再压缩S-CO2布雷顿循环性能分析及多目标优化

doi:10.11949/0438-1157.20240080

摘要/Abstract

摘要：

结合储热的太阳能热发电技术输出稳定、调峰能力强，引入超临界二氧化碳（S-CO₂）布雷顿循环可进一步提升热电转换效率。既有研究大多采用单一指标对S-CO₂循环进行性能评估，结果相对片面，因而有必要开展多指标综合性能评价以客观反映循环性能状况。建立了35 MW再压缩式S-CO₂循环的热力学和经济性模型，考察了关键参数对循环性能的影响。构建了反向传播神经网络结合遗传算法的优化方法（BP-GA），对循环性能进行多目标优化。结果表明，回热器总热导率的增加可提升循环效率，但存在上限；透平入口温度、循环最低和最高压力、分流比与循环性能分别存在显著的非单调作用关系，优化后的设计值依次为639.14℃、8.10 MPa、29.74 MPa和0.70。与初始设计值下的循环性能相比，优化后的循环系统度电成本降低了11.1%，循环热效率和比功分别提高了5.1%和27.6%。

关键词: 超临界二氧化碳, 再压缩布雷顿循环, 遗传算法, 整体优化, 热力学

Abstract:

The solar thermal power generation technology combined with heat storage has stable output and strong peak shaving capabilities. The introduction of supercritical carbon dioxide (S-CO₂) Brayton cycle can further improve thermoelectric conversion efficiency. Most of the existing studies evaluated the performance of S-CO₂ cycle based on a single index, leading to inconsistent evaluation results. Hence, it is necessary to carry out multi-index comprehensive evaluation to objectively reflect the cycle performance. In the present paper, mathematical models were established to investigate the thermodynamic performance and economy of a 35 MW recompression S-CO₂ cycle, and the effects of critical parameters on cycle performance was analyzed. A BP-GA optimization method of back propagation neural network combined with elitist nondominated sorting genetic algorithm was constructed for multi-objective optimization of cycle performance. The results indicate that the cycle efficiency increases with an increasing total thermal conductivity of the recuperators, but there is a ceiling on growth. There are significant non-monotonic relations between turbine inlet temperature, minimum cycle pressure, maximum cycle pressure, split ratio and cycle performance, and the corresponding optimal values are 639.14℃, 8.10 MPa, 29.74 MPa and 0.70, respectively. Compared with the cycle performance based on the design conditions, the optimized cycle shows a reduction of 11.1% in LCOE, and an increase of 5.1% and 27.6% in efficiency and specific work, respectively.

Key words: supercritical carbon dioxide, recompression Brayton cycle, genetic algorithm, global optimization, thermodynamics

中图分类号:

TK 122

李子扬, 郑楠, 方嘉宾, 魏进家. 再压缩S-CO₂布雷顿循环性能分析及多目标优化[J]. 化工学报, 2024, 75(6): 2143-2156.

Ziyang LI, Nan ZHENG, Jiabin FANG, Jinjia WEI. Performance analysis and multi-objective optimization of recompression S-CO₂ Brayton cycle[J]. CIESC Journal, 2024, 75(6): 2143-2156.

图/表 22

图1 再压缩再热循环布局图

Fig.1 Layout of RCRHC

图2 设计点的循环温熵图

Fig.2 Design points on T-s diagram

表1 系统分析的初始设计参数

Table 1 Initial design parameters for system analysis

参数	数值
主压缩机入口温度CIT/℃	35
循环最低压力p_min /MPa	7.5
循环最高压力p_max /MPa	25
低压透平入口压力p_mid /MPa	16.25
高/低压透平入口温度TIT/℃	650
压缩机等熵效率η_s,c/%^[31-33]	89
透平等熵效率η_s,t/%^[31-33]	93
分流比SR	0.65
高温回热器的热导率占比UAR/%	50
回热器总热导率UA /(MW/K)	20
输出功W_net /MW	35

表2 再压缩循环各部件的能量关系

Table 2 Energy relations of main devices in recompression cycle

系统部件	能量关系
高压透平	$η_{s, t} = (h_{1} - h_{2}) / (h_{1} - h_{2, s}), W_{H P T} = m_{C O_{2}} (h_{1} - h_{2})$
低压透平	$η_{s, t} = (h_{3} - h_{4}) / (h_{3} - h_{4, s}), W_{L P T} = m_{C O_{2}} (h_{3} - h_{4})$
主压缩机	$η_{s, c} = (h_{8, s} - h_{7}) / (h_{8} - h_{7}), W_{M C} = S R \times m_{C O_{2}} (h_{8} - h_{7})$
再压缩机	$η_{s, c} = (h_{9 ", s} - h_{6}) / (h_{9 "} - h_{6}), W_{R C} = (1 - S R) m_{C O_{2}} (h_{9 "} - h_{6})$
混合过程	$h_{9} = S R h_{9'} + (1 - S R) h_{9 "}$
高温回热器	$Q_{H T R} = m_{C O_{2}} (h_{4} - h_{5}) = m_{C O_{2}} (h_{10} - h_{9})$
低温回热器	$Q_{L T R} = m_{C O_{2}} (h_{5} - h_{6}) = S R m_{C O_{2}} (h_{9'} - h_{8})$
主加热器	$Q_{M H} = m_{C O_{2}} (h_{1} - h_{10}) = m_{s 1} (h_{s 1, i n} - h_{s 1, o u t})$
再热器	$Q_{R H} = m_{C O_{2}} (h_{3} - h_{2}) = m_{s 2} (h_{s 2, i n} - h_{s 2, o u t})$
冷却器	$Q_{P C} = S R \times m_{C O_{2}} (h_{6} - h_{7}) = m_{a i r} (h_{a i r, i n} - h_{a i r, o u t})$
净功	$W_{n e t} = W_{H P T} + W_{L P T} - (W_{M C} + W_{R C})$

表2 再压缩循环各部件的能量关系

Table 2 Energy relations of main devices in recompression cycle

系统部件	能量关系
高压透平	$η_{s, t} = (h_{1} - h_{2}) / (h_{1} - h_{2, s}), W_{H P T} = m_{C O_{2}} (h_{1} - h_{2})$
低压透平	$η_{s, t} = (h_{3} - h_{4}) / (h_{3} - h_{4, s}), W_{L P T} = m_{C O_{2}} (h_{3} - h_{4})$
主压缩机	$η_{s, c} = (h_{8, s} - h_{7}) / (h_{8} - h_{7}), W_{M C} = S R \times m_{C O_{2}} (h_{8} - h_{7})$
再压缩机	$η_{s, c} = (h_{9 ", s} - h_{6}) / (h_{9 "} - h_{6}), W_{R C} = (1 - S R) m_{C O_{2}} (h_{9 "} - h_{6})$
混合过程	$h_{9} = S R h_{9'} + (1 - S R) h_{9 "}$
高温回热器	$Q_{H T R} = m_{C O_{2}} (h_{4} - h_{5}) = m_{C O_{2}} (h_{10} - h_{9})$
低温回热器	$Q_{L T R} = m_{C O_{2}} (h_{5} - h_{6}) = S R m_{C O_{2}} (h_{9'} - h_{8})$
主加热器	$Q_{M H} = m_{C O_{2}} (h_{1} - h_{10}) = m_{s 1} (h_{s 1, i n} - h_{s 1, o u t})$
再热器	$Q_{R H} = m_{C O_{2}} (h_{3} - h_{2}) = m_{s 2} (h_{s 2, i n} - h_{s 2, o u t})$
冷却器	$Q_{P C} = S R \times m_{C O_{2}} (h_{6} - h_{7}) = m_{a i r} (h_{a i r, i n} - h_{a i r, o u t})$
净功	$W_{n e t} = W_{H P T} + W_{L P T} - (W_{M C} + W_{R C})$

图3 迭代程序计算流程图

Fig.3 Iterative program calculation flow chart

表3 模型验证的参数设置［30］

Table 3 Parameter settings for model validation［30］

参数名称	数值
循环最高压力p_max /MPa	25
透平入口温度TIT/℃	650
主压缩机入口温度CIT /℃	50
透平等熵效率η_s,t /%	93
压缩机等熵效率η_s,c /%	89
输出功W_net/MW	35
回热器总热导率UA/(MW/K)	变化值

表4 本文的模型结果和文献［30］结果比较

Table 4 Comparison of model results in this work and literature［30］ results

UA/ (MW/K)	η/%			ΔT_MH/℃
UA/ (MW/K)	文献	本文	误差	文献	本文	误差
5	47.17	47.17	0	138	137.98	0.01%
10	50.39	50.39	0	114.2	114.16	0.04%
15	51.59	51.58	0.02%	109.5	109.0	0.46%

表5 主要组成部件的成本函数［36］

Table 5 Cost functions of main components［36］

系统组件	成本函数	单位	年(CEPCI)
压缩机	C_com=49511.08 W_com^0.7865	CNY	2003(402.0)
透平	C_tur=55913.50 W_tur^0.6842	CNY	2003(402.0)
回热器	C_recup=8.9720 UA_recup	CNY	1994(368.1)
加热器	C_heater=25.1216 UA_heater	CNY	1994(368.1)
冷却器	C_cooler=16.5085 UA_cooler	CNY	1994(368.1)

图4 BP-GA优化方法流程图

Fig.4 BP-GA optimization method flow chart

图5 隐含层单元数和层数对LCOE神经网络性能的影响

Fig.5 Effect of the number of hidden layer units and layers on the performance of LCOE neural networks

表6 神经网络性能指标

Table 6 Performance of neural network

优化目标	R²	MSE	训练总耗时/s	Epoch
η	0.99998	3.14×10^-6	6.36	228
w	0.99999	4.54×10^-7	8.31	289
LCOE	0.99804	3.79×10^-5	2.19	76

图6 不同循环最高压力下循环效率随回热器总热导率的变化

Fig.6 Variation of cycle efficiency with total heat conductance of recuperator at different cycle maximum pressure

图7 循环最低压力对循环性能的影响

Fig.7 Effect of minimum pressure on cycle performance

图8 循环最高压力对循环性能的影响

Fig.8 Effect of maximum pressure on cycle performance

图9 主压缩机入口温度对循环性能的影响

Fig.9 Effect of main compressor inlet temperature on cycle performance

图10 透平入口温度对循环性能的影响

Fig.10 Effect of turbine inlet temperature on cycle performance

图11 回热器热导率分配比对循环性能的影响

Fig.11 Effect of heat conduction ratio of regenerator on cycle performance

图12 分流比对循环性能的影响

Fig.12 Effect of shunt ratio on cycle performance

表7 决策变量范围

Table 7 Range of decision variables

参数	下限	上限
透平入口温度TIT/℃	500	650
主压缩机入口温度CIT/℃	32	52
循环最低压力P_min/MPa	7.5	10.0
循环最高压力P_max/MPa	15	30
分流比SR	0.45	0.95

图13 多目标优化的Pareto前沿解

Fig.13 Pareto frontier solution of multi-objective optimization

表8 RCRHC循环参数多目标优化结果

Table 8 Multi-objective optimization results of RCRHC cycle parameters

参数	初始值	优化后	相对变化
TIT/℃	650	639.14	-1.67%
CIT/℃	35	32.33	-7.6%
p_min /MPa	7.5	8.10	+8%
p_max /MPa	25	29.74	+19.0%
SR	0.65	0.70	+7.7%
η/%	52.23	54.90	+5.1%
w/(kW/kg)	121.37	154.91	+27.6%
LCOE/(CNY/(kW·h))	1.0694	0.9506	-11.1%

表9 多目标优化结果验证

Table 9 Validation of multi-objective optimization results

项目	η/%	w/(kW/kg)	LCOE/(CNY/(kW·h))
优化后结果	54.90	154.91	0.9506
迭代程序计算结果	54.87	154.51	0.9498
相对误差	0.06%	0.26%	0.08%

参考文献 38

1	国家能源局. 国家能源局2023年一季度新闻发布会文字实录[EB/OL]. [2023-08-15]. .
	National Energy Administration. Text transcript of the National Energy Administration's news release conference in the first quarter of 2023[EB/OL]. [2023-08-15]. .
2	Ahn Y, Bae S J, Kim M, et al. Review of supercritical CO₂ power cycle technology and current status of research and development[J]. Nuclear Engineering and Technology, 2015, 47(6): 647-661.
3	White M T, Bianchi G, Chai L, et al. Review of supercritical CO₂ technologies and systems for power generation[J]. Applied Thermal Engineering, 2021, 185: 116447.
4	Rogalev N, Rogalev A, Kindra V, et al. Review of closed SCO₂ and semi-closed oxy-fuel combustion power cycles for multi-scale power generation in terms of energy, ecology and economic efficiency[J]. Energies, 2022, 15(23): 9226.
5	Wu D C, Wei M S, Tian R, et al. A review of flow and heat transfer characteristics of supercritical carbon dioxide under cooling conditions in energy and power systems[J]. Energies, 2022, 15(23): 8785.
6	Marchionni M, Bianchi G, Tassou S A. Review of supercritical carbon dioxide (sCO₂) technologies for high-grade waste heat to power conversion[J]. SN Applied Sciences, 2020, 2(4): 611.
7	孙铭泽, 马宁, 李浩然, 等. 中低温超临界CO₂及其混合工质布雷顿循环热力学分析[J]. 化工学报, 2022, 73(3): 1379-1388.
	Sun M Z, Ma N, Li H R, et al. Thermodynamic analysis of Brayton cycle of medium and low temperature supercritical CO₂ and its mixed working medium[J]. CIESC Journal, 2022, 73(3): 1379-1388.
8	Yin J M, Zheng Q Y, Peng Z R, et al. Review of supercritical CO₂ power cycles integrated with CSP[J]. International Journal of Energy Research, 2020, 44(3): 1337-1369.
9	Fan Y H, Tang G H, Li X L, et al. General and unique issues at multiple scales for supercritical carbon dioxide power system: a review on recent advances[J]. Energy Conversion and Management, 2022, 268: 115993.
10	Xu J L, Liu C, Sun E H, et al. Perspective of S-CO₂ power cycles[J]. Energy, 2019, 186: 115831.
11	Crespi F, Gavagnin G, Sánchez D, et al. Supercritical carbon dioxide cycles for power generation: a review[J]. Applied Energy, 2017, 195: 152-183.
12	Dunham M T, Iverson B D. High-efficiency thermodynamic power cycles for concentrated solar power systems[J]. Renewable and Sustainable Energy Reviews, 2014, 30: 758-770.
13	Dyreby J, Klein S, Nellis G, et al. Design considerations for supercritical carbon dioxide Brayton cycles with recompression[J]. Journal of Engineering for Gas Turbines and Power, 2014, 136(10): 101701.
14	Reyes-Belmonte M A, Sebastián A, Romero M, et al. Optimization of a recompression supercritical carbon dioxide cycle for an innovative central receiver solar power plant[J]. Energy, 2016, 112: 17-27.
15	Zheng N, Li Z Y, Fang J B, et al. Supercritical CO₂ mixture Brayton cycle with floating critical points for concentrating solar power application: concept and thermodynamic analysis[J]. Energy Conversion and Management, 2023, 284: 116989.
16	Al-Sulaiman F A, Atif M. Performance comparison of different supercritical carbon dioxide Brayton cycles integrated with a solar power tower[J]. Energy, 2015, 82: 61-71.
17	赵柄锡, 袁奇, 朱光宇. 多目标超临界CO₂循环设计与优化[J]. 中国电机工程学报, 2018, 38(7): 2046-2054, 2219.
	Zhao B X, Yuan Q, Zhu G Y. Multi-objective designing and optimization of Rankine cycle using supercritical CO₂ [J]. Proceedings of the CSEE, 2018, 38(7): 2046-2054, 2219.
18	Zhou T, Liu Z X, Li X J, et al. Thermodynamic design space data-mining and multi-objective optimization of SCO₂ Brayton cycles[J]. Energy Conversion and Management, 2021, 249: 114844.
19	Liang Y Z, Chen J S, Yang Z, et al. Economic-environmental evaluation and multi-objective optimization of supercritical CO₂ based-central tower concentrated solar power system with thermal storage[J]. Energy Conversion and Management, 2021, 238: 114140.
20	Ma Y N, Hu P, Jia C Q, et al. Thermo-economic analysis and multi-objective optimization of supercritical Brayton cycles with CO₂-based mixtures[J]. Applied Thermal Engineering, 2023, 219: 119492.
21	余廷芳, 宋凌. 超临界CO₂布雷顿循环余热回收系统性能分析与优化[J]. 浙江大学学报(工学版), 2023, 57(2): 404-414.
	Yu T F, Song L. Performance analysis and optimization of supercritical CO₂ Brayton cycle waste heat recovery system[J]. Journal of Zhejiang University (Engineering Science), 2023, 57(2): 404-414.
22	曹越, 陈然璟, 展君, 等. 基于神经网络的燃气-超临界CO₂联合循环变工况特性快速预测及优化[J]. 中国电机工程学报, 2023, 43(11): 4178-4190.
	Cao Y, Chen R J, Zhan J, et al. Rapid prediction and optimization for off-design performance of gas and supercritical carbon dioxide combined cycle based on neural network[J]. Proceedings of the CSEE, 2023, 43(11): 4178-4190.
23	肖晓伟, 肖迪, 林锦国, 等. 多目标优化问题的研究概述[J]. 计算机应用研究, 2011, 28(3): 805-808, 827.
	Xiao X W, Xiao D, Lin J G, et al. Overview on multi-objective optimization problem research[J]. Application Research of Computers, 2011, 28(3): 805-808, 827.
24	Li Q, Erqi E, Qiu Y, et al. Conceptual design of novel He-SCO₂ Brayton cycles for ultra-high-temperature concentrating solar power[J]. Energy Conversion and Management, 2022, 260: 115618.
25	Wang K, Li M J, Guo J Q, et al. A systematic comparison of different S-CO₂ Brayton cycle layouts based on multi-objective optimization for applications in solar power tower plants[J]. Applied Energy, 2018, 212: 109-121.
26	Li H, Su W, Cao L Y, et al. Preliminary conceptual design and thermodynamic comparative study on vapor absorption refrigeration cycles integrated with a supercritical CO₂ power cycle[J]. Energy Conversion and Management, 2018, 161: 162-171.
27	Tang J R, Zhang Q G, Zhang Z P, et al. Development and performance assessment of a novel combined power system integrating a supercritical carbon dioxide Brayton cycle with an absorption heat transformer[J]. Energy Conversion and Management, 2022, 251: 114992.
28	Qiu Y, Erqi E, Li Q. Triple-objective optimization of SCO₂ Brayton cycles for next-generation solar power tower[J]. Energies, 2023, 16(14): 5316.
29	Lemmon E, McLinden M, Huber M. NIST standard reference database 23: reference fluid thermodynamic and transport properties-REFPROP, version 9.1[DB/OL]. Gaithersburg, MD: Natl Std. Ref. Data Series (NIST NSRDS), National Institute of Standards and Technology, 2013[2024-01-13]. .
30	Neises T, Turchi C. A comparison of supercritical carbon dioxide power cycle configurations with an emphasis on CSP applications[J]. Energy Procedia, 2014, 49: 1187-1196.
31	Kulhánek M, Dostál V. Thermodynamic analysis and comparison of supercritical carbon dioxide cycles[C]//Proceedings of Supercritical CO2 Power Cycle Symposium. Boulder, Colorado, USA, 2011.
32	Mecheri M, Le Moullec Y. Supercritical CO₂ Brayton cycles for coal-fired power plants[J]. Energy, 2016, 103: 758-771.
33	Yang J Z, Yang Z, Duan Y Y. Part-load performance analysis and comparison of supercritical CO₂ Brayton cycles[J]. Energy Conversion and Management, 2020, 214: 112832.
34	Na S I, Kim M S, Baik Y J, et al. Optimal allocation of heat exchangers in a supercritical carbon dioxide power cycle for waste heat recovery[J]. Energy Conversion and Management, 2019, 199: 112002.
35	Mohagheghi M, Kapat J. Thermodynamic optimization of recuperated S-CO₂ Brayton cycles for solar tower applications[C]//Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. San Antonio, Texas, USA, 2013.
36	Carlson M D, Middleton B M, Ho C K. Techno-economic comparison of solar-driven SCO₂ Brayton cycles using component cost models baselined with vendor data and estimates[C]//Proceedings of ASME 2017 11th International Conference on Energy Sustainability Collocated with the ASME 2017 Power Conference Joint with ICOPE-17, the ASME 2017 15th International Conference on Fuel Cell Science, Engineering and Technology, and the ASME 2017 Nuclear Forum. Charlotte, North Carolina, USA, 2017
37	Engineering Chemical. 2023 CEPCI updates: July (prelim.) and June (final)[EB/OL]. [2023-10-15]. .
38	Khodaei E, Yari M, Mohammad S Mahmoudi S. Thermoeconomic optimization for a solar power generating system capable of storing energy by using calcium looping process[J]. Energy Conversion and Management, 2023, 293: 117403.

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再压缩S-CO₂布雷顿循环性能分析及多目标优化

Performance analysis and multi-objective optimization of recompression S-CO₂ Brayton cycle

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