Transcritical CO2 Research Articles

A novel dual-split layout for transcritical CO2 power cycle adapted to variable heat sources

Transcritical CO2 power cycle is widely used as the bottom cycle of natural gas engine to recover waste heat. However, owing to the large variation in waste heat sources caused by changes in engine operating conditions, the adaptability of the CO2 power cycle is poor, reflected in severe performance deterioration in thermal match, components and system power output. Hence, to improve the adaptability of the CO2 power cycle to wide-range fluctuation in heat sources, a novel dual-split configuration is proposed in this paper. The freedom of regulation is effectively enhanced by the supplementary split branches, and the mass flow rate through different heat exchangers can be actively adjusted with high flexibility. Furthermore, off-design performance models and a calculation procedure are built to present the off-design performance of the different cycles under the engine operational profile. The results indicate that the proposed configuration can improves the adaptability of the CO2 cycle to fluctuating heat sources effectively. Specifically, for all engine operational conditions, the invalidated operating region was contracted from eight to four points, with the engine coolant and exhaust gas utilisation rates exceeding 90 % and 97.4 % respectively. In addition, under low engine operating conditions, the cycle pressure ratio and mass flow rate were maintained at relatively high values, contributing to enhanced pump and turbine efficiencies. The maximum net power output increased by 8.3 kW, and the minimum brake-specific fuel consumption decreased by 16.9 %.

Adaptive fuzzy PI control for the dynamic operation of the transcritical CO2 thermal system in electric vehicles

Process control is essential for ensuring the stable and efficient operation of EVs’ transcritical CO2 thermal management systems. Traditional PI control generally shows an insufficient dynamic response for the variable and complex operating conditions and then causes fluctuant process control. This study proposed an adaptive fuzzy PI control strategy to provide real-time varying PI gains for fast-tracking response and fluctuation suppression, considering the compressor discharge pressure, coolant, and air outlet temperature. A high-fidelity transcritical CO2 thermal model in EVs was first built in the Amesim platform to simulate real-time operation, and the adaptive fuzzy PI control algorithm was then developed to optimize the process control. The co-simulation is conducted to validate the effectiveness and adaptability of the proposed control methodology by comparing it with a benchmark traditional PI control strategy. The results indicated that the proposed adaptive fuzzy PI could provide a 9.22 % overshoot suppression for discharge pressure, a maximal 22.29 % overshoot inhibition and 86 s settling time reduction for the air outlet temperature, and a 25 % settling time reduction for the coolant temperature control. In addition, the fuzzy PI improved the start-up characteristics by avoiding excessive response. Such findings demonstrate that the proposed fuzzy PI control algorithm can effectively optimize the dynamic operation of the transcritical CO2 thermal system in EVs.

Analysis of green energy-saving retrofit for air-conditioning system in UHVDC converter stations

Abstract The air-conditioning system in ultra-high-voltage direct current (UHVDC) converter stations uses hydrofluorocarbons (HFCs) as refrigerants currently, which pose a certain environmental hazard. Moreover, the cooling system of the converter valves contains a great deal of low-grade thermal energy, with waste heat being directly discharged into the air, resulting in significant energy wastage and air pollution. In light of the functional characteristics and energy wastage situation of current converter station buildings, a green energy-saving retrofit scheme for the air-conditioning system in UHVDC converter stations is proposed. It adopts a transcritical CO2 cycle system for building cooling and introduces an ejector into the system to improve its performance. Simultaneously, the heat pump technology is used to elevate the grade of waste heat from the converter valves, which is then utilized for heating in the control building. Simulation results demonstrate that this scheme is effective in enhancing ecological and environmental benefits while promoting green development of the converter station.

Performance assessment and multi-objective optimization of a novel transcritical CO2 Rankine cycle for engine waste heat recovery

In this study, a novel self-condensing transcritical CO2 Rankine cycle, which integrates the three-stage expansion process with an ejector cycle, is proposed to recover engine waste heat deeply and overcome the condensation issue caused by the relatively low critical temperature of CO2. Thermodynamic and economic mathematical models are developed, and the detailed parametric analysis is carried out to investigate the effect of main parameters on both thermodynamic and economic performances of the system. Thereafter, a multi-objective optimization is conducted to trade off the two different performances. Results show that the proposed system could operate under higher temperature cold source conditions with desirable performance. The increases of turbine1 inlet pressure and LT gas heater outlet temperature, the decreases of LT gas heater outlet pressure and turbine3 back pressure are beneficial to achieve better thermodynamic and economic performances. On the basis of multi-objective optimization, the maximum net power output is 70.04 kW, which is a 10.20 % improvement compared to the reference cycle. Meanwhile, the engine power output could be increased by 7.03 % through adopting the novel system. Furthermore, the optimal exergy efficiency and unit net power cost are 37.02 % and 0.1567$/kWh, respectively.

Numerical simulation of heat transfer phenomena in a microchannel evaporator for a transcritical CO2 air conditioning system

This study presented a numerical simulation of heat transfer characteristics in a microchannel evaporator for a transcritical CO2 air conditioning system, and the simulated results have been validated by the experimental data. The evaporator consists of 6 passes with 29 flat tubes. Each flat tube has 10 microchannels having a 1.2 × 0.6 mm cross-section. The two-phase flow was simulated in the range of evaporation temperatures from 5 to 15 °C; the mass flow rates of 24.16, 30, and 34.96 g/s; and inlet vapor qualities of 0.5, 0.61, and 0.75, respectively. The results show that the two-phase flow with the evaporative temperature at the inlet of 5, 10, and 15 °C became superheated at the 3rd, the 4th, and the 5th pass, respectively. At the evaporation temperature of 15 °C, the heat transfer coefficient decreases from 8.1 to 3.6 kW/m2 K as the vapor quality increases from 0.75 to 1. With the mass flow rate of 30 g/s, in the tube length range from 0 to 1.1 m, the heat flux achieved around 1.55 kW/m2. The numerical cooling capacity gets the maximum value of 2.85 kW at the evaporative temperature of 10 °C. The numerical results are in good agreement with those obtained from the experimental results and the other published results, with a deviation of less than 10%.

Mapping the techno-economic potential of next-generation CSP plants running on transcritical CO[formula omitted]-based power cycles

Although the thermodynamic potential of transcritical/supercritical power cycles running on CO2 mixtures for next generation Concentrated Solar Power plants has been already confirmed in literature, further investigation to assess the actual feasibility of this technology from a techno-economic standpoint is needed. In fact, large uncertainty is found when it comes to the estimation of the CapEx of the power block, and the same can be said for the solar subsystem when higher-than-SoA operating temperature are considered. In this paper, two CSP schemes, with different maximum operating temperatures, are studied: one employing molten salts and another based on solid particles.To overcome the high uncertainty in terms of cost estimation, a two-step analysis is developed: firstly, the CapEx of the entire plant, except for the power block, is calculated assuming correlations from literature. As a result, the minimum power block cost allowing an LCoE lower than a certain target is identified. Secondly, an inverse methodology is applied, setting the power block cost and assessing the minimum CapEx of the solar subsystem. As a result, a map is obtained showing the target CapEx to be accomplished by sCO2+CSP if a clear reduction of the LCoE of this technology is to be achieved.

Performance analysis of sub-cooled transcritical CO2 refrigeration system using vapour absorption refrigeration system and dew point evaporative cooling

Shifting towards natural refrigerants is expected to reduce the environmental damage in terms of refrigerants leaks, as they have zero ozone depletion potential as well as minimal global warming potential. A CO2 transcritical cycle is analysed thermodynamically in this study. Further, to improve the performance of the CO2 system, a vapour absorption refrigeration system (driven by the heat available at the exit of the compressor) has been integrated with it. Also, to counter the effects of hot climatic conditions, in Indian context, a dew point evaporative cooling system is further utilized to take up the heat from the gas-cooler. A thermodynamic and economic study of the proposed integrated system is performed. The effect of various performance parameters; such as ambient dry bulb temperature, relative humidity, evaporator temperature has been studied on the overall performance of the system. Compared to the base case, the coefficient of performance is improved in the range of 40%–270 %, for the hybrid systems, under the different climatic conditions. Moreover, the proposed system provided a low-cost performance of about 0.024 $/kWh, as compared to the base case consumption of about 0.05 $/kWh.

Effect of Inter-Stage Pressure on Performances of Two-Stage Transcritical CO2 Refrigeration Cycle with Dedicated Absorption Dual-Subcooling and Mechanical Recooling

Effect of Inter-Stage Pressure on Performances of Two-Stage Transcritical CO2 Refrigeration Cycle with Dedicated Absorption Dual-Subcooling and Mechanical Recooling

Thermodynamic analysis of a modified two-stage transcritical CO2 refrigeration cycle with an ejector and a subcooler

In the application scope of large-scale supermarkets, the practicality of transcritical CO2 refrigeration device has been confirmed to be quite satisfying. A modified two-stage transcritical CO2 refrigeration cycle with an ejector and a subcooler (MTC) is proposed in this paper. In the modified cycle, the ejector recovers expansion works and reduces irreversible losses in the throttling process. The subcooler provides subcooling degree for the CO2 entering the low-temperature (LT) evaporator, thus increasing the refrigeration capacity and improving the COP of the modified cycle. Thermodynamic analysis has shown that the exergy efficiency (ηex) and COP of MTC under given operating condition has been enhanced by 13.7 % and 14.2 % compared to BTC. The discharge temperature at the outlet of high-pressure compressor in MTC is decreased by 8.3℃. Under typical operating condition, the optimal discharge pressure of MTC is 9.07 MPa, which is lower than that of BTC. The correlation to calculate optimal discharge pressure for single-stage CO2 refrigeration cycle is also suitable for MTC under given operating conditions. The MTC has also shown better performance under variable operating conditions. For MTC, when the temperature at the outlet of gas cooler increases from 35 – 45℃, the COP and ηex are enhanced by 14.1 % - 16.1 % and 12.8 % - 14.2 % compared to BTC, respectively. When gas cooler outlet pressure decreases from 11.0 to 7.5 MPa, the COP and ηex are enhanced by 14.0 % - 22.8 % and 13.4 % - 18.7 %. As the evaporating temperature at the cold side of subcooler increases from -25 to -15℃, the COP and ηex increase from 1.82 to 1.98 and 27.4 % to 29.7 %. With the ratio of refrigeration capacity (Rec) between medium-temperature evaporator and low-temperature evaporator varies from 0.7 to 1.2, the COP and ηex are improved by 10.7 % - 16.3 % and 10.7 % - 15.4 % compared to BTC. There is the maximum exergy loss at gas cooler in the MTC, whereas that of BTC is located in the expansion valve before LT evaporator. The economic analysis shows the cost per unit of exergy of MTC is decreased by 11.5 % under typical operation condition. According to simulation results, the modified cycle has better performance in severe working conditions such as high gas cooler outlet temperature and low gas cooler outlet pressure in the given range of working conditions compared to BTC.

Optimal high-pressure correlation for transcritical CO2 cycle in direct expansion solar assisted heat pumps

Heat demand may be met sustainably by a solar-assisted heat pump that CO2 as a refrigerant. This is made possible by the employment of an ecologically benign refrigerant and a renewable energy source that enhances system performance. At the ideal high pressure, the CO2 heat pump running in a transcritical cycle will function at its highest coefficient of performance (COP). In that way, this study aims to present correlations for calculating the optimum high pressure in a CO2 direct expansion solar assisted heat pump (DX-SAHP). In this study a mathematical model for compressor, solar evaporator and gas cooler was developed and validated experimentally. The mean difference between the mathematical model and experimental results are −3.9%. Two new equations are proposed to calculate the optimum high pressure in a CO2 DX-SAHP. The first one considered environment temperature, water outlet temperature and evaporating temperature, which are easy to measure. These facilities the use of correlation to control the heat pump. The second one considered environment temperature, water outlet temperature and solar radiation, which are more suitable for designing CO2 DX-SAHP. A data base with 100 optimum points was used to curve fitting. Another data base with 50 optimum points was used to compare the results obtained from curve fitting and correlations for the optimum high pressure available in the literature. The proposed correlations shown a maximum error lower than 10.2% despite of the correlations available in the literature from which the errors are about 30%.

Refrigerant charge estimation method based on data-physic hybrid-driven model for the fault diagnosis of transcritical CO2 heat pump system

The transcritical CO2 heat pump system is a promising and excellent heating scheme. However, the operating pressure of the transcritical CO2 heat pump system is high, and refrigerant leakage is a frequent problem. It is worth noting that the operating principle of CO2 heat pump systems is unique. Thus, conventional refrigerant charge estimation methods for subcritical systems cannot be directly applied to transcritical systems. In this study, a novel refrigerant charge estimation method for the transcritical CO2 heat pump system is proposed. Based on the heat and mass transfer characteristics of the transcritical system, the grey box model constrained by physical laws is constructed. Based on the machine learning algorithm, the correction model of the grey box model is built. The hybrid model combines the advantages of the high generalization ability of the physic-driven model and the nonlinear fitting ability of the data-driven model. The results show that the novel estimation method can accurately predict the refrigerant charge, enabling fault diagnosis of refrigerant leakage. The data-driven correction model can improve the prediction accuracy of the grey box model. The Mean Relative Error of the hybrid-driven model can be controlled within 5 %.

Transcritical CO2 mixture power for nuclear plant application: Concept and thermodynamic optimization

The conventional steam power cycle suffers from lower thermal efficiency, larger size, and inadequate cold source matching, failing to meet the demands for high efficiency, compactness, and adaptability required by new-generation underwater power plants. Consequently, the T-CO2 mixture power cycle has been proposed for technological innovation in underwater nuclear plants. Thermodynamic model of the recuperated, precompression, recompression and partial cooling cycles is developed based on the first law of thermodynamics. And the thermodynamic performance of five CO2 mixtures, including CO2/SO2, CO2/H2S, CO2/butane, CO2/propane, and CO2/cyclohexane in the four cycles coupled with a pressurized water reactor (PWR) and an advanced high-temperature reactor (AHTR) is investigated. The findings reveal that when optimized for thermal efficiency, the CO2/cyclohexane is better suited for recuperated and precompression cycles, while CO2/H2S and CO2/propane are more suitable for recompression and partial cooling cycle. Furthermore, regarding the T-CO2 mixture power cycle incorporating PWR and AHTR, the recompression cycle of CO2/propane and CO2/H2S should be opted to achieve maximum thermal efficiencies of 33.07 % and 46.07 %, respectively. Conversely, selecting the precompression cycle of CO2/H2S can yield maximum specific work of 98.61 kJ/kg and 161.62 kJ/kg, respectively. Therefore, investing in reforming nuclear power with new technologies is a feasible policy choice. Additionally, policymakers need to closely monitor the reform requirements of nuclear power plants.

Performance analysis and prediction of a modified precompression transcritical CO2 power generation cycle

The efficient utilization of biomass energy and the optimal operation of integrated renewable energy sources in virtual power plants have become critical issues to achieve carbon neutrality targets in rural areas. In the rural areas of Northeast China, a large amount of electricity can be generated from biomass. It is very important to develop biomass power generation equipment for this rural area. Due to the high thermal efficiency and its compact system without freezing process like water, CO2 thermal cycle is an appropriate option for this kind of power generation equipment. According to whether the flow is separated, CO2 cycles can be divided into the single flow layouts and split flow layouts. Compared to the single flow layouts, split flow layouts have higher efficiency, but more complex structures and lower heat transfer power per unit area. Considering the climatic characteristics of Heilongjiang Province and the seasonality of straw biomass utilization, this study proposes a modified scheme for the precompression transcritical CO2 cycle in the single flow layout to meet the simple structure requirement of the small power plants in cold areas like Northeast China. Through energy analysis, the study calculates the thermal efficiencies of the two cycles when the inlet pressure of the main compressor is 5 MPa, the turbine inlet temperature is 550 °C and the pressure ratios of the main compressor are in the range of 4.5–5.5. The optimal efficiency of the traditional precompression cycle is 43.55 % when the main compressor pressure ratio is 5.5, while the modified precompression cycle is 44.86 % when the pressure ratio is 5.0266. The modified precompression cycle has a higher efficiency than the traditional precompression cycle at a lower pressure ratio of the main compressor.

Energy and Exergy Analysis of Transcritical CO2 Cycles for Heat Pump Applications

Energy and Exergy Analysis of Transcritical CO2 Cycles for Heat Pump Applications

A Novel Thermally Integrated CO2-Carnot Battery (TI-PTES) utilizing Cold Thermal Storage

Abstract The growing integration of renewable energy sources in the energy grid presents intermittency and negative pricing challenges, necessitating large-scale energy storage solutions. Pumped Thermal Energy Storage (PTES) can address these issues by storing and delivering substantial energy whenever required. High-temperature heat pump development is crucial to deploying PTES for storing heat at sink temperatures that are well above the ambient temperature(>450°C) to ensure a reasonable round-trip efficiency(RTE). Currently, however, it is not a technological possibility for heat pumps to achieve these temperatures even with the support of freely available heat (200°C to 400°C) as source temperatures. This study explores a potential layout of the TI-PTES system that exploits commercially available equipment by storing heat below the ambient temperature while still being able to utilize the freely available heat source(Solar, Waste heat, biomass, etc.) to support the overall RTE. The charging phase employs a well-established CO2-refrigeration cycle to accumulate energy below the ambient temperature in cold thermal storage. While the discharging phase runs a trans-critical CO2 power cycle between the freely available heat source and the cold thermal storage. Overall, offering a practically implementable model for the PTES system with market-available components. The study investigates the design of this innovative system presenting the relevance of different operating and machine parameters as well as the contribution of freely available heat sources to the overall performance. Finally benchmarking the technology with other long-duration energy storages.

Refrigerant charge influence on the performance of a transcritical CO2 system with flash-tank for low-temperature refrigeration

While the use of CO2 as a natural refrigerant become widespread, there is a scarcity of research on refrigerant charge effects in transcritical CO2 refrigeration applications, especially for systems with flash-tank and two-stage compressors. In this work, an experimental investigation of the effect of the Normalized Refrigerant Charge (NRC) on the parameters and performance of a Flash-Tank Vapor Injection (FTVI) CO2 refrigeration system is carried out. Within the explored NRC range of −0.02 to 0.247, an optimal NRC of 0.18 was identified that yields a maximum COP regardless of operating conditions. Results suggest that typical operating parameters such as temperature and pressure are not being affected by the NRC because of the charge buffering function of the flash-tank. However, the liquid–vapor separation capacity of the flash-tank causes a reduction in the refrigeration capacity when the system is not charged properly. This refrigeration capacity detriment related to undercharged conditions becomes more severe under high ambient temperatures, with a maximum COP penalty of 20 % when comparing the lowest charge versus the optimal charge performances at a gas cooler outlet temperature of 40 °C.

Design and Performance Evaluation of Multi-Generation System based on Transcritical CO2 Rankine Cycle and Helium Gas Turbine with Hydrogen Production

The advancement in nuclear energy embodied by the gas-cooled modular reactor (GCMR), incorporating the transcritical CO2 Rankine cycle (tRC) and a helium turbine (He tur.) for hydrogen (H2) production, signifies a substantial leap forward in this domain. This research endeavor aimed to amalgamate various technologies to enhance energy conversion efficiency and generate clean hydrogen, a versatile energy carrier. Helium, selected as the GCMR coolant, boasts advantageous properties such as superior heat transfer capabilities, chemical inertness, and the capacity to operate at elevated temperatures. These attributes facilitate effective heat extraction from the reactor core, mitigating corrosion risks while boosting both power output and energy efficiency. A pivotal aspect of this design lies in integrating the tRC with the helium turbine, maximizing energy conversion efficiency and resource utilization by harnessing waste heat from the He turbine to generate additional power through the CO2 Rankine cycle. Furthermore, the system incorporates a hydrogen production module, enabling the clean generation of hydrogen as a byproduct of the nuclear power generation process. According to analysis results, the net power obtained from the Helium turbine was calculated as 241679 kW, and the net power produced from the tRC was calculated as 9902 kW. Additionally, with this developed system, 23.11 kg/h H2 and 183.4 kg/h O2 can be produced. The energetic and exergetic performance of the overall system is computed as 41.8% and 54.28%, while the total amount of exergy destruction is determined as 212199 kW. Moreover, analytical findings reveal that the reactor core exhibits the highest exergy destruction among system components at 91282 kW, whereas the heat exchanger (HEx) registers the lowest exergy destruction at 3.56 kW. In addition, in this study, parametric analyses are also performed to determine the effect of helium outlet temperature analysis and pressure ratio on system performance.

Energetic, exergetic and economic analysis of a trans-critical solar hybrid CCHP system

A solar hybrid CCHP (combination of cooling, heating and power) system was proposed to organically integrate the Brayton and reverse Carnot cycle by trans-critical CO2 working medium. The transient thermal storage in a solar hybrid CCHP system (SCCHP) was designed to overcome the energy coupling challenges in regions rich in solar and gas resources. Moreover, the incorporation of an optimally efficient throttling expander in cooling cycle was designed to enhance energy utilization efficiency. The thermodynamic performance of the SCCHP system was systematically evaluated by comparing with the ejector hybrid CCHP system from energetic, exergetic, and economic perspectives. The results suggest that elevating the intake pressure of both the high-pressure compressor from 5.2 kW to 6.4 kW and turbine from 7.3 kW to 7.8 kW, led to an enhancement in the COP of the SCCHP system. Moreover, raising the turbine intake temperatures from 483.15 K to 503.15 K yielded a significant improvement in system energy efficiency from 0.66 to 0.71 and COP from 1.58 to 1.72. Furthermore, in contrast to the ECHP system, the components in the SCCHP system demonstrated not only less exergy efficiency variation to the influence of ambient temperature but also lower hourly economic costs. The SCCHP has an average hourly investment cost that is 5.70 USD (kgh)−1 lower than ECHP, and its economic efficiency improves with higher ambient temperatures.

Genetic algorithm-based optimization of combined supercritical CO2 power and flash-tank enhanced transcritical CO2 refrigeration cycle for shipboard waste heat recuperation

The shipping industry significantly contributes to global trade and economy, but is also responsible for approximately ∼3 % of global greenhouse gas (GHG) emissions. Harnessing waste heat from marine vessels to perform useful work is a potential solution to reduce these emissions. Although the Organic Rankine Cycle (ORC) and CO2 cycles have been studied separately for waste heat recovery, a combined power and refrigeration systems, utilizing both cycles have not been reported. Herein, a combined system, “Marine Energy Recovery System (MERS)”, that integrates the supercritical CO2 Brayton power cycle with a flash-tank-enhanced transcritical CO2 refrigeration cycle, is proposed, aiming to generate power and provide cooling simultaneously. The power cycle incorporates an ORC, and a flash-tank is introduced within the refrigeration cycle to improve system performance. Both cycles share a low-temperature recuperator and a gas cooler to further utilize the heat between them. The MERS is evaluated from both a 1st and 2nd law perspective against various performance metrics under different operating conditions, such as: gas cooler pressure, evaporation temperature, and turbine inlet temperature and pressure. Results elucidated that the MERS achieved energy and exergy efficiencies of 54.62 % and 54.90 %, respectively, representing significant improvements over similar systems. The net work output improved by 717.55 kW and the net cooling capacity by 515.7 kW relative to the reference system. Furthermore, a COP of 2.99 outlines its potential as a cooling system. To further enhance MERS’s performance, a multi-objective optimization approach is employed, utilizing Artificial Neural Network (ANN) and Genetic Algorithm (GA). Optimal operational conditions yielded an energy efficiency of 74.95 % while maintaining a net work output of 6890.55 kW with gas cooler pressure, turbine inlet temperature, and gas cooler outlet temperature being 9.5 MPa, 461.76°C and 50°C respectively. These findings support the reliability and improved design of the MERS for future marine applications.

Thermodynamic and parametric analyses of a zero-carbon emission SOFC-based CCHP system using LNG cold energy

A novel zero-carbon emission combined cooling, heating and power (CCHP) system is currently proposed. The thermal energy of the solid oxide fuel cell (SOFC) exhaust is recovered in a transcritical CO2 (T- CO2) power cycle. Relying on the efficient utilization of liquefied natural gas (LNG) cold energy, CO2 capture has been achieved at low energy consumption. The thermodynamic performance is evaluated by using energy and exergy analysis methods for this hybrid process. The electrical, exergy, and CCHP efficiencies are obtained as 60.37 %, 62.83 %, and 79.09 %, respectively. The CO2 condenser, with the largest exergy destruction ratio (18.60 %) and a low exergy efficiency (37.16 %), is regarded as the weakest point in terms of thermodynamic perfectibility. In addition, the influences of the current density, stack temperature and pressure, and fuel utilization rate have also been studied from different aspects of system performance. The current density, stack temperature, stack pressure, and fuel utilization rate are recommended as 0.3 A/cm2∼0.4 A/cm2, 900 °C, 5 bar, and 85 %, respectively. This research provides practical reference and pragmatic guidance for the integration, analysis, and optimization of SOFC-based CCHP systems.