Thermodynamic Performance of Geothermal Energy Cascade Utilization for Combined Heating and Power Based on Organic Rankine Cycle and Vapor Compression Cycle

Abstract

A large population and rapid urbanization dramatically promote the heating supply demand, the combined heating and power (CHP) system for energy cascade utilization came into being. However, the research on the recovery and utilization of condensing heat, the exploration of the coupling law between power generation and heating supply, and the influence of heat source parameters on thermo-economic performance are still insufficient. To this end, two combined heating and power (CHP) systems coupled with an organic Rankine cycle (ORC) and vapor compression cycle (VCC) are proposed, and their thermodynamic and economic performances are optimized and analyzed by the laws of thermodynamics. Results show that the increase of the volume flow will increase the power generation and heating supply quantity of the system, and there is an optimal evaporation temperature range of 130–140 °C to optimize the performance of the system. The increase of heat source temperature will improve the economic performance of the system, but it will reduce the exergetic efficiency. Therefore, two factors should be comprehensively considered in practical engineering. There is mutual exclusivity between the net power output of the system and the heating supply quantity, it should be reasonably allocated according to the actual needs of users in engineering applications. In addition, the exergetic efficiency of the two systems can reach more than 60%, and the energy utilization rate is high, which indicates that the cascade utilization mode is reasonable.

1. Introduction

With the continuous reduction of fossil fuels and the growing demand for energy, energy issues have received increasing attention from the international community. Exploring renewable energy and improving energy utilization efficiency have become two important ways to solve future energy problems [1]. Compared with the intermittency of the most renewable energies such as solar, wind, etc., geothermal energy can provide more continuous and stable energy. Additionally, large reserves and wide distribution are also its significant advantages. Geothermal energy has become one of the most potential renewable energy in the 21st century [2]. As of 2018, about 82 countries around the world are using geothermal energy directly, with a total installed thermal power of about 70.88 GW, an annual growth rate of 7.9%, and a load utilization factor of about 0.265 [3]. Therefore, the study of geothermal energy development and utilization technology plays an important role in enhancing safe energy supply and environmental protection in the future. At present, the most common forms of utilization mainly include heating supply, power generation, hot spring bathing, agricultural drying, and domestic water [4,5,6]. Moreover, it is worth noting that, although the heat source of geothermal power plant is clean and pollution-free, it still produces some pollutants or greenhouse gases during plant development, operation, and construction. However, the main purpose of this paper is not to analyze the environmental impact of geothermal power plants [7,8], so it will not be described in detail.

Rapid population growth and the accelerated pace of urbanization have led to a substantial increase in heating supply demand in recent years. At present, China often adopts the methods of direct heating supply and indirect heating supply, but they all have certain defects. Direct heating supply has large irreversible losses, while indirect heating supply consumes a lot of electricity. Therefore, in order to reduce irreversible losses and achieve self-powering of the system, related researchers have proposed a form of energy cascade utilization to improve its utilization efficiency [9,10]. First, the energy enters the first cascade system to generate electricity; then it enters the second cascade system for cooling or heating supply; finally, it is directly used in the third cascade system [11]. The above energy cascade utilization strategies correspond to different subsystems, such as organic Rankine cycle (ORC), vapor compression cycle (VCC) and combined heat and power (CHP).

The ORC technology plays an important role in the utilization of geothermal energy due to its simple structure and commercial feasibility [12,13]. Lee et al. [14] proposed a complete flash system, which can significantly reduce the irreversible losses caused by the evaporation process. Wang et al. [15] believed that the use of flash technology in an ORC system can effectively improve its performance, while the improvement was limited, as the enhanced thermal efficiency was only 6.04%. Similarly, Liu et al. [16] also introduced the flash technology in the ORC, and the results showed the thermal efficiency was only 5.1%. In order to further improve the system efficiency of the ORC, Paixãoet al. [17] studied the regenerative ORC, and the results showed that the performance of regenerative ORC is better than that of ORC, where the effect is more obvious than that of the flash technology. However, the enhanced thermal efficiency was also only on average 10%. Zheng et al. [18] showed that the double-pressure evaporation technology has a better promotion effect on improving the performance of the ORC system. White et al. [19] indicated that the power output of the two-phase ORC is about 1.3 times that of the ORC, and this conclusion was also illustrated by Sindu et al. [20].

As an important energy-saving technology, the VCC is mainly used in refrigeration and heating supply in daily life. In order to further improve its coefficient of performance (COP), a lot of research has been done in the relevant literature works. Wang et al. [21] compared the vapor compression refrigeration cycle in series and parallel form, and the results showed that the COP of the series form was 7.8% higher than that of the parallel form. Grauberger et al. [22,23] studied the organic Rankine cycle–vapor compression cycle (ORC-VCC) through experiments. The COP of the VCC is about 5.25 at the design temperature. Increasing the inlet temperature of the heat source and decreasing the outlet temperature of the condenser could effectively improve the COP of the ORC-VCC. Ashwni et al. [24] indicated that when the mass fraction of a zeotropic mixture (R245fa and hexane) is 0.5, the maximum COP of a multi evaporator vapor compression refrigeration system is 0.425. In addition, the research on improving the COP of heating systems based on heat pump principle has never been interrupted. Zhang et al. [25] found that two-stage throttling intermediate cooling can enable a two-stage heat pump cycle to achieve higher COP. Liu et al. [26] showed that the ejector-vapor compression cycle technology can significantly improve the COP of a dual temperature air source heat pump system. Subha et al. [27] also indicated that a low-grade thermally driven ejector between the compressor outlet and the condenser inlet can improve the COP of the system. Wang et al. [28] found that the COP is 4.3 when the hot water outlet temperature of the parallel cycle and condenser series heat pump system reaches 85 °C through experiments. Self et al. [29] showed that the condenser pressure has the greatest influence on the COP of the heat pump system, followed by the evaporator pressure, and the superheat degree has the least influence. It is worth mentioning that, although VCC is widely used in refrigeration or heat pump system, it is not self-powered and requires an additional power supply, which reduces its application potential.

The CHP technology is one of the important ways to improve energy efficiency and reduce carbon emissions [30,31,32]. Braimakis et al. [33] and Wang et al. [34] pointed out that the irreversible loss of the CHP system mainly occurs in the heat transfer process. Wang et al. [35] indicated that the use of interstage extraction gas can help improve the peak regulating performance of CHP systems. Liu et al. [36] pointed out that adding an ejector to the CHP system can also optimize its peak regulating capability. Ebadollahi et al. [37] found that, compared with the Kalina-CHP system, the ORC-CHP system has higher total efficiency and exergetic efficiency, and at the same time, its investment cost is also higher. Sun et al. [38] presented a new CHP system based on ejector heat exchangers and absorption heat pumps, which is more conducive to cost recovery and environmental protection compared to conventional CHP system. Mehregan et al. [39] proposed a CHP system using dual prime movers, which can reduce the operating cost by 67.52% and save fuel by 49.08%. Benalcazar et al. [40] show that integrating thermal energy storage has a positive contribution to mitigating fuel and environmental costs. Bao et al. [41] proposed a scheduling coordination approach with an adaptive constraint strategy for CHP system. The approach takes full advantage of heat network flexibility to improve operational economics. On this basis, a common CHP system is mainly coupled with power plants, and its waste heat is used for the heating supply, while the condensing heat is lost to the environment in the cooling tower and has not been effectively used.

Combined with the above literature, each subsystem has different energy supply advantages. ORC is quite competitive in the field of medium–low temperature energy generation, but its system efficiency is low. In addition, VCC heating supply systems can expand the temperature range of heating fluids and have good heating supply potential even at low heat sources, but the need for an additional power supply limits their application scenarios. In contrast, the CHP system is coupled with the power generation and heating supply systems, which ensures self-power while improving the efficiency of its own system and improves the independence of the system. At present, the research on the production mode of the three sub-systems coupling is very limited, and the coupling relationship between the reduced power generation and the increased heat supply in the CHP system of condensing heat recovery due to the increase of the back-pressure of the turbine is not clear. Meanwhile, there are few studies on the influence of heat source flow rate on system performance. Relatively, although there are many studies on the heat source temperature, the investigation on the optimum performance and corresponding working condition of the CHP varied with the heat source temperature is rarely found.

In response to this research gap, the organic Rankine cycle and vapor compression cycle–combined heating and power system (ORC-VCC-CHP) and the two-stage organic Rankine cycle and vapor compression cycle–combined heating and power system (TORC-VCC-CHP) are proposed. The effects of the operating parameters such as the evaporation temperature, heat source temperature as well as heat source flow on the thermodynamic and techno-economic performance of the two systems are discussed, and in particular, the coupling relationship between net power output and heating supply quantity is studied.

2. Physical Modeling

Figure 1 shows the physical modeling of the ORC-VCC-CHP, which consists of three sub-cycles: the organic Rankine cycle-combined heating and power cycle, the recooling heating supply cycle and the vapor compression heating supply cycle. Additionally, the specific workflow can be divided into three stages.

The first stage can be described as: the geothermal water from the production well flows into evaporator Ⅰ under the action of the pressure difference and heat transfer occurs with the organic working fluid, and the high-temperature and high-pressure organic working fluid enters the turbine to convert thermal energy into kinetic energy, and drives the generator to produce electricity. Then, the superheated organic working fluid flows into condenser Ⅰ to heat the return water, and finally enters evaporator Ⅰ again under the action of working fluid pump Ⅰ to complete a cycle. The heated return water flows to the household for heating supply.

The second stage is relatively simple. The geothermal water from evaporator Ⅰ flows into the recooler to heat the return water for heating supply to the households.

The third stage is as follows: the low temperature, low pressure organic working fluid is heated by the geothermal water from the recooler in evaporator Ⅱ, then the high temperature, low pressure working fluid is pressurized into a high temperature, high pressure state in the compressor, then heat transfer occurs in the working fluid with the return water in condenser Ⅱ, and finally, the pressure is reduced by the expansion valve to complete a cycle. The heated return water flows to the household for heating supply. Numbers 1–13 in the figure indicate the thermodynamic state points.

Figure 2 is the physical modeling of the TORC-VCC-CHP, which has one more organic Rankine cycle-combined heating and power sub-cycle than the ORC-VCC-CHP system. Additionally, the cycle process can be divided into four stages, the first and second stages are similar to the first stage of the ORC-VCC-CHP system, its third stage is similar to the second stage of the ORC-VCC-CHP system, and finally, its fourth stage is similar to the third stage of the ORC-VCC-CHP system. Numbers 1–21 in the figure indicate the thermodynamic state points.

Figure 3 and Figure 4 are the T-s diagram of the ORC sub-cycle and lg P-h diagram of the VCC sub-cycle in the two systems, respectively.

3. Mathematical Modeling

In this section, the thermodynamic analytical model and techno-economic model are established, and the simulation calculation is conducted in Matlab™ by linking to REFPROP 9.1. To simplify the calculation, the following assumptions are made:

(1)

The systems are modeled under steady state conditions [42];

(2)

The heat loss of the system and the flow resistance loss of working fluid are ignored [42];

(3)

The changes in kinetic and potential energy in the system are not considered [41];

(4)

The isentropic efficiency of the working fluid pump and turbine remain unchanged [43].

3.1. Thermodynamic Modeling

In order to analyze the thermodynamic performance of the ORC-VCC-CHP and TORC-VCC-CHP systems, the related thermodynamic parameter equations of each equipment are described.

The relevant mathematical models of each device in the two systems are shown in

Table 1. The relevant mathematical models of each device in the two systems.

Components		ORC-VCC-CHP	TORC-VCC-CHP
			Primary ORC Sub-Cycle	Secondary ORC Sub-Cycle
ORC sub-cycle	Evaporator	$Q_{\mathrm{e}1}=m_{\mathrm{wf}1}(h_1-h_6)$	$Q_{\mathrm{e}1}=m_{\mathrm{wf}1}(h_1-h_6)$	$Q_{\mathrm{e}2}=m_{\mathrm{wf}2}(h_9-h_{14})$
	turbine	$W_{\mathrm{t}1}=m_{\mathrm{wf}1}(h_1-h_2)$	$W_{\mathrm{t}1}=m_{\mathrm{wf}1}(h_1-h_2)$	$W_{\mathrm{t}2}=m_{\mathrm{wf}2}(h_9-h_{10})$
	Condenser	$Q_{\mathrm{c}1}=m_{\mathrm{wf}1}(h_2-h_5)$	$Q_{\mathrm{c}1}=m_{\mathrm{wf}1}(h_2-h_5)$	$Q_{\mathrm{c}2}=m_{\mathrm{wf}2}(h_{10}-h_{13})$
	Working fluid pump	$W_{\mathrm{p}1}=m_{\mathrm{wf}1}(h_6-h_5)$	$W_{\mathrm{p}1}=m_{\mathrm{wf}1}(h_6-h_5)$	$W_{\mathrm{p}2}=m_{\mathrm{wf}2}(h_{14}-h_{13})$
VCC sub-cycle	Evaporator	$Q_{\mathrm{e}2}=m_{\mathrm{wf}2}(h_9-h_{13})$	$Q_{\mathrm{e}3}=m_{\mathrm{wf}3}(h_{17}-h_{21})$
	Compressor	$W_{\mathrm{com}}=m_{\mathrm{wf}2}(h_{10}-h_9)$	$W_{\mathrm{com}}=m_{\mathrm{wf}3}(h_{18}-h_{17})$
	Condenser	$Q_{\mathrm{c}2}=m_{\mathrm{wf}2}(h_{10}-h_{12})$	$Q_{\mathrm{c}3}=m_{\mathrm{wf}3}(h_{18}-h_{20})$
Recooler		$Q_{\mathrm{rc}}=m_{\mathrm{rcw}}(h_{\mathrm{rcw},\mathrm{out}}-h_{\mathrm{rcw},\mathrm{in}})$

.

In Table 1, where Q is the heat transfer quantity, kW; m is the mass flow rate, kg/s; h is the specific enthalpy, kJ/kg; and W is the power, kW. The subscripts “wf1”, “wf2” and “wf3” are the working fluids of the primary ORC sub-cycle, the secondary ORC sub-cycle and the VCC sub-cycle. The subscripts “e1”, “t1”, “c1” and “p1” represent evaporator Ⅰ, turbine Ⅰ, condenser Ⅰ and working fluid pump Ⅰ; the subscripts “e2”, “t2”, “c2” and “p2” represent evaporator Ⅱ, turbine Ⅱ, condenser Ⅱ and working fluid pump Ⅱ; the subscripts “e3”, “com”, “c3” and “rc” represent evaporator Ⅲ, compressor, condenser Ⅲ and recooler; the subscript “rcw” represents the return water in the recooler; the “in” and “out” represent the inlet and outlet; and the subscript numbers represent the status points.

The calculation formulas of the heating supply exergy are shown in

Table 2. The calculation formulas of heating supply exergy.

Components	Exergy/kW
Condenser Ⅰ	$E_{\mathrm{c}1}=m_{\mathrm{cw}1}[(h_{\mathrm{cw}1,\mathrm{out}}-h_{\mathrm{cw}1,\mathrm{in}})-T_0(s_{\mathrm{cw}1,\mathrm{out}}-s_{\mathrm{cw}1,\mathrm{in}})]$
Condenser Ⅱ	$E_{\mathrm{c}2}=m_{\mathrm{cw}2}[(h_{\mathrm{cw}2,\mathrm{out}}-h_{\mathrm{cw}2,\mathrm{in}})-T_0(s_{\mathrm{cw}2,\mathrm{out}}-s_{\mathrm{cw}2,\mathrm{in}})]$
Recooler	$E_{\mathrm{rc}}=m_{\mathrm{rcw}}[(h_{\mathrm{rcw},\mathrm{out}}-h_{\mathrm{rcw},\mathrm{in}})-T_0(s_{\mathrm{rcw},\mathrm{out}}-s_{\mathrm{rcw},\mathrm{in}})]$
Condenser Ⅲ (Only for TORC-VCC-CHP)	$E_{\mathrm{c}3}=m_{\mathrm{cw}3}[(h_{\mathrm{cw}3,\mathrm{out}}-h_{\mathrm{cw}3,\mathrm{in}})-T_0(s_{\mathrm{cw}3,\mathrm{out}}-s_{\mathrm{cw}3,\mathrm{in}})]$
Heating supply exergy	$E_{\mathrm{hs}}=E_{\mathrm{c}1}+E_{\mathrm{c}2}+E_{\mathrm{c}3}+E_{\mathrm{rc}}$

.

In Table 2, where E is the exergy, kW; s is the specific entropy, kJ/kg·K; and T₀ is the ambient temperature, K. The subscripts “cw1”, “cw2” and “cw3” represent the return waters of primary ORC sub-cycle, the secondary ORC sub-cycle and VCC sub-cycle.

The calculation formulas of relevant evaluation parameters of the two systems are shown in

Table 3. The calculation formulas of the relevant evaluation parameters of the two systems.

Parameters	ORC-VCC-CHP	TORC-VCC-CHP
Power consumption of cooling water pump/kW	$W_{\mathrm{cp},\mathrm{i}}=m_{\mathrm{cw},\mathrm{i}}g{H}_{\mathrm{cp},\mathrm{i}}/(1000{\eta }_{\mathrm{cp},\mathrm{i}})$ (i = 1,2,3)	$W_{\mathrm{cp},\mathrm{i}}=m_{\mathrm{cw},\mathrm{i}}g{H}_{\mathrm{cp},\mathrm{i}}/(1000{\eta }_{\mathrm{cp},\mathrm{i}})$ (i = 1,2,3,4)
Heating supply quantity/kW	$Q_{\mathrm{hs}}=Q_{\mathrm{c}1}+Q_{\mathrm{c}2}+Q_{\mathrm{rc}}$	$Q_{\mathrm{hs}}=Q_{\mathrm{c}1}+Q_{\mathrm{c}2}+Q_{\mathrm{c}3}+Q_{\mathrm{rc}}$
Power output of turbine/kW	$W_{\mathrm{t}}=W_{\mathrm{t}1}$	$W_{\mathrm{t}}=W_{\mathrm{t}1}+W_{\mathrm{t}2}$
Net power output/kW	$W_{\mathrm{net}}={\eta }_{\mathrm{m}}{\eta }_{\mathrm{g}}{W}_{\mathrm{t}}-W_{\mathrm{p}1}-W_{\mathrm{p}2}-W_{\mathrm{cp},\mathrm{i}}-W_{\mathrm{com}}$
Geothermal water heat release/kW	$Q_{\mathrm{gw}}=m_{\mathrm{gw}}(h_{\mathrm{gw},\mathrm{in}}-h_{\mathrm{gw},\mathrm{out}})$
Power generation efficiency/%	${\eta }_{\mathrm{pow}}=W_{\mathrm{net}}/Q_{\mathrm{gw}}$
Total efficiency/%	${\eta }_{\mathrm{tot}}=(W_{\mathrm{net}}+Q_{\mathrm{hs}})/Q_{\mathrm{gw}}$
Geothermal water exergy/kW	$E_{\mathrm{gw}}=m_{\mathrm{gw}}[(h_{\mathrm{gw},\mathrm{in}}-h_{\mathrm{gw},\mathrm{out}})-T_0(s_{\mathrm{gw},\mathrm{in}}-s_{\mathrm{gw},\mathrm{out}})]$
Exergetic efficiency/%	${\eta }_{\mathrm{ex}}=(W_{\mathrm{net}}+E_{\mathrm{hs}})/E_{\mathrm{gw}}$

.

In Table 3, where g is the acceleration of gravity, m/s²; H is the head of pump, m; and η is the efficiency,%. The subscripts “cp” and “gw” represent the cooling water pump and geothermal water; and the subscript “hs” represents the heating supply. The η_m, η_g, η_pow and η_tot are the mechanical efficiency, generator efficiency, power generation efficiency and total efficiency,%.

3.2. Techno-Economic Modeling

In order to analyze the techno-economic performance of the ORC-VCC-CHP and TORC-VCC-CHP systems, a related techno-economic model is established. First, the cost of each component was calculated through the 2001 price model (As shown in

Table 4. The each equipment cost calculation formulas of two systems in 2001.

Components	Components Module Cost Models
Evaporator (plate heat exchanger)	$C_{\mathrm{ei}}=(B_1+B_2\cdot F_{\mathrm{M}}\cdot F_{\mathrm{ei},\mathrm{plate}})\cdot C_{\mathrm{p},\mathrm{ei},\mathrm{plate}}$	$\begin{array}{l}\lg C_{\mathrm{p},\mathrm{ei},\mathrm{plate}}=K_1+K_2\cdot \lg A_{\mathrm{ei},\mathrm{plate}}\\ +K_3{\left[\lg A_{\mathrm{ei},\mathrm{plate}}\right]}^2\end{array}$	$\begin{array}{l}\lg F_{\mathrm{ei},\mathrm{plate}}=C_1+C_2\cdot \lg P_{\mathrm{ei},\mathrm{plate}}\\ +C_3{\left[\lg P_{\mathrm{ei},\mathrm{plate}}\right]}^2\end{array}$
Condenser (plate heat exchanger)	$C_{\mathrm{ci}}=(B_1+B_2\cdot F_{\mathrm{M}}\cdot F_{\mathrm{p},\mathrm{ci},\mathrm{plate}})\cdot C_{\mathrm{ci},\mathrm{plate}}$	$\begin{array}{l}\lg C_{\mathrm{p},\mathrm{ci},\mathrm{plate}}=K_1+K_2\cdot \lg A_{\mathrm{ci},\mathrm{plate}}\\ +K_3{\left[\lg A_{\mathrm{ci},\mathrm{plate}}\right]}^2\end{array}$	$\begin{array}{l}\lg F_{\mathrm{ci},\mathrm{plate}}=C_1+C_2\cdot \lg P_{\mathrm{ci},\mathrm{plate}}\\ +C_3{\left[\lg P_{\mathrm{ci},\mathrm{plate}}\right]}^2\end{array}$
Working fluid pump	$C_{\mathrm{pi}}=(B_1+B_2\cdot F_{\mathrm{M}}\cdot F_{\mathrm{pi}})\cdot C_{\mathrm{p},\mathrm{pi}}$	$\begin{array}{l}\lg C_{\mathrm{p},\mathrm{pi}}=K_1+K_2\cdot \lg W_{\mathrm{pi}}\\ +K_3{\left[\lg W_{\mathrm{pi}}\right]}^2\end{array}$	$\begin{array}{l}\lg F_{\mathrm{pi}}=C_1+C_2\cdot \lg P_{\mathrm{pi}}\\ +C_3{\left[\lg P_{\mathrm{pi}}\right]}^2\end{array}$
Recooler (plate heat exchanger)	$C_{\mathrm{rc}}=(B_1+B_2\cdot F_{\mathrm{M}}\cdot F_{\mathrm{rc},\mathrm{plate}})\cdot C_{\mathrm{p},\mathrm{rc},\mathrm{plate}}$	$\begin{array}{l}\lg C_{\mathrm{p},\mathrm{rc},\mathrm{plate}}=K_1+K_2\cdot \lg A_{\mathrm{rc},\mathrm{plate}}\\ +K_3{\left[\lg A_{\mathrm{rc},\mathrm{plate}}\right]}^2\end{array}$	$\begin{array}{l}\lg F_{\mathrm{rc},\mathrm{plate}}=C_1+C_2\cdot \lg P_{\mathrm{rc},\mathrm{plate}}\\ +C_3{\left[\lg P_{\mathrm{rc},\mathrm{plate}}\right]}^2\end{array}$
Cooling water pump	$C_{\mathrm{cpi}}=(B_1+B_2\cdot F_{\mathrm{M}}\cdot F_{\mathrm{cpi}})\cdot C_{\mathrm{p},\mathrm{cpi}}$	$\begin{array}{l}\lg C_{\mathrm{p},\mathrm{cpi}}=K_1+K_2\cdot \lg W_{\mathrm{cpi}}\\ +K_3{\left[\lg W_{\mathrm{cpi}}\right]}^2\end{array}$	$\begin{array}{l}\lg F_{\mathrm{cpi}}=C_1+C_2\cdot \lg P_{\mathrm{cpi}}\\ +C_3{\left[\lg P_{\mathrm{cpi}}\right]}^2\end{array}$
turbine	$C_{\mathrm{ti}}=F_{\mathrm{bm},\mathrm{t}}\cdot C_{\mathrm{p},\mathrm{ti}}$	$\lg C_{\mathrm{p},\mathrm{ti}}=K_1+K_2\cdot \lg W_{\mathrm{ti}}+K_3{\left[\lg W_{\mathrm{ti}}\right]}^2$
Compressor	$C_{\mathrm{com}}=[(727.4235\cdot m_{\mathrm{wf},\mathrm{VCC}})/(0.8996-{\eta }_{\mathrm{tot}})]\cdot (p_{\mathrm{out}}/p_{\mathrm{in}})\cdot \ln (p_{\mathrm{out}}/p_{\mathrm{in}})$
Expansion valve	$C_{\mathrm{ev}}=114.5\cdot m_{\mathrm{wf},\mathrm{VCC}}$

), and then revised to the 2018 price by a chemical engineering plant cost index (CEPCI) [44,45,46].

The coefficients in cost calculation of each equipment are shown in

Table 5. The coefficients in cost calculation of each equipment.

Components	Coefficients
	K1	K2	K3	C1	C2	C3	B1	B2	FM	Fbm
Evaporator	4.3247	−0.3030	0.1634	0.03881	−0.11272	0.08183	1.63	1.66	1.0	/
Condenser	4.3247	−0.3030	0.1634	0.03881	−0.11272	0.08183	1.63	1.66	1.0	/
Working fluid pump	3.3892	0.0536	0.1538	−0.3935	0.3957	−0.00226	1.89	1.35	1.5	/
Recooler	4.3247	−0.3030	0.1634	0	0	0	1.63	1.66	1.0	/
Cooling water pump	3.3892	0.0536	0.1538	0	0	0	1.89	1.35	1.5	/
turbine	2.7051	1.4398	−0.1776	/	/	/	/	/	/	3.5

.

The total equipment cost calculation formula of the ORC-VCC-CHP system in 2001 is:

$$Cos{t}_{2001}=C_{\mathrm{e}1}+C_{\mathrm{e}2}+C_{\mathrm{c}1}+C_{\mathrm{c}2}+C_{\mathrm{p}1}+C_{\mathrm{t}1}+C_{\mathrm{rc}}+C_{\mathrm{cp}1}+C_{\mathrm{cp}2}+C_{\mathrm{cp}3}+C_{\mathrm{ev}}+C_{\mathrm{com}}$$

(1)

The total equipment cost calculation formula of the TORC-VCC-CHP system in 2001 is:

$$Cos{t}_{2001}=C_{\mathrm{e}1}+C_{\mathrm{e}2}+C_{\mathrm{e}3}+C_{\mathrm{c}1}+C_{\mathrm{c}2}+C_{\mathrm{c}3}+C_{\mathrm{p}1}+C_{\mathrm{p}2}+C_{\mathrm{t}1}+C_{\mathrm{t}2}+C_{\mathrm{rc}}+C_{\mathrm{cp}1}+C_{\mathrm{cp}2}+C_{\mathrm{cp}3}+C_{\mathrm{cp}4}+C_{\mathrm{ev}}+C_{\mathrm{com}}$$

(2)

where Cost₂₀₀₁ is the total equipment cost in 2001; C is the each equipment cost; and the subscript “ev” means expansion valve.

The total equipment cost calculation formula of two systems in 2018 is:

$$Cos{t}_{2018}=Cos{t}_{2001}\frac{CEPC{I}_{2018}}{CEPC{I}_{2001}}$$

(3)

where Cost₂₀₁₈ is the total equipment cost in 2018; CEPCI₂₀₁₈ = 648.7 and CEPCI₂₀₀₁ = 397 [47].

The calculation of system related investment cost is shown in

Table 6. The total investment cost of the system.

Parameters	Expressions
Total investment cost, Ctotal	$C_{\mathrm{total}}=C_{\mathrm{TDC}}+C_{\mathrm{startup}}$
Total depreciable capital, CTDC	$C_{\mathrm{TDC}}=C_{\mathrm{DPI}}+C_{\mathrm{cont}}$
Cost of contingencies and contractor’s fee, Ccont	$C_{\mathrm{cont}}=0.18 \times C_{\mathrm{DPI}}$
Total direct permanent investment, CDPI	$C_{\mathrm{DPI}}=\mathit{Cost}2018+C_{\mathrm{site}}+C_{\mathrm{sf}}$
Cost of site preparation, Csite	$C_{\mathrm{site}}=0.05 \times \mathit{Cost}2018$
Cost of service facilities, Csf	$C_{\mathrm{sf}}=0.05 \times \mathit{Cost}2018$
Cost of plant startup, Cstartup	$C_{\mathrm{startup}}=0.1 \times \mathrm{CTDC}$

.

The expression for the capital recovery factor is:

$$CRF=\frac{i{(1+i)}^T}{{(1+i)}^T-1}$$

(4)

where CRF represents capital recovery factors; i is the annual loan interest rate, assume i = 5% [47], T is life cycle time, and suppose T = 20 years [47,48].

The expression for the annual electricity sales revenue is:

$$S_{\mathrm{annual}}=C_1\times H_{\mathrm{annual}}\times W_{\mathrm{t}}$$

(5)

where S_annual is the annual electricity sales revenue, C₁ is the electricity price, and assume C₁ = 0.1 $/kW·h [49].

The expression for the annual electricity production time is:

$$H_{\mathrm{annual}}=0.9\times 24\times 365$$

(6)

where H_annual is the annual electricity production time.

The expression for the levelized cost of electricity (LCOE) is:

$$LCOE=\frac{\left[{\displaystyle \sum _{t=1}^n{C}_{\mathrm{total}}\times \frac{CRF}{{(1+i)}^{\mathrm{t}}}}\right]}{\left[{\displaystyle \sum _{t=1}^n\frac{S_{\mathrm{annual}}}{{(1+i)}^{\mathrm{t}}}}\right]}$$

(7)

The expression for the payback period (PBP) is:

$$PBP=\frac{C_{\mathrm{total}}}{S_{\mathrm{annual}}}$$

(8)

For the economical difference between heating supply and electricity, the economic thermal efficiency (η_ec,th) and economic exergetic efficiency (η_ec,ex) are defined in this paper, and economic thermal efficiency is expressed as:

$${\eta }_{\mathrm{ec},\mathrm{th}}=\frac{W_{\mathrm{net}}+\alpha Q_{\mathrm{hs}}}{Q_{\mathrm{gw}}}$$

(9)

where α is the ratio of heating price to electricity price under the same measurement unit, assume α = 0.5 [50].

The expression for the economic exergetic efficiency is:

$${\eta }_{\mathrm{ec},\mathrm{ex}}=\frac{W_{\mathrm{net}}+\alpha E_{\mathrm{hs}}}{E_{\mathrm{gw}}}$$

(10)

3.3. System Parameters

Table 7. Relevant parameters of the simulation calculation conditions of two systems.

Parameter	tgw/°C	Vgw/m3·h−1	tcw,in/°C	tcw,out/°C	ηiso,t/%	ηise,com/%	ηise,p/%	tsh/°C	tsc/°C	Δtpp/°C	ηm/%	ηg/%	T0/K	P0/kPa
value	100–200	50–100	35	45	75	75	60	3	3	5	95	95	277.25	72.19

below shows the relevant parameters of the simulation calculation conditions of the two systems. The environmental parameters are the measured values in the Gonghe Basin of Qinghai in November 2021. The R601 is used as working fluid of ORC sub-cycle and VCC sub-cycle, and its thermodynamic parameters are shown in

Table 8. Thermodynamic properties of R601.

Substance	Physical Data				Environmental Date		Source
R245fa	M/g·mol−1	Tb/°C	Tcri/°C	Pcri/Mpa	ODP	GWP/100yr	[51,52]
	72.15	36.10	196.60	3.37	0	−20

.

3.4. Validation

By consulting and comparing a large number of references, it is found that the thermodynamic model studied in reference [50] has a high similarity with the model established in this paper. Therefore, its calculation conditions are brought into the model of this paper, total efficiency of system, exergetic efficiency and economic exergetic efficiency are used as verification indicators, and the relevant results are shown in

Table 9. The reference value and validation value.

Parameter	ηtot/%	ηex/%	ηec,ex/%
Reference value	154.7	81.68	32.10
Validation value	158.3	77.94	33.10

. By comparison, it is found that the calculation results of the model established in this paper are in good agreement with the calculation results of the reference [50], and the error range is −4.58–3.12%. Thus, the accuracy of the model established in this paper is verified.

4. Results and Discussion

In this part, the volume flow (v_gw), evaporation temperature (t_e) and heat source temperature (t_gw,in) are used as independent variables, and net power output (W_net), heating supply quantity (Q_hs), power generation efficiency (η_pow), exergetic efficiency (η_ex), total efficiency (η_tot), economic thermal efficiency (η_ec,th), economic exergetic efficiency (η_ec.ex), levelized cost of electricity (LCOE) and payback period (PBP) are used as dependent variables, and the ORC-VCC-CHP system and the TORC-VCC-CHP system will be compared in terms of thermodynamics and techno-economic performance.

4.1. Thermodynamic Performance

4.1.1. The Influence of Volume Flow Rate

As shown in Figure 5, it shows the change of net power output, heating supply quantity, power generation efficiency, exergetic efficiency and total efficiency of two systems with the volume flow rate. As can be seen from the figure, the volume flow rate has the same effect on the performance of the two systems. Since the parameters that affect the enthalpy value of each state point such as temperature and pressure have not changed, the enthalpy difference between the inlet and outlet of each component remains unchanged. However, the increase in volume flow leads to a proportional increase in the power output of the turbine and the power consumption of other components. Therefore, there is a proportional relationship between the net power output and the volume flow. Similarly, the increase in volume flow increases the heating supply quantity of each sub-cycle, so the system heating supply quantity is also proportional to the volume flow. According to the relevant calculation formulas of the efficiencies in Table 3, their influencing parameters all increase at the same rate with the increase of the volume flow. Therefore, the change of the volume flow will not have effect on the power generation efficiency, exergetic efficiency and total efficiency.

4.1.2. The Influence of Evaporation Temperature

Figure 6 shows the effect of the evaporation temperature on the thermodynamic performance of the two systems. For the ORC-VCC-CHP system, with the increase of the evaporation temperature, the net power output, power generation efficiency and exergetic efficiency first increase and then decrease, while the variation trend of heating supply quantity and total efficiency are just opposite. The increase of the evaporation temperature increases the specific enthalpy difference between the inlet and outlet of the turbine and decreases the mass flow rate of the working fluid; therefore, the product of the specific enthalpy difference and mass flow rate has a peak value. The increase of the evaporation temperature has no effect on the heating supply quantity of condenser Ⅱ, but the heating supply quantity of condenser Ⅰ decreases and the heating supply quantity of the recooler increases. The coupling effect of the heating supply quantities of condenser Ⅰ and the recooler makes the total heating supply quantity of the system have a minimum value. Since the evaporation temperature has no effect on the heat absorption of the system and the heat source exergy, the change of the power generation efficiency only depends on the net power output, and exergetic efficiency is determined by net power output and heating supply exergy, and the change of the total efficiency not only depends on the net power output, but also depends on the heating supply quantity.

From Figure 6(b1,b3,b4), the TORC-VCC-CHP system is similar to ORC-VCC-CHP system, the net power output, power generation efficiency and exergetic efficiency have similar trends. Their specific changing trends are described as follows: (i) As the primary evaporation temperature (t_e1) increases, they first increase and then decrease when the secondary evaporation temperature (t_e2) is less than 110 °C; (ii) they are positively correlated with the primary evaporation temperature when the secondary evaporation temperature is greater than or equal to 110 °C; (iii) when the primary evaporation temperature is less than or equal to 127 °C, they have a negative correlation with the secondary evaporation temperature; and (iv) when the primary evaporation temperature is greater than 127 °C, they all have a peak value. The reason for the above change trends is that the net power output is related to the working fluid mass flow of the primary and secondary ORC sub-cycles and the specific enthalpy difference between the inlet and outlet of the turbine. The primary and secondary evaporation temperatures do not affect the system heat absorption and heat source exergy, so the power generation efficiency is only affected by the net power output, while the exergy efficiency is related to the net power output and heating supply exergy.

Figure 6(b2) shows the variation of the heating supply quantity of the TORC-VCC-CHP system with the primary and secondary evaporation temperatures. As the primary evaporation temperature increases, the heating supply quantity of condenser Ⅰ and the recooler decreases, while that of condenser Ⅱ increases, and that of condenser Ⅲ remains unchanged, so that the total heating supply quantity has the following trends: When the secondary evaporation temperature is less than 110 °C, there is a minimum value. On the contrary, when it is greater than or equal to 110 °C, the heating supply quantity is inversely proportional to the primary evaporation temperature. As the secondary evaporation temperature increases, the heating supply quantity of condenser Ⅰ and condenser Ⅲ remains unchanged, while that of condenser Ⅱ decreases, and that of the recooler increases, so that the total heating supply quantity has the following trends: When the primary evaporation temperature is less than 132 °C, the heating supply quantity is proportional to the secondary evaporation temperature. On the contrary, when it is greater than or equal to 132 °C, the heating supply quantity first decreases and then increases. In general, combined with Figure 6(a,b1,b2), there is an obvious mutual exclusivity between the net power output and heating quantity of the two systems. In other words, when the net power output is large, the heating supply quantity is insufficient, and vice versa.

The change in total efficiency can be seen from Figure 6(b5). Similarly, since the primary and secondary evaporation temperatures do not affect the system heat absorption; therefore, the trend of total efficiency is generated by the coupling of net power output and heating supply quantity, as follows: Taking the primary evaporation temperature as 155 °C as the cut-off point, (i) when it is less than the cut-off point, the secondary evaporation temperature is positively correlated with the total efficiency; and (ii) when it is greater than the cut-off point, the total efficiency first decreases and then increases with the increase of the secondary evaporation temperature. As the primary evaporation temperature increases, the total efficiency changes as follows: (i) It is increased when the secondary evaporation temperature is less than 100 °C and not equal to 60 °C; (ii) when the secondary evaporation temperature is in the range of 100–120 °C and equal to 60 °C, it first decreases and increases; and (iii) it is decreased when the secondary evaporation temperature is greater than 125 °C. It is worth noting that due to the existence of the VCC sub-cycle, which is actually a heat pump cycle that can obtain more heating supply quantity from heat source by consuming part of the power output, the total efficiency of system can be greater than 100%. This point has also been confirmed by Lo Basso et al. [53].

4.1.3. The Influence of Heat Source Temperature

The variation of each parameter with the heat source temperature is shown in Figure 7. Similar to the effect of volumetric flow, the heat source temperature has a similar effect on the ORC-VCC-CHP system and the TORC-VCC-CHP system. The coupling effect of the mass flow rate of the working fluid and the specific enthalpy difference between the inlet and outlet of the turbine makes the power output of the turbine increase with the increase of the heat source temperature, which in turn increases the net power output. As the heat source temperature increases, the heat absorbed by the system increases, and therefore, the heat provided to the occupants also increases. Since the increase rate of the net power output is greater than that of the heat absorption of the system, the power generation efficiencies of the two systems both tend to increase. In addition, the system exergetic efficiency is reduced because the growth rate of the sum of net power output and heating supply exergy is less than that of the heat source exergy. Similarly, under the coupling effect of net power output, heating supply quantity and system heat absorption, the total efficiency also shows a downward trend.

The maximum net power output, heating supply quantity, power generation efficiency, exergetic efficiency and total efficiency at each heat source temperature are shown in

Table 10. The optimal thermodynamic parameters of two systems at each heat source temperatures.

tgw,in/°C	ORC-VCC-CHP System					TORC-VCC-CHP System
	Wnet,max /kW	Qgr,max /kW	ηpow,max /%	ηex,max /%	ηtot,max /%	Wnet,max /kW	Qgr,max /kW	ηpow,max /%	ηex,max /%	ηtot,max /%
100	10.41	7443	0.1554	67.57	111.2	31.29	7439	0.4672	68.96	111.2
110	60.07	8510	0.7739	65.55	109.7	91.59	8506	1.180	67.28	109.6
120	121.0	9555	1.374	64.01	108.5	161.7	9545	1.835	65.88	108.4
130	193.3	10,577	1.964	62.81	107.5	242.8	10,603	2.468	64.77	107.5
140	277.2	11,584	2.555	61.89	106.8	333.4	11,582	3.073	63.82	106.7
150	372.9	12,552	3.149	61.21	106.1	433.0	12,554	3.657	63.02	106.1
160	480.8	13,525	3.754	60.72	105.6	541.9	13,505	4.230	62.35	105.6
170	601.5	14,447	4.737	60.41	105.2	660.5	14,434	4.801	61.83	105.1
180	735.9	15,381	5.013	60.27	104.8	789.4	15,343	5.378	61.43	104.7
190	885.3	16,248	5.683	60.30	104.5	930.0	16,238	5.970	61.19	104.4
200	1052	17,138	6.393	60.50	104.2	1087	16,989	6.606	61.13	104.0

. As the heat source temperature increases, the maximum net power output, heating supply quantity, and power generation efficiency at each heat source temperature increase, and the change in maximum total efficiency is just the opposite. However, there is a difference in the change of the maximum exergetic efficiency of the two systems. In addition, the net power output and power generation efficiency only reflect the power generation performance, and the heating supply quantity only reflects the heat supply performance. The difference between the total efficiency of the two systems is very little, the maximum difference does not exceed 0.2%. Therefore, comparing the two systems with exergetic efficiency, it is found that the exergetic efficiency of TORC-VCC-CHP is higher than that of the ORC-VCC-CHP system, which increased by an average of 1.49%, it means that the thermodynamic performance of the TORC-VCC-CHP is better.

4.2. Techno-Economic Performance

4.2.1. The Influence of Volume Flow Rate

The effect of volume flow on the economic performance of the ORC-VCC-CHP system is shown in Figure 8a. Since the ratio of heating price to electricity price is constant at 0.5, the influencing factors of economic thermal efficiency are net power output, heating supply quantity and heat absorption, and economic exergetic efficiency is related to net power output, heating supply exergy, and heat source exergy. As the volume flow increases, these influencing parameters increase almost at the same rate. Therefore, the economic thermal efficiency remains unchanged at 54.46%, while the economic exergy efficiency fluctuates between 40.42–40.43%. The LCOE and PBP are important indicators to evaluate the economics of the system. Since the influencing factors of LCOE and PBP are both net power output and system investment cost, the two evaluation indicators have the same change trend, which is that the larger the volume flow, the lower the LCOE, and the shorter the PBP.

From Figure 8b, since the factors affecting the economic thermal efficiency, economic exergetic efficiency, LCOE and PBP of the TORC-VCC-CHP system are similar to those of the ORC-VCC-CHP system, their changing trends are similar to those in the ORC-VCC-CHP system. As the volume flow increased from 50 m³/h to 100 m³/h, LCOE and PBP decreased from 0.05969 $·(kW·h)⁻¹ and 6.762 yr to 0.04233 $·(kW·h)⁻¹ and 4.796 yr, respectively; and the economic thermal efficiency remains unchanged at 54.49%, and the economic exergetic efficiency fluctuates around 40.83%.

4.2.2. The Influence of Evaporation Temperature

Figure 9 shows the economic performance of the two systems as a function of the evaporating temperature.

From Figure 9a, there is a peak value in both the economic thermal efficiency and economic exergetic efficiency of the ORC-VCC-CHP system. The reason is that the evaporation temperature does not cause changes in the heat absorption and heat source exergy of the system, the ratio of heating price to electricity price is constant at 0.5, the net power output first increases and then decreases with the evaporation temperature, and the changes of heating supply quantity and heating supply exergy are just the opposite. Therefore, their coupling effect contributes to the changing trend of economic thermal efficiency and economic exergetic efficiency, and the two peaks are 54.54% and 41.35%, respectively. Since the influencing factors of LCOE and PBP are the same, the two evaluation indicators have similar changing rules. The increase of evaporation temperature leads to the peak value of net power output and system investment cost. Under the coupling effect of the two factors, both LCOE and PBP have a minimum value, which are 0.03342 $·(kW·h)⁻¹ and 3.786 yr, respectively, under the conditions shown in the legend.

The factors affecting each economic performance evaluation index in the TORC-VCC-CHP system are the same as those in the ORC-VCC-CHP system. Therefore, the following change trends can be obtained from Figure 9b.

From Figure 9(b1,b2), the changing law of economic thermal efficiency and economic exergetic efficiency: (i) As the primary evaporation temperature increases, when the secondary evaporation temperature is less than 110 °C, they first increase and then decrease. On the contrary, they decrease when it is greater than or equal to 110 °C. (ii) As the secondary evaporation temperature increases, except for extreme conditions (the primary evaporation temperature is less than 127 °C), when the primary evaporation temperature is greater than or equal to 127 °C, they also tend to increase first and then decrease.

From Figure 9(b3,b4), the LCOE and PBP share the same trend, which is described as follows: (i) As the primary evaporation temperature increases, when the secondary evaporation temperature is 60 °C, LCOE and PBP first decrease and then increase. When the secondary evaporation temperature is greater than 60 °C and less than 75 °C, the LCOE and PBP first decrease, then increase and finally decrease. When the variation range of the secondary evaporation temperature is 75–155 °C, the variation trend of LCOE and PBP is opposite to that when it is equal to 60 °C. When the secondary evaporation temperature is greater than 155 °C, they are decreased. (ii) As the secondary evaporation temperature increases, when the primary evaporation temperature is less than 132 °C, the LCOE and PBP decrease. When the variation range of the primary evaporation temperature is 132 °C −153 °C, LCOE and PBP change in a single hump. When it is greater than 153 °C and less than 157 °C, they change in a double hump. When the variation range of the primary evaporation temperature is 157–170 °C, they show a valley-to-peak change. Finally, they change in a single valley when it is greater than 170 °C.

4.2.3. The Influence of Heat Source Temperature

Figure 10 indicates the effect of the heat source temperature on the economic performance of the two systems. The trends of the evaluation parameters in the two systems are similar. With the increase of the heat source temperature, the net power output, heating supply quantity, system heat absorption, heating supply exergy and heat source exergy all increase. According to Equation (9) of the economic thermal efficiency, since the increase rate of the sum of net power output and heating supply quantity is less than that of the system heat absorption, the economic thermal efficiency is inversely proportional to the temperature of the heat source. However, it can be seen from Equation (10) that the coupling effect of net power output, heating supply exergy and heat source exergy makes the economic exergetic efficiency change in a single peak with the heat source temperature. In addition to that, the investment cost of the system also increases with the heat source temperature, but because the increase rate in net power output is greater than the that in investment cost, so the LCOE and PBP decrease.

The maximum economic thermal efficiency and economic exergetic efficiency, the minimum LCOE and PBP at each heat source temperature is shown in

Table 11. The optimal thermal economy parameters of two systems at each heat source temperature.

tgw,in/°C	ORC-VCC-CHP System				TORC-VCC-CHP System
	ηec,th,max /%	ηec,ex,max /%	LCOEmin /$·(kW·h)−1	PBPmin /yr	ηec,th,max /%	ηec,ex,max /%	LCOEmin /$·(kW·h)−1	PBPmin /yr
100	55.60	34.19	0.1692	19.17	55.72	35.69	0.1571	17.80
110	55.02	34.70	0.1288	14.60	55.18	36.57	0.1186	13.44
120	54.64	35.24	0.1029	11.65	54.84	37.26	0.09425	10.68
130	54.40	35.82	0.08482	9.609	54.62	37.92	0.07743	8.772
140	54.25	36.43	0.07157	8.108	54.49	38.50	0.06509	7.375
150	54.18	37.08	0.06144	6.961	54.43	39.04	0.05575	6.316
160	54.17	37.81	0.05345	6.055	54.43	39.56	0.04847	5.491
170	54.20	38.57	0.04700	5.325	54.48	40.09	0.04267	4.835
180	54.28	39.40	0.04168	4.722	54.56	40.66	0.03803	4.309
190	54.39	40.32	0.03722	4.217	54.68	41.27	0.03438	3.895
200	54.54	41.35	0.03342	3.786	54.80	42.04	0.03191	3.615

. As the heat source temperature increases, the minimum LCOE and PBP at each heat source temperature both decrease, and the maximum economic exergetic efficiency increase, the maximum economic thermal efficiency first decreases and then increases. The economic thermal efficiency and economic exergetic efficiency of the TORC-VCC-CHP are higher than those of the ORC-VCC-CHP system, and the LCOE and PBP of the TORC-VCC-CHP are smaller than those of the ORC-VCC-CHP system, whose LCOE and PBP are relatively improved by about 8.2%, which means that the economic performance of the TORC-VCC-CHP is better.

5. Conclusions

The organic Rankine cycle and vapor compression cycle–combined heating and power system (ORC-VCC-CHP) and the two-stage organic Rankine cycle and vapor compression cycle–combined heating and power system (TORC-VCC-CHP) are established in this paper, the optimization of the thermo-economic performance of the two systems has been carried out, and the optimal performance and operating parameters under different heat source temperatures have also been revealed. The following conclusions are mainly drawn:

(1)

The increase of volume flow will make the net power output and heating supply quantity of the system increase and LCOE and PBP decrease. Hence, the system performance will be better. In addition, when the heat source parameters are optimal, the system possesses excellent thermo-economic performance with the evaporation temperature that varies in the range 130–140 °C depending on the optimization objective function chosen.

(2)

The condition with lower heat source temperature has higher exergy efficiency and total efficiency, while the condition with higher heat source temperature has lower LCOE and PBP. Therefore, it is not only necessary to pursue whether the performance of a certain aspect is optimal in practical engineering applications, but two aspects of thermodynamics and economic performance should be considered comprehensively.

(3)

Both systems can achieve high energy utilization, and the exergetic efficiency can reach more than 60%. However, by comparing the exergetic efficiency and economic evaluation indicators of the two systems, the thermodynamic and economic performance of the TORC-VCC-CHP system is better than that of the ORC-VCC-CHP system.

(4)

There is a conflicting relationship between the net power output and heating supply quantity for both systems, the higher the net power output, the lower the heating supply quantity, vice versa. Therefore, in engineering applications, it is necessary to allocate between them according to the actual needs of users.