution of investments on a hydro-power plant.

B. Ogayar, P.G. Vidal / Renewable Energy 34 (2009) 6–13 7

The constants a, b, c are obtained through the followingexpressions.

a ¼ e�DC (10)

b ¼ �AC

(11)

c ¼ �BC

(12)

Since costs are determined by the independent variables, powerand net head, as well as by the typology of turbines, it will be alsonecessary to discriminate between different types of turbines todeterminate the value of the constants.

The cost includes the ex-works market price of the electro-mechanical equipment (turbine, alternator, automatic valve,aspiration and pneumatic regulation elements). The maintenancecost is not included.

For this analysis, we have used, among others, data from thesmall plants included in the project Study on Feasibility andPotential for refurbishment of Hydro-power Plants in the Prov-ince of Jaen, carried out on request of AGENER (Agency of EnergyManagement in the province of Jaen), as well as those includedin Determination and Feasibility of Small Hydro-power Plants inthe Andalusian Autonomous Community, project financed by theAndalusian Energy Agency, organization belonging to theMinistry for Innovation, Science and Enterprise of the Andalu-sian Regional Government. The location of the plants is shown inFig. 2.

Obtained results for each type of turbine are described below.

3. Pelton turbines

Carrying out the linear correlation, we obtain the plane

Z ¼ 9:78098þ 0:635275X � 0:281735Y ; (13)

with a quite good fit of R2¼ 93.16%.Once the equation Z is obtained, and according to Eqs. (10)–(12)

searched constants would value

a ¼ e9:7809 ¼ 17:693b ¼ 0:635275c ¼ �0:281735

(14)

Cost equation for these constant values would be the following1

1 Cost is expressed in V/kW and referred as of 1st January 2008.

COST ¼ 17:693P�0:3644725H�0:281735ðV=kWÞ: (15)

The graphic representation of the afore-mentioned surface isshown in Figs. 3 and 4. In these figures, it is noticeable how the costis proportional to power and head, except in low heads, where thecost increases noticeably.

Comparing real cost with that obtained through Eq. (15), thedegree of approximation or error of the equation can bedetermined. The different plants whose committed error wascalculated are shown in Table 2.

In the above table, it is noticeable that errors range between�23.83% and þ20.015%, so they are limited to a fluctuation rangeof �20%. They are completely acceptable figures for a previousstudy.

4. Francis turbines

Carrying out linear correlation:

Z ¼ 10:1542þ 0:439865X � 0:127243Y�

R2 ¼ 72:26%�

(16)

a ¼ e10:1542 ¼ 25:698b ¼ 0:439865c ¼ �0:127243

(17)

COST ¼ 25:698P�0:560135H�0:127243ðV=kWÞ: (18)

The cost function of a Francis turbine (18) is graphically shownin Figs. 5 and 6; a strong cost increase for high power levels andheads lower than 100 m is noticeable.

Incurred errors have ranged betweenþ22.27% and�15.83%. Thelargest errors appear within the band of power level ranging from300 to 400 kW (Table 3).

5. Kaplan–semiKaplan turbines

The different constants for Kaplan and semiKaplan turbineshave been obtained carrying out linear correlation in a similar wayto that for Pelton and Francis turbines. Those constants are listed inTable 4.

Cost equations would therefore be

COST ¼ 19:498P�0:58338H�0:113901ðV=kWÞ (19)

COST ¼ 33:236P�0:58338H�0:113901ðV=kWÞ (20)

The cost function of a semiKlapan turbine (19) and Kaplanturbine (20) are graphically shown in Figs. 7 and 8, respectively.

In the same way, errors incurred using cost equations areshown in Table 5. These errors are similar to those obtained forPelton and Francis turbines, since they range between þ23.50%and �18.53%.

6. Summary of results

The Table 6 lists the results obtained, including cost equationsper power unit, their R2 related and error range, for each type ofmachine.

Table 1Cost functions found in literature

Cost function Country Year Author

(2) COSTð$Þ ¼ 9000P0:7H�0:35 Canada 1978 Gordon and Penman [3,4]

(3) COSTð$Þ ¼ 97:436P0:53H�0:53 Sweden 1979 Lasu and Persson [10]

(4) COSTð$Þ ¼ 9600P0:82H�0:35 USA 1984 Gulliver [6]

(5) COSTð$=kWÞ ¼ 31:500P0:25H�0:75 United Kingdom 1988 Whittington [14]

(6) COSTð$Þ ¼ 40:000P0:70H�0:35 Greece 2000 Voros [13]

(7) COSTðFRSÞ ¼ 103ð34:12þ 16:99,P0:91H�0:14Þ Switzerland 2000 Chenal [2]

(8) COSTð$=kWÞ ¼ 12:9P0:82H�0:246 Canada 2003 Gordon [5]

(9) COSTðV=kWÞ ¼ 3:300ðP�0:122H�0:107Þ Greece 2007 Kaldellis [8,9]

B. Ogayar, P.G. Vidal / Renewable Energy 34 (2009) 6–138

7. Validation of results

Equations obtained for every type of turbine have been vali-dated among engineering companies working in the design andassembly of small plants. It is noticeably that all of them perfectlyfulfil all manufacturing standards and that cost deviation is that

Fig 2. Map of loca

expected in every studied case for different types of realinstallations.

These companies have provided the following actual costs ofelectro-mechanical equipment plants located in Europe andNorthern Africa. We have simulated the various costs, using equa-tions of Table 6, and then determined the various errors. In the

tion of plants.

2000Power kw

1000

0

200000

400000

600000

800000

CO

ST

€

5001000

1500

200

400

600

800Head m

Fig 3. Graphic representation of the cost of Pelton turbines.

500 10002000

Power kW

2004006008001000

Head m

200000

0

400000

600000

800000

CO

ST

€

1500

Fig 4. Graphic representation of the cost of Pelton turbines.

Table 2Errors incurred by the use of Eq. (15)

Name of the plant P (kW) H (m) Real cost (V/kW) Simulated cost (V/kW) Error (%)

Santa Isabel 25 88 1400.00 1549.29 �10.66Santa Isabel 2 30 88 1233.33 1449.62 �17.54Ntra. Sra. de Tiscar 58 85 1034.48 1151.00 �11.26Rıo Frıo 80 155 1062.50 864.23 18.66Sp-P3 93 100 1021.51 925.55 9.39Mata Bejid 100 80 1200.00 959.86 20.01Sp-P2 113 180 796.46 730.51 8.28Sp-P1 178 75 786.52 792.08 �0.71La Toba 190 80 763.16 759.52 0.48Cerrada de Utrero 365 160 465.75 492.40 �5.72Acequia Hijuela de la Maja 400 165 473.30 472.11 0.25Valdepenas 510 109 392.16 485.62 �23.83Rıo Frıo 600 145 405.68 422.31 �4.10Cerrada de Utrero 750 160 360.61 378.65 �5.00Acequia Almegijar 750 225 353.40 343.97 2.67Valdepenas 900 110 420.71 393.74 6.41Alhori II 900 112 420.71 391.74 6.88Rıo Frıo 1000 155 390.66 344.00 11.94Sabinar 1000 200 288.49 320.16 �10.98Sabinar 2 1000 300 265.05 285.60 �7.75

B. Ogayar, P.G. Vidal / Renewable Energy 34 (2009) 6–13 9

500 1000 1500

Power kW

100200300

Head m

100000

200000

300000

400000

500000

CO

ST

€

2000

Fig 5. Graphic representation of the cost of Francis turbines.

1500

2000

100

200

300

Head m

100000200000300000

400000

500000

CO

ST

€

500

1000Power kW

Fig 6. Graphic representation of the cost of Francis turbines.

Table 3Errors incurred by the use of the Eq. (18)

Name of the Plant P (kW) H (m) Real cost(V/kW)

Simulated cost(V/kW)

Error (%)

Cristo de la Fe 200 29 788.83 860.89 �9.13Sp-F1 235 25 744.68 801.52 �7.63Potril 250 32 880.00 750.28 14.74Sp-F3 263 84 760.46 645.00 15.18Cubillas 300 12 720.00 767.49 �6.60Sp-F2 313 50 511.18 625.01 �22.27Pinos Puente 350 14 840.00 690.33 17.82Lojena 350 35.8 805.71 612.59 23.97Moclın 400 70 473.30 521.95 �10.28San Clemente 450 36 471.19 531.77 �12.86Nuevo Alcazar 500 85 424.07 449.39 �5.97Moclın 550 70 377.00 436.68 �15.83El Portillo 2 750 55.5 353.40 378.04 �6.97Rumblar 1000 47 315.53 328.66 �4.16El Portillo 1 1000 55.5 302.91 321.78 �6.23Rıo Frıo 1000 155 317.00 282.36 10.93Valdepenas 1500 116 260.00 233.45 10.21

B. Ogayar, P.G. Vidal / Renewable Energy 34 (2009) 6–1310

analysis, it has been included the results obtained by theseequations that have been recently developed for European countryand Canada.

Analyzing the results in Table 7, it should be noted that theerrors incurred using the equations developed in this paper liewithin a band of fluctuation between þ19.52% and �9.50%. Asshown in Fig 9, the costs have been compared using the proposedequation and real cost for the plants considered.

The errors incurred by the equations reviewed in this paper arehigher than those incurred by our equations. However, the functionproposed by Kaldellis [8,9] and Voros [13] matches real costreasonably well (Fig 10).

Table 4Constants calculated in Kaplan–semiKaplan turbines

a b c R2

SemiKaplan 1.9498 0.41662 �0.113901 91.70Kaplan 3.1196 0.41662 �0.113901 91.72

5002000

Power kW

5101520

Head m

100000

200000

300000

400000

CO

ST

€

1000 1500

Fig 7. Graphic representation of the cost of semiKaplan turbines.

500

1000

1500

2000

Power kW

5

10

15

20

Head m

200000

400000

600000

CO

ST

€

Fig 8. Graphic representation of the cost of Kaplan turbines.

Table 5Errors incurred using cost Eqs. (19) and (20)

Name of the Plant P (kW) H (m) Real cost(V/kW)

Simulated cost(V/kW)

Error (%)

D-642-AET 9.4 1.5 6170.21 4971.08 19.43D-862-AEC 15.9 1.5 3710.69 3646.89 1.72D-646-AEV 53.4 5 1573.03 1557.00 1.02D-972-AET 60.2 3 1362.13 1537.73 �12.89D-13112-AES 62.9 1.8 1701.11 1588.25 6.63D-5310-AEV 65.4 9 1467.89 1292.20 11.97Puente del Obispo 100 2.5 1100.00 1164.14 �5.83D-13112-AEC 118.9 3 874.68 1029.63 �17.71D-868-AEV 142.7 7 840.93 839.59 0.16Electra San Juan 145 7 827.59 831.72 �0.50Purısima Concepcion 150 18 700.00 732.11 �4.59D-8610-AEV 163.3 13 887.94 722.66 18.61D-15132-AES 178 3 747.19 811.72 �8.64Las Chozuelas 186 6.25 698.92 727.52 �4.09D-12140-AET 203.2 4.6 659.45 715.11 �8.44Las Chozuelas 220 6.25 659.09 658.99 0.02Electra San Juan 225 7 622.22 641.98 �3.18D-15134-AEC 300.7 4.6 478.88 567.63 �18.53D-16144-AES 311.9 4 461.69 564.44 �22.26D-1088-AEV 325.2 9 445.88 502.13 �12.61D-7512-AEV 365.9 18 409.95 432.86 �5.59Las Chozuelas 530 5.4 405.66 399.09 1.62San Rafael 1000 4 360.61 284.07 21.23Casas Nuevas 1500 6.17 278.33 212.91 23.50

B. Ogayar, P.G. Vidal / Renewable Energy 34 (2009) 6–13 11

8. Conclusions

We have obtained equations which facilitate the determinationof the cost of electro-mechanical equipment from easily availableparameters in any small hydro-power plant: net head and power.These expressions have been differentiated for the most commontypes of turbines: Pelton, Francis, Kaplan and semiKaplan, and fora power range below 2 MW. All equations fit the original costs quitewell, as R2 exceeds 75% in all cases.

Table 6Summary cost equations, error range and R2

Turbinetype

Cost function (V/kW) Errorrange (%)

R2 (%)

Pelton (21) COST ¼ 17:693P�0:3644725H�0:281735 �23.83,þ20.015

93.16

Francis (22) COST ¼ 25:698P�0:560135H�0:127243 þ22.27,�15.83

72.26

Kaplan (23) COST ¼ 33:236P�0:58338H�0:113901 þ23.50,�18.53

91.70

SemiKaplan (24) COST ¼ 19:498P�0:58338H�0:113901 þ23.50,�18.53

91.72

Allth

asw

ellas

those

prop

tth

eequ

ations

prop

turb

ines

and

do

not

gThof

the

electro-m

echtom

aticvalve,

aspir

em

ainten

ance

costTh

pd

etermin

eth

ein

itiaw

hen

plan

nin

grefu

ro-p

ower

plan

tsw

ithAal

installation

sexist

in)

asw

ellas

inoth

e,Portu

gal)an

dA

fricer

than

20

%;

Table 7Validation of results and errors incurred

Turbine type P (kw) H (m) Real cost(V/kw)

Simulatedcost(V/kw)

Vorosequation(V/kw)

Chenalequation(V/kw)

Gordonequation(V/kw)

Kaldellisequation(V/kw)

Errorsimulation(%)

Errorchenal(%)

Errorvoros(%)

Errorgordon(%)

Errorkaldellis(%)

Senhora – Italy Francis 400 92 550 504 409 1330 361 979 �8.36 141.85 �25.72 �34.43 78.06La frasnee – France Francis 80 50 1375 1341 820 1754 179 1272 �2.45 27.56 �40.39 �86.97 �7.48Sailant – France Francis 450 24 544 560 631 1582 884 1115 2.84 190.59 15.93 62.46 104.73Oum er rbia-Morocco Francis 240 26 938 788 741 1671 518 1193 �15.93 78.26 �20.95 �44.75 27.28Dronero – Italy Francis 420 28 655 571 611 1560 805 1106 �12.84 138.19 �6,76 22,91 68.87El portillo – Spain Francis 2753 70.64 209 177 251 1145 2995 796 �15.24 448.35 20.33 1334.35 281.33Ferreras – Spain Francis 2342 53.28 172 201 291 1209 2811 837 16.85 603.38 69.37 1535.83 386.97Sauvage – France Kaplan 102 2.5 1225 1173 2174 2535 457 1702 �4.28 106.89 77.42 �62.72 38.86Navas – Spain Kaplan 300 3,1 1000 984 1459 2188 1049 1458 �1.59 118.76 45.90 4.94 45.79Sp1 – kaplan Kaplan 485 3 701 745 1278 2095 1569 1380 6.26 198.84 82.28 123.76 96.82Sp2 – kaplan Kaplan 900 3 589 590 1061 1974 2604 1280 0.14 235.28 80.25 342.25 117.28Acheres – France Kaplan 450 8 367 420 927 1842 1159 1254 14.61 402.37 152.85 216.,08 241.92Saltos dellocca – Italy Kaplan 260 3 827 649 1541 2230 941 1489 �21.48 169.67 86.31 13.77 80.04Castrillo – Spain Kaplan 200 3 875 758 1667 2292 759 1537 �13.39 161.98 90.49 �13.29 75.68Valgode – Portugal Kaplan 670 7 410 337 862 1805 1660 1211 �17.78 339.73 110.05 304.41 195.15Zennegat – Belgium Kaplan 110 5.05 1591 1016 1662 2284 409 1564 �36.15 43/59 4.46 �74.30 �1.70Trooz- Belgium Kaplan 300 3.9 700 579 1346 2119 992 1423 �17.26 202.76 92.34 41.69 103.22Mor 1 – Morocco Pelton 200 90 775 721 507 1440 329 1068 �6.96 85.80 �34.60 �57.60 37.84Manteigas – Portugal Pelton 300 178 583 513 354 1253 387 945 �12.01 114.81 �39.40 �33.58 62.03Cartignano – Italy Pelton 300 150 567 539 375 1283 404 963 �4.95 126.37 �33.77 �28,68 69.88Muceres – Portugal Pelton 170 170 882 640 426 1347 246 1018 �27.51 52.69 �51.72 �72.12 15.37Palencia – Spain Semikaplan 500 3 500 452 2026 2089 1608 1375 �9.50 317.75 305.18 221.66 174.93

0

500

1000

1500

2000

2500

3000

3500

SENHORA-ITALYLA FRASNEE-FRANCE

SAILANT-FRANCEOUM ER RBIA-MOROCCO

DRONERO-ITALYEL PORTILLO-SPAIN

FERRERAS-SPAINSAUVAGE-FRANCE

NAVAS-SPAINSP1-KAPLANSP2-KAPLAN

ACHERES-FRANCESALTOS DELLÓCCA-ITALY

CASTRILLO-SPAINVALGODE-PORTUGALZENNEGAT-BELGIUM

TROOZ- BELGIUMMOR 1-MOROCCO

MANTEIGAS-PORTUGALCARTIGNANO-ITALY

MUCERES-PORTUGALPALENCIA-SPAIN

COST (€/kW)

REAL C

OST (€/kW

)KALD

ELLIS EQU

ATION

(€/kW)

VOR

OS EQ

UATIO

N (€/kW

)G

OR

DO

N EQ

UATIO

N (€/kW

)C

HEN

AL EQU

ATION

(€/kW)

Fig10.

Real

costvs.equation

san

alyzed.

0

500

1000

1500

2000

2500

3000

3500

ORA-ITALYEE-FRANCENT-FRANCE-MOROCCOERO-ITALYILLO-SPAINRAS-SPAINE-FRANCEVAS-SPAINP1-KAPLANP2-KAPLANES-FRANCECCA-ITALY

ILLO-SPAIN-PORTUGALT-BELGIUM

TROOZ- BELGIUMMOR 1-MOROCCO

MANTEIGAS-PORTUGALCARTIGNANO-ITALY

MUCERES-PORTUGALPALENCIA-SPAIN

COST (€/Kw)

REAL C

OST (€/kW

)SIM

ULATED

CO

ST (€/kW)

B.Ogayar,P.G

.Vidal

/Renew

ableEnergy

34(2009)

6–1312

ereview

edequ

ations

do

not

match

reald

ataosed

inth

isp

aper.

This

isd

ue

toth

efact

tha

osedh

eretake

into

accoun

td

ifferent

types

ofen

eralise.e

cost

inclu

des

the

ex-works

market

price

anical

equ

ipm

ent

(turb

ine,

alternator,

auation

and

pn

eum

aticregu

lationelem

ents).Th

isn

otin

clud

ed.

eresu

ltsofth

eseequ

ations

canb

eu

sedto

hel

lin

vestmen

tat

ap

revious

stud

ylevel

bish

men

tor

new

constru

ctionof

small

hyd

rou

td

evelopin

ga

comp

letep

roject.ll

expression

sh

aveb

eenvalid

atedw

ithre

ing

inth

ep

rovinces

ofJaen

and

Gran

ada

(Spa

rcou

ntries

inEu

rope

(France,

Italy,B

elgium

a(M

orocco),w

ithcom

mitted

errorslow

SENHLA FRASN

SAILAOUM ER RBIA

DRONEL PORT

FERRESAUVAG

NASS

ACHERSALTOS DELLÓ

CASTRVALGODEZENNEGA

Fig9.

Real

costvs.sim

ulatedcost.

B. Ogayar, P.G. Vidal / Renewable Energy 34 (2009) 6–13 13

a completely acceptable percentage for a previous study on therefurbishment of small plants.

Acknowledgments

We would like to thank all companies and organizations whichhave verified the validity of the equations obtained in this work,specially Saltos Del Pirineo, Hydroship and the Institute for EnergyDiversification and Saving (IDAE).

Appendix. Cost analysis methodology

The expression of initial cost of electro-mechanical equip-ment is

COST ¼ aPbHcðVÞ (25)

Applying logarithms in the of expression (25), it is obtained

log COST ¼ log�

aPbHc�¼ log aþ ðb� 1Þlog P þ clog H;

(26)

Carrying out a variable change

Z ¼ log COSTX ¼ log PY ¼ log H

;

Expression (26) will remain the following way

Z ¼ log aþ bX þ cY; (27)

Substituting data of cost, power and head of every plant whosedata are known in the previous expression, it is obtained

Z1 ¼ log aþ bX1 þ cY1Z2 ¼ log aþ bX2 þ cY2Zn ¼ log aþ bXn þ cYn

(28)

Then we proceeded to search the plane AXþ BYþ CZþD¼ 0with the best fit to data (Xk, Yk, Zk) using Eq. (28) and carrying outa multiple regression between the independent variables (X, Y)and (Z)

AX þ BY þ CZ þ D ¼ 0 (29)

Working out the value of Z, supposing C s 0 without restrictionas the plane would not be vertical,

Z ¼ ��

DC

���

AC

�X �

�BC

�Y; (30)

Constants a, b, c are obtained by comparing Eqs. (27) and (30)through the following expressions

a ¼ e�DC

b ¼ �AC

c ¼ �BC

(31)

The function of cost per power unit will be

COST ¼ aPb�1HcðV=kWÞ (32)

References

[1] Anagnostopoulos JS, Papantonis DE. Optimal sizing of a run-of-river smallhydropower plant. Energy Convers Manag 2007;48(10):2663–70.

[2] Raymond Chenal. Evaluation du co}ut de construction d’une petite centralehydro-electrique nouvelle et complete et du prix de revient du kwh (p< d1000 kw). Suisse: MHylab. Available from: http://www.mhylab.com/fr/pages/pdf/cout_PCH.pdf; 2000.

[3] Gordon JL, Penman AC. Quick estimating techniques for small hydro potential.Int Water Power Dam Construction 1979;31(9):46–51.

[4] Gordon JL. Dissertation on site development and cost. WATERPOWER XII. SaltLake City, Utah ,USA 2001.

[5] Gordon JL. Determining ‘‘Ballpark’’ costs for a proposed project. Hydro Rev2003;11(1):37–41.

[6] Gulliver JS, Avry D. Cost estimated for hydropower at existing dams. J EnergyEng 1984;10(3):204–14.

[7] IDAE (Instituto para la diversificacion y Ahorro de la Energıa). MinicentralesHidroelectricas. Madrid: IDAE; 2007.

[8] Kaldellis JK, Vlachou DS, Korbakis G. Tecno-economic evalution of small hydropower plants in Greece: a complete sensitivity analysis. Energy Pol 2005;33(15):1969–85.

[9] Kaldellis JK. The contribution of small hydro power stations to the electricitygeneration in Greece: technical and economic considerations. Energy Pol2007;35(4):2187–96.

[10] Lasu S, Persson T. Mini power station in Sweden. Internationale Fachtagunguber Umbau und Erweitrung von Wasserkraftanlagen 1979:34.

[11] Montanari R. Criteria for the economic planning of a low power hydroelectricplant. Renew Energy 2003;28(13):2129–45.

[12] Sheldon LH. Cost analysis of hydraulic turbines. Int Water Power Dam Const1981:33.

[13] Voros NG, Kiranoudis CT, Maroulis ZB. Short-cut design of small hydroelectricplants. Renew Energy 2000;19(4):545–63.

[14] Whittinton HW, Wallace AR, Henderson DS. An economic analysis of capitalcosts in micro-hydro. In: Third international conference on small hydro,Cancun, Mexico, Hydro-88; p. 182–197.

[15] Willer David C. Powerhouse and small hydropower project cost estimated. In:Gulliver Johns S, editor. Hydropower engineering handbook. New York:McGraw-Hill; 1991. pp. 6.1–6.58.