Exergy Analysis of 500 MW Power Unit Based on Direct Measurement Data

Abstract

This paper presents an exergy analysis of a 500 MW unit based on actual measurement data. The mathematical model of the system was built in the Aspen HYSYS 2.4 software. The analysis was carried out for two operating states of the unit, at nominal load and at minimum technical load, based on data from two measurement campaigns carried out specifically for this study. The use of measurement data allows an accurate representation of the unit’s current operating conditions, which is crucial for the accuracy of the analysis and the practical implementation of the results obtained. The results show that the dominant sources of exergy losses are the irreversibilities associated with combustion and boiler heat transfer, which account for more than 60% of total exergy losses. The article makes an important contribution to sustainability by identifying opportunities to increase the operating efficiency of the power unit and reduce CO₂ emissions. Proposed technical modifications, such as the modernisation of air heaters, the use of inverters in ventilation systems, or the optimisation of heat exchangers in the turbine system, can significantly improve energy efficiency and reduce the unit’s environmental impact. The analysis provides a valuable resource for the development of energy technologies that promote efficiency and sustainable resource use.

1. Introduction

The concept of exergy has gained considerable interest in the thermodynamic analysis of thermal processes and energy systems, as it was found that an analysis based on the first law of thermodynamics was insufficient from the energy efficiency standpoint [1]. The energy balance of a system is not sufficient to possibly identify system inadequacies by itself, and the most important benefits of exergy analyses are as follows [2]:

• Exergetic efficiency is always a measure of true excellence and provides more meaningful information when assessing the performance of energy systems. In addition, exergetic losses clearly identify the locations, causes, and sources of deviations from ideal processes in a system that are directly related to a unit’s CO₂ emissions.
• Exergy methods can help to assess the thermodynamic values of product energy forms in complex systems with multiple products (e.g., cogeneration and trigeneration plants).
• Exergy-based methods can be used to improve economic and environmental assessments, thereby influencing sustainability issues in the energy sector and economy.
• Exergy can improve understanding of terms such as energy conservation and the energy crisis.
• Exergetic methods can assist in optimisation efforts.

With regard to the arguments cited above, it seems expedient to carry out an exergy analysis for the evaluation and improvement of the energy unit that is the subject of this study by defining the facility’s actual sources of thermodynamic inadequacy.

In the available literature on exergy analysis of power units, one can find works with different levels of detail [3,4,5,6,7,8,9]. Some of the works focus on the exergy analysis of the turbine unit, while the boiler is treated there as a whole [6,10]. Quite a few of the available studies deal exclusively with the boiler [3,4,5]. Only a few papers with similar details of the whole system can be found in the literature [11,12,13,14,15,16,17,18,19], although these papers are not supported by experimental data.

In recent years, exergy analyses have been carried out on units of different capacities and configurations. The exergy analysis of the solar-aided coal-fired power generation (SAPG) plant was carried out in [11]. The paper uses a 330 MW SAPG plant as a case study to perform a comprehensive exergy analysis under off-design conditions. The results show that efficiency degradation at partial loads is primarily caused by the steam turbine’s governing stage and slip-pressure operation. Furthermore, variations in solar input led to substantial alterations in crucial operating parameters, including exhaust flow rate and the pressure at each turbine stage.

In [12], a new CCS (CO₂ capture and storage) system was proposed for a 300 MW coal-fired power plant (CFPP), featuring two strategies: (1) a CCS system that integrates a (CRC) CO₂ refrigeration cycle (CFPP-CCS-CRC), and (2) a CCS cogeneration (CHP—Combined Heat and Power) plant that also incorporates a CO₂ refrigeration cycle (CHP-CCS-CRC). The performance of these proposed systems was assessed using energy, exergy, and economic (3E) analyses. The findings showed that across a range of CO₂ capture rates (13.1% to 72.9%), the CHP-CCS-CRC system achieved 1.2% to 5.6% higher energy utilisation efficiency and 7.7% to 25.8% greater exergy efficiency compared with a conventional CCUS (CO₂ capture, utilisation, and storage) system. In [14], a power-to-heat TES (thermal energy storage) system was integrated into a coal-fired power plant (CFPP), with the stored heat utilised to warm live steam (scheme C1), reheat steam (scheme C2), and high-pressure heater feedwater (scheme C3). The results indicate that the power-to-heat process can enable zero output from CFPPs, although it experiences an exergy loss coefficient exceeding 40%. When the boiler operates at 75% of its rated thermal load, schemes C1, C2, and C3 can increase power output by a maximum of 150.0 MW, 96.5 MW, and 50.0 MW, corresponding to 25.0%, 16.1%, and 8.3% of the rated load, respectively. Scheme C2 achieves the highest equivalent round-trip efficiency at 50.81%, slightly surpassing scheme C1’s 50.74%. Scheme C1 also has the lowest total cost for equipment and storage materials at 63.68 million USD, with a net present value of 25.0 million USD and a payback period of 13.5 years.

Article [15] introduces an innovative metric called the Exergy Return on Environment and Energy Investment (ExROEEI). This concept evaluates energy quality and broadens the analytical scope to include the exergy required for CO₂ removal from fuel combustion and the environmental impacts of waste streams. When this advanced approach is applied to a coal-fired power plant utilising amine-based post-combustion CO₂ capture, the analysis from [15] reveals an ExROEEI ratio of 2.06:1. The plant’s exergy output is 250.52 PJ, while the exergy input is 121.46 PJ, with the exergy dedicated to CO₂ capture and compression accounting for 35.58% of the input value.

Ref. [16] presents a model of a CaL-CSP system (Ca (calcium) looping with concentrated solar power), which integrates a conventional calcium looping CO₂ capture process with concentrated solar power designed for a 500 MW coal-fired power plant. Additionally, two steam cycles were developed to efficiently harness available heat sources. The system’s performance was assessed using energy, exergy, and economic analyses. With a CO₂ capture efficiency of 93%, the calciner required 1293 MWth of thermal power, which was provided by a heliostat field operating at an efficiency of 88.56%. The overall net electrical efficiency of the system was calculated at 33.22%, and the levelized cost of electricity was 120.27 USD/MWh. Exergy analysis revealed that the calciner had a lower exergy efficiency of 82.61% compared with the carbonator’s 88.51%, attributed to greater exergy destruction occurring in the calciner reactor and the compression unit.

In [17], a coal chemical looping combustion (CLC) power plant with a power of 600 MW and integrated CO₂ capture was developed and validated. The operational parameters and conditions of the CLC process were examined and optimised. A heat exchange network (HEN) was designed and improved using a combined pinch and exergy analysis approach to match and integrate different energy levels from flue gas and exhaust steam waste heat, aiming to maximise the energy efficiency of the CLC power plant. A subsequent techno-economic evaluation and exergy distribution analysis indicated that the net energy efficiency of the CLC power plant was 34.8%, an improvement of 1.9% and 2.4% higher compared with a monoethanolamine (MEA)-based ultra-supercritical coal power plant, which achieved 32.4% efficiency at the same CO₂ capture rate of 90%. Additionally, the CLC power plant demonstrated a lower electricity cost (ranging from 0.088 to 0.127 $/kWh) and reduced coal consumption (381 g/kWh) in comparison to the MEA-based power plant (0.143 $/kWh and 408 g/kWh, respectively).

The performance of a solar-aided coal-fired power plant (SACFPP) under fluctuating solar irradiance was examined in [18]. Dynamic and exergy analysis models were developed to assess the performance of the SACFPP during transient processes caused by changes in solar irradiance and subsequent system adjustments. The study simulated an SACFPP that integrates a trough collector system (TCS) in parallel with the HP2 (high-pressure) and HP3 heaters of a 660 MW coal-fired power plant. The impact of variations in solar irradiance and the feedwater ratio to the TCS on SACFPP performance was analysed, including both step-change scenarios and typical solar days. During dynamic processes, the solar-to-power exergy efficiency showed significant fluctuations, rising from 32.62% to 57.25% and then dropping to 28.1% as solar irradiance decreased from 700 to 400 W/m². The highest accumulations of additional power and exergy destruction were observed during the Autumn Equinox. To enhance efficiency, control strategies for feedwater flow to the TCS were proposed and compared. The findings suggest that the feedwater flow should be adjusted in response to decreasing solar irradiance within a dynamic period of less than 200 s to minimise additional exergy destruction.

In [19], a thermodynamic analysis was performed on a coal-fired power plant integrated with a carbon capture system under varying load conditions. The findings indicate that the exergy efficiency penalty increases as the power load ratio decreases. Specifically, the exergy efficiency of the plant drops by 8.29% and 10.02% at 100% and 30% load ratios, respectively, when integrated with the carbon capture system. Additionally, the irreversibility of the carbon capture system rises as the load ratio decreases. A pressure-sliding operation strategy is proposed to enhance the performance of the integrated system under load-cycling conditions. Increasing the absorber pressure when the load ratio is below 75% improves system performance while reducing the stripper pressure helps lower energy consumption. This strategy enhances exergy efficiency by 0.23%, 0.31%, 0.3%, and 0.37% at load ratios of 100%, 75%, 50%, and 30%, respectively.

The paper [6] presents an energy and exergy analysis of a 660 MWe supercritical power plant unit at 100, 80, and 60% load. The analysis allowed the determination of energy losses and exergy destruction in the main components of the system, such as the boiler, high-pressure, medium-pressure, and low-pressure parts of the turbine, and the condenser, as well as in auxiliary equipment such as pumps, deaerators, etc. The analysis showed that the highest energy destruction was in the boiler, with less energy destruction when the turbine unit was under-loaded. The energy destruction in the turbine at 100/80/60% load was 49.16/43.22/43.92 MW for constant system pressure, respectively.

The authors of [7] carried out an in-depth exergy analysis of the entire plant, including auxiliary equipment, in order to find fuel consumption reduction opportunities in a large coal-fired power plant. With access to data from ultra-supercritical and subcritical facilities, they carried out a comparison of the possible savings in different types of steam power plants. The results show a detailed distribution of exergy destruction and energy losses for the three operating ranges of the unit and for the different types of heat exchangers included in the system. However, the authors found that the potential for energy savings both at the system level and at the individual equipment level through improvement is not proportional to the amount of exergy destruction. Furthermore, due to the diversity of equipment and optimisation strategies, it is not possible to clearly identify the reduction in exergy destruction resulting from optimisation of individual components of the steam system.

In [9], an exergy analysis of the power plant system was carried out using a simulation model developed in Aspen Plus software. The results obtained made it possible to determine the main losses in the thermal cycle, as well as to analyse the influence of the plant’s operating parameters, such as combustion temperature, excess air ratio, steam temperature, and pressure. The main source of exergy losses is the conversion of the chemical energy of the fuel into heat. The high-pressure part of the turbine shows the lowest exergetic efficiency in the whole turbine but has the highest power output efficiency of 37.08%.

The authors of [20] performed an energy and exergy analysis of a small power plant of 82 MW. The analysis showed that the boiler, steam turbines, deaerator, and condenser, in turn, have the highest exergy destruction. In the case of the boiler, the burners are responsible for 50% of the exergy destruction. The greatest energy loss occurs sequentially in the boiler and in the condenser, as well as in the tubes, due to wall friction. The exergy efficiency was determined to be 42% for the boiler, 84% for the turbines, 38% for the condenser, and 60% for the deaerator. In this paper, the authors also analysed the effect of key parameters on plant efficiency.

In [21], the authors performed an energy and exergy analysis of a gas–steam system in a CHP plant based on the design parameters of the unit. The results indicated large temperature drop losses occurring in the high-pressure steam generator, affecting the irreversibility of the process. The medium-pressure steam superheater was characterised by a smaller temperature drop and, therefore, less process irreversibility. The greatest energy destruction occurred in the steam turbine system, followed by the heat regeneration system, the turbine itself, and the condenser. The exergetic efficiency of the steam turbine system was determined to be 92%, whereas that of the condenser was 63%.

It is also possible to find research on the boiler only [3,4,5,8], whereby some authors such as [3] carried out an exergy analysis of existing installations with the aim of demonstrating the low energy efficiency of a 350 MW boiler, while typical efficiency tests carried out according to standards did not give adequate results. The authors showed that the direct impact on the reduced efficiency of the boiler could be determined by an exergy analysis under different operating variants, taking into account the amount of fuel consumed and the thermal energy obtained.

The authors of the paper [4] dealt with a similar case by presenting the sources of irreversibility of the energy conversion process in a boiler serving a 348.5 MWe turbine generator set. The paper presents an exergy analysis in combination with the economic impact.

In the paper [8], the authors focused on the analysis of a biomass boiler operating under co-firing with coal, feeding four different biomass fuels and two different types of coal (hard coal and lignite). The exergetic efficiencies of the plant were determined for different fuel mixtures and for two different operating states of the boiler. The analysis showed that the exergetic efficiency of both the boiler and the entire installation decreases with increasing biomass content in the fuel mixture. The authors then presented the exergetic efficiencies as a function of the proportion of specific fuels at a constant fuel flow into the plant and at a constant heat flow into the steam cycle. Results were obtained showing that the exergetic efficiencies of the system range from 31.54% to 33.82% at a constant fuel flow with different fuel mixtures in co-combustion shares from 0 to 30% and from 31.45% to 33.05% at a constant heat input to the steam cycle.

In [22], an exergy analysis is presented for a 650 MW thermal power plant. The relationship between power plant exergy and thermal efficiency for two different loads is shown. In addition, the effects of a decrease in condenser pressure, pressure at the inlet of the medium-pressure part of the turbine, and an increase in superheated steam temperature at the inlet to both the high-pressure part of the turbine and the medium-pressure part were investigated. In [23], an energy and exergy analysis of a biomass-fired CHP plant for ultra-supercritical steam parameters was carried out. The performance of the plant was assessed using sensitivity analyses covering a wide range of heat demand scenarios for industrial applications.

In [24], an energy and exergy analysis was carried out for a conventional steam power plant (CSPP) and a supercritical carbon dioxide (S-CO₂) power plant. An analysis of the exergy distribution and optimisation methods was carried out for different variants for the construction of a supercritical carbon dioxide unit: Cycle-Internal-Split-Flow (CISF) and Connected-Top-Bottom-Cycle (CTBC). The results show that the exergy loss due to heat exchange for a supercritical CO₂ power plant (SCO2PP) is lower than for a conventional steam power plant (CSPP).

The authors [25] carried out an exergy analysis of a CHP plant using different fuels, including biodiesel. The main objective was to understand the impact of design parameters and chemical dissociation of combustion products on energy and exergetic efficiency. Mass, energy, and exergy analyses were carried out on the main components of the system, considering six different sources of irreversibility: combustion chamber, heat transfer process, steam condensation, flue gas emission to the atmosphere, pumping, and overheating in the steam turbine due to friction.

In [26], a system integrating a biomass-fuelled gas generator with an external combustion gas turbine coupled to a Molten Carbonate Fuel Cell (MCFC), an Organic Rankine Cycle (ORC) system, and a cryogenic CO₂ separation system was modelled. Exergetic and exergoeconomic analyses were performed on the developed thermodynamic model, including parametric analysis of critical design parameters. The overall exergetic efficiency of the system is 40.76%, the LCOE (Levelised Cost Of Energy) is 77.74 USD/MWh, and the specific CO₂ emission value is 133.3 kgCO₂/kWh.

By using real measurement data, the analysis presented in this paper differs from analyses of this class found in the literature. The use of real measurement data allows the theory of exergy analysis and its benefits to be put into practice. Power units, especially those that have undergone modifications over the years, rarely operate at design parameters. Therefore, carrying out the analysis on real data provides more precise data on the current state of the unit and ensures greater accuracy of results.

In analyses based on actual measurements, an appropriate data acquisition system describing the operation of the object under consideration is essential. Examples of data acquisition systems are described in [27,28]. The benefits of using actual measurement data to analyse the operation of already constructed objects result from the fact that these objects often (especially over time) differ from the design assumptions. This may result from both minor differences after the construction of the system and from the degradation processes of the system elements during system operation.

The unit was divided into two sub-systems, the boiler and the steam turbine unit, in order to calculate the losses and exergy destruction. These sub-systems were then subdivided into individual machines and equipment, for which exergy balances were carried out in a subsequent step. It was, therefore, necessary to analyse the structure of the block and the individual machines and equipment involved in the exergy analysis accordingly. The analysis of the block structure made it possible to determine the balance limits for the individual machines and equipment and to examine the connections between the analysed elements. This made it possible to determine the exergy flows between the individual elements of the system under consideration. The analysis considered two variants of the power unit’s operation—at full load and at the technical minimum.

The analytical process consisted of several key stages, starting with the analysis of the technical documentation and structure of the unit, through the collection and processing of operational data, to the construction of mathematical models of the equipment and their integration into one coherent model of the power unit. Next, balance calculations were carried out for both selected operating variants to identify the locations with the highest exergy losses and exergy destruction in the system. The next step was to compare the results of the exergy analysis with the classical energy analysis, which made it possible to indicate in which areas the exergy analysis provides more valuable information than traditional methods.

The aim of the study is not only to identify the exact locations of exergy losses but also to identify potential areas where improvements and optimisations can be implemented to increase the exergy efficiency of the entire system. The analysis also allows for the development of practical recommendations that can contribute to increasing the overall energy efficiency of the analysed unit. Thus, this work can make a significant contribution to the development of more efficient and environmentally responsible energy technologies, as well as provide valuable guidance for the practical application of exergy analysis in energy engineering in its broadest sense.

Exergy analyses of other energy systems can also be found in the authors’ previous articles [29,30,31,32].

2. Materials and Methods

The modelling process followed several main steps. The first was to analyse the technical documentation and the unit structure in terms of exergetic analysis. This was followed by the power unit model, which consists of sub-models of the energy installations. Utilising the model implemented in the numerical environment, an energy and exergy analysis was carried out for two power levels of the unit: operational minimum and maximum.

The operating data prepared in advance were used as boundary conditions for the model. One must also consider that the mass and energy balances for the instantaneous values measured via the power unit measurement system may need to be met due to measurement errors and inertia. Therefore, in order to minimise the impact of these phenomena, the measurement data were processed. For the steady-state unit, operating data were collected at minimum and maximum load. Records corresponding to a power other than ±1 MW were then discarded. From the remaining records, averages were determined for each of the analysed parameters based on the probability density of a normal distribution.

2.1. Data Preparation from Direct Measurements

Both energy and exergy analysis of a power unit requires the definition of a specific operating state of the unit and then isolating the values of the unit parameters corresponding to this state. In the case of the analysed unit, two operating states were selected:

• Operation at nominal (maximum) power conditions—100% load.
• Operation at minimal power conditions—45% load.

After determining the operating states of the unit, two measurement campaigns (Figure 1) were carried out in which the unit operated at 100% (maximum) and 45% (minimum) power. The duration of the measurement campaigns is shown in

Table 1. Measurement campaign parameters of 500 MW class unit.

Parameter	Measurement Campaign 1	Measurement Campaign 2
Measurement duration	53 h	72 h
No. of records	3180	4320
Number of records corresponding to minimum power (45% load)	820	1312
Number of records corresponding to maximum power (100% load)	1757	2365
Number of records rejected in the filtering process	603	643
Number of parameters analysed	99	99

.

The records of the unit’s operating parameters were derived in a data matrix containing information such as the measurement time, the unit’s power, and the measured parameter values. The measurement frequency is 60 s. The number of records for each measured parameter is presented in Table 1.

An analysis of the measurement data was carried out to determine the values of the parameters that best correspond to the operation of the block under steady conditions, i.e., at specific power levels of the unit. As two operating states of the 500 MW class unit were studied as part of the energy and exergy analyses, the first step in analysing the measurement data was to observe the correlation of the measured parameters with the unit power. Diagrams showing the correlation of the selected parameter with the unit power are shown in Figure 2. As the data refer to the unit’s operation over a wide power range, the next step was to determine the records corresponding to the unit’s operation with maximum and minimum loads and to discard the records corresponding to the unit’s operation with intermediate power values. In each of the periods studied, records corresponding to minimum and maximum power ±1 MW were selected. The filtering process results are shown in Table 1.

To calculate the average values of the performance parameters, the data corresponding to the specified power were analysed according to the following scheme:

• The minimum and maximum values of the measured parameter were determined ($w_{min},w_{max}$).
• The analysed data range was determined as $w={<w}_{min},w_{max}>$.
• The histogram interval length $l$ was determined as $l=\frac{w_{max}-w_{min}}{n}$, where $n$ is the number of histogram intervals. The number of intervals equalled 12, and it was determined using Sturges’ rule: the number of intervals was calculated as $k=1+{log}_2\left(i\right)$, where $i$ is the number of observations.
• The histogram intervals were determined using Formula (1), where $i=\mathrm{1,2},3\dots n$

  $$k_i=<w_{min}+\left(i-1\right)l,w_{min}+il>,$$

  (1)
• The number of records per histogram interval was calculated.
• The interval with the highest record number was determined as $k_{max}$.
• The average value of the analysed parameter was determined (Equation (2))

  $$k_{s max}={(w}_{min}+\left(i-1\right)l+w_{min}+il)/2,$$

  (2)

The scheme presented above was used to analyse each of the measured unit parameters. Graphs showing histograms of selected parameters are shown in Figure 3. They represent the probability density of measurements occurring within the designated intervals. Some of the histograms have the characteristics of a normal distribution.

2.2. Mathematical Model and Energy Analysis

Within the power unit case study, a model was developed for the unit, including the steam and air–flue gas circuits, without taking into account the auxiliary installations. The model implemented in the numerical environment consisted of submodels, including turbine stages, fans, heat exchangers, valves, and pipelines. The analysed plant under consideration uses three main working mediums during steady-state operation: water, air, and exhaust gas. Two working medium models were used in the power unit model. The Peng–Robinson model [20] was used for flue gas and air. Since the water/steam part of the system requires a much more accurate model dedicated exclusively to this medium, the ASME Steam model [21] was used for this part. The analysis included a series of balance calculations based on the constructed system model. These calculations made it possible to determine the key thermodynamic parameters in the system and the fluid flow values, which were then used to carry out energy and exergy analyses. The calculations were made for two system operating conditions corresponding to the minimum and maximum unit load.

A graphical interpretation of the model is given in Figure 4, Figure 5 and Figure 6. The primary steam system (Figure 4), the reheated steam system (Figure 5), and the air–fume system (Figure 6) are shown. The diagrams indicate points corresponding to specific locations in the system for which the values of thermodynamic parameters and flows were determined. For each of the examined operating states of the boiler system, the values of the above parameters are included in Appendix A. The fluid mass flow, temperature, pressure and enthalpy are shown at each point. The designations of the points in the system are shown in Appendix A. Figure 4 shows a primary steam diagram, including the evaporator and feedwater heater. The sub-system includes a feedwater heater, an evaporator, a drum, four primary steam lines, desuperheater chambers, and a section of the injection water feed system. Figure 5 shows a schematic of the reheated steam described in sections 1.53 to 1.90. The modelled sub-system includes four lines of reheated steam, desuperheater chambers, and a section of the injection water feed system. A schematic diagram of the air and flue gas system is shown in Figure 6, which is described in sections 1.91 to 1.118. The modelled sub-system includes the boiler heat exchange and the system of three air and flue gas lines, together with rotary air heaters, flue gas fans, and air fans.

Following the mathematical model of the unit and after determining the values of thermodynamic parameters and flows at key points in the system, the unit’s energy balances were carried out for minimum and maximum loads. The energy balance results are presented in Figure 7.

The steam turbine set model with its cooling system was implemented in the Aspen HYSYS 2.4 programme. The diagram of the steam part of the modelled system is shown in Figure 8.

This system consists of a steam turbine (high-pressure part HP with control stage HR, medium-pressure part MP, and two low-pressure parts LPI and LPII). There is a reheater between the high-pressure and medium-pressure parts of the turbine, and the exhaust steam from the low-pressure parts of the turbine goes to separate condensers CO₁ and CO₂. The turbine has an extensive high-pressure regeneration carried out by six heat exchangers, XH1A-XH3B. Medium-pressure regeneration is carried out by the heat exchanger XL3 (and deaerator), and low-pressure regeneration by the heat exchangers XL1 and XL2. The main feedwater pump is driven by the steam turbine TP with a separate condenser CC. All condensers are cooled by a cooling tower. The energy balance of the steam turbine set is shown in Figure 9.

This balance shows that the largest source of losses in the turbine set from the point of view of energy analysis is condensers CO₁ and CO₂. These losses, for a minimum load, constitute 26% each in the energy balance for condensers CO₁ and CO₂.

This balance shows that the largest source of losses in the turbine set, for maximum load, from the point of view of energy analysis are also condensers CO₁ and CO₂. These losses, for maximum load, constitute 26% and 25% of the energy balance for capacitors CO₁ and CO₂, respectively.

2.3. Exergy Analysis

By adapting the mathematical models presented above to exergy analysis, it is possible to calculate the exergy balances of individual systems. The exergy balance can be described in a general way by the Gouy–Stodola equation [1,33]:

$$\delta B=T_0\sum \Delta S,$$

(3)

In order to calculate the exergy destruction using the formula (Equation (3)), one needs to know the working medium entropy. The real gas entropy (the working medium model for flue gas and air) is calculated by adding the residual entropy to the perfect gas entropy. The difference between the real gas entropy according to the Peng–Robinson model and the perfect gas entropy can be represented by the following formula (Equation (4)) [34]:

$${\left(S^{GR}-S^{GD}\right)}_{p,T}=R\ln \left(Z-B\right)+\frac{\frac{da}{dT}}{2\sqrt{2b}}\ln \left[\frac{Z+\left(1+\sqrt{2}\right)B}{Z+\left(1-\sqrt{2}\right)B}\right],$$

(4)

The correlations for the individual coefficients in the second (Equation (4)) equation are as follows:

$$Z=\frac{pV}{RT},$$

(5)

$$B=\frac{pb}{RT}$$

(6)

$$A=\frac{pa}{R^2{T}^2}$$

(7)

$$a\left(T\right)=0.45724\frac{R^2{T}_c^2}{p_c}\alpha \left(T\right)$$

(8)

$$b=0.0778\frac{R{T}_c}{p_c}$$

(9)

$$\sqrt{\alpha }=1+\kappa \left(1-\sqrt{\frac{T}{T_c}}\right)$$

(10)

$$\kappa =0.37464+1.54226\omega -0.26992{\omega }^2$$

(11)

Steam and liquid water entropy were calculated using the ASME equations [35]. The correlations used to calculate the exergy destruction in the modelled system elements are described in Equations (12)–(15). The exergy loss in fans, compressors, and pumps was calculated according to Equation (12).

$$\delta B={\mathrm{B}}_2-{\mathrm{B}}_1-{\mathrm{E}}_{\mathrm{m} \mathrm{s}}$$

(12)

Exergy loss in turbine/turbine section (Equation (13)):

$$\delta B={\mathrm{B}}_2-{\mathrm{B}}_1+{\mathrm{E}}_{\mathrm{m} \mathrm{t}}$$

(13)

Exergy loss in heat exchangers (Equation (14)):

$$\delta B={\mathrm{B}}_{2 \mathrm{z}}+{\mathrm{B}}_{2 \mathrm{g}}-{\mathrm{B}}_{1 \mathrm{z}}-{\mathrm{B}}_{1 \mathrm{g}}$$

(14)

Exergy loss in valves and vessels (Equation (15)):

$$\delta B={\mathrm{B}}_2-{\mathrm{B}}_1$$

(15)

The boiler system exergy analysis was based on a previously developed mathematical model, using flow rates and thermodynamic parameters at key points in the system. The analysis was made using literature-based correlations [8]. The boiler exergy balance was calculated based on Equation (16):

$$\dot{B_F}=\dot{B_P}+\dot{\delta B_L}+\dot{\delta B_D}$$

(16)

The exergy feeding the boiler, i.e., the fuel exergy $\dot{B_F}$, is calculated using Equation (17):

$$\dot{B_F}=\dot{m_F}{b}_F$$

(17)

The chemical exergy of fuel $b_f$ was determined based on Equation (18) [10]:

$$b_f=(W_d+rg)\beta +(b_s-W_{d,S})g_s+b_p·g_p+b_w·g$$

(18)

The increase in utility product exergy in the boiler corresponds to the increase in exergy of primary steam and reheated steam calculated from the formula (Equation (19)):

$$\dot{B_P}=\dot{m_p}[\left(h_2-h_1\right)-T_{ot}\left(s_2-s_1\right)]$$

(19)

External exergy loss $\dot{B_L}$ includes components such as outlet exergy loss and chemical and physical losses in slag and fly ash. Internal exergy destruction $\dot{B_D}$ refers to destruction resulting from irreversible processes such as combustion, media mixing, or heat transfer. The values of the detailed coefficients and the relationships used for the calculations described in this article were adopted from [8,21].

3. Results

The parameter values determined necessary for the exergetic analysis at each point in the system at minimum and maximum load are shown in Appendix A. The fluid mass flux, temperature, and entropy are shown at each point. The exergetic balance of the boiler system is shown in the Sankey diagram in Figure 10 and Figure 11. According to the Sankey diagrams showing the boiler system exergy balance, one can notice that the dominant exergy fluxes are the medium exergy gain and the exergy destruction due to the combustion irreversibility and the heat exchange.

At minimum load, exergy destruction accounts for 54.79% of the total flows, while at maximum load, it drops to 53.89%. Such a difference indicates a slightly higher exergetic efficiency at higher boiler loads. This information allows us to state that from the operator’s point of view; it is more efficient both exergy-wise and energetically to run the unit with nominal power or close to nominal power, which is obvious information. However, the relatively small difference in exergy loss provides information about the fact that losses in the case of operation with minimum load are relatively small (about 1% in relation to nominal power), which is positive information due to the current nature of operation of power units, which, due to the relatively large share of energy from renewable sources, often have to operate with nominal load. In both cases, the main exergy flow is associated with superheated steam, reaching 37.30% and 37.69% for minimum and maximum loads, respectively. The irreversibility of the combustion process, which is an important source of exergy loss, remains similar for both loads, being 34.62% at minimum and 34.76% at maximum load. The stability of this parameter, despite the difference in load, indicates that the characteristics of the combustion process in terms of exergy efficiency are unchanged.

Analysing the exergy destruction flux through heat exchange in the boiler, which is 20.17% at minimum load and 19.13% at maximum load, one can see an improvement in exergy efficiency at higher loads. Other exergy losses, such as those due to fly ash and slag, also show stability, with values of 0.26% and 0.27% for ash and a constant 0.07% for slag at minimum and maximum load. Exergy loss in exhaust gases is noticeably higher in the minimum load case. The Sankey diagrams (Figure 12 and Figure 13) detail the distribution of exergy loss and destruction in the boiler, distinguishing the individual exchangers in the system.

In Figure 12, for a minimum load, exergy destruction in the boiler system is dominant over losses, which account for 2.49%. The irreversibility of the combustion process reaches 61.62%, which is the dominant factor in the distribution of losses and exergy destruction. Destruction through heat exchange in the boiler is 35.89%, of which a significant share is allocated to the evaporator due to the high-temperature differences in the heat exchange process. Exergy losses in other components, such as fly ash, slag, and flue gas, are very low, 0.46%, 0.12%, and 1.91%, respectively.

At maximum load, the exergy loss drops slightly to 2.24%. The irreversibility of the combustion process is slightly higher than at minimum load, reaching 63.06%. It is worth noting that heat exchange in the boiler drops to 34.70%, indicating an increase in heat exchange efficiency at higher loads. Other exergy losses in components such as fly ash, slag, and flue gas remain at similar levels, with minimal differences compared with the minimum load. Furthermore, slight changes in exergetic efficiency at the above-mentioned points of the system, indicating a slight deterioration in system efficiency at minimum power, point to the potentially good preparation of the system for operation at minimum power, which is important given the current significant share of renewable sources in the European energy system.

The exergy balance of the steam turbine set for minimum load is shown in Figure 14.

It is worth noting that the exergy efficiency of the steam turbine set is very high compared with the exergy efficiency of the boiler and amounts to 77.59% for the minimum load.

A similar graph (Figure 15) shows isolated exergy losses and destructions in the steam part of the system.

Quite a large share of exergy losses are those included in the group of leakages and others—5.49%. The graph also shows “other” small exergy losses and destructions (none of which exceed 0.3% individually). This item accounts for 1.51% of exergy losses and destructions.

The exergy balance of the steam turbine set for the maximum load is shown in Figure 16.

It is important to highlight that the exergy efficiency of the steam turbine set is significantly higher than that of the boiler, reaching 83.68% at maximum load.

Compared with the total exergy flow, items other than those related to turbine power appear to be very small. Therefore, a separate graph shows isolated exergy losses and destructions in the steam part of the system—Figure 17.

For this case, leaks account for 2.17% of exergy losses. The sum of other small losses and exergy destruction in this case is 1.98%.

A comparison of the percentage shares of exergy destruction in the total exergy destruction of the steam turbine set for maximum and minimum load shows that for low load, the greatest exergy destruction occurs on the VLZ-1 and VLZ-2 control valves. This is the result of throttling on these valves. The situation is completely opposite for full load—exergy destruction on the control valves is then negligible, while exergy destruction on the heat exchangers (especially on the CO₁ and CO₂ condensers) increases. This is because for a full load, we have a much larger flow of steam and water (in the case of CO₁ and CO₂ condensers, the cooling water flow is constant, and the steam flow is greater), and the heat exchange surface is the same. As a result, for full loads, we have larger temperature differences on the heat exchangers than for partial loads.

Therefore, for low load, the greatest source of exergy destruction is throttling, and for full load, it is exergy destruction on the condensers.

4. Discussion

As indicated in the previous section, it is possible to identify the locations of thermodynamic imperfections for the system under consideration. The components of the system responsible for this thermodynamic imperfection are not obvious when energy analysis is applied, but they can be seen thanks to the methods of exergy analysis.

Based on the exergy analysis of the boiler system, it can be stated that in both analysed operating states, exergy destruction resulting from the irreversibility of the combustion process is dominant, amounting to over 60% of all exergy losses/destruction in the system. The second dominant factor is exergy destruction resulting from heat exchange in the boiler, the largest part of which is heat exchange in the evaporator. This results from the fact that the evaporator has the largest temperature difference between exhaust gases and water/steam, and at the same time, it takes over the dominant amount of heat from exhaust gases.

As part of the work carried out, the percentage shares of the power of individual exchangers in the boiler and the percentage shares of exergy destruction in the same exchangers were analysed. The values of the exergy destruction shares are not directly related to the power of the exchangers. The key factor influencing the value of exergy destruction is the temperature difference in exhaust gases and steam/water exchanging heat in the area of the analysed sub-system.

Exergy destruction due to the combustion process and heat exchange is inevitable in boilers and results from the nature of the boiler operation; at the same time, it constitutes almost 98% of the exergy losses of the system. The remaining exergy losses, constituting more than 2%, are the exhaust loss and loss in slag and fly ash. Among the above losses, the exhaust exergy loss shows the greatest possibility of reduction. Currently, at nominal load, the exhaust gas temperature is about 155 °C, and the exergy loss of the boiler system does not exceed 2%. When the exhaust gas temperature is reduced to 140 °C, a reduction in the exergy loss can be expected by a maximum of several MW. However, such a change is associated with the modification of the rotary air heater. The second possibility of a slight improvement in the exergy efficiency is the installation of inverters for air fan systems, which show a significant decrease in both energy and exergy efficiency at a lower block load. A comparison of percentage shares of exergy destruction in the total exergy destruction of the steam turbine set for the full load and the minimum load shows that for a low load, the greatest exergy destruction occurs on the VLZ-1 and VLZ-2 control valves. This is the result of throttling on these valves. The situation is completely opposite for a full load—exergy destruction on the control valves is then negligible, while exergy destruction on the heat exchangers (especially on the CO₁ and CO₂ condensers) increases. This is because, for a full load, we have much larger flows of factors (in the case of CO₁ and CO₂ condensers, only the steam flow is larger), and the heat exchange surface is the same. As a result, for a full load, we have greater temperature differences on the heat exchangers than for partial loads. In the case of a low-load turbine set, the greatest source of exergy destruction is throttling, and for a full load, exergy destruction occurs in the condensers. It is worth emphasising that the exergetic efficiency of the steam turbine set is very high compared with the exergetic efficiency of the boiler and amounts to 77.59% for the minimum load and 83.68% for the maximum load.

As part of this study (in the case of the turbine set), three modifications were indicated that may lead to obtaining certain savings: the use of an additional pump to increase the pressure before the auxiliary turbine condenser; replacement of the auxiliary turbine seals with telescopic seals; replacement of the condenser tubes with titanium tubes.

Unfortunately, these modifications lead to a slight reduction in exergy losses and destruction and thus to small increases in the turbine set’s power.

The possibilities of a slight reduction in exergy losses presented above should be subject to a feasibility analysis and economic evaluation, which may significantly affect the justification for carrying out activities aimed at improving the exergetic efficiency in the analysed system.

Due to the fact that the calculations carried out in this study revealed only slight possibilities of reducing exergy losses and destruction, it can be said that the analysed block has good properties from the point of view of exergy analysis in comparison with other subcritical blocks of similar power.

In summary, the modification recommendations for the boiler are as follows:

• Modification of the rotary air heater.
• Installation of inverters for air fan systems, which shows a significant decrease in both energy and exergy efficiency at lower block load.

As a result of the energy and exergy analyses conducted in the previous sections, the following modifications to the steam power unit can be indicated as interesting:

• Replacing the CO₁ and CO₂ condenser tubes with titanium ones;
• Replacing the auxiliary turbine seals;
• Providing an additional pump for the auxiliary turbine condenser cooling water in order to avoid unnecessary pressure increases in the entire cooling system and thus reduce the power of the main cooling water pumps.

Assuming that the steam unit operates for 3500 h a year at full power (which is typical in Poland today), the proposed modifications can result in the following reductions in CO₂ emissions:

• Modification of the rotary air heater—10,500 tCO₂/year;
• Installation of inverters for air fan systems—500 tCO₂/year;
• Replacing the CO₁ and CO₂ condenser tubes with titanium ones—7326.9 tCO₂/year;
• Replacing the auxiliary turbine seals—161.0 tCO₂/year;
• Providing an additional pump for the auxiliary turbine condenser cooling water—2077.2 tCO₂/year.

These are noticeable savings but too small to justify the significant investment costs associated with them.