Optimization of a novel cogeneration system including a gas turbine, a supercritical CO2 recompression cycle, a steam power cycle and an organic Rankine cycle

Optimization of a novel cogeneration system including a gas turbine, a supercritical CO2 recompression cycle, a steam power cycle and an organic Rankine cycle

Energy Conversion and Management 172 (2018) 457–471 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www...

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Energy Conversion and Management 172 (2018) 457–471

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Optimization of a novel cogeneration system including a gas turbine, a supercritical CO2 recompression cycle, a steam power cycle and an organic Rankine cycle

T



Shengya Houa, Yaodong Zhoua, Lijun Yua, , Fengyuan Zhanga, Sheng Caoa, Yuandan Wub a b

Institute of Thermal Energy Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China AECC Hunan Aviation Powerplant Research Institute, Zhuzhou 412000, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Cogeneration system Gas turbine Supercritical CO2 recompression cycle Steam power cycle Organic Rankine cycle Multi-objective optimization

According to the principles of energy grade recovery and cascade utilization, a novel cogeneration system including a gas turbine, a supercritical CO2 (S-CO2) recompression cycle, a steam power cycle and an organic Rankine cycle (ORC) is proposed. In particular, a part of waste heat from the supercritical CO2 recompression cycle is used to preheat the steam power cycle, and ORC uses the zeotropic mixture as working fluid. Comprehensive thermodynamic and exergoeconomic analyses are presented for the proposed cogeneration system. Parametric studies are conducted to study the effects of key system design parameters as pressure ratio of gas turbine, pressure ratio of the S-CO2 cycle, split ratio of the S-CO2 cycle, evaporation temperature of the steam power cycle, mass fraction of isopentane in the zeotropic mixture, evaporation temperature of ORC and pinch point temperature difference in the ORC evaporator on the exergy efficiency and total product unit cost. The optimum system parameters are obtained through the multi-objective optimization method based on GA (genetic algorithm) and TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) decision making. The optimization results indicate that the optimum values of exergy efficiency and total product unit cost are 69.33% and 10.77$/GJ, respectively. Furthermore, the superiority of the proposed cogeneration system is verified by comparison with other seven forms of power generation systems.

1. Introduction Due to the increase in fuel price and the reduction of fossil fuel resources, the optimal operation and management of energy system are crucial. Gas turbine power generation has a series of advantages such as high efficiency, small footprint, short construction period, low water consumption, quick startup, and flexible operation. Therefore, it has received increasing attention from many countries [1]. However, a stand-alone gas turbine emits high-grade heat into the atmosphere, resulting in low thermal efficiency. It is an effective way to improve the efficiency of gas turbines by constructing combined cycle to recover the waste heat [2]. At present, the conventional gas turbine waste heat recovery way is to design a gas-steam combined power generation system. Sahu [3] carried out the comparisons between the stand-alone gas turbine and the gas-steam combined cycle and found that the combined cycle has 21.16% higher exergy efficiency while the cost of electricity is only 13.3% higher. However, as the exhaust temperature range of gas turbine is large, gas-steam combined cycle may not be the



best way to recover the waste heat of gas turbine [4]. According to the principles of energy grade recovery and cascade utilization, the temperature of gas turbine exhaust can be divided into three grades: high, medium, and low. Each level of waste heat can be recovered through its corresponding most suitable power cycle to achieve higher efficiency. The supercritical carbon dioxide (S-CO2) cycle is used to recover high-grade waste heat, which is very attractive as a replacement of the steam power cycle when the heat source temperature is higher than 500 °C [5]. The S-CO2 cycle has the advantages of high efficiency, compactness, simplicity, better economy and safety priority [6]. Kouta et al. [7] conducted the performance and cost analyses of the solar power tower integrated with S-CO2 cycle. They found that the S-CO2 recompression cogeneration cycle has a lower levelized cost of energy than the S-CO2 regeneration cogeneration cycle. Cao et al. [8] proposed a novel combined gas turbine and CO2 cycle and showed that it has better thermodynamic performance than the gas-steam combined cycle. Nami et al. [9] proposed and optimized a combined cycle including a gas turbine, a supercritical CO2 recompression cycle, an organic

Corresponding author. E-mail address: [email protected] (L. Yu).

https://doi.org/10.1016/j.enconman.2018.07.042 Received 27 April 2018; Received in revised form 8 July 2018; Accepted 13 July 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature

Subscripts

Glossary

0 1, 2··· cr D o F H i in k net P ph q W

A CRF cp,tot e Ė f h ṁ ORC P PRc Q rp S-CO2 s T W x Z Ż

heat transfer area, m2 capital recovery factor total product unit cost, $/GJ specific exergy, kJ/kg exergy rate, kW exergoeconomic factor specific enthalpy, kJ/kg mass flow rate, kg/s organic Rankine cycle pressure, bar compressor pressure ratio heat capacity, kW pressure ratio of compressor1 supercritical carbon dioxide specific entropy, kJ/kg·K temperature, °C output power, kW split ratio capital cost, $ capital cost rate, $/s

ambient (temperature) state points critical destruction outlet fuel heat exchanger inlet input k-th component net power product physical exergy heat power

Greek symbols η ηi ΔT φ

exergy efficiency isentropic efficiency pinch point temperature difference correction factor

and the ORC are suitable for recovering high-temperature, mediumtemperature and low-temperature waste heat, respectively. For gas turbine waste heat recovery, it would be possible to achieve good results if the three power cycles could be combined according to this characteristic. However, the studies on recovering waste heat from gas turbine through the combination of the S-CO2 recompression cycle, steam power cycle and ORC have not been reported yet. Thus, in this paper, according to the principles of grade recovery and cascade utilization, a novel cogeneration system including a gas turbine, a supercritical CO2 recompression cycle, a steam power cycle and an ORC is proposed. The supercritical CO2 recompression cycle, steam power cycle and ORC are used to recover high, medium, and low grades waste heat from the gas turbine, respectively. Detailed thermodynamic analysis and exergoeconomic analysis are performed. The multi-objective optimization method is selected to obtain the optimum system parameters.

Rankine cycle (ORC) and a heat recovery steam generator. The result showed that the average product unit cost of the optimized condition is lower by 0.56 $/GJ than that of the basic condition. ORC can be used to recover low-grade waste heat, which is more suitable for heat source below 200 °C than steam power cycle [10–12]. The thermodynamic and the economic optimization of ORC is performed by Quoilin et al. [13]. Result indicated that the optimal economics profitability and thermodynamic efficiency are obtained at different fluids and evaporation temperatures. Khaljani et al. [14] proposed a new cogeneration cycle which combines a gas turbine and an ORC through an HRSG (heat recovery steam generator) and assessed thermodynamic, exergo-economic and environmental impacts. They found that the most exergy destruction occurred in the combustion chamber. Pan et al. [15] introduced an ORC and Kalina cycle combined power generation system using the exhaust gas from solid oxide fuel cell and gas turbine as the heat source. Result indicated that the thermal efficiency and the annual power generation of the system are 53% and 1.964 MkW∙h/a. Kosmadakis et al. [16] compared 33 organic working fluids and concluded that R245fa is the most appropriate fluid. The comparisons between the pure and zeotropic mixture fluids of ORC was investigated by Heberle et al. [17]. Result showed that the use of mixtures leads to higher efficiency than pure fluids. At present, in order to meet the practical application environment, researchers began to optimize the system using multi-objective optimization method and obtained good results. Multi-objective optimization considering exergy efficiency and total cost rate of gas turbine is conducted by Ahmadi et al. [18] who reported 4% increase in exergy efficiency and 5% reduction in environmental impacts by optimization. Ganjehkaviri et al. [19] performed multi-objective optimization for gassteam combined cycle and found that the optimal quality of the vapor at steam turbine outlet is 88%. Hou et al. [20] reported multi-objective optimization for a cogeneration system including a gas turbine, a supercritical CO2 regenerative cycle and an ORC. Result showed that the optimal values of the system parameters could be obtained by the multiobjective optimization method based on genetic algorithm. Garg et al. [21] investigated mixture R245fa/Isopentane as ORC working fluids and reported that the ORC could achieve cycle efficiency of 10–13% at an optimum expansion ratio of 7–10. Therefore, the S-CO2 recompression cycle, the steam power cycle

2. Cycle description and assumptions Fig. 1 shows the schematic diagram of the novel cogeneration system which includes a gas turbine, a supercritical CO2 recompression cycle, a steam power cycle and an ORC. Supercritical CO2 recompression cycle, steam power cycle and ORC recover high, medium, and low grades gas turbine waste heat in turn. In addition, a part of the waste heat of the supercritical CO2 recompression cycle is used to preheat the steam power cycle. As shown in Fig. 1, air at ambient conditions is compressed in the compressor (C1). The compressed air and fuel are mixed and combusted in the combustion chamber (CC). The high-temperature gas exiting combustion chamber enters the gas turbine (GT) to drive C1 and generator. Gas turbine exhaust is the hot source of supercritical CO2 recompression cycle, steam power cycle and ORC. The high-temperature exhaust discharged from gas turbine first enters heat exchanger (H1) to heat CO2. The heated CO2 expands in the S-CO2 turbine (T1) to generate power and then flows into the high temperature recuperator (HTR) and low temperature recuperator (LTR) to sequentially heat the stream 12 and the stream 10. Stream 17 exiting LTR is split into two streams: stream 18 and stream 20. Stream 20 enters the evaporator to preheat the water of steam power cycle and 458

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Fig. 1. Schematic diagram of the proposed system.

then flows to the cooler1 before being compressed in the S-CO2 compressor (C2). Stream 18 is compressed in the S-CO2 compressor (C3) and then joins stream 11 exiting from LTR. Mixed stream 12 is preheated in HTR before being heated in the H1. The exhaust exiting H1 flows to the heat exchanger (H2) to heat water of the steam power cycle. The superheated steam from H2 flows to the steam turbine (T2) to produce power and enters the cooler (Cooler2) where it condenses into water. Stream 24 exiting Cooler2 is compressed by the water pump (Pump1). The exhaust exiting H2 flows to the heat exchanger (H3) to heat organic working fluid of ORC. The heated organic working fluid expands in the ORC turbine (T3) to produce power. The expanded organic working fluid enters the ORC regenerator (RE) to preheat the stream 32. The stream 36 exiting RE is cooled in the cooler (Cooler3) before being compressed by the ORC pump (Pump2). The T-S diagrams of supercritical CO2 recompression cycle, steam power cycle and ORC are shown in Fig. 2. In order to simplify the model of the combined cycle, the following assumptions are adopted:

the actual application process, the system designers need to use the method given in this paper to obtain the result according to the actual situation. 3.1. Thermodynamic analysis The conservations of mass and energy, as well as the exergy balance, are applied to each component as follows [24]:

∑ ṁ i Q̇ +

=

∑ ṁ e

∑ ṁ i hi = Ẇ

EQ̇ +

∑ ṁ i ei = EẆ

(1)

+

∑ ṁ e he

+

∑ ṁ e ee + EḊ

(2) (3)

where subscripts i and e refer to the inlet and outlet of control volume, respectively; EẆ , EQ̇ and EḊ denote the exergy rate related to mechanical power, heat transfer and destruction, respectively. Exergy consists of exergy and chemical exergy. Since there is no chemical reaction in the proposed system, only physical exergy need to be analyzed [15]. The physical exergy of each stream is expressed as [24]:

(1) The cogeneration system operates at steady state condition. (2) The temperature and pressure of ambient condition are 25 °C and 1.013 bar, respectively. (3) The cooling water enters cooler1, cooler2 and cooler3 under ambient condition. (4) The changes in potential and kinetic energies are negligible [9]. (5) The isentropic efficiencies of GT1, T1, T2 and T3 are 90%, 90%, 85% and 85% [3,9,22], respectively. (6) The isentropic efficiencies of C1, C2, C3, water pump and ORC pump are 88%, 85%, 85%, 80% and 80% [3,9,22], respectively.

eph = (h−h 0)−T0 (s−s0)

(4)

The exergy efficiency for the cogeneration system is defined as [9]:

η=

Eṗ ̇ Ein

(5)

where Ė p and Ėin are the total produced exergy and the total exergy entering the system, respectively. 3.2. Exergoeconomic analysis

3. Mathematical modeling Exergoeconomic is a branch of engineering analysis. It combines exergy analysis with economic principles to provide system designers with crucial information that not available by traditional energy analysis and economic assessments [25]. The cost balance equation of each component generating power and receiving heat transfer is expressed as [25]:

In order to obtain the optimal design parameters of the cogeneration system, thermodynamic models and exergoeconomic models are developed in Matlab software. The required thermophysical properties of the working fluids are obtained by calling the REFPROP Version 9.0 [23]. The model uses the assumptions listed in Section 2, which are specific to the situation and do not affect the regularity of the study, but have an impact on the numerical outcomes of the study. Therefore, in

∑ Cȯ ,k + CẆ ,k = ∑ Ci̇ ,k + Cq̇ ,k + Zk̇ 459

(6)

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Fig. 2. The T-S diagrams: (a) supercritical CO2 recompression cycle, (b) steam power cycle, (c) ORC.

For the combustion chamber:

where

Ċ = cE ̇

(7)

Zcc =

and c is the cost per unit of each exergy stream. The cost rate of the kth component is defined as [26]:

Zk̇ = Zk ·CRF ·φ /(N × 3600)

i (1 + i)n (1 + i)n−1

39.5ṁ 1 (rp )ln(rp) 0.9−ηC1

ZGT =

P2 P1

(12)

266.3ṁ 3 ⎛ P3 ⎞ ln (1 + exp(0.036T3−54.4)) 0.92−ηGT ⎝ P4 ⎠ ⎜



(13)

where ηGT is the isentropic efficiency of GT. For C2, C3 and T1 of the S-CO2 cycle:

(9)

ZC 2 =

71.1ṁ 9 (PR c ) ln(PR c ) 0.9−ηC 2

(14)

ZC3 =

71.1ṁ 18 (PR c ) ln(PR c ) 0.9−ηC3

(15)

ZT 1 =

479.34ṁ 14 ln(PR c )(1 + exp(0.036T14−54.4)) 0.92−ηT 1

(16)

where ηC2, ηC3 and ηT1 are the isentropic efficiencies of C2, C3 and T1, respectively; PRc is the pressure ratio of the C2 and C3, which is defined as:

(10)

where ηC1 is the isentropic efficiency of C1; rp is the pressure ratio of C1, which is defined as:

rp =

(1 + exp(0.018T3−26.4))

For the gas turbine: (8)

where i and n are the interest rate (10%) and the system operation years (20 years), respectively. The capital costs of power machineries in the cogeneration system can be expressed as follows [3,27,28]: For the C1:

ZC1 =

P

2

where Zk is the purchase cost of the kth component; φ is the maintenance factor (1.06); N refers to the annual number of operating hours (7446 h); CRF is the capital recovery factor, which is defined as:

CRF =

25.65ṁ 2 0.995− P3

PR c = (11)

P10 P9

(17)

The split ratio refers to the ratio of the mass flow into C2 to the total

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mass flow, which is expressed as:

ṁ x = 20 ṁ 17

where CEPCI refers to the chemical engineering plant cost index. CEPCI2001 = 394, CEPCI2018 = 638.1 [26]. SPECO (specific exergy costing) method is used to solve the exergoeconomic analysis [29]. Table 1 shows the definition for fuel and product of the cogeneration system. Assuming cooling water comes from the environment, its cost rate is negligible, i.e. c22 = c29 = c37 = 0. Table 2 presents the exergy cost rate balances and auxiliary equations for each component. Several parameters play an important role in the exergoeconomic analysis, which include the average cost per unit exergy of fuel (cF,k), average cost per unit exergy of product (cP,k), cost flow rate associated with the exergy destruction (ĊD,k ), exergoeconomic factor (fk), and total product unit cost (cP,tot). The parameters are defined as follows [24]:

(18)

For T2 and water pump of the steam power cycle: 3

266.3m27 ⎞ ⎛ ZT 2 = 3880.5P27 ⎜1 + ⎛⎜ ⎟ 0.92−ηT 2 ⎠ ⎝ ⎝

T −866 ⎞ ⎞⎛ ⎞ ⎛ 28 ⎟ 1 + 5 exp ⎝ 10.42 ⎠ ⎝ ⎠ ⎠

0.2 ⎞ ⎛ ZPump1 = 705.48P25 ⎜1 + 1−ηPump1 ⎟ ⎝ ⎠

(19)

(20)

where ηT2 and ηPump1 are the isentropic efficiencies of T2 and water pump, respectively. For T3 and ORC pump of the ORC:

cF , k =

CḞ , k EḞ , k

(27)

479.34ṁ 34 ⎛ P34 ⎞ ln (1 + exp(0.036T34−54.4)) ZT 3 = 0.92−ηT 3 ⎝ P35 ⎠

(21)

cP, k =

Zpump2 = 3540Ẇ pump2 0.71

CṖ , k EṖ , k

(28)

(22)





where ηT3 is the isentropic efficiency of T3. The capital costs of heat exchangers in the cogeneration system can be defined as follows [28]:

lg CH , k = K1, H , k + K2, H , k lg AH , k + K3, H , k (lg AH , k )2

CḊ , k = cF , k EḊ , k

(29)

Zk̇ Zk̇ + CḊ , k

(30)

fk =

(23)

lg FH , k = C1, H , k + C2, H , k lg PH , k + C3, H , k (lg PH , k )2

(24)

ZH , k = CH , k (B1, H , k + B2, H , k FM , H , k FH , k ) j

(25)

cp, tot =

̇ Zk̇ + Cfuel np ̇ ∑ Epi

(31)

i=1

The exergoeconomic factor reveals the relative importance of the component cost to the exergy destruction cost. The total product unit cost is the objective function of the exergoeconomic optimization.

where AH,k and PH,k are the area and operating pressure of the kth heat exchange, respectively; Ki,H,k, Ci,H,k, are coefficients related to the area and operating pressure of the kth heat exchange, respectively; Bi,H,k and FM,H,k are coefficients related to the type and material of heat exchanger, respectively. The capital costs of heat exchangers are based on commodity prices in 2001 and can be converted to 2018 through the cost index coefficient which is expressed as:

j = CEPCI2018/ CEPCI2001

n ∑i =k 1

3.3. Model validation In order to validate the developed model for the cogeneration system, data reported in literatures is used. Since there is no literature on the proposed cogeneration system model, the system model is split and verified according to the existing literatures. Table 3 compares the

(26)

Table 1 Definition for fuel and product of the cogeneration system.

Table 2 Exergy cost rate balances and auxiliary equations for each component.

Component

Fuel exergy rate (kW)

Product exergy rate (kW)

Component

Exergy cost rate balance equation

C1

̇ WC1 E2̇ + E8̇ E3̇ −E4̇

E2̇ −E1̇

C1

̇ ̇ ̇ C1̇ + CW C1 + ZC1 = C2

PleaseCheck

E3̇ ̇ WGT

CC

c8 = 4$/GJ

E4̇ −E5̇ E5̇ −E6̇

̇ −E13 ̇ E14 ̇ −E13 ̇ E14

̇ = C3̇ C2̇ + C8̇ + ZCC ̇ ̇ ̇ C4̇ + CW GT = C3 + ZGT

H1

E6̇ −E7̇ ̇ −E15 ̇ E14

̇ −E33 ̇ E34 ẆT1

H3

̇ −E16 ̇ E15 ̇ −E17 ̇ E16

̇ −E12 ̇ E13 ̇ −E10 ̇ E11

HTR

̇ WC2 ̇ WC3 ̇ −E21 ̇ E20

̇ −E9̇ E10 ̇ −E18 ̇ E19 ̇ −E25 ̇ E26

̇ −E9̇ E21 ̇ −E28 ̇ E27

̇ −E22 ̇ E23 ẆT2

Cooler1

̇ −E24 ̇ E28 Ẇ p1

̇ −E29 ̇ E30 ̇ −E24 ̇ E25

̇ −E35 ̇ E34 ̇ −E36 ̇ E35

ẆT3 ̇ −E32 ̇ E33

̇ −E31 ̇ E36 Ẇ p2

̇ −E37 ̇ E38 ̇ −E31 ̇ E32

CC GT H1 H2 H3 T1 HTR LTR C2 C3 H4 Cooler1 T2 Cooler2 Pump1 T3 RE Cooler3 Pump2

GT

c3 = c 4

̇ = C4̇ + C13 ̇ + ZḢ 1 C5̇ + C14 ̇ = C5̇ + C26 ̇ + ZḢ 2 C6̇ + C27

c4 = c5

̇ = C6̇ + C33 ̇ + ZḢ 3 C7̇ + C34 ̇ + CW ̇ ̇ ̇ C15 T 1 = C14 + ZT 1 ̇ + C13 ̇ = C15 ̇ + C12 ̇ + ZHTR ̇ C16

c6 = c 7

c16 = c17

C2

̇ + C17 ̇ = C10 ̇ + C16 ̇ + ZLTR ̇ C11 ̇ ̇ ̇ C9̇ + CW C 2 + ZC 2 = C10

C3

̇ + CW ̇ ̇ ̇ C18 C 3 + ZC 3 = C19

cWC 3 = cWT 1

H4

̇ + C26 ̇ = C20 ̇ + C25 ̇ + ZḢ 4 C21 ̇ = C21 ̇ + C22 ̇ + ZCooler1 ̇ C9̇ + C23

PleaseCheck

c27 = c28

Pump1

̇ + CW ̇ ̇ ̇ C28 T 2 = C27 + ZT 2 ̇ + C30 ̇ = C28 ̇ + C29 ̇ + ZCooler2 ̇ C24 ̇ + CW ̇ ̇ ̇ C24 + ZPump1 = C25

T3

̇ + CW ̇ ̇ ̇ C35 T 3 = C34 + ZT 3

c34 = c35

RE

̇ + C36 ̇ = C32 ̇ + C35 ̇ + ZRE ̇ C33 ̇ + C38 ̇ = C36 ̇ + C37 ̇ + ZCooler3 ̇ C31 ̇ + CW ̇ ̇ ̇ C31 + ZPump2 = C32

c35 = c36

H2 T1 LTR

T2 Cooler2

Cooler3 Pump2

461

Auxiliary equation

p1

p2

c5 = c6

c14 = c15 PleaseCheck cWC 2 = cWT 1

PleaseCheck PleaseCheck

cWP1 = cWT 2

PleaseCheck cWp2 = cWT 3

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Table 3 Model validation for the combined gas turbine and steam cycle using the data reported by Sahu [3]. Decision and performance parameters Input values

The The The The The

compressor pressure ratio turbine inlet temperature isentropic efficiency of compressor isentropic efficiency of gas turbine isentropic efficiency of steam turbine

Output values

The net power The exergetic efficiency The cost of electricity

Sahu [3]

Present work for the Sahu M K’s configuration

10 1500 K 88% 90% 85%

10 1500 K 88% 90% 85%

48.71 MW 39.44% 3.33cent/(kW·h)

48.53 MW 39.29% 3.42cent/(kW·h)

Table 6 The key input data used in the analysis.

Table 4 Model validation for the combined S-CO2 and ORC using the data reported by Wang [22]. Decision and performance parameters

Wang [22]

Present work for the Wang’s configuration

Input values

2.84

2.84

72.32 °C

72.32 °C

3.03 °C

3.03 °C

0.09 °C CO2/R245fa

0.09 °C CO2/R245fa

263.96 MW 60.92%

262.14 MW 60.50%

9.60$/GJ

9.73$/GJ

Output values

The compressor pressure ratio The evaporation temperature The pinch point temperature difference The degree of superheat The working fluid The net power The second law efficiency The total unit cost of system products

Parameters

Values

T0 (°C) P0 (bar) T3 (°C) P9 (bar) T9 (°C) T22 (°C) T29 (°C) T37 (°C) Fuel cost ($/GJ)

25 1.013 1247 [25] 74 [7] 32 [7] 25 25 25 4 [30]

the molar mass, critical temperature (Tcr), critical pressure (Pcr), temperature range of applicability, ozone depletion potential (ODP), global warming potential (GWP) and safety group. Table 6 outlines the key input parameters used in the analysis.

results obtained by the present model and those reported by Sahu [3] for the combined gas turbine and steam cycle. Table 4 presents the comparison between the data obtained from present model to that of Wang [22] for the combined S-CO2 and ORC. As shown in Tables 3 and 4, there is a good agreement between the obtained results with the developed model and those reported by the literatures.

4.1. Exergoeconomic analysis The results of exergoeconomic analysis and system improvement recommendations based on exergoeconomic analysis that can provide the reference for system designers are shown in this section. Table 7 shows the system parameters, exergy flow rates, unit exergy costs and cost flow rates for the streams of the proposed cogeneration system. As shown in Table 7, the temperatures of points 4, 5, 6 are 631 °C, 446 °C and 204 °C, which are also the heat source temperatures of S-CO2 cycle, steam power cycle, and ORC, respectively. This also echoes the appropriate heat source temperatures for the three power cycles in the Introduction. The unit exergy costs of power machineries of the gas turbine, S-CO2 cycle, steam power cycle, and ORC are 6.33$/GJ, 12.41$/GJ, 14.43$/GJ and 13.09$/GJ, respectively, indicating that steam power cycle has the highest unit exergy cost among the power cycles. Exergoeconomic parameters for the proposed cogeneration system components are presented in Table 8. As shown in Table 8, the combustion chamber (CC) has the highest values of ED and Z + CD among all the components and has the lowest exergoeconomic factor which indicates that its exergy destruction overwhelms the owning and operating cost. After the combustion chamber, gas turbine (GT) has the highest values of ED and Z + CD. The exergoeconomic factor of GT is 70.49%, indicating that the owning and operating cost dominates the exergy destruction cost. Meanwhile, the GT has a high exergy efficiency

4. Results and analysis The results of exergoeconomic analysis, parametric study, multiobjective optimization and comparative analysis are presented in this section. The key system parameters including pressure ratio of C1 (rp), pressure ratio of S-CO2 cycle (PRc), split ratio of S-CO2 cycle (x), evaporation temperature of steam power cycle (TE), mass fraction of isopentane in the zeotropic mixture (fm), evaporation temperature of ORC (Te) and pinch point temperature difference in the ORC evaporator (ΔTe), which have significant effect on system performance parameters, are selected as the decision variables. The objective functions of the present work are exergy efficiency and total product unit cost. The exergy efficiency represents thermodynamics performance while the total product unit cost represents exergoeconomic performance of the system. ORC uses isopentane/R245fa as working fluid. This zeotropic mixture not only has good thermal properties but also overcomes the disadvantages of R245fa’s GWP and isopentane’s flammability [21]. Table 5 shows the properties of organic working fluids, which include Table 5 Properties of the organic working fluids [23]. Fluids

Isopentane R245fa

Molar mass (g/mol)

72.15 135.05

Tcr (°C)

187.2 154.01

Pcr (MPa)

3.378 3.651

Range of applicability Tmin (°C)

Tmax (°C)

−160.5 −102.1

226.85 166.85

462

ODP

GWP

Safety group

0 0

20 1030

A3 B1

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Table 7 System parameters, exergy flow rates, unit exergy costs and cost flow rates for the streams of the proposed cogeneration system. State

Fluid

T (°C)

P (bar)

m (kg/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 WC1 WGT WC2 WC3 WT1 Wpump1 WT2 Wpump2 WT3

N2, O2, CO2, H2O N2, O2, CO2, H2O N2, O2, CO2, H2O N2, O2, CO2, H2O N2, O2, CO2, H2O N2, O2, CO2, H2O N2, O2, CO2, H2O Methane CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2 Water Water Water Water Water Water Water Water Water Isopentane, R245fa Isopentane, R245fa Isopentane, R245fa Isopentane, R245fa Isopentane, R245fa Isopentane, R245fa Water Water

25 404 1247 631 446 204 81 25 32 110 255 255 416 601 450 271 120 120 255 120 50 25 30 35 35 110 416 35 25 30 30 31 57 130 70 36 25 30

1.01 15.02 14.27 1.10 1.10 1.10 1.10 12.00 74.00 254.57 254.57 254.57 254.57 254.57 74.00 74.00 74.00 74.00 254.57 74.00 74.00 3.00 3.00 0.06 38.19 38.19 38.19 0.06 3.00 3.00 1.68 16.52 16.52 16.52 1.68 1.68 3.00 3.00

55.5, 16.8, 55.5, 16.8, 55.5, 10.2, 55.5, 10.2, 55.5, 10.2, 55.5, 10.2, 55.5, 10.2, 1.6 52.1 52.1 52.1 70.6 70.6 70.6 70.6 70.6 70.6 18.5 18.5 52.1 52.1 171.4 171.4 7.3 7.3 7.3 7.3 7.3 742.7 742.7 17.2, 13 17.2, 13 17.2, 13 17.2, 13 17.2, 13 17.2, 13 394.3 394.3

E (MW)

c ($/GJ)

C ($/s)

0.03, 0.9 0.03, 0.9 4.6, 4.6 4.6, 4.6 4.6, 4.6 4.6, 4.6 4.6, 4.6

0 27.53 85.25 24.40 14.03 3.95 1.21 66.01 11.25 13.39 17.42 23.61 30.95 41.08 28.58 20.95 16.61 4.36 6.20 12.25 11.40 0.03 0.06 0.00 0.03 0.34 8.87 0.58 0.15 0.28 0.20 0.26 0.35 2.52 0.54 0.41 0.08 0.15 29.12 58.61 2.42 2.01 11.95 0.03 7.14 0.07 1.72

0 7.73 5.60 5.60 5.60 5.60 5.60 4 11.00 11.62 11.93 11.91 11.92 11.00 11.00 11.00 11.00 11.00 11.86 11.00 11.00 0 45.14 11.04 23.83 31.14 11.04 11.04 0 35.81 10.26 12.65 16.05 10.26 10.26 10.26 0 33.32 6.33 6.33 12.41 12.41 12.41 14.43 14.43 13.09 13.09

0 0.21 0.48 0.14 0.079 0.022 0.007 0.26 0.12 0.16 0.21 0.28 0.37 0.45 0.31 0.23 0.18 0.048 0.074 0.13 0.13 0 0.003 5E−05 0.0008 0.011 0.10 0.006 0 0.01 0.002 0.003 0.006 0.03 0.006 0.004 0 0.005 0.18 0.37 0.030 0.025 0.15 0.0005 0.10 0.0009 0.02

Table 8 Exergoeconomic parameters for the proposed cogeneration system components. Component

EF (MW)

EP (MW)

ED (MW)

ε%

CD ($/h)

Z ($/h)

Z + CD ($/h)

f (%)

C1 CC GT H1 H2 H3 T1 HTR LTR C2 C3 H4 Cooler1 T2 Cooler2 Pump1 T3 RE Cooler3 Pump2 Overall

29.12 93.54 60.85 10.37 10.07 2.75 12.50 7.64 4.34 2.42 2.01 0.84 0.16 8.30 0.57 0.03 1.99 0.13 0.21 0.07 66

27.53 85.25 58.61 10.13 8.53 2.18 11.95 7.34 4.03 2.14 1.84 0.31 0.03 7.14 0.13 0.03 1.72 0.09 0.07 0.06 45.77

1.59 8.29 2.24 0.24 1.54 0.57 0.55 0.30 0.31 0.28 0.17 0.53 0.13 1.15 0.44 0.01 0.27 0.04 0.14 0.01 20.23

94.54 91.14 96.32 97.70 84.70 79.25 95.57 96.07 92.82 88.29 91.43 36.64 19.13 86.12 22.49 80.66 86.61 69.07 32.83 80.38 69.33

36.22 152.06 45.12 4.81 31.07 11.50 21.89 11.89 12.34 12.68 7.70 21.16 4.97 45.76 17.63 0.35 9.82 1.51 5.16 0.66 454.30

102.59 2.67 107.77 88.52 111.32 17.78 39.13 13.39 16.57 6.31 2.25 2.11 4.23 41.34 12.92 0.80 7.75 3.51 9.94 0.95 591.87

138.81 154.74 152.89 93.32 142.39 29.28 61.03 25.28 28.91 18.99 9.95 23.27 9.20 87.11 30.55 1.15 17.57 5.02 15.10 1.61 1046.17

73.91 1.73 70.49 94.85 78.18 60.73 64.12 52.98 57.33 33.24 22.57 9.07 45.97 47.46 42.28 69.54 44.10 70.00 65.82 59.15 56.58

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exchanger with higher efficiency can improve the exergoeconomic performance. The third lowest value of exergoeconomic factor in the proposed cogeneration system belongs to the C3 which is the recompression compressor of S-CO2 cycle. The Cooler2 and the T3 have the lowest exergoeconomic factor in the components of the steam power cycle and the ORC, respectively. Therefore, employing higher efficiencies components is suggested for exergoeconomic performance enhancement. Opposite to the combustion chamber, the H1 has the highest exergoeconomic factor and exergy efficiency, which is the evaporator of S-CO2 cycle. Therefore, replacing the H1 with another one with a lower purchasing cost at the expense of heat exchanger exergy efficiency can improve the economic performance of the system. The exergoeconomic factor value of the overall cogeneration system is

of 96.32%, indicating that it has high equipment purchasing cost. Therefore, replacing the gas turbine with another one with a lower purchasing cost at the expense of exergy efficiency can improve the economic performance of the system, which can be achieved by lowering the isentropic efficiency. The third highest values of ED and Z + CD in the proposed cogeneration system belong to the H2 which is the evaporator of S-CO2 cycle. The exergy efficiency and exergoeconomic factor of H2 are 84.70% and 78.18%, indicating that the component purchasing cost is higher and therefore a decrease in the purchasing cost of H2 is recommended at the expense of exergy efficiency. The second lowest value of exergoeconomic factor is H4 for which the exergy efficiency is 36.64%, indicating that the exergy destruction cost is dominant. Therefore, employing more expensive heat

Fig. 3. Effects on the system performance parameters of the system design parameters (a) rp, (b) PRc, (c) x, (d) TE, (e) fm, (f) Te, (g) ΔTe. 464

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Table 11 Values of objective and decision variables for points A-C on the Pareto frontier.

Table 9 Decision variables and their lower and upper boundaries. Lower bound

Upper bound

rp PRc [27] x TE mass fraction Te ΔTe

5 2.2 0 100 0 70 5

25 4.2 1 350 1 140 30

Table 10 Main parameters used for the genetic algorithm. Parameters

Values

Population size Crossover fraction Migration fraction Pareto front population fraction Generations size

15 * 7 0.8 0.2 1 100

η (%)

cp,tot

rp

PRc

x

TE (°C)

fm

Te (°C)

ΔTe (°C)

A B C

68.28 69.33 69.75

10.66 10.77 10.95

12.27 14.83 18.02

3.63 3.44 3.47

0.83 0.74 0.72

252.11 247.63 233.71

1 0.57 0.49

129.16 128.73 126.57

15.84 12.98 12.74

effect of the key system design parameters on the system performance parameters. The key system design parameters include pressure ratio of C1 (rp), pressure ratio of S-CO2 cycle (PRc), split ratio of S-CO2 cycle (x), evaporation temperature of steam power cycle (TE), mass fraction of isopentane in the zeotropic mixture (fm), evaporation temperature of ORC (Te) and pinch point temperature difference in the ORC evaporator (ΔTe). In addition, the exergy efficiency of the whole system (η) and total product unit cost (cp,tot) are adopted as the system performance parameters. When analyzing the effect of a particular parameter on system performance, all other parameters remain unchanged. Fig. 3 shows effects on the system performance parameters of the system design parameters. Variation in exergy efficiency and total product unit cost with pressure ratio of C1 (rp) is shown in Fig. 3a. As the pressure ratio of C1 increases, the exergy efficiency first increases rapidly and then tends to grow smoothly. Fig. 3a also indicates that as the rp increases, the total product unit cost decreases at first and then increases, reaching the minimum value when the rp is 12.5. The reason for this is that as the rp increases, the wall thickness of components and the requirements for sealing and manufacturing processes increase, which leads to an increase in cost. Variation in exergy efficiency and total product unit cost with the pressure ratio of S-CO2 cycle (PRc) is shown in Fig. 3b. Fig. 3a and b show that with the increase of rp and PRc, the change trend of the objective function curve is similar. The reason is that the mechanism of the change in system performance caused by the two decision variables is similar. Fig. 3c illustrates the variation of total product unit cost and exergy efficiency with the split ratio of S-CO2 cycle (x). As shown in Fig. 3c, the exergy efficiency curve decreases continuously with the increase in the split ratio. This can be explained as follows: T4 decreases with the increase of the split ratio, resulting in a drop in the mass flow of CO2 under the same heat source conditions, which in turn leads to a decrease in the net work. Fig. 3c also indicates that the value of total product unit cost is minimized at the particular split ratio (x = 0.83). Fig. 3d shows the variation of exergy efficiency and total product unit cost with the evaporation temperature of steam power cycle (TE). As shown in Fig. 3d, as the TE increases, the exergy efficiency increases at first and then decreases, while the total product unit cost decreases first and then increases. Exergy efficiency and total product unit cost have optimum values when the TE is equal to 250 °C and 260 °C, respectively. The reason for this is that as the TE increases, the thermal efficiency of the steam power cycle and the outlet temperature of the exhaust increase at the same time, resulting in the net work increasing at first and then decreasing. The variation of exergy efficiency and total product unit cost with the mass fraction of isopentane in the zeotropic mixture (fm) is presented in Fig. 3e. Referring to Fig. 3e, exergy efficiency and total product unit cost have optimum values when the fm is 0.1 and 1, respectively. This illustrates that isopentane/R245fa (0.1/0.9) has the highest thermal efficiency while isopentane/R245fa (1/0) has the lowest total product unit cost. Fig. 3f illustrates the variation of exergy efficiency and total product unit cost with the evaporation temperature of ORC (Te). The exergy efficiency increases first and then decreases, reaching a maximum value when the Te is 118 °C. The total product unit cost decreases first and then increases, reaching a minimum value when the Te is 130 °C. Fig. 3g represents the variation of exergy efficiency and total product unit cost with pinch point temperature difference in the ORC evaporator (ΔTe). As shown in Fig. 3g, the curve of exergy efficiency has

Fig. 3. (continued)

Decision variables

Point

Fig. 4. Pareto frontier of total product unit cost with exergy efficiency.

56.58%, indicating that 43.42% of the cogeneration system cost is associated with the exergy destruction. 4.2. Parametric study Parametric study is conducted in this section to investigate the 465

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the negative slope as with ΔTe increases. Fig. 3g also indicates that the total product unit cost decreases at first and then increases with the increase of ΔTe and has the minimum value when the ΔTe is 18 °C. The reason for this trend is that the reduction of pinch point temperature

difference in the heat exchanger would increase the net power, but this will also lead to an increase in the area of the heat exchanger and thus increase the cost. Therefore, it can be concluded that the optimal thermodynamic

Fig. 5. Scatter distribution of decision variables with population: (a) rp, (b) PRc, (c) x, (d) TE, (e) fm, (f) Te, (g) ΔTe.

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where X is the vector of decision variables to be optimized which are the key system design parameters; F(X) and f(X) denote the multi-objective function vector and single-objective function, respectively; gj(X) and hk(X) are the inequality constraints and equality constraints, respectively. The method used for solving the multi-objective optimization problem in this paper is the genetic algorithm (GA) which imitates the principle of biological evolution and uses iterative random search strategy to find the optimal solution [32]. The goal of multi-objective optimization is to obtain Pareto frontier solutions which are nondominant optimization solutions. In order to further obtain the optimum design point amongst the Pareto front solutions, TOPSIS [28] (Technique for Order Preference by Similarity to Ideal Situation) decision making is applied. TOPSIS defines the ideal point where each objective has its optimum value and the non-ideal point where each objective has its worst value. The ideal point and the non-ideal point don’t locate on the Pareto frontier. The final optimal point has the minimum distance from the ideal point and the maximum distance from the non-ideal point. In the optimization process, the values of decision variables must be within a reasonable range. The lower and upper boundaries of decision variables are listed in Table 9. Table 10 outlines the main parameters used for the genetic algorithm. Referring to Table 10, the population size uses the default value, which is 15×(number of decision variables). Fig. 4 shows the scattered distribution of Pareto frontier of total product unit cost with exergy efficiency. Referring to Fig. 4, the total product unit cost increases with the increase of exergy efficiency, indicating the apparent trade-off between exergoeconomic performance and thermodynamic performance. As shown in Fig. 4, the minimum total product unit cost (10.66$/GJ) exists at point A, while the exergy efficiency (68.28%) is also the minimum at this point. In contrast, the maximum exergy efficiency (69.75%) occurs at point C, while total product unit cost (10.95$/GJ) is also the maximum at this point. Therefore, point C is the optimal solution when exergy efficiency is the single objective function, on the other hand, point A is the optimal solution when total product unit cost is the single objective function. In the multi-objective optimization process, in order to obtain the final optimal solution, it is necessary to use the ideal point that simultaneously has the maximum exergy efficiency and the minimum total product unit cost. The ideal point does not locate on the Pareto frontier

Fig. 5. (continued)

(exergy efficiency) and exergoeconomic (total product unit cost) performance are achieved with different decision variables including rp, PRc, x, TE, fm, Te and ΔTe. 4.3. Multi-objective optimization According to the previous parametric study, there is no set of key system design parameters that can simultaneously satisfy the maximization of exergy efficiency and the minimization of the total product unit cost. Multi-objective optimization has been widely used to simultaneously minimize or maximize multiple objective functions, which can be expressed as follows [31]:

min F (X ) = [f1 (X ), f2 (X ), f3 (X ). ..fm (X )]T

(32)

Subject to

gj (X ) ⩽ 0, j = 1, ...,J hk (X ) = 0, k = 1, ...,K

Fig. 6. Configuration of the gas turbine combined with S-CO2 cycle and steam power cycle (system VV). 467

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Fig. 7. Configuration of the gas turbine combined with S-CO2 cycle and ORC (system VI).

Fig. 8. Configuration of the gas turbine combined with steam power cycle and ORC (system VII).

as shown in Fig. 4. According to TOPSIS decision making, the final optimal solution is the closest point to the ideal point, which is marked with point B. The exergy efficiency and total product unit cost of point B are 69.33% and 10.77$/GJ, respectively. Table 11 outlines the values of objective functions and decision variables for points A-C on the Pareto frontier. Fig. 5 shows the scatter distribution of decision variables with the population. The area surrounded by the dotted red line is the scope of the decision variable. As shown in Fig. 5a, the optimal pressure ratio range of C1 (rp) is 12.2–18. Fig. 5 also indicates that the optimal pressure ratio (PRc) and the split ratio (x) of S-CO2 cycle locate in the range of 3.43–3.64 and 0.71–0.83, respectively. The optimal evaporation temperature of steam power cycle (TE) locates in the range of 233.7–252.2 °C as shown in Fig. 5d. It also can be observed in Fig. 5 that the optimal mass fraction of isopentane, evaporation temperature and

pinch point temperature difference of ORC locate in the range of 0.49–1, 126.6–129.6 °C and 12.5–15.9 °C, respectively. 4.4. Comparative analysis The comparison between the proposed cogeneration system and other forms of power generation systems is carried out in this section. According to different layout configurations of bottoming cycles, there are several types of power generation: stand-alone gas turbine power generation (system I), gas turbine combined with S-CO2 cycle (system II), traditional gas-steam combined power generation (system III), gas turbine combined with ORC (system IV), gas turbine combined with SCO2 cycle and steam power cycle (system V), gas turbine combined with S-CO2 cycle and ORC (system VI), gas turbine combined with steam power cycle and ORC (system VII). System I is a simple gas 468

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namely system V, system VI and system VII. The Schematic diagrams of system V, system VI and system VII are shown in Figs. 6, Fig. 7 and Fig. 8, respectively. In order to effectively compare the proposed cogeneration system and other seven forms of power generation systems, similar optimizations are performed for the other systems described above. The optimization results are shown in Fig. 9. The apparent trade-off between exergoeconomic performance and thermodynamic performance of these seven systems is similar to that of the proposed cogeneration system which is shown in Fig. 4. The maximum exergy efficiency and

turbine power generation system without a waste heat recovery. System II, system III and system IV use the S-CO2 recompression cycle, the steam power cycle, and ORC as the bottoming cycle of the gas turbine, respectively. System V uses the combined S-CO2 cycle and steam power cycle as the bottom cycle of the gas turbine for recovering the waste heat of the gas turbine. System VI employs the combined S-CO2 cycle and ORC as the bottom cycle of gas turbine. System VII adopts the combined steam power cycle and ORC as the bottom cycle of gas turbine. Since the first four system configurations are relatively simple, this section only gives the schematic diagrams of the last three systems,

Fig. 9. Pareto frontier of total product unit cost with exergy efficiency for (a) system I, (b) system II, (c) system III, (d) system IV, (e) system V, (f) system VI, (g) system VII. 469

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5. Conclusion A novel cogeneration system including a gas turbine, a supercritical CO2 recompression cycle, a steam power cycle and an ORC is proposed. Detailed thermodynamic analysis, exergoeconomic analysis and parametric studies are successfully performed for the cogeneration system. The optimum system parameters are obtained through the multi-objective optimization method based on the GA and TOPSIS decision making. The main conclusions are drawn below: (1) The exergoeconomic analysis results show that the unit exergy costs of power machineries of the gas turbine, S-CO2 cycle, steam power cycle, and ORC are 6.33$/GJ, 12.41$/GJ, 14.43$/GJ and 13.09$/ GJ, respectively. Furthermore, the exergoeconomic factor value for the overall cogeneration system is 56.58%, indicating that 43.42% of the cogeneration system cost is associated with the exergy destruction. (2) Parametric studies indicate that optimal exergy efficiency and total product unit cost are achieved with different decision variables. The optimal exergy efficiency and total product unit cost obtained by the multi-objective optimization method are 69.33% and 10.77$/ GJ. The corresponding decision variables including pressure ratio of C1 (rp), pressure ratio of S-CO2 cycle (PRc), split ratio of S-CO2 cycle (x), evaporation temperature of steam power cycle (TE), mass fraction of isopentane in the zeotropic mixture (fm), evaporation temperature of ORC (Te) and pinch point temperature difference in the ORC evaporator (ΔTe) are 14.83, 3.44, 0.74, 247.63 °C, 0.57, 128.73 °C and 12.98 °C, respectively. (3) The comparative analysis reveals the superiorities of the proposed novel cogeneration system to other seven forms of power generation systems. The exergy efficiency and total product unit cost of the proposed cogeneration system increased and decreased by 43.29% and 18.24% compared with that of the stand-alone gas turbine power generation system, respectively.

Fig. 9. (continued)

Fig. 10. Comparison of performance parameters of different systems.

References the minimum total product unit cost of the system I, system II, system III, system IV, system V, system VI and system VII are (49.31%, 13.08$/ GJ), (61.43%, 11.53$/GJ), (68.32%, 11.18$/GJ), (58.78%, 11.63$/ GJ), (67.75%, 10.83$/GJ), (63.84%, 10.96$/GJ), (69.51%, 11.17$/ GJ), respectively. In addition, the optimal exergy efficiency and total product unit cost of the system I, system II, system III, system IV, system V, system VI and system VII are (48.38%, 13.17$/GJ), (60.54%, 11.65$/GJ), (67.75%, 11.25$/GJ), (57.92%, 11.75$/GJ), (67.43%, 11.04$/GJ), (63.48%, 11.06$/GJ), (68.84%, 11.25$/GJ), respectively. In order to display the comparison results more intuitively, the performance parameters including exergy efficiency and total product unit cost of the proposed cogeneration system are set to 1, and the performance parameters of the other seven systems are given in accordance with the proportion of the proposed cogeneration system, as shown in Fig. 10. The system 0 in Fig. 10 refers to the novel proposed cogeneration system. According to Fig. 10, the exergy efficiency of the proposed cogeneration system is higher than other systems while the total product unit cost of the proposed cogeneration system is lower than other systems. The exergy efficiency and total product unit cost of the proposed cogeneration system increased and decreased by 43.29% and 18.24% compared with that of the stand-alone gas turbine power generation system (system I), respectively. In addition, the exergy efficiency and total product unit cost of the proposed cogeneration system increased and decreased by 2.33% and 4.26% compared with that of the traditional gas-steam combined power generation system (system III), respectively. Therefore, the superiority of the proposed cogeneration system is verified through comparison.

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