Stochastic Multicriteria Acceptability Analysis for Evaluation of Combined Heat and Power Units
Abstract
:1. Introduction
2. Combined Heat and Power Units and Evaluation Criteria
2.1. Combined Heat and Power Units
- S1: compression engines diesel 200 kWe (industry).
- S2: compression engines diesel 20 MWe (industry).
- S3: gas engines—Otto cycle 1 kWe (household).
- S4: gas engines—Otto cycle 13 MWe (industry).
- S5: GT 500 kWe (industry).
- S6: GT 225 MWe (industry).
- S7: micro-turbines (CHP) 10 kWe (industry).
- S8: micro-turbines (CHP) 500 kWe (industry).
- S9: combined cycle gas turbines (CCGT) 8 MWe (industry).
- S10: CCGT 750 MWe (industry).
- S11: ST 500 kWe (coal) (hot water) (industry).
- S12: ST 500 kWe (fuel oil) (hot water) (industry).
- S13: ST 500 kWe (natural gas) (hot water) (industry).
- S14: ST 150 MWe (coal) (hot water) (industry).
- S15: ST 150 MWe (fuel oil) (hot water) (industry).
- S16: ST 150 MWe (natural gas) (hot water) (industry).
CHP | Electrical output (kWe) | Power to heat ratio | Efficiency (%) | Installation cost (€/kWe) | Maintenance cost (c€/kW·he) | Electricity cost (c€/kW·he) | Heat cost (c€/kW·hth) | CO2 production (kg/MW·he) | Footprint (m2/kWe) |
---|---|---|---|---|---|---|---|---|---|
S1 | 200 | 1.00 | 85 | 500 | 1 | 5.64 | 7.74 | 623.53 | 0.02 |
S2 | 20,000 | 1.23 | 88 | 1,500 | 0.5 | 2.30 | 4.84 | 545.96 | 0.011 |
S3 | 1 | 0.45 | 85 | 500 | 2 | 32.82 | 17.85 | 758.17 | 0.3 |
S4 | 13,000 | 0.90 | 88 | 2,500 | 0.7 | 3.81 | 4.84 | 479.80 | 0.014 |
S5 | 500 | 0.45 | 80 | 500 | 0.8 | 15.93 | 7.74 | 805.56 | 0.015 |
S6 | 225,000 | 0.70 | 90 | 1,200 | 0.2 | 4.37 | 4.72 | 539.68 | 0.0045 |
S7 | 10 | 0.29 | 75 | 1,500 | 1 | 33.84 | 9.61 | 1,186.21 | 0.05 |
S8 | 500 | 0.60 | 85 | 1,100 | 0.5 | 10.12 | 7.74 | 627.45 | 0.02 |
S9 | 8,000 | 0.96 | 73 | 1,000 | 0.8 | 5.78 | 5.18 | 559.36 | 0.03 |
S10 | 750,000 | 1.25 | 90 | 500 | 0.2 | 1.73 | 4.72 | 400 | 0.025 |
S11 | 500 | 0.25 | 82 | 2,000 | 0.5 | 2.23 | 0.51 | 2,042.68 | 0.06 |
S12 | 500 | 0.25 | 82 | 2,000 | 0.45 | 8.23 | 2.18 | 1,615.85 | 0.05 |
S13 | 500 | 0.25 | 82 | 2,000 | 0.4 | 28.35 | 7.74 | 1,219.51 | 0.027 |
S14 | 150,000 | 0.60 | 85 | 1,100 | 0.25 | 0.77 | 0.51 | 1,050.98 | 0.06 |
S15 | 150,000 | 0.60 | 85 | 1,100 | 0.2 | 2.82 | 2.18 | 831.37 | 0.05 |
S16 | 150,000 | 0.60 | 85 | 1,100 | 0.15 | 5.98 | 4.72 | 627.45 | 0.027 |
2.2. Properties and Measurements of Criteria
Criteria | Efficiency | Installation cost | Maintenance cost | Electricity cost | Heat cost | CO2 production | Footprint |
---|---|---|---|---|---|---|---|
Criteria No. | C1 | C2 | C3 | C4 | C5 | C6 | C7 |
Property 1 | ▲ | ▼ | ▼ | ▼ | ▼ | ▼ | ▼ |
Uncertainty | ±5% | ±10% | ±10% | ±10% | ±10% | ±10% | ±10% |
3. Weighting Method Based on a Complementary Judgment Matrix
3.1. Complementary Judgment Matrix
Description | aij | aji |
---|---|---|
ith criterion is equally important compared with jth | 0.5 | 0.5 |
ith criterion is a little more important compared with jth | 0.6 | 0.4 |
ith criterion is important compared with jth | 0.7 | 0.3 |
ith criterion is very important compared with jth | 0.8 | 0.2 |
ith criterion is extremely important compared with jth | 0.9 | 0.1 |
3.2. Feasible Weight Space
4. Stochastic Multicriteria Acceptability Analysis
4.1. The Stochastic Multicriteria Acceptability Analysis-2 Model
4.2. Handling the Uncertainties
4.2.1. Uncertainties in Criteria Measurements
4.2.2. Uncertainties in Weighting
5. Results and Discussion
Weight type | No. | Description |
---|---|---|
No weight information | (a) | The FWS is the general weight space with seven criteria, i.e., a six-dimensional simplex |
Interval constraints of weights | (b) | The FWS shown in Figure 5 |
5.1. Results
CHP | pc | ah | b1 | b2 | b3 | b4 | b5 | b6 | b7 |
S1 | 6.2 | 30.7 | 0.4 | 8.8 | 7.8 | 6.9 | 7.5 | 9.2 | 12.6 |
S2 | 7.1 | 39.9 | 1.1 | 5.6 | 21.8 | 15.9 | 14.5 | 16.7 | 9.5 |
S3 | 0 | 2.5 | 0 | 0 | 0 | 0.1 | 0.1 | 0.1 | 0.1 |
S4 | 4.2 | 22.7 | 0.3 | 1.1 | 3.8 | 8.0 | 6.2 | 7.4 | 11.7 |
S5 | 6.3 | 16.3 | 0.1 | 1.0 | 2.5 | 2.0 | 2.2 | 2.8 | 3.9 |
S6 | 23.9 | 62.4 | 10.3 | 47.6 | 17.2 | 11.0 | 6.9 | 3.7 | 1.9 |
S7 | 0 | 1.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S8 | 0.7 | 21.9 | 0 | 0.1 | 0.7 | 2.1 | 4.6 | 8.4 | 15.6 |
S9 | 0.5 | 14.7 | 0 | 0.2 | 0.6 | 1.3 | 2.0 | 3.2 | 5.2 |
S10 | 99.4 | 92.5 | 80.1 | 12.8 | 3.9 | 1.8 | 0.8 | 0.3 | 0.2 |
S11 | 11.0 | 10.9 | 0.1 | 0.3 | 0.4 | 0.7 | 1.0 | 1.8 | 3.4 |
S12 | 0 | 10.1 | 0 | 0 | 0.1 | 0.1 | 0.2 | 0.6 | 1.4 |
S13 | 0 | 5.6 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1 |
S14 | 53.1 | 40.8 | 5.4 | 10.0 | 12.2 | 13.4 | 13.9 | 12.2 | 10.0 |
S15 | 11.5 | 40.3 | 1.6 | 7.4 | 14.7 | 18.6 | 18.8 | 15.5 | 10.8 |
S16 | 4.8 | 39.0 | 0.6 | 5.1 | 14.2 | 18.1 | 21.2 | 18.1 | 13.5 |
CHP | b8 | b9 | b10 | b11 | b12 | b13 | b14 | b15 | b16 |
S1 | 14.4 | 14.0 | 7.1 | 5.4 | 3.3 | 1.6 | 1.0 | 0 | 0 |
S2 | 5.7 | 4.6 | 3.7 | 0.8 | 0 | 0 | 0 | 0 | 0 |
S3 | 0.2 | 0.5 | 2.0 | 4.5 | 5.2 | 3.3 | 7.6 | 15.1 | 61.0 |
S4 | 10.7 | 10.9 | 9.2 | 13.1 | 6.4 | 6.0 | 2.5 | 1.2 | 1.4 |
S5 | 6.1 | 11.1 | 18.7 | 17.6 | 12.7 | 17.4 | 1.9 | 0 | 0 |
S6 | 1.0 | 0.3 | 0.1 | 0 | 0 | 0 | 0 | 0 | 0 |
S7 | 0 | 0 | 0 | 0.3 | 1.8 | 3.5 | 7.1 | 60.2 | 27.1 |
S8 | 24.0 | 22.2 | 12.7 | 5.6 | 3.1 | 0.8 | 0.1 | 0 | 0 |
S9 | 8.6 | 11.3 | 19.5 | 15.1 | 10.1 | 9.5 | 9.9 | 3.4 | 0.2 |
S10 | 0.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S11 | 4.8 | 5.5 | 10.1 | 13.2 | 15.1 | 16.6 | 12.5 | 7.1 | 7.3 |
S12 | 2.9 | 4.9 | 8.9 | 16.9 | 28.5 | 23.7 | 7.6 | 3.8 | 0.3 |
S13 | 0.3 | 0.7 | 1.7 | 4.4 | 13.4 | 17.6 | 49.8 | 9.2 | 2.6 |
S14 | 7.8 | 7.8 | 4.3 | 2.6 | 0.3 | 0.1 | 0 | 0 | 0 |
S15 | 7.0 | 3.8 | 1.5 | 0.3 | 0 | 0 | 0 | 0 | 0 |
S16 | 6.3 | 2.3 | 0.6 | 0.1 | 0 | 0 | 0 | 0 | 0 |
CHP | pc | ah | b1 | b2 | b3 | b4 | b5 | b6 | b7 |
S1 | 0 | 27.1 | 0 | 0 | 1.3 | 6.2 | 9.5 | 14.5 | 25.4 |
S2 | 0 | 51.6 | 0 | 2.0 | 73.3 | 14.8 | 6.4 | 2.9 | 0.6 |
S3 | 0 | 3.8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S4 | 0 | 27.7 | 0 | 0 | 1.2 | 11.9 | 10.6 | 12.2 | 18.5 |
S5 | 0 | 13.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S6 | 2.5 | 70.0 | 1.8 | 95.8 | 2.2 | 0.1 | 0 | 0 | 0 |
S7 | 0 | 0.0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S8 | 0 | 20.7 | 0 | 0 | 0 | 0.2 | 1.0 | 3.0 | 9.4 |
S9 | 0 | 7.8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S10 | 99.1 | 99.5 | 98.2 | 1.8 | 0 | 0 | 0 | 0 | 0 |
S11 | 0 | 8.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S12 | 0 | 9.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S13 | 0 | 4.2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S14 | 0 | 33.8 | 0 | 0.1 | 5.8 | 17.4 | 21.2 | 22.8 | 18.9 |
S15 | 0 | 37.1 | 0 | 0.1 | 8.5 | 25.4 | 26.4 | 21.3 | 12.6 |
S16 | 0 | 36.5 | 0 | 0.1 | 7.6 | 23.9 | 24.9 | 23.3 | 14.6 |
CHP | b8 | b9 | b10 | b11 | b12 | b13 | b14 | b15 | b16 |
S1 | 27.9 | 15.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S3 | 0 | 0 | 0.2 | 4.6 | 4.9 | 10.4 | 23.8 | 55.6 | 0.3 |
S4 | 22.4 | 23.0 | 0.2 | 0 | 0 | 0 | 0 | 0 | 0 |
S5 | 0 | 0.2 | 69.1 | 17.9 | 11.8 | 1.0 | 0 | 0 | 0 |
S6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.3 | 99.7 |
S8 | 30.7 | 55.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S9 | 0 | 0.1 | 8.0 | 25.9 | 11.7 | 27.3 | 12.2 | 15.0 | 0 |
S10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S11 | 0 | 0 | 12.4 | 19.6 | 29.0 | 27.1 | 7.7 | 4.2 | 0 |
S12 | 0 | 0 | 10.1 | 31.3 | 39.7 | 16.7 | 1.8 | 0.3 | 0 |
S13 | 0 | 0 | 0 | 0.7 | 2.9 | 17.4 | 54.4 | 24.6 | 0 |
S14 | 9.8 | 4.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S15 | 4.5 | 1.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
S16 | 4.7 | 0.8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
5.2. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Abbreviations
AHP | Analytical hierarchy process |
CC | Combined cycle |
CCGT | Combined cycle gas turbine |
CHP | Combined heat and power |
CJM | Complementary judgment matrix |
DM | Decision maker |
FWS | Feasible weight space |
GT | Gas turbine |
MCDA | Multicriteria decision analysis |
SMAA | Stochastic multicriteria acceptability analysis |
ST | Steam turbine |
Letter Symbols
A | Complementary judgment matrix |
aij | Element of a judgment matrix |
aih | Holistic acceptability index of alternative i |
pic | Confidence factor of alternative i, % |
W | Weight space |
Wir | Favorable ranking weights |
w | Weight |
w | Weight vector |
wic | Central weight vector |
Subscripts and Superscripts
e | Electricity |
th | Thermal |
c | Cent |
Conflicts of Interest
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Wang, H.; Jiao, W.; Lahdelma, R.; Zhu, C.; Zou, P. Stochastic Multicriteria Acceptability Analysis for Evaluation of Combined Heat and Power Units. Energies 2015, 8, 59-78. https://doi.org/10.3390/en8010059
Wang H, Jiao W, Lahdelma R, Zhu C, Zou P. Stochastic Multicriteria Acceptability Analysis for Evaluation of Combined Heat and Power Units. Energies. 2015; 8(1):59-78. https://doi.org/10.3390/en8010059
Chicago/Turabian StyleWang, Haichao, Wenling Jiao, Risto Lahdelma, Chuanzhi Zhu, and Pinghua Zou. 2015. "Stochastic Multicriteria Acceptability Analysis for Evaluation of Combined Heat and Power Units" Energies 8, no. 1: 59-78. https://doi.org/10.3390/en8010059
APA StyleWang, H., Jiao, W., Lahdelma, R., Zhu, C., & Zou, P. (2015). Stochastic Multicriteria Acceptability Analysis for Evaluation of Combined Heat and Power Units. Energies, 8(1), 59-78. https://doi.org/10.3390/en8010059