# Energy-Saving Benefits of Air-Source Heat Pump-Assisted Solar Water Heating Systems in Large Stadiums

Authors: Xinghua Yang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

With the rising trend of national sports, sports events are more and more favored by people and many large stadiums have emerged as the times require. Due to the particularity of sports, large stadiums are often equipped with independent hot water preparation systems for the convenience of sports enthusiasts. However, the traditional hot water preparation process not only consumes a lot of energy but also brings a lot of potential environmental pollution, which seriously violates the original intention of hot water preparation. Solar energy is clean energy that can be recycled and has a promising market prospect, but its heat production is greatly affected by the weather. Based on this, the paper has proposed a new solar water heating system (SWHS) that relies on the assistance of an air source heat pump (ASHP), aiming to solve the problem of hot water preparation in large sports stadiums from both economic and stability aspects. Taking the Xi’an Olympic Sports Center as an example, the article established the ASHP-aided SWHS and analyzed the differences between the system and other hot water preparation methods in terms of energy efficiency and benefits in terms of economy and environment. The results of the study showed that the energy replacement factor of the ASHP-aided SWHS reached 0.91, which was equivalent to replacing 91% of the annual conventional energy use in one year with this system, with significant energy-saving benefits. This demonstrates the high applicability and energy efficiency of the ASHP-aided SWHS in large sports stadiums.


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## Body

## 1. Introduction

With the development of society, the wave of sports and fitness has opened the door of large stadiums, forcing the stadiums to continuously upgrade their internal facilities and increase the experience of residents. The hot water system is one of the necessary facilities for large stadiums, which embodies the level of the stadiums. The heat sources of traditional hot water systems mainly rely on boilers, electricity, and gas. This preparation method has major drawbacks, in which the use of boilers and gas to prepare hot water not only consumes a lot of energy in vain but also brings serious environmental problems. Although the use of electric energy to prepare hot water will not cause environmental pollution, it will increase a lot of economic costs. Based on this, this paper uses the air source heat pump as the auxiliary and solar energy as the main heat source of the hot water system and proposes a new solar water heating system relying on the air source heat pump. On the one hand, the energy used in the system is mainly renewable solar energy, so its running costs are almost zero. On the other hand, in times of bad weather, the use of the air source heat pump system will not bring about a substantial increase in cost, but will further increase the stability of the hot water supply system.The combination of air source heat pumps and solar energy provides a new opportunity for hot water preparation. Zeng and Sun [1] built a dynamic simulation model and retuned and optimized the key parameters of the network. To test the practical effects of the optimization, they used the example of a hot water system in a city student residence [1]. Yuan and Sun [2] used the cluster analysis method to analyze the operating mode of an SWHS assisted by an air source heat pump. Using this method, they analyzed the meteorological data of Xichang city and proposed a new control strategy [2]. et al. [3] analyzed the operational characteristics of the ASHP-assisted SWHS. They also pointed out that the system has a promising market with a high return on investment compared to other heating systems [3]. Wang et al. [4] pointed out that the ASHP-assisted SWHS can work just as well in solar-shortage areas. To verify their view, they improved and upgraded the original system [4]. The abovementioned scholars further demonstrated the effectiveness of the combination of air source heat pump and solar energy, but they did not analyze the energy-saving benefits of the system.Large stadiums are the cornerstone of the development of sports, and more and more scholars are paying attention to them. Hu et al. [5] pointed out that the development of stadiums is closely related to stadium safety and interior comfort. In order to ensure safety and comfort, they proposed a new management strategy and used a two-parameter estimation method to quantify the relevant factors [5]. Yu [6] pointed out that large stadiums are the basis for sports. In order to make the development of stadiums keep pace with the times, he analyzed the possibility of commercialization of stadiums from the perspective of economics [6]. Schmidt et al. [7] pointed out that the environmental impact of large and medium-sized buildings is enormous. To this end, they used a different approach to analyzing the environment of the stadium [7]. Lyubimova et al. [8] discussed the possibility of increasing the efficiency of the use of sports stadiums. On the basis of the comprehensive analysis, they also considered the extreme utilization situation of the stadium and the situation under the effect of the highest utilization rate [8]. The abovementioned experts and scholars have analyzed the development of large-scale stadiums and put forward many targeted suggestions, but they have not optimized the interior of the stadiums for the energy-saving concept.The article analyses the application of SWHS in a large sports stadium with the aid of an ASHP and provides an in-depth portrayal of the energy-saving benefits of the system. During the research process, the article compares the energy-saving benefits of different preparation methods. The comparison results showed that different hot water preparation schemes have different calorific values and energy consumption. Among them, it can be seen that the calorific value of natural gas has reached 39.2kWh, ranking first.


## 2. Preparation Methods of Hot Water in Large Stadiums

Large-scale stadiums are mainly composed of stadiums and gymnasiums [9]. Large stadiums are one of sports stadiums that undertake large regional competitions. In sports stadiums, because most sports have a certain load, people’s bodies tend to sweat and heat up after exercising, which can easily lead to a cold or another physical discomfort in sports groups. Under this circumstance, the hot water provided by the sports stadiums solves the urgent need for the majority of sports groups [10]. Nowadays, large stadiums are basically equipped with hot water supply systems, and sports enthusiasts can choose whether they need to take a bath after exercising. Not only large stadiums, but now many regional small and medium-sized stadiums have also added hot water supply systems to provide convenience for sports groups. In the process of hot water preparation, the preparation method of large stadiums is often different from that of other venues. The basic flow of hot water supply in the stadium is shown in Figure 1.Figure 1
Basic process of hot water supply in stadiums.As can be seen throughout the heating process, the main source of hot water supply to the stadium is from the indoor storage tanks [11]. During the design of the tanks, sensors are embedded into each tank. Once the water level is lower than the water level line, the water inlet pipe will receive instructions to replenish the water body in time for the water tank. At the same time, once the water temperature is lower than the temperature set by the controller, the controller will deploy the thermal device to work [12]. Then, if someones need to use hot water in the stadium, they only need to turn on the hot water switch, and the water will be injected into the water facilities of the stadium through a dedicated supply pipe under the action of pressure. In the whole process, the timeliness and stability of hot water supply are the basic criteria to measure the hot water supply system.


### 2.1. Hot Water Preparation Methods

In daily life, hot water does not exist naturally. It is obtained through a series of preparation methods. Different from other preparation methods, hot water preparation does not obtain new substances or components, but the temperature of the object has changed significantly [13]. In real life, there are many ways to obtain hot water. Generally speaking, hot water preparation methods are mainly divided into the following three types:


#### 2.1.1. Combustion Preparation

Combustion is a relatively violent method of material transformation, which can rapidly increase the temperature of an object. In the process of hot water preparation, the combustion preparation method mainly ignites combustible substances such as coal and then heats the water when the object releases a large amount of temperature [14]. This preparation method is suitable for use in places with sufficient fuel, so it has been popularized and promoted in domestic use. However, due to site and environment limitations, the preparation method cannot be used in some confined spaces.


#### 2.1.2. Electricity Preparation

With the discovery of new energy sources, more convenient methods of preparing hot water are gradually being discovered. Electricity has been favored since its inception, so it also appears in the production of hot water. Nowadays, electric water heaters, electric kettles, etc. emerge in an endless stream, and the hot water preparation method based on electric energy has basically been popularized [15]. At the same time, due to the limitation of the power source itself, the power preparation method is often only suitable for small-scale hot water preparation.


#### 2.1.3. Energy Conversion Preparation

Electricity preparation is convenient and simple, but it cannot realize large-scale hot water preparation [16]. In the large-scale hot water preparation process, a heat pump is a common preparation method. During the preparation process, the compressor inside the electric pump can convert electrical energy into heat energy or power potential energy to realize hot water preparation. Referring to this energy conversion method, it is gradually discovered that solar energy can also be used to realize thermal production. In the process of this change, equipment such as solar water heaters gradually emerged, but the solar hot water preparation method is highly susceptible to weather, which exacerbates the instability of the hot water supply.Although the abovementioned several hot water preparation methods are not the same, there are certain similarities in principle [17]. Based on the basic principle of hot water preparation, the article combines the electric power preparation method with the solar power preparation method in energy conversion preparation and proposes the SWHS with the aid of ASHP.


### 2.2. Solar Water Heating Systems Relying on Air Source Heat Pumps

In order to realize the efficient use of resources, the paper adopts a parallel design when designing a new solar water heating system that relies on an air source heat pump. During the design process, the heating unit is connected in parallel with the ASHP unit [18]. At the same time, in order to ensure the 24-hour convenience of large stadiums, the article also especially sets up two water collection tanks. One of the tanks is connected to the solar collector and the other tank forms a series relationship with ASHP. The schematic diagram of the ASHP-assisted SWHS is shown in Figure 2.Figure 2
Schematic diagram of ASHP-assisted SWHS.In this hot water supply system, the water tank will heat the tap water stored inside according to a designed program [19]. Before the second heat, the water tank will be filled with water in advance. Then the system cycles like this. During the cycle, the system will preferentially use solar collectors for heating.In the specific design process, the performance of the ASHP-assisted SWHS is mainly determined by the accuracy of the control unit [20]. During this process, if the ASHP is frequently started when the solar energy is abundant, then this will not only fail to save energy but may also directly cause resource waste. Precise control of different control units of the system is therefore an important measure to achieve resource savings. Among them, the control flow of the solar water heating system assisted by the air source heat pump is shown in Figure 3.Figure 3
Control flow of the solar water heating system assisted with an air source heat pump.In the abovementioned control process, the controller takes an essential part in the regulation. In the solar system control, once the solar collector starts to work, the controller will issue a stop instruction to the air source heat pump, and then the air source heat pump is in the dormant stage [21]. During the solar heating phase, the heating converter has a built-in temperature sensor and a water temperature detector which will start the heating converter as soon as the water temperature inside the tank is found to be below the minimum temperature set by the controller. In this process, the solar collector has both a heat collection function and a control function.In the temperature control process, the temperature is mainly regulated by the temperature control unit. Once the water temperature in the water tank is lower than this temperature, the water tank controlled by the solar thermal collector will immediately fill the water tank with water. In this constant temperature water tank, the controller sets up two water level lines in advance, one of which is the lowest water level line and the other is the highest water level line [22]. If the water level in the tank falls below the minimum water line, the collector tank will fill its level with water. The highest water level line exists to prevent the water level control unit from failing. Once the water level exceeds the highest water level line, the alarm connected to the water level line will sound an alarm, and the controller will immediately disconnect the fuse connected between the water tanks for emergency power off. Through the control and adjustment of many of the abovementioned links, the air source heat pump-assisted solar water heating system can dynamically control the preparation process of hot water, and it also has better heating performance.


### 2.3. Calculation of Energy-Saving Benefits of Hot Water Preparation

The article describes the energy conservation advantages of ASHP-assisted SWHS in the preparation process on a theoretical level, but there is no data to support this claim. In order to fully demonstrate the advantages of the hot water system proposed in the article in terms of energy saving, the article aims to analyze the energy conservation benefits from a numerical and theoretical perspective.


#### 2.3.1. Energy Substitution Amount

Energy is the direct source of heat and power and is critical to the operation of all systems. In the process of hot water preparation, energy consumption is unavoidable. Among them, the calculation process of energy substitution amount is as follows:(1)Ctdl=CatlCmtl∗Pstd,(2)Pstd=Ri+Rjq·yce,(3)Qk=12SbLnx.Among them,Ctdl represents the actual energy replacement amount of the system. Pstd represents the standard coal amount consumed in the process of preparing hot water. Meanwhile, this value can also be obtained jointly by solar energy supply Ri and heat pump function Rj.


#### 2.3.2. Energy Consumption Ratio

Energy consumption ratio is the proportion of energy consumption, that is, the energy consumed per unit of output value in the process of hot water preparation. Through the calculation of energy substitution, the article unifies the form and type of energy expression. Among them, the calculation formulas of the energy consumption ratio in the hot water preparation process are as follows:(4)D=JaCtdl·Lmpx,(5)Lm=Px·Qx+Jj−Ctdl2.In formulas (4) and (5), D represents the energy consumption ratio of the hot water preparation process. Ja and Lm represent the type of energy and the actual consumption of energy, respectively.


#### 2.3.3. Environmental Benefits

In the field of energy analysis, there are many indicators related to environmental protection, which is not conducive to the classification research of the article. Therefore, this paper selects carbon dioxide emissions, sulfur dioxide emissions, and dust emissions as the calculation indicators. The calculation process is as follows:(6)HCO2=ZPstd,(7)HSO2=aPstd,(8)HDST=gPstd.Among them,Z, a and g represent the impact factor, respectively. In the abovementioned description process, the emission of different gases or suspended solids is closely related to the actual atmospheric conditions, so different factor changes can directly affect the emission value.


#### 2.3.4. Economic Benefits

Economic benefits are often the concentrated expression of measuring the value of the system. At the same time, it can also reflect the energy-saving benefits of the system on the side. The formulas for calculating the economic benefits of the system are as follows:(9)Zh=Ma+i1+b2h+12−1Pstd,(10)W=PI2−kFij.In formulas (9) and (10), Zh represents the total cost of the system. Ma represents the actual investment amount. With the increase of the number of years k, the maintenance cost W of the system is also increasing. The direct relationship between the two is described as follows:(11)r=Zh·T2WxPstd−WaWx.In formula (11), r describes the algebraic relationship between the two. This fully shows that with the increase of years, the maintenance cost and total cost of the system will continue to increase. There is a half-normal distribution between the total cost and the maintenance cost. Based on this, the paper preliminarily describes the energy-saving benefits of the hot water preparation system from four levels and analyzes the energy-saving benefits of SWHS relying on air source heat pumps from a mathematical point of view. Next, the article will focus on this as the basis for the preliminary exploration of the energy-saving benefits of the hot water preparation system.


## 2.1. Hot Water Preparation Methods

In daily life, hot water does not exist naturally. It is obtained through a series of preparation methods. Different from other preparation methods, hot water preparation does not obtain new substances or components, but the temperature of the object has changed significantly [13]. In real life, there are many ways to obtain hot water. Generally speaking, hot water preparation methods are mainly divided into the following three types:


### 2.1.1. Combustion Preparation

Combustion is a relatively violent method of material transformation, which can rapidly increase the temperature of an object. In the process of hot water preparation, the combustion preparation method mainly ignites combustible substances such as coal and then heats the water when the object releases a large amount of temperature [14]. This preparation method is suitable for use in places with sufficient fuel, so it has been popularized and promoted in domestic use. However, due to site and environment limitations, the preparation method cannot be used in some confined spaces.


### 2.1.2. Electricity Preparation

With the discovery of new energy sources, more convenient methods of preparing hot water are gradually being discovered. Electricity has been favored since its inception, so it also appears in the production of hot water. Nowadays, electric water heaters, electric kettles, etc. emerge in an endless stream, and the hot water preparation method based on electric energy has basically been popularized [15]. At the same time, due to the limitation of the power source itself, the power preparation method is often only suitable for small-scale hot water preparation.


### 2.1.3. Energy Conversion Preparation

Electricity preparation is convenient and simple, but it cannot realize large-scale hot water preparation [16]. In the large-scale hot water preparation process, a heat pump is a common preparation method. During the preparation process, the compressor inside the electric pump can convert electrical energy into heat energy or power potential energy to realize hot water preparation. Referring to this energy conversion method, it is gradually discovered that solar energy can also be used to realize thermal production. In the process of this change, equipment such as solar water heaters gradually emerged, but the solar hot water preparation method is highly susceptible to weather, which exacerbates the instability of the hot water supply.Although the abovementioned several hot water preparation methods are not the same, there are certain similarities in principle [17]. Based on the basic principle of hot water preparation, the article combines the electric power preparation method with the solar power preparation method in energy conversion preparation and proposes the SWHS with the aid of ASHP.


## 2.1.1. Combustion Preparation

Combustion is a relatively violent method of material transformation, which can rapidly increase the temperature of an object. In the process of hot water preparation, the combustion preparation method mainly ignites combustible substances such as coal and then heats the water when the object releases a large amount of temperature [14]. This preparation method is suitable for use in places with sufficient fuel, so it has been popularized and promoted in domestic use. However, due to site and environment limitations, the preparation method cannot be used in some confined spaces.


## 2.1.2. Electricity Preparation

With the discovery of new energy sources, more convenient methods of preparing hot water are gradually being discovered. Electricity has been favored since its inception, so it also appears in the production of hot water. Nowadays, electric water heaters, electric kettles, etc. emerge in an endless stream, and the hot water preparation method based on electric energy has basically been popularized [15]. At the same time, due to the limitation of the power source itself, the power preparation method is often only suitable for small-scale hot water preparation.


## 2.1.3. Energy Conversion Preparation

Electricity preparation is convenient and simple, but it cannot realize large-scale hot water preparation [16]. In the large-scale hot water preparation process, a heat pump is a common preparation method. During the preparation process, the compressor inside the electric pump can convert electrical energy into heat energy or power potential energy to realize hot water preparation. Referring to this energy conversion method, it is gradually discovered that solar energy can also be used to realize thermal production. In the process of this change, equipment such as solar water heaters gradually emerged, but the solar hot water preparation method is highly susceptible to weather, which exacerbates the instability of the hot water supply.Although the abovementioned several hot water preparation methods are not the same, there are certain similarities in principle [17]. Based on the basic principle of hot water preparation, the article combines the electric power preparation method with the solar power preparation method in energy conversion preparation and proposes the SWHS with the aid of ASHP.


## 2.2. Solar Water Heating Systems Relying on Air Source Heat Pumps

In order to realize the efficient use of resources, the paper adopts a parallel design when designing a new solar water heating system that relies on an air source heat pump. During the design process, the heating unit is connected in parallel with the ASHP unit [18]. At the same time, in order to ensure the 24-hour convenience of large stadiums, the article also especially sets up two water collection tanks. One of the tanks is connected to the solar collector and the other tank forms a series relationship with ASHP. The schematic diagram of the ASHP-assisted SWHS is shown in Figure 2.Figure 2
Schematic diagram of ASHP-assisted SWHS.In this hot water supply system, the water tank will heat the tap water stored inside according to a designed program [19]. Before the second heat, the water tank will be filled with water in advance. Then the system cycles like this. During the cycle, the system will preferentially use solar collectors for heating.In the specific design process, the performance of the ASHP-assisted SWHS is mainly determined by the accuracy of the control unit [20]. During this process, if the ASHP is frequently started when the solar energy is abundant, then this will not only fail to save energy but may also directly cause resource waste. Precise control of different control units of the system is therefore an important measure to achieve resource savings. Among them, the control flow of the solar water heating system assisted by the air source heat pump is shown in Figure 3.Figure 3
Control flow of the solar water heating system assisted with an air source heat pump.In the abovementioned control process, the controller takes an essential part in the regulation. In the solar system control, once the solar collector starts to work, the controller will issue a stop instruction to the air source heat pump, and then the air source heat pump is in the dormant stage [21]. During the solar heating phase, the heating converter has a built-in temperature sensor and a water temperature detector which will start the heating converter as soon as the water temperature inside the tank is found to be below the minimum temperature set by the controller. In this process, the solar collector has both a heat collection function and a control function.In the temperature control process, the temperature is mainly regulated by the temperature control unit. Once the water temperature in the water tank is lower than this temperature, the water tank controlled by the solar thermal collector will immediately fill the water tank with water. In this constant temperature water tank, the controller sets up two water level lines in advance, one of which is the lowest water level line and the other is the highest water level line [22]. If the water level in the tank falls below the minimum water line, the collector tank will fill its level with water. The highest water level line exists to prevent the water level control unit from failing. Once the water level exceeds the highest water level line, the alarm connected to the water level line will sound an alarm, and the controller will immediately disconnect the fuse connected between the water tanks for emergency power off. Through the control and adjustment of many of the abovementioned links, the air source heat pump-assisted solar water heating system can dynamically control the preparation process of hot water, and it also has better heating performance.


## 2.3. Calculation of Energy-Saving Benefits of Hot Water Preparation

The article describes the energy conservation advantages of ASHP-assisted SWHS in the preparation process on a theoretical level, but there is no data to support this claim. In order to fully demonstrate the advantages of the hot water system proposed in the article in terms of energy saving, the article aims to analyze the energy conservation benefits from a numerical and theoretical perspective.


### 2.3.1. Energy Substitution Amount

Energy is the direct source of heat and power and is critical to the operation of all systems. In the process of hot water preparation, energy consumption is unavoidable. Among them, the calculation process of energy substitution amount is as follows:(1)Ctdl=CatlCmtl∗Pstd,(2)Pstd=Ri+Rjq·yce,(3)Qk=12SbLnx.Among them,Ctdl represents the actual energy replacement amount of the system. Pstd represents the standard coal amount consumed in the process of preparing hot water. Meanwhile, this value can also be obtained jointly by solar energy supply Ri and heat pump function Rj.


### 2.3.2. Energy Consumption Ratio

Energy consumption ratio is the proportion of energy consumption, that is, the energy consumed per unit of output value in the process of hot water preparation. Through the calculation of energy substitution, the article unifies the form and type of energy expression. Among them, the calculation formulas of the energy consumption ratio in the hot water preparation process are as follows:(4)D=JaCtdl·Lmpx,(5)Lm=Px·Qx+Jj−Ctdl2.In formulas (4) and (5), D represents the energy consumption ratio of the hot water preparation process. Ja and Lm represent the type of energy and the actual consumption of energy, respectively.


### 2.3.3. Environmental Benefits

In the field of energy analysis, there are many indicators related to environmental protection, which is not conducive to the classification research of the article. Therefore, this paper selects carbon dioxide emissions, sulfur dioxide emissions, and dust emissions as the calculation indicators. The calculation process is as follows:(6)HCO2=ZPstd,(7)HSO2=aPstd,(8)HDST=gPstd.Among them,Z, a and g represent the impact factor, respectively. In the abovementioned description process, the emission of different gases or suspended solids is closely related to the actual atmospheric conditions, so different factor changes can directly affect the emission value.


### 2.3.4. Economic Benefits

Economic benefits are often the concentrated expression of measuring the value of the system. At the same time, it can also reflect the energy-saving benefits of the system on the side. The formulas for calculating the economic benefits of the system are as follows:(9)Zh=Ma+i1+b2h+12−1Pstd,(10)W=PI2−kFij.In formulas (9) and (10), Zh represents the total cost of the system. Ma represents the actual investment amount. With the increase of the number of years k, the maintenance cost W of the system is also increasing. The direct relationship between the two is described as follows:(11)r=Zh·T2WxPstd−WaWx.In formula (11), r describes the algebraic relationship between the two. This fully shows that with the increase of years, the maintenance cost and total cost of the system will continue to increase. There is a half-normal distribution between the total cost and the maintenance cost. Based on this, the paper preliminarily describes the energy-saving benefits of the hot water preparation system from four levels and analyzes the energy-saving benefits of SWHS relying on air source heat pumps from a mathematical point of view. Next, the article will focus on this as the basis for the preliminary exploration of the energy-saving benefits of the hot water preparation system.


## 2.3.1. Energy Substitution Amount

Energy is the direct source of heat and power and is critical to the operation of all systems. In the process of hot water preparation, energy consumption is unavoidable. Among them, the calculation process of energy substitution amount is as follows:(1)Ctdl=CatlCmtl∗Pstd,(2)Pstd=Ri+Rjq·yce,(3)Qk=12SbLnx.Among them,Ctdl represents the actual energy replacement amount of the system. Pstd represents the standard coal amount consumed in the process of preparing hot water. Meanwhile, this value can also be obtained jointly by solar energy supply Ri and heat pump function Rj.


## 2.3.2. Energy Consumption Ratio

Energy consumption ratio is the proportion of energy consumption, that is, the energy consumed per unit of output value in the process of hot water preparation. Through the calculation of energy substitution, the article unifies the form and type of energy expression. Among them, the calculation formulas of the energy consumption ratio in the hot water preparation process are as follows:(4)D=JaCtdl·Lmpx,(5)Lm=Px·Qx+Jj−Ctdl2.In formulas (4) and (5), D represents the energy consumption ratio of the hot water preparation process. Ja and Lm represent the type of energy and the actual consumption of energy, respectively.


## 2.3.3. Environmental Benefits

In the field of energy analysis, there are many indicators related to environmental protection, which is not conducive to the classification research of the article. Therefore, this paper selects carbon dioxide emissions, sulfur dioxide emissions, and dust emissions as the calculation indicators. The calculation process is as follows:(6)HCO2=ZPstd,(7)HSO2=aPstd,(8)HDST=gPstd.Among them,Z, a and g represent the impact factor, respectively. In the abovementioned description process, the emission of different gases or suspended solids is closely related to the actual atmospheric conditions, so different factor changes can directly affect the emission value.


## 2.3.4. Economic Benefits

Economic benefits are often the concentrated expression of measuring the value of the system. At the same time, it can also reflect the energy-saving benefits of the system on the side. The formulas for calculating the economic benefits of the system are as follows:(9)Zh=Ma+i1+b2h+12−1Pstd,(10)W=PI2−kFij.In formulas (9) and (10), Zh represents the total cost of the system. Ma represents the actual investment amount. With the increase of the number of years k, the maintenance cost W of the system is also increasing. The direct relationship between the two is described as follows:(11)r=Zh·T2WxPstd−WaWx.In formula (11), r describes the algebraic relationship between the two. This fully shows that with the increase of years, the maintenance cost and total cost of the system will continue to increase. There is a half-normal distribution between the total cost and the maintenance cost. Based on this, the paper preliminarily describes the energy-saving benefits of the hot water preparation system from four levels and analyzes the energy-saving benefits of SWHS relying on air source heat pumps from a mathematical point of view. Next, the article will focus on this as the basis for the preliminary exploration of the energy-saving benefits of the hot water preparation system.


## 3. Preliminary Exploration of Energy-Saving Benefits of Solar Water Heating Systems Relying on Air Source Heat Pumps

Xi’an Olympic Sports Center is one of the most representative large-scale sports venues in China. It consists of two stadiums and a supporting outdoor sports field, which can accommodate up to 18,000 people. In order to explore the actual energy-saving benefits of the solar water heating system assisted by the air source heat pump, the article took Xi’an Olympic Sports Center as an example. The benefits of different hot water preparation methods based on the stadiums of Xi’an Olympic Sports Center were studied. In the research process, the article comprehensively compared the energy saving of different hot water preparation systems. The calorific value and energy consumption distributions under different preparation methods are shown in Tables1 and 2.Table 1
Calorific value under different hot water preparation methods.
ModeCalorific value (kWh)Theoretical energy consumption (kWh)Type of energyAir source heat pumps4.392.0ElectricityElectricity3.41.6ElectricitySolar + air source heat pump (system in this paper)3.23.21Solar + electricityGas39.21.2Natural gasTable 2
Energy consumption under different preparation schemes.
ModesAnnual consumption (kWh)Unit consumption (kgce/t)Average consumption (kWh)Air source heat pumps11034.983.912.22Electricity20721.352.1512.9System in this paper8954.223.611.80Gas20589.057.2321.7Solar electric assist12384.241.0611.09The experimental data show that different hot water preparation schemes had different calorific values and energy consumption. Among them, it can be seen that the calorific value of natural gas has reached 39.2 kWh, ranking first. At the same time, through data research and analysis, it can be found that there was a certain correlation between the calorific value and energy consumption of the hot water preparation system.In order to further study the benefits of SWHS relying on ASHP, the paper calculated the pollutant emissions brought by different systems according to the method in the formulas. Among them, the pollutant emissions in different systems are shown in Table3.Table 3
Pollutant emissions in different systems.
Contrasting optionsAir source heat pumpsElectricitySystem in this paperGasSolar electric assistCarbon dioxide (t)1.111.020.151.010.57Sulphur dioxide (t)00000Dust (t)0.310.010.030.010.03Others (t)1.330.010.050.10.04Table3 shows that there were obvious differences in the pollution emissions caused by different hot water systems. Among them, in terms of carbon dioxide emissions, the emission of solar water heating systems relying on air source heat pumps was only 0.15 t/year, which was much lower than that of other hot water systems. In terms of sulfur dioxide emissions, the emissions of the five hot water systems were all zero, which meant that none of the five hot water systems would bring about sulfur dioxide emissions. In terms of dust emission, the SWHS emission relying on ASHP was only 0.03 t/year. Although its value was not the lowest, it was within the qualified line.Economic benefits are directly linked to environmental benefits. Therefore, the article conducted experiments and pieces of research on the annual input costs of different schemes. Among them, the comparison of the annual input costs of each scheme is shown in Table4.Table 4
Comparison of annual input costs of various programs.
Contrasting optionsAir source heat pumpsElectricitySystem in this paperGasSolar electric assistStarting costs (million)6.072.135.603.5820.52Equipment age (years)1515151010Operating costs (million)3.837.126.0111.2113.05Maintenance costs (million)5.047.155.037.126.24Energy prices (million)0.220.220.225.233.22Table4 shows that there were large differences in the cost input of different schemes. Among them, in terms of initial investment, the investment cost of electric hot water systems and natural gas hot water systems was the lowest, only 21,300 yuan and 35,800 yuan. In comparison, the initial investment of a new solar water heating system that relied on an air source heat pump reached 56,000 yuan. In terms of equipment service life, the service life of each scheme was roughly the same, and it was concentrated in 10 years and 15 years. At the same time, through quantitative analysis, it is also found that the investment cost directly determines the comprehensive cost of the hot water preparation system.


## 4. Energy-Saving Benefit of Solar Water Heating System Relying on Air Source Heat Pumps

In the course of the abovementioned experiments, it can be found that SWHS, which depends on air source heat pumps, has advantages in many areas. In order to focus on analyzing the energy-saving benefits of the system, the paper analyzes and expounds on its energy-saving benefits from the aspects of energy substitution, energy consumption ratio, environmental benefits, and economic benefits.


### 4.1. Quantity of Energy Substitution

Energy substitution is an important measure to realize the transformation and upgrading of the energy structure and promote economic development. In order to achieve green energy substitution, hot water preparation systems use conventional energy such as electricity, natural gas, or solar energy to prepare hot water. The energy substitution amount of different preparation methods are shown in Figure4.Figure 4
Energy substitution of different preparation methods.Figure4 shows that there were obvious differences in the amount of energy substitution under different preparation methods. Among them, in terms of coal energy substitution, the energy substitution amount of the system proposed in this paper reached 3.09kWh, and the substitution coefficient reached 0.91. The reason is that the energy used by solar water heating systems relying on air source heat pumps is mainly solar energy, which can minimize the use of conventional energy. It can be seen that using this system for one year is equivalent to replacing 91% of the coal energy in the whole year, so it has good energy-saving benefits.


### 4.2. Energy Consumption Ratio

The energy consumption ratio is the proportion of energy consumed in the production or operation process and refers to the specific energy consumed per unit of output value. Generally speaking, the lower the energy consumption ratio is, the lower the energy consumption will be in the production process, and the greater the resource-saving will be. Among them, the energy consumption ratio distribution of different schemes is shown in Figure5.Figure 5
Energy consumption ratio of different preparation methods.Figure5 shows that the distribution of energy consumption ratios under different preparation methods is relatively discrete. Among them, the annual energy consumption ratio and the average energy consumption ratio of solar water heating systems relying on air source heat pumps were relatively low, which were 2034.79 and 921.05, respectively. In terms of physical consumption, the consumption ratio of the solar water heating system relying on the air source heat pump reached 6.21, which was relatively higher than other preparation methods. This showed that in terms of physical consumption, the energy consumption of the system was relatively high, and the energy consumption was relatively huge. However, in terms of unit energy consumption and annual energy consumption, the energy consumption ratio of the system was at a low level. This indicated that under the comprehensive conditions, the solar water heating system relying on the air source heat pump has a lower energy consumption ratio, lower energy consumption, and relatively good energy-saving benefits.


### 4.3. Environmental Benefits

In the process of using resources, environmental benefits measure the consequences or benefits of the natural ecology in the production process. In the process of benefits evaluation, bringing greater economic value with less environmental impact is a necessary measure in line with sustainable development. Among them, the environmental benefits of different preparation methods are shown in Figure6.Figure 6
Environmental benefits of different preparation methods.Figure6 shows that solar water heating systems relying on air source heat pumps had less polluting emissions. Among them, in terms of carbon dioxide emissions, the system emissions were only 1.03 t/year. In contrast, the emissions of other systems basically reached 1.34 t/year. In terms of dust and haze particle emissions, the system’s emissions reached 1.53 t/year and 1.02 t/year, which basically met the pollution emission standards. It can be seen that in terms of pollution emissions, the environmental benefits of SWHS relying on air source heat pumps are significant. In turn, the excellent environmental benefits of SWHS relying on air source heat pumps will continue to promote the system to achieve self-upgrade, thereby enhancing its energy-saving benefits.


### 4.4. Economic Benefits

Economic benefits refer to the comparison between the energy consumed in the production process of the system and the benefits. Economic benefits embody the operating results and social value of the system. Among them, the distribution of economic benefits of different preparation methods is shown in Figure7.Figure 7
Economic benefits of different preparation methods.Figure7 shows that solar water heating systems relying on air source heat pumps had good economics. In terms of investment, the ratio of investment to the output of the system was 0.75 and 0.65. This showed that the system can generate other economic benefits besides the daily hot water preparation, and its economic value reached 86.6%. Moreover, with the gradual increase in energy prices, the economic cost of other hot water systems will continue to rise, and the economic benefits will be directly affected. It can be seen that the solar water heating system relying on the air source heat pump can overcome the influence of energy and other factors, which has good economic advantages.


## 4.1. Quantity of Energy Substitution

Energy substitution is an important measure to realize the transformation and upgrading of the energy structure and promote economic development. In order to achieve green energy substitution, hot water preparation systems use conventional energy such as electricity, natural gas, or solar energy to prepare hot water. The energy substitution amount of different preparation methods are shown in Figure4.Figure 4
Energy substitution of different preparation methods.Figure4 shows that there were obvious differences in the amount of energy substitution under different preparation methods. Among them, in terms of coal energy substitution, the energy substitution amount of the system proposed in this paper reached 3.09kWh, and the substitution coefficient reached 0.91. The reason is that the energy used by solar water heating systems relying on air source heat pumps is mainly solar energy, which can minimize the use of conventional energy. It can be seen that using this system for one year is equivalent to replacing 91% of the coal energy in the whole year, so it has good energy-saving benefits.


## 4.2. Energy Consumption Ratio

The energy consumption ratio is the proportion of energy consumed in the production or operation process and refers to the specific energy consumed per unit of output value. Generally speaking, the lower the energy consumption ratio is, the lower the energy consumption will be in the production process, and the greater the resource-saving will be. Among them, the energy consumption ratio distribution of different schemes is shown in Figure5.Figure 5
Energy consumption ratio of different preparation methods.Figure5 shows that the distribution of energy consumption ratios under different preparation methods is relatively discrete. Among them, the annual energy consumption ratio and the average energy consumption ratio of solar water heating systems relying on air source heat pumps were relatively low, which were 2034.79 and 921.05, respectively. In terms of physical consumption, the consumption ratio of the solar water heating system relying on the air source heat pump reached 6.21, which was relatively higher than other preparation methods. This showed that in terms of physical consumption, the energy consumption of the system was relatively high, and the energy consumption was relatively huge. However, in terms of unit energy consumption and annual energy consumption, the energy consumption ratio of the system was at a low level. This indicated that under the comprehensive conditions, the solar water heating system relying on the air source heat pump has a lower energy consumption ratio, lower energy consumption, and relatively good energy-saving benefits.


## 4.3. Environmental Benefits

In the process of using resources, environmental benefits measure the consequences or benefits of the natural ecology in the production process. In the process of benefits evaluation, bringing greater economic value with less environmental impact is a necessary measure in line with sustainable development. Among them, the environmental benefits of different preparation methods are shown in Figure6.Figure 6
Environmental benefits of different preparation methods.Figure6 shows that solar water heating systems relying on air source heat pumps had less polluting emissions. Among them, in terms of carbon dioxide emissions, the system emissions were only 1.03 t/year. In contrast, the emissions of other systems basically reached 1.34 t/year. In terms of dust and haze particle emissions, the system’s emissions reached 1.53 t/year and 1.02 t/year, which basically met the pollution emission standards. It can be seen that in terms of pollution emissions, the environmental benefits of SWHS relying on air source heat pumps are significant. In turn, the excellent environmental benefits of SWHS relying on air source heat pumps will continue to promote the system to achieve self-upgrade, thereby enhancing its energy-saving benefits.


## 4.4. Economic Benefits

Economic benefits refer to the comparison between the energy consumed in the production process of the system and the benefits. Economic benefits embody the operating results and social value of the system. Among them, the distribution of economic benefits of different preparation methods is shown in Figure7.Figure 7
Economic benefits of different preparation methods.Figure7 shows that solar water heating systems relying on air source heat pumps had good economics. In terms of investment, the ratio of investment to the output of the system was 0.75 and 0.65. This showed that the system can generate other economic benefits besides the daily hot water preparation, and its economic value reached 86.6%. Moreover, with the gradual increase in energy prices, the economic cost of other hot water systems will continue to rise, and the economic benefits will be directly affected. It can be seen that the solar water heating system relying on the air source heat pump can overcome the influence of energy and other factors, which has good economic advantages.


## 5. Conclusions

The SWHS relying on air source heat pumps is fully adaptable to the needs of large sports stadiums and has shown excellent energy-saving benefits in practical application. Taking Xi’an Olympic Sports Center as an example, this paper has analyzed the energy-saving benefits of SWHS assisted by ASHP. In the SWHS design of the ASHP-assisted air source heat pump, the paper adopted the double water tank design. Taking advantage of the characteristics of solar heat collection, the paper directly connected the water collecting tank with the solar heat collector, so that the system could fully adapt to the frequent hot water use needs of large stadiums. Meanwhile, the article conducts a series of studies and experiments on the proposed system.In the course of the study, the environmental and economic benefits of various hot water preparation systems were compared. The results of the comparison showed that the ASHP-assisted SWHS has great environmental and economic benefits. Due to time constraints, the article was unable to provide a comprehensive analysis of the ASHP-assisted SWHS or to profoundly reveal the core factors affecting the change of its energy-saving benefits. In the future, the article will continue to delve into the energy-saving benefits of this system and propose a more general approach.



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*Source: 4593271-2022-09-06.xml*