A novel method for building air conditioning energy saving potential pre-estimation based on thermodynamic perfection index for space cooling

ABSTRACT The construction energy consumption (CEC) is about 35% of entire energy consumption (EC), of which 50% is for cooler air-conditioner. The practical cooling EC is relevant to the dynamic thermal performance of cooler air-conditioner. Analyzing the difference in cooling efficiency and energy-saving potential (ESP) of the same equipment is significant to cutting down building EC. Using the concept of thermodynamic perfectness, a thermal model of refrigeration equipment is established to analyze the deviation from the ideal refrigeration cycle. At the same time, to explore the internal connection between its energy conservation and climate adaptability, five typical cities in different thermal climate zones were selected. Dynamic load model of an office building is established and the cooling EC throughout the year of each city is simulated separately. Preliminary research results show that the thermodynamic perfectness does not have a single-valued function relationship with their cooling efficiency; Guangzhou has the highest cooling demand, with a total cooling load 14.3% higher than Wuhan, and its cooling EC is lower than Wuhan. Through the establishment of a thermodynamic model and preliminary application, the calculation of the cooling ESP in different climatic regions in Chinese summer is greatly important to the usage of air conditioner. Graphical Abstract


Introduction
In the last few decades, with the acceleration of modernization and urbanization, CEC has increased sharply at a mean yearly rate of over 10% (Pérez-Lombard, Ortiz, and Pout 2008;AIE 2009). The proportion of the public construction expenditure of energy is approximately 40% of the entire primary energy use of buildings among them (Tsinghua University Building Efficiency Research Center 2014). The usage of electric energy for building refrigeration and dehumidification accounts for an increasing ratio of the entire primary energy used in the building sectors. Therefore, nowadays, the search, which is looking for more low carbon emission and energy-efficient systems and technologies, has been stimulated by the factors, which is the increasing requirement for energy supply in commonable facilities and in severe environmental issues (Deng, Wang, and Han 2011). Based on the existing statistical datum, the HVAC (heating, ventilation and air conditioning) systems still constitute the predominant role in CEC (Tsinghua University Building Efficiency Research Center 2014). Therefore, it is incredibly vital and literally necessary to optimize the design and operation of HVAC systems to reduce CEC.
Traditional HVAC design is improved on the reverse Carnot cycle absorption refrigeration system and systems of compression refrigeration. The EC of the HVAC system is related to the building's indoor and outdoor environment and system design. There is no doubt that HVAC systems have significant ESP, and plenty of recent scientific papers regard HVAC systems as research objects.
Extensive review articles on HVAC energy saving technology, especially on the optimization of heat source and frequency conversion technology, have been presented by many people (Ma 2015;Xie 2016;Qian and Li 2012;Zhao, Hu, and Bo et al. 2015;Zeng and Lu 2013;Fu 2017). In terms of building cooling and energy conservation, many people have studied the direction of reducing cooling EC through passive building energy saving. Wang et al. (Wang, Wei, and Jiang 2010) established the classification and energy efficiency index system of typical air-conditioning (AC) systems and proposed a diagnosis method based on sub-item electricity consumption and cooling capacity data. Yu et al. (Yu 2018) based on the reversed Carnot cycle analyzed the working principle of the heat pump of air source and calculated the efficiency of the air source heat pump. Its similarities and differences between the entropy minimization theory and the heat and mass transfer process optimization theory were compared by Chen et al. (Chen and Xia, 2019). At the same time, they pointed out that the pursuit of the unity of physical models, the universality of optimization methods, and the universality of optimization results are the development trends of generalized thermodynamic optimization theory.
Many people have conducted theoretical research based on the reverse Carnot cycle and the second law of thermodynamics. Xing et al. (Xing 2016) based on the second law of thermodynamics discussed the conservation of heat conduction. Chimal-Eguia et al. (Chimal-Eguia, Paez-Hernández, and Pacheco-Paez 2021), against the theory of linear irreversible thermodynamics, analyzed the Blancano cycle from the perspective of stochastic models. Chen et al. (Chen and Li 2016) in the process of energy transfer attempt to give a quantifiable expression of the second law of thermodynamics, according to calculating the available energy change. Chen et al. (Chen and Li 2016) defines the available energy consumption coefficient as the ratio of the available energy consumption rate to the heat transfer rate.
In the research on building refrigeration and climate zones, many people have studied the division of climate zones and the calculation methods of climate data. In five major Chinese climate zones, some typical cities were selected and the COP and SEER, when the two-stage compression supermarket refrigeration system uses R134a refrigerant and CO2 refrigerant under different climatic conditions, were analyzed by Li et al. (Li, Shun, and Chui et al. 2019). Cui et al. (Cui, Yan, and Ma 2017) compared the generation methods of the typical summer in the Chinese code and the American ASHRAE manual, and proposed two typical generation methods of the new generation in the typical summer. Dong et al. (Dong, Yan, and Wei 2016) in view of the wide distribution of cold winter and hot summer areas, large differences in climatic characteristics, heating problems in winter, starting from the interior thermal environment in winter and the residential requirements, the necessity of heating partitions was analyzed. Besides, Dong et al. (Dong, Yan, and Wei 2016) analyzed the necessity of heating partitions and used cluster analysis method to divide the cold winter and hot summer areas into the northern high-heat area one, the central heating transition area two, and the southern low-heat area three and proposed suitable heating modes. Fu et al. (Fu, Zhang, and Huang 2008) according to the relationship between climatic sectors and building ES, determined its climatic factors affecting building energy consumption. Fu et al. (Fu, Zhang, and Huang 2008) took the first-level indicators, which is 18°C heat degree days and 26°C refrigeration degree days, and taking winter solar radiation, summer relative humidity and coldest monthly average temperature as the second-level indicators, the country is divided into eight climate regions, and the climatic characteristics of each region are discussed. Xiong et al. (Xiong, Yao, and Li et al. 2019) used the clustering method to further subdivide the climate into hot summer and cold winter regions.
Because building indoor thermal environment and outdoor climate conditions and envelope structure has an impact on building cooling demand, many persons analyzed the passive energy saving in building cooling (Aboelata 2021;Hoffmann, Šuklje, and Kozamernik et al. 2021;Feng, Yang, and Liu et al. 2021;Zhuang, Gao, and Zhao et al. 2021). The greening of the building exterior can effectively cool the building itself and the surrounding environment. Karin A. Hoffmann et al. (Hoffmann, Šuklje, and Kozamernik et al. 2021) proposed and applied a validated numerical heat transfer model to describe the relevant building types to study the building types suitable for the use of building exterior greening.
Han et al. (Han, Sun, and Wei et al. 2021) proposed an evaporative cooling compound ACs to get the aim, which is to improve the energy efficiency. Enzo et al. (Zanchini and Naldi 2019) analyzed the ESP obtained by combining the commercially available M-cycle evaporative cooling system with the traditional refrigeration cycle. They concluded that it reduces the energy extracted by the refrigeration cycle by 37.6%, the heat energy by 76%, and the total electricity usage by 38% under the assumption of electric heating.
However, under the practical HVAC system in the single thermal environment, the effective research almost concentrates on an investigation of the energysaving effect. Distinction between the practical irreversible cooling cycle and the ideal cycle and the dynamic cooling energy consumption in different climatic zones was seldom focused.
Most of the existing research on thermal perfection is based on theoretical research and does not pay attention to the difference between thermal perfection and refrigeration theoretical cycle and actual cycle; in terms of the ESP of AC, most people study the performance of AC equipment itself. The amount of energy saved is lack of research to analyze the ESP of AC equipment from the perspective of thermal perfection. In addition, we also analyzed the difference in thermodynamic perfectness of the same equipment in different climate zones. We regarded thermal perfection as a strong connection point, linking actual refrigeration with theoretical refrigeration, and also associate ESP with climate zoning, and fully study the relationship between building models and thermodynamic models.
Existing studies lack the full-year dynamic ESP of HVAC based on the reversed Carnot cycle; the majority of studies are conducted in a steady-state environment, and no one proposed the specific gap between practical refrigeration and theoretical refrigeration. Besides, existing research lack the analysis of the impact of climate zones on HVAC, only the energysaving analysis of a single device in a single climate zone. On the one hand, the thermodynamic perfectness can measure the gap between the refrigeration cycle from reversible to irreversible, reflect the difference between the practical refrigeration cycle and the theoretical refrigeration cycle, which can be called an ESP. On the other hand, the dynamic refrigeration model estimates the practical energy consumption more accurately than traditional research methods, and analyzing the dynamic energy consumption in different climate zones can command the use of HVAC. Therefore, how to estimate the dynamic ESP of HVAC in different climatic zones is problem, which is vital and unsolved.
Based on the concept of thermodynamic perfectness, a simplified thermal model of refrigeration equipment was established to analyze its deviation from the ideal refrigeration cycle. At the same time, to explore the internal connection between its energy conservation and climate adaptability, five typical cities in different thermal climate zones were selected: Qiqihar, Wuhan, Tianjin, Guangzhou and Guizhou, dynamic load model of an office building was established and the hourly cooling EC throughout the year was simulated of each city separately. This work can guide practical HVAC system optimization design and the use of HVAC systems in different climatic zones. All in all, the main research of this paper is to pre-evaluate the operating power consumption of a certain airconditioning equipment in a certain climate zone, which plays a guiding role in the selection of airconditioning equipment in different climatic zones and different buildings. Except the above, the research of this paper is also to calculate and analyze its existing energy saving potential from the theoretical model of the heat pump. For example: when the performance of a heat pump equipment is improved by 5%, its energy consumption reduction degree is different in different regions. It is cost-effective to improve the performance of equipment in places with high energy saving potential, and conversely, the economic benefits brought by places with low energy saving potential are low.

Model
In this article, various articles about building models and thermodynamics were presented. To simplify the research, the authors have verified the models (Zhang, Lin, and Zhang et al. 2006;Wang, Cheng, and Zeng et al. 2014;Jiang, Wang, and Zhang 2012;Zhang, Zhang, and Wang et al. 2013;Zhang, Wang, and Hu 2018). The main academic value of the work lies in the proposed analysis approach to pre-estimate the building cooling energy saving potentials with equipped air conditioning devices. In fact, it is a combined comprehensive numerical method consisting of two key parts. One is the established dynamic model for cooling equipment based on thermodynamic perfection index. The other is the simplified Double-Layer building thermal model for building cooling load evaluation, which was put forward and validated in previous works (please see citations for references in the manuscript). Thus, it is a thermodynamic-perfection-indexbased method, integrated with building thermal modeling.

Air conditioner system
This article refers to the air conditioning system model in the previous paper and combines the outdoor dynamic temperature problem studied in this article to improve the original model (Zhang, Wang, and Hu 2018). As Figure 1 shows, it is an office building with mechanical HVAC systems. In summer times, when the indoor operating temperature t in,op is greater than the set point (t H ), which is able to meet the people's comfort needs for indoor thermal environment, switch on AC to cool the space and keep the room thermally comfortable (Zhang, Wang, and Hu 2018).

Mechanical ventilation
The h rad is the radiant heat transfer, which is the heat transfer process of mutual emission and absorption of radiant energy between objects; the h coe means the convective heat transfer coefficient, which means the heat exchange capacity between the fluid and the solid surface.; the t ar means the average temperature of radiant surface. For instance, the cooling loads in office buildings are mainly distributed in the daylight. The main advantage of a mechanical HAVC system is that it can meet the ventilation demands of a building during the day. This is because the outdoor fresh air has a higher temperature than the indoor air. As an evident consequence, the method mentioned above absolutely makes a growth in the refrigeration duty. By comparison, turn off the AC in the evening and turn on the ventilator to introduce low-temperature fresh air, which is able to cut down the demand of loading on the following working day. In this case, because the outdoor temperature changes significantly during the day, in some cities, when the outdoor temperature drops to meet the indoor thermal comfort conditions, mechanical ventilation or natural ventilation can be used to achieve natural cooling of the building. In this way, it is possible to provide a better premise for the thermal comfort of the building's interior for the next day and reduce the air conditioning and refrigeration load. As a consequence, how to take full advantage of natural ventilation or mechanical ventilation in the summer night, to achieve natural cooling in the office buildings, and to guide the mechanical ventilation strategy and set the hourly air exchange rate (ACH) that is able to achieve the highest energy efficiency, is extraordinary considerable for HVAC systems and refrigeration ES. For purpose of studying the ESP of this HVAC system, it is essential to create a dynamic system optimization thermal model (Zhang, Wang, and Hu 2018).

Building thermal model
In this paper, based on the building thermodynamic model established in the previous article, referring to the previous model, combined with the outdoor dynamic temperature problem studied in this paper, the original model is improved (Zhang, Wang, and Hu 2018). To simplify the analysis, the models with two board houses which have been previously verified in the building simulation were used (Zhang, Lin, and Zhang et al. 2013;Wang, Cheng, and Zeng et al. 2014;Jiang, Wang, and Zhang 2012). Without considering the long-wave radiation, Figure 2 shows the relationship that, the walls, which are the outer parts, are considered to be one of the internal boards, and entire inherent envelopes are concentrated in another boards (Yu, Heiselberg, and Lei et al. 2015;Zhang, Wang, and Hu 2018).
(1) Walls The transient heat transfer equation and boundary conditions can be expressed by: where ρ wall means the wall density, whose unit is (kg/ m3); c p,wall means the wall specific heat, whose unit is (J/(kg°C)); q r , in is the indoor heat gains of people, equipment and solar radiation penetrated from the windows, whose unit is (W/m 2 ); k wall means the thermal conductivity, whose unit is (W/(m°C)); while q r , out contains outdoor heat gains of solar radiation, longwave radiation from the ground and sky, whose unit is (W/m 2 ) (Zhang, Wang, and Hu 2018). Figure 3 shows the heat transfer processes in external building envelopes. The convective heat transfer coefficient of the outer surface of the wall is usually taken as a constant in the heat transfer calculation of the building (h wall,out = 23.3 W/(m 2 .°C)) (Zhang, Lin, and Zhang et al. 2013  obtained through the formula recommended in the ASHRAE Handbook: The transient heat transfer equation can be expressed by (Zhang, Wang, and Hu 2018): where ρ w means the window density, whose unit is (kg/m 3 ); Δx means the glass thickness, whose unit is (m); q r,w,1 and q r,w,2 are the radiation heat gains of external and internal surfaces, respectively, whose unit is (W/m 2 ); c p,w means the specific heat, whose unit is (J/(kg.°C)). h w,1-2 represent the heat transfer coefficient between the two glass layers, whose unit is (W/(m 2 .°C)), and it can be expressed by (Zhang, Wang, and Hu 2018): The h w,out and h w,in represent the equivalent heat transfer coefficient of the window exterior and interior surfaces (W/(m 2 .°C)); and the U w refers to the overall heat transfer coefficient of the glass window (W/ (m 2 .°C)); (3) Indoor air The energy conversation equation can be expressed by (Zhang, Wang, and Hu 2018): where Q dis is indoor heat disturbance (W); Q ACH means the ventilation heat gains; Q c is the cooling power provided by the AC, which has two situations, one is when t air,in is less than t H and the other is when t air,in is greater than t H ; Q wall means the indoor air heat convection with walls (W); Q w represent indoor air heat convection with window (W), which can be expressed by (Zhang, Wang, and Hu 2018): Q ACH ¼ V room ACHρ a c p;a ðt air;out À t air;in Þ=3600 (13)

Cooling equipment model
(1) Ideal refrigeration process The reversed Carnot cycle serves as the ideal refrigeration process, which means that a refrigeration system has the maximum possible coefficient of performance (COP). The equation expression this is: where T e ,T c means the evaporation and condensation temperature, respectively. For an ideal reverse cycle, both the heat-charge and discharge processes facilitate under isothermal conditions without any irreversible losses. Theoretical refrigerating coefficient of performance of AC is COP con , the Q means the rated cooling amount of AC; w means the rated energy consumption by the compressor of AC.
(2) Practical refrigeration process However, the ideal cycle assuming that there is no temperature difference when the refrigerant exchanges heat with the heat source and the cold source, it will mean that the area of the heat exchanger should be infinite, which is impractical.
In fact, in the heat absorption process, the T air,in (the summer indoor AC designed temperature) of the refrigerant is always lower than the T e of the object, which need cool; in the heat release process, its T air,out (the outdoor dry-bulb temperature) is always higher than the T c . (ambient temperature). Besides, in the actual refrigeration cycle, the temperature of heat source may change. The actual reverse cycle has external and internal irreversible losses. The degree of irreversibility is measured by thermodynamic perfectness. Therefore, the actual refrigerating coefficient of AC, COP p , can be expressed by: where COP i means the ideal refrigerating coefficient of AC. In this study, to simplify the study, some substitutes were made. This paper involves many classic articles related to absorption chillers and absorption heat pumps. The focus is on the dynamic relationship between the ACs and the external thermal environment of the building. It cares only for the changes in outdoor and indoor environment temperatures but does not discuss the changes in the internal solution parameters of the air conditioning system. What is more, this method has been cited a lot in similar analyzes and has been proved to be accurate. Therefore, it is more reliable to use this method when doing heat pump performance-related research Xiong et al. 2019;Zhang, Shi, and Zhang 2006;Chua, Toh, and Kc 2002).
Therefore, according to the Equation (14), to simplify analysis, the heat source temperature, T e , and the cold source temperature, T c , are substituted for T air,in (the summer indoor AC designed temperature) and T air,out (the outdoor dry-bulb temperature), respectably. Hence, the COP i of the ideal refrigerating coefficient of AC can be obtained by using the simplified thermodynamic model: where X is the thermodynamic perfectness of AC.
X ¼ COP con =COP con:ll (18) COP con:ll ¼ T air;in;ll = T air;out;ll À T air;in;ll À � where COP con.ll ,T air,in,ll ,T air,out,ll ,T room mean the theoretical refrigeration coefficient under AC testing conditions, the designed indoor temperature t in,de , the local outdoor dry-bulb temperature in summer and the indoor temperature, where P p ,P i ,E q , mean the actual refrigerating input power, ideal refrigerating input power and practical refrigerating demand of the room. The mathematical Equation (16) and Equation (18) are similar, but their actual meanings and uses are completely different. In order to calculate the thermodynamic perfectness of the AC, COP con:ll (the theoretical refrigeration coefficient under AC testing conditions) and COP con (the theoretical refrigeration coefficient of normal testing conditions) are used to inversely calculate the thermodynamic perfectness by Equation (18). After the thermal perfection X and the COP i of the building model AC under ideal conditions are calculated by Equation (17), the COP p of the actual dynamic AC we need can be calculated by Equation (16). Therefore, the difference between equation (16) and equation (18) is their purpose, Equation (16) is used to calculate the COP p , and it needs the X and COP i ; Equation (18) explained how to calculate the X. In this paper, there is no temperature difference caused by heat transfer, which may lead to errors in thermodynamic perfectness value and the data based on this value. Through this iterative method, although there were certain errors in the calculation process, the errors in the final results were offset by each other. The dynamic relationship between the power consumption and ESP of ACs and the outdoor temperature t out will not be affected.
In this paper, we used Equations (15), (16), (17), (18), (19) to calculate the COP p . First, we got the rated refrigerating capacity and rated refrigerating power from the studied AC to calculate COP con (the theoretical refrigerating coefficient of performance of AC) by Equation (15); at the same time, according to the summer AC outdoor design dry bulb temperature in five studied cities, we calculated the COP con.ll by Equation (19). Therefore, the thermodynamic perfectness was calculated by the Equation (18) easily. In the end, we were able to get the T air.in and T air,out from the simulation model and calculate the COP i by Equation (17). To sum up, the COP p was calculated by the Equation (16).
(3) Energy saving potential In this article, the cooling energy consumption corresponding to the practical refrigeration cycle minus the energy consumption of the theoretical cycle is defined as the ESP, which can be expressed by: With the development of refrigeration technology, the gap between the practical refrigeration cycle and the theoretical refrigeration cycle will be smaller, and the energy consumption difference between the practical cycle and ideal cycle is the energy consumption that the air conditioning can reduce.

Typical building
The typical building thermal model is established for simulation and case study, and Figure 4 shows the simulation model. This public building model is a north-south and one-story frame structure with a construction area of 35.27 m 2 . Table 1 shows the basic parameters of the building model. Apart from the thermal-physical properties of the building, climatic conditions have a vital role in determining the indoor environment and cooling load for certain cases. Thus, based on the same modeling building, some typical cities in China were chosen to investigate and compare the thermal performances and energy consumptions under different ambient parameters.
The t room of the building model is affected by heat transfer factors, such as t out , solar radiation. The outside and inside temperature of the building model will also change the operating environment of the air conditioning unit and affect the condensation temperature, evaporation temperature and the refrigeration coefficient of the air conditioning unit. The main connection between the models is to maintain the thermal inertia of the heat transfer and the heat transfer of the structure (Figure 4(a)).

Climate conditions
Nowadays, there are only two standards for building zoning in the China industry: GB50178-93 "Building Climate Zoning Standard" (Xie 1994) and GB50176-16 "Civil Building Thermal Design Code"(Li and Gao 2019). The architectural climate zoning reflects the relationship close between architecture and climate, mainly reflecting the temporal and spatial distribution characteristics of various basic meteorological elements and their direct effects on architecture. The building climate zoning is to make the buildings more fully utilize and adapt to the different climatic conditions in our country and to adopt measures to local conditions. In this paper, the latter one is chosen to analyze the correlation between the climatic conditions and the COP of the AC.
To analyze the variety of COP in the different climatic conditions, Qiqihar, Tianjin, Wuhan, Guiyang and Guangzhou as the typically studied cities were chosen to represent five climatic areas. Figure 5 shows the location of the five cities. Figure 6 shows the typical summer day hourly t out . The typical summer day hourly t out is obtained by Average Method (Cui, Yan, and Ma 2017;Dan 1989;Lu 2008). By comparing the typical summer days hourly t out , it is obvious that the typical characteristics of summer temperature in the five climatic regions can be found. Figure 7(a-e) shows that the hourly t out and the simulated natural room temperature t room throughout a whole typical year. According to the AC design standards or handbooks, the indoor setting temperature or cooling triggering point for air conditioning is often 26°C on summer days. It is clear that for five studied cities, curve of the hourly t room and t out variation trend approach to sine triangular function curves, and the five studied cities' yearly average temperature mainly lies in the range 4°C and 23°C. Besides, it can be seen that there are wider ranges of the temperature difference between day and night in Guangzhou and Guiyang, and there are large fluctuations in the curve of the two cities' t out , and the curves of the rest three cities are more likely to be fitting the trigonometric  Figure 5. Location of the five studied cities in different climatic regions in China.  function curve better and smoother. The differential in the temperature difference between day and night may be a significant element in the simulation of the buildings' dynamic thermal process. Due to the natural heat transfer processes through building envelopes, the t room can be higher than the t out for a long period. Because of the design-parameter air change rate, a fraction of them is lower than the t out . It can be seen that, in the majority time of Guangzhou and Wuhan in summer, the t room is higher than the indoordesign temperature t in,de , and their demand for refrigerating are higher than other studied cities, and compared with the other three cities, the t room of Guiyang (Temperate) and Qiqihar (Severe Cold) are generally lower, which means that these two cities have lower demand for air conditioning cooling capacity.

AC and cooling performance simulation
The research object of this study is a general public residential building, and the AC equipment of typical AC brands on the Chinese market was investigated. The existing AC equipment on the market and the nature of the building model were considered. Finally, according to China's classification and price of AC energy efficiency, a universal equipment among all the ACs was selected, which can represent the vast majority of ACs on the market. Table 2 shows the performance parameters of chosen AC. The energy efficiency rating of this AC belongs to Class I energy efficiency, according to local standards, which is the highest energy efficiency rating for commercial ACs in China, and it is an ordinary type of AC with representative research significance.
In this paper, the dynamic thermal process of the studied building is simulated by the DeST, and the practical t room and t out are given by this software. Combining the thermodynamic perfectness model and outdoor meteorological parameters, the thermal process of the AC can be calculated in this paper. In this way, the practical COP and ESP can be expressed throughout a year.
In this paper, a typical AC was chosen as a research tool to build a dynamic energy consumption model. But this study only used the basic parameters of this AC, such as the rated refrigerating capacity and rated refrigerating power. Instead of establishing an operating model for the equipment, the basic parameters of the equipment are brought into the model that is established dynamic energy consumption.

Cooling load
The relationship between t room and the practical COP on the 26°C t in,de premise is shown in Figure 8. It is easy to calculate the practical COP of five studied cities according to the Equation (16); in the same way, the ESP of five studied cities can be calculated by the Equation (23). To solve the aforementioned problems, where the t room is higher than the t in,de 26°C and the t out is lower than the t in,de 26°C, only when both the t room and the t out are higher than the t in,de can the practical COP and the ESP be calculated. In Figures 8 and 9, many values that do not meet the actual situation have been discarded, where COP is over 40, because in these situations, the value of Δt(Δt = T air,out -T air,in in Equation (17)) is pretty small, leaving the values of practical COP do not match the practical situation.
It can be seen that Wuhan, Tianjin and Guangzhou have longer AC using time, especially the Tianjin and the Guangzhou, and this leads to higher power consumptions and ESP. In these three cities, it is clear that the practical AC using time of Guangzhou is more concentrated and continuous than Wuhan and Tianjin, and the operating conditions of the ACs in these three cities change with the t room of the year. In summer, the AC will reach the peak stage of use, where t room is much higher than the t in,de , and the actual operating COP changes continuously, and it can be seen that Guangzhou and Tianjin have a longer and more continuous AC using time throughout the year, especially Guangzhou's air-conditioner service period lasts for seven months from April. In contrast, Guiyang and Qiqihar have a small period of time when the t room is higher than the t in,de . Figure 9 shows the relationship between the t room and the ESP. Due to the different variations of the five studied cities' t out , such as the diurnal temperature variation and the maximum temperature in summer, the ESP of the five studied cities manifested in five different forms. It is obvious that the histogram of ESP of the five cities is approximately a normal distribution, and the maximum point of ESP in a year occurs in July. The changing trend of ESP in a year is the same as that of t room . Due to the calculation method of the refrigeration coefficient and the t in,de , the relationship between the t room and the refrigeration coefficient and ESP is an inverse function, so the refrigeration coefficient is the closest to the actual situation and the smallest moment at the time when ESP is the largest. Since the COP is affected by the t room , thermodynamic perfectness and t in,de , especially the t room , under different climatic conditions, t in,de and thermal perfection, the ESP of air-conditioner equipment ought to show different forms of variety. Under the condition, which the t in,de of five research cities are all 26°C, since the indoor natural temperature rise trends of the five cities are different, according to Equation (23), it is apparently clear that different t out change trends will be different ESP and refrigeration coefficient change trend; because of the difference between t out and t room , the refrigeration requirements of the building models of the five cities will also be different, which is also an important reason for the different ESP. It is apparently clear that the ESP of Guiyang and Qiqihar are mainly concentrated in July and are much smaller than the other three cities, especially Qiqihar; on the contrary, the ESP of the other three cities are evenly distributed in the four months from June to September.

Comprehensive analysis of ESP
To further analyze and quantify the AC use time in five different cities, the t room and t out of the five cities were counted. The ratio of the number of hours that the t room is higher than t in.de to the number of annual hours is called X o . The ratio of the number of hours that the t out is higher than the t in.de to the number of annual hours is called X n . When the above two conditions are met at the same time, the number of hours divided by the number of annual hours is called Y.     Figure 10 show the t out and t room annual distribution statistics. Guangzhou has the highest AC using time 31.16%. In contrast, Guiyang and Qiqihar have a small part of the year when the t room is higher than the t in,de , so the air-conditioner use time in these two cities is only 4.97% (Qiqihar) and 6.75% (Guiyang), respectively. The use time of air conditioning in Guangzhou is about six times that of Qiqihar.
The t o and t n means the t out and t room .
In this paper, the research method of directly taking the constant thermodynamic perfectness has not been adopted, instead of the meteorological data of different cities (climate regions) to calculate the corresponding thermal perfection. Based on the Design code, the t out,de of AC in summer of five studied cities was obtained. Because of the t out,de of AC in summer of Wuhan is the highest in the five cities, the thermodynamic perfectness is the highest, which was calculated by Equation (15), Equation (18) and Equation (19).
The value of number E/W is used to represent the operation of the equipment in five cities, which is the required cooling capacity compared to the total energy consumed, which is the "energy conversion efficiency". In this case, the equipment has the highest thermal perfection in Wuhan, which is used to measure similarity between the practical cycle and the theoretical cycle.
The concept of the coefficient of refrigeration is the rate of the heat absorbed by the working fluid from constant temperature cold source to the mechanical work consumed; therefore, the value of number E/W can be used instead of COP to indicate the efficiency of the AC. When comparing the economics of two refrigeration cycles, if the T c and T p of the two are the same, the coefficient of refrigeration (COP) and the thermodynamic perfectness is equivalent for comparison; if the T c and T p of the two are not equal, it is meaningful to use thermodynamic perfectness to compare. In this paper, the economic benefits of refrigeration cycles in five cities were analyzed. Though the evaporating temperature T e is same, the condensing temperature of the five cities varies differently according to climate. So the comparison is not between two simple refrigeration cycles, it is a comprehensive calculation of the annual refrigeration cycle in five cities.
According to Table 4 and Table 5, the E/W is used to compare the air-conditioning performance in the refrigerating cycle; it can be seen that the AC's cooling efficiency of Tianjin is the highest among the five cities, which is 7.7% to 30.13% higher than the cooling efficiency of the other four cities, but the ESP and the thermodynamic perfectness were not the largest. At the same time, this AC has the least operating  conditions and largest ESP in Wuhan; therefore, the use of this AC in Wuhan is dissatisfied with the dual requirements of economy and energy saving.

Cooling efficiency and climate
The distribution of t room in Wuhan and Guangzhou and the distribution of COP values during air conditioning operation were counted. It was found that the temperature distribution in the city has a vital impact on the overall cooling efficiency. Under the same t room , it is clear that Wuhan (with a thermal perfection degree of 0.16) has a higher cooling efficiency. But in this article, when t room or t out of the building model is very close to t in,de , according to the Equation (16) and (17), the calculated AC cop will be far from the actual situation. In this case, the refrigeration coefficient obtained is very large, resulting in a large E/W. Therefore, it can be seen from the Table 6 that because the number of times the t room in Guangzhou is in the interval from 26°C to 30°C is greater than that of Wuhan (or even Guangzhou) (The interval from 30°C to 34°C is also greater than Wuhan), so it is apparently clear that, in Table 7, Guangzhou has a greater proportion of COP>10 than Wuhan. Therefore, under such an overall situation, the annual E/W ratio of Guangzhou is obtained. Wuhan is big, but Guangzhou's thermal perfection is less than Wuhan. Through the analysis, it is apparently clear that the change of t out not only affects the thermodynamic perfectness of the AC but also affects the overall cooling efficiency of the equipment. The principles are worthy of in-depth study.

Conclusion and prospects
Cooling energy consumption accounts for the most electricity usage for indoor environment control in China. The specific values highly depend on both the thermal performance of the used AC and dynamic climatic conditions for a given building in certain places. In this article, the simplified thermodynamic model of the cooling device is established based on the designated perfectness of the cooling cycle, which depicts the irreversibility and disparity for practical equipment from an ideal one. Furthermore, the dynamic energy consumptions for a modeling building are investigated and compared for five typical cities in China under different climatic conditions. For the studied cases based on the proposed model, the conclusions are as follows: (1) The thermodynamic perfectness of AC and its E/ W do not lie in a monotonous linear relationship. When the outdoor climate environment of the city is fully considered, such as the annual tout distribution and maintenance structure, Y, which the same air condition operating in different cities, cannot represent the overall practical energy-consuming conditions of it. The higher the thermal perfectness, that is, the single actual operating condition of the AC is closer to the theoretical operating condition, which does not mean that the actual annual operating effect is better or the refrigeration coefficient is higher.
(2) The relationship between the climatic environment and actual energy consumption by cooling experiment is different for the five cities. The expected demand for refrigeration E in Guangzhou is 14.3% higher than Wuhan's. However, the practical energy consumption in Guangzhou is lower instead. The operation of the same equipment in cities with different climate zones may be significantly different, and the main reason for this situation might be composed of two parts, one is the setting of AC operating parameters, the other is the climate conditions of the city, such as the day and night temperature difference, variation amplitude of tout throughout the year and the t in,de , This is a question worthy of further study.
(3) For the evaluation of refrigeration and ESP, the AC shows less accumulated power consumption in Qiqihar (Severe cold) and Guiyang (Temperate) throughout the whole cooling season, due to the relatively moderate ambient temperature in summer (the refrigeration demand of Qiqihar and Guiyang is 22.68% and 14.19% of Guangzhou's respectively). The AC has a maximal E/W in Tianjin (Cold) and the E/W of Tianjin is 7.7%~30.13% higher than the E/W of the other four cities. In all, the studied cooling equipment shows the most ESP in Guangzhou and Wuhan.
The work at this stage simply discusses a typical case to show the established thermodynamic model and building model to predict the summer cooling energy consumption and energy saving potential in different climate regions of China. When processing and calculating the actual air conditioning energy consumption, it will be affected by many factors, such as building type, refrigeration equipment, climatic conditions, thermal comfort of the building environment, and air quality of the building environment. In addition, as mentioned above, the ventilation and airconditioning systems of different types of public buildings are very different, and the actual working performance of the equipment is likely to deviate to a certain extent from the calculations calculated by the model assumptions in this article. Such limitations also arise some future research works for further investigation: (1) A simple public office room is chosen as the case building here, with certain geometric and thermal parameters. Changes of building types (residential, public, factory etc.), room geometry (location, facing direction, ratio of window to wall etc.), and thermalproperties of building envelopes (thermal conductivity, density, specific heat, solar radiation absorption ratio etc.) can contribute to different indoor air environment and air conditioning loads.
(2) Climatic conditions play a significant role in determining building energy consumption, in terms of impacting both indoor load demands and coefficient of performance of air conditioning devices. Only five typical cities in different climatic zones in China are discussed here for space cooling. While for building space heating in other places located in various global climatic regions, the situations should be quite different even with the same heat pump equipment.
(3) The proposed method is mainly based on the reverse Carnot cycle and thermal perfection index, approaching to an ideal one of any refrigeration cycles. In practical engineering, the thermal perfection index may not remain unchanged for different certain equipment and could vary with changing working conditions.
Although the specific results obtained in typical cases may not meet all the conditions under different conditions, the analysis methods used in this article are of reference value. The results at this stage can not only guide the optimization design of the actual building refrigeration system but also optimize the existing airconditioning system.