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

doi:10.11949/0438-1157.20240080

Abstract

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

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

CLC Number:

TK 122

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.

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.

Figures/Tables 22

Fig.1 Layout of RCRHC

Fig.2 Design points on T-s diagram

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

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	$W_{n e t} = W_{H P T} + W_{L P T} - (W_{M C} + W_{R C})$

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	$W_{n e t} = W_{H P T} + W_{L P T} - (W_{M C} + W_{R C})$

Fig.3 Iterative program calculation flow chart

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

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%

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)

Fig.4 BP-GA optimization method flow chart

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

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

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

Fig.7 Effect of minimum pressure on cycle performance

Fig.8 Effect of maximum pressure on cycle performance

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

Fig.10 Effect of turbine inlet temperature on cycle performance

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

Fig.12 Effect of shunt ratio on cycle performance

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

Fig.13 Pareto frontier solution of multi-objective optimization

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%

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%

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

再压缩S-CO₂布雷顿循环性能分析及多目标优化

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