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Optimisation and techno-economic analysis of autonomous

photovoltaicwind hybrid energy systems in comparison

to single photovoltaic and wind systems

A.N. Celik *

Department of Mechanical Engineering, School of Engineering and Architecture, Mustafa Kemal University,31050 Antakya, Hatay, Turkey

Received 30 June 2001; accepted 26 November 2001

Abstract

A techno-economic analysis for autonomous small scale photovoltaicwind hybrid energy systems is

undertaken for optimisation purposes in the present paper. The answer to the question whether a hybrid

photovoltaicwind or a single photovoltaic or wind system is techno-economically better is also sought.

Monthly analysis of 8 year long measured hourly weather data shows that solar and wind resources vary

greatly from one month to the next. The monthly combinations of these resources lead to basically threetypes of months: solar-biased month, wind-biased month and even month. This, in turn, leads to energy

systems in which the energy contributions from photovoltaic and wind generators vary greatly. The

monthly and yearly system performances simulations for different types of months show that the system

performances vary greatly for varying battery storage capacities and different fractions of photovoltaic and

wind energy. As well as the system performance, the optimisation process of such hybrid systems should

further consist of the system cost. Therefore, the system performance results are combined with system cost

data. The total system cost and the unit cost of the produced electricity (for a 20 year system lifetime) are

analysed with strict reference to the yearly system performance. It is shown that an optimum combination

of the hybrid photovoltaicwind energy system provides higher system performance than either of the

single systems for the same system cost for every battery storage capacity analysed in the present study. It is

also shown that the magnitude of the battery storage capacity has important bearings on the systemperformance of single photovoltaic and wind systems. The single photovoltaic system performs better than

a single wind system for 2 day storage capacity, while the single wind system performs better for 1.25 day

storage capacity for the same system cost.

2002 Elsevier Science Ltd. All rights reserved.

Energy Conversion and Management 43 (2002) 24532468

www.elsevier.com/locate/enconman

* Tel.: +90-532-2277353; fax: +90-326-2455499.

E-mail address: [email protected] (A.N. Celik).

0196-8904/02/$ - see front matter

2002 Elsevier Science Ltd. All rights reserved.P I I : S0196- 8904( 01) 00198- 4
http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/


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Keywords: Solar energy; Wind energy; Single system; Hybrid system; Solar-biased month; Optimisation of the hybrid

energy system; Techno-economic analysis; Unit cost of electricity

1. Introduction

The search for a more reliable and less costly renewable energy system has brought about thehybrid use of two energy sources: solar and wind energy. For a photovoltaicwind hybrid system,the techno-economical efficiency is mainly dependent on the solar and wind energy resources,

which are highly variable in time and site specific. The problems caused by the variable nature ofthese resources can be partially overcome by integration of the two resources into an optimumcombination. The strength of one source could overcome the weakness of the other during a

certain period of time. This is apparent by realising the fact that in many areas, more solar ra-

diation and less wind are available during the summer months, and similarly, more wind and lesssolar radiation are available during the winter. The primary aim of combining more than one

renewable converter is then to design techno-economically more effective systems. As stated byKellogg et al. [1] and Seeling-Hochmuth [2], reduction, to a minimum, in the required storage

capacity, when one of the optimum combinations of photovoltaic and wind energy is used, isanother advantage of hybrid systems for a given site.

Single or hybrid systems of different energy sources (solar, wind, Diesel, etc.) are the only way

to generate electricity in some regions of developing countries. On the other hand, they are analternative way to supply electricity, especially in remote areas of developed countries. However,

only limited experience exists with the operation of photovoltaicwind hybrid energy systems.Protogeropoulos et al. [3] state that the benefits of combining solar and wind energy resources are

obvious. However, there are also problems that stem from the increased complexity of the systemin comparison with single energy systems. This complexity, brought about by the use of twodifferent resources together, makes the hybrid systems more difficult to analyse. The solar radi-ation and wind speed being highly location dependent, the sizing of such hybrid systems requires

comprehensive analysis of these variables for a given location in relation to the system cost fordifferent combinations of the two converters.

The use of either a single or a hybrid system is strongly dependent on the solar radiation and

wind speed potentials and the load demand in a given location. It is necessary to establish thephotovoltaic and wind energy contributions to the load in the case of a hybrid system for opti-

misation purposes. Once decided in favour of a hybrid system, the optimisation of the hybrid

system gains importance to run the hybrid system effectively. This is because a certain ratio of energyto load (ELR) can be obtained from several different combinations of photovoltaic panels and windturbines. Therefore, one of the optimum combinations amongst many different ones must be used.Otherwise, the hybrid system will not be satisfactory in terms of performance cost effectiveness.

2. A literature survey: hybrid energy systems as alternative to single systems

The fact that the electrical energy requirements for remote applications may be too great toallow the cost effective use of autonomous single photovoltaic or single wind systems has moti-

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vated researchers to develop more effective systems combining these power sources to form a

hybrid system. The system performance and optimisation of such hybrid systems have been thesubjects of research in this field.

Protogeropoulos et al. [3] present a general methodology for the sizing and optimisationof solar photovoltaicwind power systems. Two scenarios are examined to illustrate calcu-lation of the relative contributions of photovoltaic and wind energy for stand alone hybridsystems. Scenario 1 uses the annual average monthly values. With Scenario 2, the renewable

components are sized with respect to the worst renewable months. Both scenarios take into ac-count the actual energy yield from the renewable energy sources in combination with the en-ergy demand by systematically varying the relative sizes of the renewable energy components

size determined by availability of components on the market. A techno-economic combina-tion is then found by applying cost data to disclose the system with the lowest overall system

cost.Beyer and Langer present a simplified design method in [4] for photovoltaicwind hybrid en-

ergy systems. They first develop equations for the performance curves of photovoltaic and windsystems separately. An approach is then presented that focuses on determination of the combi-nations of generators and storage battery that ascertain a given system reliability in a hybrid

system. Beyer and Langer conclude that, using the simple measure of investment costs as anoptimisation criterion, photovoltaicwind hybrid energy systems are recommended for an average20 W load in the entire region of northwestern Europe for the two random sources of energy,

which are individually less reliable, could, as a whole, have higher reliability. However, in theMediterranean region, the hybrid solution is restricted to a smaller number of sites with betterwind conditions. Markvart describes a procedure in [5] that theoretically determines the sizes of

the photovoltaic array and wind turbine in a photovoltaic and wind hybrid energy system. Using

the measured values of solar and wind energy at a given location, the method employs a simplegraphical construction of the two generators that satisfies the energy demand throughout the year.If d is assumed to be the average daily load demand, the daily energy condition is given by the

following equation,

d6Waw Sas; 1

where Wand Sare the available yearly average wind and solar energy and aw and as are the sizesof the wind and solar converters, respectively. The main aim is to establish the range of values ofaw and as which fulfil the equation at all times of the year using the average values of W, Sand d.

The system cost is given by

hybrid generator cost csas cwaw should be minimum; 2

where cs and cw represent the costs of photovoltaic and wind energy generators per unit power ofthe output rating. Considering just winter and summer, if a graph is drawn showing aw and as atdifferent co-ordinates, the boundary of the two lines connecting the winter and summer conditions

defines the solution region for the hybrid system. This could be repeated for each of the 12months. Again, the optimum system is within the boundary of the 12 lines. Combining the

A.N. Celik / Energy Conversion and Management 43 (2002) 24532468 2455


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technical and economical analyses, finally, an optimum solution is derived. Markvart [5] con-cludes that for a range of costs of the solar and wind energy systems, the hybrid system represents

the most cost effective solution. In this model, the system is sized where the energy to load ratio

(ELR, i.e. ratio of energy produced by the renewable components to energy demand) is equal tounity. Although the model theoretically proves that the hybrid system is less costly than the single

photovoltaic or wind system, the inefficiency of the model lies in the fact that it gives no insightinto the level of loss-of-load and the storage problem.

Obviously, a photovoltaicwind combination is not the only hybrid system available. Either of

them could be effectively combined with other types of power generators, such as the photovol-taicDiesel [6] and windDiesel [7] generator. Furthermore, depending on the requirement and the

availability of energy sources, more than two of the sources could be combined, such as photo-voltaicwindDiesel generator [8]. The selection process for hybrid power sources at a given site

is dependent on a combination of many factors, including the load demand, site topography,seasonal availability of energy sources, cost of energy storage and delivery, seasonal energy re-quirements, etc.

3. Energy contribution of the components and system performance definitions

3.1. Photovoltaic and wind fractions

In a hybrid photovoltaicwind energy system the term total produced energy is non-specific in

the sense that the photovoltaic and wind contributions are not known. The term fraction

specifies this contribution. The photovoltaic fraction fPV and wind fraction fWG are given by thefollowing:

fPV EPV

ET; 3a

fWG EWG

ET: 3b

Then knowing from

ET EPV EWG 4

that the total energy (ET) is determined from the photovoltaic and wind energies (EPV and EWG,respectively), the following is written,

fPV fWG 1; 5

where the point fPV 1 corresponds to a single photovoltaic system in which all the energy iscontributed by the photovoltaic system. Similarly, the point fPV 0 corresponds to a single windsystem. Therefore, except for these boundary combinations, the remaining combinations corre-spond to a hybrid system.



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3.2. Autonomy definition

The system performance is defined by the term autonomy, which is one minus the ratio of the

total number of hours in which loss-of-load occurs to the total hours of operation, given by

A 1 HLOL

Htot: 6

In the present paper, the photovoltaicwind energy system simulation program of the Solar En-ergy Unit (SEUARES) of Cardiff University has been used [3]. The same system settings as in theexperimental hybrid system, as described by Celik in [9], installed at Tal-y-Bont (TyB, a remote

site near Cardiff, UK) are assumed for the system investigated in this paper. The validated powercurves of the photovoltaic modules and the wind generator with respect to solar radiation and

wind speed are used in the simulation program.

4. Optimal and non-optimal combinations

The optimum combination of photovoltaic and wind energy in a hybrid system varies as the

solar radiation and wind speed potentials vary during the time in question: for example, hourly,monthly, seasonally or yearly. Therefore, if the system is designed to supply electricity throughout

a year, the hybrid energy system should be designed according to the yearly solar and wind re-sources rather than those of any other period of time. Similarly, if the system is to supply power in

a predetermined season or a month, then the seasonal or monthly solar and wind resources shouldbe considered. Eight year long measured hour-by-hour weather data from five different locations

(Cardiff, Canberra, Davos, Athens and Ankara) have been used in the present paper for analysingthe optimal and non-optimal combinations of photovoltaic and wind resources in a hybrid sys-tem. The monthly statistics of the available 8 year long solar radiation and wind speed data showthat the resources vary greatly from one month to the next. This section establishes the funda-

mentals for defining the terms optimal and non-optimal combinations in a photovoltaicwindenergy system on a monthly basis. The monthly average daily specific energies produced by thephotovoltaic and wind generators are presented in Fig. 1 for three different months representing

three main combinations of solar and wind resources, which are:

Fig. 1. Three different months representing three main combinations of solar and wind resources.



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1. May of Cardiff 1991, in which the solar energy resource almost equals the wind energy resourcein terms of available energy per square metre. This month typifies an optimum combination inwhich the system performance is enhanced by the use of a hybrid system.

2. January of Cardiff 1996, in which the solar energy resource is very little, while the wind speedpotential is quite high. This is an example of a wind-biased month and the lack of solar energyis rectified by the wind energy.

3. August of Canberra, in which the solar energy resource is much higher than the wind energyresource. This is an example of a solar-biased month in which the solar energy rectifies the lackof wind energy.

Photovoltaic fraction statistics, consisting of a total of 96 months, are shown in Table 1. The

specific photovoltaic energy (photovoltaic energy output per square metre) is quite comparable tothe specific wind energy for 52% of the months, similar to May shown in Fig. 1. For 33% of the

months, the specific photovoltaic energy is much smaller than the specific wind energy. Thesemonths are comparable to January shown in Fig. 1. For the remaining 15% of the months, thespecific photovoltaic energy is quite high compared to the specific wind energy, similar to August

in Fig. 1. It should be noted that 55% of the months analysed are wind-biased and the remaining45% are solar-biased in terms of the specific energies. Therefore, in 55% of the months, a possiblehybrid system is wind-biased, and in the rest of the months, 45%, it is solar-biased, providing thesame amount of photovoltaic and wind converters are used. Overall, a 55% and 45% distribution

shows a relatively uniform distribution in terms of the specific photovoltaic and wind energyoutputs. The system performances corresponding to each type of month will be analysed next for

a varying range of photovoltaic and wind fractions.

4.1. Optimal combination

The first of the three main combinations is the May of Cardiff 1991 data, in which the specificsolar and wind energy outputs are nearly equal. This is an example month in which the hybrid use

of photovoltaic and wind energy is most efficient. Fig. 2 shows some possible combinations ofphotovoltaic and wind energy, including single photovoltaic and wind systems, for the battery toload ratio (BLR) of 1.5. The simulations are run assuming a 24 h constant 15 W load. Each

continuous line represents a fixed value of the photovoltaic fraction. Along any curve, thephotovoltaic and wind energy contribution to the hybrid system is constant. The bottom curvescorrespond to the photovoltaic fraction values of 0.0 and 1.0, respectively, while the upper curves

belong to the photovoltaic fractions of 0.4, 0.5 and 0.6. The photovoltaic fraction values of 0.4,0.5 and 0.6 are the optimal combinations of photovoltaic and wind energy for ELRs larger than a

Table 1

Photovoltaic fraction statistics consisting of a total of 96 months

fPV Percentage

0.080.4 33%0.40.6 52%

0.60.7 15%



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certain limit. The increase in system autonomy brought about by the hybrid use of photovoltaicand wind energy is evident. After the ELR of 1.0 the hybrid system offers 2025% more autonomythan the single systems do. However, it is noted that at low ELRs (0.20.7), the single photo-

voltaic system provides higher autonomy figures than a hybrid system. This must be considered ina system that can afford an autonomy level as low as 70%. The hybrid system autonomies, ingeneral, are higher than the single system autonomies for the same values of ELR. This confirms

that the use of two different energy resources at the same time generally leads to a more consistentsystem performance. This is because the wind energy is distributed over 24 hours, which com-plements the solar energy prevailing only during daylight. Thus, the produced energy and the load

demand match more closely, and the system works more efficiently.

4.2. Wind-biased month

Fig. 3 shows the monthly autonomy values of the photovoltaic and/or wind energy system for a

highly wind-biased month, January of Cardiff 1996, for the BLR of 1.5. The single photovoltaicsystem can provide a maximum of 27% monthly autonomy, whereas the single wind systemprovides monthly autonomy values as high as 81% for the ELR of 2.0. The high wind speed

prevailing during this month results in 10 times more specific wind energy than the specificphotovoltaic energy. Therefore, in order to acquire the same amount of photovoltaic energy(i.e. to obtain an fPV value of 0.5) within the hybrid system in this month, 10 times as much

Fig. 2. Monthly autonomy versus the ELR for different fractions of photovoltaic and wind energy for an even month.

Fig. 3. Monthly autonomy versus the ELR for different fractions of photovoltaic and wind energy for a wind-biased

month.



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photovoltaic converter as wind converter should be used. Even then, as seen from the figure, the

autonomy of the hybrid system for the fPV value of 0.5 is well under that of the single wind system(fPV 0). Evidently, in the case of using such a large size of photovoltaic converter for the sake of

a month, a possible hybrid system would be immensely oversized for the rest of the year. Thesystem cost would be extensively high too. Two important points are worth making. The first isthe advantage of a hybrid system over the single systems. If a hybrid system was not an option andthe project had to use only the photovoltaic converter, a high level of autonomy could be achieved

only by excessively increasing the photovoltaic converter size or/and the storage capacity. Thelatter possibility would not contribute to achieving a high level of autonomy, knowing that theprevious month was December, which is a poor solar month. Therefore, the battery storage would

have most probably been depleted. The only option left is to increase both the photovoltaicconverter size and the battery storage size, which will, in turn, result in too costly a system. The

second point is that the single wind system is already able to achieve a monthly system autonomylevel as high as 81%. While the best option is the single wind system for this highly wind-biased

month, the photovoltaic fraction values between 0.2 and 0.0 also produce as high autonomyfigures as the single wind system.

4.3. Solar-biased month

The monthly autonomy values of the photovoltaic and/or wind energy system for a solar-biasedmonth, February of Canberra, are presented in Fig. 4 for the BLR of 1.5. During this month, the

specific photovoltaic energy output was more than twice that of the specific wind energy output.Compared to 10 times the difference in the wind-biased month, a ratio of 2 is the case for thesolar-biased month. The single photovoltaic system provides autonomy values up to 91%, while

the bottom curve represents the single wind system, providing up to 66% of monthly autonomy.The top curves correspond to the photovoltaic fraction values between 0.7 and 0.95, supplying

over 95% monthly autonomy values for the ELR of 2.0 and higher. The highest monthly au-tonomy values occur where the fPV 0:77. For the lower ELRs (less than 0.6), the single windsystem returns higher autonomy figures than the hybrid and single photovoltaic systems.

It is observed from Figs. 24 that the monthly system autonomies rise rapidly where the ELR isbetween 0.2 and 1.0. A slow increase in the system autonomy follows up to an ELR of 2.0. After

Fig. 4. Monthly autonomy versus the ELR for different fractions of photovoltaic and wind energy for a solar-biased

month.



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this point, the system autonomies increase slightly. Therefore, it could be concluded that systems

must be sized for ELRs between 1.0 and 2.0. Beyond the ELR of 2.0, the system cost wouldincrease sharply to gain a further few percent of autonomy. Therefore, systems sized beyond the

ELR of 2.0 would be techno-economically non-optimal.

5. Annual system autonomy simulations

Having analysed the optimal and non-optimal combinations of solar and wind resources in ahybrid energy system on a monthly basis, the system autonomy is studied on a yearly basis in this

part of the paper. One year long measured hourly weather data of Cardiff 1996, measured at theTyB site, in which the yearly average specific photovoltaic and wind energy outputs were 1.90 and

2.52 kWh/m2, is used. The monthly photovoltaic and wind energy outputs are given in Fig. 5. Theannual autonomy values are presented for various photovoltaic fractions for the BLR of 1.5 in

Fig. 6. It is observed from the figure that while the lower curves represent the boundary com-binations of solar and wind resources (0.0, 0.1, 0.9, 1.0), the upper curves correspond to the

optimum photovoltaic fraction range where the fPV values are between 0.4 and 0.5. The differencebetween the upper and the lower curve autonomy levels is as high as 16%, accentuating the im-portance of the photovoltaic fraction used. It is observed that the hybrid system provides a higher

autonomy value than a single photovoltaic or a single wind system at this ELR. At small

Fig. 5. Monthly energy outputs of Cardiff 1996 weather data.

Fig. 6. Yearly system autonomies versus ELR for different fractions of photovoltaic energy for the BLR of 1.5.



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ELRs (0.00.5), the single photovoltaic and the hybrid systems with high photovoltaic fraction

values (0.90.8) provide higher autonomy figures than the hybrid energy system with lowerphotovoltaic fractions (0.4, 0.5, 0.6). At this low ELR, therefore, a single photovoltaic or a hybrid

system with a high photovoltaic fraction value (0.90.8) should be preferred. It should, however,be noted that the autonomy level at this ELR range is too small for an autonomous hybrid systemfor many applications.

6. Performancetotal cost analysis for hybrid and single systems

It was shown that at high ELRs, the hybrid photovoltaicwind energy system provides moreautonomy than the single systems. However, the performance analysis alone is insufficient, for thesystem cost is mostly the governing design criterion. Therefore, the performance data are com-

bined with the cost data in this part of the paper. The costs are 58.75 per photovoltaic panel(rated output of 10 W at 1 kW h/m2) of 0.3 m2 each and 327 per wind generator (rated output of

50 W at 10 m/s) of 0.65 m2 swept area. The characteristic parameters for a 24 A h lead acid batterywith a unit cost of 25 will be used. A total of 200 battery controller cost is also added into thecost of the system. The component capital costs refer to 2001 prices in the UK. In calculating thecost of the system a 20 year lifetime and a 5% installation, maintenance and engineering cost of

the initial hardware cost are also assumed.In the following figures of cost versus performance for varying BLRs, each data point, of a total

of four, along the lines is determined by a different sizing scenario. The first point is by the yearly

average scenario, which sizes the systems at a point where the ELR is equal to unity. The secondpoint is sized by the plus standard deviation scenario. This scenario uses the yearly average areas

of photovoltaic and wind converters (as in the yearly average scenario) plus the correspondingstandard deviations (rPV and rWG) of the monthly areas. The third point is by the worst month

scenario. This scenario chooses the worst month in which the largest total area of photovoltaicand wind generator occurs. The fourth point is by the worst months scenario. The worst monthsare the ones in a year that require the largest photovoltaic and wind converter sizes to meet the

load.Fig. 7 shows the yearly autonomy levels and the corresponding system costs for the single

photovoltaic, single wind and one of the near optimal combinations of the hybrid energy system

for the BLR of 2. For the same system cost, the hybrid system returns the highest annual au-tonomy values and proves most optimal in terms of the performancecost relationship. For ex-ample, looking at Fig. 7, for the cost of 3000, the hybrid system provides 97% yearly autonomy,

while the single photovoltaic system provides 90% and the single wind system provides only 73%.The single photovoltaic system returns higher autonomy figures than the single wind system for

the same system cost. For example, 80% autonomy level is achieved with a 1600 system costfor the photovoltaic system, while the same system autonomy can be achieved with 3600 for the

wind system. On average, the hybrid system provides 96% autonomy while the single photovoltaicand wind systems supply 87% and 77%, respectively, for the BLR of 2. One of the most importantpoints Fig. 7 shows is that achieving a further small increase in the system autonomy in the high

autonomy region (over 95%) means a sharp increase in the system cost, especially for the hybridand single photovoltaic systems. For example, the hybrid system can achieve 97% yearly au-



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tonomy level with a system cost of 3000, and an extra 2% autonomy requires an extra 1500investment.

A similar analysis for a lower BLR (1.50) shows that the hybrid system is still superior to thesingle systems, as shown in Fig. 8. In comparison to the previous figure the hybrid system supplieseven higher autonomy values than the single systems. On average, the hybrid system provides 86%

autonomy, while the single photovoltaic and wind systems supply 67% and 68%, respectively. Themost noticeable difference, when compared to the previous BLR, is that amongst the singlesystems, the photovoltaic system no longer provides higher autonomy values than the wind energy

system at all cost levels. At around 3700, where the photovoltaic and wind lines intersect, thephotovoltaic and the wind energy systems both provide the same level of yearly autonomy.

Therefore, the photovoltaic system with the total cost less than 3700 would have provided moreyearly autonomy than the single wind system for this particular location. Beyond the total system

cost of 3700, the wind system provides higher autonomy values than the photovoltaic system.The yearly system autonomy values and the system cost for single photovoltaic, single wind and

hybrid energy systems for the BLR of 1.25 are presented in Fig. 9. For this BLR, the single windsystem is now superior to the single photovoltaic system. The hybrid energy system still returns

Fig. 7. Yearly system autonomy versus system cost for single photovoltaic, single wind and hybrid energy systems for

the BLR of 2.0.


the BLR of 1.5.



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higher autonomy values in comparison to the single systems. While the single wind system pro-vides, on average, 59% yearly autonomy, the photovoltaic system provides only 46%, 13% less

yearly autonomy than the single wind system, thus being the least likely option to choose for thisBLR. The hybrid system, with an optimal combination of photovoltaic and wind generator,

provides an average of 71% yearly autonomy for the BLR of 1.25.

7. Performanceunit cost analysis for hybrid and single systems

Unit cost of the produced energy is analysed as a function of the yearly system autonomy for

single photovoltaic, single wind and hybrid energy systems for varying BLRs. Fig. 10 shows the

unit cost of the produced energy versus the yearly system autonomy for single photovoltaic, singlewind and hybrid energy systems for the BLR of 2.0. For the same yearly system autonomy, theunit cost of electricity is most by the single wind system and least by the hybrid system. It is seenfrom the same figure that the hybrid system returns the lowest unit cost values to supply the same

level of autonomy as the single systems. In other words, the hybrid system supplies more au-tonomy than the single systems for the same unit cost value. For example, as seen in the figure,


the BLR of 1.25.

Fig. 10. Unit cost of the produced energy versus the yearly system autonomy for single photovoltaic, single wind and

hybrid energy systems for the BLR of 2.0.



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with the unit cost of 1.4 the single wind system supplies only 58% yearly autonomy, while the

single photovoltaic system supplies 92%. For the same unit cost value, the hybrid system provides98% yearly system autonomy. For the single photovoltaic system, the unit cost of electricity rises

sharply from 1.0 to over 1.5 between the yearly autonomy levels of 87% and 92%. This meansthat the unit cost of the electricity rises sharply in return for a little increase in the system au-tonomy. A similar sharp increase is observed for the hybrid system too: the unit cost is doubledfrom 0.85 to 1.70 between the yearly system autonomy values of 89% and 99%. Another notable

point in the figure is that the unit cost of electricity for 80% yearly system autonomy is 0.75 whenproduced by the single photovoltaic system, while the unit cost is 1.75 for the same level of yearlyautonomy when produced by the single wind system.

The unit cost of the produced electricity versus the yearly system autonomy for single photo-voltaic, single wind and hybrid energy systems for the BLR of 1.5 is presented in Fig. 11. The

hybrid system is the best option for this BLR, for it produces the least costly electricity for thesame level of yearly autonomy. For this particular BLR and location, if an autonomous system is

expected to supply a yearly autonomy level of 90%, the hybrid system is the only option becausethe single systems cannot supply that level of autonomy. The single photovoltaic system supplies60% yearly system autonomy with a unit cost of 1.0. It is 1.7 when the same level of yearly

autonomy is supplied by the single wind system. At around the yearly autonomy level of 73%, theelectricity produced by the single photovoltaic and wind systems both costs 2.0. Beyond this levelof autonomy, the single wind system produces the electricity at a lower cost.

Fig. 12 shows the unit cost of the produced energy versus the yearly system autonomy for singlephotovoltaic, single wind and hybrid energy systems for the BLR of 1.25. The hybrid systemprovides much higher yearly system autonomies than the single systems for the same unit cost of

electricity. For example, with a unit cost of 1.8, the single photovoltaic and wind systems return

44% and 46% yearly autonomies, respectively, while the hybrid system provides 75% yearly au-tonomy. Overall, the single photovoltaic system produces the most costly electricity for this BLR.As the yearly autonomy level goes from 40% to 50%, the unit cost of the electricity increases

rapidly from 1.35 to 2.85. The unit cost of the electricity by the single photovoltaic systemincreases exponentially for an autonomy level more than 50%. The cost of the electricity from thesingle wind system increases from 1.75 to 2.25 linearly between the autonomy levels of 43% and





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64%. Beyond this level of autonomy, the unit cost of the electricity rises sharply for the single windsystem.A further design parameter that combines the unit cost and yearly system autonomy is defined

here as the cost per percent autonomy, which is calculated over a 20 year system lifetime. Theratios of cost to the system autonomy (cost per percent autonomy) are presented in Table 2 forsingle photovoltaic, single wind and hybrid energy systems for varying BLRs. The cost per percent

autonomy increases as the BLR decreases for the single and hybrid systems. This is especiallyaccentuated in the single photovoltaic system, where the cost per percent autonomy increases 87%as the BLR decreases from 2.0 to 1.25. The cost per percent autonomy increases only 28% for the

single wind system, while it increases 39% for the hybrid energy system from the BLR of 2.0 to1.25. Overall, the per percent autonomy is least costly when produced by the hybrid system for

every BLR and highest when produced by the single wind system. This is due to the fact that thesite studied is a typical poor wind site with the yearly average hourly wind speed value of 2.18 m/s.

8. Conclusions

This paper has addressed the optimisation of photovoltaicwind hybrid energy systems in terms

of a performancecost relationship. A similar performancecost relationship analysis has beenperformed to determine whether the hybrid photovoltaicwind energy system or the single



Table 2

For a 20 year lifetime, the ratio of cost to the system autonomy (cost per percent autonomy) for single photovoltaic,

single wind and hybrid energy systems for varying BLRs

Battery to load ratio (BLR)

2.0 1.5 1.25

Photovoltaic system 1.55 1.99 2.90

Wind system 1.45 1.65 2.02

Hybrid system 2.07 2.31 2.65



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photovoltaic or wind system is better. The numerical analysis has been based on 1996 weather

data from the TyB site of Cardiff, UK, and considers the basic system settings at this experimentalsite.

Three main combinations of solar and wind energy have been analysed on a monthly basis: aneven month, a highly wind-biased month and a solar-biased month. The system autonomies havebeen derived for each case, using an example month. For the even month, it was shown that thephotovoltaic fractions of 0.4, 0.5 and 0.6 are the optimal combinations for the hybrid photo-

voltaicwind energy system. The example month for the wind-biased case has shown that thesmaller values of the photovoltaic fraction (0.00.2) provide the highest autonomy figures. For thesolar-biased month, it was observed that the photovoltaic fraction values between 0.7 and 0.9 offer

the highest monthly autonomy values.A careful examination of the monthly and yearly autonomy curves suggests that the optimum

design point is in the range where the ELR is between 1.0 and 2.0 for any BLR. Therefore, thephotovoltaicwind hybrid energy systems sized beyond this point would fall into the non-optimal

range, resulting in techno-economically ineffective systems. Hybrid systems sized within the op-timum range of ELR return, on average, 93% annual autonomy, while the single photovoltaic andwind systems supply 87% and 65%, respectively, for the BLR of 2, for the same system cost.

However, as the BLR decreases to 1.5, the difference between the single photovoltaic and windsystem reduces to 8%. The single wind system supplies 5% more autonomy than the singlephotovoltaic system for the BLR of 1.25 for the same system cost.

The second design parameter used to evaluate the quality of the system in terms of techno-economics has been the unit cost of the produced electricity. Amongst the BLRs analysed, the unitcost of the produced electricity is lowest for 2 day battery storage. For this BLR, the single wind

system returns the highest unit cost values. For the single photovoltaic system, the unit cost of

electricity rises sharply from 1.0 to over 1.5 between the yearly autonomy levels of 87% and92%. This means that the unit cost of the electricity rises sharply in return for a little increase inthe system autonomy. Overall, the hybrid system returns the lowest unit cost values. Looking

at the relationship between the system performancesystem cost and system performanceunitcost, the hybrid system proves to be techno-economically better than either of the single systemsfor every BLR analysed in the present paper. This is a consequence, as expected, of the more

reliable hybrid system behaviour by combining two less reliable resources.

References

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