Measuring the relative efficiency of hydrogen energy technologies ...

Author's personal copyinternational journal of hydrogen energy 36 (2011) 12655e12663 12657Fig. 1 e Execution flowchart.natural language expression rather than crisp numbers inmaking assessments. The fuzzy set theory deals with ambiguoussituations or situations that are not well defined. Thedata is presented to show human thoughts and perceptionsusing approximate information and uncertainty in order togenerate reasonable alternatives in decision-makingproblems.The concept of fuzzy theory was introduced by Zadeh in1965 [7]. Fuzzy theory includes fuzzy sets, membership functions,and fuzzy numbers to change vague data into usefuldata efficiently.Fuzzy set theory implements groups of data with boundariesthat are not sharply defined. The merit of using thefuzzy approach is that it expresses the relative importance ofalternatives and criteria with fuzzy numbers instead of crispnumbers because most decision making in the real worldtakes place in situations where pertinent data and thesequences of possible actions are not precisely known.Triangular and trapezoidal fuzzy numbers are generallyused to capture the vagueness of the parameters related toselect the alternatives. TFN is expressed with boundariesinstead of crisp numbers to reflect the fuzziness as decisionFig. 2 e Hierarchy of the fuzzy AHP.

Author's personal copyinternational journal of hydrogen energy 36 (2011) 12655e12663 12659W ¼ðdðA 1 Þ; dðA 2 Þ; .; dðA n ÞÞ T (11)where W is a non-fuzzy number.4.2. DEAThe DEA approach is a nonparametric MCDM assessment toolused in conjunction with decision-making units (DMUs) toeffectively solve many decision-making problems by simultaneouslyintegrating multiple inputs and outputs. Thismathematical method has been used to solve a wide range ofapplications since 1978. The DEA is generally applied not onlyto assess the service productivity of banks [12], insurancecompanies [13], hospitals [14], universities [15] and restaurants,but also to evaluate the efficiency of R&D programs[16e18].Fig. 3 shows the hierarchy structure of the DEA process,which consists of a single input factor and multiple outputfactors. The input factor consists of the DC associated with thedevelopment of hydrogen economy technologies. The fouroutput factors are EI, CP, IC, and TS. The relative weightscalculated using the fuzzy AHP approach are applied inconjunction with the output factors employed as part of theDEA approach.The DEA ration form was first proposed by Charnes,Cooper, and Rhodes (CCR) [19], and was designed to measurethe relative efficiency or productivity of a specific DMU k . TheDEA formulation is given as follows:Suppose there is a set of n DMUs to be analyzed, each ofwhich uses m common inputs and s common outputs.Let k (k ¼ 1,., n) denote the DMU whose relative efficiencyor productivity is to be maximized, as represented byP sr¼1Max h k ¼u rkY rkP mi¼1 v (12)ikX ikP sr¼1s:tu rkY rkP mi¼1 v 1; for j ¼ 1; .; n (13)ikX iku rk > 0; for r ¼ 1; .; s (14)v ik > 0; for i ¼ 1; .; m (15)where u rk is the variable weight given to the rth output of thekth DMU, v ik is the variable weight given to the ith input of thekth DMU, u rk and v ik are decision variables determining therelative efficiency of DMU k , Y rj is the rth output of the jth DMU,and X ij is the ith input of the jth DMU. This also assumes thatall Y rj and X ij are positive. The value h k is the efficiency score,which is less than and equal to 1. When the efficiency score ofh k is 1, DMU k is regarded as an efficient frontier.The two types of CCR models are the input-oriented model,in which the inputs are maximized, and the output-orientedmodel, in which the outputs are maximized. Given that thefocus is on maximizing multiple outputs, this paper used thefollowing output-oriented CCR model:min px 0 (16)s:t qy 0 ¼ 1 (17)pX þ qY 0 (18)p 0; q 0; (19)where x 0 and y 0 are the input and output vectors of DMU o ,respectively. In Equation 18, X and Y variables refer tomatrices of inputs and outputs, respectively. Let an optimalsolution of LP 0 be (v*, u*). Then, an optimal solution of theoutput-oriented model is obtained fromp ¼ v =q ; q ¼ u =q : (20)Fig. 3 e Hierarchy of the DEA approach.

Author's personal copy12660international journal of hydrogen energy 36 (2011) 12655e12663Table 2 e Classification of hydrogen energy technologies.High-level Mid-level Low-Level Core technologiesTechnologies for thehydrogen economyHydrogen Tech Hydrogen production Natural gas hydrogen production techThermochemical hydrogen production techWater electrolyzer hydrogen production techHydrogen separation& StorageChemical storage tech of solidHigh purity hydrogen production techFuel cell Tech PEMFC Portable fuel cell techFuel cell vehicle techHoem/Industry system techMicro fuel cellDMFCLaptop’s fuel cell techPortable fuel cell techSOFCFuel cell for power generationFuel cell for home & APUClearly, (p*, q*) is feasible for LP 0 . The optimal solutioncomes from Equation 21, presented asp x 0 ¼ v x 0 =q ¼ h (21)^x 0 ¼ x 0 t (22)In the first stage, we weigh the relative priority of low levelsof hydrogen energy technologies using the fuzzy AHPapproach. We then measure the relative efficiency of 13shortlisted hydrogen energy technologies on the second stageby using the DEA approach.^y 0 ¼ h y 0 þ t þ (23)where t * and t þ * are the slack variables of inputs and outputsrelated to DMU 0 , respectively.6. Numerical examples6.1. Priority of criteria5. Classification of hydrogen energytechnologies for the hydrogen economyHydrogen energy technologies are composed of five low levelsof hydrogen energy technologies considered under Korea’senergy environment. The classified hydrogen energy technologiesof the hydrogen economy are shown in Table 2.We made pairwise comparisons of four criteria to assess thehydrogen energy technologies in the sector of the hydrogeneconomy. Table 3 shows the fuzzy evaluation matrix withresponse to the goal.The result of the fuzzy evaluation of criteria, which is themean value, is shown in Table 4.We calculated TFN values of the four criteria by using thefuzzy evaluation values in Table 4. The TFN values of thecriteria are as follows:Table 3 e Fuzzy evaluation of the goal.EI CP IC TSEI (1, 1, 1) (1, 1, 1) (1, 1, 1) (2/3, 1, 3/2)(1, 1, 1) (2/3, 1, 3/2) (1, 1, 1) (2/3, 1, 3/2)(1, 1, 1) (1, 1, 1) (2/3, 1, 3/2) (3/2, 2, 5/2)- - - -- - - -CP (1, 1, 1) (1, 1, 1) (1, 1, 1) (2/3, 1, 3/2)(2/3, 1, 3/2) (1, 1, 1) (2/3, 1, 3/2) (1, 1, 1)(1, 1, 1) (1, 1, 1) (2/3, 1, 3/2) (3/2, 2, 5/2)- - - -- - - -IC (1, 1, 1) (1, 1, 1) (1, 1, 1) (2/3, 1, 3/2)(1, 1, 1) (2/3, 1, 3/2) (1, 1, 1) (2/3, 1, 3/2)(2/3, 1, 3/2) (2/3, 1, 3/2) (1, 1, 1) (2/3, 1, 3/2)- - - -- - - -TS (2/3, 1, 3/2) (2/3, 1, 3/2) (2/3, 1, 3/2) (1, 1, 1)(2/3, 1, 3/2) (1, 1, 1) (2/3, 1, 3/2) (1, 1, 1)(2/5, 1/2, 2/3) (2/5, 1/2, 2/3) (2/3, 1, 3/2) (1, 1, 1)- - - -- - - -- denotes that there is another value for another expert’s fuzzyevaluation of criteria.S 1 ðEIÞ ¼ð3:97; 4:60; 5:40Þ5ð1=20:20; 1=16:60; 1=14:01Þ¼ ð3:97 1=20:2; 4:60 1=16:60; 5:40 1=14:01Þ¼ð0:20; 0:28; 0:39ÞS 2 ðCPÞ ¼ð3:97; 4:60; 5:40ÞÞ5ð1=20:20; 1=16:60; 1=14:01Þ¼ð0:20; 0:28; 0:39ÞS 3 ðICÞ ¼ð3:23; 3:80; 4:67ÞÞ5ð1=20:20; 1=16:60; 1=14:01Þ¼ð0:16; 0:23; 0:33ÞTable 4 e Fuzzy evaluation of criteria.EI CP IC TSEI (1.00, 1.00,1.00)CP (0.93, 1.00,1.10)IC (0.81, 0.90,1.03)TS (0.56, 0.80,1.17)(0.93, 1.00,1.10)(1.00, 1.00,1.00)(0.75, 0.90,1.13)(0.63, 0.80,1.07)(1.03, 1.20,1.40)(0.97, 1.20,1.50)(1.00, 1.00,1.00)(0.67, 1.00,1.50)(1.00, 1.40,1.90)(1.07, 1.40,1.80)(0.67, 1.00,1.50)(1.00, 1.00,1.00)

Author's personal copyinternational journal of hydrogen energy 36 (2011) 12655e12663 12661Table 5 e Values of V(S j ‡S i ).V(S 1 S i ) value V(S 2 S i ) valueTable 7 e 10-point scale for EI.ScaleDefinitionV(S 1 S 2 ) 1.00 V(S 2 S 1 ) 1.00V(S 1 S 3 ) 1.00 V(S 2 S 3 ) 1.00V(S 1 S 4 ) 1.00 V(S 2 S 4 ) 1.00V(S 3 S i ) value V(S 4 S i ) valueV(S 3 S 1 ) 0.72 V(S 4 S 1 ) 0.70V(S 3 S 2 ) 0.74 V(S 4 S 2 ) 0.70V(S 3 S 4 ) 1.00 V(S 4 S 3 ) 0.94S 4 ðTSÞ ¼ð2:85; 3:60; 4:73ÞÞ5ð1=20:20; 1=16:60; 1=14:01Þ¼ð0:14; 0:22; 0:34ÞWe compared the values of S i and calculated the degree ofpossibility of S j ¼ (l j , m j , u j ) S i ¼ (l i , m i , u i ) using Equation (8).Table 5 shows the values of V(S j S i ).We calculated the minimum degree possibility d 0 (i) ofVðS j S i Þ for i,j ¼ 1,2,..,k.D 0 ð1Þ ¼min VðS 1 S 2 ; S 3 ; S 4 Þ¼min ð1:00; 1:00; 1:00Þ ¼1:00D 0 ð2Þ ¼min VðS 2 S 1 ; S 3 ; S 4 Þ¼min ð1:00; 1:00; 1:00Þ ¼1:00D 0 ð3Þ ¼min VðS 3 S 1 ; S 2 ; S 4 Þ¼min ð0:72; 0:74; 1:00Þ ¼0:72D 0 ð4Þ ¼min VðS 4 S 1 ; S 2 ; S 3 Þ¼min ð0:70; 0:70; 0:94Þ ¼0:70The weight vector is as follows:W 0 ¼ ð1:00; 1:00; 0:72; 0:70Þ TWe normalized the weight vectors as follows:W ¼ð0:29; 0:29; 0:21; 0:20Þ TThe final weights of EI, CP, IC, and TS, are 0.29, 0.29, 0.21, and0.20, respectively. Among the four criteria, EI and CP arepreferred over the other two.6.2. Quantitative data of shortlisted hydrogen energytechnologiesShortlisted hydrogen energy technologies to foster thehydrogen economy are classified based on a 10-point scale.Table 6 shows the 10-point scale for IC and TS. The numbers 2,2 Potential energy saving is less than10,000 TOE/year,CO 2 emission reduction is less than10,000 tCO 2 /year4 Potential energy saving is between10,000 and 500,000 TOE/year,CO 2 emission reduction is between10,000 and 500,000 tCO 2 /year6 Potential energy saving is between500,000 and 1,000,000 TOE/year,CO 2 emission reduction is between500,000 and 1,000,000 Tco 2 /year8 Potential energy saving is between1,000,000 and 2,000,000 TOE/year,CO 2 emission reduction is between1,000,000 and 5,000,000 tCO 2 /year10 Potential energy savings is greater than2,000,000 TOE/year,CO 2 emission reduction is greater than5,000,000 tCO 2 /year1, 3, 5, 7, 9 Intermediate values are used tocompromise between two judgments4, 6, 8, and 10, which correspond to the extent of preference forone element over others, are used as scaling ratios. Forexample, a technology with a score of 10 can be regarded asexhibiting a degree of IC and TS much higher than that of theother technologies. Conversely, a score of 2 means that oneenergy technology ranks much lower than the others in termsof a particular criterion.Tables 7 and 8 display the 10-point scale for the EI and the CP,respectively. A score of 10 for EI implies potential energy savingsof more than 2 million TOE/year, or a reduction in CO 2 emissionsgreater than 5 million tCO 2 /year. Meanwhile, a score of 10for the possibility of commercialization indicates that a particularenergy technology is currently at the technology disseminationphase, and that core patents and the dissemination ofthe energy technology can be secured within three years.Table 9 shows a single input and multiple outputs data, whichare shortlisted energy technologies in the sector of the hydrogeneconomy. It describes the data multiplied by the fuzzy AHPresults for measuring the relative efficiency of energy technologiesin the hydrogen economy using the DEA approach.Table 6 e 10-point scale for IC and TS.ScaleDefinition2 Inner capacity and technical spin-off areat an extremely low level4 Inner capacity and technical spin-off areat a low level6 Inner capacity and technical spin-off areat a medium level8 Inner capacity and technical spin-off areat a high level10 Inner capacity and technical spin-off areat an extremely high level1, 3, 5, 7, 9 Intermediate values are used tocompromise between two judgmentsTable 8 e 10-point scale for CP.ScaleDefinition2 Phase of quickening technology development, needarises to research new technological concepts4 Phase of technology development, componenttechnologies need to be developed6 Core patent acquirement phase8 Commercialization phase, core patents can beobtained and technologies commercializedwithin 3e5 years10 Technological dissemination phase, core patentscan be acquired and technologies disseminatedwithin 3 years1, 3, 5, 7, 9 Intermediate values are used to compromisebetween two judgments

Author's personal copy12662international journal of hydrogen energy 36 (2011) 12655e12663Table 9 e Single input and multi outputs data of shortlisted hydrogen energy technologies.Low-level Shortlisted energy tech Inputs OutputsDevelopment cost(mil.KRW) EI CP IC TCHydrogen Production tech Hydrogen production tech from natural gas 500 8.0 7.0 9.0 8.0Thermalchemical hydrogen production tech 500 7.0 4.0 7.0 7.0Water electrolysis hydrogen production tech 500 6.0 5.0 6.0 7.0Hydrogen separation & storage tech Chemical storage tech of solid 500 7.0 5.0 7.0 7.0High purity hydrogen separation tech 500 7.0 4.0 7.0 7.0PEMFC tech Portable fuel cell tech 540 8.0 8.0 9.0 8.0Fuel cell vehicle tech 540 8.0 8.0 9.0 9.0Home/Industry system tech 500 8.0 7.0 8.0 8.0DEFC tech Micro fuel cell tech 500 6.0 6.0 8.0 7.0Laptop’s fuel cell tech 500 6.0 7.0 8.0 7.0Portable power fuel cell tech 500 6.0 7.0 8.0 7.0SOFC tech Power generation fuel cell tech 540 6.0 7.0 4.0 4.0Home/APU fuel cell tech 540 6.0 7.0 4.0 4.0Table 10 e Preferred data applied to the fuzzy AHP results.Low-level Shortlisted energy tech Inputs OutputsDevelopment cost(mil.KRW) EI CP IC TSHydrogen Production tech Hydrogen production tech from natural gas 500 2.32 2.04 1.90 1.64Thermalchemical hydrogen production tech 500 2.04 1.17 1.48 1.44Water electrolysis hydrogen production tech 500 1.75 1.46 1.27 1.44Hydrogen separation& storage techChemical storage tech of solid 500 2.04 1.46 1.48 1.44High purity hydrogen separation tech 500 2.03 1.17 1.48 1.44PEMFC tech Portable fuel cell tech 540 2.34 2.34 1.90 1.64Fuel cell vehicle tech 540 2.34 2.34 1.90 1.85Home/Industry system tech 500 2.34 2.04 1.69 1.64DEFC tech Micro fuel cell tech 500 1.75 1.75 1.69 1.44Laptop’s fuel cell tech 500 1.75 2.04 1.69 1.44Portable power fuel cell tech 500 1.75 2.04 1.69 1.44SOFC tech Power generation fuel cell tech 540 1.75 2.04 0.84 0.82Home/APU fuel cell tech 540 1.75 2.04 0.84 0.82Table 10 shows the preferred data applied to the fuzzy AHPcriteria’ relative weights, wherein four multiple inputs dataare changed.6.3. Relative efficiency of hydrogen energy technologiesWe calculated the relative efficiency of hydrogen energytechnologies by using the DEA approach in the second stage.Table 11 shows the relative efficiency scores and the ranks ofhydrogen energy technologies.An efficiency score of 1.000 means an energy technologyhas been determined to belong to the efficient frontier groupusing the DEA model. In addition, an efficiency score of 1.000is the optimal status considering the ratio of output variablesover input variables from benefit cost analysis concept. If anefficiency score of portable fuel cell technology of PEMFC isTable 11 e Relative efficiency scores and ranks.Low-level Shortlisted energy tech Efficiency score RankHydrogen Production Tech Hydrogen production tech from natural gas 1.000 1Thermalchemical hydrogen production tech 0.875 8Water electrolysis hydrogen production tech 0.840 13Hydrogen separation & storage tech Chemical storage tech of solid 0.875 8High purity hydrogen separation tech 0.875 8PEMFC tech Portable fuel cell tech 1.000 1Fuel cell vehicle tech 1.000 1Home/Industry system tech 1.000 1DEFC tech Micro fuel cell tech 0.889 7Laptop’s fuel cell tech 0.951 5Portable power fuel cell tech 0.951 5SOFC tech Power generation fuel cell tech 0.875 8Home/APU fuel cell tech 0.875 8

Author's personal copyinternational journal of hydrogen energy 36 (2011) 12655e12663 126631.000, there is no need for addition increase of output performanceand input increase. If an efficiency score of micro fuelcell technology of DEFC is 0.889, in that case, there is needed toconsider the quantity increase of outputs and the quantitydecrease of inputs for having the efficiency score 1.000 as anefficient frontier group.The efficient frontier group, consisting of hydrogen energytechnologies, includes four technologies achieving relativeefficiency scores of 1.000: hydrogen production technologyfrom natural gas, portable fuel cell technology, fuel cellvehicle technology, and home/industry system. The othernine hydrogen energy technologies have been found to berelatively inefficient DMUs, following a comparison with therelative efficiency scores.7. ConclusionsIn this research, have expounded on how hydrogen energytechnologies measure relative efficiency using the DEAapproach based on performance and productivity. In the firststage, we allocated the relative weights of low levels ofhydrogen energy technologies using the fuzzy AHP approach.In the second stage, we measured the efficiency scores usingthe DEA approach. Fuzzy AHP effectively reflects humanthoughts with vagueness of real world decision-makingproblems compared with AHP, which only evaluates therelative weights with crisp numbers.4 hydrogen energy technologies, hydrogen productiontechnology from natural gas in the sector of hydrogenproduction and portable fuel cell technology, fuel cell vehicletechnology, home/industry system technology in the sector ofPEMC, are the most efficient technologies that should befocused on strategically with a view point of productivity andperformance. The other 9 hydrogen technology have to beadjusted the quantity values of input and output variables forbeing the efficiency frontier group.The results of this research can provide energy policymakers with optimal alternatives for resource allocation andfor implementing well-focused R&D as they establish andevaluate the priority and efficiency of hydrogen energy technologiesin the hydrogen economy sector. We plan to carry outfurther studies using the hybrid fuzzy AHP/DEA scale efficiencyapproach and slack-based measurement [20].AcknowledgmentThis work was supported by the KIER Basic Fund and by theHERC. The author would also like to express his gratitude to theexperts who participated in establishing the hydrogen ETRM.NomenclatureAHPCPDEADEFCDMUAnalytic hierarchy processCommercial potentialData envelopment analysisDirect ethanol fuel cellDecision-making unitEIETRMICMCDMPEMFCSOFCTSEconomic impactEnergy technology roadmapInner capacityMulti-criteria decision-makingPolymer electrolyte membrane fuel cellSolid oxide fuel cellTechnical spin-offreferences[1] Year book of energy statistics 2010. Ministry of KnowledgeEconomy; 2010.[2] KEPCO in brief 2009. Korea Electric Power Corporation; 2009.[3] Lee WY. Activities of hydrogen fuel cells in Korea. In:Proceeding of 3rd fuel cells and hydrogen; 2010.[4] Lee SK, Kim JW. World energy outlook and measures. KIER-A52417; 2005:299e354.[5] Lee SK, Mogi G, Kim JW. Energy technology roadmap for thenext 10 years: the case of Korea. Energy Policy 2009;37:588e96.[6] Lee SK, Mogi G, Lee SK, Kim JW. 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