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Frontiers in Energy

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Front. Energy    2024, Vol. 18 Issue (5) : 665-683    https://doi.org/10.1007/s11708-024-0922-z
Capacity-operation collaborative optimization of the system integrated with wind power/photovoltaic/concentrating solar power with S-CO2 Brayton cycle
Yangdi Hu, Rongrong Zhai(), Lintong Liu
School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China
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Abstract

This paper proposes a new power generating system that combines wind power (WP), photovoltaic (PV), trough concentrating solar power (CSP) with a supercritical carbon dioxide (S-CO2) Brayton power cycle, a thermal energy storage (TES), and an electric heater (EH) subsystem. The wind power/photovoltaic/concentrating solar power (WP−PV−CSP) with the S-CO2 Brayton cycle system is powered by renewable energy. Then, it constructs a bi-level capacity-operation collaborative optimization model and proposes a non-dominated sorting genetic algorithm-II (NSGA-II) nested linear programming (LP) algorithm to solve this optimization problem, aiming to obtain a set of optimal capacity configurations that balance carbon emissions, economics, and operation scheduling. Afterwards, using Zhangbei area, a place in China which has significant wind and solar energy resources as a practical application case, it utilizes a bi-level optimization model to improve the capacity and annual load scheduling of the system. Finally, it establishes three reference systems to compare the annual operating characteristics of the WP−PV−CSP (S-CO2) system, highlighting the benefits of adopting the S-CO2 Brayton cycle and equipping the system with EH. After capacity-operation collaborative optimization, the levelized cost of energy (LCOE) and carbon emissions of the WP−PV−CSP (S-CO2) system are decreased by 3.43% and 92.13%, respectively, compared to the reference system without optimization.
Keywords wind power/photovoltaic/concentrating solar power (WP−PV−CSP)      supercritical carbon dioxide (S-CO2) Brayton cycle      capacity-operation collaborative optimization      sensitive analysis     
Corresponding Author(s): Rongrong Zhai   
Online First Date: 26 January 2024    Issue Date: 16 October 2024
 Cite this article:   
Yangdi Hu,Rongrong Zhai,Lintong Liu. Capacity-operation collaborative optimization of the system integrated with wind power/photovoltaic/concentrating solar power with S-CO2 Brayton cycle[J]. Front. Energy, 2024, 18(5): 665-683.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-024-0922-z
https://academic.hep.com.cn/fie/EN/Y2024/V18/I5/665
Fig.1  WP−PV−CSP (S-CO2) integrated energy system.
Fig.2  Operation strategy of WP−PV−CSP (S-CO2) system. DNI indicates direct normal irradiance; GI indicates global horizontal irradiance; HT indicates hot tank.
Parameter Value Parameter Value
AMOD/m2 1.675 Tc,ref/°C 25
G INOMC/(W·m−2) 800 TNOMC/°C 46
ηINV/% 97.8 Ta,NOMC/°C 20
fPV/% 80 UL,NOMC 9.5
ηPV,NOM/% 14.9 τ ?α 0.8
Tab.1  Values of the corresponding parameters in PV model
Parameter Value
prated/MW 1.675
vcut,in/(m·s−1) 3.5
vcut,out/(m·s−1) 25
vrated/(m·s−1) 12
h2/m 70
Tab.2  Values of corresponding parameters in WP model
Parameter Value Parameter Value
Heat transfer oil temperature/K 668 Turbine isentropic efficiency/% 93
Turbine inlet temperature/K 623 Compressor isentropic efficiency/% 89
Turbine inlet pressure/MPa 25 Generator efficiency/% 97
Compressor inlet temperature/K 308 Motor efficiency/% 90
Compressor inlet pressure/MPa 8.06 Power cycle efficiency/% 36.92
Tab.3  Design parameters of S-CO2 Brayton cycle at different installed capacities
Parameter Capacity/MW
1 10 50 100 200
Heater heat transfer capacity UAheater/(kW·K−1) 121.12 1211.20 6056.01 12112.02 24224.04
Recuperator heat transfer capacity UArecup/(kW·K−1) 61.62 616.18 3080.88 6161.76 12323.52
Pre-cooler heat transfer capacity UAcooler/(kW·K−1) 64.45 644.48 3222.40 6444.80 12889.60
Tab.4  Heat transfer capacity of heat exchangers in S-CO2 Brayton cycle at different capacities
Input parameters Collection efficiency
DNI/(W·m−2) Tin/K Calculated data/% Reference data/% Error/%
600 490 81.93 81.90 0.03
600 510 79.92 80.26 0.34
600 530 77.91 77.84 0.07
600 550 75.51 74.47 1.04
600 570 69.16 69.98 0.82
600 590 62.11 64.19 2.08
700 490 82.58 82.29 0.29
700 510 80.64 81.00 0.36
700 530 78.94 79.14 0.20
700 550 75.31 76.55 1.24
700 570 74.54 73.12 1.42
700 590 69.53 68.72 0.81
Tab.5  Relevant data for collector model validation
Fig.3  Algorithm flowchart of bi-level optimization.
Parameter Decision variable Unit Boundary condition
Ri,1 NLoop − [165, 776]
Ri,2 CCSP MW [0, 200]
Ri,3 CTES h [0, 20]
Ri,4 CEH MW [0, 60]
Ri,5 CPV MW [0, 200]
Ri,6 NWT − [0, 66]
Tab.6  Boundary condition for decision variable
Fig.4  Model validation of NSGA-II algorithm.
Fig.5  Hourly meteorological data and load demand for the case.
Parameter Value Unit
PV
　Investment costs (ICs) 1003 $/kW
　Operation and maintenance (O&M) costs 2.15 $/(kW·a)
　Auxiliary equipment 350 $/kW
　Inverter 105 $/kW
WP
　ICs 909.98 $/kW
　O&M costs 0.857 $/(kW·a)
　Auxiliary equipment 35 $/kW
　Inverter 105 $/kW
SF
　ICs 242 $/m2
　Auxiliary equipment 0.285 × IC $/m2
　O&M costs 0.017 × IC $/(m2·a)
TES
　ICs 31.4 $/kWh
　Auxiliary equipment 0.285 × IC $/kWh
　O&M costs 0.017 × IC $/(kWh·a)
S-CO2 Brayton cycle
　IC of compressor 6898 ×(WC×1000)0.7865 $
　IC of turbine 7790 ×(WT×1000)0.6842 $
　IC of heater 3500 ×U Aheater $
　IC of recuperator 1200 ×U Arecup $
　IC of cooler 2300 ×U Acooler $
　Auxiliary equipment 340 $/kW
　Fixed O&M costs 66 $/(kW·a)
　Variable O&M costs 3500 $/kWh
Tab.7  Main economic data of the WP−PV−CSP (S-CO2) system
Fig.6  Pareto front curve of WP−PV−CSP (S-CO2) system.
Number NLoop CCSP/MW CTES/h CEH/MW CPV/MW NWT LCOE/($·kWh−1) CO2 emissions/(104 t·a−1)
1 165 10 14 27 23 0 0.1360 2.6299
…
24 165 12 14 33 34 13 0.1446 2.0756
…
55 291 26 14 42 48 26 0.1736 1.5584
…
108 659 74 12 60 104 50 0.2727 0.6406
…
163 395 169 5 40 74 17 0.3936 0.1208
…
200 456 178 4 39 186 43 0.5259 0.0021
Tab.8  Pareto optimal solution set
Weight NLoop CCSP/MW CTES/h CEH/MW CPV/MW NWT LCOE/($·kWh−1) CO2 emissions/(104 t·a−1)
[0.45, 0.55] 257 64 14 59 117 49 0.2581 0.7186
[0.29, 0.71] 776 98 13 60 132 49 0.3342 0.3647
[0.21, 0.79] 395 170 5 39 79 18 0.3975 0.0914
[0.17, 0.83] 456 167 5 43 68 22 0.3990 0.0831
[0.14, 0.86] 456 167 5 43 68 22 0.3990 0.0831
[0.12, 0.88] 456 167 6 46 71 23 0.4088 0.0501
[0.10, 0.90] 456 167 7 45 72 19 0.4196 0.0370
[0.09, 0.91] 456 167 7 45 72 19 0.4196 0.0370
[0.08, 0.92] 456 167 7 45 72 19 0.4196 0.0370
Tab.9  Compromise solutions corresponding to different weights
Fig.7  Daily output electricity power of WP-PV-CSP (S-CO2) system.
Item Reference System 1 Reference System 2 Reference System 3 WP−PV−CSP (S-CO2) system
Capacity configuration
　　 NLoop 456 456 395 456
　　 CCSP/MW 167 167 130 167
　　 CTES/h 7 7 8 7
　　 CEH/MW 0 45 20 45
　　 CPV/MW 72 72 80 72
　　 NWT 19 19 30 19
Economic parameter
　　LCOE/($·kWh−1) 0.4319 0.4401 0.4345 0.4196
System operation result
　　 PPV/MW 50576 50576 49821 50576
　　 PWP/MW 18555 18555 24596 18555
　　 PCSP/MW 77021 81280 58611 82003
　　 Ppurchase/MW 6531 2273 19656 1550
　　 Pab/MW 67358 31750 59014 32039
　　 QHT/MW 22109612 25757981 18107612 25487392
　　CO2 emissions/(t·a−1) 1563 543.97 4704 370
Tab.10  Annual performance comparison of WP−PV−CSP (S-CO2) system with other systems
Fig.8  Effect of N Loop on LCOE and CO2 emissions of WP−PV−CSP (S-CO2) system.
Fig.9  Effect of (a) C CSP and (b) C PV on LCOE and CO2 emissions of WP−PV−CSP (S-CO2) system.
Fig.10  Effect of C TES on LCOE and CO2 emissions of WP−PV−CSP (S-CO2) system.
Fig.11  Effect of N WT on LCOE and CO2 emissions of WP−PV−CSP (S-CO2) system.
Fig.12  Effect of C EH on LCOE and CO2 emissions of WP−PV−CSP (S-CO2) system.
Abbreviations
CSP Concentrating solar power
EH Electric heater
HT Hot tank
PV Photovoltaic
S-CO2 Supercritical carbon dioxide
SF Solar field
TES Thermal energy storage
WP Wind power
WT Wind turbine
Variables
A Area/m2
B Coal consumption/t
C Capacity/MW
DNI Direct solar irradiation/(W·m−2)
GI Global irradiance/(W·m−2)
h Height/m
IC Investment costs/$
LCOE Levelized cost of electricity/($·kWh−1)
m Mass flow rate/(kg·s−1)
P Power/MW
Q Quantity of heat/MW
T Temperature/°C
v Wind speed/(m·s−1)
W Work/MW
η Efficiency
Subscripts
a Ambient
ab Abandoned
C Compressor
c Charge
d Discharge
HE Heat exchanger
INV Inverterin input
NOM Normal
O&M Operation and maintenance
out Output
ref Reference
s Standard
T Turbine
  
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