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Frontiers in Energy

Front. Energy    2020, Vol. 14 Issue (3) : 649-665     https://doi.org/10.1007/s11708-018-0548-0
RESEARCH ARTICLE
Multi-objective optimization in a finite time thermodynamic method for dish-Stirling by branch and bound method and MOPSO algorithm
Mohammad Reza NAZEMZADEGAN1, Alibakhsh KASAEIAN1, Somayeh TOGHYANI1, Mohammad Hossein AHMADI2(), R. SAIDUR3, Tingzhen MING4
1. Department of Renewable Energies, Faculty of New Science and Technologies, University of Tehran, Tehran, 1417466191, Iran
2. Faculty of Mechanical Engineering and Mechatronic, Shahrood University of Technology, Shahrood 3619995161, Iran
3. Faculty of Science and Technology, Sunway University, No. 5, Jalan Universiti, Bandar Sunway, 47500 Petaling Jaya, Malaysia; Department of Engineering, Lancaster University, Lancaster, LA1 4YW, UK
4. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China
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Abstract

There are various analyses for a solar system with the dish-Stirling technology. One of those analyses is the finite time thermodynamic analysis by which the total power of the system can be obtained by calculating the process time. In this study, the convection and radiation heat transfer losses from collector surface, the conduction heat transfer between hot and cold cylinders, and cold side heat exchanger have been considered. During this investigation, four objective functions have been optimized simultaneously, including power, efficiency, entropy, and economic factors. In addition to the four-objective optimization, three-objective, two-objective, and single-objective optimizations have been done on the dish-Stirling model. The algorithm of multi-objective particle swarm optimization (MOPSO) with post-expression of preferences is used for multi-objective optimizations while the branch and bound algorithm with pre-expression of preferences is used for single-objective and multi-objective optimizations. In the case of multi-objective optimizations with post-expression of preferences, Pareto optimal front are obtained, afterward by implementing the fuzzy, LINMAP, and TOPSIS decision making algorithms, the single optimum results can be achieved. The comparison of the results shows the benefits of MOPSO in optimizing dish Stirling finite time thermodynamic equations.

Keywords dish-Stirling      finite time model      branch and bound algorithm      multi-objective particle swarm optimization (MOPSO)     
Corresponding Author(s): Mohammad Hossein AHMADI   
Just Accepted Date: 12 February 2018   Online First Date: 03 April 2018    Issue Date: 14 September 2020
 Cite this article:   
Mohammad Reza NAZEMZADEGAN,Alibakhsh KASAEIAN,Somayeh TOGHYANI, et al. Multi-objective optimization in a finite time thermodynamic method for dish-Stirling by branch and bound method and MOPSO algorithm[J]. Front. Energy, 2020, 14(3): 649-665.
 URL:  
http://journal.hep.com.cn/fie/EN/10.1007/s11708-018-0548-0
http://journal.hep.com.cn/fie/EN/Y2020/V14/I3/649
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Mohammad Reza NAZEMZADEGAN
Alibakhsh KASAEIAN
Somayeh TOGHYANI
Mohammad Hossein AHMADI
R. SAIDUR
Tingzhen MING
Fig.1  Thermodynamic cycle of Stirling
Decision variables Objectives
j x AR TH Th f P h S
Max(f) 1.000 0.478 1.491 1400.0 998.290 0.190 0.312 0.333 0.000465
Max(P) 1.000 0.475 10.000 1400.0 850.000 0.100 0.531 0.344 0.000790
Max(h) 1.000 0.450 10.000 1100.0 850.000 0.060 0.315 0.408 0.000285
Min(S) 1.000 0.450 0.250 1100.0 850.000 0.046 0.051 0.323 0.000046
Tab.1  Results of single-objective optimization
Decision variables Objectives
j x AR TH Th f P h S
1.000 0.450 10.000 1400.0 876.6 0.100 0.528 0.36 0.000665
Tab.2  Results of four-objective optimization with pre-expression of preferences
Decision variables Objectives
j x AR TH Th f P h S
Fuzzy 1.003 0.4602 2.0689 1292.4 949.096 0.155 0.339 0.373 0.000395
Linmap 1.0026 0.4802 4.1062 1391.2 907.0816 0.172 0.332 0.363 0.000401
Topsis 1.0411 0.4603 2.9210 1349.7 931.4148 0.183 0.337 0.351 0.000423
Tab.3  Results of four-objective optimization with post-expression of preferences
Fig.2  Pareto frontier of three-objective (f, P,h) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th f P h
Fuzzy 1.0019 0.452 3.232 1286.2 932.82 0.145 0.423 0.364
LINMAP 1.0026 0.468 6.396 1310.2 897.80 0.158 0.431 0.355
TOPSIS 1.0303 0.475 5.061 1364.9 929.26 0.177 0.384 0.348
Tab.4  Results of three-objective (f, P,h) optimization with post-expression of preferences
Fig.3  Pareto frontier of three-objective (f, P, S) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th f P h
Fuzzy 1.0031 0.4800 1.9688 1335.1 925.26 0.1412 0.357 0.000411
Linmap 1.0080 0.4636 4.5553 1220.8 938.81 0.1629 0.341 0.000404
Topsis 1.0080 0.4636 4.5553 1220.8 938.81 0.1629 0.341 0.000404
Tab.5  Results of three-objective (f, P, S) optimization with post-expression of preferences
Fig.4  Pareto frontier of three-objective (f, h, S) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th f h S
Fuzzy 1.0027 0.4750 2.4029 1229.5 974.21 0.1430 0.3784 0.000237
Linmap 1.0171 0.4504 1.4500 1214.7 948.59 0.1426 0.3640 0.000213
Topsis 1.0014 0.4542 3.9563 1139.6 984.06 0.1415 0.3608 0.00208
Tab.6  Results of three-objective (f, h, S) optimization with post-expression of preferences
Fig.5  Pareto frontier of three-objective (P, h, S) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th P h S
Fuzzy 1.0054 0.4504 6.4309 1128.7 868.23 0.309 0.407 0.000280
Linmap 1.0008 0.4503 7.9711 1137.7 850.00 0.315 0.407 0.000285
Topsis 1.0008 0.4503 7.9711 1137.7 850.00 0.315 0.407 0.000285
Tab.7  Results of three-objective (P, h, S) optimization with post-expression of preferences
Fig.6  Pareto frontier of two-objective (f, P) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th f P
Fuzzy 1.0000 0.4726 3.0483 1399.9 945.86 0.1533 0.4423
Linmap 1.0005 0.4836 4.1740 1400.0 929.26 0.1609 0.4275
Topsis 1.0002 0.4605 1.9859 1399.9 977.11 0.1738 0.3973
Tab.8  Results of two-objective (f, P) optimization with post-expression of preferences
Fig.7  Pareto frontier of two-objective (f, h) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th f h
Fuzzy 1.0003 0.4584 1.7197 1252.4 934.53 0.1500 0.3799
LINMAP 1.0005 0.4801 3.3165 1284.5 940.28 0.1812 0.3571
TOPSIS 1.0002 0.4750 3.0802 1326.8 965.14 0.1883 0.3507
Tab.9  Results of two-objective (f, h) optimization with post-expression of preferences
Fig.8  Pareto frontier of two-objective (P, h) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th P h
Fuzzy 1.0001 0.4520 9.9352 1152.3 852.47 0.4523 0.3845
LINMAP 1.0000 0.4542 9.9471 1299.5 858.50 0.5074 0.3674
TOPSIS 1.0000 0.4500 9.9586 1264.8 850.00 0.5283 0.3596
Tab.10  Results of two-objective (P, h) optimization with post-expression of preferences
Fig.9  Pareto frontier of two-objective (f, S) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th f S
Fuzzy 1.0079 0.4500 0.7250 1240.2 984.29 0.1520 0.000235
LINMAP 1.0000 0.4519 0.5000 1276.9 960.01 0.1425 0.000211
TOPSIS 1.0007 0.4523 1.4500 1262.3 955.29 0.1275 0.000175
Tab.11  Results of two-objective (f, S) optimization with post-expression of preferences
Fig.10  Pareto frontier of two-objective (P, S) optimization with post-expression of preferences
Decision variables Objectives
j x AR TH Th P S
Fuzzy 1.0005 0.4816 9.6704 1339.3 857.53 0.3790 0.000391
LINMAP 1.0000 0.4711 9.3228 1209.7 865.87 0.3571 0.000358
TOPSIS 1.0059 0.4929 10.0000 1377.8 850.00 0.3227 0.000308
Tab.12  Results of two-objective (P, S) optimization with post-expression of preferences
Fig.11  Pareto frontier of two-objective (η, S) optimization with past-expression of preferences
Decision variables Objectives
j x AR TH Th h S
Fuzzy 1.0000 0.4502 1.9978 1100.2 853.18 0.3903 0.000152
LINMAP 1.0000 0.4500 2.5461 1100.6 865.72 0.3686 0.000092
TOPSIS 1.0005 0.4502 4.5771 1100.9 859.37 0.3618 0.000118
Tab.13  Results of two-objective (h, S) optimization with post-expression of preferences
Fig.12  Optimum absorber temperature and concentrating ratio of the system (Adapted with permission from Ref. [22])
Fig.13  Pareto optimal frontier in objectives’ space (thermal efficiency- dimensionless objective function)
Decision variable or objective function In this paper In the references
TH 1100 1100
hm 0.35<<0.40 0.37<<0.41
Tab.14  Verification of decision variables of x and TH [22,30]
Ares Absorber area
Aapp Aperture area
C Concentration ratio
F Dimensionless objective function
f Dimensionless economic factor
h Heat transfer coefficient/(W•K–4 or W•m–2•K–1)
I Direct solar flux intensity/(W•m–2)
i ith objective
j jth solution
n Mole number of the working fluid/mol
P Dimensionless output power
Q Heat transfer/J
R Universal gas constant/(J•mol–1•K–1)
S Dimensionless entropy
T Temperature/K
W Work/J
V Volume
t Cyclic period/s
x Temperature ratio of the Stirling engine
Greek letter
l Ratio of volume during the regenerative processes
h Thermal efficiency
є Emissivity factor
s Entropy
d Stefan–Boltzmann coefficient
Subscripts
H Absorber (heater)
h High temperature side heat exchanger
L Heat sink
c Low temperature side heat exchanger
m Entire solar dish Stirling system
t Stirling engine
0 Ambient condition, optics
1–4 Process states
  
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