Hydrogen energy which has been recognized as an alternative instead of fossil fuel has been developed rapidly in fuel cell vehicles. Different hydrogen energy systems have different performances on environmental, economic, and energy aspects. A methodology for the quantitative evaluation and analysis of the hydrogen systems is meaningful for decision makers to select the best scenario. principal component analysis (PCA) has been used to evaluate the integrated performance of different hydrogen energy systems and select the best scenario, and hierarchical cluster analysis (CA) has been used to verify the correctness and accuracy of the principal components (PCs) determined by PCA in this paper. A case including 11 different hydrogen energy systems for fuel cell vehicles has been studied in this paper, and the system using steam reforming of natural gas for hydrogen production, pipeline for transportation of hydrogen, hydrogen gas tank for the storage of hydrogen at refueling stations, and gaseous hydrogen as power energy for fuel cell vehicles has been recognized as the best scenario. Also, the clustering results calculated by CA are consistent with those determined by PCA, denoting that the results calculated by PCA are scientific and accurate.
Due to air pollution, energy shortage and climate change, the exploration of cleaner alternative transportation fuel is of vital importance [
Hydrogen fuel cell vehicles have the potential to be the most energy-efficient vehicles and to reduce polluting emissions and other harmful emissions on a well-to-wheel basis [
In order to search the best hydrogen energy system for fuel cell vehicles, we face an important question: how to determine the best hydrogen energy system for fuel cell vehicles among the alternatives according to the corresponding performances?
Searching for the best option among the pool of different hydrogen energy options through a set of decision criteria including environmental, economic, and energy aspects, multi-criteria methodology can assess the integrated performance of different energy approaches accurately. However, the methodologies that include many different indicators are difficult to compare the superiority among the different energy options because some indicators in energy option
Principal component analysis (PCA) is a multivariable technique in which the numbers of variables are reduced to a smaller number of factors that describe the principal variability or joint behavior of the data set [
Principal component analysis (PCA) has been used as a mathematical tool to evaluate and analyze the integrated performance of 11 hydrogen energy systems for fuel cell vehicles, and cluster analysis has also been used to verify the correctness of the principal components determined by PCA.
PCA is a mathematical tool which performs a reduction in data dimensionality and allows the visualization of underlying structure in experimental data and relationships between data and samples [
Collect the data about the characteristics (criteria) of the samples, and let the original decision-making matrix
Transform all the criteria in the original decision-making matrix to benefit type. The transformation can be carried out according to the type of the characteristic (criteria). Consider
Standard transformation
Calculate the correlation coefficient matrix. The element of correlation coefficient matrix can be calculated by (
Consider
Solve the eigenvalue and eigenvector, then calculate the contribution rate
Express the principal component. Select the first
Consider
Calculate the weight of the principal component.
Consider
Determine the evaluation function of each sample
Rank the sequence of the samples according to the rule that the larger the score of the evaluation function, the better the sample.
In order to verify the correctness of principal component analysis for determining the principal components, cluster analysis of the original variables (criteria) is helpful to judge the accuracy of the results by PCA.
The hierarchical agglomeration algorithm for clustering has been used in this paper, and the main thought of this methodology is assuming there are m observations, then the algorithm starts with
Determine the distance between all the observations.
Link the two observations that correspond to the lowest distance to conform a new cluster.
Compare the two observations that form part of the newly formed group with the remaining observations.
Repeat Step
The framework of multi-criteria decision making on hydrogen energy systems has been shown in Figure
Framework of multicriteria decision making on hydrogen energy systems.
determining the alternatives of hydrogen energy systems
determining the criteria for the assessment of the hydrogen energy systems (
using principal component analysis and cluster analysis to analyze the hydrogen energy systems, determining the PCs, the evaluation functions, and the clusters.
comparing the results determined by principal component analysis and cluster analysis. If they are consistent, turn to Step
ranking the sequence of the alternatives from the best to the worst.
In this section, principal component analysis has been applied for evaluating the performance of 11 plants of hydrogen energy systems for fuel cell vehicles provided by Feng et al. [
Steam reforming of natural gas (central factory) for hydrogen production, hydrogen gas cylinder by trucks for transportation, hydrogen cylinder for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume gaseous hydrogen;
Steam reforming of natural gas (central factory) for hydrogen production, pipeline for transportation, hydrogen gas tank for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume gaseous hydrogen;
Steam reforming of natural gas (central factory) for hydrogen production, liquid hydrogen tank by trucks for transportation, liquid hydrogen tank for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume liquid hydrogen;
Steam reforming of natural gas (central factory) for hydrogen production,
Coal gasification (central factory) for hydrogen production, hydrogen gas cylinder by trucks for transportation, hydrogen cylinder for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume gaseous hydrogen;
Coal gasification (central factory) for hydrogen production, pipeline for transportation, hydrogen gas tank for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume gaseous hydrogen;
Coal gasification (central factory) for hydrogen production, liquid hydrogen tank by trucks for transportation, liquid hydrogen tank for the storage of hydrogen at refueling stations, fuel cell vehicles in Peking consume liquid hydrogen;
Coal gasification (central factory) for hydrogen production,
Water electrolysis with industrial electricity at refueling stations for hydrogen production, no transportation, hydrogen gas tank for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume gaseous hydrogen;
Water electrolysis with valley electricity at refueling stations for hydrogen production, no transportation, hydrogen gas tank for the storage of hydrogen at refueling stations, and fuel cell vehicles in Peking consume gaseous hydrogen;
Methanol synthesis via natural gas (methanol factory), methanol tank by trucks for the storage, methanol tank for the storage of methanol, and fuel cell vehicles in Peking consume methanol (methanol reforming onboard).
The environmental, economic, and energy performances of the hydrogen energy systems have been shown in Table
The environmental, economic, and energy performance of the 11 scenarios [
Aspect | Environment | Economic | Energy | |||||||
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Criterion | SO2 | CO2 |
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CO | CH4 | Dust | Waste water | Waste solids | Costs | Energy |
Unit | kg | kg | kg | kg | kg | kg | kg | kg | ¥ | MJ |
Option 1 | 0.062 | 16.659 | 0.059 | 0.022 | 0.072 | 0.224 | 1011 | 4783 | 15.18 | 185.17 |
Option 2 | 0.053 | 15.761 | 0.048 | 0.020 | 0.072 | 0.188 | 822 | 3884 | 23.56 | 176.68 |
Option 3 | 0.160 | 26.573 | 0.103 | 0.019 | 0.074 | 0.623 | 2950 | 13994 | 18.56 | 219.66 |
Option 4 | 0.182 | 28.222 | 0.114 | 0.023 | 0.072 | 0.706 | 3350 | 15880 | 24.22 | 222.95 |
Option 5 | 0.130 | 37.664 | 0.084 | 0.016 | 0.000 | 0.453 | 2124 | 10071 | 19.84 | 294.26 |
Option 6 | 0.132 | 37.807 | 0.079 | 0.014 | 0.000 | 0.461 | 2144 | 10163 | 28.84 | 289.53 |
Option 7 | 0.232 | 48.243 | 0.130 | 0.013 | 0.000 | 0.865 | 4122 | 19562 | 23.43 | 331.96 |
Option 8 | 0.252 | 49.257 | 0.140 | 0.017 | 0.000 | 0.941 | 4488 | 21285 | 28.95 | 331.96 |
Option 9 | 0.616 | 59.532 | 0.316 | 0.020 | 0.000 | 2.475 | 11882 | 56340 | 41.66 | 683.47 |
Option 10 | 0.616 | 59.537 | 0.316 | 0.020 | 0.000 | 2.475 | 11883 | 56343 | 25.07 | 683.48 |
Option 11 | 0.083 | 21.244 | 0.074 | 0.021 | 0.110 | 0.275 | 1277 | 6011 | 14.68 | 270.74 |
¥ represents Yuan which is the basic monetary unit of China, 1 Yuan = 0.16 $.
The processed data of the 11 scenarios.
Aspect | Environment | Economic | Energy | |||||||
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Criterion | SO2 | CO2 |
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CO | CH4 | Dust | Waste water | Waste solids | Costs | Energy |
Option 1 | 0.9840 | 0.9795 | 0.9590 | 0.1000 | 0.3455 | 0.9843 | 0.9829 | 0.9829 | 0.9815 | 0.9832 |
Option 2 | 1.0000 | 1.0000 | 1.0000 | 0.3000 | 0.3455 | 1.0000 | 1.0000 | 1.0000 | 0.6709 | 1.0000 |
Option 3 | 0.8099 | 0.7530 | 0.7948 | 0.4000 | 0.3273 | 0.8098 | 0.8076 | 0.8073 | 0.8562 | 0.9152 |
Option 4 | 0.7709 | 0.7153 | 0.7537 | 0.0000 | 0.3455 | 0.7735 | 0.7714 | 0.7713 | 0.6464 | 0.9087 |
Option 5 | 0.8632 | 0.4997 | 0.8657 | 0.7000 | 1.0000 | 0.8841 | 0.8823 | 0.8821 | 0.8087 | 0.7680 |
Option 6 | 0.8597 | 0.4964 | 0.8843 | 0.9000 | 1.0000 | 0.8806 | 0.8805 | 0.8803 | 0.4752 | 0.7773 |
Option 7 | 0.6821 | 0.2580 | 0.6940 | 1.0000 | 1.0000 | 0.7040 | 0.7017 | 0.7011 | 0.6757 | 0.6936 |
Option 8 | 0.6465 | 0.2348 | 0.6567 | 0.6000 | 1.0000 | 0.6707 | 0.6686 | 0.6683 | 0.4711 | 0.6936 |
Option 9 | 0.0000 | 0.0001 | 0.0000 | 0.3000 | 1.0000 | 0.0000 | 0.0001 | 0.0001 | 0.0000 | 1.9732 |
Option 10 | 0.0000 | 0.0000 | 0.0000 | 0.3000 | 1.0000 | 0.0000 | 0.0000 | 0.0000 | 0.6149 | 0.0000 |
Option 11 | 0.9467 | 0.8747 | 0.9030 | 0.2000 | 0.0000 | 0.0000 | 0.9589 | 0.9595 | 1.0000 | 0.8144 |
The standard transformed data of the 11 scenarios.
Aspect | Environment | Economic | Energy | |||||||
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Criterion | SO2 | CO2 |
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CO | CH4 | dust | Waste water | Waste solids | Costs | Energy |
Option 1 |
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Option 2 |
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Option 5 |
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Option 11 |
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The correlation coefficient matrix.
SO2 | CO2 |
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CO | CH4 | Dust | Waste water | Waste solids | Costs | Energy | |
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SO2 |
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CO2 |
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CO |
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CH4 |
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Dust |
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Waste water |
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Waste solids |
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Costs |
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Energy |
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Then, the main results of PCA analysis of the 11 scenarios have been shown in Table
Main results of PCA of the 11 scenarios for the criteria.
PC1 | PC2 | PC3 | |
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SO2 | 0.3932 | 0.0980 | 0.0704 |
CO2 | 0.3723 | −0.2342 | 0.0693 |
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0.3899 | 0.1320 | 0.0809 |
CO | −0.0372 | 0.6783 | 0.0233 |
CH4 | −0.2697 | 0.5125 | 0.0473 |
Dust | 0.2767 | 0.3352 | 0.2261 |
Waste water | 0.3912 | 0.1135 | 0.0686 |
Waste solids | 0.3913 | 0.1130 | 0.0685 |
Costs | 0.3099 | −0.0979 | −0.4888 |
Energy | −0.0438 | −0.2186 | 0.8256 |
Eigenvalue | 6.2472 | 1.9040 | 1.2453 |
Variance (%) | 62.472 | 19.040 | 12.453 |
Cumulative variance (%) | 62.472 | 81.513 | 93.966 |
Weights | 0.6648 | 0.2026 | 0.1325 |
From the eigenvectors acquired in the principal component analysis, and according to (
For the purpose of checking the accuracy of principal component analysis for determining the principal components, the hierarchical agglomeration algorithm has been used to group the ten original variables. The data after standard transformation as shown in Table
The result of cluster analysis of the original variables has been shown in Figure
The result of cluster analysis of the original variables.
Meanwhile, each cluster can further be grouped into sub-clusters, for instance, cluster A can divided into subcluster A1 (SO2, CO2, NO
Then, the values of the principal component for the 11 hydrogen energy systems for fuel cell vehicles have been calculated, as shown in Table
The values of the principal components for the 11 hydrogen energy systems.
PC1 | PC2 | PC3 | |
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Option 1 | 2.5778 | −0.9118 | 0.1037 |
Option 2 | 2.3416 | −0.3616 | 0.7212 |
Option 3 | 1.3222 | −0.4495 | −0.0601 |
Option 4 | 0.8951 | −1.2432 | 0.2088 |
Option 5 | 0.8796 | 1.4576 | −0.0915 |
Option 6 | 0.4944 | 1.9931 | 0.5209 |
Option 7 | −0.4432 | 1.9464 | −0.2624 |
Option 8 | −0.8212 | 1.1215 | 0.0141 |
Option 9 | −5.0105 | −1.2034 | 2.1727 |
Option 10 | −4.1428 | −0.47455 | −2.4606 |
Option 11 | 1.9070 | −1.8746 | −0.8667 |
The weights of the three principal components have been shown in Table
With (
The final score and the sequence of the 11 hydrogen energy systems.
Score | Rank | |
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Option 1 | 1.5427 | 2 |
Option 2 |
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1 |
Option 3 |
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5 |
Option 4 | 0.3708 | 7 |
Option 5 | 0.8679 | 3 |
Option 6 |
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Option 7 | 0.0649 | 8 |
Option 8 |
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Option 9 | −3.2869 | 11 |
Option 10 | −3.1763 | 10 |
Option 11 | 0.7731 | 6 |
The sequence of the scenarios from the best to the worst is Option 2, Option 1, Option 5, Option 6, Option 3, Option 11, Option 4, Option 7, Option 8, Option 10, and Option 9. The best scenario determined by PCA is Option 2, followed by Option 1 and Option 5. Consequently, the hydrogen energy system for fuel cell vehicles with steam reforming of natural gas for hydrogen production, pipeline for the transportation, hydrogen cylinder for the storage at refueling stations and gaseous hydrogen as power energy for fuel cell vehicles has been recognized as the best one which has the best integrated performance.
The growing concern on the negative effects on environmental, economic, and energy aspects of traditional vehicles has promoted the decision makers to pay significant attention on clean and environment-friendly ones, and hydrogen energy systems for fuel cell vehicles are promising and attractive technologies in the future. However various methodologies of production, storage, transportation, and utilization will lead to different impacts on economic, environmental, and energy aspects. It is difficult for the stakeholders to determine the best one directly from various hydrogen energy systems. Therefore, developing a multicriteria decision making methodology on hydrogen energy systems is meaningful and valuable for the selection of the best system.
A hybrid multi-criteria decision making methodology integrating principal component analysis and cluster analysis has been proposed to assess the hydrogen energy systems in this paper. Principal component analysis has been used to determine the principal components and the evaluation functions of the systems, and cluster analysis has been used to verify the principal components determined by principal component analysis. When the results determined by principal component analysis and cluster analysis are consistent, the sequence of the alternatives from the best to the worst can be determined according to the value of the evaluation function for each system.
Eleven hydrogen energy systems for fuel cell vehicles have been assessed and analyzed by the proposed method, the sequence of the systems has been ranked, and the system using steam reforming of natural gas for hydrogen production, pipeline for transportation, hydrogen cylinder for the storage, and gaseous hydrogen for the consumption of fuel cell vehicles has been recognized as the best scenario. The clusters determined by CA are consistent with the principal components determined by PCA, indicating that the PCs for the evaluation of hydrogen energy systems are scientific and accurate. The proposed methodology can also be popularized.