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

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.

Graphical abstract

Keywords

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

1 Introduction

Electricity, an integral part of modern economies, supports a range of critical services, such as transportation, healthcare, and banking [1]. Electrification continues worldwide and the amount of final energy being electrified leads to the fact that the power sector is playing an increasingly central role in ‎the global energy system [2]. The share of electricity in the final consumption is less than half that of oil today and is predicted to overtake oil by 2040. Moreover, approximately 36.3% of the electricity was generated by burning fossil fuels in thermal power plants in 2019 [3]. Efficiency enhancement of thermal power plants has been increasingly applied to overcome challenges of affordability, sustainability, and security [4], apart from developing renewable energy sources, such as solar [5,6], biomass [7], geothermal resources [8], and wind energies [9].

Many comprehensive studies have been conducted to enhance the efficiency of thermal power plants. According to basic thermodynamics, the efficiency of thermal power plants can be enhanced by using hot- and cold-end system optimization to reduce external irreversibility of the cycle. Temperature and pressure optimization of working fluid [10] and reheating [11,12] belong to the hot-end system optimization, while back pressure [13] and operation optimization [14] are included in the cold-end system design. As a result, thermal power plants prefer high hot-end parameters and large capacities. Many technologies, such as waste heat recovery [15], solar-aided coal-fired units [16], and poly-generation systems [17] are applied to conventional thermal power plants to enhance efficiency but lead to increasingly complex power system configurations. Combined optimization of cold- and hot-end systems is essential to achieving the optimal overall performance of thermal power plants because hot-end systems in these comprehensive studies have become increasingly complex and expensive [18].

Cold-end systems aim to cool the working fluid to the cold-end temperature under the constraint of environmental conditions. Natural sources, such as air and water, can generally be used for cooling [19]. As a potential measure for enhancing efficiency, the optimization of the cold-end system of thermal power plants includes the two aspects of design and operation optimization.

Many comprehensive studies on the optimization of cold-end systems considering geographic locations of thermal power plants have been performed. Bustamante et al. [20] pointed out that hybrid wet/dry cooling system technologies can improve performance at high ambient temperatures. Deng et al. [21] highlighted the advantages of using air-cooled condensers in coal-rich but water-insufficient areas. Different criteria are used as optimization objectives, including loss of available work, entropy generation rate [22,23], exergy loss [24], and costs of maintaining, building, and operating [25]. Khalifeh Soltan et al. [26] proposed an objective function based on total costs of transfer area and cooling water pump power to determine the optimum baffle spacing for segmentally baffled shell and tube condensers. Chen et al. [27] used a novel vertical arrangement of air-cooled condensers based on a direct dry cooling power plant and found that this arrangement can weaken adverse wind effects and utilize wind power to improve the cooling capacity of air-cooled condensers. Xia et al. [28] showed that optimizing the number of cooling water pumps in cold-end systems can save $243310 per year. Hajabdollahi et al. [29] presented the thermo-economic optimization of a shell and tube condenser and found that optimal design parameters could be reached with genetic and particle swarm algorithms.

Many comprehensive studies have been carried out concerning the operation optimization of the cold-end system. Changes in cooling temperature (inlet temperature and the cooling water mass flow rate) affect the power consumption of the cooling water pump [30], the steam condenser performance [31], and the condensing steam pressure [32], and subsequently influence the operation of low-pressure (LP) turbine [33]. Li et al. [34] investigated the optimal operating fan frequency and the corresponding backpressure of a typical large-scale air-cooled coal-fired power plant in different boundary conditions. Laskowski et al. [35] indicated that when the correct mass flow rate of cooling water is selected, the output power of the unit increases by approximately 1 MW. Haseli et al. [36] analyzed the influence of several operating parameters, such as the inlet and outlet cooling water and condensation temperatures, and revealed the relationship between characteristics of the cooling water and the minimization of exergy destruction of the condensation process. Yang et al. [37] examined the economic impact of condenser fouling of power plants through the minimization of exergy destruction, and indicated that costs can reach $0.93 million/a (USD 2009), or 0.88% of revenue for a baseline 550 MW installation with an overdesign factor of 0.85 and a moderate temperature and load profile. Golkar et al. [38] indicated the excellent performance of genetic algorithms (GAs) in the optimization hybrid wet-/dry-cooling systems of power plants. Increasingly robust and heuristic searching methods, such as GAs [39–41] and particle swarm optimization [42], have been applied and explored for energy system optimization or energy-resource scheduling and planning because the system structure typically differs for specific design targets.

Cold-end systems are composed of condensers, pumps, and pipelines. Design and operation optimization aims to reduce the irreversibility that occurs in cold-end systems due to the heat transfer in the finite heat transfer area and pressure drop in frictional pipes [43]. Cold-end systems have become increasingly complex and multi-pressure condensers have been widely applied in recent years [44]. Multiple parameters, such as area distribution, steam distribution in the condenser, and cooling water flow rate, should be optimized while considering detailed entropy generations in cold-end systems. Therefore, entropy generation minimization (EGM) has been applied to optimize cold-end systems in this study. To the best of the authors’ knowledge, this study is the first to apply multiparameter optimization with EGM on cold-end systems with multiple-pressure condensers, in which EGM models for single- and multi-pressure cold-end systems of thermal power plants are developed; components that exhibit considerable irreversibility in the overall cold-end system are identified; the quantitative relationship between the area allocation and steam distribution of dual- and quadruple- cold-end systems is determined; and a new multi-pressure optimization scheme is proposed to reduce the energy dissipation and improve the performance of cold-end systems.

2 Model development

In this study, cold-end systems with different condensers are optimized using EGM and then compared. In addition, thermo-economic models are developed. In this section, the optimization method is introduced.

2.1 Thermodynamic analysis models

Figure 1 illustrates a thermal power plant with a wet cooling system. The difference between the single-pressure cold-end system, the dual-pressure cold-end system, and the quadruple-pressure cold-end system lies in the connections between the low-pressure turbines (LPTs) and the condensers (CONDs). The cold-end system includes 6 types of devices: steam turbine, condenser, cooling water pump (CWP), condensate pump (CP), and regenerative heaters (RHs). The once-through cooling system is adopted in the cold-end system in this study, and the cooling water comes from a river, lake, or sea which passes once through the condenser. The heated cooling water is then sent back to its source. The exhaust steam of the LPTs enters the condenser, and the condensate water flows into CP. After being pressurized by the CP, the condensate water is fed into the heat regenerative system and heated step by step in RHs after pressurization by the CP.

Thermodynamic optimization aims to minimize the total entropy generation in the cold-end system with some constraints. The following total entropy generation rate for the cold-end system is the sum of the components:

(1)\dot{S}{g}_{\mathrm{tot}}=\dot{S}{g}_{\mathrm{st}}+\dot{S}{g}_{\mathrm{cond}}+\dot{S}{g}_{\mathrm{pump}}+\dot{S}{g}_{\mathrm{fdh}},

where \dot{S}{g}_{\mathrm{tot}}, \dot{S}{g}_{\mathrm{st}}, \dot{S}{g}_{\mathrm{cond}}, \dot{S}{g}_{\mathrm{pump}}, \dot{S}{g}_{\mathrm{fdh}} are the entropy generation rates of the cold-end system, the turbine, the condenser, the pump, and the RH (RH7), kW/K, respectively.

Therefore, models are developed in the following sections to calculate \dot{S}{g}_{\mathrm{st}}, \dot{S}{g}_{\mathrm{cond}}, \dot{S}{g}_{\mathrm{pump}}, and \dot{S}{g}_{\mathrm{fdh}}.

2.1.1 Steam turbine models

A steam turbine, which has one steam entrance and one steam exit, is shown in Fig. 2. It is difficult to obtain exhaust steam enthalpy because the exhaust steam of LPT is wet and its dryness ratio is unknown. However, the superheated steam enthalpy can be achieved using the known pressure and temperature. The isentropic efficiency of the last stage of the LPT is assumed to be constant. Therefore, the exhausted steam enthalpy can be directly obtained using

(2)h_{\mathrm{st}}^{\mathrm{out}}=h_{\mathrm{st}}^{\mathrm{in}}-{\eta }_{\mathrm{st}}(h_{\mathrm{st}}^{\mathrm{in}}-h_{\mathrm{st}}^{\mathrm{t}}),

where h is the steam enthalpy, kJ/kg; η_st is the isentropic efficiency of the turbine, %; the superscripts in, out, and t denote the inlet, the outlet, and the theoretical value, respectively.

The exergy equation in the steam turbine based on the advanced exergy analysis proposed in Ref. [45] can be written as

(3){\dot{E}}_{\mathrm{F,st}}\mathrm{=}{\dot{E}}_{\mathrm{P,st}}\mathrm{+}{\dot{E}}_{\mathrm{D,st}},

where Ė_F,st is the exergy fuel of the steam turbine, kW; Ė_P,st is the exergy product of the steam turbine, kW; and Ė_D,st is the exergy destruction of the steam turbine, kW.

The exergy fuel of steam turbines is produced by the inlet steam as

(4){\dot{E}}_{\mathrm{F,st}}={\dot{m}}_{\mathrm{st}}^{}·e_{\mathrm{st}}^{\mathrm{in}}-{\dot{m}}_{\mathrm{st}}^{}·e_{\mathrm{st}}^{\mathrm{out}},

where ṁ_st is the mass flow rate of the steam turbine, kg/s; e_{\mathrm{st}}^{\mathrm{in}} is the exergy of the inlet steam, kJ/kg; and e_{\mathrm{st}}^{\mathrm{out}} is the exergy of the outlet steam, kJ/kg.

The product of the steam turbine is calculated as

(5){\dot{E}}_{\mathrm{P,st}}={\dot{m}}_{\mathrm{st}}^{}·h_{\mathrm{st}}^{\mathrm{in}}-{\dot{m}}_{\mathrm{st}}^{}·h_{\mathrm{st}}^{\mathrm{out}},

where h_{\mathrm{st}}^{\mathrm{in}} is the enthalpy of the inlet stream, kJ/kg, and h_{\mathrm{st}}^{\mathrm{out}} is the enthalpy of the outlet stream, kJ/kg.

The internal irreversibility in the steam turbine can be calculated as

(6){\dot{E}}_{\mathrm{D,st}}=T_{\mathrm{0}}·\dot{S}{g}_{\mathrm{st}},

(7)\dot{S}{g}_{\mathrm{st}}={\dot{m}}_{\mathrm{st}}(s_{\mathrm{st}}^{\mathrm{out}}-s_{\mathrm{st}}^{\mathrm{in}}),

where s is the specific entropy, kJ/(kg·K); T₀ is the ambient temperature, K; and the superscripts in and out denote the inlet and the outlet, respectively.

2.1.2 Condenser models

The single pass, single-zone condenser is the most widely applied condenser in industries, and it may have one, two, or many shells depending on the number of low-pressure turbines. Three condensers, i.e., the single-pressure condenser (scond), the dual-pressure condenser (dcond), and the quadruple-pressure condenser (qcond) are considered in the condenser models, which are demonstrated in Fig. 3. The steam condenses into water, and then the condensate water flows into the high-pressure condenser chamber step by step, and finally affluxes into the condensate tank.

The condenser is a shell-and-tube heat exchange in which cooling water flows inside tubes while the steam condenses on the outer surface of tubes. Calculations involving the condenser are performed using the model developed by the Heat Exchange Institute [4].

Heat rejection of exhausted steam can be expressed as

(8)h_{\mathrm{cond}}^{\mathrm{in}}=h_{\mathrm{st}}^{\mathrm{out}},

(9){\dot{Q}}_{\mathrm{cond}}={\dot{m}}_{\mathrm{s}}·h_{\mathrm{cond}}^{\mathrm{in}}-{\dot{m}}_{\mathrm{s}}·h_{\mathrm{cond}}^{\mathrm{out}}=K_{\mathrm{cond}}{A}_{\mathrm{cond}}\mathrm{\Delta }{t}_{\mathrm{m}}={\dot{m}}_{\mathrm{cw}}{c}_{\mathrm{cw}}\mathrm{\Delta }t,

where ṁ_s is the mass flow rate of the steam into condensers, kg/s; {\dot{Q}}_{\mathrm{cond}} is the heat transfer in the condenser, kW; K_cond is the heat transfer coefficient, W/(m²·°C); A_cond is the condenser area, m²; Δt is the cooling water temperature difference, °C; and Δt_m is the log mean temperature difference in the condenser, °C, where the Δt_m can be calculated as

(10)\mathrm{\Delta }{t}_{\mathrm{m}}={\displaystyle \frac{t_{\mathrm{cw}}^{\mathrm{out}}-t_{\mathrm{cw}}^{\mathrm{in}}}{\ln {\displaystyle \frac{t_{\mathrm{s}}-t_{\mathrm{cw}}^{\mathrm{in}}}{t_{\mathrm{s}}-t_{\mathrm{cw}}^{\mathrm{out}}}}}},

(11)t_{\mathrm{s}}=t_{\mathrm{cw}}^{\mathrm{in}}+\mathrm{\Delta }t+{\displaystyle \frac{\mathrm{\Delta }t}{{\mathrm{e}}^{\left(\frac{K_{\mathrm{cond}}·A_{\mathrm{cond}}}{c_{\mathrm{cw}}·{\dot{m}}_{\mathrm{cw}}}\right)}-\mathrm{1}}},

where t_s is the steam saturation temperature, °C; and t_{\mathrm{cw}}^{\mathrm{in}} is the inlet temperature of the cooling water inlet.

The condenser model is depicted in Fig. 4. The condenser model calculation satisfies the principle of energy conservation. The inlet enthalpy of the condenser is determined by the saturation temperature of the condenser.

The increase in water enthalpy in the single-pressure condenser can be expressed in the differential form as [46]

(12)\mathrm{d}h=\mathrm{\delta }q+\mathrm{d}p/\rho .

The entropy increment is expressed as

(13)\mathrm{d}s={\displaystyle \frac{\mathrm{\delta }q}{T}}.

The pressure loss per unit length on the waterside can be expressed as

(14)\mathrm{d}p=-\lambda {\displaystyle \frac{{\rho }_{\mathrm{cw}}{v}_{\mathrm{cw}}^{\mathrm{2}}}{\mathrm{2}}}{\displaystyle \frac{\mathrm{d}x}{D_{\mathrm{h}}}},

where ρ_cw is the density, kg/m³; v_cw is the velocity of the cooling water, m/s; λ is the flow resistance coefficient on the cooling waterside; and D_h is the hydraulic diameter on the waterside, D_{\mathrm{h}}=d_i.

The following mass flow rate of the water flowing through the steam condenser can be obtained from the density, fluid velocity, and cross section through which the cooling water flows:

(15){\dot{m}}_{\mathrm{cw}}={\rho }_{\mathrm{cw}}{v}_{\mathrm{cw}}F{\dot{m}}_{\mathrm{cw}},

where ṁ_cw is the mass flow rate of the cooling water, kg/s; and F is the cross section of the cooling water mass, m².

Substituting Eqs. (13) − (15) into Eq. (12), Eq. (16) is obtained.

(16)\mathrm{d}s={\displaystyle \frac{c_{\mathrm{cw}}\mathrm{d}T}{T}}+{\displaystyle \frac{\lambda {\dot{m}}_{\mathrm{cw}}^{\mathrm{2}}}{\mathrm{2}T{\rho }_{\mathrm{cw}}^{\mathrm{2}}{F}^{\mathrm{2}}}}{\displaystyle \frac{\mathrm{d}x}{d_i}}.

Integrating Eq. (16) between the inlet and the outlet, Eq. (17) is obtained.

(17)\mathrm{\Delta }s={\displaystyle {\int }_{T,\mathrm{in}}^{T,\mathrm{out}}{\displaystyle \frac{c_{\mathrm{cw}}\mathrm{d}T}{T}}}+{\displaystyle {\int }_{\mathrm{0}}^L{\displaystyle \frac{\lambda {\dot{m}}_{\mathrm{cw}}^{\mathrm{2}}}{\mathrm{2}T{\rho }_{\mathrm{cw}}^{\mathrm{2}}{F}^{\mathrm{2}}}}}{\displaystyle \frac{\mathrm{1}}{d_i}}\mathrm{d}x.

The entropy generation rate of the condenser is expressed as [47]

\dot{S}{g}_{\mathrm{sp}}\mathrm{=}-{\displaystyle \frac{{\dot{Q}}_{\mathrm{sp}}}{T_{\mathrm{sp}}}}+{\dot{m}}_{\mathrm{cw}}{c}_{\mathrm{cw}}\ln \left({\displaystyle \frac{T_{\mathrm{cw}}^{\mathrm{in}}}{T_{\mathrm{cw}}^{\mathrm{out}}}}\right)

(18)+{\displaystyle \frac{\lambda {\dot{m}}_{\mathrm{cw}}^{\mathrm{3}}}{\mathrm{2}{T}_{\mathrm{cw}}{\rho }_{\mathrm{cw}}^{\mathrm{2}}{A}_{\mathrm{sp}}^{\mathrm{2}}}}{\displaystyle \frac{\mathrm{1}}{d_i}}{L}_{\mathrm{sp}},

where \dot{S}{g}_{\mathrm{sp}} is the entropy generation rate of the single-pressure condenser, kW/K; {\dot{Q}}_{\mathrm{sp}} is the heat transfer in the single-pressure condenser, kW; d_i is the tube inner diameter, m; c_cw is the specific heat capacity of the cooling water, J/(kg·K); L_sp is the tube length of the single-pressure condenser, m; A_sp is the area of the single-pressure condenser, m²; T_{\mathrm{cw}}^{\mathrm{in}} is the inlet temperature of the cooling water, K; and T_{\mathrm{cw}}^{\mathrm{out}} is the outlet temperature of the cooling water, K.

The dual-pressure condenser has low- and high-pressure chambers, which are numbered 1 and 2 with increasing pressure, as shown in Fig. 3(b). The quadruple-pressure condenser has four chambers, which are numbered 1 to 4 with increasing pressure, as shown in Fig. 3(c). Each chamber is represented numerically.

(19)A_{\mathrm{cond}}={\displaystyle \sum _{i=\mathrm{1}}^n{A}_i},

where A_i is the heat transfer area of the ith chamber, m².

The entropy generation rate of the multi-pressure condenser is the sum of the entropy generation rate of all chambers,

(20)\dot{S}{g}_{\mathrm{cond}}\mathrm{=}{\displaystyle \sum _{i=\mathrm{1}}^n\dot{S}{g}_i},

where \dot{S}{g}_{\mathrm{cond}} is the entropy generation rate of condensers, kW/K; and \dot{S}{g}_i is the entropy generation rate of the ith chamber, kW/K.

The entropy generation calculation models of each steam chamber in the multi-pressure condenser is similar to that of the single-pressure condenser,

\dot{S}{g}_i\mathrm{=}-{\displaystyle \frac{{\dot{Q}}_i}{T_i}}+m_{\mathrm{cw}}{c}_{\mathrm{cw}}\ln \left({\displaystyle \frac{T_{\mathrm{cw}}^{i\mathrm{,in}}}{T_{\mathrm{cw}}^{i\mathrm{,out}}}}\right)

(21)+{\displaystyle \frac{\lambda {\dot{m}}_{\mathrm{cw}}^{\mathrm{3}}}{\mathrm{2}{T}_{\mathrm{cw}}{\rho }_{\mathrm{cw}}^{\mathrm{2}}{A}_i^{\mathrm{2}}}}{\displaystyle \frac{\mathrm{1}}{d_i}}{L}_i,

where {\dot{Q}}_i is the flow rate of the heat transferred in the ith chamber, kW; T_i is the steam saturation temperature in the ith chamber, K; L_i is the tube length of the ith chamber, m; T_{\mathrm{cw}}^{i\mathrm{,in}} is the inlet temperature of the cooling water in the ith chamber, K; and T_{\mathrm{cw}}^{i\mathrm{,out}} is the outlet temperature of the cooling water in the ith chamber, K, respectively.

The condenser is a dissipative component in the cold-end system. Therefore, the waste heat of the Rankine cycle in the steam power plant is normally discharged by the condenser. The exergy balance equations are expressed as

(22){\dot{E}}_{\mathrm{cond}}^{\mathrm{in}}\mathrm{=}{\dot{E}}_{\mathrm{cond}}^{\mathrm{out}}\mathrm{+}{\dot{E}}_{\mathrm{D,cond}}^{},

where {\dot{E}}_{\mathrm{cond}}^{\mathrm{in}}is the inlet exergy of condensers, kW; {\dot{E}}_{\mathrm{cond}}^{\mathrm{out}}is the outlet exergy of condensers, kW; and Ė_D,cond is the exergy destruction of condensers, kW.

The two inlet streams in condensers are the cooling water and n stream steam. Therefore, the inlet exergy can be expressed as

(23){\dot{E}}_{\mathrm{cond}}^{\mathrm{in}}={\dot{E}}_{\mathrm{cond}}^{\mathrm{cw,in}}+{\displaystyle \sum _{i=\mathrm{1}}^n{\dot{E}}_{\mathrm{cond,i}}^{\mathrm{stm,in}}},

where {\dot{E}}_{\mathrm{cond}}^{\mathrm{cw,in}} is the exergy of the inlet cooling water, kW, and {\dot{E}}_{\mathrm{cond,}i}^{\mathrm{stm,in}} is the inlet steam exergy of the ith chambers, kW.

(24){\dot{E}}_{\mathrm{cond}}^{\mathrm{out}}={\dot{E}}_{\mathrm{cond}}^{\mathrm{cw,out}}+{\dot{E}}_{\mathrm{cond}}^{\mathrm{wat,out}},

where {\dot{E}}_{\mathrm{cond}}^{\mathrm{cw,out}} is the exergy of the outlet cooling water, kW, and {\dot{E}}_{\mathrm{cond}}^{\mathrm{wat,out}} is the exergy of condensate water, kW.

(25){\dot{E}}_{\mathrm{D,cond}}=T_{\mathrm{0}}·\dot{S}{g}_{\mathrm{cond}},

where \dot{S}{g}_{\mathrm{cond}} represents the entropy generation rate of the condenser, kW/K.

2.1.3 Pump models

A pump, which has one water inlet and one water outlet, converts the electrical energy into the enthalpy increase of fluid. The pump exergy balance is expressed as

(26){\dot{E}}_{\mathrm{F,pump}}\mathrm{=}{\dot{E}}_{\mathrm{P,pump}}\mathrm{+}{\dot{E}}_{\mathrm{D,pump}},

where Ė_F,pump is the exergy fuel of pumps, kW; Ė_P,pump is the exergy product of pumps, kW; and Ė_D,pump is the exergy destruction of pumps, kW.

The inlet electric power is equal to the exergy fuel in the pump, which is expressed as

(27){\dot{E}}_{\mathrm{F,pump}}={\dot{W}}_{\mathrm{pump}},

where Ẇ_pump is the electric power, kW.

The changes in the working fluid exergy is indicated by the product exergy, as

(28){\dot{E}}_{\mathrm{P,pump}}={\dot{m}}_{\mathrm{pump}}^{}{e}_{\mathrm{pump}}^{\mathrm{out}}-{\dot{m}}_{\mathrm{pump}}^{}{e}_{\mathrm{pump}}^{\mathrm{in}},

where ṁ_pump is the mass flow rate in pumps, kg/s; e_{\mathrm{pump}}^{\mathrm{out}} is the outlet exergy of the pump, kJ/kg; and e_{\mathrm{pump}}^{\mathrm{in}} is the inlet exergy of the pump, kJ/kg.

The exergy destruction and entropy generation in pumps can be calculated as

(29){\dot{E}}_{\mathrm{D,pump}}=T_{\mathrm{0}}·\dot{S}{g}_{\mathrm{pump}},

(30)\dot{S}{g}_{\mathrm{pump}}\mathrm{=}{\dot{m}}_{\mathrm{pump}}(s_{\mathrm{st}}^{\mathrm{out}}-s_{\mathrm{st}}^{\mathrm{in}}),

where \dot{S}{g}_{\mathrm{pump}} is the entropy generation rate of pumps, kW/K; s_{\mathrm{st}}^{\mathrm{in}} is the outlet specific entropy of the pump, kJ/(kg·K); and s_{\mathrm{st}}^{\mathrm{out}}is the outlet specific entropy of the pump, kJ/(kg·K).

2.1.4 Regenerative heater models

The process in RHs can be divided into hot and cold sides. The fluid process is illustrated in Fig. 5. RH7 is considered in the cold-end system in this study. Steam is extracted from the steam turbine and led to the hot side of the RH. The heat is then transferred from the steam to the feedwater. The exergy balance of the RH is expressed as

(31){\dot{E}}_{\mathrm{F,fdh}}\mathrm{=}{\dot{E}}_{\mathrm{P,fdh}}\mathrm{+}{\dot{E}}_{\mathrm{D,fdh}},

where Ė_F,fdh is the exergy fuel of the RH, kW; Ė_P,fdh is the entropy product of the RH, kW; and Ė_D,fdh is the exergy destruction of the RH, kW.

According to the fluid flow and heat transfer in the RH, the fuel exergy of the RH is the sum of the inlet exergy and expressed as

(32){\dot{E}}_{\mathrm{F},\mathrm{fdh}}={\dot{m}}_{\mathrm{hot,stm}}^{\mathrm{in}}·e_{\mathrm{hot,stm}}^{\mathrm{in}}+{\dot{m}}_{\mathrm{hot,wat}}^{\mathrm{in}}·e_{\mathrm{hot,wat}}^{\mathrm{in}}-{\dot{m}}_{\mathrm{hot,wat}}^{\mathrm{out}}·e_{\mathrm{hot,wat}}^{\mathrm{out}},

where {\dot{m}}_{\mathrm{hot,stm}}^{\mathrm{in}} is the flow rate of the steam, kg/s; {\dot{m}}_{\mathrm{hot,wat}}^{\mathrm{in}} is the inlet flow rate of the drain water, kg/s; {\dot{m}}_{\mathrm{hot,wat}}^{\mathrm{out}} is the outlet flow rate of the drain water, kg/s; e_{\mathrm{hot,stm}}^{\mathrm{in}}is the exergy of the steam, kJ/kg; e_{\mathrm{hot,wat}}^{\mathrm{in}} is the inlet exergy of the drain water, kJ/kg; and e_{\mathrm{hot,wat}}^{\mathrm{out}}is the outlet exergy of the drain water, kJ/kg.

(33){\dot{E}}_{\mathrm{P},\mathrm{fdh}}={\dot{m}}_{\mathrm{cold,fdh}}^{\mathrm{out}}·e_{\mathrm{cold,fdh}}^{\mathrm{out}}-{\dot{m}}_{\mathrm{cold,fdh}}^{\mathrm{in}}·e_{\mathrm{cold,fdh}}^{\mathrm{in}},

where {\dot{m}}_{\mathrm{cold,fdh}}^{\mathrm{in}}is the inlet feedwater flow rate of the RH, kg/s ; {\dot{m}}_{\mathrm{cold,fdh}}^{\mathrm{out}}is the outlet feedwater flow rate of the RH, kg/s; e_{\mathrm{cold,fdh}}^{\mathrm{in}} is the inlet exergy of the feedwater, kJ/kg and e_{\mathrm{cold,fdh}}^{\mathrm{out}} is the outlet exergy of the feedwater, kJ/kg.

(34){\dot{E}}_{\mathrm{D},\mathrm{fdh}}=T_{\mathrm{0}}·\dot{S}{g}_{\mathrm{fdh}},

(35)\dot{S}{g}_{\mathrm{fdh}}=-{\displaystyle \frac{{\dot{Q}}_{\mathrm{fdh}}}{T_{\mathrm{fdh}}}}\mathrm{+}{\dot{m}}_{\mathrm{cold,fdh}}·c_{\mathrm{cold,fdh}}·\ln \left({\displaystyle \frac{T_{\mathrm{cold},\mathrm{fdh}}^{\mathrm{in}}}{T_{\mathrm{cold,fdh}}^{\mathrm{out}}}}\right),

where \dot{S}{g}_{\mathrm{fdh}}is the entropy generation rate of the RH, kW/K; {\dot{Q}}_{\mathrm{fdh}} is the heat transferred in the RH, kW; T_fdh is the steam saturation temperature in the RH, K; T_{\mathrm{cold},\mathrm{fdh}}^{\mathrm{in}}is the inlet temperature of the feedwater, K; and T_{\mathrm{cold,fdh}}^{\mathrm{out}}is the outlet temperature of the feedwater, K.

The cooling water is the only exergy loss in the cold-end system that can be calculated as

(36){\dot{E}}_{\mathrm{L},\mathrm{tot}}={\dot{E}}_{\mathrm{L},\mathrm{en}}={\dot{m}}_{\mathrm{cw}}\left(e_{\mathrm{cw}}^{\mathrm{out}}-e_{\mathrm{cw}}^{\mathrm{in}}\right),

where Ė_L,tot is the exergy loss of the cold-end system; e_{\mathrm{cw}}^{\mathrm{out}} is the outlet exergy of the cooling water, kJ/kg; and e_{\mathrm{cw}}^{\mathrm{in}} is the inlet exergy of the cooling water, kJ/kg.

2.2 Objective function and optimization method

The optimization process based on EGM is exhibited in Fig. 6. The condenser pressure is achieved by the environmental conditions and the cooling water flow rate. For the multi-pressure condensers, the average condenser pressure is also determined by area distribution A_i and steam distribution ṁ_i. The entropy generation rate of each component is then determined via the pressure in the chambers of the multi-pressure condenser. The condenser model contains four inputs, i.e., the exhaust steam flow rate, the exhaust steam enthalpy, the cooling water temperature, and the cooling water flow rate. The saturated temperature of working fluid and outlet temperature are the outputs of the model. The objective function described in Eq. (1) is nonlinear. GA was first proposed by John Holland to find good solutions to a problem that were otherwise computationally intractable [48]. Therefore, GA is utilized in this study for optimization, whose process is displayed in Fig. 7.

2.3 Economic analysis models

The adoption of multi-pressure condensers changes the backpressures of steam turbines and then affects the power output of the power plant. The additional income model is proposed to evaluate the economic benefits caused by the differences in power output. Purchased-equipment costs are listed in Table 1, and coefficients are adjusted according to the method used in Refs. [49,50] and true investment data.

The total investment capital (TIC) is calculated using the obtained PECs of all components [51]. The TIC of a typical 660 MW ultra-supercritical power plant in China is approximately $ 828 million [52]. Only the change in the cold-end system caused by the change in condenser pressure is considered and the investment cost (excluding the cost of the cold-end system) amounts to $ 110.36 million. Given the constant parameters at the hot end, the constant coal consumption of 85 $/t and the average price of coal with LHV of 29270 MJ/kg lead to the maximum levelized fuel cost of 91.6 M$.

To simplify, levelized cost of electricity (LCOE) is expressed as

(37)\mathrm{LCOE}=\mathrm{2}\mathrm{.5131}+\mathrm{100}{\displaystyle \frac{{\mathrm{CC}}_{\mathrm{L}}+{\mathrm{OMC}}_{\mathrm{L}}}{{\dot{W}}_{\mathrm{net}}·\mathrm{R}\mathrm{T}·\omega }},

where Ẇ_net is the net output power, kW, and subscript L indicates the levelized value.

The levelized carrying (CC_L) and operating and maintenance (OMC_L) costs [43] can be calculated using the capital recovery factor (CRF) and the constant-escalation levelization factor (CELF) as

(38)\mathrm{TCI}=\mathrm{110.36}+\mathit{\gamma }{\displaystyle \sum \mathrm{P}}{\mathrm{EC}}_k,

(39){\mathrm{CC}}_{\mathrm{L}}=\mathrm{TCI}·\mathrm{CRF,}

(40){\mathrm{OMC}}_{\mathrm{L}}=\varphi ·\mathrm{TCI}·\mathrm{CELF,}

(41)\mathrm{CELF}={\displaystyle \frac{\mathrm{1}+r_{\mathrm{n}}}{i_{\mathrm{eff}}-r_{\mathrm{n}}}}\left(\mathrm{1}-{\left({\displaystyle \frac{\mathrm{1}+r_{\mathrm{n}}}{\mathrm{1}+i_{\mathrm{eff}}}}\right)}^n\right)\mathrm{CRF,}

(42)\mathrm{CRF}={\displaystyle \frac{i_{\mathrm{eff}}{\left(\mathrm{1}+i_{\mathrm{eff}}\right)}^{n-\mathrm{1}}}{{\left(\mathrm{1}-i_{\mathrm{eff}}\right)}^n-\mathrm{1}}}.

The excess revenue (ER) from using different cold-end systems is expressed as

(43)\mathrm{ER}={\displaystyle \frac{\mathrm{1}}{\mathrm{100}}}·(C_{\mathrm{e}}-\mathrm{LCOE})·\mathrm{R}\mathrm{T}·{\dot{W}}_{\mathrm{e}}·\omega ,

where ER is the excess revenue, $/a, and Ẇ_e is the additional power output compared with the base case, kW.

3 Results and discussion

The influence of main parameters on the performance of the cold-end system will be evaluated in this section using a reference case. The influence of boundary conditions mainly on the cooling water temperature, cooling water flow rate, and condenser area are then discussed. Moreover, influences on the entropy generation rate and exergy destruction are analyzed with cooling water mass flow rates, area distribution A_i, and steam distribution ṁ_i. Furthermore, the economic performance of the thermal power plant with the cold-end system is presented.

3.1 Reference case

A typical advanced 660 MW ultra-supercritical power plant with a single-pressure condenser is the reference case of this study. The ambient temperature is the inlet temperature of the cooling water, and the atmospheric pressure is 0.1 MPa. The design values of the single-pressure cold-end system on the benchmark condition are listed in Table 2. In the thermo-economic analyses of this study, it is assumed that the steam condensates at constant temperature and pressure; there is no sub-cooling in the condensers, i.e., the condensate leaving the condenser is at saturation temperature; the changes in kinetic and potential energies and exergies are negligible; and the heat losses of cold-end system are neglected.

3.2 Influence of parameters on performance of cold-end systems

The application of the multi-pressure cold-end system has an effect on the turbine exhaust steam mass flow rate and pressure, resulting in the change of the average condenser pressure, which should be analyzed in detail.

3.2.1 Cooling water temperature

Changes in the average condenser pressure due to the temperature change when the total condenser area is 40000 m² and the cooling water mass flow rate is 23305 kg/s are plotted in Fig. 8. The pressure of the single-, the dual-, and the quadruple-pressure cold-end system when the cooling water temperature is 10°C is 2.19, 1.98, and 1.89 kPa, respectively. This finding suggests that the average condenser pressure of the multi-pressure cold-end system is lower than that of the single-pressure condenser cold-end system. Moreover, the pressure of the dual-pressure condenser is higher than that of the quadruple-pressure condenser. The average condenser pressure increases with the increase in inlet water temperature. The entropy generation rate of the single-, the dual-, and the quadruple-pressure cold-end system when the cooling water temperature is 10°C is 105.6, 103, and 102.1 kW/K, respectively. This finding indicates that the entropy generation rate of the cold-end system decreases with the increase of the cooling water temperature. The increase in the inlet temperature of the cooling water results in the decrease in the temperature difference between the outlet water temperature of the cooling water and the saturated water temperature of the condenser, thereby reducing the irreversible loss.

3.2.2 Cooling water flow rate

The influence of the cooling water mass flow rate on the performance of the cold-end system is illustrated in Fig. 9. The average pressure of the single-, the dual-, and the quadruple-pressure cold-end system when the cooling water flow rate is 20000 kg/s is 2.34, 2.25, and 2.22 kPa, respectively. The average pressure of the single-, the dual-, and the quadruple-pressure cold-end system when the cooling water flow rate is 30000 kg/s is 2, 1.96 and 1.94 kPa, respectively. The condenser pressure decreases with the increase of the cooling water flow rate. However, the mean pressure difference between the single- and multi-pressure condensers becomes increasingly small when the cooling water flow rate increases. The entropy generation rate of the single-, the dual-, and the quadruple-pressure cold-end system when the cooling water flow rate is 20000 kg/s is 107.00, 103.79, and 102.62 kW/K, respectively. The entropy generation rate of the single-, the dual-, and the quadruple-pressure cold-end system when the cooling water flow rate is 30000 kg/s is 103.78, 101.95, and 101.27 kW/K, respectively. The entropy generation of the cold-end system decreases continuously but the decreasing rate slows down with the increase of the cooling water flow rate.

3.2.3 Condenser area

The influence of the condenser area on cold-end systems when the cooling water flow rate is fixed (23305 kg/s) and the cooling water temperature is 10°C is presented in Fig. 10. The condenser pressure decreases with the increase of the condenser area. The average pressure of the single-, the dual-, and the quadruple-pressure cold-end system when the condenser area is 30000 m² is 2.47, 2.4, and 2.37 kPa, respectively. The average pressure of the single-, the dual-, and the quadruple-pressure cold-end system when the condenser area is 40000 m² is 2.19, 2.13, and 2.1 kPa, respectively. The pressure difference among the three cold-end systems decreases as the area increases. Entropy generation decreases gradually with the increase of the condenser area. The entropy generation rate of the single-, the dual-, and the quadruple-pressure cold-end system when the condenser area is 30000 m² is 131.9, 128.9, and 127.65 kW/K, respectively. The entropy generation rate of the single-, the dual-, and the quadruple-pressure cold-end system when the condenser area is 40000 m² is 105.6, 103, and 102.05 kW/K, respectively. However, the entropy generation in the multipressure cold-end system is less than that in the single-pressure cold-end system with the same condenser area.

3.3 Thermodynamic optimization and comparison

As discussed above, boundary conditions significantly influence the performance of cold-end systems. The optimization of multiple parameters under a certain boundary condition is discussed in this section. The optimization process is divided into two aspects. First, two parameters, i.e., the area A_i of the chambers and the inlet steam mass flow rate ṁ_i of the condenser, are optimized while other parameters remain constant. Second, all parameters are optimized. Third, the different condensers are compared.

3.3.1 Optimization of the area A_i of the chambers and the inlet steam mass flow rate ṁ_i

EGM is performed using the constant total condenser area and ambient temperature. The total condenser area and the cooling water inlet temperature are assumed to be 40000 m² and 10°C, respectively. The area A_i of the chambers and the inlet steam mass flow rate ṁ_i are the two main variables that influence the performance of the cold-end system. The influences of the area A_i of the chambers and the inlet steam mass flow rate ṁ_i when the cooling water flow rate is 23305 kg/s are illustrated in Fig. 11 using the dual-pressure condenser as an example. The x-axis is the ratio of the area of the low-pressure steam chamber to the total area and denoted as α_A, where {\alpha }_{\mathrm{A}}=A_{\mathrm{dl}}/A_{\mathrm{cond}}. The y-axis is the ratio of the steam flow rate of the low-pressure steam chamber to the total area and denoted as α_m, where {\alpha }_{\mathrm{m}}=m_{\mathrm{dl}}^{\mathrm{in}}/m_{\mathrm{cond}}^{\mathrm{in}}. The entropy generation rate reaches the minimum when the steam flow rate of the low-pressure steam chamber and the area distribution are both in the range of 0.35–0.65.

The exergy analysis is also performed on all components of the cold-end system to quantify the location and magnitude of exergy destruction occurred in the cold-end system. The optimal entropy generation rate of the single-, the dual-, and the quadruple-pressure cold-end system is 105.6, 102.2, and 101.4 kW/K and the average pressure of each cold-end system is 2.19, 2.13, and 2.16 kPa, respectively, under boundary conditions of a cooling flow rate of 23305 kg/s, a condenser area of 40000 m², and a cooling water inlet temperature of 10°C when the area distribution and condenser inlet steam flow rate are optimized. The entropy generation rate of the cold-end system decreases gradually with the increase of the number of condenser steam chambers. Furthermore, the exergy destruction among the three cold-end systems is illustrated in Fig. 12. The optimal values with the entropy generation minimization of the cold-end systems are listed in Table 3. The exergy destruction of condensate pumps and circulating pumps nearly remain constant because the exergy destruction of the pump is related to the water flow rate. The exergy destruction of the condenser and return water heater decreases as the number of condenser steam chambers and steam turbines increases. Moreover, the total entropy generation rate decreases with the increasing number of condenser steam chambers.

3.3.2 Optimization of all parameters

Parameters, including the area A_i of chambers, the inlet steam mass flow rate ṁ_i, and the cooling water flow rate, with a total condenser area of 40000 m², are optimized with GA based on EGM in this section. Entropy generation rates of cold-end systems with different parameters optimized is shown in Fig. 13. The only parameter optimized in the single-pressure cold-end system is the cooling water flow rate. The cooling water flow rate of the optimal single-pressure cold-end system is 29354 kg/s, which is 6408 kg/s higher than the benchmark condition. The condenser pressure changes by 0.18 kPa, the entropy generation decreases by 0.6 kW/K, and the turbine power output increases by 1698 kW as the cooling water flow rate changes. Moreover, the exergy loss and destruction decrease by 336 kW but the exergy efficiency increases by 0.13% in the cold-end system.

The dual- and the quadruple-pressure condenser cold-end systems are optimized. Parameters for optimization include the area A_i of chambers, the inlet steam mass flow rate ṁ_i, and the cooling water flow rate. First, the area A_i of the chambers of the dual- and the quadruple-pressure condensers is optimized. Second, the inlet steam mass flow rate ṁ_i of the dual- and the quadruple-pressure condensers is optimized. Third, the cooling water flow rate of the dual- and the quadruple-pressure cold-end systems is optimized. Finally, the area A_i of chambers, the inlet steam mass flow rate ṁ_i, and the cooling water flow rate are optimized. As shown in Fig. 13, the entropy generation rate of the system can be reduced using the dual- or the quadruple-pressure cold-end system. The entropy generation rate of the dual- and the quadruple-pressure cold-end system is 103.9 and 103.0 kW/K, respectively. The optimization of all parameters can obtain the minimum total entropy generation, while that of the cooling water flow rate exerts the maximum influence on the total entropy generation.

3.3.3 Comparison of cold-end systems with different condensers

The comparison of cold-end systems with different condensers with optimal parameters is shown in Figs. 14 and 15. The single-, the dual-, and the quadruple-pressure cold-end system demonstrates a condenser pressure of 2.02, 2.02, and 2.06 kPa and an entropy generation of 103.92, 102.23, and 101.45 kW/K, respectively, as manifested in Fig. 14. The optimal results are listed in Table 4. The temperature distribution in the condenser is shown in Fig. 15. The outlet temperature of the dual- and the quadruple-pressure cold-end system is higher than that of the single-pressure cold-end system. This finding indicates that the irreversibility of heat transfer between the exhaust steam and cooling water decreases with the decrease of their difference and results in the reduction of the entropy generation rate of the condenser.

3.4 Economic comparison

The basic symbols and assumptions for the economic analysis are summarized in Table 5. The method of total revenue requirement is applied to calculate the LCOE (¢/kWh).

The LCOE of the reference case is 5.2400 cent/kWh, and calculated data are the same as those in Ref. [53]. The comparison between the LCOE and ER of the optimal single-, the dual-, and the quadruple-pressure cold-end system is shown in Fig. 16. The ER of the single-pressure cold-end system increases by 559815 $/a compared with that of the benchmark condition. This finding illustrates that the adoption of the multi-pressure cold-end system can reduce the LCOE and thus increase the profit. The LOCE will decrease by 0.002 cent/(kW·h) and the ER will increase by 15610 $/a when the dual-pressure cold-end system is used. Compared with the single-pressure cold-end system, the LOCE of the quadruple-pressure cold-end system decrease by 0.0004 and the ER increase by 5286 $/a.

4 Conclusions

Optimization models of cold-end systems with multi-pressure condensers based on EGM were developed in this study. The thermo-economic performance of the single- and the multi-pressure cold-end system is investigated. Influences of design parameters, such as cooling water temperature, cooling water flow rate, and condenser area, on the thermodynamic performance of cold-end systems are analyzed in this study. The following conclusions can be drawn from this study.

When the cooling water flow rate increases gradually, the difference in entropy generation among the cold-end systems decreases. The entropy generation rates of the single-, the dual-, and the quadruple-pressure cold-end systems are nearly the same when the cooling water flow is sufficiently large (>100000 kg/s) while that of the cold-end system decreases with the increase of the cooling water temperature and condenser area.

The entropy generation rate of the dual- and quadruple-pressure cold-end systems decreases by 2.6 and 1.0 kW/K, respectively, compared with that of the single-pressure cold-end system when the area A_i of the chambers, the inlet steam mass flow rate ṁ_i, and the cooling water mass flow rate are optimized. The cooling water flow rate is the dominant factor that affects the change of the entropy generation rate.

The adoption of multi-pressure cold-end systems will increase the ER of the power plant and reduce the LCOE when the total area is the same. ER that can be gained by using dual- and quadruple-pressure cold-end systems is 575 and 580 k$/a, respectively, compared with that of using the single-pressure cold-end system.

References

[1] Yin J, Liu M, Zhao Y, Dynamic performance and control strategy modification for coal-fired power unit under coal quality variation. Energy, 2021, 223: 120077

[2] Liu R, Liu M, Zhao Y, Thermodynamic study of a novel lignite poly-generation system driven by solar energy. Energy, 2021, 214: 119075

[3] Zhang Y L, Li J J, Liu H, Environmental, social, and economic assessment of energy utilization of crop residue in China. Frontiers in Energy, 2021, 15(2): 308–319

[4] Zhang K, Liu M, Zhao Y, Entropy generation versus transition time of heat exchanger during transient processes. Energy, 2020, 200: 117490

[5] Yan H, Li X, Liu M, Performance analysis of a solar-aided coal-fired power plant in off-design working conditions and dynamic process. Energy Conversion and Management, 2020, 220: 113059

[6] Zou C Z, Feng H Y, Zhang Y P, Geometric optimization model for the solar cavity receiver with helical pipe at different solar radiation. Frontiers in Energy, 2019, 13(2): 284–295

[7] Ye B Q, Zhang R, Cao J, Thermodynamic and economic analyses of a coal and biomass indirect coupling power generation system. Frontiers in Energy, 2020, 14(3): 590–606

[8] Liu Q, Shang L L, Duan Y Y. Performance analyses of a hybrid geothermal-fossil power generation system using low-enthalpy geothermal resources. Applied Energy, 2016, 162: 149–162

[9] Fateh L, Ahmed O, Amar O, Modeling and control of a permanent magnet synchronous generator dedicated to standalone wind energy conversion system. Frontiers in Energy, 2016, 10(2): 155–163

[10] Liu M, Zhang X, Yang K, Optimization and comparison on supercritical CO₂ power cycles integrated within coal-fired power plants considering the hot and cold end characteristics. Energy Conversion and Management, 2019, 195: 854–865

[11] Wang Z, Liu M, Zhao Y, Comparison on thermodynamic characteristics of single- and double- reheat boilers under off-design working conditions and during transient processes. Applied Thermal Engineering, 2020, 179: 115620

[12] Wang Z, Liu M, Zhao Y, Flexibility and efficiency enhancement for double-reheat coal-fired power plants by control optimization considering boiler heat storage. Energy, 2020, 201: 117594

[13] Wang C, Liu M, Zhao Y, Dynamic modeling and operation optimization for the cold end system of thermal power plants during transient processes. Energy, 2018, 145: 734–746

[14] Ahmadi M H, Ahmadi M A, Aboukazempour E, Exergetic sustainability evaluation and optimization of an irreversible Brayton cycle performance. Frontiers in Energy, 2019, 13(2): 399–410

[15] Zhang H S, Zhao H B, Li Z L. Performance analysis of the coal-fired power plant with combined heat and power (CHP) based on absorption heat pumps. Journal of the Energy Institute, 2016, 89(1): 70–80

[16] Wu J, Hou H, Hu E, Performance improvement of coal-fired power generation system integrating solar to preheat feedwater and reheated steam. Solar Energy, 2018, 163: 461–470

[17] Rivarolo M, Cuneo A, Traverso A, Design optimisation of smart poly-generation energy districts through a model based approach. Applied Thermal Engineering, 2016, 99: 291–301

[18] Bugge J, Kjær S, Blum R. High-efficiency coal-fired power plants development and perspectives. Energy, 2006, 31(10–11): 1437–1445

[19] Akpan P U, Fuls W F. Application and limits of a constant effectiveness model for predicting the pressure of steam condensers at off-design loads and cooling fluid temperatures. Applied Thermal Engineering, 2019, 158: 113779

[20] Bustamante J G, Rattner A S, Garimella S. Achieving near-water-cooled power plant performance with air-cooled condensers. Applied Thermal Engineering, 2016, 105: 362–371

[21] Deng H, Liu J, Zheng W. Analysis and comparison on condensation performance of core tubes in air-cooling condenser. International Journal of Heat and Mass Transfer, 2019, 135: 717–731

[22] Bejan A. Entropy generation minimization, exergy analysis, and the constructal law. Arabian Journal for Science and Engineering, 2013, 38(2): 329–340

[23] Bejan A.Fundamentals of exergy analysis, entropy generation minimization, and the generation of flow architecture. International Journal of Energy Research, 2002, 26(7): 0–43

[24] Yang B, Chen L G, Sun F R. Exergetic performance optimization of an endoreversible variable-temperature heat reservoirs intercooled regenerated Brayton cogeneration plant. Journal of the Energy Institute, 2016, 89(1): 1–11

[25] d’Accadia M D, Vanoli L. Thermoeconomic optimisation of the condenser in a vapour compression heat pump. International Journal of Refrigeration, 2004, 27(4): 433–441

[26] Khalifeh Soltan B, Saffar-Avval M, Damangir E. Minimizing capital and operating costs of shell and tube condensers using optimum baffle spacing. Applied Thermal Engineering, 2004, 24(17–18): 2801–2810

[27] Chen L, Yang L, Du X, A novel layout of air-cooled condensers to improve thermo-flow performances. Applied Energy, 2016, 165: 244–259

[28] Xia L, Liu D, Zhou L, Optimal number of circulating water pumps in a nuclear power plant. Nuclear Engineering and Design, 2015, 288: 35–41

[29] Hajabdollahi H, Ahmadi P, Dincer I. Thermoeconomic optimization of a shell and tube condenser using both genetic algorithm and particle swarm. International Journal of Refrigeration, 2011, 34(4): 1066–1076

[30] Gololo K V, Majozi T. On synthesis and optimization of cooling water systems with multiple cooling towers. Industrial & Engineering Chemistry Research, 2011, 50(7): 3775–3787

[31] Anozie A N, Odejobi O J. The search for optimum condenser cooling water flow rate in a thermal power plant. Applied Thermal Engineering, 2011, 31(17–18): 4083–4090

[32] Chuang C C, Sue D C. Performance effects of combined cycle power plant with variable condenser pressure and loading. Energy, 2005, 30(10): 1793–1801

[33] O’Donovan A, Grimes R. A theoretical and experimental investigation into the thermodynamic performance of a 50 MW power plant with a novel modular air-cooled condenser. Applied Thermal Engineering, 2014, 71(1): 119–129

[34] Li X, Wang N, Wang L, Identification of optimal operating strategy of direct air-cooling condenser for Rankine cycle based power plants. Applied Energy, 2018, 209: 153–166

[35] Laskowski R, Smyk A, Lewandowski J, Selecting the cooling water mass flow rate for a power plant under variable load with entropy generation rate minimization. Energy, 2016, 107: 725–733

[36] Haseli Y, Dincer I, Naterer G F. Optimum temperatures in a shell and tube condenser with respect to exergy. International Journal of Heat and Mass Transfer, 2008, 51(9–10): 2462–2470

[37] Yang T, Wang W, Zeng D, Closed-loop optimization control on fan speed of air-cooled steam condenser units for energy saving and rapid load regulation. Energy, 2017, 135: 394–404

[38] Golkar B, Naserabad S N, Soleimany F, Determination of optimum hybrid cooling wet/dry parameters and control system in off design condition: case study. Applied Thermal Engineering, 2019, 149: 132–150

[39] Wang L, Yang Y, Dong C, Systematic optimization of the design of steam cycles using MINLP and differential evolution. Journal of Energy Resources Technology, 2014, 136(3): 031601

[40] Chen C, Xie D, Xiong Y, Optimization of turbine cold-end system based on BP neural network and genetic algorithm. Frontiers in Energy, 2014, 8(4): 459–463

[41] Demirkaya G, Besarati S, Vasquez Padilla R, Multi-objective optimization of a combined power and cooling cycle for low-grade and midgrade heat sources. Journal of Energy Resources Techno-logy, 2012, 134(3): 032002

[42] Liu M, Wang S, Yan J. Operation scheduling of a coal-fired CHP station integrated with power-to-heat devices with detail CHP unit models by particle swarm optimization algorithm. Energy, 2021, 214: 119022

[43] Bhattacharyya S, Pathak M, Sharifpur M, Heat transfer and exergy analysis of solar air heater tube with helical corrugation and perforated circular disc inserts. Journal of Thermal Analysis and Calorimetry, 2021, 145(3): 1019–1034

[44] Fu Y, Liu M, Wang L Y, Thermo-economic optimization of the dual-pressure condenser for 700°C ultra-supercritical coal-fired power plants. In: Proceedings of the ASME 2020 Power Conference Collocated with the 2020 International Conference on Nuclear Engineering, Virtual, 2020, online, doi:10.1115/POWER2020-16302

[45] Kelly S, Tsatsaronis G, Morosuk T. Advanced exergetic analysis: approaches for splitting the exergy destruction into endogenous and exogenous parts. Energy, 2009, 34(3): 384–391

[46] Liu J, Hu Y, Zeng D, Optimization of an air-cooling system and its application to grid stability. Applied Thermal Engineering, 2013, 61(2): 206–212

[47] Cheng X. Entropy resistance minimization: an alternative method for heat exchanger analyses. Energy, 2013, 58: 672–678

[48] McCall J. Genetic algorithms for modelling and optimisation. Journal of Computational and Applied Mathematics, 2005, 184(1): 205–222

[49] Ameri M, Ahmadi P, Hamidi A. Energy, exergy and exergoeconomic analysis of a steam power plant: a case study. International Journal of Energy Research, 2009, 33(5): 499–512

[50] Xiong J, Zhao H, Zhang C, Thermoeconomic operation optimization of a coal-fired power plant. Energy, 2012, 42(1): 486–496

[51] Bejan A, Tsatsaronis G, Moran M J. Thermal Design and Optimization. New York: John Wiley & Sons, 1995

[52] Wang L. Thermo-economic evaluation, optimization and synthesis of large-scale coal-fired power plants. Dissertations for the Doctoral Degree. Berlin: Technische Universitaet Berlin (Germany), 2016

[53] Wang L, Yang Y, Dong C, Parametric optimization of supercritical coal-fired power plants by MINLP and differential evolution. Energy Conversion and Management, 2014, 85: 828–838

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