Sizing a hybrid wind-diesel stand-alone system on the basis of minimum long-term electricity...

APPLIED

Applied Energy 83 (2006) 1384–1403

www.elsevier.com/locate/apenergy

ENERGY

Sizing a hybrid wind-diesel stand-alone system onthe basis of minimum long-term

electricity production cost

J.K. Kaldellis a,*, E. Kondili b, A. Filios c

a Laboratory of Soft Energy Applications and Environmental Protection, TEI of Piraeus,

P.O. Box 41046, Athens 12201, Greeceb Optimisation of Production Systems Laboratory, Mechanical Engineering Department, TEI of Piraeus,

P.O. Box 41046, Athens 12201, Greecec Fluid Mechanics and Turbomachines Laboratory, School of Pedagogical and Technological Education,

P.O. Box 41046, Athens 12201, Greece

Received 17 October 2005; received in revised form 29 December 2005; accepted 14 January 2006Available online 3 April 2006

Abstract

Hybrid wind-diesel systems are an interesting solution for the electrification of isolated consum-ers. The proposed system, including a properly sized battery, leads to a significant reduction of thefuel consumption, in comparison with a diesel-only installation, also protecting the diesel generatorfrom excessive wear. On the other hand, a properly designed wind-diesel installation remarkablyreduces the required battery capacity, in relation to a wind-only based stand-alone system, especiallyin medium-low wind potential areas. In this context, a complete sizing model, based on a long-termenergy production cost analysis is developed, able to predict the optimum configuration of a hybridwind-diesel stand-alone system on the basis of minimum long-term cost. According to the applica-tion results obtained for representative wind potential cases, the proposed hybrid system guaranteesone year’s long energy autonomy of a typical remote consumer, presenting a significant cost advan-tage in relation either to a diesel-only or to a wind-based stand-alone system.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Hybrid wind-diesel system; Stand-alone; Optimum system sizing; Energy cost; Long-term operationalcost

0306-2619/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apenergy.2006.01.006

* Corresponding author. Tel.: +30 210 5381237; fax: +30 210 5381348.E-mail address: [email protected] (J.K. Kaldellis).URL: www.sealab.gr (J.K. Kaldellis).

mailto:[email protected]

www.sealab.gr

J.K. Kaldellis et al. / Applied Energy 83 (2006) 1384–1403 1385

1. Introduction

Stand-alone wind-power systems provide an interesting solution for the electrificationof various isolated consumers [1,2]. One important technical problem of similar installa-tions results by the highly fluctuating power-output of the wind turbine, which is generallyincompatible with the demand of typical domestic or commercial users. To face this prob-lem, an appropriate energy-storage device is usually incorporated, which however signif-icantly increases the initial cost of stand-alone installations [3].

On the other hand, diesel-electric generator sets, while being relatively inexpensive topurchase, are generally expensive to operate and maintain, especially at partial-load levels[4]. In the absence of energy storage, a high start–stop cycling frequency is evident. Thiswill lead to an increased wear of the diesel and, therefore, to an increased demand of main-tenance [5].

A hybrid wind-diesel system (with energy storage) reimburses the capital cost of thewind turbine and the operating costs of the diesel-electric generator, while remarkablydecreasing the battery bank size [6,7]. In this context, a hybrid wind-diesel system, includ-ing a properly-sized battery bank, leads to a significant reduction in the start–stop cyclingfrequency of the diesel, along with fuel consumption shrinkage, compared with the diesel-only operation system. Besides, the proposed hybrid system remarkably reduces therequired battery capacity in relation with a wind-based stand-alone system, especially inrelatively low wind potential areas.

Thus far, optimal sizing of stand-alone systems is usually based on simplified cost anal-ysis, mainly concentrated on the initial installation cost. Although this analysis provides afirst estimation, a long-term cost investigation is required, including maintenance andoperation cost. Thus, in this paper a complete long-term energy-production cost methodof a wind-diesel hybrid system is developed. This method considers the fixed and variablecosts of maintenance, operation and financing, in addition to initial costs. By using theproposed model, the optimum configuration of a hybrid stand-alone system may bedefined based on minimum long-term cost.

2. Proposed solution

A typical wind-diesel hybrid system (Fig. 1), able to meet the electricity requirements ofisolated consumers, comprises of:

(a) A micro wind-converter of rated power ‘‘N0’’ and given power curve N = N(V) forstandard day conditions [2].

(b) A small internal combustion engine of ‘‘N*’’ kW, able to meet the consumptionpeak-load demand ‘‘Np’’ (i.e. N* P Np), presenting a typical specific-fuel-consump-tion curve versus partial loading of the engine [4].

(c) A lead-acid battery storage system for ‘‘h0’’ hours of autonomy, or equivalent totalcapacity of ‘‘Qmax’’, operation voltage ‘‘Ub’’ and maximum depth of discharge‘‘DODL’’.

(d) An AC/DC rectifier of ‘‘N0’’ kW and UAC/UDC operation voltage values.(e) A DC/DC charge controller of ‘‘N0’’ rated power, charge rate ‘‘Rch’’ and charging

voltage ‘‘UCC’’.

Fig. 1. Proposed autonomous wind-diesel hybrid system.

1386 J.K. Kaldellis et al. / Applied Energy 83 (2006) 1384–1403

(f) A UPS (uninterruptible power supply) of ‘‘Np’’ kW, frequency of 50 Hz, autonomytime ‘‘dt � 2 min’’ and operation voltage 220/380 V. The UPS utilization – betweenthe installed wind-turbine and the AC load – is optional and it is proposed here inorder to stabilize the wind-turbine’s output as well as to protect the sensitive devicesfrom undesired power-fluctuations.

(g) A DC/AC inverter of maximum power ‘‘Np’’ able to meet the consumption peakload demand, frequency of 50 Hz and operational voltage 220/380 V.

This system should be capable of satisfying the electricity demand of a remote consumer(e.g. a four to six member family), with rational first installation and long-term opera-tional costs. The specific remote consumer investigated (see also [8–10]) presents a loadprofile described in Fig. 2. This is basically a rural household profile (not an average loadtaken from typical users) selected among several profiles provided by the Hellenic Statis-tical Agency [2,6]. More precisely, the numerical load values vary between 30 W (refriger-ator load) and 3300 W. According to the consumption profile approved, the annual peak

Typical Weekly Electricity Demand Profile

0

500

1000

1500

2000

2500

3000

3500

4000

0 24 48 72 96 120 144 168

Time (hours)

Load

Dem

and

(W)

Winter Consumption

Summer Consumption

Fig. 2. Typical electricity demand profile of the remote consumer analyzed.


load ‘‘Np’’ does not exceed 3.5 kW, while the annual energy consumption ‘‘Ey’’ is almost4750 kW h.

Thus, the annual electricity consumption, on an hourly basis, being also dependent onthe portion of the year analysed (i.e. winter, summer, other), is the first input of the presentanalysis, see also Fig. 2. Additionally, the corresponding wind-potential and ambient tem-perature and pressure are also necessary to integrate the system sizing calculations.Finally, the operational characteristics of all the components (e.g. wind-power curve atstandard-day conditions, diesel generator specific-fuel-consumption, inverter efficiency,battery-bank characteristic, etc.) composing the hybrid system under investigation are alsorequired.

During the operation of the system the following energy-production scenarios exist:

� The energy (AC current) is produced by the micro wind-converter and it is directly sentto consumption via the UPS.� The energy (AC current) is produced by the small diesel-electric generator and it is for-

warded to the consumer.� The energy output of the wind turbine (not absorbed by the consumption-energy sur-

plus) is transformed to DC current (via AC/DC rectifier) and it is subsequently storedin the batteries via the charge controller.� The battery is used to cover the energy deficit via the charge controller and the DC/AC

inverter.

For estimating the appropriate configuration of the proposed wind-diesel hybridsystem, three governing parameters should be defined: the rated power ‘‘N0’’ of the windturbine used, the battery’s maximum necessary capacity ‘‘Qmax’’ and the annual fuel-consumption ‘‘Mf’’. For the solution of this problem, the already presented [2,11]computational algorithm ‘‘WINDREMOTE-II’’ is hereby expanded to include a smalldiesel-electric generator. This new numerical code ‘‘WIND-DIESEL I’’ is applied to carry


out the necessary parametrical analysis on an hourly energy production-demand basis, tar-geting to estimate the wind turbine rated power ‘‘N0’’ and the corresponding batterycapacity ‘‘Qmax’’ given the annual permitted oil-consumption ‘‘Mf’’; see also Fig. 3.

Fig. 3. WIND-DIESEL-I algorithm.


More specifically, given the ‘‘Mf’’ value – for each ‘‘N0’’ and ‘‘Qmax’’ pair – the ‘‘WIND-DIESEL I’’ algorithm is executed for all the time-period selected (e.g. for one month, six-months, one year or even for three years) and emphasis is laid on obtaining zero-loadrejection operation. Using the proposed algorithm, for every (N0, Q*, Mf) combinationensuring the energy autonomy of the remote system, a detailed energy-production anddemand-balance are available along with the corresponding time-depending battery depthof discharge, ‘‘DOD’’ and diesel-oil consumption time evolution. The optimum configura-tion is subsequently predicted on the basis of the minimum long-term cost configuration.

3. Cost-benefit analysis of the proposed solution

The present value of the entire investment cost of a stand-alone wind-diesel hybrid sys-tem operating for a n-years period is a combination of the initial installation cost and thecorresponding maintenance and operation cost [12].

3.1. First installation cost

The initial investment cost ‘‘IC0’’ includes the market (ex-works, i.e. not including theinstallation cost) price of the installation components (wind turbine, ICWT; diesel genera-tor, ICd; battery, ICbat; inverter, UPS, rectifier, charge controller, ICelec) and the corre-sponding balance of the plant cost, expressed as a fraction ‘‘f’’ of the wind-turbine’spurchase cost. Thus one may write:

IC0 ¼ ICWT þ ICd þ ICbat þ ICelec þ f � ICWT ð1ÞUsing the analysis of previous studies [13,14] the following expression is assumed valid:

IC0 ¼a

bþ Nx0

þ c� �

� N 0 � ð1þ f Þ þ u � N d þ n � Q1�xmax þ k � N 1�s

p þ B � N 0 ð2Þ

where ‘‘N0’’ is the wind-turbine’s rated power, ‘‘Nd’’ is the diesel-electric generator nom-inal power, ‘‘Np’’ is the consumption peak-load demand (including an appropriate safetyfactor, e.g. 1.3) and ‘‘Qmax’’ is the battery capacity. Besides ‘‘a, b, x and c’’ are numericalconstants used to convey [13] the ex-works price of small wind-converters (up to 100 kW)in the local market. Their numerical values are equal to 8.7 · 105 Euro/kW, 621, 2.05 and700 Euro/kW, respectively. Similarly, parameters ‘‘n and x’’ are instructed [14] to describethe battery bank initial cost: thus n = 5.04 Euro/Ah and x = 0.078, while ‘‘u’’ representsthe diesel-electric generator specific purchase cost (e.g. u = 150–250 €/kW). Finally,parameters ‘‘k, s and B’’ are respectively equal to 483 Euro/kW, 0.083 and 380 Euro/kW, used also to assess [14] the electronic devices initial-cost.

3.2. Maintenance and operation cost

During long-term operation of a hybrid wind-diesel system, the maintenance and oper-ation (M&O) cost can be split [12] into the fixed ‘‘FCn’’ and the variable ‘‘VCn’’ mainte-nance cost. Usually, the annual fixed M&O cost of a stand-alone wind-power system isexpressed as a fraction ‘‘m’’ of the initial capital invested. On top of this, an annual increaseof the fixed M&O cost is taken into account (M&O cost mean annual inflation rate ‘‘gm’’),incorporating the annual changes of labor cost and the corresponding spare-parts.


In a wind-diesel hybrid system, one should also consider the diesel generator M&Ocost, expressed as a function of the annual diesel-oil consumption ‘‘Mf’’. Besides, the cor-responding specific price ‘‘c0’’ includes any lubricant consumption. In this context, onemay write:

FCn ¼ m � IC0 � x � ð1þ xþ x2 þ � � � þ xn�1Þ þ c0 �M f � y � ð1þ y þ y2 þ � � � þ yn�1Þð3Þ

with

x ¼ 1þ gm

1þ ið4Þ

and

y ¼ 1þ e1þ i

ð5Þ

where ‘‘i’’ is the local market capital cost, while ‘‘e’’ is the diesel-oil price mean annualescalation-rate.

The variable maintenance and operation cost ‘‘VCn’’ mainly depends [3] on the replace-ment of ‘‘k0’’ installed major parts, sustaining a shorter lifetime ‘‘nk’’ than the completeinstallation. Using the symbol ‘‘rk’’ for the replacement-cost coefficient of each one ofthe ‘‘k0’’ major parts (battery, diesel generator, rotor blades, etc.) the ‘‘VCn’’ term canbe expressed as:

VCn ¼ IC0 �W ð6ÞBear in mind that ‘‘VCn’’ takes into consideration the diesel-electric generator ‘‘rdIC0’’ andthe battery ‘‘rbIC0’’ replacement cost every ‘‘nd’’ and ‘‘nb’’ years respectively (nd � 4–6 andnb � 5–7 years), while ‘‘gd’’ and ‘‘gb’’ describe the diesel-electric generator/battery pur-chase cost mean annual inflation rate.

It is important to note that the ‘‘W’’ term expresses the replacement cost of specific(major) parts of the installation, given as a fraction of the initial installation cost. For exam-ple, at the end of the fifth year, the diesel-electric generator should be replaced, taking intoconsideration its expected purchase-cost increase (or decrease) and the corresponding cap-ital cost impact (since the present value model is adopted here). Similarly, the installationbatteries should be replaced at the end of the seventh year. Thus one may write:

W¼ 0 for n6 nd ¼ 5

W¼ rd �1þ gd

1þ i

� �nd

for ndþ 16 n6 nb ¼ 7

W¼ rd �1þ gd

1þ i

� �nd

þ rb �1þ gb

1þ i

� �nb

for nbþ 16 n6 2nd ¼ 10

W¼ rd �1þ gd

1þ i

� �nd

þ rd �1þ gd

1þ i

� �2nd

þ rb �1þ gb

1þ i

� �nb

for 2ndþ 16 n6 2nb ¼ 14

W¼ rd �1þ gd

1þ i

� �nd

þ rd �1þ gd

1þ i

� �2nd

þ rb �1þ gb

1þ i

� �nb

þ rb �1þ gb

1þ i

� �2nb

for 2nbþ 16 n6 3nb ¼ 15


W¼ rd �1þ gd

1þ i

� �nd

þ 1þ gd

1þ i

� �2nd

þ 1þ gd

1þ i

� �3nd

" #þ rb �

1þ gb

1þ i

� �nb

þ 1þ gb

1þ i

� �2nb

" #

for 2ndþ 16 n6 nmax ¼ 20 ð7Þ

3.3. Long-term cost of the hybrid system

Using the analysis of Sections 3.1 and 3.2, one may estimate the long-term cost of awind-diesel hybrid system in present values as follows:

Cn ¼ IC0 � ð1� cÞ þ m � x � xn � 1

x� 1þ c0 �M f

IC0

� y � yn � 1

y � 1þW

� �ð8Þ

The proposed model also includes the diesel only solution (i.e. IC0 = uNd, N0 = 0, rb = 0,Mf = Mmax) as well as the wind-only configuration (i.e. ICd = 0, rd = 0, Mf = 0).

Finally, ‘‘c’’ is the subsidy percentage (e.g. 30%–40%) by the Greek State, according tothe current development law (e.g. 3299/04) or the corresponding National OperationalCompetitiveness Program [12].

4. Optimum configuration prediction for various typical cases

4.1. Final equations used

According to Eqs. (1) and (2), the initial cost ‘‘IC0’’ of the proposed hybrid station is afunction of the wind turbine rated power ‘‘N0’’, the battery capacity ‘‘Qmax’’ and the cor-responding peak load demand ‘‘Np’’, while there is no contribution of the oil cost. On theother hand, the total operational cost ‘‘Cn’’ takes into account the system M&O cost aswell as the annual oil consumption cost, whilst it is also influenced by the local marketinflation rate, the capital cost and the oil price annual escalation rate.

Subsequently, considering the replacement cost of the diesel-electric generator and thesystem batteries every ‘‘nd’’ and ‘‘nb’’ years respectively, a significant modification of theoptimum solution values (N �0, Q�max, M�

f ) is expected in comparison with the one basedon the initial cost minimization only [15].

In the following, the 10-year and the 20-year total operational cost (in present values) ofthe hybrid station under consideration is to be used as the dominant choice criterion,expressed as follows:

C10 ¼ IC0 � ð1� cÞ þ m � x � x10 � 1

x� 1þ c0 �M f

IC0

� y � y10 � 1

y � 1þ rd � x5 þ rb � x7

� �ð9Þ

and

C20 ¼ IC0 � ð1� cÞ þ m � x � x20 � 1

x� 1þ c0 �M f

IC0

� y � y20 � 1

y � 1

�

þrd � ðx5 þ x10 þ x15Þ þ rb � ðx7 þ x14Þ�

ð10Þ

accepting that gd � g and gb � g.


4.2. High wind potential case

The first case analyzed concerns a remote consumer located at a high wind potentialarea, e.g. the island of Andros. Andros is a medium-sized island (the second biggestone) of the Cyclades complex (population 12,000 habitants, area of 384 km2), located inthe middle of the Aegean Sea. The local terrain is very intense, including several rockymountains with relative sharp slopes. The island has one of the best wind potential inGreece (annual mean wind speed, �V � 10 m=s), since the minimum monthly average windspeed [16] exceeds the 6.5 m/s, Fig. 4. At the same time, the number of zero-wind-produc-tion days (daily average wind speed below 4.0 m/s) is minimum, see also Fig. 5, underlin-ing the fact that the maximum calm spell period of the island is 37 h.

Applying the proposed solution for the Andros case, one may obtain the (Qmax � N0)distribution that guarantees one year energy autonomy for various typical annual oilquantities (i.e. Mf = 0 kg/year up to Mf = 1000 kg/year); see Fig. 6. Bear in mind thatapproximately 2000 kg of oil are necessary in order the diesel-electric generator to meetthe electricity requirements of the specific consumer under investigation without any otheradditional energy source. Rationally, the dimensions of the hybrid system are remarkablyreduced as the contribution of diesel oil is increased. In fact, this reduction is greater whensmall quantities of diesel oil are used, while for larger oil quantities the battery bank size isslightly decreased for given wind turbine rated power.

Accordingly, the constant initial cost (IC0 = ct) curves are drawn in the same Fig. 6,which however does not take into account the annual oil quantity consumed. In this con-text, one should certainly select the maximum diesel oil consumption solution, since thischoice minimizes the initial cost of the hybrid station. In Fig. 7, however, one has theopportunity to investigate the 10-year cost variation for selected representative cases.More specifically, Fig. 7 presents:

MONTHLY-AVERAGED WIND-SPEED VALUES AT ANDROS ISLAND

0

2

4

6

8

10

12

14

16

18

20

Janu

ary

Febr

uary

Mar

chApr

ilM

ayJu

ne July

Augus

t

Septe

mbe

r

Octobe

r

Novem

ber

Decem

ber

Month

Win

d S

peed

(m

/s)

Mean Value

Mean Value+Standard Deviation

Mean Value-Standard Deviation

Fig. 4. Wind-speed values at Andros island.

0

2

4

6

8

10

12

14

16

18

20

22

24

1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211 225 239 253 267 281 295 309 323 337 351 365

Days of Year

Win

d S

peed

(m

/s)

Fig. 5. Daily mean wind-speed at Andros island.

ANDROS ISLAND (24Volt, DOD=70%, DOD1=40%)

0

5000

10000

15000

20000

25000

0 2000 4000 6000 8000 10000 12000 14000 16000

Wind Power (Watt)

Bat

tery

Cap

acity

(A

h)

Mf=0

Mf=25

Mf=50

Mf=100

Mf=500

Mf=1000

ICo=20000Euro

ICo=30000Euro

ICo=40000Euro

Fig. 6. Energy autonomous configuration for a wind-diesel hybrid system, including the first installation cost,Andros island.


(i) The autonomous wind-battery solution (Mf = 0 kg/year).(ii) The diesel only solution (Mf = Mfmax = 2000 kg/year).

(iii) The 5% annual diesel-oil penetration (Mf = 100 kg/year).(iv) The 12.5% annual diesel-oil penetration (Mf = 250 kg/year).(v) The 25% annual diesel-oil penetration (Mf = 500 kg/year).

(vi) The 50% annual diesel oil penetration (Mf = 1000 kg/year).

ANDROS ISLAND WIND-DIESEL STAND ALONE SYSTEM

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 2000 4000 6000 8000 10000 12000 14000

Wind-Turbine Rated Power (Watt)

Ten

Yea

rs C

ost (

Eur

o)

Mf=0(kg/year)

Mf=100(kg/year)

Mf=250(kg/year)

Mf=500(kg/year)

Mf=1000(kg/year)

Diesel Only System

Fig. 7. Ten-year cost analysis of a wind-diesel hybrid system, Andros island.

Table 1Numerical values of the parameters of Eqs. (7) and (9)

Parameter Symbol Value

nd Diesel-electric generator service period 5 (years)nb Lead-acid battery replacement period 7 (years)ICd Diesel-electric generator purchase cost (5 kW) 750 (€)gd Mean annual increase of diesel-electric generator purchase cost 2%gb Mean annual increase of lead-acid battery purchase cost 2%m Installation annual M&O cost coefficient 2%c0 Diesel-oil specific cost 1.5 (€/kg)x see Eq. (4) 0.9444y see Eq. (5) 0.9815i Mean annual capital cost 8%


After a closer inspection of the calculation results and considering the numerical valuesof Table 1 regarding parameters of Eqs. (7) and (9), we may state the following commentsfor the 10-year cost solution:

� The optimum zero-oil solution should be based on a 4 kW wind turbine and 7100 Ahbattery capacity, while the corresponding 10-year cost is fairly higher than 35,300€.� In any case the zero-oil solution is slightly more expensive than the diesel-only solution,

i.e. by almost 5000€ (�15%), on the 10-year basis.� By increasing the diesel oil contribution the 10-year cost is remarkably reduced, being

quite lower than the diesel-only solution.� For each Mf = ct configuration there is a minimum cost area, which leads to lower bat-

tery capacity and wind turbine rated power as the diesel-oil penetration increases.

Using also Fig. 8, one may estimate the optimum diesel oil contribution that minimizesthe 10-year system cost. Hence, the corresponding optimum configuration for the specific


0

5000

10000

15000

20000

25000

30000

35000

40000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Fuel Mass Flow (kg/year)

Ten

Yea

rs C

ost (

Eur

o)ANDROS ISLAND WIND-DIESEL STAND ALONE SYSTEM

0

5000

10000

15000

20000

25000

30000

35000

40000

0 200 400 600 800 1000 1200 1400 1600 1800 2000


Ten

Yea

rs C

ost (

Eur

o)

Fig. 8. Minimum 10-year cost of a wind-diesel hybrid system, Andros island.


hybrid system under investigation is based on a 2 kW wind turbine and a battery bank of1000 Ah, while the annual fuel consumption is 500 kg/year and the minimum 10-years costapproximates the 17,300€ in present values, being less than 60% of the diesel-only solution(�29,300€).

This situation is quite different in case that a 20-year time horizon is concerned. More pre-cisely, even the autonomous wind power solution is less expensive than the diesel-only sys-tem operation, Fig. 9. Additionally, the 20-year system cost diminishes as the oil penetrationincreases. This situation is inversed after a minimum cost point is achieved, Fig. 10. Thus the


0

20000

40000

60000

80000

100000

120000

140000

0 2000 4000 6000 8000 10000 12000 14000

Wind-Turbine Rated Power (Watt)

Twen

ty Y

ears

Cos

t (E

uro)

Mf=0(kg/year)

Mf=100(kg/year)

Mf=250(kg/year)

Mf=500(kg/year)

Mf=1000(kg/year)

Diesel Only System

Fig. 9. Twenty-year cost analysis of a wind-diesel hybrid system, Andros island.


optimum configuration system is based on a 2.5 kW wind turbine, 1700 Ah battery capacity,300 kg/year diesel-oil consumption, while the corresponding 20-year cost in present values is26,300€, less than 50% of the one corresponding to the diesel only solution.

Recapitulating, one may state that in this high wind potential area, a wind-diesel hybridsystem presents a competitive advantage in comparison with a diesel only or a wind powerstand-alone system. The optimum system configuration is based on 2–2.5 kW wind tur-bines and on 1000–1700 Ah battery capacity. These solutions annually save over 75% ofthe fuel required by a diesel-only system in order to obtain full energy autonomy of theinstallation, while the corresponding 10-year or 20-year total operational cost rangesbetween 60% and 50% of the diesel-only configuration, respectively.

4.3. Low wind potential case

The second case analyzed concerns a remote consumer located at a relatively low windpotential area, e.g. the island of Kea. Kea is a small island (2300 habitants, area 103 km2)close to Athens. The topography of the island is typically Aegean, i.e. gentle slopes,absence of flat fields, low mountains and sparse vegetation, while the main economic activ-ities of the local society are agriculture, cattle breeding, beekeeping and tourism. The cor-responding wind potential [16] although quite lower than the one of Andros, is goodenough (annual mean wind speed �6.0 m/s, Fig. 11) to feed contemporary wind turbines,for electricity production. In this case, the number of zero wind production days (dailyaverage wind speed below 4.0 m/s) is quite remarkable, see also Fig. 12, therefore the max-imum calm spell period of the island is approximately 170 h (almost one week).

Applying the proposed methodology for the Kea case, one may obtain the (Qmax � N0)distribution that guarantees one year energy autonomy for various typical annual diesel-oil quantities (i.e. Mf = 0 kg/year up to Mf = 1500 kg/year); see Fig. 13. As in the Androscase, the dimensions of the hybrid system are remarkably reduced as the contribution of


0

10000

20000

30000

40000

50000

60000

0 200 400 600 800 1000 1200 1400 1600 1800 2000


Tw

enty

Yea

rs C

ost (

Eur

o)

Fig. 10. Minimum 20-year cost of a wind-diesel hybrid system, Andros island.

MONTHLY AVERAGED WIND-SPEED VALUES IN KEA ISLAND

0

2

4

6

8

10

12

14

Janu

ary

Febru

ary

Mar

chApr

ilM

ayJu

ne July

Augus

t

Septe

mbe

r

Octobe

r

Novem

ber

Decem

ber

Month

Win

d S

peed

(m

/s)

Mean Value

Mean Value+Standard Deviation

Mean Value-Standard Deviation

Fig. 11. Kea monthly mean wind-speed.

Daily Mean Wind-Speed for Kea Island

0

2

4

6

8

10

12

14

16

18

20

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361

Days of Year

Win

d S

peed

(m

/s)

Fig. 12. Kea daily mean wind-speed.


diesel oil is increased. In fact, this reduction is greater when over 100 kg of diesel-oil is con-sumed per year, since for lower diesel oil quantities the system size is not seriously mod-ified. Obviously, for given wind turbine rated power, the battery bank size is notanalogically decreased as larger oil quantities are used. In fact after the Mf = 1000 kg/yearvalue the battery capacity convergences to the same – very low – value of 450 Ah.

Accordingly, the constant initial cost (IC0 = ct) curves are drawn in the same Fig. 13,not including the annual diesel-oil consumption. Since the fuel cost is excluded, it is quite

KEA ISLAND (24Volt, DOD=70%, DOD1=40%)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

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Fig. 13. Energy autonomous configuration for a wind-diesel hybrid system, including first installation cost, Keaisland.


rational that the minimum initial cost solution is the one that uses the maximum diesel-oilquantity. On the other hand, by examining the 10-year cost variation in Fig. 14 for selectedannual diesel-oil consumption quantities, one can easily extract the following conclusions:

� There is no optimum zero-oil solution under the precondition that the wind turbinerated power is less than 15 kW. For bigger wind turbines (15 kW 6 N0 6 20 kW) a min-imum cost solution may be achieved.� The diesel-only solution is almost the most cost effective choice, excluding the high die-

sel-oil penetration solutions (i.e. Mf P 1000 kg/year).� There is a considerable 10-year cost reduction by increasing the annual diesel-oil

penetration.� For each Mf = ct configuration there is a minimum cost area, which leads to lower bat-

tery capacity and wind turbine rated power as the diesel penetration increases.

Using also Fig. 15, one may estimate the optimum diesel oil contribution that mini-mizes the 10-years system cost. Hence, the corresponding optimum configuration forthe specific hybrid system located in this medium-low wind potential area consists of a1.5 kW wind turbine and a battery bank of 1300 Ah, while the annual fuel consumptionis 1250 kg/year and the minimum 10-year cost approximates 28,500€ in present values,being slightly below the diesel only solution (�29,300€).

This situation is somewhat different in case that a 20-year time horizon is concerned.More precisely, in this long-term analysis one may use lower diesel-oil annually in orderto obtain the minimum cost operation, Fig. 16. Thus, initially the 20-years system costdiminishes as the oil penetration increases. This situation is inversed after a minimum costpoint is achieved, Fig. 17. Thus the optimum configuration system is based on a 2.5 kW

KEA ISLAND WIND-DIESEL STAND ALONE SYSTEM

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Mf=0 (kg/year)Mf=100 (kg/year)Mf=250 (kg/year)Mf=500 (kg/year)Mf=1250 (kg/year)Mf=1500 (kg/year)Diesel Only System

Fig. 14. Ten-year cost analysis of a wind-diesel hybrid system, Kea island.


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Fig. 15. Minimum 10-year cost of a wind-diesel hybrid system, Kea island.


wind turbine, 3500 Ah battery capacity, 1000 kg/year diesel-oil consumption, while thecorresponding 20-year cost in present values is 43,000€, almost 20% lower than the die-sel-only solution case.

Summarizing, even in this medium-low wind potential area, a wind-diesel hybrid systemis less expensive than a diesel only solution (especially for a long-term time horizon basis),while it is definitely more cost effective than a stand-alone wind power one. Of course, one

KEA ISLAND WIND-DIESEL STAND-ALONE SYSTEM

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Fig. 16. Twenty-year cost analysis of a wind-diesel hybrid system, Kea island.

KEA ISLAND WIND-DIESEL STAND-ALONE SYSTEM

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Fig. 17. Minimum 20-year cost of a wind-diesel hybrid system, Kea island.


should not disregard the fact that the proposed hybrid system presents additional environ-mental and increased reliability advantages that may compensate the increased first instal-lation and operational cost.

5. Discussion of the results

Considering the calculation results regarding two extreme wind potential cases, a wind-diesel stand-alone system presents significant cost advantages in comparison with diesel-


only or wind power stand-alone systems. These advantages are more obvious for highwind potential areas and for long-term operation. More specifically the mean annual costfor Andros island is almost the 40% of the corresponding cost of Kea island; see Fig. 18.Additionally, the minimum 10-year annual cost for Andros island is 1700€ forMf � 500 kg/year, while the corresponding value for Kea island is 2800€, while the annualdiesel-oil consumption is approximately 1250 kg/year. The electricity production cost dif-ference is more obvious in case of low diesel-oil penetration, due to the wind potential var-iation between the two islands examined.

The same behaviour is also valid for the 20-year operation of the wind-diesel installa-tion. It is interesting to note that the optimum system configuration for both islands isrealized for lower diesel-oil penetration than the 10-year optimum solution. On top of this,as time passes the mean annual cost becomes lower for both islands, hence the correspond-ing 20-year mean annual value is 1300€ and 2200€, respectively. Finally, the optimumsolution is moving towards lower diesel-oil penetration values, underlining the competitiveadvantage of power stations based on renewable energy sources, if a life-cycle cost analysisis considered.

Interesting conclusions may be derived by analyzing the 10-year minimum cost distri-bution; see Figs. 19 and 20. As it originates from these figures, for low diesel-oil penetra-tion the main cost contribution is due to the high battery cost (including the variable M&Ocost-battery replacement) and the fixed M&O cost. One cannot also disregard the windpower contribution, which represents approximately 15% of the total system cost. Onthe other hand, for high diesel-oil penetration, diesel-oil purchase cost represents over50% of the entire system cost. On top of this, for the optimum system configurationsthe diesel-oil and the battery bank correspond to 40% and 35% of the total system costin Andros island, while for the low potential case (i.e. Kea island) the optimum systemconfiguration, diesel-oil represents almost the 2/3 of the system total cost. In both cases,the wind turbine ex-works price does not exceed 15% of the system 10-year total cost.

Wind-Diesel Stand-Alone Systems

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Fig. 18. Comparison of mean annual cost of typical wind-diesel hybrid configurations on 10-year or 20-yearbasis.

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Andros Island Wind-Diesel Stand-Alone System10-Year Cost Analysis

Wind Turbine Cost Electronic Equipment CostBattery Cost Installation CostM&O Cost Fuel CostVariable M&O Cost

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Fig. 19. Total 10-year cost analysis of a typical wind-diesel hybrid system, high wind potential case.

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Kea Island Wind-Diesel Stand-Alone System10-Year Cost Analysis


Fig. 20. Total 10-year cost analysis of a typical wind-diesel hybrid system, medium-low wind potential case.


6. Conclusions

The central target of the present study is to estimate the optimum dimensions of ahybrid wind-diesel stand-alone system based on the minimum long-term electricity pro-duction cost. For this purpose, first the proposed energy production configuration is


described along with an appropriate algorithm that estimates the combinations of windturbine rated power, the corresponding battery capacity and the annual oil consumptionrequired in order to guarantee energy autonomy of the entire stand-alone installation.

Accordingly, a total energy production cost calculation model is developed. The appli-cation of the developed model gives the opportunity to define the optimum size of thehybrid system under investigation on a 10-year or on a 20-year long minimum electricityproduction cost basis. Finally, the application of the complete analysis on two selected lowand high wind potential regions indicates that the proposed hybrid system is more reliableand cost effective than a diesel-only installation or a wind-only based stand-alone system.

Recapitulating and considering the representative long-term results of the presentstudy, one may state that a hybrid wind-diesel stand-alone system is a motivatingtechno-economic solution to meet the electricity demand of remote consumers, especiallyin regions with medium or low wind potential. In this context, an appropriately sizedhybrid system should replace diesel-only generators, minimizing also the usage ofimported oil and avoiding the environmental impact accompanying the operation of inter-nal combustion engines.

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[10] Notton G, Muselli M, Poggi P, Louche A. Sizing reduction induced by the choice of electrical appliancesoptions in a stand-alone photovoltaic production. Renew Energy 1998;15:581–4.

[11] Kaldellis JK, Tsesmelis M. Integrated energy-balance analysis of a stand-alone wind-power system, forvarious typical Aegean Sea regions. Wind Energy J 2002;5(1):1–17.

[12] Kaldellis JK, Gavras TJ. The economic viability of commercial wind plants in Greece. A complete sensitivityanalysis. Energy Policy J 2000;28:509–17.

[13] Kaldellis JK, Tsesmelis M. Optimum stand-alone wind-power system, on the basis of minimum installationcost. In: International Conference on Wind Power for the 21st Century, paper VP8.6, Kassel, Germany,2000.

[14] Tsesmelis M, Kaldellis JK. Validation of autonomous wind energy solution, for remote consumers, includingfinancial aspects. In: European Wind Energy Conference and Exhibition 2001, paper PG6.12, Copenhagen,Denmark, 2001.

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