Comparative Exergy Analysis of Thermal Power Plant Systems

Abstract

The concept of exergy, derived from the second law of thermodynamics, becomes a valuable source tool in analyzing thermal systems’ performance. Several terms encountered in the literature are synonymous or closely related to exergy, which are available energy, essergy, utilizable energy, and availability. The thermal efficiency of the power plants can be increased by adopting supercritical and ultra-supercritical conditions. Pressures exceeding 221.2 bar and steam temperatures exceeding 374.5°C are being used for supercritical thermal power plants, whereas the corresponding values for ultra-supercritical conditions are greater than or equal to 250 bar and 600°C. So, there is ample scope to enhance the steam conditions and optimize power plant configurations further to improve the plant efficiency. The power plant cycle is simulated by using Cycle Tempo version 5.0 software. It is used for advanced thermal energy system optimization. In the present work, for the thermodynamic analysis of supercritical—660 MW, and ultra-supercritical—800 MW power plant, cycle capacities are carried out and compared with subcritical power plant capacity of 500 MW. The important conclusions drawn from the current research work are the improvement in feed water temperature, optimum steam extraction pressures, and comparison of exergy efficiency of various thermal systems.

1. Introduction

Exergy was introduced by Z. Rant in 1956 [1]. It is preferred over energy analysis, because it cannot detect most thermodynamic imperfections, mainly irreversible heat transfer in system components. Exergy offers engineers a refined perspective on energy utilization. In the grand tapestry of engineering principles, the concept of exergy is grounded in understanding that not all energy is created equal [2]. Energy can exist in various forms—thermal, mechanical, chemical—but exergy takes a discerning approach, focusing on the energy that possesses the potential to perform work [3, 4].

2. Energy vs exergy

Energy is a broad measure of the capacity to do work, while exergy narrows the focus to the portion of energy that can be converted into useful work. In simpler terms, energy is like a raw resource, and exergy is the refined, usable portion extracted for practical applications [5].

Exergy is a measure of the quality or usefulness of energy. It is only conserved when there are no irreversible processes in a system and its surroundings, which is never the case [6]. Exergy is always destroyed when irreversibility happens. By doing an exergy analysis on a plant like a power station, a chemical plant, nuclear or a cooling system, we can quantify the thermodynamic inefficiencies as exergy destructions and/or exergy losses, which indicate how much exergy is consumed (or depleted) in the system [7, 8, 9]. Exergy analysis considers the different thermodynamic values of different types of energy and amounts, such as work and heat. The exergy transfer with shaft work is the same as the shaft work. The exergy transfer with heat transfer, however, depends on how the temperature of the heat transfer compares to the temperature of the environment [10].

3. The need for exergy analysis

Traditional energy analyses, while informative, may fall short in pinpointing inefficiencies within a system. Exergy analysis, on the other hand, provides a more granular understanding of energy transformations, revealing the areas where exergy losses occur. Considering a steam power plant. Traditional energy analysis would highlight the overall energy input and output, offering insights into the plant’s efficiency. However, exergy analysis dives deeper, scrutinizing each component of the system. It identifies inefficiencies in the steam generator, turbine, and condenser, shedding light on specific areas where exergy losses occur [11]. Armed with this knowledge, engineers can implement targeted improvements, such as better insulation or more efficient turbines, to enhance the overall system efficiency. Some of the applications of exergy include:

1. Exergy analysis: This is a method of thermodynamic analysis that uses exergy as a basis for evaluating the performance and improvement potential of energy systems. Exergy analysis can identify the sources and causes of exergy destruction and loss and provide insights for enhancing the system design and operation [12, 13, 14, 15, 16].

2. Exergy optimization: This is a method of optimizing the design and operation of energy systems by minimizing the exergy destruction and loss or maximizing the exergy output or efficiency [17, 18]. Exergy optimization can be performed using mathematical models, numerical methods, or heuristic algorithms.

3. Exergy economics: This is a branch of thermoeconomics [19, 20] that uses exergy as a common currency for evaluating the cost and benefit of energy systems. Exergy economics can account for the quality and availability of energy resources, as well as the environmental impact of energy use.

4. Exergy sustainability: This is a concept that relates exergy to the sustainability of energy systems and human activities. Exergy sustainability can be defined as the ratio of exergy input to exergy output, or the ratio of exergy consumption to exergy production. Exergy sustainability can be used to measure the degree of compatibility between energy use and environmental preservation [21, 22, 23, 24].

The thermal power is the largest source of India. Coal and lignite [25] have accounted as 60% of India’s total installed capacity. India’s electricity sector consumption about 72% of the coal produced. In India, the total installation capacity of thermal power production has 207.77 GW. The coal-based power plants are based on the Rankine cycle. The main components of a cycle consist of steam generator, steam turbines, condenser, feed water heaters and several pumps. Power plant optimization can be done by any of the methods below.

1. Steam generator Optimization.

2. Condenser Pressure Reduction.

3. Reduction of steam generator pressure losses and leakages.

4. Minimization of combustion air excess.

5. Thermal losses minimization.

6. Improvement of steam generator efficiency & steam turbine components.

7. Main Steam Parameters Optimization.

8. Proper reheat pressure Optimization.

9. Feed water heater pressure optimization.

10. Steam turbine blade optimization.

3.1 Classification of power plant cycles

The power plants are classified into subcritical, supercritical, and ultra-supercritical, based on operating conditions and plant capacity. The classification of the coal fired power plants, and their steam parameters are summarized [26] shown in Table 1. The temperature-entropy plot presentation for subcritical, supercritical, and ultra supercritical cycle is mentioned in Figure 1.

Power plant cycle	Unit size (MW)	Main steam pressure (bar)	Main steam temperature (°C)	Reheat steam temperature (°C)
Subcritical	500	166	538	538
Supercritical	660	247	538	565
Ultra- supercritical	800	270	565	593

Table 1.

Classification of the coal fired power plants.

Figure 1.

Temperature – Entropy plane of three different power plant cycles [26].

3.2 Efficiency of the power plants

Thermal efficiency is very important to economic gain and it’s an important engineering effort over 250 years by applying various techniques and technologies implemented in thermal sector [27]. American Electric Power’s (AEP), Philo Plant Unit 6, steam generator is the first commercial supercritical unit, in service early in 1957. Philo 6th unit, a double reheat design, delivered 120 MW, operating at a steam flow rate of 85 kg/s, main steam pressure (MSP) 310 bar, MST/SRH/DRH 621/565°C and 538°C. The technology was supplied by the Babcock & Wilcox Company (B&W). In 1959, Philadelphia Electric Company’s Eddy stone, steam generator with a double reheat supplied by Combustion Engineering, Inc., delivered the net power output of 325 MW and the net plant thermal efficiency has 39.99% based on the higher heating value (HHV), at a flow rate of 252 kg/s under the main steam pressure of 345 bar, MST/SRH/DRH of 649/565°C and 565°C [28, 29, 30, 31, 32]. To investigate the efficiency of power plants by varying the steam parameters, authors have used various modern tools for simulation of power plant configurations are discussed in literature reviews are 1. Ebsilon, 2. Cycle Tempo, 3. IAPWS- Microsoft Excel 4. Gate Cycle, 5. Steam Pro, 6. Reference Prop 8.0 7. Engineering Equation Solver (EES), 8. MATLAB, 9. IPSE-PRO.

4. Mathematical modeling equations

Mathematical formulations, pertaining to thermal power plant cycles are presented in terms of exergy analysis. The formulation of power plant processes is inherently non-convex, nonlinear by nature, which means that a good initial starting point and feasible bounds, for variables, must be provided to guarantee a good solution. To explore the benefits of steam parameters and structural changes in the process, it may be possible to build a general layout, containing all the possible process options and subjecting them to optimization. Therefore, it is essential to find a systematic way of building a general layout, which includes all the promising alternatives without being too large. The traditional way of designing power plants is to maximize the thermal efficiency of the plant [33].

4.1 Exergy analysis

Exergy is a property and is associated with the state of the system and the environment. It is not conserved. Once it is wasted, it can never be recovered. The useful work potential of a system is the amount of energy extracted as useful work. The useful work potential of a system at a specified state is called exergy. Exergy destruction or loss is proportional to the increase in entropy of the system together with its surroundings. The loss of exergy or irreversibility provides a quantitative measure of process inefficiency. Exergy efficiency does provide a measure of approach to ideality and exergy loss does provide measures of the deviation from ideality.

Exergy analysis [34, 35, 36, 37, 38, 39] is a powerful tool for evaluating the performance of energy conversion processes. It is based on the concept of exergy, which is the maximum amount of work that can be obtained from a system or a flow of matter and energy when it is brought into equilibrium with a reference environment. Exergy analysis allows us to identify the sources and causes of irreversibilities, losses, and inefficiencies in any process, and to quantify them in terms of exergy destruction. Exergy analysis can also help us to design more efficient and sustainable systems, and to optimize the use of available resources.

The exergy rate entering the system is equal to the sum of the exergy rate leaving the system plus the amount of exergy destruction rate during the process.

$${\mathrm{\Sigma Ex}}_{\text{in}}={\mathrm{\Sigma Ex}}_{\text{out}}+{\mathrm{\Sigma Ex}}_{\text{destroyed}}$$E1

The calculation of exergy for different primary energy sources depends on the definition of the reference environment and the thermodynamic properties of the substances involved. For fossil fuels, such as coal, oil, and natural gas, the exergy is equal to their lower heating value, which is the amount of heat released when they are completely burned.

Exergy efficiency is a measure of how effectively a process converts exergy input into exergy output. It is defined as the ratio of exergy output to exergy input, multiplied by 100. Exergy efficiency can be used to compare different processes or systems that have different types and qualities of energy inputs and outputs. Exergy efficiency can also be used to assess the improvement potential of a process or system, by comparing it with an ideal or reversible process that has the same input and output conditions. Exergy efficiency is an important indicator of thermodynamic performance, environmental impact, and economic viability in various fields of industry. The different components of a power plant cycle and its exergy efficiency terms are mentioned below with mathematical equations.

4.1.1 Steam generator

Steam generator is a closed vessel converts water into steam based on the pressure and temperature maintained in the generator by absorbing heat from the burnt coal [38]. The schematic diagram of steam generator shown in Figure 2.

Figure 2.

Schematic diagram of steam generator.

Exergy flow of streams for a steam generator can be calculated as.

$$\dot{\mathrm{\psi }}=\dot{\mathrm{m}}\mathrm{x}\left[\left(\mathrm{h}‐{\mathrm{h}}_0\right)‐{\mathrm{T}}_0\mathrm{x}\left(\mathrm{s}‐{\mathrm{s}}_0\right)\right]$$E2

Where, h and s represent the specific enthalpy and entropy of steam respectively, 0: dead state condition (atmospheric pressure and temperature).

In the exergetic performance analysis, exergy efficiency gives a measure of the performance of a system or a component.

Exergy absorbed in steam generator.

$${\dot{\mathrm{\psi }}}_{\mathrm{SG}}=\frac{\dot{\mathrm{m}}\mathrm{x}\left[\left({\mathrm{h}}_{\mathrm{o}}‐{\mathrm{h}}_{\mathrm{i}}\right)‐{\mathrm{T}}_0\mathrm{x}\left({\mathrm{s}}_{\mathrm{o}}‐{\mathrm{s}}_{\mathrm{i}}\right)\right]}{{\mathrm{\eta }}_{\mathrm{SG}}}$$E3

Exergy destruction or loss in steam generator can be calculated by

$$\begin{array}{l}{\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{SG}}={\dot{\mathrm{\psi }}}_{\mathrm{f}}‐{\dot{\mathrm{\psi }}}_{\mathrm{p}},{\dot{\mathrm{\psi }}}_{\mathrm{f}}={\dot{\mathrm{\psi }}}_1+{\dot{\mathrm{\psi }}}_2+{\dot{\mathrm{\psi }}}_3+{\dot{\mathrm{\psi }}}_5,{\dot{\mathrm{\psi }}}_{\mathrm{p}}={\dot{\mathrm{\psi }}}_4‐{\dot{\mathrm{\psi }}}_6\end{array}$$E4

Where ${\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{SG}}$ is the exergy destruction or loss in steam generator, ${\dot{\mathrm{\psi }}}_{\mathrm{f}}$ is called exergy of fuel and it is always destroyed or consumed, whereas ${\dot{\mathrm{\psi }}}_{\mathrm{p}}$ is called exergy of product and it is the amount of exergy which are produced.

$$\begin{array}{l}\text{Exergy efficiency}{\mathrm{\phi }}_{\mathrm{SG}}=\left(\left({\dot{\mathrm{\psi }}}_4‐{\dot{\mathrm{\psi }}}_3\right)+\left({\dot{\mathrm{\psi }}}_6‐{\dot{\mathrm{\psi }}}_5\right)\right)/\left({\dot{\mathrm{\psi }}}_1+{\dot{\mathrm{\psi }}}_2\right)\end{array}$$E5

Where ${\mathrm{\phi }}_{\mathrm{SG}}$: exergy efficiency in steam generator, ${\dot{\mathrm{\psi }}}_1$: Exergy of coal, ${\dot{\mathrm{\psi }}}_2$: Exergy of air, ${\dot{\mathrm{\psi }}}_3$: feed water in, ${\dot{\mathrm{\psi }}}_5$: Cold reheat or steam entering in to the reheater, ${\dot{\mathrm{\psi }}}_4$: Main steam, ${\dot{\mathrm{\psi }}}_6$: Hot reheat or superheated steam outlet from reheater.

4.1.2 Steam turbine

Steam turbine is driven with high pressure steam produced by a steam generator. It is a heat engine which converts the thermal energy of steam into mechanical work [40]. It is used to generate electricity by harnessing the power of steam in a power plant. The schematic diagram of steam turbine is shown in Figure 3.

Figure 3.

Schematic diagram of steam turbine.

Exergy destruction or loss in steam turbines shown in Figure 3 can be calculated by.

$${\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{T}}={\dot{\mathrm{\psi }}}_1‐{\dot{\mathrm{\psi }}}_2‐{\dot{\mathrm{\psi }}}_3‐\dot{\mathrm{W}}$$E6

Where ${\dot{\mathrm{\psi }}}_1$: Exergy of main steam flow in to steam turbine,

${\dot{\mathrm{\psi }}}_2$, ${\dot{\mathrm{\psi }}}_3$: Steam extractions for feed water heating,

$\dot{\mathrm{W}}$: Work output from steam turbine.

Exergy efficiency of the steam turbine can be calculated by.

$${\mathrm{\phi }}_{\mathrm{T}}=\frac{\dot{\mathrm{W}}}{\left({\dot{\mathrm{\psi }}}_1‐{\dot{\mathrm{\psi }}}_2‐{\dot{\mathrm{\psi }}}_3\right)}$$E7

4.1.3 Steam condenser

A steam condenser is a heat exchanger applied to convert low pressure exhaust steam from the steam turbine to water. The schematic diagram of steam condenser is shown in Figure 4.

Figure 4.

Schematic diagram of steam condenser.

Exergy destruction or loss in steam condenser shown in Figure 4 can be calculated as.

$${\dot{\mathrm{\psi }}}_{\text{destr},\text{COND}}={\dot{\mathrm{\psi }}}_1+{\dot{\mathrm{\psi }}}_3‐{\dot{\mathrm{\psi }}}_2‐{\dot{\mathrm{\psi }}}_4$$E8

Exergy efficiency in steam condenser can be calculated by Eq. (9)

$${\mathrm{\phi }}_{\text{COND}}=\frac{\left({\dot{\mathrm{\psi }}}_4‐{\dot{\mathrm{\psi }}}_3\right)}{\left({\dot{\mathrm{\psi }}}_1‐{\dot{\mathrm{\psi }}}_2\right)}$$E9

4.1.4 Feed water heater

A feedwater heater is a power plant component used to preheat water delivered to a steam generator. This process helps to improve the steam generator efficiency and reduces the fuel costs. The schematic diagram of feedwater is shown in Figure 5.

Figure 5.

Schematic diagram of one feed water heater.

Exergy destruction or loss in feed water heater shown in Figure 5 calculated as.

$${\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{FWH}}={\dot{\mathrm{\psi }}}_1+{\dot{\mathrm{\psi }}}_3‐{\dot{\mathrm{\psi }}}_2‐{\dot{\mathrm{\psi }}}_4$$E10

$${\dot{\mathrm{m}}}_1+\sum _{\mathrm{x}=11}^{18}{\dot{\mathrm{m}}}_{\mathrm{x}}={\dot{\mathrm{m}}}_{10}+{\dot{\mathrm{m}}}_{26}$$E11

$${\dot{\mathrm{m}}}_1{\mathrm{h}}_1+\sum _{\mathrm{x}=11}^{18}{\dot{\mathrm{m}}}_{\mathrm{x}}{\mathrm{h}}_{\mathrm{x}}‐{\dot{\mathrm{m}}}_{10}{\mathrm{h}}_{10}‐{\dot{\mathrm{m}}}_{26}{\mathrm{h}}_{26}={\dot{\mathrm{Q}}}_{\mathrm{FWH}}$$E12

$${\dot{\mathrm{m}}}_1{\mathrm{\psi }}_1+\sum _{\mathrm{x}=11}^{18}{\dot{\mathrm{m}}}_{\mathrm{x}}{\mathrm{\psi }}_{\mathrm{x}}‐{\dot{\mathrm{m}}}_{10}{\mathrm{\psi }}_{10}‐{\dot{\mathrm{m}}}_{26}{\mathrm{\psi }}_{26}‐{\dot{\mathrm{\psi }}}_{{\dot{\mathrm{Q}}}_{\mathrm{FWH}}}={\dot{\mathrm{\psi }}}_{\text{dest},\mathrm{FWH}}$$E13

A power plant cycle consists of open feed water heaters (OFWH) called direct contact heat exchanger and closed feed water heaters called indirect contact heat exchanger. The closed feed water heaters are classified as low pressure closed feed water heaters (LPFWHs) and high-pressure feed water heaters (HPFWHs). The layout of different feed water heaters is shown in Figure 6. Part of steam is extracted from various steam turbines called low pressure, intermediate and high-pressure steam turbine to raise the condensed water temperature from steam condenser.

Figure 6.

Schematic layout of eight feed water heaters (LPFWHs and HPFWHs).

Exergy efficiency for high pressure feed water heaters ${\mathrm{\phi }}_{\mathrm{FWH}}$ calculated as

$$\frac{{\dot{\mathrm{\psi }}}_{10}-{\dot{\mathrm{\psi }}}_9}{{\dot{\mathrm{\psi }}}_{18}-{\dot{\mathrm{\psi }}}_{19}}$$E14

$$\text{HPFWH2}=\frac{{\dot{\mathrm{\psi }}}_9-{\dot{\mathrm{\psi }}}_8}{{\dot{\mathrm{\psi }}}_{17}+{\dot{\mathrm{\psi }}}_{19}-{\dot{\mathrm{\psi }}}_{20}}$$E15

$$\text{HPFWH1}=\frac{{\dot{\mathrm{\psi }}}_8-{\dot{\mathrm{\psi }}}_7}{{\dot{\mathrm{\psi }}}_{16}+{\dot{\mathrm{\psi }}}_{20}-{\dot{\mathrm{\psi }}}_{21}}$$E16

$$\text{For Open feed water heaters}\left(\mathrm{DEA}\right)=\frac{{\dot{\mathrm{\psi }}}_6}{{\dot{\mathrm{\psi }}}_{15}+{\dot{\mathrm{\psi }}}_5+{\dot{\mathrm{\psi }}}_{21}}$$E17

Exergy efficiency ${\mathrm{\phi }}_{\mathrm{FWH}}$ for low pressure feed water heaters calculated as

$$\text{LPFWH}4=\frac{{\dot{\mathrm{\psi }}}_5-{\dot{\mathrm{\psi }}}_4}{{\dot{\mathrm{\psi }}}_{14}-{\dot{\mathrm{\psi }}}_{22}}$$E18

$$\text{LPFWH}3=\frac{{\dot{\mathrm{\psi }}}_4-{\dot{\mathrm{\psi }}}_3}{{\dot{\mathrm{\psi }}}_{13}+{\dot{\mathrm{\psi }}}_{22}-{\dot{\mathrm{\psi }}}_{23}}$$E19

$$\text{LPFWH}2=\frac{{\dot{\mathrm{\psi }}}_3-{\dot{\mathrm{\psi }}}_2}{{\dot{\mathrm{\psi }}}_{12}+{\dot{\mathrm{\psi }}}_{23}-{\dot{\mathrm{\psi }}}_{26}}$$E20

$$\text{LPFWH}1=\frac{{\dot{\mathrm{\psi }}}_{24}-{\dot{\mathrm{\psi }}}_1}{{\dot{\mathrm{\psi }}}_{11}+{\dot{\mathrm{\psi }}}_{26}-{\dot{\mathrm{\psi }}}_{28}}$$E21

4.1.5 Feed water pump

Feed water pump is a power plant component used to pump the feed water coming from various feed water heaters into the steam generator and its schematic diagram is shown in Figure 7.

$$\text{Exergy destruction or loss in pump}{\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{P}}={\dot{\mathrm{\psi }}}_1‐{\dot{\mathrm{\psi }}}_2+{\dot{\mathrm{W}}}_{\mathrm{p}}$$E22

$$\text{Exergy efficiency in pump}{\mathrm{\phi }}_{\mathrm{P}}=\frac{\left({\dot{\mathrm{\psi }}}_2‐{\dot{\mathrm{\psi }}}_1\right)}{{\dot{\mathrm{W}}}_{\mathrm{p}}}$$E23

Figure 7.

Schematic diagram of feed water pump.

Total exergy destruction or loss in the plant can be determined as sum of exergy destruction rates of components:

$${\dot{\mathrm{\psi }}}_{\text{destr},\text{total}}=\sum {\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{i}}={\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{SG}}+{\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{T}}+{\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{C}}+{\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{P}}+{\dot{\mathrm{\psi }}}_{\text{destr},\mathrm{FWH}}$$E24

For the whole thermal power plant, the exergy efficiency can be given.

$$\mathrm{\phi }=\frac{{\dot{\mathrm{W}}}_{\mathrm{net}}}{{\dot{\mathrm{m}}}_{\text{coal}}{\mathrm{x\psi }}_{\text{coal}}}$$E25

Where ${\mathrm{\psi }}_{\text{coal}}$: specific exergy of coal, ${\dot{\mathrm{m}}}_{\text{coal}}$: Mass of the coal.

${\dot{\mathrm{W}}}_{\mathrm{net}}$: Network output from turbines.

4.2 Quasi-Newton optimization

The process to get maximum thermal efficiency of a cycle describes the optimization steps in Cycle Tempo. Quasi-Newton optimization technique in Cycle Tempo 5.0 is recognized today as one of the most powerful tools for feeding steam extraction pressures optimization from steam turbines. It usually converges fast, and sometimes converges even without step length control. In the initial step, give the input values to the components presented in the cycle diagram. In the second step, start with initial guess values by giving starting steam extraction pressures from turbines X_i, Let i = 1. In the third step, it calculates the mass & energy balance equations. In the fourth step, it computes the objective function f(X_i) as η of thermal power plant cycle. In the fifth step, it generates a new solution X_i + 1 as steam extraction pressures from the turbines. In the sixth step, it computes the objective function f (X_i + 1) as thermal efficiency (η) of power plant. In the seventh step, it checks for convergence on efficiency of plant. In the eighth step, it will check for maximum efficiency of a plant. In the ninth step, if it is ok that gives the message as success and updates the geometry as an optimal solution.

5. Result and discussions – Case study

The simulation and optimization of three different thermal power plant cycles are carried out, with Cycle Tempo 5.0 simulation software tool for energy systems. The following parameters have been studied for 500, 660 and 800 MW power plant cycles. The performance of the power plant cycle configuration is mentioned in Tables 2–6 and shown in Figures 8–12. In the current study exergy analysis was used as a tool to identify the thermodynamic losses and exergy efficiencies in various components of the power plant cycle with the help of Cycle Tempo 5.0. [41].

MSP (bar)	Net thermal and exergy efficiency (%)
	500°C		600°C		700°C
200	41.33	38.96	42.30	39.88	43.59	41.09
220	41.49	39.11	42.85	40.39	44.09	41.56
240	41.60	39.21	43.03	40.56	44.29	41.75
260	41.67	39.28	43.16	40.69	44.47	41.92
280	41.71	39.32	43.27	40.79	44.62	42.06
300	41.70	39.31	43.33	40.86	44.79	42.13

Table 2.

Net thermal and exergy efficiency of plant (%) at different main steam temperatures and pressures.

Main steam pressure (bar)	Main steam temperature
	500°C	600°C	700°C
200	752.54	677.73	603.51
250	810.35	696.86	614.06
300	847.91	718.93	631.77

Table 3.

Variation of steam consumption (kg/s) at different main steam pressures and temperatures.

Main steam pressure (bar)	Main steam temperature
	500°C	600°C	700°C
200	453	443	430
250	452	438	422
300	450	433	418

Table 4.

Variation of coal consumption in tonnes per hour at different main steam pressures and temperatures.

MST	Subcritical	Supercritical	Ultra-supercritical
	Auxiliary power consumption (MW)
500°C	6.65	8.77	10.64
600°C	6.17	8.12	9.54
700°C	5.75	7.84	8.75

Table 5.

Comparative auxiliary power consumption in three different power plant cycles.

Feed water heaters	Subcritical	Supercritical	Ultra-supercritical
	Steam extraction pressures (bar)
LPFHW1	0.32	0.34	0.36
LPFWH2	0.87	0.96	0.98
LPFWH3	1.96	2.26	2.50
LPFWH4	4.04	4.78	5.78
DEA(OFWH)	7.96	9.59	12.01
HPFWH1	14.62	18.35	23.34
HPFWH2	31.21	39.80	48.94
HPFWH3	75.61	92.31	107.58
Feed Water temperature (°C)	290.65	304.40	315.34

Table 6.

Comparison of steam extraction pressure (bar) optimization in three different power plant cycles.

Figure 8.

Exergy absorbed in steam generator for three power plant cycles.

Figure 9.

Exergy loss of different components in three different power plants.

Figure 10.

Exergy loss in closed feed water heaters of three different power plant cycles.

Figure 11.

Exergetic loss variations of different components of three different power plant cycles.

Figure 12.

Variation of exergy efficiency of power plant components in three different power plant cycles.

The key output parameters which can be observed to see for changed input parameters are exergy absorbed in steam generator and reheater, Exergy loss/Total exergy input in steam generator, reheater and steam turbines, Exergy loss in different components, Exergy loss and rate of heat transfer in closed regenerative feed water heaters, Thermal and exergy efficiency, Impact of condenser pressure variation on exergy efficiency, Auxiliary power consumption and pipe exergy losses, Coal, and steam consumption. All these parameters are based on steam extraction pressure optimization from feed water heaters to get maximum plant cycle efficiency.

Efficiency of the Rankine cycle can be improved by increasing the average temperature of heat addition or by decreasing the average temperature of heat rejection [42].

In thermal power plants, the average heat addition is increased, by setting number of feed water heaters. The feed water enters the steam generator (Evaporator), through economizer. The performance of a power plant is characterized by its power output, efficiency, heat rate, steam rate, fuel rate, etc., In the present work, the efficiency of thermal power plant cycles (subcritical, supercritical and ultra-supercritical) is analyzed by considering, the key input parameters of, main steam pressure (MSP), main steam temperature (MST), reheat temperature and condenser pressure, etc., Figure 13 shows, the schematic layout of thermal power plant, contains combustor (air + coal) releases the flue gases and passes through the various heat exchangers like (evaporator, superheaters), where feed water gets converted to steam according to the steam parameters maintained in a power plant cycle called as steam generator (SG). The steam and then passes into the high-pressure turbine (HPT), reheater to low pressure turbine (LPT), condenser (COND), four closed feed water heaters (four low pressure feed water heaters (LPFWHs) and three high pressure feed water heaters (HPFWHs)), one open feed water heater (OFWH) called as deaerator (DEA) called feed water heater section and various pumps (Boiler feed pump, water pumps). The feed water from feed water heater section into the economizer and then passes into the evaporator, where it gets converted into steam based on steam parameters.

Figure 13.

Process flow sheet layout of thermal power plant cycle [41].

The assumptions considered for the thermal power plant cycle shown in Figure 13 are available in Table 7. Before the analysis, any power plant components should be given some assumptions to evaluate the performance of the system.

S. no	Component	Value
1	Pressure drops in steam generator	3%
2	Efficiency of steam generator	92%
3	Pressure drops in reheater	1%
4	Pressure drops of main steam	4%
5	Isentropic efficiency of high-pressure turbine	90%
6	Isentropic efficiency of a low-pressure turbine	90%
7	Mechanical efficiency of a feed pump turbine	98%
8	Isentropic efficiency of a feed pump	78%
9	Isentropic efficiency of a main condensate pump	78/75%
10	Generator efficiency	98%
11	Atmospheric temperature/pressure	30°C/1.01 bar
12	TTD on high side/low side for LPFWHs	3/5 K
13	TTD on high side/low side for HPFWHs	0/7 K
14	Condenser pressure	0.09 bar
15	Calorific value of coal	34,000 kJ/kg

Table 7.

Assumptions of a power plant components [41].

Table 2 shows the effect of main steam pressure on thermal and exergy efficiency of a plant cycle. It shows that the exergy efficiency of a cycle is less than thermal efficiency of cycle and this is due to chemical exergy of coal is greater than the calorific value of coal. As the main steam pressure is raised, the thermal efficiency increases up to a pressure of 280 bar for subcritical power plant cycle and there after it decreases. This shows that the optimum limit of efficiency increases. After 280 bar, the efficiency decreases due to less work output from the turbines and increase of pump work.

Variation of steam consumption (kg/s) at different main steam pressures and temperatures are shown in Table 3. It shows the steam consumption increases when the main steam pressure is raised due to reduced enthalpy of steam. Steam consumption decreases when the main steam temperature is raised at a particular pressure of 200 bar due to high enthalpy of steam. To meet the required power plant capacity of 500MW with high enthalpy steam content can reduce steam consumption.

The coal consumption in tonnes per hour (TPH) for a power plant operating at different steam conditions is shown in Table 4. It shows that coal consumption decreases, both with the increase of main steam pressures and temperatures. But the decrease of coal consumption is little bit less when main steam pressure is raised as compared to the different main steam temperatures.

The comparison of auxiliary power consumption results is shown in Table 5. The auxiliary power consumption decreases, as the main steam temperatures have increased from 500–700°C. The auxiliary power consumption decreases to all the power plant cycles, because it depends on the specific volume of steam and quality of steam entering pumps when the main steam temperature is raised. The cooling water required by the condenser also decreases when main steam temperatures are raised. Auxiliary power consumption increases, with the increase of the power plant capacity.

The percentage of auxiliary power consumption has increased 24%, compared to subcritical plant, whereas the same value is increased to 14.8%, compared to supercritical power plant cycle. But overall, 35% auxiliary power consumption is increased compared to subcritical power plant cycle.

The comparison of steam extraction pressure optimization of 8 regenerative feed water heater stages and feed water temperatures, in the power plant cycles are shown in Table 6. It shows that the optimum steam extraction pressures and feed water temperatures are increased. This is due to the increase in steam flow rate. The feed water temperature improvement is 4.51%, compared to subcritical steam power plant cycle, 3.47% compared to supercritical power plant cycle and overall, 7.82% compared to subcritical power plant cycle.

The variation of exergy absorbed in steam generator is shown in Figure 8. It shows the exergy absorbed in steam generator increases gradually, as the main steam temperature is raised. This is due to the increase in entropy of steam.

Exergy is how much work output is possible to convert on using heat content of steam. But overall, the exergy absorbed both in steam generator and reheater decreases due to constant reheat temperature. The exergy absorbed in steam generator is 21.47% compared to subcritical power plant, 15.46% compared to supercritical, and overall, the exergy absorbed in steam generator is 33.62% between ultra-supercritical to subcritical cycle at a main steam temperature of 600°C.

The exergy loss, measured in megawatt (MW) of different plant cycle components, for three different power plants capacity are shown in Figure 9. It shows the exergy loss increases to all components. The major exergy loss found in steam generator but in reheater, steam turbine and in condenser it decreases. When the power plant capacity rises the difference in exergy loss increases. The difference in exergy loss in terms of percentage increases in steam generator between subcritical and supercritical up to 19.87%. Whereas the same value in between the supercritical and ultra-supercritical is 41.10%. The overall difference in exergy loss is 31.17% between the subcritical and ultra-supercritical. The difference in exergy loss in percentage is increased in reheater between subcritical and supercritical is 27.10% whereas the same value in between the supercritical and ultra-supercritical is 21.67%. The overall difference in percentage exergy loss between the subcritical and ultra-supercritical is 42.90%.

The difference in exergy loss in percentage is increased in feed pump turbine between subcritical and supercritical is 40.70% whereas the same value in between the supercritical and ultra-supercritical is 33.36%. The overall difference in percentage exergy loss between the subcritical and ultra-supercritical is 60.48%. The difference in exergy loss in terms of percentage found less in feed water heater and then in condenser.

The exergy loss in feed water heaters is up to 8 regenerative stages which are shown in Figure 10. As the number of feed water heaters increases the exergy loss decreases. The difference in exergy loss percentage is increased in regenerative feed water heaters between subcritical and supercritical is 22.92%. The same value between the supercritical and ultra-supercritical is 4.47%. The overall difference in exergy loss (%) between the sub and ultra-supercritical is 26.37%.

The percentage exergetic loss in steam generator, steam turbines and condenser decrease from subcritical to ultra-supercritical power plant cycles shown in Figure 11. The major percentage exergetic loss occurs in steam generator and its value in subcritical state is 50.79% and the same value in supercritical state is 49.99%. It shows the percentage of exergetic loss decreases in between subcritical to supercritical is 1.60% and the same in between supercritical and ultra-supercritical is only 1.52%.

The overall percentage difference between ultra-supercritical and subcritical is 3.14%. The exergetic loss also decreases in steam turbines and in condenser. But the overall reduction in percentage is very small.

The exergy efficiency of individual components like steam generator, reheater, different turbines, feed water heaters and pumps are shown in Figure 12. It shows the exergy efficiency increases in all the components except feed pump. The energy efficiency of steam generator and reheater lie in the range of 48 to 51%. HPT and HPFWHs show the high exergy efficiency in the range of 90 to 95%. LPT and LPFWHs show the exergy efficiency in the range of 80 to 90% and feed pump shows the exergy efficiency in the range of 65 to 70%. Only the feed pump turbine has constant exergy efficiency in all power plant cycles. The power producing device shows more exergy efficiency. The feed water heaters have more exergy efficiency because of the heat transfer between steam and feed water. In deaerators the exergy efficiency decreases as the main steam temperature have raised. But when main steam pressure is raised, the exergy efficiency of deaerator increases.

6. Conclusions

From the aforementioned information in tables and figures, the following conclusions may be drawn as

1. As the main steam temperature is raised by keeping reheat temperature as constant the optimum steam extraction pressure values for 8 regenerative stages decreases.

2. Auxiliary power consumption decreases as the main steam temperature is raised for a main steam pressure to all power plant capacities.

3. The energy and exergy absorbed in steam generator increases to three power plant capacities.

4. Exergy loss in steam generator decreases from subcritical power plant cycle to ultra-supercritical power plant cycle.

5. Comparing the rates of heat transfer in feed water heaters from subcritical to ultra-supercritical power plant cycle, more heat transfer is possible between subcritical to supercritical compared to supercritical and ultra-supercritical steam conditions.

6. The exergy efficiency of a steam generator increases as the main steam input parameters are raised.

7. The feed water temperature of a plant can be improved by raising the steam input pressures.

8. The exergy analysis reveals that the subcritical units are less efficient to utilize the available exergy of coal compared with supercritical and ultra-supercritical units.

9. Specific steam and coal consumption decreases when higher steam input parameters are used.

10. Simulation and exergy analysis are useful in system optimization. They not only indicate the direction of system optimization, but also provide a theoretical basis for the system optimization.

11. The average cooling water requirement in condenser/MW for subcritical plant capacity of 500 MW is 40 kg/s, for supercritical 660 MW, it is 38 kg/s and for ultra-supercritical 800 MW capacity, it is 37 kg/s.

Acknowledgments

The authors would like to thank the ASIMPTOTE – Cycle Tempo 5.0 licensed software, Delft University of technology, Netherlands for carrying out the exergy analysis of thermal power plants in the year 2016–2017.

Conflict of interest

The authors declare no conflict of interest.

Nomenclature

$\dot{\mathrm{\psi }}$	exergy flow rate (MW)
$\dot{\mathrm{Q}}$	heat flow rate (MW)
$\dot{\mathrm{W}}$	work (MW)
$\mathrm{\psi }$	specific exergy (kJ/kg)
h	enthalpy (kJ/kg)
LHV	lower heating value (kJ/kg)
HHV	higher heating value (kJ/kg)
$\dot{\mathrm{m}}$	mass flow rate (kg/s)
${\dot{\mathrm{m}}}_{\mathrm{s}}$	mass flow rate of steam (kg/s)
s	entropy (kJ/kg K)
T	temperature (K or °C)
${\mathrm{\eta }}_{\mathrm{th}}$	thermal efficiency (%)
$\mathrm{\phi }$	exergy efficiency (%)
${\dot{\mathrm{\psi }}}_{\mathrm{f}}$	exergy of the fuel (MW)
${\dot{\mathrm{\psi }}}_{\mathrm{p}}$	exergy of the product (MW)

Subscripts

a	air
aux, ele	auxiliary electrical equipment
ext	extraction
destr	destruction or loss
f	fuel
fw	feed water
FWH	feed water heater
gross	gross
loss	loss in components
ms	main steam
net	net
pump	pump
rs	reheated steam
SG	steam generator
COND	condenser
i	inlet
o	outlet
p	product
rh	reheat
S	steam
T	turbine
total	total
th	thermal

Abbreviations

APC	auxiliary power consumption
BFP	boiler feed pump
BFPT	boiler feed pump turbine
CEP	condensate extraction pump
COND	condenser
CT	cooling tower
CWP	cooling water pump
DEA	deaerator
FPT	feed pump turbine
FWH	feed water heater
FWT	feed water temperature
GW	Gigawatt
HHV	higher heating value
HPFWH	high pressure feed water heaters
HPT	high pressure turbine
LHV	lower heating value
LPFWH	low pressure feed water heater
LPT	low pressure turbine
MW	Megawatt
MSP	main steam pressure
MST	main steam temperature
OFWH	open feed water heater (DEA)
SG	steam generator
SRH	single reheater
TBFP	turbine driven boiler feed pump
TPH	tonnes per hour
TTD	terminal temperature difference