Optimization of cold-end system of thermal power plants based on entropy generation minimization

doi:10.1007/s11708-021-0785-5

Front. Energy

2022, Vol. 16

Issue (6) : 956-972 https://doi.org/10.1007/s11708-021-0785-5

RESEARCH ARTICLE

Optimization of cold-end system of thermal power plants based on entropy generation minimization

Yue FU, Yongliang ZHAO, Ming LIU(

), Jinshi WANG, Junjie YAN

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

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Abstract

Cold-end systems are heat sinks of thermal power cycles, which have an essential effect on the overall performance of thermal power plants. To enhance the efficiency of thermal power plants, multi-pressure condensers have been applied in some large-capacity thermal power plants. However, little attention has been paid to the optimization of the cold-end system with multi-pressure condensers which have multiple parameters to be identified. Therefore, the design optimization methods of cold-end systems with single- and multi-pressure condensers are developed based on the entropy generation rate, and the genetic algorithm (GA) is used to optimize multiple parameters. Multiple parameters, including heat transfer area of multi-pressure condensers, steam distribution in condensers, and cooling water mass flow rate, are optimized while considering detailed entropy generation rate of the cold-end systems. The results show that the entropy generation rate of the multi-pressure cold-end system is less than that of the single-pressure cold-end system when the total condenser area is constant. Moreover, the economic performance can be improved with the adoption of the multi-pressure cold-end system. When compared with the single-pressure cold-end system, the excess revenues gained by using dual- and quadruple-pressure cold-end systems are 575 and 580 k$/a, respectively.

Keywords cold-end system entropy generation minimization optimization economic analysis genetic algorithm (GA)

Corresponding Author(s): Ming LIU

Online First Date: 15 October 2021 Issue Date: 17 January 2023

Cite this article:

Yue FU,Yongliang ZHAO,Ming LIU, et al. Optimization of cold-end system of thermal power plants based on entropy generation minimization[J]. Front. Energy, 2022, 16(6): 956-972.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-021-0785-5
https://academic.hep.com.cn/fie/EN/Y2022/V16/I6/956

Fig.1 Thermodynamic system diagram of cold-end systems.

Fig.2 Exergy analysis of a steam turbine.

Fig.3 Diagram of the condensers.

Fig.4 Schematic diagram of the condenser model.

Fig.5 Fluid flow in feedwater preheater.

Fig.6 Objective function based on EGM.

Fig.7 Process of GA.

Component	Cost functions and the adjusted coefficients	Remarks
Steam turbine	$PEC st = 1180.088 × F T × F η × W ˙ st 0 .7,$ $F T = (1 + 5 × exp ((t i − t r) / 10.42)),$ $F η = (1 + ((1 − η st,r) / (1 − η st)) 3),$	?_st is the turbine power generation (kW); t_i is the inlet steam temperature (°C); η_st is the isentropic efficiency; η_st,r, and t_r are 0.95 and 886, respectively
Condenser	$PEC cond = 46.479 × A cond + 123.5 × m ˙ cw + 10.67 × Q ˙ × (− 0.6936 × log (t cw,a − t r) + 2.19),$ $t cw,a = (h cw out − h cw in) / (s cw out − s cw in)$	t_cw,a is the thermodynamic average temperature of the cooling water (°C); t_r is 15°C
Pump	$PEC pump = 708.88 × W ˙ pump 0 .71 × (1 + ((1 − η pump,r) / (1 − η pump)) 3)$	?_pump is the power required (kW); η_pump is the isentropic efficiency with its reference value (0.85)
Feedwater preheater	$P E C fph = 6.6 × Q ˙ fph × (1 Δ t up + 4) 0.1$	Δt_up is the upper terminal temperature difference (°C)

Tab.1 Cost for system components [49,50]

Item	Symbol	Unit	Value
Cold-end system inlet steam mass flow rate	?_in	kg/s	425
Cold-end system inlet steam pressure	P_in	kPa	2.31
Cold-end system inlet steam temperature	t_in	°C	63
Cold-end system outlet steam mass flow rate	?_out	kg/s	425
Cold-end system outlet steam pressure	P_out	kPa	8.16
Cold-end system outlet steam temperature	t_out	°C	63
Cooling water inlet temperature	$t cw in$	°C	10
Number of condensers tubes	N_cond	–	36500
Tube outer diameter in condensers	d_o	mm	25
Tube inner diameter in condensers	d_i	mm	20
Tube length in condensers	L_cond	m	14
Heat transfer surface area of condensers	A	m²	40000
Cooling water mass flow rate in condensers	?_cw	kg/s	23305
Condenser pressure	P_cond	kPa	2.2

Tab.2 Thermodynamic parameter of the single-pressure cold-end system

Fig.8 Influence of cooling water temperature on cold-end systems.

Fig.9 Influence of cooling water flow rate on cold-end systems.

Fig.10 Influence of condenser area on cold-end systems.

Fig.11 Entropy generation rate due to the steam flow rate distribution and area allocation.

Tab.3 Optimal values of cold-end systems at a fixed cooling water flow rate

Fig.12 Exergy destruction of each cold-end system.

Fig.13 Entropy generation rates of cold-end systems with different parameters being optimized.

Tab.4 Multi-parameter optimal solution

Fig.14 Comparison of optimal cold-end systems.

Fig.15 Temperature distribution in condensers.

Tab.5 Basic symbols and assumptions for the economic analysis [53]

Fig.16 Economic comparison of cold-end systems.

A_cond	The condenser area/m²
A_sp	The area of single-pressure condenser/m²
c_cw	The specific heat capacity of the cooling water/(J·(kg·K)⁻¹)
CC_L	The levelized carrying cost/$
d_i	The tube inner diameter/m
D_h	The hydraulic diameter on the waterside/m
e	The specific entropy/(kJ·kg⁻¹)
Ė_F	The exergy fuel/kW
Ė_D	The exergy destruction/kW
Ė_P	The exergy product/kW
Ė_L,tot	The exergy loss in the cold-end system/kW
ER	The excess revenue/$
F	The cross section of the cooling water mass/m²
h	The steam enthalpy/(kJ·kg⁻¹)
L_sp	The tube length of single-pressure condenser/m
?	The mass flow rate/(kg·s⁻¹)
?_s	The mass flow rate of the steam into condensers/(kg·s⁻¹)
K_cond	The heat transfer coefficient/(W·(m²·°C)⁻¹)
OMC_L	The operating and maintenance cost/$
PEC	The purchased-equipment cost/$
T	The temperature/K
T₀	The ambient temperature/K
TIC	The total investment capital/$
$Q ˙$	The heat transfer in the condenser/kW
$S ˙ g tot$	Entropy generation rate on the cold-end system/(kW·K⁻¹)
$S ˙ g$	Sentropy generation rate/(kW·K⁻¹)
t_s	The steam saturation temperature/°C
t	The temperature/°C
v_cw	The velocity of the cooling water/(m·s⁻¹)
η_st	The isentropic efficiency of the turbine/%
Δt	The cooling water temperature difference/°C
Δt_m	The log mean temperature difference in the condenser/°C
λ	The flow resistance coefficient on the cooling waterside
ρ_cw	The density/(kg·m⁻³)
i_eff	Average interest rate/%
r_n	The nominal escalation ratio for OMC/%
r_nf	The nominal escalation ratio for FC/%
n	Plant economic life/a
RT	Annual operation hours/(h·a⁻¹)
Load	Annual capacity factor
ϕ	Maintenance factor (OMC/TCI)
C_e	A feed-in tariff/(cent·(kW·h)⁻¹)
ω	Annual capacity factor
γ	TCI/ΣPEC_k
Subscript
st	Steam turbine
cond	Con
pump	Pump
fdh	Regenerative heater
cw	Cooling water
in	Inlet
out	Outlet
t	Theoretical value

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