Source Heat Pump Unit Research Articles

Performance of air source heat pump units with different wettability evaporators

The air source heat pumps (ASHPs) for winter heating have the advantages of high efficiency and environmental protection. However, the outside evaporator’s frosting negatively impacts the performance of heat pump systems in low-temperature and high-humidity environments. In this paper, we fabricated the superhydrophobic evaporator and mounted it on a commercial ASHP unit, expanding the use of superhydrophobic surface modification technology from heat exchangers in the laboratory to the ASHP units. Then we investigated the operating characteristics of two ASHP units equipped with hydrophilic and superhydrophobic evaporators respectively under six distinct outdoor and indoor environmental conditions experimentally. In the non-frosting conditions, film condensation formed on the surface of the hydrophilic evaporator and the evaporation temperature decreased with the formation of water film, resulting in a decrease in heat production and COP. In the frosting conditions, the time of forming the frost layers with the same thickness on the superhydrophobic surface was more than 4 times longer than that on the hydrophilic surface. The COP of the superhydrophobic evaporator unit was improved by 2.9% to 8.2% under the non-frosting conditions, by 11.5% under the continuous heating conditions and by 14.28% when the hydrophilic unit performed two defrosting cycles, respectively. During the period in which the hydrophilic evaporator unit completed two frosting/defrosting cycles, the energy loss coefficient caused by the defrosting process was 31.65% compared to the superhydrophobic evaporator unit. This work extended the experimental method of superhydrophobic heat exchanger, contributing to the application of superhydrophobic finned-tube evaporators in ASHP units.

Applying neural network model to real-time frosting detection and intelligent defrosting control for air source heat pump

Periodic defrosting is essential for efficient operation of air source heat pump to avoid the attenuation of performance caused by frosting. However, the mal-defrosting phenomena in practice, which are no defrosting progress when necessary and unnecessary defrosting operation under no frosting, happen occasionally. To improve the accuracy of defrosting, a convolutional neural network model based on deep learning with YOLOv5 is introduced for frosting detection in this paper. Firstly, the evaluation method of frosting degree combining fractal dimension and heating capacity attenuation is constructed. Then, an image dataset is built based on frosting degree evaluation. The optimized YOLOv5-frost network is constructed, which improves the accuracy of frosting detection by iterative training. Thirdly, a novel defrosting control method based on YOLOv5-frost network is proposed, in which the defrosting initiation and termination points are investigated. Finally, comparative experiments are conducted between the proposed defrosting control method and traditional methods. The results indicate that the mal-defrosting phenomena are effectively avoided under the proposed method. The COP and total heating capacity are increased by 11.83 % and 7.42 % respectively, as well as the defrosting frequency and energy consumption are decreased by 75.00 % and 88.24 %, respectively. Additionally, the time consumption, memory overhead, and central processing unit overhead of the proposed method are 2.72 %, 71.58 %, and 74.07 % of those for the traditional methods, respectively. The performance of air source heat pump unit in real-time frosting detection and on-demand defrosting in complex conditions can be effectively improved with the proposed method.

Research on energy-saving and carbon-reducing technologies for water-ground source heat pump units

Abstract The heat pump industry’s energy consumption as a percentage of total energy consumption is constantly increasing. Research on energy-saving and carbon-reducing technologies, and manufacturing high-efficiency units of heat pump with water-ground source has become the main trend of the current heat pump industry. With proposal of the national “dual-carbon” strategy goal, enhancing the energy efficiency of units of heat pump with water-ground source has become a key way to transform and upgrade the refrigeration and air conditioning industry. The aim of this study is to combine current studies on energy-saving and carbon-reducing technologies for units of heat pump with water-ground source and applying these technologies. Through experimental tests, the energy efficiency of units of heat pump with water-ground source is more than 15% higher than that of ordinary units.

Seawater source heat pump system based on capillary heat exchanger for seepage in submarine tunnel: a case study

Abstract The discharge of seepage water from undersea tunnel structures, often treated as wastewater, inherently carries a substantial reservoir of untapped low-grade thermal energy. Unfortunately, comprehensive investigations into harnessing this latent potential remain notably limited. This study introduced an innovative strategy through the design of an undersea tunnel seepage seawater source heat pump system. Distinguished by the integration of a capillary front-end heat exchanger, this system aimed to effectively exploit the frequently disregarded low-grade thermal energy present in the seepage water of undersea tunnel structures. The seawater seepage from the tunnel is transported to the car park at the tunnel entrance, and a seawater energy pool is constructed by storing seawater in its underground space. The use of capillary network placed in the energy pool in the front heat exchanger, water source heat pump units, circulating water pumps and fan coil end device composed of underground undersea tunnel seepage seawater source heat pump system for the building heating and cooling. Furthermore, a comparative assessment was conducted, contrasting this novel system with the traditional air-conditioning setup that utilizes chillers and gas boilers as cooling and heating sources. The aim was to evaluate its capacity for energy conservation and emission reduction. The findings from the study strongly affirmed the viability of the proposed seepage seawater source heat pump system within undersea tunnels. It boasted the potential to achieve annual savings of 53.55 tce, highlighting a noteworthy energy-saving rate of 21.2%. Concurrently, reductions in CO2, SO2, and particulate emissions amounted to 132.28 t/a, 1.07 t/a, and 0.54 t/a, respectively. This study not only stands as a reference for the strategic utilization of seepage seawater from undersea tunnel structures, prioritizing energy conservation and emission reduction, but also pioneers innovative approaches toward resource optimization and environmental sustainability, meeting the inherent needs of carbon peaking and carbon neutrality goals.

Advanced Exergy Assessment of an Air Source Heat Pump Unit

Conventional exergy-based analysis methods are used for evaluating the performance of the energy conversation systems. Conventional exergy-based analyses identify the sources, amounts, and reasons of irreversibilities (exergy destructions), costs and environmental effects, and provide a general direction for improvement. However, interactions between system components (endogenous/exogenous) and technical limitations (avoidable/unavoidable) cannot be identified with any conventional analysis. Hence, the real potential for improvement and optimization strategies can be misguided. Advanced exergy based analysis seeks to overcome this limitation. An air source heat pump unit was assessed applying conventional and advanced exergy analysis approaches respectively. Avoidable/unavoidable and endogenous/exogenous exergy destructions, modified exergy efficiencies and modified exergy losses ratios were calculated for every single component of the system. The results showed that while the evaporator and condenser efficiencies could be upgraded via constructional enhancements to the overall system and other system components, internal operating conditions were mainly responsible of the inefficiencies regarding with the compressor. The analysis demonstrated that while it was possible to improve evaporator and condenser efficiency by making constructive enhancements to whole system design, the efficiency of the compressor was mainly determined by the internal conditions in which the compressor operated.

A simulation study on the heating characteristics of residential buildings using intermittent heating in Hot-Summer/Cold-Winter areas of China

Radiant air conditioning system is an important heating method with better thermal comfort, less noise and greater energy-saving potential. However, different intermittent heating modes may significantly impact both the heating efficiency and indoor thermal comfort, which has been neglected in existing studies. Therefore, to obtain optimal intermittent heating modes for achieving higher energy efficiency and better indoor thermal comfort for the residential buildings in Hot Summer and Cold Winter areas, a TRNSYS model of the radiant air conditioning system was developed and validated. The indoor thermal comfort and energy consumption characteristics during the coldest day and entire heating season were simulated and analyzed based on four different intermittent heating modes. The results demonstrated that the supply water temperature of the air source heat pump unit and the radiant terminals stabilized at the set temperature in about 1 h during the start-up stage, and the indoor air temperature stabilized at 24.0 °C after 7.5 h during the shutdown stage. The proportion of time that meets first-level thermal comfort under the four intermittent heating modes was above 90.1% and even higher at over 96.1% when considering the sleeping period. Compared to the continuous heating mode, the four intermittent heating modes saved 22.3%, 25.8%, 40.4% and 48.4% of energy. Overall, the preferred intermittent heating mode for residential buildings with the radiant air conditioning system in Hot Summer and Cold Winter areas was identified as switching on from 7:00 to 15:00 and 19:00 to 3:00, while switching off from 15:00 to 19:00 and 3:00 to 7:00. This model not only considered the immediate benefits of improved indoor thermal comfort and energy efficiency, but also showed great advantages in developing sustainable construction.

A field study on the impacts of cold island effect on operating performances of air source heat pump array for space heating

Connecting multiple air source heat pump units in parallel to form an air source heat pump array (ASHP-A) is an important heating approach for central heating in small areas. At a low wind speed, the colder air stream exhausted by outdoor coils of ASHP units cannot effectively mixed with the ambient air and repeatedly return to the outdoor coil for heat exchange, resulting in the local air temperature inside the ASHP-A lower and lower and forming the cold island effect (CIE). CIE may seriously deteriorate the heating efficiency of ASHP units in buildings. However, the impacts of CIE on the operating performances of an ASHP-A were insufficiently studied in existing studies but necessary for developing a reasonable installation standard and efficient control strategy. Therefore, to reveal the impacts of CIE on the operating performances of ASHP units in ASHP-A, the characteristics of CIE, and its impacts on the operating performances of the field ASHP-A were experimentally carried out. The results demonstrated that CIE significantly existed in the field ASHP-A and resulted in frequent defrosting operations and lower heating performances. The defrosting frequency of Unit 1 having a more severe CIE was increased by 243.5 %. The averaged output heating capacity and COP in Unit 1 declined by 27 % and 27.7 %, and these for Unit 2 by 13.6 % and 14.8 %, respectively. The frosting-defrosting loss coefficient for Unit 1 was increased by 519 % relative to Unit 2. This study is valuable to promote the development of installation standards by taking the CIE into consideration for improving heating efficiency of ASHP-A in buildings.

Experimental study on the effects of melted frost icing on the operating performances of air source heat pump

Defrosting operation is always used to solve its frosting problem at a high humidity environment for air source heat pump units (ASHPs), and at the end of defrosting operation, the residual melted frost may exist on the surface of outdoor coil and freeze into ice in sequent frosting. However, till now, as the residual melted frost icing environment is difficult to create, its quantitative influences on the heating performance of ASHPs is still unknown, especially at different icing levels. To resolve this issue, a control strategy was firstly proposed to make it possible for the residual melted frost to ice. Then, based on the control strategy, the effect of five different icing levels on operating performances of an ASHP unit were investigated. Results indicated that ice can promote the frost formation, and the operating performances of ASHP unit were significantly affected by different icing levels. When the percentage of iced outdoor coil surface was increased from 0% to 15% and 35%, the output heating capacity of ASHP unit was decreased by 11.2% and 23.8%, and meanwhile the COP of ASHP unit was decreased by 7.7% and 16.1%, respectively. The results can assist with the defrosting control optimization of practical products.

Experimental study of relative humidity effect on the edge effect of frosting characteristics on a vertical cold plate surface

As a common phenomenon, frosting often brings negative impacts in various fields. To gain more insight into the frosting process on a vertical cold plate considering the edge effect, a specific experimental system is designed and built to perform frosting experiments under forced convection conditions with relative humidity varying from 40% to 80%. The results show that as the relative humidity increases, the droplet solidification stage period in the unaffected region decreases, but the equivalent width of edge-affected region, area-average equivalent contact diameter of droplets, and coverage area ratio of droplets increases and then decreases. The area-average equivalent diameter of droplets in edge-affected region increases by 41.25%, 214.63%, 137.98%, 159.03%, and 30.30%, when compared to the unaffected region from Case 1 to Case 5, respectively. Besides, the difference between the droplet distribution density in the edge-affected and unaffected regions gradually decreases, but the average frost layer thickness in the edge-affected region increases significantly as the relative humidity increases. The frost layer growth rate decreases first and then increases as relative humidity increases. From Case 1 to Case 5, the frost growth rates at 1,800 s decrease by 90.05%, 70.19%, 56.08%, 62.28%, and 82.39%, respectively, compared to the initial ones. Results of this study can provide a reference for the anti-frosting and defrosting control technologies in the field such as refrigeration and air source heat pump units.

Study on the Performance of a New Ultra-Low Temperature Air Source Heat Pump (ASHP) Unit in Cold Regions

Low air temperature and frosting have been reported as the critical factors that greatly attenuate the efficiency and performance of the ASHP in cold regions. In order to ensure the potential prevalence of the ASHP in cold regions of China, a new ultra-low temperature ASHP unit was developed, and the field measurement was carried out in an office building where these ASHP units were installed in Shanxi Province. Results showed that a coefficient of performance (COP) of 1.83 was obtained at the ultra-low environmental temperature of −25 °C. Meanwhile, measured results indicated significant frosting suppression and improved heating performance under three typical frosting conditions. In addition, long-term measurement results revealed that the mean COP and COPsys reached up to 3.34 and 2.63, respectively, indicating a higher performance in the cold regions of China. Consequently, the corresponding CO2 emission reached 11.3 kg per year and per square meter, and the annual total cost on the unit reduced by 15.8% compared with the conventional ASHP, which meant that the total investment could be covered in the second year. The reduced CO2 emission and the annual cost implied that the ASHP unit could produce better environmental and economic benefits. Findings of this study revealed that this ultra-low temperature ASHP unit had a better performance under cold environment, which offered a possibility for the prevailing of the ASHP in cold or extremely cold regions, as well as could contribute to the carbon peaking and neutralization.

A novel variable speed ASHP frosting suppression operation method based on the frosting suppression performance map

For variable speed (VS) space heating air source heat pump (ASHP) unit, its different operation speed combinations may significantly affect the frosting suppression and heating performances. However, currently there is no frosting suppression operation method for VS ASHP units, so that their frosting suppression ability using different speed combinations is not fully utilized. Therefore, a novel frosting suppression operation method based on the frosting suppression performance map for VS ASHPs has been proposed, and its development through experimental is reported in this paper. Firstly, a novel operation method to guide the frosting suppression operation for VS ASHPs is proposed. Secondly, an experimental setup with two VS experimental ASHP units, test conditions, and nine study cases are described. Thirdly, the speed combinations that led to different frosting suppression potentials but with the same output heating capacity were determined using the developed frosting suppression performance map, and comparative tests were carried out. It is shown that the use of the proposed novel frosting suppression operation method with the optimal coefficient of performance (COP), which can increase the total output heating capacity (Q) by 15% and the COP by 25%. The proposed novel operation method was straightforward and simple to implement, which could contribute to the further development of frosting suppression operation for ASHPs.

Energy, exergy and economic analysis of an integrated ground source heat pump and anaerobic digestion system for Co-generation of heating, cooling and biogas

This study designed and simulated a feasible polygeneration system, which integrated with a ground source heat pump and anaerobic digestion units to co-generate cooling, heating, and biogas for buildings as well as to utilize biomass residues in rural areas. The quantitative investigation of the energy, economics, and exergy of such a system was conducted in a village in Chongqing, China. The results indicated that by incorporating an anaerobic digestion unit, the integrated system could save 21.6% and 32.2% of primary energy, as well as 35.6% and 34.4% of annual costs, when compared to the separated and current systems, respectively. A Sankey diagram of exergy flow showed that exergy efficiency was 32.2%, and the anaerobic digester and heat pump units were the main exergy destruction components. Increasing the operating supplied temperature of the heat pump for the anaerobic digester from 45 °C to 60 °C improved exergy efficiency from 32.2% to 40.7% but decreased the overall energy efficiency ratio from 4.09 to 3.83. In addition, increasing the coefficient of performance (COP) of heat pump units was an effective way to enhance energy and exergy efficiency. The study may aid designers and decision-makers in optimizing the system and its components.

Field studies on indoor thermal environment and start-stop characteristics of the radiant air conditioning system during intermittent heating

With the improvement of social economy, the heating demand of residents in Hot Summer and Cold Winter (HSCW) areas in China is increasing. The radiant air conditioning (A/C) system, is popular as a heating way due to its high comfort, low noise and high energy saving potential. There is still a lack of field research on the system under the intermittent heating mode in the HSCW area. To provide a guide for the operation mode of the radiant A/C system during intermittent heating in HSCW areas, this paper focused on the radiant A/C system with the fresh air system, and then studied system's practical operational parameters and dynamic characteristics in winter. The indoor and outdoor air temperatures and relative humidity, the water temperatures of inlet and outlet of the air source heat pump (ASHP) unit, the supply and return water temperatures of radiant terminals, as well as supply air temperature were analyzed in three stages, i.e., the initial start-up stage, the intermittent shutdown stage and the intermittent start-up stage. The results show that, it took 7 h and 50 min for the indoor air temperature to reach the set indoor temperature during the initial start-up stage. Compared to the initial start-up stage, the intermittent start-up stage reduced the time for the indoor air temperature to reach the set indoor temperature by 4 h and increased the indoor air temperature rise rate by 97%. The indoor air temperature rise rate was 0.46 oC/h and 0.91 oC/h, during the initial start-up and the intermittent start-up stage, respectively. The indoor air temperature decrease rate was 0.23 oC/h during the shutdown period. During the entire winter season, the ASHP unit switched on and off intermittently 10 times. The longest shutdown lasted for 111 h, and the indoor air temperature dropped to 17.2oC.

A method for sizing air source heat pump considering the joint effect of outdoor air temperature and relative humidity

When operated in a highly humid environment, frost may accumulate on the surface of the outdoor coil in air source heat pump units (ASHPs), leading to a reduction in its output heating capacity. Currently, the existing methods for sizing ASHPs only considered the effect of outdoor air temperature, Ta, without taking into account the effect of relative humidity, RH, on output heating capacity. This often resulted in an insufficient heating capacity from an ASHP selected. To resolve this issue, a model for predicting the output heating capacity of ASHPs, Qh, was established firstly. Then, considering the variation in the rated output heating capacity of ASHPs, a method for sizing ASHPs considering the joint effect of Ta and RH has been developed. Besides, for practical application, a capacity design correction factor, K, was proposed, evaluated, and plotted as a cloud picture. Evaluating results indicated that K can be used for sizing ASHPs accurately. When the effect of frosting on Qh was considered, the maximum rates of decrease in the output heating capacity correction factor, KQ, was between 43.8% and 50.0%, and the outdoor air design temperatures for space heating in six typical Chinese cities were decreased by 1.8–3.5 °C, with the average of 2.8 °C. For highly humid cities, such as Qiannan area China, even if its outdoor air design temperature was 1.4 °C higher than that in Chongqing City, the K value was 0.24 lower.

A modelling study on the frosting characteristics of a novel dual-fan outdoor coil in an Air Source Heat Pump unit

Uneven frosting along the airflow direction in a traditional outdoor coil in air source heat pumps (ASHPs) was inevitable due to a fixed one-way outdoor airflow direction, causing a rapid deterioration in heating performances of ASHPs. To alleviate this uneven frosting phenomenon, a novel dual-fan outdoor coil where air flow direction can be alternately reversed was proposed in a previous experimental study. To more effectively and comprehensively study the operating characteristics of ASHPs having the dual-fan outdoor coil at different fan operating modes, with different configurations and under different operating ambient conditions, a dynamic mathematical model for the experimental ASHP having the dual-fan outdoor coil was developed and experimentally validated. Then a follow-up modelling study for different operating modes of the two fans, fin pitches and operating ambient conditions was carried out using the validated model. The modelling results demonstrated that by optimizing fan operating mode, the difference in frost thickness between the windward and leeward sides of the dual-fan outdoor coil can be reduced by up to 77.3 %, the averaged output heating capacity and COP improved by up to 11.1 % and 12.7 %, respectively, and the number of switching operation of the two fans decreased by 55.6 %. Besides, the recommendations for using the dual-fan outdoor coil at different operating modes of the two fans, different fin pitches and operating ambient conditions were also made. The model can be used as a useful tool in helping achieve higher operating efficiency for ASHPs having the novel dual-fan outdoor coil.

Technical measures for improving the cold island effect of air source heat pump unit array

In recent years, in response to the call for energy conservation and emission reduction, the air source heat pump systems have been widely applied in regional centralized heating engineering.However, due to the existence of cold island effect, the heat pump unit operation in winter has the problems of low efficiency, high operation cost and insufficient production.This paper takes the heat source station combined with gas source heat pump and electric boiler as an example, and its heat pump unit array was simulated and calculated by analyzing relevant test data and using the numerical calculation method. Some technical measures were put forward to improve the cold island effect, and then the advantages and application scope of these measures are also analyzed.

An experimental study on improving defrosting performances of air source heat pump unit based on hot-gas bypass method

ABSTRACT A novel hot-gas bypass defrosting method for an air source heat pump (ASHP) unit has been presented in a previous work, which can satisfy defrosting and uninterrupted heating simultaneously. To further improve the novel hot-gas bypass defrosting performances, the effects of electronic expansion valve (EEV) on both the defrosting and uninterrupted heating performances are experimentally investigated. The results showed that the defrosting period and consumption decreased by 64.7% from 510 to 180 s and 19.7% from 1133.8 to 910.2 kJ when the opening of a 500-step EEV increased from 120-step to 480-step. Although the defrosting period for EEV opening of 480-step was the shortest, the period of blowing cold air was the longest which lasted for around 60 s. Besides, the percentage of consumed energy amount used for defrosting and the average heating capacity during defrosting period ranged from 65.2%~81.7% and 1178 ~ 903 W, respectively, with five EEV openings. The maximum average COP was 0.57 with EEV opening of 120-step, while the minimum value was 0.36 with EEV opening of 280-step. The results can help to optimize the defrosting control strategy of the ASHP units using the novel hot-gas bypass defrosting method and facilitate the development of ASHP technology.

Optimal design strategy of selection and combination to multi-air source heat pump units for central heating

The air source heat pump (ASHP), as an energy-saving and environmentally friendly heating technology, has been widely used in central heating projects. The initial selection scheme of ASHP plays a crucial role in improving partial load performance, especially for fixed frequency ASHP units. To improve the performance of an ASHP scheme, where the scheme contains a number of ASHP units, the design and operation of several ASHP units in central heating systems were studied. Combined with field test results, the simulation calculation of different schemes was carried out and the optimal selection scheme which had both stability and high performance was obtained. By choosing units that have different nominal heating capacities, this can improve performance by up to 6% compared with the traditional scheme where all units have equal nominal heating capacity. By calculating performance under different building loads, it was concluded that the highest coefficient of performance (COP) can be achieved when the number of units is three and the nominal heating capacity ratio of the different units is 2:3:4. At the same time, a new concept was proposed to evaluate the overall operating load of the unit.

A modeling study on developing the condensing-frosting performance maps for a variable speed air source heat pump

For a variable speed (VS) space heating air source heat pump (ASHP) unit, to comprehensive study its frosting suppression and heating performances, a condensing-frosting performance map has been proposed. An experimental study using an experimental VS ASHP unit to obtain condensing-frosting performance maps was previously reported. However, obtaining such performance maps experimentally was time consuming and costly, and it was therefore considered highly necessary to develop a mathematical model to obtain performance maps through modeling study. In this paper, therefore, a mathematical model for the experimental VS ASHP unit was firstly developed by referring to previously published mathematical models for VS air conditioners. The developed model was experimentally validated using reported experimental data. The average relative errors between the measured and predicted total output heating capacity and COP were at 3.7% and 3.6%, respectively, and the average error between the measured and predicted outdoor coil surface temperature was at 0.2 °C. A follow-up modeling study was then carried out using the validated model to obtain condensing-frosting performance maps for the experimental VS ASHP unit having different outdoor coil surface areas and at different outdoor operating conditions. The modeling study results suggested that by increasing outdoor coil surface area of the experimental VS ASHP unit from 50% to 150%, its surface temperature on average was increased by more than 1.37 °C, which was inducive to a better frost suppression performance, and the total output heating capacity by more than 11.07%, but at a higher initial manufacturing cost. The modeling study results also indicated that the developed model can be a useful tool in studying the characteristics of VS ASHPs during both frosting and frost-free operations, which was important for guiding the design and control of ASHPs for their efficient and reliable operations.

Field research on the trinity energy storage and heating system of villa in cold area

Since the implementation of changing coal into clean energy heating in the Beijing–Tianjin–Hebei region, there has been a tremendous change in terms of air quality during the winter in the north. On the basis of field research for resort sample room setting up in the Yanqing district , Beijing, this paper mainly expounds the cold and heat sources and system solutions used by resort villas to meet the needs of hot water, heating, and cooling throughout the year, and introduces a new type of solar energy ‘The heat pump direct floor radiant heating system’ (called “Trinity”), which can combine air source heat pump-solar system and direct floor radiant heating to ensure the efficient and stable operation of the heating system while making full use of solar energy. Moreover, with the combination of modeling analysis on the annual load via DeST software, the result of actual measurement sees “Trinity” system as the optimal solution not only by means of comparing the heating scheme of the original single air source heat pump unit and the solar energy + air source heat pump unit’s simulation comparison, it was concluded that the initial investment of scheme two was 16,969 yuan and the initial investment of scheme two was 17,352 yuan. The annual operating cost of the second option is 3577.8 yuan, and the annual operating cost of the second option is only about one-half of the annual operating cost of the second option. Based on the calculation of the investment recovery period, the cost savings of the second option after only 0.15 years is net income. Therefore, the “Trinity” scheme is selected as the best scheme.