# Realistic Energy, Exergy, and Exergoeconomic (3E) Characterization of a Steam Power Plant: Multi-Criteria Optimization Case Study of Mashhad Tous Power Plant

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## Abstract

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## 1. Introduction

_{2}emissions. Mohammadpour et al. [15] performed an energy and exergy (2E) analysis for an oxy-fuel regenerative gas turbine. They considered two distinct streams for CO

_{2}, including primary and dilution. The highest exergy destruction in the system happens in the combustion chamber. In another investigation, Abuelnuor et al. [16] applied fundamental 2E thermodynamic analysis in a 180 MW combined power plant in Khartoum. The energy and exergy efficiency of the power plant were 38% and 49%. Bai et al. and Yan et al. [17,18] tried to investigate the performance of coal-fired power plants based on 2E thermodynamic analyses. The former study reported 1.046% exergy efficiency increase after enhancing the recompression supercritical CO

_{2}cycle; the total exergy, energy, and power efficiency were 53.41%, 94.68%, and 48.06%. The latter work simulated the integration of a trough collector system in a coal-fired power plant with a nominal electricity output of 660 MW. The exergy efficiency of the combined system highly depends on daily solar irradiance. With 300 $\mathrm{W}\xb7{\mathrm{m}}^{-2}$ variations in the solar intensity, the exergy efficiency fluctuates from about 33% to 57%. In [19], a geothermal power plant accompanied by non-condensable gases in two distinct site conditions, including subcritical and supercritical, was analytically investigated. The exergy efficiencies of the subcritical and supercritical modes were 50.5% and 52%, respectively. They concluded that turbine inlet pressure has an indirect relation with the exergy performance of the supercritical cycle, while the subcritical cycle’s performance first increases and then reduces. The analysis reveals the levelized cost of energy for the subcritical and supercritical systems by 5.52 $\mathrm{EUR}\xb7\mathrm{KW}{\mathrm{h}}^{-1}$ and 6.96 $\mathrm{EUR}\xb7\mathrm{KW}{\mathrm{h}}^{-1}$, respectively. Elhelw and Al Dahma [20] studied the exergetic performance of the new Abu Qir thermal steam power plant in Alexandria with 650 MW nominal output power. The investigation was divided into full and half loads. The exergy destruction share of the boiler, turbine, and condenser is 75%, 15%, and 6%, respectively. The half load’s exergy destruction for the same devices in order is 78%, 14%, and 5%. Khaleel et al. [21] studied the energy and exergy performance of a steam coal-fired power plant. The sensitivity analysis of the superheater pressure and temperature was investigated. Doubling the superheater pressure leads to enhanced net power output by about 8%. The superheater temperature had the same trend. Increasing the steam temperature from 539.8 to 580 °C, the net power increases by 6%. The overall energy and exergy efficiencies of this 589.47 MW power plant are 30.41% and 62.20%, respectively. Ahmadi et al. [22] used energy, exergy, and exergoenvironmental analyses to evaluate the performance of a CHP power plant in Isfahan Petrochemical Complex, Iran. The complex aims to generate Benzene, Orthoxylene, Toluene, and Xylene. The CHP’s net power is about 18 MW. The energy and exergy efficiency of the plant are 8.22% and 7.87%. The boiler possesses the highest exergy destruction rate at 65,571 kW. Adnan et al. [23] delved into two waste fuel power plants in two cities in Bangladesh. Taking 3 million metric tons (MMT) of municipal solid waste, Dhaka’s power plant’s net power is 169 MW, and Chattogram’s output is 83 MW. The environmental analysis shows that burning solid waste curbed carbon emissions by about 1 MMT for Dhaka and 0.5 MMT for Chattogram. Hao et al. [24] conducted an energy and exergy analysis, along with an economic exergy analysis, of Huadian Kemen Power Plant based on its operational efficiency and its impact on the discharged heat to the surrounding environment. Their findings indicated that the construction of heat-retaining and -diversion facilities within the power plant reduced the intake water temperature and improved heat distribution, although regions with higher temperatures also experienced an increase.

- Utilizing energy, exergy, and ecoexergy equations for the Tous power plant;
- Optimizing effective parameters through a multi-objective optimization method;
- The best ambient temperature has been selected based on exergy efficiency, work, and capital cost under various loads;
- Employing experimental results for the validation and modeling of a power plant.

## 2. Materials and Methods

#### 2.1. Mashhad Tous Power Plant Topology

#### 2.2. Thermodynamic Modeling

#### 2.2.1. Energy and Exergy Analysis

#### 2.2.2. Exergoeconomic Analysis

#### 2.3. Multi-Criteria Optimization

## 3. Results

#### 3.1. Validation

#### 3.2. Energy and Exergy Results

#### 3.3. Exergoeconomic Results

#### 3.4. Optimization Results

## 4. Conclusions

- Ambient temperature has a greater impact on intermediate and low loads compared to high loads;
- In optimal conditions, the highest exergy efficiency of 42.15% occurs at the intermediate heat load;
- The power plant’s output at a high thermal load stands at 145 MW, and after optimization this value escalates to 151 MW;
- The greatest improvement in power plant output is 16.37% for low thermal loads.
- The lowest cost reduction is related to the intermediate thermal load.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

c | cost per exergy (USD∙${\mathrm{k}\mathrm{J}}^{-1}$) |

${\dot{\mathrm{Ex}}}_{\mathrm{D}}$ | exergy destruction ($\mathrm{kW}$) |

ex | specific exergy ($\mathrm{kJ}\xb7{\mathrm{kg}}^{-1}$) |

i | interest |

$\dot{\mathrm{m}}$ | mass flow rate ($\mathrm{kg}\xb7{\mathrm{s}}^{-1}$) |

n | operating years |

P | pressure ($\mathrm{MPa}$) |

$\dot{\mathrm{Q}}$ | heating power ($\mathrm{kW}$) |

s | specific entropy ($\mathrm{kJ}\cdot {\mathrm{kg}}^{-1}\xb7{\mathrm{K}}^{-1}$) |

h | specific enthalpy ($\mathrm{kJ}\cdot {\mathrm{kg}}^{-1}$) |

T | temperature (°C) |

$\dot{\mathrm{W}}$ | shaft power ($\mathrm{kW}$) |

Z | purchase cost of the component ($\mathrm{USD}$) |

Subscripts | |

b | boiler |

c | condenser |

en | energy |

ex | exergy |

in | inlet |

out | outlet |

RSH | re-super heat |

SH | super heat |

Greek letters | |

$\mathsf{\psi}$ | calorific value of fuel ($\mathrm{kW}\cdot \mathrm{k}{\mathrm{g}}^{-1}$) |

${\mathsf{\eta}}_{\mathrm{t}\mathrm{h}}$ | energy efficiency |

${\mathsf{\eta}}_{\mathrm{e}\mathrm{x}}$ | exergy efficiency |

$\gamma $ | maintenance factor |

$\tau $ | operating hour per year |

Acronyms | |

HPH | high-pressure heater |

LPT | high-pressure turbine |

IPT | intermediate-pressure turbine |

LPH | low-pressure heater |

BFP | boiler feed pump |

CRF | capital recovery factor |

CI | capital investment |

OM | operating and maintenance |

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**Figure 6.**Variation in total exergy destruction with HP turbine inlet pressure (

**A**) and ambient temperature (

**B**).

**Figure 11.**Work output, exergy efficiency, and cost analysis for different heat loads before and after optimization.

Operating Conditions | Value |
---|---|

Power produced | 150 ($\mathrm{MW}$) |

Mass flow rate of fuel | 39.8 ($\mathrm{N}\xb7{\mathrm{m}}^{3}\xb7{\mathrm{h}}^{-1}$) |

Stack flue gas temperature | 110 (°C) |

Steam temperature, main line | 540 (°C) |

Steam flow rate, main line | 520 ($\mathrm{Ton}\cdot {\mathrm{h}}^{-1}$) |

Number of induced and draft fans | 2 |

Number of burners | 9 |

Pump/motor efficiency | 95% |

Points | $\mathbf{T}\text{}\mathbf{\left(}\mathbf{\xb0C}\mathbf{\right)}$ | $\mathbf{P}\text{}\mathbf{\left(}\mathbf{MPa}\mathbf{\right)}$ | $\dot{\mathbf{m}}$$\text{}\mathbf{(}\mathbf{kg}\cdot {\mathbf{s}}^{-1}\mathbf{)}$ | $\mathbf{h}\text{}\mathbf{(}\mathbf{kJ}\cdot \mathbf{k}{\mathbf{g}}^{-1}\mathbf{)}$ | $\mathbf{s}\text{}\mathbf{(}\mathbf{kJ}\cdot \mathbf{k}{\mathbf{g}}^{-1}\cdot {\mathbf{K}}^{-1}\mathbf{)}$ | $\mathbf{ex}$$\text{}\mathbf{\left(}\mathbf{kJ}\xb7\mathbf{k}{\mathbf{g}}^{-1}\mathbf{\right)}$ |
---|---|---|---|---|---|---|

1 | 243 | 13.684 | 145 | 1053 | 2.707 | 889.3 |

2 | 538 | 12.919 | 145.1 | 3439 | 6.571 | 3179 |

3 | 355 | 3.633 | 145.1 | 3113 | 6.656 | 2851 |

4 | 353 | 3.627 | 10.1 | 3108 | 6.649 | 2846 |

5 | 353 | 3.544 | 132.1 | 3110 | 6.662 | 2848 |

6 | 538 | 3.239 | 135 | 3540 | 7.304 | 3261 |

7 | 452 | 1.804 | 7.6 | 3365 | 7.341 | 3085 |

8 | 356 | 0.837 | 7.44 | 3173 | 7.407 | 2892 |

9 | 244 | 0.3201 | 8.01 | 2954 | 7.461 | 2672 |

10 | 226 | 0.2686 | 110 | 2920 | 7.473 | 2637 |

11 | 128 | 0.09225 | 4.7 | 2733 | 7.545 | 2449 |

12 | 65 | 0.02482 | 99 | 2618 | 7.833 | 2326 |

13 | 63 | 0.05572 | 112.5 | 263.7 | 0.8687 | 146.3 |

14 | 65 | 0.056 | 113.3 | 272.1 | 0.8935 | 154.1 |

15 | 66 | 1.358 | 113.3 | 277.4 | 0.9051 | 159.1 |

16 | 67.5 | 1.317 | 113.3 | 283.6 | 0.9236 | 164.8 |

17 | 69.7 | 1.2 | 113.3 | 292.7 | 0.9506 | 173.3 |

18 | 95 | 0.08825 | 12.8 | 398 | 1.25 | 271.1 |

19 | 92.5 | 1.114 | 113.3 | 388.3 | 1.221 | 262.1 |

20 | 134 | 0.3157 | 8.01 | 563.5 | 1.677 | 425.9 |

21 | 134 | 0.08825 | 7.7 | 2745 | 7.596 | 2460 |

22 | 132 | 1.280 | 113.3 | 555.6 | 1.655 | 418.6 |

23 | 170 | 0.8374 | 133 | 719.3 | 2.042 | 572.6 |

24 | 173.5 | 17.732 | 133 | 743.9 | 2.055 | 596.8 |

25 | 178.5 | 1.753 | 17.1 | 757 | 2.124 | 608.3 |

26 | 178 | 1.540 | 17.09 | 754.7 | 2.119 | 606.1 |

27 | 207 | 15.401 | 133.7 | 889.3 | 2.375 | 734.3 |

28 | 212 | 3.527 | 10.3 | 907.3 | 2.441 | 750.6 |

29 | 207 | 1.752 | 10.13 | 2799 | 6.395 | 2544 |

**Table 3.**Equipment energy and exergy equations [28].

Equipment | Energy and Exergy Formula |
---|---|

Boiler | ${\dot{\mathrm{Q}}}_{\mathrm{Boiler}}={\dot{\mathrm{m}}}_{1}\left({\mathrm{h}}_{2}-{\mathrm{h}}_{1}\right)+{\dot{\mathrm{m}}}_{5}\left({\mathrm{h}}_{6}-{\mathrm{h}}_{5}\right)$ ${\dot{\mathrm{Q}}}_{\mathrm{fuel}}={\dot{\mathrm{m}}}_{\mathrm{fuel}}\xb7{\mathsf{\psi}}_{\mathrm{fuel}}$ ${\mathsf{\eta}}_{\mathrm{en},\text{}\mathrm{Boiler}}=\frac{{\dot{\mathrm{m}}}_{1}\left({\mathrm{h}}_{2}-{\mathrm{h}}_{1}\right)+{\dot{\mathrm{m}}}_{5}\left({\mathrm{h}}_{6}-{\mathrm{h}}_{5}\right)}{{\dot{\mathrm{Q}}}_{\mathrm{fuel}}}$ ${\mathsf{\eta}}_{\mathrm{ex},\text{}\mathrm{Boiler}}=\frac{{\dot{\mathrm{m}}}_{1}\left({\mathrm{ex}}_{2}-{\mathrm{ex}}_{1}\right)+{\dot{\mathrm{m}}}_{5}\left({\mathrm{ex}}_{6}-{\mathrm{ex}}_{5}\right)}{{\dot{\mathrm{Q}}}_{\mathrm{fuel}}\left(1-\frac{{\mathrm{T}}_{0}}{{\mathrm{T}}_{\mathrm{b}}}\right)}$ |

Turbine | ${\dot{\mathrm{W}}}_{\mathrm{Turbine},\text{}\mathrm{hp}}={\dot{\mathrm{m}}}_{2}\left({\mathrm{h}}_{2}-{\mathrm{h}}_{3}\right)$ ${\mathsf{\eta}}_{\mathrm{en},\text{}\mathrm{Turbine},\text{}\mathrm{hp}}=\frac{{\dot{\mathrm{W}}}_{\mathrm{turbine},\text{}\mathrm{hp}}}{{\dot{\mathrm{m}}}_{2}\left({\mathrm{h}}_{2}-{\mathrm{h}}_{3}\right)}$ ${\mathsf{\eta}}_{\mathrm{ex},\text{}\mathrm{Turbine},\text{}\mathrm{hp}}=\frac{{\dot{\mathrm{W}}}_{\mathrm{turbine},\text{}\mathrm{hp}}}{{\dot{\mathrm{m}}}_{2}\left({\mathrm{ex}}_{2}-{\mathrm{ex}}_{3}\right)}$ $\mathrm{E}{\mathrm{x}}_{\mathrm{D},\text{}\mathrm{Turbine},\text{}\mathrm{hp}}={\dot{\mathrm{m}}}_{2}\left({\mathrm{ex}}_{2}-{\mathrm{ex}}_{3}\right)-{\dot{\mathrm{W}}}_{\mathrm{Turbine},\text{}\mathrm{hp}}$ |

Condenser | ${\dot{\mathrm{Q}}}_{\mathrm{Condenser}}={\dot{\mathrm{m}}}_{12}\left({\mathrm{h}}_{12}-{\mathrm{h}}_{13}\right)$ $\mathrm{E}{\mathrm{x}}_{\mathrm{D},\text{}\mathrm{Condenser}}={\dot{\mathrm{m}}}_{12}\left({\mathrm{ex}}_{12}-{\mathrm{ex}}_{13}\right)-{\dot{\mathrm{Q}}}_{\mathrm{Condenser}}\left(1-\frac{{\mathrm{T}}_{0}}{{\mathrm{T}}_{\mathrm{c}}}\right)$ |

BFP | ${\dot{\mathrm{W}}}_{\mathrm{BFP}}={\dot{\mathrm{m}}}_{23}\left({\mathrm{h}}_{24}-{\mathrm{h}}_{23}\right)$ ${\mathsf{\eta}}_{\mathrm{en},\text{}\mathrm{BFP}}=\frac{{\dot{\mathrm{m}}}_{23}\left({\mathrm{h}}_{24}-{\mathrm{h}}_{23}\right)}{{\dot{\mathrm{W}}}_{\mathrm{BFP}}}$ ${\mathsf{\eta}}_{\mathrm{ex},\text{}\mathrm{BFP}}=\frac{{\dot{\mathrm{m}}}_{23}\left({\mathrm{ex}}_{23}-{\mathrm{ex}}_{24}\right)}{{\dot{\mathrm{W}}}_{\mathrm{BFP}}}$ |

Pump_{cond} | ${\dot{\mathrm{W}}}_{{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}={\dot{\mathrm{m}}}_{14}\left({\mathrm{h}}_{15}-{\mathrm{h}}_{14}\right)$ ${\mathsf{\eta}}_{\mathrm{en},\text{}{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}=\frac{{\dot{\mathrm{m}}}_{14}\left({\mathrm{h}}_{15}-{\mathrm{h}}_{14}\right)}{{\dot{\mathrm{W}}}_{{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}}$ ${\mathsf{\eta}}_{\mathrm{ex},\text{}{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}=\frac{{\dot{\mathrm{m}}}_{14}\left({\mathrm{ex}}_{15}-{\mathrm{ex}}_{14}\right)}{{\dot{\mathrm{W}}}_{{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}}$ |

Deaerator | ${\mathsf{\eta}}_{\mathrm{en},\text{}\mathrm{Deaerator}}=\frac{{\dot{\mathrm{m}}}_{23}{\mathrm{h}}_{23}}{{\dot{\mathrm{m}}}_{8}{\mathrm{h}}_{8}+{\dot{\mathrm{m}}}_{22}{\mathrm{h}}_{22}+{\dot{\mathrm{m}}}_{26}{\mathrm{h}}_{26}}$ ${\mathsf{\eta}}_{\mathrm{ex},\text{}\mathrm{Deaerator}}=\frac{{\dot{\mathrm{m}}}_{23}{\mathrm{ex}}_{23}}{{\dot{\mathrm{m}}}_{8}{\mathrm{ex}}_{8}+{\dot{\mathrm{m}}}_{22}{\mathrm{ex}}_{22}+{\dot{\mathrm{m}}}_{26}{\mathrm{ex}}_{26}}$ $\mathrm{E}{\mathrm{x}}_{\mathrm{D},\text{}\mathrm{Deaerator}}={\dot{\mathrm{m}}}_{8}{\mathrm{ex}}_{8}+{\dot{\mathrm{m}}}_{22}{\mathrm{ex}}_{22}+{\dot{\mathrm{m}}}_{26}{\mathrm{ex}}_{26}-{\dot{\mathrm{m}}}_{23}{\mathrm{ex}}_{23}$ |

Component | Cost Function |
---|---|

Boiler | ${\mathrm{Z}}_{\mathrm{Boiler}}={\mathrm{a}}_{1}{\left({\dot{\mathrm{m}}}_{1}\right)}^{{\mathrm{a}}_{2}}{\mathsf{\beta}}_{\mathrm{p}}{\mathsf{\beta}}_{\mathrm{T}}{\mathsf{\beta}}_{\mathsf{\eta}}{\mathsf{\beta}}_{\mathrm{SH}/\mathrm{RSH}}$ |

${\mathsf{\beta}}_{\mathrm{p}}=\mathrm{exp}\left(\frac{{\mathrm{P}}_{2}-{\stackrel{\mathrm{-}}{\mathrm{P}}}_{\mathrm{e}}}{{\mathrm{a}}_{3}}\right)$, ${\mathsf{\beta}}_{\mathrm{T}}=1+{\mathrm{a}}_{5}\mathrm{exp}\left(\frac{{\mathrm{T}}_{2}-{\stackrel{\mathrm{-}}{\mathrm{T}}}_{\mathrm{e}}}{{\mathrm{a}}_{6}}\right)$, ${\mathsf{\beta}}_{\mathrm{eta}}=1+{\left(\frac{1-{\stackrel{\mathrm{-}}{\mathsf{\eta}}}_{1}}{1-{\mathsf{\eta}}_{1}}\right)}^{{\mathrm{a}}_{4}}$ | |

${\mathsf{\beta}}_{\mathrm{SH}/\mathrm{RSH}}=1+\frac{{\mathrm{T}}_{2}-{\mathrm{T}}_{1}}{{\mathrm{T}}_{2}}+\frac{{\dot{\mathrm{m}}}_{6}}{{\dot{\mathrm{m}}}_{1}}\frac{{\mathrm{T}}_{6}-{\mathrm{T}}_{5}}{{\mathrm{T}}_{6}}$ | |

${\stackrel{\mathrm{-}}{\mathrm{T}}}_{\mathrm{e}}=593\text{}(\xb0\mathrm{C})$, ${\stackrel{\mathrm{-}}{\mathrm{P}}}_{\mathrm{e}}=28\text{}\left(\mathrm{bar}\right)$, ${\stackrel{-}{\mathsf{\eta}}}_{1}=0.9$, ${\mathrm{a}}_{1}=\mathrm{208,582}\text{}(\$\cdot \mathrm{k}{\mathrm{g}}^{-1}\cdot {\mathrm{s}}^{-1})$ | |

${\mathrm{a}}_{2}=0.8$, ${\mathrm{a}}_{3}=150\text{}\left(\mathrm{bar}\right)$, ${\mathrm{a}}_{4}=7$, ${\mathrm{a}}_{5}=5$, ${\mathrm{a}}_{6}=10.42\text{}(\xb0\mathrm{C})$ | |

Turbine | ${\mathrm{Z}}_{\mathrm{Turbine}}={\mathrm{a}}_{7}{\dot{\mathrm{W}}}_{\mathrm{Turbine}}^{0.7}\left(1+{\left(\frac{0.05}{1-{\mathsf{\eta}}_{\mathrm{Turbine}}}\right)}^{3}\right)\left(1+5\mathrm{exp}\left(\frac{{\mathrm{T}}_{\mathrm{in}}-866\text{}{\mathrm{K}}^{-1}}{10.42\text{}{\mathrm{K}}^{-1}}\right)\right)$ |

${\mathrm{a}}_{7}=3880.5\text{}(\$\cdot \mathrm{k}{\mathrm{W}}^{-0.7})$ | |

Condenser | ${\mathrm{Z}}_{\mathrm{Condenser}}=1773{\dot{\mathrm{m}}}_{12}$ |

BFP/Pump_{cond} | ${\mathrm{Z}}_{\mathrm{Pump}}=705.48{\dot{\mathrm{W}}}_{\mathrm{Pump}}^{0.71}\left(1+\left(\frac{0.2}{1-{\mathsf{\eta}}_{\mathrm{Pump}}}\right)\right)$ |

Deaerator | ${\mathrm{Z}}_{\mathrm{Deaerator}}={\mathrm{a}}_{8}{\dot{\mathrm{m}}}_{22}^{{\mathrm{a}}_{9}}$ |

${\mathrm{a}}_{8}=\mathrm{143,315}\text{}(\$\cdot \mathrm{k}{\mathrm{W}}^{-0.7})$, ${\mathrm{a}}_{9}=0.7$ | |

Heaters (LPH1, LPH2, HPH1, HPH2, HE1, and HE2) | ${\mathrm{Z}}_{\mathrm{Heater}}=2020\times 3.3\mathrm{Q}{\left(\frac{1}{{\mathrm{T}}_{\mathrm{D}}}\right)}^{0.1}{\left(10\u2206{\mathrm{P}}_{\mathrm{t}}\right)}^{-0.08}{\left(10\u2206{\mathrm{P}}_{\mathrm{s}}\right)}^{-0.04}$ |

**Table 5.**Cost balance and auxiliary equations [35].

Component | Equation |
---|---|

Boiler | ${\mathrm{c}}_{\mathrm{fuel}}{\dot{\mathrm{Ex}}}_{\mathrm{fuel}}+{\mathrm{Z}}_{\mathrm{Boiler}}={\mathrm{c}}_{2}{\dot{\mathrm{Ex}}}_{2}-{\mathrm{c}}_{1}{\dot{\mathrm{Ex}}}_{1}+{\mathrm{c}}_{6}{\dot{\mathrm{Ex}}}_{6}-{\mathrm{c}}_{5}{\dot{\mathrm{Ex}}}_{5}$ |

${\mathrm{c}}_{6}={\mathrm{c}}_{2}$ | |

Turbine | ${\mathrm{c}}_{2}{\dot{\mathrm{Ex}}}_{2}-{\mathrm{c}}_{4}{\dot{\mathrm{Ex}}}_{4}-{\mathrm{c}}_{5}{\dot{\mathrm{Ex}}}_{5}+{\dot{\mathrm{Z}}}_{\mathrm{Turbine}}={\mathrm{c}}_{\mathrm{Work}}{\dot{\mathrm{Ex}}}_{\mathrm{Work},\text{}\mathrm{Turbine}}$ |

${\mathrm{c}}_{4}={\mathrm{c}}_{2}$, ${\mathrm{c}}_{5}={\mathrm{c}}_{2}$ | |

Condenser | ${\mathrm{c}}_{12}{\dot{\mathrm{Ex}}}_{12}+{\dot{\mathrm{Z}}}_{\mathrm{condenser}}={\mathrm{c}}_{13}{\dot{\mathrm{Ex}}}_{13}$ |

${\mathrm{c}}_{13}={\mathrm{c}}_{14}$ | |

BFP | ${\mathrm{c}}_{23}{\dot{\mathrm{Ex}}}_{23}+{\dot{\mathrm{Z}}}_{\mathrm{BFP}}+{\mathrm{c}}_{\mathrm{work}}{\dot{\mathrm{Ex}}}_{\mathrm{Work},\text{}\mathrm{BFP}}={\mathrm{c}}_{24}{\dot{\mathrm{Ex}}}_{24}$ |

Pump_{cond} | ${\mathrm{c}}_{14}{\dot{\mathrm{Ex}}}_{14}+{\dot{\mathrm{Z}}}_{{\mathrm{P}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}+{\mathrm{c}}_{\mathrm{work}}{\dot{\mathrm{Ex}}}_{\mathrm{Work},\text{}{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}}={\mathrm{c}}_{15}{\dot{\mathrm{Ex}}}_{15}$ |

Deaerator | ${\mathrm{c}}_{8}{\dot{\mathrm{Ex}}}_{8}+{\mathrm{c}}_{26}{\dot{\mathrm{Ex}}}_{26}-{\mathrm{c}}_{23}{\dot{\mathrm{Ex}}}_{23}+{\dot{\mathrm{Z}}}_{\mathrm{Deaerator}}={\mathrm{c}}_{23}{\dot{\mathrm{Ex}}}_{23}-{\mathrm{c}}_{22}\dot{\mathrm{Ex}}\_22$ |

${\mathrm{c}}_{23}={\mathrm{c}}_{22}$ | |

Heater | ${\mathrm{c}}_{9}{\dot{\mathrm{Ex}}}_{9}+{\dot{\mathrm{Z}}}_{\mathrm{Heater}}-{\mathrm{c}}_{20}{\dot{\mathrm{Ex}}}_{20}={\mathrm{c}}_{22}{\dot{\mathrm{Ex}}}_{22}-{\mathrm{c}}_{19}{\dot{\mathrm{Ex}}}_{19}$ |

${\mathrm{c}}_{20}={\mathrm{c}}_{19}$ |

**Table 6.**Exergoeconomic parameters [36].

Parameter | Equation |
---|---|

Average cost per unit exergy of fuel | ${\mathrm{c}}_{{\mathrm{F}}_{\mathrm{k}}}=\frac{{\dot{\mathrm{C}}}_{{\mathrm{F}}_{\mathrm{k}}}}{{\dot{\mathrm{E}}}_{{\mathrm{F}}_{\mathrm{k}}}}$ |

Average cost per unit exergy of product | ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{k}}}=\frac{{\dot{\mathrm{C}}}_{{\mathrm{p}}_{\mathrm{k}}}}{{\dot{\mathrm{E}}}_{{\mathrm{p}}_{\mathrm{k}}}}$ |

Cost rate of exergy destruction | ${\dot{\mathrm{C}}}_{{\mathrm{D}}_{\mathrm{k}}}={\mathrm{c}}_{{\mathrm{F}}_{\mathrm{k}}}{\dot{\mathrm{E}}}_{{\mathrm{D}}_{\mathrm{k}}}$ |

Exergoeconomic factor | ${\mathrm{f}}_{\mathrm{k}}=\frac{{\dot{\mathrm{Z}}}_{\mathrm{k}}}{{\dot{\mathrm{Z}}}_{\mathrm{k}}+{\dot{\mathrm{C}}}_{{\mathrm{D}}_{\mathrm{k}}}}$ |

Relative cost difference (%) | ${\mathrm{r}}_{\mathrm{k}}=\frac{{\mathrm{c}}_{{\mathrm{p}}_{\mathrm{k}}}-{\mathrm{c}}_{{\mathrm{F}}_{\mathrm{k}}}}{{\mathrm{c}}_{{\mathrm{F}}_{\mathrm{k}}}}\mathrm{\ast}100$ |

Heat Load (MW) | Site Actual Work (MW) | Calculated Work (MW) |
---|---|---|

214 | 75 | 76.259 |

311 | 112.5 | 123.053 |

423 | 150 | 154.377 |

Q = 214 MW | |||||||

Component | C_{f} (USD∙GJ^{−1}) | Cp (USD∙GJ^{−1}) | Ċ_{D} (USD∙h^{−1}) | Ż_{k} (USD∙h^{−1}) | Ċ_{D} + Ż_{k} (USD∙h^{−1}) | f (%) | r (%) |

Boiler | 0.002621 | 0.6403 | 12.25 | 3.21 | 15.46 | 0.1429 | 2442 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{H}\mathrm{P}}$ | 0.000256 | 0.001493 | 0.4032 | 0.06841 | 0.47161 | 0.1451 | 4.835 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{I}\mathrm{P}}$ | 0.000006144 | 0.00002458 | 0.009083 | 0.06715 | 0.076233 | 0.8809 | 3 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{L}\mathrm{P}}$ | 0.000006144 | 0.00001229 | 0.01016 | 0.01451 | 0.02467 | 0.5882 | 1 |

Condenser | 0.000006144 | 0.00009125 | 0.2409 | 0.0004219 | 0.2413219 | 0.001748 | 13.85 |

Pump_{cond} | 0.00008801 | 0.00009125 | 0.05181 | 0.0006064 | 0.0524164 | 0.01157 | 0.03691 |

LPH1 | 0.000005359 | 0.000006144 | 0.0004206 | 0.00001759 | 0.00043819 | 0.04014 | 0.1465 |

LPH2 | 0.000006144 | 0.000006364 | 0.00144 | 0.00005773 | 0.00149773 | 0.03854 | 0.0357 |

Deaerator | 0.00000507 | 0.000005578 | 0.0008694 | 0.01131 | 0.0121794 | 0.9286 | 0.1001 |

BFP | 0.000005201 | 0.000005516 | 0.02145 | 0.002486 | 0.023936 | 0.1039 | 0.06048 |

HPH1 | 0.000005099 | 0.000006144 | 0.001166 | 0.00004126 | 0.00120726 | 0.0001529 | 0.205 |

HPH2 | 0.001291 | 0.001238 | 0.3384 | 0.00005173 | 0.33845173 | 0.0401 | 0.0415 |

Q = 311 MW | |||||||

Component | C_{f} (USD/GJ) | Cp (USD/GJ) | Ċ_{D} (USD/h) | Ż_{k} (USD/h) | Ċ_{D} + Ż_{k} (USD/h) | f (%) | r (%) |

Boiler | 0.0006933 | 0.9296 | 69 | 11.77 | 80.77 | 0.1457 | 1340 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{H}\mathrm{P}}$ | 0.0006853 | 0.003275 | 1.506 | 0.06239 | 1.56839 | 0.03979 | 3.779 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{I}\mathrm{P}}$ | 0.000007992 | 0.00003197 | 0.01764 | 0.1088 | 0.12644 | 0.8605 | 3 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{L}\mathrm{P}}$ | 0.000007992 | 0.00001598 | 0.01552 | 0.04612 | 0.06164 | 0.7482 | 1 |

Condenser | 0.000007992 | 0.0001131 | 0.4422 | 0.0005968 | 0.4427968 | 0.001348 | 13.15 |

Pump_{cond} | 0.0001091 | 0.0001131 | 0.09041 | 0.0008004 | 0.0912104 | 0.008775 | 0.03602 |

LPH1 | 0.000006732 | 0.000007992 | 0.001414 | 0.00005694 | 0.00147094 | 0.03871 | 0.1871 |

LPH2 | 0.000007992 | 0.000007884 | 0.00166 | 0.00003532 | 0.00169532 | 0.02084 | 0.01353 |

Deaerator | 0.000006212 | 0.000007075 | 0.005906 | 0.01467 | 0.020576 | 713 | 0.1388 |

BFP | 0.000006382 | 0.000006418 | 0.03226 | 0.003232 | 0.035492 | 0.09105 | 0.005638 |

HPH1 | 0.000006485 | 0.000007992 | 0.001319 | 0.00002784 | 0.00134684 | 0.02067 | 0.2323 |

HPH2 | 0.002703 | 0.00259 | 1.095 | 0.00007558 | 1.09507558 | 0.00006903 | 0.04204 |

Q = 423 MW | |||||||

Component | C_{f} (USD/GJ) | Cp (USD/GJ) | Ċ_{D} (USD/h) | Ż_{k} (USD/h) | Ċ_{D} + Ż_{k} (USD/h) | f (%) | r (%) |

Boiler | 0.0006377 | 1.285 | 85.45 | 17 | 102.45 | 0.166 | 2014 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{H}\mathrm{P}}$ | 0.0006351 | 0.002489 | 1.987 | 0.04944 | 2.03644 | 0.02428 | 2.919 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{I}\mathrm{P}}$ | 0.000002632 | 0.00001053 | 0.008034 | 0.1743 | 0.182334 | 0.9559 | 3 |

${\mathrm{T}\mathrm{u}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}}_{\mathrm{L}\mathrm{P}}$ | 0.000002632 | 0.000005263 | 0.00651 | 0.03631 | 0.04282 | 0.848 | 1 |

Condenser | 0.000002632 | 0.00003643 | 0.561 | 0.0008049 | 0.5618049 | 0.001441 | 12.85 |

Pump_{cond} | 0.00003604 | 0.00003643 | 0.01281 | 0.0008923 | 0.0137023 | 0.06514 | 0.01103 |

LPH1 | 0.000002148 | 0.000002632 | 0.0008285 | 0.00009175 | 0.00092025 | 0.0997 | 0.2252 |

LPH2 | 0.000002632 | 0.000002763 | 0.002083 | 0.000174 | 0.002257 | 0.07711 | 0.04993 |

Deaerator | 0.000002279 | 0.000002459 | 0.00523 | 0.01837 | 0.0236 | 0.7784 | 0.07891 |

BFP | 0.000002344 | 0.000002508 | 0.01368 | 0.002984 | 0.016664 | 0.1791 | 0.07001 |

HPH1 | 0.000001669 | 0.000002632 | 0.0005317 | 0.00005685 | 0.00058855 | 0.0966 | 0.5763 |

HPH2 | 0.001233 | 0.001854 | 0.3256 | 0.00004935 | 0.32564935 | 0.0001515 | 0.504 |

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## Share and Cite

**MDPI and ACS Style**

Tavana, M.; Deymi-Dashtebayaz, M.; Dadpour, D.; Mohseni-Gharyehsafa, B.
Realistic Energy, Exergy, and Exergoeconomic (3E) Characterization of a Steam Power Plant: Multi-Criteria Optimization Case Study of Mashhad Tous Power Plant. *Water* **2023**, *15*, 3039.
https://doi.org/10.3390/w15173039

**AMA Style**

Tavana M, Deymi-Dashtebayaz M, Dadpour D, Mohseni-Gharyehsafa B.
Realistic Energy, Exergy, and Exergoeconomic (3E) Characterization of a Steam Power Plant: Multi-Criteria Optimization Case Study of Mashhad Tous Power Plant. *Water*. 2023; 15(17):3039.
https://doi.org/10.3390/w15173039

**Chicago/Turabian Style**

Tavana, Mashar, Mahdi Deymi-Dashtebayaz, Daryoush Dadpour, and Behnam Mohseni-Gharyehsafa.
2023. "Realistic Energy, Exergy, and Exergoeconomic (3E) Characterization of a Steam Power Plant: Multi-Criteria Optimization Case Study of Mashhad Tous Power Plant" *Water* 15, no. 17: 3039.
https://doi.org/10.3390/w15173039