Heat Pump Capacity Research Articles

Matching analysis between the heating/cooling capacity of PVT heat pumps and the heating/cooling demand of residential buildings across various regions in China

PVT-HP (Photovoltaic-Thermal Heat Pump) is a novel type of energy saving technology. Existing researches on PVT-HP technology focuses only on its operating performance under some specific conditions, ignoring the matching of its energy supply capacity with the energy demand of buildings, which is very important for its engineering design and application. In this paper, the matching relationship between the heating/cooling capacity of the PVT-HP system and the heating/cooling demand of residential buildings in major cities of China has been analyzed. To achieve this goal, a novel prediction model used to calculate the heating/cooling performance of the PVT-HP system has been proposed. And the daily heating guarantee rate and daily cooling guarantee rate have been put forward to evaluate the matching relationship. Based on the evaluation indexes, the applicable matching relationship between the installed capacity of the PVT-HP system and the heating/cooling area of residential buildings has been analyzed. The result of case study shows that for the selected cities of Shenyang, Beijing and Wuhan, the heating/cooling area of residential building for PVT-HP system with installed capacity of 1hp should not exceed 17m2, 31m2 and 25m2, respectively. Further matching analysis of major cities in China shows that the PVT-HP system is more suitable for application in hot summer and cold winter zones of China, in where the suggested heating/cooling area for the PVT-HP system with installed capacity of one horse power is within the range of 30m2 to 37m2.

A study of capacity demands for heat pumps intermittent heating of China’s residences

Heat pump heating is one of the most promising solutions for transitioning residential heating in China’s cold regions, as well as hot summer and cold winter regions from centralized, continuous heating to decentralized, intermittent heating, promoting low-carbon transformation. However, the fundamental issue of the actual capacity requirements for heat pumps in intermittent heating has not yet been addressed. In view of this, this study developed a numerical model that considers the dynamic coupling characteristics between the heat pump and the building environment. Using the model, the worst startup conditions for heat pumps in intermittent heating, actual heat pump capacity demands, and the differences in capacity compared to continuous heating mode for residential buildings in 230 Chinese cities are analyzed. The findings revealed an exponential relationship between intermittent heating capacity demands and time constraints, as well as a linear relationship with heating temperature. Specifically, the impact of the set temperature on capacity demands in cold regions and hot summer and cold winter regions is 22.8 W/(m2·°C) and 32 W/(m2·°C), respectively. These findings provide insights into the planning and design of future intermittent heating renovation projects in China.

Effect of thermoelectric subcooling on COP and energy consumption of a propane heat pump

The building sector has an important impact on the environment, being responsible for 30 % of the total greenhouse gas emissions. Knowing that the energy consumption devoted to HVAC systems accounts for 50 % of the total energy consumption of buildings, it is paramount to develop environmentally friendly technologies able to provide green space heating to the building sector. To that purpose, this manuscript presents a computational study on propane vapor compression heat pumps which include thermoelectric subcooling to boost their operation. The combination of these technologies has been proven in the past to be very beneficial for refrigeration systems and this study concludes for the first time that propane heat pumps can highly benefit from thermoelectric subcooling. The widely conducted research includes the following parameters: ambient temperatures from −20 to 15 °C, voltage supplies to the thermoelectric modules from 0.5 to 10 VDC, number of thermoelectric subcooling blocks from 1 to 8 and two water inlet temperatures, 40 and 55 °C to study their influence on heating capacity, compressor and thermoelectric power consumptions, subcooling degree, propane mass flow, compressor capacity, COP, energy consumption and SCOP of the combined heat pump. The obtained results are very conclusive, COP enhancements up to 12.29 % are achieved when a thermoelectric subcooler with 16 modules is included in a propane heat pump already provided with an internal heat exchanger for an ambient temperature of −20 °C and a water inlet temperature of 55 °C. Additionally, improvements in Seasonal COP up to 9.98 % are achieved if the above-mentioned technologies integration between a vapor compression heat pump and a thermoelectric subcooler substitutes a conventional propane heat pump with an internal heat exchanger for space heating a single-story two-family house.

A simplified model for correcting the heating capacity of air source heat pumps in high-altitude plateau areas

The performance of air source heat pumps (ASHPs) is typically evaluated in plain areas, leaving limited insight into their performance in high-altitude plateau areas. To address this, a simplified fitting model is proposed to correct ASHP heating capacity in plateau areas. The structure of the fitting model is deduced based on physical principles. Then we regress the model on simulation data calculated by a complex model from previous study. Finally, the fitting model is validated by both simulation data and field test data from four ASHP projects comprehensively. Utilizing the fitting model, the influence of outdoor temperature and altitudes on the correction factor are fully discussed. Results show that the proposed fitting model is easy to facilitate in practical engineering. Only three sets of experiments are required to determine the constant coefficients of the fitting model, thus eliminating the necessity of establishing a complex calculation model for ASHP systems. The heating capacity and correction factors of ASHPs in the plateau areas can be accurately calculated by the proposed fitting model. The maximum error is around 0.5 % compared with the model in a previous study. When compared with the monitored data from real projects, approximately 80 %∼85 % of the points fall within the ±20 % error line. For every 1000 m increase in altitude, the heating capacity decreases by approximately 3.9 %–5.1 %. The proposed fitting model offers simplicity and convenience for designing ASHP heating systems in high-altitude plateau areas.

Covering District Heating Demand with Waste Heat from Data Centres

Currently, the huge potential of data centre waste heat for the decarbonization of the heating sector is often ignored. Here, a feasibility study is presented for covering the heat demand of two districts of Frankfurt (Germany) mainly by data centre waste heat. Contrary to many existing projects, the waste heat shall supply existing buildings, the total heat demand is very high (144 GWh/a) and it should be covered almost exclusively by waste heat usage. In this study, the potential and demand are estimated, a heating supply concept is presented and evaluated regarding costs, heat pump capacity, and storage size. As a result, the utilisation of data centre waste heat is not only possible, but it’s the most promising way for decarbonizing the heating sector in this area. With high-capacity heat pumps (37 MWth), gas boilers (20 MWth) and a storage for daily peaks, 97.5 % of the heat demand can be covered by waste heat usage. It is economically favourable compared to decentralized heat pumps for all types of buildings and with the proposed concept, CO2-emissions in the network area are reduced by 78 % on average. Laws to oblige the waste heat usage of data centres are recommended.

Optimization of solar-air source heat pump hybrid heating system

Abstract In order to construct a versatile, complementary, low-carbon, clean, and efficient heating system, this study explores the potential of a solar-air source heat pump (SAHP) hybrid heating system. A simulation model is established in TRNSYS, and the particle swarm algorithm (PSO) and genetic algorithm (GA) from GENOPT and MATLAB are employed. With the aim of minimizing the annual cost, optimization is conducted on the key parameters and operational strategies of the system. Comparative analysis between the two algorithms reveals that PSO slightly outperforms in cost reduction, while GA exhibits a slight advantage in enhancing system performance. Significantly improved energy savings are achieved by appropriately reducing the rated heating capacity of the air source heat pump and increasing the volume of the water tank.

Heating performance of a vapor compression heat pump cascaded with a thermoelectric heat pump

Air source heat pumps (ASHPs) are widely utilized for heating and cooling in residential buildings; however, their effectiveness in heating mode is compromised during extreme weather conditions. Extensive research endeavors have been undertaken to develop, test, and assess a cost-effective vapor compression ASHP suitable for cold climate regions. This study takes an innovative approach by developing component and system prototypes for a cold climate heat pump. This design combines a thermoelectric heat pump (TEHP) with a traditional residential split ASHP to augment heating capacity in low ambient temperature conditions. The component and system prototypes underwent experimental testing in the psychrometric chambers. The experimental findings revealed a 13.6 % to 13.7 % increase in total heat pump heating capacity, accompanied by a 3.1 % to 5.0 % decrease in the coefficient of performance (COP) at ambient temperatures of −15 °C and −19 °C, when compared to the original ASHP. The COP of the TEHP is relatively constant, ranging from 1.63 to 1.76. This prototype offers a solution to address the challenges associated with reduced heat pump capacity at low ambient temperatures. The experimental results indicated that the lower the ambient temperature, thermoelectric heat pump auxiliary heating can increase the heating efficiency 60 % in comparison to electric resistance.

Dynamic characteristics of refrigerant evaporation temperature in air-water heat source heat pump

In order to improve the problem of reduced heat capacity and unstable heating ability of air source heat pump (ASHP) in the heating mode during the cold season, a heat pump evaporator using air and surface water as a heat source is designed in this paper. A heat transfer unit's calculation model of an air–water heat source evaporator is established. Experimental tests and simulation studies are conducted on the refrigerant evaporation temperature and heat pump heating performance. On this basis, a refrigerant evaporation temperature prediction model is constructed using a multiple linear regression (MLR) model. The trend of refrigerant evaporation temperature under air–water heat source is analyzed by taking the winter meteorological parameters in Xiangtan City as an example. The results show that the air–water heat source heat pump (A-WSHP) has a higher refrigerant evaporation temperature and a smaller temperature fluctuation range than the ASHP. The average values of refrigerant evaporation temperatures under the experimental conditions were 5.3 °C and 4.6 °C, respectively. The temperature fluctuation ranges were 3.8 °C-6.7 °C and 2.8 °C-7.0 °C, respectively. The A-WSHP has higher heating capacity and heating stability. Air temperature, air velocity, water spray temperature and water spray flow rate are all important parameters that affect the refrigerant evaporation temperature of a heat pump. Evaporation temperature changes are positively correlated with these factors. In the refrigerant evaporation temperature prediction model, the air temperature change has the most significant effect on the evaporation temperature, followed by spray water temperature, air velocity, and spray flow rate, whose influence weights are 82.5 %, 38.8 %, 29.4 %, and 25.3 %, respectively. Selecting different temperatures of spray water and adjusting the evaporator's inlet spray flow rate can improve the refrigerant evaporation temperature and heat pump heating stability.

Influence of Geology, Hydrogeology, and Climate on Ground Source Heat Pump Distribution in Slovenia and Selected European Countries

Shallow geothermal energy (SGE) is a renewable energy that could contribute to the decarbonatization of the heating and cooling sector. SGE is predominantly harnessed through ground source heat pump (GSHP) systems. The choice of which type of GSHP system depends on various factors. Understanding these factors is crucial for optimizing the efficiency of GSHP systems and fostering their implementation. In this paper, we have analysed the spatial distribution of GSHPs in Slovenia. We identified 1073 groundwater and 1122 ground-coupled heat pump systems with a total heat pump capacity of almost 30 MW. We quantitatively assessed the influence of geological, hydrogeological, and climate conditions on their spatial distribution. Using the χ2 test and information value method, we identified hydrogeological conditions as the most influential factor for the GSHP systems’ spatial distribution. We also performed the spatial analysis of geological and hydrogeological data in 22 European countries, including Slovenia. We collected the reported numbers of installed GSHP units in 2020 and were able to distinguish the shares of groundwater and ground-coupled heat pump systems for 12 of these countries. The analysis showed that ground-coupled heat pumps predominate in most countries, even if the natural conditions are favourable for groundwater heat pumps.

Research on the effect of the refrigerant charge in a variable capacity heat pump

Current energy efficiency regulations have led to the development of heat pumps equipped with variable speed compressors (VSC) and electronic expansion valves (EEV). To reduce the amount of refrigerant charge, heat pump manufacturers are developing units without a liquid receiver. As a result, the amount of refrigerant charge has a direct impact on the unit performance and needs to be optimized. Previous studies have shown the existence of an optimum refrigerant charge that maximizes the COP at a given operating condition. However, with VSC it is not clear if the optimum charge at a given compressor speed is the adequate one at other speed values. This paper analyzes the effects of the refrigerant charge amount on the performance of a brine-to-water heat pump equipped with a VSC and an EEV. For a given compressor speed, the variation of the COP with the charge showed similar trends and an optimum refrigerant charge could be identified. The charge for the maximum COP changes slightly with the compressor speed. The seasonal coefficient of performance (SCOP) is proposed as a better metric for evaluating the optimum charge. Results show that the SCOP is quite stable with the refrigerant charge.

Assessing the Flexibility Potential of Industrial Heat–Electricity Sector Coupling through High-Temperature Heat Pumps: The Case Study of Belgium

Thermal processes represent a significant fraction of industrial energy consumptions, and they rely mainly on fossil fuels. Thanks to technological innovation, highly efficient devices such as high-temperature heat pumps are becoming a promising solution for the electrification of industrial heat. These technologies allow for recovering waste heat sources and upgrading them at temperatures up to 200 °C. Moreover, the coupling of these devices with thermal storage units can unlock the flexibility potential deriving from the industrial sector electrification by means of Demand-Side Management strategies. The aim of this paper is to quantify the impact on the energy system due to the integration of industrial high-temperature heat pumps and thermal storage units by means of a detailed demand–supply model. To do that, the industrial heat demand is investigated through a set of thermal process archetypes. High-temperature heat pumps and thermal storage units for industrial use are included in the open-source unit commitment and optimal dispatch model Dispa-SET used for the representation of the energy system. The case study analyzed is Belgium, and the analysis is performed for different renewable penetration scenarios in 2040 and 2050. The results demonstrate the importance of a proper sizing of the heat pump and thermal storage capacity. Furthermore, it is obtained that the electrification of the thermal demand of industrial processes improves the environmental impact (84% reduction in CO2 emissions), but the positive effect of the energy flexibility provided by the heat pumps is appreciated only in the presence of a very high penetration of renewable energy sources.

EVALUATION OF THE ENERGY EFFICIENCY OF HEAT SUPPLY SYSTEMS OF A RESIDENTIAL BUILDING WITH HEAT PUMPS BASED ON COMPUTER SIMULATION

This article presents an analysis of the energy efficiency of the heating system of a single-family residential building with the integration of a heat pump (HP) using climate data for Kyiv city. Specialized software complexes for calculation (GeoT*SOL), dynamic energy modeling (DesignBuilder/EnergyPlus), and techno-economic justification of HP systems implementation (RETScreen) were used for this purpose. The analysis was conducted for two types of HPs: air-to-water (air-based) and ground-source (ground-based), considering various temperature regimes of the indoor heating system. Based on the modeling results, it was determined that for an air-to-water HP with a nominal capacity of 7 kW, the average seasonal efficiency rating could be approximately 3.6 for the HP itself and 2.7 for the overall system. For a ground-source HP with a nominal capacity of 6 kW, the average seasonal efficiency rating is 4.7 for the HP itself and 3.75 for the overall system. The total electricity consumption varies within the range of 4800–5700 kWh for air-based HP and 3200–4300 kWh for ground-based HP. Depending on the HP capacity, the share of heating energy coverage ranges from 85-98% for ground-based HP and 79-98% for air-based HP. The simple payback period of the HP-based heating system compared to electric convectors is 15.2–17.0 years.

Whether the off-design characteristics of equipment should be considered in integrated energy system optimization design models – A case study

The operational performance of integrated energy systems (IESs) varies with their configuration. The equipment model directly influences the capacity configuration of IESs. The conventional static model assumes that equipment efficiency is constant, ignoring its off-design characteristics. For this reason, this paper establishes a dynamic model considering the off-design characteristics of the equipment. Based on the dynamic and static models, bi-level optimization models with the minimum total cost as the optimization objective are established to optimize the configuration of IESs, and the optimization results are System 1 and System 2, respectively. Then, the operational performance of the two systems under the dynamic optimal scheduling model is compared. The results demonstrate that the capacity of the absorption chiller (ABC), combined heating and power (CHP) unit in System 1 are larger than in System 2 owing to the difference in equipment models, whereas the capacity of ground source heat pumps (GSHPs) shows the opposite trend. The larger capacity of the GSHP increases the grid power consumption of System 2 but also reduces its operating efficiency. The greater operation energy consumption and grid power consumption make the operating cost, carbon tax, and total cost of System 2 under the design condition higher than that of System 1, with an increased rate of 1.38%, 3.47%, and 1.14%, respectively. As with the design condition, the carbon tax, operating cost, and total cost of System 2 are higher than those of System 1 under both summer and winter operating conditions, particularly under summer operating conditions, where the carbon tax, operating cost, and total cost increase by 2.27%, 1.24%, and 0.88% respectively. Even if the energy price changes, the carbon tax, operating cost and total cost of System 2 in a typical year are still greater than those of System 1. Therefore, it is necessary to consider the off-design characteristics of equipment in the bi-level optimization design model.

Modeling of thermal processes in vertical heat exchangers of ground-source heat pump

The basic directions for perfection heat supply systems are the tendency of transition to the low-temperature heating systems based at application heat pump installations. We consider heat supply systems with ground-source heat pump. The paper considers modeling the efficiency of ground-source heat pumps with the account of Ukrainian climate conditions. The paper presents the energy performance criteria which show the way to rational implementation of ground-source heat pumps for heating. A computational model based at non-stationary heat exchange processes in elements of ground-source heat pumps is developed. Generalization and analysis of theoretical and experimental dates allow establishing nature of dependence thermophysical properties on temperature insoil around ground heat exchangers during long term operation of the system. Numerical simulation of thermal processes in vertical ground pipes for ground-source heat pump working with low-temperature heating systems has been worked out. The results of numerical modeling demonstrated perfection and technical adaption of ground-source heat pump for low-temperature heating systems with rational using ground energy potential. The novelty of our method is complex usage theoretical and experimental results which enable to prevent freezing in the ground during long term exploitation This provides insights at effects of different resource mixes and may serve as a new approach to analysis of future heat pump systems using ground source energy development.The proposed method contributes to the field of creation and implementation the sustainable heating technologies using renewable energy sources. The ground heat exchange pipes quantities that are necessary for effective operation heat pump installation, capacity and coefficient of performance with the account of climate conditions are calculated.

Thermodynamic and economic seasonal analysis of a transcritical CO2 supermarket with HVAC supply through ice thermal energy storage (ITES)

A real case of a supermarket where a CO2 refrigerating plant also supplies heating, air conditioning and hot water is considered. Ice thermal energy storage (ITES) is used both as latent storage in summer and as sensible thermal energy storage (TES) in winter to partially cover the space cooling/heating load of the supermarket. In particular, it allows to reduce peaks in the electrical power use, when the refrigeration and HVAC systems are running at full power together with ovens and heaters for meals. A thermodynamic analysis, including a detailed theoretical model of the formation and melting of ice on the coils, is carried out to predict the behaviour of ITES during the charging and the discharging phases. A daily energy analysis for both a winter and a summer typical day, and an annual analysis are carried out for the whole system. In summer, two cases are evaluated, i.e. supplying the whole AC demand in the morning or partially covering the AC demand to reduce the design capacity of the reversible heat pump. In all cases, the use of ITES aimed at shaving electrical peaks leads to a higher electrical energy use, also on an annual basis. However, the cost analysis reveals significant benefits, including a reduction in the required capacity of the reversible heat pump, better exploitation of tariffs and the avoidance of installing an electrical transformer in a dedicated room. This results in savings €58,699 over 10 years €47,888 over 15 years, making the choice of ITES more economically advantageous within the typical lifetime of these systems.

Multi-objective optimization of micro-gas turbine coupled with LCPV/T combined cooling, heating and power (CCHP) system based on following electric load strategy

A distributed energy system integrated with solar and natural gas can achieve cascade energy utilization, high efficiency and energy-saving, and significantly reduce carbon emissions, which is receiving increasing attention. Therefore, this paper establishes an optimization model for primary energy consumption saving rate (PECSR), annual total cost saving rate (ATCSR), carbon dioxide emission reduction rate (CDERR) and exergy efficiency of micro-gas turbine coupled with low-concentrating photovoltaic/thermal (LCPV/T) CCHP system, and analyzes the influence of the parameters, such as solar irradiation, LCPV/T inlet temperature, LCPV/T inlet flow, LCPV/T area, low-temperature water source heat pump capacity, high-temperature water source heat pump capacity, the heat transfer efficiency of waste heat recovery boiler (WHRB) and gas boiler capacity, on the objective functions. The analysis results indicate that when the heat exchange efficiency of WHRB reaches 0.71, the CCHP system is most economical. Based on this, the Strength Pareto Evolutionary Algorithm-II (SPEA-II) optimization algorithm and decision-making method combining Technique for order preference by similarity to an ideal solution (TOPSIS) and weight entropy method are employed to solve the model comprehensively, and acquire the optimum solution. After multi-objective optimization and selection, the system exergy efficiency remains around 25 %. Compared with the separation production system, the PECSR and CDERR of the CCHP system are improved by more than 24 % and 41 %, respectively.

Adaptive model predictive control of a heat pump-assisted solar water heating system

Full electrification of building energy systems makes that the electricity-driven heat pump and solar heat become the most promising heating sources for hot water production in the future. The heat pump assisted solar water heater will be a good solution to jointly use these two heating sources. The system has large potential in demand response because of large capacity thermal storage tank which requires reasonable optimal control. In this context, this paper presents an adaptive model predictive control (AMPC) to achieve demand response with adaptive boundary and linear time-varying heat pump efficiency. Using adaptive parameters, the controller improves the adaptability and achieves optimal control under various disturbance conditions. The results demonstrated the AMPC realize 20% cost saving and 12% energy saving compared with PID, which are 7% reduction in costs and a 3% decrease in energy consumption compared to conventional MPC methods. Furthermore, a detailed analysis research was conducted on the controller parameters and disturbances, considering equipment parameters, electricity pricing models, weather conditions, and load types. Notably, the MPC exhibited even greater performance improvements in scenarios involving real-time pricing, concentrated loads, and low heat pump capacity.

Parametric analysis and multi-objective optimization of a heat pump dryer based on working conditions and using different refrigerants

Considering Heat pump dryers are extensively used in the food industry, evaluating and optimizing their performance can be beneficial. Therefore, a comprehensive model is presented in this study using for waste food with considerations of energy, exergy, and exergoeconomy. Several influential parameters, such as evaporator and condenser temperatures, heat pump capacity, dry and wet-basis moisture content, along with the product mass and refrigerant types, are considered in the investigation. Five environmentally-friendly refrigerants of, R134a, R1234yf, R1234ze, R717, and R152a, are used as the working fluid of the heat pump. The parametric study shows that evaporator and condenser temperatures and heat pump capacity have significant effects on the heat pump COP, exergy efficiency, drying time, and cost of dried product. Hence, assuming these four objective functions, a multi-objective optimization model based on the TOPSIS method is presented. According to this, the optimal point of the system is found at the evaporator and condenser temperatures of 10.32 °C and 69.68 °C, respectively. Results of the refrigerant analysis demonstrate that although R717 has the best energetic performance, using R1234yf results in the shortest drying time and lowest cost of dried product.

Experimental and energy saving potential analysis of GSHP and ASAC systems using normalized sensitivity technique in cooling mode operation

ABSTRACT The current investigation examines the experimental and energy-conservation analyses of 17.5 kW cooling capacity of a ground-source heat pump (GSHP) system and an air-source air-conditioning system (ASAC) of the same cooling capacity. Using experimental data and a sensitivity technique, the thermal efficiency of both the systems were evaluated. During the experiments conducted for cooling period in June 2022, the data for six-day operation were collected and the coefficient of performance of both the systems were evaluated. Notably, the GSHP system exhibited an average cooling capacity of 10 to 15 kW, whereas the ASAC maintained a range of 9 and 13 kW. The coefficient of performance (COP) for the GSHP system was obtained as 3.8, while the ASAC system COP was 2.9. The results indicate that the use of GSHP system results in an energy-saving of 10–40% in comparison to the ASAC system. Moreover, the present study included uncertainty and propagation analyses, along with sensitivity evaluations, with the objective of identifying the most influencing parameter on the derived parameters. Sensitivity analysis indicates outlet temperature of air from the evaporator is the most influencing parameter for the performance of both the systems.

Research on multi-objective optimization of control strategies and equipment parameters for a combined heating system of geothermal and solar energy in cold and arid regions based on TRNSYS

Focusing on the multiple objectives of maximum solar heating capacity, maximum COP of heat pump and minimum soil heating capacity, a model of one typical building and two heating strategies was established in the TRNSYS. Non-dominated Sorting Genetic Algorithm (NSGA) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) based on entropy weight are used to optimize operation parameters. Optimized control strategies and equipment parameters of a combined geothermal and solar system in cold and arid regions were taken as the research objects. The final optimized strategy and the original strategy of the single ground source heat pump heating system were compared. Research results show that the optimized control strategy of the geothermal solar heating system transforms solar hot water from the storage tank to heating terminals in the heating season and transforms solar hot water to the ground heat exchanger in the non-heating season. Compared to GSHP, the optimizing strategy saves 16.8 MWh annually, and the energy saving rate is 20.59%. Soil temperature drop increases from 2.74 °C to 0 °C. The annual electricity saving cost intensity is about 4 yuan/m2, and the CO2 emission reduction intensity is 4.3 kg CO2/m2. This study provides a solution for soil temperature reduction in one year and low-cost operation in cold and arid regions during ground source heat pump applications.