General sustainability indicator of renewable energy system based on grey relational analysis

SHORT COMMUNICATION

General sustainability indicator of renewable energysystem based on grey relational analysisGang Liu*,†, Ali M. Baniyounes, M.G. Rasul, M.T.O. Amanullah and M.M.K. Khan

Central Queensland University, Power and Energy Research Group, Rockhampton, QLD4702, Australia

SUMMARY

This research answers the question of how to measure the sustainability of a renewable energy systems (RESs) as a physicalparameter. Renewable energy is considered as a solution for mitigating the energy crisis, climate change and environmentalpollution; however, an important problem of its application is that it is very difficult to evaluate the sustainability of RESs.This study develops a general sustainability indicator which is a tool to evaluate sustainability of RESs precisely and com-prehensively. Based on the Triple Bottom Line approach, 11 Basic Sustainability Indicators with different dimensions andvarious units are selected from environmental, economic and social sustainability assessment criteria. In order to deal withthe uncertainties in the definition and the assessment of sustainability, the grey regression analysis method is employed toquantify the basic indicators and to aggregate them into the general indicator. In addition, for explaining application of thegeneral indicator, the cases of four RESs in hot-arid Australia are presented. In the case study, the grey indicator is used toassess the sustainability of four systems with different combinations of grid, solar photovoltaic and wind renewable energy.The final results are compared with the general indicator based on fuzzy sets theory developed in previous studies. It isfound that for the case of Australian system, the grey sustainability indicator has a good linear correlation to the fuzzyindicator results. The grey indicator is an effective way to assess the sustainability of RESs and provides a good tool fordesigners, users, decision makers and researchers. Copyright © 2013 John Wiley & Sons, Ltd.

KEY WORDS

general sustainability indicator; renewable energy system; grey relational analysis; solar photovoltaic; wind energy

Correspondence

*Gang Liu, Central Queensland University, Power and Energy Research Group, Rockhampton, QLD4702, Australia.†E-mail: [email protected]

Received 23 June 2012; Revised 10 December 2012; Accepted 22 December 2012

1. INTRODUCTION

With the increasing concern of climate change, the electricitygeneration from renewable energy and renewable energysystems (RESs) are encouraged by government incentives ofmany countries and regions. The usage of RESs brings bothadvantages (e.g., cleaner and less emissions) and shortcom-ings (e.g., higher financial cost) for electricity generation,and, therefore, a big issue is that it is quite difficult to compre-hensively assess the sustainability of RESs. Since sustainabil-ity is a complex concept including environmental, economicand social considerations, it is impossible to use eitherenvironmental criteria or economic criteria separately forindividual assessment. Therefore, what is needed is thedevelopment of a general sustainability indicator (GSI) shouldconsider all the aspects of sustainability is required so thatengineers, energy consultants, system users, designers anddecision makers have a tool to measure sustainability andmake a decision on RESs.

The methods of decision making on RESs based onsustainability considerations have been highlighted in a number

of research projects, based on either multi-criteriadecision-making (MCDM) methods, such as AnalyticalHierarchy Processing (AHP) [1–5], Technique for OrderPreference by Similarity to Ideal Solution [6,7]), Prefer-ence Ranking Organisation METhod for EnrichmentEvaluation [8–10] and Elimination Et Choice TranslatingREality [11–13], or the combination of fuzzy methodologyand MCDM [14–19]. Overall, these studies are all able tochoose the best system among many system options, but fewof them are able to supply a score of sustainability for the eval-uated RESs. While an increasing number of studies concen-trate on the MCDM of RESs, there appear to be few studieson a common tool of sustainability measurement which couldbe called as GSI. In essence, the existing studies did not give ameasurement tool which is able to assess the sustainability ofRESs comprehensively.

There are three main challenges in the development ofsustainability indicators. First, it is difficult to select thecriteria for the sustainability assessment of RESs, becausesustainability is a very wide concept and has a large num-ber of criteria used in the previous studies covering a range

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2013; 37:1928–1936

Published online 12 March 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3016

Copyright © 2013 John Wiley & Sons, Ltd.1928

of aspects including economic, technological, environmen-tal, social considerations and so on. For example, [20]proposed energy generation efficiency as the singlecriterion to assess the sustainability of an electricity gener-ator. Emission is closely related to the environmentalassessment and therefore was considered as a main sustain-ability indicator in previous literature [21–26]. The ther-modynamics definitions of entropy [27–29] and exergy[30–33] were also used as the methods of sustainabilityquantification; costs of systems were also used to assessthe economic performance of sustainability [34]. The seconddifficulty in indicator development is the quantificationof the indicators. The indicators mentioned above eachreflect some aspect of sustainability but have different dimen-sions. While the unit of emission is expressed in kg/yr,entropy and energy efficiency are, respectively, J/(K � kg)and percent. Third, it is a hard task to aggregate all the indica-tors with different dimensions into an integrated indicator. Inanother words, there is not a practical methodology to modelthe sustainability indicator. The dimensions, which a GSI hasto have, were often used individually in single criterionassessment but not in a comprehensive sustainability assess-ment [35,36].

This paper presents a novel sustainability indicator, whichis developed based on grey relational analysis, to assess thesustainability degree of RESs. The selected 11 Basic Sustain-ability Indicators (BSIs), based on Triple Bottom Line (TBL)sustainability assessment criteria, are integrated into the GSI.Using the developed indicator, four typical configurations ofan Australian system for a small electricity user (consuming100 kWh/day) are evaluated and compared. In addition, theresults of the grey GSI will be compared to a GSI based onour fuzzy sets theory which was published previously [37].

The developed GSI of this study can provide RES users,system designers and renewable energy consultants with atool for sustainability assessment and a reference fordecision making. It is also expected that this tool can formthe basis for forming relevant government policies andrenewable regulations.

2. SELECTION OF BSIS

The procedures of sustainability assessment not only dependon the system performance itself and the accepted sustainabil-ity definition, but also on the local policies, existing statisticalcapabilities, availability and quality of energy and otherrelevant data [38,35]. The first step is to select all the basicindicators based on the sustainability definition and its assess-ment. Since the definition of sustainable development was firstcoined by the World Commission on Environment andDevelopment [39], sustainability has become a popular buzz-word when discussing energy, resources use and environmen-tal policy [40].

In practical terms, the phrase TBL is coined to explainsustainability considerations [41]. The TBL approach aimsto extend the traditional reporting framework to take intoaccount environmental and social performance in addition

to economic performance. A number of indicators, likeprice of electricity generation, greenhouse gas emissions,availability and technological limitations, efficiency ofenergy generation, land use, water consumption and socialimpacts have been proposed to assess renewable energytechnologies [42]; however, these indicators work individ-ually but are not integrated into a GSI.

In this paper, the TBL approach is used to select basicindicators. The 1992 Rio Declaration suggested thatsustainable development is about balancing these threedimensions and achieving some kind of trade-off amongthem in the prioritisation process [43]. Therefore, theindication from an individual criterion is impossible to beaccepted, and here the environmental indicators, economicindicators and social indicators are all considered in theselection of basic indicators of GSI’s development.

2.1. Environmental indicators

Environmental indicators in a GSI reflect the impacts of anRES on the environment. Due to the global greenhouseeffect and acid rain, the monitoring of greenhouse gasesand acid rain gases have been used with increasing impor-tance in the assessment of RESs. Any design of powersystem has to incorporate those features which are relatedto the low emission of SO2, CO2 and NOx per unit of elec-tricity generated. The environmental indicators in thisstudy are composed of these three elements. Both CO2

and NOx indicators are represented by the green housegas emissions per year, and SO2 indicator is relative tothe air pollution by acid rain, represented by the emissionsper year.

Moreover, the environmental indicators for RESs alsopresent the performance of energy resource conservation.Renewable fraction, which means the proportion of elec-tricity generated by renewable energy resources dividedby the total electricity generation, is needed as an indicator.In addition, in order to evaluate the quality of the energyresources, an indicator of energy conversion ratio is usedin this study. This indicator is to present the effectivenessof energy conversion from resources to electricity.

2.2. Economic indicators

Economic indicators are measures of the microeconomicefficiency of RESs. The costs vary from one type of RESto another, even though the systems generate the sameamount of electricity. Therefore, the cost analysis of aRES is very important in sustainability assessment.

The economic indicator of RESs comprises three sets ofdata, namely net present cost, cost of energy and return oninvestment. The net present cost includes the initial cost ofthe system components, and the cost of any componentreplacements within the whole lifetime of the system[44]; and the cost of energy means all the costs (withinthe whole lifetime) of generating electricity for a systemin $/kWh; the return on investment is defined as the ratio

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1929Int. J. Energy Res. 2013; 37:1928–1936 © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er

of money gained or lost (whether realised or unrealised) onan investment relative to the amount of money invested.

2.3. Social indicators

The social indicators reflect the social impacts of thesystems, which includes two aspects: the areas benefitedfrom the systems and the new jobs which the systemscan supply. They are abbreviated as households indicatorand jobs indicator, respectively.

To sum up, the indicators of environmental, economicand social aspects, as well as the weightings of these indi-cators which have been determined by our previous study[37] are listed in Table I. The environmental indicatorand its BSIs take up the largest weightings (0.5414) ofall, and the economic and social indicators account for0.4531 and 0.0056, respectively.

3. SUSTAINABILITY INDICATORMODELLING BY GREY RELATIONALANALYSIS

Since the grey system theory was put forward in 1982, ithas been widely applied in various fields of sciencebecause of its advantages in evaluating complex systemswith multiple criteria [26]. The theory is able to deal withuncertainties in the development of sustainability indica-tors, where some information is incomplete. The uncertain-ties, which are the main challenges of the development ofthe GSI, include the unknown relationship between theGSI and BSIs. The function shown in Equation 1 can beused to describe the relationship between the output(GSI) and inputs (BSIs).

GSI ¼ f BSI1;BSI2; . . . ;BSImð Þ (1)

However, the expression of the function f(xi) isunknown. The only three ‘knows’ are those:

• for positive BSIs, the larger their value, the larger thesustainability indicator value;

• for negative BSIs, the larger their value, the smallerthe sustainability indicator value;

• for nominal BSIs, the closer to the desired value, thelarger the sustainability indicator value.

Except for these three expressions, nothing is clear inthe sustainability indicator modelling. While a grey systemmeans that a system in which part of the information isknown and part of the information is unknown, for theGSI, the origin values of all the BSIs are known clearlybut the sustainability judgements corresponding to suchBSIs are unknown. Consequently, the GSI can be consid-ered as a grey system because it has all the characteristicsof a grey system.

The grey relational analysis is employed to model theGSI through carrying out the procedures shown in Figure 1.The first step is to determine the BSIs and the hierarchy ofthe GSI. Then, it is to normalise all the BSIs into values onthe interval [0, 1]. After that, the grey relational coeffi-cients are calculated, and then, using the given weightingsof BSIs to compute the grey relational evaluation results.The final procedure is to analyse the evaluation resultsvector and process final scores of the GSI.

3.1. Determination of the hierarchy

As shown in Figure 2, there are three layers in the indicatorhierarchy: the top layer is the GSI; the criteria layerincludes the TBL criteria (economic, environmental andsocial criterion); and the bottom layer includes all the BSIs(as shown in Table I). When aggregating the lower layersinto the upper layers, all the components in the lowerlayers have different weightings (wij). Based on the previ-ous studies, these weightings can also be determined byMCDM methods, such as pair-wise comparison, AHPand Simos [45].

3.2. Normalisation of BSIs

The BSIs involved in this GSI cannot be compared orintegrated directly because they have different dimensionsand magnitudes [46], so normalisation is needed to transfer

Table I. The criteria of sustainability indicators.

Ci of sustainability Cij Meaning of Cij Unit Weighting

C1: Economic, (0.4531) C11 net present cost $ 0.1521C12 cost of energy $/kWh 0.1117C13 return on investment percent 0.6639C14 energy generation kW 0.0724

C2: Environmental, (0.5414) C21 renewable fraction percent 0.2563C22 CO2 emissions kg/year 0.6206C23 SO2 emissions kg/year 0.0434C24 NOx emissions kg/year 0.0127C25 conversion efficiency percent 0.0696

C3: Social, (0.0056) C31 households benefited number 0.5C32 new jobs created number 0.5

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the original sequence to a comparable which is generallydimensionless. A linear normalisation method [47] is usedto translate the original sequence (xij) into the comparablesequence (x0ij) as shown in Equations 2 to 4.

x0ij¼

xij �min xij; i ¼ 1; 2; . . . ;m� �

max xij; i ¼ 1; 2; . . . ;m� ��min xij; i ¼ 1; 2; . . . ;m

� �for i ¼ 1; 2; . . . ;m; j ¼ 1; 2; . . . ; n

(2)

x0ij¼

max xij; i ¼ 1; 2; . . . ;m� �� xij

max xij; i ¼ 1; 2; . . . ;m� ��min xij; i ¼ 1; 2; . . . ;m

� �for i ¼ 1; 2; . . . ;m; j ¼ 1; 2; . . . ; n

(3)

Equation 2 is used for positive BSIs (the larger thebetter); Equation 3 is used for negative BSIs (the smallerthe better) and Equation 4 is used for the desired-valueBSIs (the closer to the desired value x�j the better).

3.3. Calculation of the grey relationalcoefficients

When converting BSIs into GSI, the grey relational coeffi-cients are calculated using Equation 5 [48], and then a grey

relational coefficients matrix is obtained Ξ= {xij}m� n.

xij ¼min

1≤i≤mmin

1≤j≤n zij� �

m�n þ rmax

1≤i≤mmax

1≤j≤m zij� �

m�n

zij þ rmax

1≤i≤mmax

1≤j≤m zij� �

m�n

(5)

where r is the distinguishing coefficient, r2 [0,1], usuallyr= 0.5; and zij is the absolute difference between theelements of the reference sequence and the elements ofeach column of the matrix, given by Equation 6.

zij ¼ x0j � xij�� (6)

where x0j is the reference sequence as x0 = (x01,x02, . . .,x0j, . . .,x0n).

3.4. Calculation of the comprehensiveevaluation vector

The result of a comprehensive evaluation of the objectivesystem, which is the final result of the GSI, is given byEquation 7.

ri ¼Xmj¼1

xij�oj (7)

whereΩ={oj} is the weighting vector of each basic indicator.

x0ij ¼ 1� xij � x�j

max max xij; i ¼ 1; 2; . . . ;m� �� x�j ; x

�j �min xij; i ¼ 1; 2; . . . ;m

� �n o

for i ¼ 1; 2; . . . ;m; j ¼ 1; 2; . . . ; n

(4)

Figure 2. The sustainability indicator hierarchy.

Figure 1. The information flow of the sustainability indicator.



In this study, the weightings of all the BSIs are borrowed fromthe (fuzzyAHP) FAHPweightingmodel [37], and the weight-ing vector result is given in Table I.

4. CASE STUDY IN AUSTRALIA

The purpose of this case study is to measure the sustainabilityof RESs by using the developed GSI. The RESs are located inAlice Springs (23.70 ∘S, 133.88 ∘E), where monthly solarirradiation is between 13.31 and 21.3 (MJ/m2)/day and meanwind speed is 7.0 m/s [37]. There are four options for thesystem configurations with different combinations of photo-voltaic (PV), wind and grid. They are, respectively:

• System A: PV/wind/grid system includes 1 kW PVpanel and one 7.5 kW DC wind turbine.

• System B: PV/grid system includes a 2 kW PV panel.• System C: wind/grid system includes one 7.5 kW DCwind turbine.

• System D: pure grid system.

The original values of BSIs of the four configurations asthe inputs of the GSI are shown in Table II. System A hasthe highest cost of all, but has the best renewable fractionand the least emissions. In contrast, System D has the leastinvestment, but has the most emissions and the lowestrenewable fraction.

The sustainability of the four optimised configurationsis measured by the grey sustainability indicator. The fol-lowing sections use the GSI to measure the sustainabilityof these four configurations and make a decision on themto choose the system having the maximum sustainabilityvalue.

4.1. The results of grey relationalcoefficients

The grey relational coefficients quantify not only the rela-tionship between various BSIs but also the relationshipbetween BSIs and GSI. The values of the coefficients ofall the BSIs, as the intermediate results of the GSI for allthe systems, are shown in Tables III to V for economic,

environmental and social BSIs, respectively. These coeffi-cients represent the scores of a specific system with itscorresponding BSI. For both positive and negative BSIs,a higher grey relational coefficient implies a higher scoringsystems’ sustainability.

4.1.1. The grey relational coefficients of economicBSIs

The grey relational coefficients of economic BSIs reflectthe sustainability level of systems in the economic view.The higher the value of the coefficients, the stronger is thesustainability. As can be seen from Table III, System A is

Table II. Origin values of BSIs of the four systems.

Cij System A System B System C System D

C11 $ 91, 702 $ 89, 246 $ 89, 949 $ 87, 720C12 0.197$/kWh 0.191$/kWh 0.193$/kWh 0.188$/kWhC13 7.25% 6.82 % 7.56 % 8%C14 45, 514 kWh 36, 868 kWh 44, 520 kWh 36, 500 kWhC21 57.3 % 9.83 % 54.5 % 0C22 13, 647 kg/yr 30, 714 kg/yr 14, 632 kg/yr 33, 726 kg/yrC23 149 kg/yr 335 kg/yr 160 kg/yr 368 kg/yrC24 191 kg/yr 429 kg/yr 204 kg/yr 471 kg/yrC25 33.02% 41.1% 35% 45%C31 3 2.5 2 2C32 5 3 2 1

Table III. The grey relational coefficients of economic BSIs forall systems.


C11 0.2857 0.5107 0.4168 1.0000C12 0.2857 0.5455 0.4186 1.0000C13 0.3863 0.2857 0.5175 1.0000C14 1.0000 0.2943 0.7839 0.2857

Table IV. The grey relational coefficients of environmental BSIsfor all systems.


C21 1.0000 0.3256 0.8911 0.2857C22 1.0000 0.3200 0.8908 0.2857C23 1.0000 0.3202 0.8884 0.2857C24 1.0000 0.3200 0.8960 0.2857C25 0.2857 0.5513 0.3240 1.0000

Table V. The grey relational coefficients of social BSIs for allsystems.


C31 1.0000 0.4444 0.2857 0.2857C32 1.0000 0.4444 0.3478 0.2857



scored 1 (full credit) in the BSI of C14. This is because thesystem generates the most electricity (45 514 kWh per year).Moreover, the sustainability of this system is scored 0.907 inthe BSI of C13 (return on investment). System A, however, isscored very low in the BSIs of C11 (net present cost) and C12

(cost of energy). As to System B and System C, the coefficientsof all the BSIs are less than 1; this is because the PV/gridsystem and the wind/grid have no superiority in theassessment of economic criteria. System D, which is apure grid system, has the least values of net present costand the cost of energy and has the best return on invest-ment (as shown in Table III). As a result, these three BSIsof System D are ranked as full credit. It would bepredicted that System D would be scored the highestsystem for the economic criteria.

4.1.2. The grey relational coefficients ofenvironmental BSIs

The grey relational coefficients indicate the sustainabilityof all the systems in regards to environmental aspects. Thegrey relational coefficients of the five BSIs of environmentalcriteria for this case are shown in Table IV. System A, thePV/wind/grid system, is scored 1 for four BSIs: C21 (renew-able fraction), C22 (CO2 emission), C23 (SO2 emission) andC24 (NOx emission). For these four BSIs, System C is alsoscored higher (0.8884–0.8960). Systems B and D are scoredvery low, 0.32 and 0.28, respectively. In terms of the BSI(C25, conversion efficiency), the pure grid system (System D)

is scored as full credit. This is due to the fact that the gridelectricity is almost exclusively based on coal, petrol and othertraditional energy resources which have higher conversionefficiency than wind and solar. In contrast, System A (PV/wind/grid system) and System C (PV/grid system), which havea solar PV component, are scored lower than other systems,because of the lower energy conversion efficiency in solar PV.To sum up, System A is the strongest sustainable system forthe environmental criteria.

4.1.3. The grey relational coefficients of socialBSIs

The grey relational coefficients of social BSIs represent thesustainability level of all the systems with regard to socialaspects. The social sustainability, from the stronger to theweaker, is found to be in the order of: System A, System B,System C and System D. Because System A creates morenew jobs and benefits to more residents, it is scored as 1 inthese two BSIs (C31 and C32). The coefficients of these twoBSIs for System D are both 0.2857.

4.2. The GSI results

The final GSI results include the results of the economicindicators, environmental indicators, and social indicators.The results of the GSIs are summarised in Figure 3. In termsof the economic indicator, as can be seen from Figure 3(a),System D has the highest score (0.9483). This is becauseSystem D needs the least financial costs and has the highest

A B C D0

0.2

0.4

0.6

0.8

1

Indi

cato

r V

alue

(−

)

Systems

(a) Economic indicator

A B C D0

0.2

0.4

0.6

0.8

1

Indi

cato

r V

alue

(−

)

Systems

(b) Environmental indicator

A B C D0

0.2

0.4

0.6

0.8

1

Indi

cato

r V

alue

(−

)

Systems

(c) Social indicator

A B C D0

0.2

0.4

0.6

0.8

1

Indi

cato

r V

alue

(−

)

Systems

(d) General sustainability indicator

Figure 3. The final results of system sustainability indicators.



return on investment, while other systems including renewableenergy components have more costs. In particular, the returnon investment takes up the biggest weighting of 0.3008, soSystem D scores higher than others since this system hassignificant superiority in this BSI. Although System D hasthe lowest annual electricity generation, this does not lead toa lower score for the economic indicator because the BSI ofelectricity generation has a very small weighting among theeleven indicators. System C has a relatively higher value inthe BSIs of return on investment as discussed above; therefore,it has the second highest score (0.5105). Moreover, System Aand System B are scored at 0.4042 and 0.3496, respectively.

The environmental indicator is the most important indi-cator of the GSI which takes up the weightings of 0.5414.It can be seen from Figure 3(b) that Systems A and C arescored higher, 0.95 and 0.8514, respectively, while Sys-tems B and D are marked as 0.3375 and 0.3355. The socialindicator results shown in Figure 3(c) for all the systemsare ranked in the order of: System A (1), B (0.4444),C (0.3168) and D (0.2857).

To sum up, the integration of all the BSIs and the resultsof GSI are shown in Figure 3(d). The sustainability ofSystem A is scored 0.7032, System B 0.3436, System C0.6940 and System D 0.6129. It is found that, under the localweather conditions, the systems’ sustainability from strongerto weaker is found to be in order of: System A (1 kW PVpanel and one 7.5 kW DC wind turbine), System C (one7.5 kW DC wind turbine), System D (pure grid) and SystemB (2 kW PV panel).

4.3. Validation: A comparison between greyindicator and fuzzy indicator

In order to validate the grey relational analysis based-GSI,the sustainability of 20 virtual RESs had been comparedwith a fuzzy GSI which is based on FAHP and fuzzy com-prehensive assessment in Ref. [37]. The linear correlationanalysis of these two GSIs is shown in Figure 4, wherethe horizontal axis represents the fuzzy GSI and the verti-cal axis represents the grey GSI. It is found from the figure

that there is a good linear correlation between these twoGSIs, where the correlation coefficient is 0.8445 and thep-value (0.0007) is less than the significance levela=0.05. This illustrates that the results of grey GSI andfuzzy GSI are quite close in spite of minor differences.The linear regelation between the two indicators can berepresented by a linear function based on the least squaremethod: y= 0.5277x+ 0.2055. The slope coefficient of theline (0.5277) indicates that, in spite of the good linearcorrelation of those two GSIs, they have different values.The fuzzy GSI just fuzzifies the original values of theperformances parameters and defuzzifies the sustainabilityjudgements; the grey GSI, however, not only considers theuncertainties of BSIs’ quantification, but also considers thegrey relation between these performances and the degreesof sustainability assessment. Consequently, the uncertain-ties in the development of sustainability indicator for RESscan be effectively solved by grey relational analysis as wellas fuzzy sets theory, and the GSI based on grey relationalanalysis is reliable.

5. CONCLUSIONS

This study develops a GSI for the sustainability assessmentof RESs in Australia. The indicator includes three levels:general indicator level, criteria level and basic indicatorslevel. Through normalising the selected eleven BSIs andcalculating the grey coefficients of the selected 11 basicindicators (including net present cost, cost of energy,return on investment, energy generation, renewable frac-tion, carbon dioxide emissions, sulfur dioxide emissions,nitrogen oxide emissions, conversion efficiency, house-holds benefited and new jobs created) of environmental,economic and social criteria of sustainability, the GSI isdeveloped based on grey relational analysis. The weightsof all the BSIs determined by FAHP in our previous study[37] are used to build the modelling of the grey GSI.

The four optimised configurations of Australian RESswith different combinations of PV, wind and grid are eval-uated using their sustainability indicators in the case study.The grey relational coefficients as the medium results andthe final results for the top layer and the criteria layer arediscussed. It is found from the case study that the systemincluding 1 kW PV panel and one 7.5 kW DC wind turbinerunning under the local weather conditions is scored0.7032 and is the best system to meet the requirement ofsustainable development.

Based on the comparison between the results of greyGSI and the previous results of fuzzy GSI, it is found thatthe grey GSI has good linear relationship to the fuzzy GSI.This proves that the grey GSI is reliable and reasonable,and it is an effective way to evaluate and rank the sustain-ability of RESs. However, this indicator is only proper forthe Australia and current policies. With the economicdevelopment and the change of economic environment,the policy bias of renewable energy would also change,and the policy incentives would also change. As a result,

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Fuzzy indicator

Gre

y in

dica

tor

Indicatorsy=0.5277x+0.2055

Figure 4. The comparison between grey indicator and fuzzy indicator.



the weightings and normalisation methods of BSIs, andeven the final results of GSI, would be different to thedescriptions as discussed above.

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General sustainability indicator of renewable energy system based on grey relational analysis