Thermodynamic-Environmental-Economic Evaluations of a Solar-Driven Supercritical CO₂ Cycle Integrated with Cooling, Heating, and Power Generation

Abstract

The combined cooling, heating, and power system is based on the principle of energy cascade utilization, which is conducive to reducing fossil energy consumption and improving the comprehensive utilization efficiency of energy. With the characteristics of a lower expansion ratio and larger recuperation of a supercritical carbon dioxide (SCO₂) power cycle, a combined cooling, heating, and power (CCHP) system is proposed. The system is based on a SCO₂ cycle and is driven by solar energy. The system is located in Qingdao and simulated by MATLAB/Simulink software (R2022b). Firstly, the thermodynamic performance of the CCHP system at the design condition is analyzed. The energy utilization efficiency of the CCHP system is 79.75%, and the exergy efficiency is 58.63%. Then, the thermodynamic, environmental, and economic performance analyses of the system under variable conditions are carried out. Finally, the solar multiple is optimized. The results show that the minimum levelized cost of electricity is 10.4 ¢/(kW·h), while the solar multiple is 4.8. The annual primary energy saving rate of the CCHP system is 85.04%, and the pollutant emission reduction rate is 86.05%, compared with the reference system. Therefore, an effective way to reduce environmental pollution and improve the utilization efficiency of solar energy is provided.

1. Introduction

The development of renewable energy is conducive to reducing the utilization of fossil energy and pollutant emissions. In recent years, the share of solar energy in the global energy structure has increased significantly. Concentrated solar thermal power generation is not only environmentally friendly but also grid-compatible [1]. Additionally, solar tower power generation has the characteristics of high concentration ratios and high thermal-to-electrical conversion efficiency, making it a research focus [2].

The development of the SCO₂ cycle in solar thermal power generation systems has become a new research hotspot. When the turbine inlet parameter is 700 °C/35 MPa, the thermal efficiency of the SCO₂ cycle reaches 51.82%, which is significantly higher than that of existing supercritical water–steam Rankine cycle power plants [3]. The density of CO₂ is relatively high at the critical point (7.38 MPa, 31.3 °C), the power consumption of compression is reduced. Thus, the combination of solar power systems with the SCO₂ power cycle has the potential for efficient utilization of solar energy at high operating temperatures. Higher cycle efficiency is achieved by modifying the SCO₂ cycle layout [4]. Through the optimization and comparative analysis of different SCO₂ power cycle layouts, it is found that the SCO₂ recompression cycle exhibits better thermodynamic performance [5,6].

To enhance energy utilization efficiency and mitigate irreversible losses in power cycles, the waste heat of the power system is utilized. There are usually two types of waste heat utilization methods. One is to combine a bottom power cycle to achieve power generation, and the other is to recover waste heat for cooling, heating, and power generation.

When the top power cycle is a SCO₂ power cycle, current investigations focus on two predominant bottom cycle configurations: the organic Rankine cycle (ORC) and the transcritical carbon dioxide (TCO₂) cycle. Studies reveal substantial performance improvements in the combined cycle. For the SCO₂ cycle combined with the ORC, Song et al. [7] demonstrated significant improvements, with the maximum power output enhancement reaching 58% and the specific investment cost reduction achieving 4% compared to SCO₂ systems. Research by Fan et al. [8] on solar-driven SCO₂-ORC system further confirmed the enhanced thermodynamic and economic performance of integrated systems. For the SCO₂ cycle integrated with the TCO₂ cycle, the thermal efficiency of the integrated system reaches up to 65.7% [9]. Advanced configurations developed by Fan et al. [10] employed two-stage cascaded SCO₂–TCO₂ cycles for waste heat recovery of gas turbines, finding that the thermal efficiency of the combined system increased by 4.32%, and the levelized cost of electricity (LCOE) decreased by 2.42% compared with the SCO₂ recompression cycle.

Recovering waste heat from the power cycle to drive cooling and heating operations is also an effective way to improve the overall energy utilization of the system. The CCHP system is based on the principle of cascaded energy utilization to achieve the output of cooling, heating and electricity. Wu et al. [11] found that the micro-CCHP system based on the integration of a gas engine and an absorption chiller is always superior to the conventional separated system for heat loads exceeding 21 kW. As the turbine inlet temperature rises, both the turbine output work and the exergy efficiency of the SCO₂ CCHP system increase [12]. However, Li et al. [13] found that the turbine inlet temperature was negatively correlated with the payback period and levelized energy cost. Therefore, it is necessary to evaluate the cogeneration system comprehensively. A novel hybrid CCHP system was introduced by Soleimani et al. [14], and its performance was evaluated from the perspectives of energy, exergy, environment and economic. The results showed that the CCHP system has higher efficiency and lower pollutant emissions than the reference system. Fan et al. [15] proposed a CCHP system integrated the SCO₂ cycle with the ORC and the ejector refrigeration cycle, and the results showed that the exergy efficiency of the CCHP system is increased by 9.17% and the unit cost of the product is decreased by 5.05%. To evaluate the matching between the output of the CCHP system and the user’s demand, Feng et al. [16] proposed five dimensionless matching parameters to analyze the performance.

The utilization of solar energy and thermal energy storage is an effective way to reduce fossil energy consumption and improve the operational performance of the CCHP system. Distributed CCHP is the mainstream for small-scale solar thermal utilization. Solar energy resources vary due to weather and geographical conditions. Wu et al. [17] studied the performance of solar CCHP system in different regions. The results showed that the CCHP system is more effective in cold regions, where solar energy resources are abundant, and the heat demand of buildings is large and stable throughout the year. The application of thermal energy storage equipment addresses the intermittent and unstable characteristics of solar energy [18]. Wang et al. [19] proposed a solar photovoltaic/thermal CCHP system, and the optimal sizing of electrical energy storage and the thermal energy storage are obtained using an upper-level optimization model. Moreover, the optimization of the operation strategy and the capacity of the thermal energy storage equipment further improve energy efficiency. A novel CCHP system integrated with solar energy is analyzed by Chen et al. [20], and it is found that the cost increased with the thermal energy storage ratio. Liu et al. [21] adjusted the operation strategy according to the variation in electricity price, and the capacity of thermal energy storage is optimized, the equivalent electricity cost of the system was reduced, and the results showed that, when the solar multiple is 8.17, the LCOE reaches its lowest value.

However, the high initial investment of CCHP system remains a limitation for large-scale applications. Secondly, the load fluctuation of CCHP system is large. Adjusting the output of cooling, heating, and power according to the actual demand is also one of the difficulties in current research [22].

This paper innovatively proposes a solar-driven SCO₂-combined cooling, heating, and power system, which adjusts the ratio of cooling, heating, and power by changing the split ratio. To cope with the intermittent and unstable characteristics of solar energy, the system integrates thermal energy storage equipment. The main contributions are summarized as follows:

(1)

A SCO₂-combined cooling, heating, and power system with thermal energy storage driven by solar energy is proposed. The cascade utilization of energy is realized, and the system model is built and verified.

(2)

The system performance under different solar multiples is analyzed, and the solar multiples is optimized with the levelized cost of electricity as the optimization objective. According to the variations in users’ demands and solar irradiance, the thermodynamic, environmental, and economic performance of the system under typical days and variable conditions are investigated.

The structure of this paper is organized as follows: Section 2 introduces the system structure, the climatic parameters and building load. In Section 3, the mathematical model for the equipment and the evaluation criteria of thermodynamic, environmental, and economic are introduced, and the model is verified. Section 4 analyzes the performance of the system under design conditions and variable operating conditions throughout the year. Finally, the conclusions are illustrated in Section 5.

2. System Descriptions

2.1. System Configuration

The system proposed in this paper is composed of a solar tower collector and a SCO₂ CCHP unit. The configuration of the solar-driven CCHP system is shown in Figure 1a. The CCHP system drives the generator to generate electricity through turbine operation and uses the medium and low-grade waste heat at the turbine outlet for cooling and heating. Power from the grid is used as a supplement when the output electricity is insufficient to meet the users’ needs. When the output cooling does not meet the users’ cooling load, the electric refrigeration unit is utilized. When the output heating energy is insufficient, heat from the heating network is purchased.

When the CO₂ at the inlet of the main compressor reaches a critical point, it is then compressed to a high-pressure state by the main compressor (MC). The compressed fluid sequentially recovers waste heat through the low temperature recuperator (LTR) (9–10) and medium temperature recuperator (MTR) (10–11), ultimately merging with the recompressed stream at node 12. The flow through the high temperature recuperator (HTR) is reheated (13–14). Solar irradiation is concentrated onto the top collector through heliostat reflection, and the low-temperature molten salt from the cold tank is heated as it passes through the collector. The heated molten salt flow subsequently diverges into two streams: one directly supplies thermal energy to unit of CCHP, while the other is stored in the hot storage tank to maintain system operation during solar insolation deficits. The CO₂ is heated by molten salt in the heater (14–1), then expands through the turbine for power generation (1–2). After releasing heat at the hot side of the HTR (2–3), the total mass flow rate is split into two streams. One stream enters the exchanger to drive absorption refrigeration (3b–4b), while the other stream flows through the MTR (3a–4a). These two streams recombine at node 5 before entering the LTR for further heat rejection (5–6). Then, the stream is split into two parts. One of the streams enters the exchanger to supply heating, while the other stream is compressed by the recompressor (RC). The CO₂ is cooled to near-critical conditions in the air cooler (7–8) to complete the cycle. The T-s diagram of the CCHP is illustrated in Figure 1b.

There are two splits in the proposed system, and the split ratios (SR) are defined as SR1 and SR2. SR1 is the ratio of the mass flow through the main compressor to the total mass flow and SR2 is defined as the percentage of mass flow through MTR to the total flow.

$$SR1={\displaystyle \frac{m_{MC}}{m_{total}}}$$

(1)

$$SR2={\displaystyle \frac{m_{MTR}}{m_{total}}}$$

(2)

SR1 is constant, while SR2 varies according to users’ load fluctuations.

The separating production (SP) system is selected as the reference system. Electricity from the power grid meets the electrical load. The cooling energy provided by the electric chiller is used to meet the cooling requirement. Heat energy from the heating network is used to supply the users.

2.2. Energy Requirement of Users

The area is situated in Qingdao City (E119°30′–E121°00′, N35°35′–N37°09′). The reason is that Qingdao belongs to a temperate climate with modest solar irradiation and four distinct seasons. The hourly environmental parameters and collection efficiency are illustrated in Figure 2. The solar tower collection efficiency is defined as the product of receiver thermal efficiency and field optical efficiency.

The building databases are sourced from the U.S. Department of Energy (DOE). The schematic diagram of building model is shown in Figure 3, which is a hotel with a total floor area of 11,345.29 m². The main parameters of the building model are shown in

Table 1. Main parameters of building model.

Items	Value
Number of above found floors	6
Number of underground floors	1
Total floor area/m2	11,345.29
Roof area/m2	1478
Number of people	1239
Window area/m2	1214

.

According to the environmental parameters and building model parameters, the annual hourly building energy consumption is calculated. The building load throughout the year is shown in Figure 4. The heating and cooling load is calculated as follows [23]:

$$Q_{\mathrm{load}}=Q_1+Q_2+Q_3+Q_4$$

(3)

$$Q_1={\displaystyle \sum _{i=1}^{N_{\mathrm{sl}}}{Q}_{\mathrm{i}}}$$

(4)

$$Q_2={\displaystyle \sum _{i=1}^{N_{\mathrm{surfaces}}}{h}_{\mathrm{i}}{A}_{\mathrm{i}}}\left(T_{\mathrm{si}}-T_z\right)$$

(5)

$$Q_3={\displaystyle \sum _{i=1}^{N_{\mathrm{zones}}}{m}_{\mathrm{i}}}{C}_{\mathrm{p}}\left(T_{\mathrm{zi}}-T_{\mathrm{z}}\right)$$

(6)

$$Q_4={\mathrm{m}}_{\inf }{C}_{\mathrm{p}}(T_{\infty }-T_z)$$

(7)

where Q₁ represents convective internal heat transfer, Q₂ represents convective heat transfer from the zone surfaces, Q₃ represents heat transfer due to inter zone air mixing, Q₄ represents heat transfer due to the infiltration of outside air.

According to the calculation results of the annual building energy consumption, the cooling and heating loads are greatly affected by seasonal fluctuations. Seasonal variations significantly influence energy requirements. The demand for cooling is more intense in summer, while the demand for heating is greater in winter. The electricity demand remains comparatively stable throughout the year. The operation strategy of the following thermal load (FTL) is applied due to the energy demand characteristics of the users. Operational priority is assigned to heat loads during peak heating demand periods. During large cooling demand periods, the cooling load is preferentially satisfied. Furthermore, the cooling, thermal, and electrical output proportions can be dynamically modulated through the adjustment of the split ratio, thereby optimizing energy allocation.

3. Calculation Model

3.1. Device Model

The system components mainly include heat exchangers and turbomachinery. Printed circuit heat exchangers (PCHE) are selected for the CCHP cycle. The heat exchanger is designed by the NTU-ε method. Each heat exchanger is divided into N sub-heat exchangers. The amount of heat exchange is calculated as follows:

$$Q={\displaystyle {\sum }_{i=1}^{N}UA}\cdot \mathrm{\Delta }T$$

(8)

where ΔT is logarithmic mean temperature difference.

The total conductance (UA) of the heat exchanger is the sum of the conductance values of all sub heat exchangers:

$$UA={\displaystyle {\sum }_{i=1}^N\left(NT{U}_i{C}_{\min ,i}\right)}$$

(9)

The number of transfer units (NTU) calculation formula of the sub heat exchanger is as follows:

$$NT{U}_i=\log \left({\displaystyle \frac{1-{\epsilon }_i{C}_{\mathrm{R},i}}{1-{\epsilon }_i}}\right)$$

(10)

$$C_{\mathrm{R}}={\displaystyle \frac{C_{\min }}{C_{\max }}}$$

(11)

$$C_{\min }=\min \left(C_{\mathrm{h},i},C_{\mathrm{c},i}\right)$$

(12)

where the C_R is the heat capacity ratio and C_min,i and C_max,i are the minimum and maximum heat capacity of the cold and hot sides of the sub-heat exchanger.

The heat transfer effectiveness of the sub heat exchanger is calculated as follows:

$${\epsilon }_i={\displaystyle \frac{h_{\mathrm{hot},\mathrm{in}}-h_{\mathrm{hot},\mathrm{out}}}{N{C}_{\min ,i}\left(T_{\mathrm{hot},\mathrm{in},i}-T_{\mathrm{cold},\mathrm{in},i}\right)}}$$

(13)

The turbine and compressor models refer to the performance of the literature published by Sandia Laboratory [24]. The compressor model is similar to the turbine model. By fitting the mechanical performance curve, the isentropic efficiency and expansion ratio are calculated as follows:

$$\phi ={\displaystyle \frac{m\sqrt{T_{\mathrm{in}}}}{P_{\mathrm{in}}}}$$

(14)

$$E{R}_{\mathrm{tur}}=3.09-0.8827\cos (\phi \times 3.113\times {10}^5)-0.5483\times \sin (\phi \times 3.113\times {10}^5)$$

(15)

$${\eta }_{\mathrm{isec}}=0.6688\times \sin \left(\phi -\pi \right)-0.1526\times {\left(\phi -10\right)}^2+105.26$$

(16)

where φ is the flow coefficient, η_isec represents the isentropic efficiency, ER_tur represent the expansion ratio of turbine.

For an irradiation condition, the calculation of the system is divided into two distinct parts: heat exchangers and rotating machinery. The calculation flowchart of heat exchanger is shown in Figure 5a, and the calculation flowchart of rotating machinery is shown in Figure 5b. For variable irradiation conditions, each irradiation point is regarded as a quasi-steady state [25].

3.2. Evaluation Criteria

The steady-state mass balance formula of the system is

$${\displaystyle \sum _i{m}_i={\displaystyle \sum _e{m}_{\mathrm{e}}}}$$

(17)

The energy balance equation is as follows:

$$Q-W={\displaystyle \sum _e{m}_e{h}_e-{\displaystyle \sum _i{m}_i{h}_i}}$$

(18)

The exergy destruction rate of a component is as follows [26]:

$$E{x}_D={\displaystyle \sum _j\left(1-\frac{T_0}{T_j}\right)Q_j}-W+{\displaystyle \sum _{i}E{x}_i}-{\displaystyle \sum _{e}E{x}_e}$$

(19)

where T₀ represents the environmental temperature, taken as 298.15 K, T_j represents the temperature of the heat source, Q_j is the heat supplied to the system, W represents the output work of the system, Ex_i is the inflow exergy, and Ex_e is the outflow exergy.

The energy analysis and exergy analysis of CCHP are carried out with the energy utilization efficiency and exergy efficiency as the evaluation criteria. The energy utilization efficiency is calculated as follows:

$${\eta }_{\mathrm{eu}}={\displaystyle \frac{\left(W_{\mathrm{net}}+Q_{\mathrm{heating}}+Q_{\mathrm{cooling}}\right)}{Q_{\mathrm{in}}}}$$

(20)

$$W_{\mathrm{net}}=W_{\mathrm{tur}}-W_{\mathrm{MC}}-W_{\mathrm{RC}}$$

(21)

where Q_in is the input heat for the system heat source, Q_cooling is the heat provided by the system to the EX1, Q_heating is the heat provided by the system to the EX2, W_tur is the work of turbine, W_MC is the power consumed in the main compressor, and W_RC is the power consumed in the recompressor.

The exergy efficiency is calculated as follows:

$${\eta }_{\mathrm{ex}}={\displaystyle \frac{W_{\mathrm{net}}+E{x}_1+E{x}_2}{E{x}_{\mathrm{in}}}}$$

(22)

where the Ex_in is the exergy of heat source input, Ex₁ is the exergy obtained on the cold side of EX1, kW; Ex₂ is the exergy obtained on the cold side of EX2.

The primary energy saving rate is selected as the energy saving evaluation criterion, which is calculated as follows:

$$PES={\displaystyle \frac{F_{\mathrm{SP}}-F_{\mathrm{CCHP}}}{F_{\mathrm{SP}}}}$$

(23)

where F_CCHP represents the primary energy consumption within the CCHP system and F_SP represents the primary energy consumption of SP system under the same load output as CCHP system.

The system is evaluated from an thermodynamics, environmental, and economic perspective. The pollutant emission reduction rate (PER) and the equivalent levelized cost of electricity (LCOE) are as given in the evaluation criteria.

Pollutant emission reduction rate is calculated as follows:

$$PER={\displaystyle \frac{1}{3}}CDER+{\displaystyle \frac{1}{3}}NOER+{\displaystyle \frac{1}{3}}SDER$$

(24)

where CDER is Carbon dioxide emissions reduction rate, NOER is Nitrogen oxides (NO_x) emissions reduction rate, and SDER is Sulfur dioxide (SCO₂) emissions reduction rate [27].

$$CDER={\displaystyle \frac{CD{E}_{\mathrm{SP}}-CD{E}_{\mathrm{CCHP}}}{CD{E}_{\mathrm{SP}}}}$$

(25)

$$NOER={\displaystyle \frac{NO{E}_{\mathrm{SP}}-NO{E}_{\mathrm{CCHP}}}{NO{E}_{\mathrm{SP}}}}$$

(26)

$$SDER={\displaystyle \frac{SD{E}_{\mathrm{SP}}-SD{E}_{\mathrm{CCHP}}}{SD{E}_{\mathrm{SP}}}}$$

(27)

The levelized cost of electricity (LCOE) [21] of the system is selected as the optimization index as follows:

$$LCOE={\displaystyle \frac{C_{\mathrm{A}}+C_{\mathrm{O}\mathrm{\&}\mathrm{M}}}{E_0^{\mathrm{ann}}}}$$

(28)

$$C_{\mathrm{O}\mathrm{\&}\mathrm{M}}=0.06C_{\mathrm{A}}$$

(29)

where C_A is the annual equipment investment amount and C_O&M is the annual equipment operation and maintenance cost.

The equivalent power of heating and cooling of the CCHP system is calculated as follows:

$$E_0^{\mathrm{ann}}=E_{\mathrm{cycle}}^{\mathrm{ann}}+{\displaystyle \frac{Q_{\mathrm{h},\mathrm{cycle}}^{\mathrm{ann}}}{CO{P}_{\mathrm{h}}}}+{\displaystyle \frac{Q_{\mathrm{c},\mathrm{cycle}}^{\mathrm{ann}}}{CO{P}_{\mathrm{ec}}}}$$

(30)

where $E_0^{\mathrm{ann}}$ is the annual equivalent power generated and COP_h is the coefficient of performance of electrical heating, the value is 4 [21].

The initial investment cost of the equipment is mainly the investment of the heliostat field, solar tower, heat storage and SCO₂ cycle equipment. The heater, HTR, MTR, EX1, EX2, and cooler are all heat exchanger equipment in the SO₂ cycle. The calculation is as follows:

$$C_{\mathrm{A}}=M(C_{\mathrm{tow}}+C_{\mathrm{helios}}+C_{\mathrm{hst}}+C_{{\mathrm{SCO}}_2})$$

(31)

$$C_{{\mathrm{SCO}}_2}=C_{\mathrm{Heater}}+C_{\mathrm{HTR}}+C_{\mathrm{MTR}}+C_{\mathrm{LTR}}+C_{\mathrm{EX}1}+C_{\mathrm{EX}2}+C_{\mathrm{Cooling}}$$

(32)

$$M={\displaystyle \frac{i}{1-{(1+i)}^{-n}}}$$

(33)

where M is annual depreciation rate of system equipment, i is the interest rate, the value is 0.05, n is the service life of the equipment, 25 years, C_helios is initial investment cost of heliostat field, C_tur is initial investment cost of turbine, C_tur is initial investment cost of compressor, C_hst is initial investment cost of thermal energy storage tank, C_exh is initial investment cost for heating heat exchanger, and C_tow is the initial investment cost of solar tower. The cost function of the initial investment cost of the CCHP system equipment is shown in

Table 2. The cost function of CCHP system equipment investment.

Components	Cost Function/$
Heat exchanger [28]	$C_{\mathrm{exh}}=2500UA$
Turbine [28]	$C_{\mathrm{tur}}=479.34m_{\mathrm{tur},\mathrm{in}}\left({\displaystyle \frac{1}{0.93-{\eta }_{\mathrm{tur}}}}\right)\left[1+\exp \left(0.036t_{\mathrm{tur},\mathrm{in}}-54.4\right)\right]\ln \left(PR\right)$
Compressor [28]	$C_{\mathrm{com}}=71.1m_{\mathrm{com},\mathrm{in}}\left({\displaystyle \frac{1}{0.92-{\eta }_{\mathrm{com}}}}\right)PR\cdot \ln \left(PR\right)$
Thermal energy storage tank [29]	$C_{\mathrm{hst}}=22Q_{\mathrm{hst},\max }$
Heliostat field [29]	$C_{\mathrm{helios}}=156A_{\mathrm{helios}}$
Tower receiver [29]	$C_{\mathrm{tow}}=100Q_{\mathrm{heater}}$

.

3.3. Verification of the Model

The system model is established based onMATLAB/Simulink software (R2022b), and the properties of the working fluid are determined using the NIST REFPROP database. The equipment models are composed of the heat exchanger model and rotating machinery model. In the calculation process of the heat exchanger, the iterative error is ensured to be less than 10⁻⁸. The fitting accuracy of the rotating mechanical performance curve is 99.95%. To illustrate the accuracy of the calculation, the verification of the calculation model is carried out. The input parameters are consistent with the literature [30], as shown in

Table 3. Input parameters for model validation.

Decision and Performance Parameters	Ref.	Input Value
MC inlet temperature	313.15 K	313.15 K
MC inlet pressure	7.80 MPa	7.80 MPa
HTR hot end inlet temperature	807.05 K	807.05 K
HTR hot end inlet pressure	8.04 MPa	8.04 MPa
HTR cold end inlet temperature	548.05 K	548.05 K
HTR cold end inlet pressure	24.61 MPa	24.61 MPa

. The validation results are shown in

Table 4. Validation results of recompression SCO₂ Brayton cycle.

Decision and Performance Parameters	Ref.	Present Model	Error
MC outlet temperature	399.95 K	397.90 K	0.51%
MC outlet pressure	24.85 MPa	24.18 MPa	2.70%
HTR hot end outlet temperature	560.95 K	554.60 K	1.13%
HTR hot end outlet pressure	7.96 MPa	7.97 MPa	0.24%
HTR cold end outlet temperature	775.55 K	792.40 K	2.17%
HTR cold end outlet pressure	24.36 MPa	24.46 MPa	0.41%

. The error is below 3%, indicating the accuracy of the model. The physical properties of CO₂ change dramatically near the critical point, consequently leading to a substantial error in the main compressor.

4. Results and Discussion

4.1. System Performances at the Design Condition

The main parameters of the design condition are summarized in

Table 5. Main parameters of design condition.

Items	Values
Heat absorption of the heater (kW)	869
The total mass flow rate (kg/s)	3.80
Turbine inlet temperature (K)	820.80
Turbine inlet pressure (MPa)	21
MC inlet temperature (K)	307.80
MC inlet pressure (MPa)	7.89
MC pressure ratio [24]	2.64
RC pressure ratio [24]	2.62
Turbine expansion ratio [24]	2.59
Split ratio 1	0.68
Split ratio 2	0
Isentropic efficiency of main compressor (%) [24]	83.85
Isentropic efficiency of recompressor (%) [24]	80.20
Isentropic efficiency of turbine (%) [24]	90

, and the irradiation at 12:00 on March 14th is selected as the design point, because the irradiation intensity at this time is close to the annual average, and the cooling, heating, and electrical loads are balanced. The area of tower heliostat field is 4016 m² in the design condition, and heat provided to the heater is 869 kW. The turbine inlet temperature of the CCHP system is 820.80 K.

The energy flow diagram of the CCHP system is shown in Figure 6a. When the energy provided by solar energy to the system is 859 kW, the electricity generation of the system is 300 kW. In addition, 130.2 kW is used for cooling, 262.9 kW is used for heating, and the energy loss during the conversion process is 175.9 kW. The largest proportion of energy is converted into electricity, accounting for 34.52%, followed by heating accounting for 30.25% and cooling accounting for 14.98%. Therefore, the energy utilization efficiency of the CCHP system is 79.75%, which is 31.30% higher than the SCO₂ power cycle driven by concentrated solar energy [31]. The exergy destructions of the components are shown in Figure 6b. The exergy efficiency is 58.63% at the design condition. Compared with the SCO₂ power cycle, the exergy efficiency of the CCHP system increases by 7.82% [32]. The reason is that the waste heat from the turbine outlet of the CCHP system is utilized to provide cooling and heating, and the irreversible loss is reduced. The total output of the system increases due to the production of cooling and heating, and the proportion of exergy destruction in each component is reduced. The exergy destruction of the heater accounts for the largest proportion of the exergy destruction in the conventional SCO₂ power cycle. The exergy destruction of heater of CCHP system is 33.45% lower than that in the SCO₂ power cycle. The CCHP system reduces the temperature difference between the hot and cold sides of the recuperator, thereby reducing the irreversible losses in the recuperators.

The largest exergy loss occurs in the heater, accounting for 15% in the CCHP system; this is because the temperature difference between the high temperature molten salt and CO₂ in the heater is large, resulting in increased irreversibility at the heat transfer process. The exergy flow of the CCHP system at the design condition is shown in Figure 6c, illustrating the input, output, and loss of exergy of each piece of equipment.

4.2. Thermodynamic Performances in Typical Days

The performance of the CCHP system under variable solar irradiation and users’ loads is investigated, and thermodynamic analyses are conducted on typical summer and winter days with a solar multiple of 4.8. The solar multiple (SM) refers to the ratio of the equivalent power that is provided by the heliostat site to the design power of the solar power plant [33].

Energy supply and demand are compared between the two seasons. The weather data including direct normal irradiance, ambient temperature, and wind speed for the summer and winter days are shown in Figure 7.

The total input mass flow rate of CO₂ remains constant under variable irradiation conditions, and the inlet temperature of turbine changes with the fluctuation of heat absorption. The variations in thermodynamic performance of the system with turbine inlet temperatures are shown in Figure 8.

With the increase in turbine inlet temperature, the energy utilization efficiency first increases and then decreases. The exergy efficiency decreases with the increase in turbine inlet temperature. This is because, as the turbine inlet temperature increases, the power generation increases and the increase in recyclable waste heat increases the heating and cooling capacity, leading to an initial rise in energy utilization efficiency. When the turbine inlet temperature is too high, the increase in the recompressor inlet temperature increases the power consumption, causing the energy utilization efficiency to decline. The exergy efficiency is significantly affected by the exergy destruction in the refrigeration heat exchanger. When the turbine outlet temperature increases, the temperature difference between the cold and hot sides of the heat exchanger grows, resulting in higher irreversible loss.

The energy demand and supply on a typical summer day are shown in Figure 9. The Q_rec,out represents the heat collection of the solar heliostat field, and Q_sto is the thermal energy storage value. When the heat collection of the solar collector exceeds the heat Q_cycle required by the system, the remaining heat is stored in the thermal energy storage tank. On the contrary, when the heat collection is not enough to meet the needs of the system, the molten salt flows out from the high-temperature storage tank to release heat; at this time, Q_sto is negative. In summer, the cooling demand is the highest and the heating demand is the lowest. Increased summer solar irradiance elevates both turbine inlet temperature and heat recovery efficiency. The solar heat collection and thermal energy storage meet the cooling and heating needs.

The peak of the power load on the day mainly occurs at 8:00 and 20:00. The higher heat output of the system leads to more waste of cooling capacity, as shown in Figure 9c. Increasing the system’s heat supply will lead to more heat and the cold energy is wasted, so the power is taken from the power grid to supplement at 20:00. The E_load in the figure is the electric load, E_cycle is the electricity output of the system, E_grid is the power obtained from the power grid, and negative represents the power that sold to the power grid. Q_c,load is the cooling load and Q_c,cycle is the cooling capacity of the system. Q_ec,c is the electric cooling capacity, a negative value represents the excess cooling capacity. Q_h,load is the heat load, Q_h,cycle is the heating capacity of the system, Q_hn,h is the heat taken from the heating network, and the negative number represents the excess waste heat.

On a typical summer day, the energy utilization efficiency and exergy efficiency of the system reached 82.74% and 58.82%, respectively. According to the operation strategy, the cooling load of the users is prioritized. Therefore, the supply and demand matching performance for cooling load is better. However, the heating capacity of the system is also high due to the high inlet temperature of the turbine.

The energy demand and supply on a typical summer day and on a typical winter day are shown in Figure 10. In winter, due to the lower solar irradiation and shorter sunshine duration, the solar energy collection period is from 9:00 to 14:00, making the system more dependent on thermal energy storage and external energy supplements. It is necessary to obtain electricity from the power grid to supplement the electric load from 20:00 to 22:00. In winter, the demand for heating is high, and there is almost no cooling demand. Therefore, solar energy heat collection and storage fulfill the cooling requirements of users as shown in Figure 10c. According to the operation strategy, the system gives priority to meeting the heat load, so the heat load also is satisfied. On typical winter days, the energy utilization efficiency and exergy efficiency of the system are 76.22% and 50.58%, respectively. The energy utilization efficiency and exergy efficiency are lower than those on typical summer days due to the lower solar irradiation intensity in winter. Additionally, because of the low turbine inlet temperature, the energy utilization efficiency is reduced, the irreversible loss of the system increases, and the exergy efficiency also decreases.

The changes in irradiation conditions affect the performance of the system. The solar collection, thermal energy storage, and thermodynamic performance of the system in a typical week in spring is shown in Figure 11. The amount of thermal energy storage is influenced by solar irradiation and users’ demand. In the typical spring week, the system achieves stable operation driven by solar energy for 132 h, as shown in Figure 11a. Furthermore, the energy utilization efficiency and exergy efficiency of the system is shown in Figure 11b, the average energy utilization efficiency of the typical spring week is 75.14%, and the average exergy efficiency of the typical spring week is 51.64%.

4.3. Annual Thermodynamic Performances

The annual thermodynamic and environmental performance of the CCHP system is analyzed. The energy efficiency and exergy efficiency in different months are shown in Figure 12. The monthly energy efficiency ranges from 62.48% to 81.06%, and the monthly exergy efficiency ranges from 43.34% to 54.91%. Due to the high turbine inlet temperature in July, the system is operating near the design condition, so the energy utilization rate in July is up to 81.06% and the efficiency in July is up to 54.91%. The energy utilization efficiency and exergy efficiency are the lowest in January, primarily due to the low irradiation in winter and the low turbine inlet temperature during the operation period of the system. The energy utilization efficiency of CCHP system in a whole year is in the range of 71.05–82.81%, and the exergy efficiency ranges from 45.03% to 59.77%. The annual energy utilization efficiency and exergy efficiency of CCHP system are 77.16% and 52.20%, respectively.

The thermodynamic and environmental performances in different months are shown in Figure 13. The primary energy saving rate and pollutant emission reduction rate are highest in May, reaching 99.58% and 99.7%, respectively. Due to the solar collection being higher this month, more user demand is met. The primary energy saving rate and pollutant emission reduction rate are relatively low in February, at 63.26% and 62.13%, respectively. Because of the low intensity of solar radiation, more external energy is needed.

Moreover, the pollutant emissions are also varied, and the CO₂, NO_x, and SO₂ reduction rates compared with reference system are shown in Figure 13. The change in CO₂ and SCO₂ emission reduction rates is similar. In January, December, and February, the NO_x emission reduction rate is lower than the CO₂ emission reduction rate and SO₂ emission reduction rate. The NOx emission of heating network is greater than the NOx emission of power generation [34]. In winter, the heating of the system output is not enough to meet the requirements of users. The increment of heat supplied by the heat network results in elevated NOx emissions, and the NOx emission reduction rate is lower. Conversely, in other months with lower heating loads, the NO_x emission reduction rate is relatively high. Compared with the separate system, the primary annual energy saving rate is 93.70% and the pollutant emission reduction rate is 94.15%.

4.4. Optimization of Solar Multiple

The size of the heliostat field area not only affects the stability of the CCHP system, but also the economic performance of the system. In order to determine the optimal heliostat field area and thermal energy storage scale, optimization is carried out, with SM as the optimization parameter and LCOE as the optimization objective.

Firstly, the actual heliostat field area of different SM is calculated. Then, the annual initial investment cost, operation and maintenance cost, and equivalent electricity of the system under different SM are calculated. Finally, the calculated LCOE of different SM is determined, and the optimal SM is determined according to the minimum LCOE. The flow chart of the optimization program is shown in Figure 14.

The variations in cost and equivalent electricity under different solar multiple are shown in Figure 15a. As the solar multiple increases from 2 to 5.6, the initial investment cost, operation and maintenance cost, and equivalent electricity of the solar heliostat field show an increasing trend. When the solar multiple increases from 4.8 to 5.6, the growth of the equivalent electricity generated by the system slows down, which is lower than the growth rate of the initial investment cost and operation and maintenance cost of the solar heliostat field. With the increase in SM, the initial investment of the solar tower and heliostat field presents a linear upward, as shown in Figure 15b. The initial investment of thermal energy storage tank increases with the increase in SM, and the magnitude of the increase becomes greater with higher SM. This is because, when the system is capable of fulfilling the majority of user requirements, additional energy will be stored with the increment of SM, thereby leading to a significant increase in capacity of thermal energy storage.

Therefore, LCOE gradually decreases with the increase in solar multiple from 2 to 4.8, which is shown in Figure 16. The reason is that, when the solar multiple is small, the increase in solar multiple leads to the increase in thermal energy storage capacity, along with the cost increase. The system is thus able to utilize solar energy more effectively, and the annual cooling, heating, and electricity supply of the system increases. The solar multiple increases from 4.8 to 5.6, and the cost growth rate is higher than the equivalent power growth rate. At this point, because the thermal energy storage scale has basically satisfied the demand of users, the increase in the scale of the thermal energy storage will only increase the initial investment cost and operating and maintenance cost. When the SM is 4.8, the LCOE is at least 10.4 ¢/(kW·h), which is 5.22% lower than that of the concentrating solar power system [35]. This is mainly due to the improvement in the output of the CCHP system. The efficiency of solar-to-electricity efficiency in the references is 14.7% and the average direct normal irradiation is close to the irradiation in this paper. The increase in the energy utilization rate in CCHP system leads to an increase in the equivalent electricity, thus reducing the LCOE. At the condition of the optimal SM, the system driven by solar energy operates for 299 days in whole year, realizing operational stability.

When the SM is 4.8, the proportion of annual costs is shown in Figure 17. The electric charge represents the cost of buying electricity from the grid minus the cost of selling electricity. The investment proportion of the heliostat field is the largest, accounting for 60%. The investment proportion of the heater is the largest among the SCO₂ cycle equipment, followed by HTR and turbine.

The thermodynamic and environmental performances of the system under different solar multiples are analyzed. The annual primary energy saving rate and pollutant emission reduction rate under different SM are shown in Figure 18. The primary energy saving rate and pollutant emission reduction rate increase as the solar multiple increases. This is because, as the solar multiple increases, the storage and utilization of solar energy increases, and the corresponding energy consumption and pollutant emissions are reduced. When the solar multiple is 4.8, the primary energy saving rate is 85.04%, and the pollutant emission reduction rate is 86.05%, the carbon dioxide emissions reduction rate is 85.06%, the nitrogen oxide emissions reduction rate is 88.20%, and the sulfur dioxide emissions reduction rate is 84.90%. Compared with the CCHP system of similar capacity, the carbon dioxide emission reduction rate is increased by 20%, which illustrates the feasibility of solar-driven SCO₂ CCHP system [36].

5. Conclusions

A solar-driven SCO₂ CCHP system is proposed. The CCHP system is evaluated from the perspectives of thermodynamic, environmental, and economic. The main conclusions are listed as follows:

(1)

The thermodynamic performance of the CCHP system under the design conditions is analyzed. Under the design conditions, the energy utilization efficiency of the CCHP system is 79.75%, which is 31.30% higher than the SCO₂ power cycle driven by concentrated solar energy. The exergy efficiency is 58.63% and the largest exergy loss occurs in the heater, accounting for 15%.

(2)

According to the changes in solar radiation and users’ loads, the thermodynamic and environmental performance of CCHP system in typical days and under annual conditions are analyzed. The annual energy utilization efficiency and exergy efficiency of CCHP system are 77.16% and 52.20%, respectively. Compared with the separating production system, the annual primary energy saving rate is 85.04%, and the pollutant emission reduction rate is 86.05%.

(3)

The system performance for different solar multiples is analyzed, and thermal storage capacity is determined. The SM is optimized with LCOE as the optimization objective, and the results show that, when the SM is 4.8, the LCOE is the lowest, at 10.4 ¢/(kW·h).

This paper considers the performance of the system under the operation strategy of following thermal load, the future works will compare the system performance with different operation strategies. Furthermore, the performance of the system in different climatic zones is also worth investigating.