Energy and Exergy Evaluations of a Combined Heat and Power System with a High Back-Pressure Turbine under Full Operating Conditions

: High back-pressure technology is a promising method for the waste heat recovery of exhaust steams in combined heat and power systems. In this research, a 300 MW coal-fired subcritical combined heat and power system was selected as the reference system, and modeled in EBSILON professional. Then, energy-based and exergy-based performances of the high back-pressure system and traditional combined heat and power system were compared under full operating conditions. Moreover, a novel exergy-based evaluation method, which considers the energy level of the heating supply, was proposed and applied to evaluate the two systems. Results show that: In design conditions, both the heating capacity and power output of the high back-pressure system were higher than those of the extraction condensing system, which led to 17.67% and 33.21% increments of the gross thermal efﬁciency and generation efﬁciency, respectively. Compared with the extraction condensing system, the exergy efﬁciencies of the high back-pressure system were 7.04–8.21% higher. According to the novel exergy-based evaluation, the exergy efﬁciencies for the generation of the high back-pressure system and extraction condensing system were 46.48% and 41.22%, respectively. This paper provides references for the thermodynamic performance evaluation of the combined heat and power system.


Introduction
Combined heat and power (CHP) is a well-proven energy-saving technology for fossil energies [1]. By the end of 2016, the gross installed capacity of CHP reached 755.2 GW and kept incrementing by 2.8% per year [2]. In China, CHP is widely used in the coal-fired power plants due to the coal-dominated resource structure [3]. The total installed capacity was 435 GW in 2018, accounting for 39.4% of the coal-fired power plants. Hence, the technological innovation of CHP technology is essential for the energy industries around the world.
In the traditional CHP system, the steam for heating is usually extracted between the medium-pressure turbine and low-pressure turbine. In the meantime, the heat loss of exhaust steam is large and hard to recover due to its low energy level. Thus, the waste heat recovery of the CHP plant has been widely focused on and considered as a significant part in future district heating (DH) system. Currently, the CHP system with a high back-pressure turbine (CHP-HBP) has drawn more and more attention [4]. In the HBP system, with the improvement of the back-pressure of the low-pressure turbine, the temperature of the exhaust steam is largely increased. Then the exhaust steam can heat the thermal network water, which leads to nearly zero heat loss of the turbine [5]. Due to

Traditional CHP System
In traditional coal-fired CHP plant, the live steam, which is generated directly from the boiler, is usually expanded in the high-pressure turbine (HPT) and medium-pressure turbine (MPT) first. Then, part of the steam will be extracted to heat the water through the thermal network heater (THN), while the rest is sent to the low-pressure turbine (LPT). This mode is also called the "extraction condensing (EC) system." By the cascade utilization of the steam and the decrease of the exhaust steam loss, the CHP system shows great advantages in energy conservation over the system that generates electricity only (power-only system). In this research, a 300 MW coal-fired subcritical single-reheat power plant was selected as the reference system, which has three high-pressure regenerative heaters, three low-pressure regenerative heaters and one deaerator, as shown in Figure 1. The pressure of the extracted steam for heating is 0.4 MPa. After the thermal network heater, the steam is cooled as the drain water of 104 • C and sent to the deaerator. The maximum mass flow of the extraction steam is 500 t/h. Tables 1 and 2 give the main technical parameters and the steam parameters of the reference system under the turbine maximum continuous rating (TMCR) conditions, respectively. Generally, the turbine heat acceptance (THA) is the normal condition for generation given by the manual of the steam turbine, while the TMCR is the base condition for the CHP process. Table 3 gives the elemental analysis of the selection coal, in which q LHV , A ar , M ar and V ar denote the lower heating value, ash, moisture and volatile contents of the coal as-received, respectively.
However, there are still improvements in the traditional CHP plant: (1) Considering the safety of the LPT, not all the steam can be extracted for heating, which means the exhaust steam loss in the condenser is inevitable. In fact, the volumetric flow rate of the steam in the LPT is usually no less than 1/3 of the designed value. (2) Besides, the energy level of the extracted steam is much higher than that of the thermal network water, which restricts the possibly performance improvement of the traditional CHP plant.

CHP System with a High Back-Pressure Turbine
CHP-HBP is a novel process for the coal-fired power plant, also known as the low vacuum system, as shown in Figure 2 [7]. In the HBP system, the back-pressure of the LPT is increased to improve the energy level of the exhaust steam. Then, the waste heat of the exhaust steam can be recovered to heat the thermal network water. By doing this, the loss of exhaust steam is eliminated and nearly zero loss of the turbine side can be achieved. Thus, the HBP system could significantly improve the heating capacity and efficiency of the power plant [22].
In this research, the back-pressure of the LPT was set as 54 kPa with the saturation temperature of 83.27 • C, by removing the last two stages of blades [23]. Compared with the traditional CHP system, the temperature of the heating steam in the HBP system is much lower. This could reduce the exergy loss between the steam and thermal network water, but make it worse in the adaption to a high-temperature thermal network. However, such characteristics cannot be reflected in the existing energy-and exergy-based evaluation method, because they are all based on the product only and care little about the energy level of the heating steam. In the following part, thermodynamic performances of the two system based on the existing evaluation methods are compared and the limitations are discussed.  Figure 2. Schematic of the coal-fired CHP-HBP system.

Modeling Method
In this research, EBSILON Professional was used to building the mathematical model, which is widely used in the design, optimization and evaluation of the general thermal process and has proved to be a reliable tool in modeling process [24,25]. Model details of the main components are listed in Table 4, and the model of the reference system in EBSILON is shown in Figure 3. In the modeling process, the shaft-packing leakage of the turbine is also considered to improve the accuracy. Some of the leakages are recovered to the gland heater (GH), while the others are sent to the seal system of the LPT. Detailed sources and destinations of the leakages can be seen in Figure 3.  High-pressure regenerative heater = 3%; Low-pressure regenerative heater = 5%; Pipeline from MPT to LPT =4.5% Feed water preheater NO. 10 Pressure loss of feed water = 5 kPa; Upper temperature difference: 1# = −1.
In the off-designed simulation of the turbine, there are two parameters that have substantial influences on the power output: (1) the inlet and outlet pressures and (2) the isentropic efficiency.
In EBSILON professional, the pressures can be deduced by Stodola's law [26]: where G is the mass flow rate the steam, kg/h; p is the inlet pressure, MPa; v denotes the specific volume, m 3 /kg. The output of the turbine stage (P s ) can be calculated as: where h 1 and h 2,is are the enthalpies of the inlet steam and outlet steam in isentropic process, kJ/kg; η is and η s,m denote the isentropic efficiency and mechanical efficiency, which are obtained in the manual of the steam turbine, %. Figure 4 gives the accuracy validation of the model, which compares the simulation results of the model with design data of the turbine manual in both power-only and CHP conditions. The maximum relative error(RE) is −0.39% in 75% THA condition, which proves that the model has high precision and can be used in the following discussion.

Energy-Based Evaluation
The most commonly used evaluation method of the CHP system is based on the first law of thermodynamics, called the energy-based evaluation [27]. This method mainly follows the mass and energy balances and can obtain primary energy savings. The typical indicators are given below.
The gross thermal efficiency (η g,CHP ): where P and Q H are the power and heat loads of the CHP system, respectively, MW; B is the coal consumption rate of the boiler, t/h. The heating efficiency (η h,CHP ): where η b,CHP and η p,CHP are the efficiencies of the boiler and pipe, %. The generation efficiency (η e,CHP ): The standard coal consumption rate of generation (b e,CHP ): The standard coal consumption rate of heating (b h,CHP ): 3.

Conventional Exergy-Based Evaluation
The energy-based evaluation presents the energy utilization condition from the quantity aspect, but ignores the energy level differences of the sources and products. By contrast, the exergy is a conception based on the second law of thermodynamics. It represents the maximum useful work the energy can generate with its environment during a reversible process, and is the measure of the energy quality. The exergy efficiency can be usually defined as the ratio of useful exergy output to the total exergy input. Hence, exergy-based evaluation covers not only the quantity but also the quality of the energy and is considered as a more objective criterion than the energy-based method [28].
The traditional exergy efficiency of the CHP system can be given as: where E H is the output exergy for heating, MW; ξ is the ratio of the exergy of the coal to its q LHV ; η ex DH is the exergy efficiency of the DH system, %. ξ can be calculated as [29]: The η ex DH can be calculated as: where T 0 and T C are the temperatures of the environment and the cold-end, • C. In this study, the temperature of the environment was set as 0 • C. In traditional exergy-based evaluation, the cold-end has different definitions. Usually, the object of the cold-end could be the heat consumer or the heat station. In this research, T C of the former was constant as 20 • C while T C of the latter was the mean temperature of the supplied-and returned-water, • C. Figure 5 gives the energy flow diagram of the two systems in the maximum heating condition. The energy from the boiler of the HBP system is 1.87 MW lower than the EC system when the mass flow of the main steam remains the same. The main losses of the EC system from the condenser, boiler, pipes and others, account for 17.72%, 7%, 1.35% and 0.35% of the input energy, respectively. Moreover, the output heating and power occupy 43.83% and 29.74%, respectively. Compared with the EC system, the HBP system has a similar energy loss distribution except for the exhaust steam loss, which is 0 in the HBP system. The output heating and power of the HBP system account for 55.61% and 35.63%, 11.78% and 5.89% higher values than those of the EC system. Table 5 gives the energy-based comparison of the two CHP modes in design conditions. The HBP system has higher heating capacity, power output, generation efficiency and exergy efficiency than the EC system. In detailed, the gross efficiencies of the HBP system reach 91.24% and 17.67% higher than the EC system. Moreover, the heating capacity of the HBP system also has a 26.58% (92.89 MW) improvement over that of the EC system. In the meantime, the power generated by the HBP system is also 46.29 MW higher. Overall, the generation efficiency of the HBP system reaches 89.98% with the standard coal consumption rate of 136.47 g/kWh, 79.84 g/kWh lower than that of the EC system. When the temperature of the cold end is set as the heat user (T C = 20 • C), the exergy efficiency of the HBP system is 6.52% higher than that of the EC system.   Figure 6 shows the gross thermal efficiencies, generation efficiencies and exergy efficiencies of the two systems in the whole feasible operational range. It can be seen that the energy-based evaluation methods (η g,CHP and η e,CHP ) show similar trends, which are that η g,CHP and η e,CHP will increase with the increment of the heat load when the live steam remains the same. With the maximum mass flow of live steam, when the heat load of the EC system changes from 0 to 249.52 MW, η g,CHP and η e,CHP are increased from 39.83% to 73.58% and from 39.83% to 56.77%, respectively. By contrast, when the heat load of the HBP system changes from 0 to 442.41 MW, η g,CHP and η e,CHP are increased from 35.70% to 91.24% and from 35.70% to 89.98%, respectively. This trend also reflects the advantage of the CHP system over the power-only system. However, a different trend is achieved when it comes to η ex g,CHP . The rise of the heat load could decrease η ex g,CHP of the EC system but increase η ex g,CHP of the HBP system. When the heat load changes from 0 to the maximum, η ex g,CHP of the EC system decreases from 38.81% to 31.89% when η ex g,CHP of the HBP system increases from 34.78% to 38.41%. Furthermore, results in Figure 6c,f also are affected by the cold-end temperature, which brings about some limitations which are discussed in Sections 4.1.3 and 4.2. Figure 6. Efficiencies in the feasible operational region: (a) η g,CHP of EC system; (b) η e,CHP of EC system; (c) η ex g,CHP of EC system (T C = 20 • C); (d) η g,CHP of HBP system; (e) η e,CHP of HBP system; (f) η ex g,CHP of HBP system (T C = 20 • C).

Exergy Analysis with Different Cold-End Temperatures
According to Equation (10), the conventional exergy-based evaluation is based not only on the CHP system but also on the temperature of the cold end. In the above section, the cold end is set as the heat user (T C = 20 • C). In this section, the cold end is the water in the DH system. Moreover, the temperatures of the returned-and supplied-water could influence the exergy-based performance. Figure 7 shows the influences of returned-and supplied-water temperatures on η ex DH . In the application, the temperatures of returned-and supplied-water are usually no more than 70/130 • C. Temperatures higher than these are for the theoretical analysis only and are presented as empty circles in the figure.
With the increment of the returned-and supplied-water temperatures, the exergy of the DH system increases. With the mean temperature of the water increases from 35 • C to 125 • C, η ex DH is raised from 11.36% to 31.40%, which means every 10 • C improvement of the mean temperature could bring about 2.23% increment of η ex DH in the given temperature range. With the returned-and supplied-water temperatures of 70/130 • C, η ex DH could reach 26.80%. Based on η ex DH given in Figure 7, Figure 8 gives the exergy efficiencies of the two systems with different returned-and supplied-water temperatures. The exergy efficiency has a similar trend as η ex DH , and increases with the improvement of the mean temperature of the thermal network water. Every 10 • C improvement of the mean temperature could bring about 1.38% increment of the exergy efficiency of the HBP system, which is 0.95% of the EC system. Compared with the EC system, the exergy efficiency of the HBP system is 7.04-8.21% higher with the same cold-end temperature.

Limitations of the Traditional Evaluations
Results above show some limitations of the traditional exergy-based evaluation: 1. The conventional exergy-based evaluation of the CHP system strongly relies on the temperatures of the cold-end and the environment, which increases the complexity of further exergy-based research. For example, each cold-end temperature will need a unique diagram to show the exergy efficiencies in the feasible operational region (Figure 6c,f). 2. The conventional exergy-based evaluation only concerns the product but ignores the heat sources.
For example, the HBP system shows great advantages over the EC system under both the energy-based and the conventional exergy-based evaluations. However, the heating steam of the EC system has a higher level, which is hard to be displayed in these evaluations. Thus, these evaluation methods have limitations when used to compare different types of CHP systems. 3. Results based on conventional exergy-based evaluation could also lead in the wrong directions.
For example, according to the results in Figures 7 and 8, the increment of the cold-end temperature could increase the exergy efficiency of the CHP system. However, this may raise the bar to recover the low-level waste heat and is opposite to the DH system in the future [30].

Proposal of the Novel Exergy-Based Evaluation
The conventional exergy-based evaluation of the CHP system has some limitations and has difficulties in guiding the improvement of CHP technology. Considering that, a novel exergy-based evaluation is proposed in this research, which is based on the exergy consumption dispatch of the heat and power.
In the novel evaluation, the main objective is to separate the exergy consumption of heating from the gross consumption scientifically. After that, the exergy consumption of the generation can be obtained, as shown in Figure 9. The new evaluation concerns the heating steam and its exergy consumption of different CHP types, so the temperatures will not influence it. The following gives the main criterion of the novel evaluation method. For the thermal network heater (TNH), the exergy efficiency can be achieved as: where E s and T S are the exergy and mean temperature of the heating steam, respectively. The exergy efficiency for heating (η ex h,CHP ): where η ex p,CHP is the exergy efficiencies of the pipe, which is 97% in this study [31]; and η ex b,CHP denotes the exergy efficiency of the boiler, which can be calculated as: where D 0 and D r are the mass flows of the live steam and reheat steam, t/h; e 0 , e f , e r,hot and e r,cold are the specific exergies of the live steam, feed water, hot and cold sides of the reheat steam, respectively, kJ/kg. Finally, the exergy efficiency for the generation (η ex e,CHP ) of the EC system can be deduced: For the HBP system, the mass flow of the exhaust steam depends on the mass flow of live steam only. That means when the live steam is constant, the exergy consumption for heating should be the same no matter whether the waste heat of the exhaust steam is fully recovered. Here, τ is defined as the mass flow ratio of the exhaust steam recovered in the heating condenser. Then, the exergy consumption for heating should be E H /(η ex h,CHP τ), and the η ex e,CHP of the HBP system is deduced as:

Exergy Analysis under Design Conditions
To show the energy level differences between the heating steam in the two systems, Figure 10 gives the T-Q diagram of the heating steam in the two systems. The heating steam of the EC system goes through several states (superheated steam, saturated steam, wet steam, saturated water, unsaturated water) in the heating process with the mean temperature of 145.87 • C. By contrast, the heating steam of the HBP system is wet steam initially, and releases heat to the saturated water with a constant temperature of 83.27 • C. Thus, although the heating capacity of the HBP system is 72.89 MW higher, the energy level of the heating steam is lower than that of the EC system.  Figure 11 gives the influences of the supplied-and returned water temperatures on the exergy efficiency of the TNH. Similar to the gross exergy efficiency shown in Figure 9, the improvement of the temperature of the thermal network water can increase η ex TNH,CHP in both systems. With the same supplied-and returned water temperatures, the η ex TNH,CHP of the HBP system is 16.00-30.32% higher than that of the EC system. Within the given range, the η ex TNH,CHP of the HBP system can reach 92.21% (80/70 • C), which is 76.98% (130/70 • C) of the EC system. Based on the results in Figure 11, Figure 12 shows the influence of the thermal network heater temperature on the exergy efficiency for heating (η ex h,CHP ). The exergy efficiency of the boiler was calculated to be 51.14%, and the exergy efficiency of the pipes was set as 97%. With the returned-water temperature increasing from 30 • C to 70 • C, the η ex h,CHP of the EC system changed from 32.71% to 38.70% with the supplied-water temperature of 130 • C; that of the HBP system changed from 36.06% to 46.35% with the supplied-water temperature of 80 • C. Then the thermodynamic comparison based on the novel exergy analysis is shown in Table 6. According to the results before, the energy of the heating steam of the HBP system is 72.89 MW higher than that of the EC system. However, the exergy of the heating steam of the HBP system is 18.32 MW lower than that of the EC system, which is caused by the energy difference of the heating steam and also leads to a 33.30 MW decrement of the exergy consumption for heating. Finally, the exergy efficiencies for generation (η ex e,CHP ) of the HBP system and EC system can be achieved, which are 46.48% and 41.22%, respectively. Compared with the power-only system, the η ex e,CHP of the HBP system and EC system are 8.10% and 2.84% higher.  Figure 13 gives the η ex e,CHP in the feasible operational region of the EC system and HBP system. Then, three features of the novel exergy-based evaluation can be deduced by comparing with the results in Figure 6e,f: (1) η ex e,CHP and η ex g,CHP are the same when the heat load is 0. Since in this condition the CHP plant can be considered as the power-only system, η ex e,CHP and η ex g,CHP will be not influenced by the heating part. (2) With the increment of the heat load, different trends are achieved. For the EC system, with the live steam mass flow unchanged, the η ex e,CHP is increased with the improvement of the heat load, when η ex g,CHP is decreased in the same condition. For the HBP system, the η ex e,CHP remains unchanged with the same mass flow of the live steam. In this condition, the change of the heat load only influences the heat dispatch of the heating condenser and cooling tower, not the coal consumption and generation characters. Thus, the trend of η ex e,CHP can reflect the characters of the CHP system clearer than η ex g,CHP .
(3) Since η ex e,CHP is based on the exergy consumption dispatch of the heat and power concerning more regarding the CHP system itself, the cold-end temperature has no influence on the results in Figure 13. With these features, the novel exergy-based evaluation is supplementary to the existing evaluation system.

Conclusions
In this study, a comprehensive thermodynamic performance evaluation of the coal-fired CHP plant with a HBP turbine was performed based on both the energy-and exergy-based evaluation methods. Compared with the traditional CHP plant with EC mode, the thermodynamic characteristics of the HBP system under full operational conditions were obtained. Then, considering the energy level differences of the heating steam, a novel exergy-based evaluation method was proposed and applied to compare the performances of different CHP systems. The main results were as follows: (1) In design conditions, both the heating capacity and power output of the HBP system were higher than those of the EC system, which led to 17.67% and 33.21% increments of the gross thermal efficiency and generation efficiency respectively, and a 79.84 g/kWh decrement of the standard coal consumption rate. Compared with the EC system, the exergy efficiencies of the HBP system were 7.04-8.21% higher with the same cold end temperature.
(2) Efficiencies in the feasible operational region were also achieved and show that the energy-based evaluation methods (η g,CHP and η e,CHP ) show similar trends: η g,CHP and η e,CHP will increase with the increment of the heat load when the live steam remains the same, while η g,CHP will show the opposite trend.
(3) According to the novel exergy-based evaluation method, the exergy efficiencies for the generation (η ex e,CHP ) of the HBP system and EC system were 46.48% and 41.22%, respectively-8.10% and 2.84% higher than those of the power-only system. η ex e,CHP in the whole feasible operational region was obtained.