Analysis of the rule of window-to-wall ratio on energy demand of residential buildings in different locations in China

Abstract

Building energy demands are influenced by the window-to-wall ratio (WWR). The impact of the WWR on the energy demand in the same area has been researched by software. However, the impact of the WWR on the energy demand of buildings in different locations of China has not been investigated using the energy balance equation. The equation for the indoor temperature variation under various internal and external disturbances was provided in this study. The relationship between parameters A and B and the change in indoor temperature was proven. China's Harbin, Beijing, and Chengdu air-conditioning and heating loads, as well as the impact of changing WWR on the rate of energy savings for air-conditioning and heating energy demand, were studied. After investigating the changes in the cooling and heating loads in various cities under various WWRs, the suitable relationship between the cooling and heating loads and the WWR of three urban units was discovered. The findings indicated that despite the three cities' various climates and the diverse energy demands for air conditioning and heating in each city, with the same change in the WWR of urban buildings, the change rate of the air conditioning and heating loads in each city was near. Meanwhile, the heating and cooling loads were linear with WWR.

1. Introduction

In China, the building energy demand is huge, which is close to 28% of the energy demand of the whole society [[1], [2], [3]]. Especially in cold areas, a significant amount of the entire building heat loss is caused by windows [[4], [5], [6]], and roughly 30% of the entire heat loss occurs through windows and air infiltration [7,8]. Generally, the window's heat transfer coefficient is 2–3 times that of the wall, and it also transfers more heat per unit area [9]. The change in the window-to-wall ratio (WWR) will lead to the rise and fall of the two parts. Therefore, one of the main factors affecting the building's energy demand is the WWR, which has a bigger impact on the energy demand of the enclosure structure [[10], [11], [12], [13]]. Different techniques were employed by some researchers to look into how the WWR affected building energy demand. In order to do time-dependent dynamic simulation, Chen [14] used the MATLAB application to examine how WWR affected building energy demand, then proposed some energy-saving suggestions. Jiang [15] explored how the WWR and orientation affected the demand for heating, cooling, and overall energy by using PKPM software. Yang [16] employed DeST simulation software to examine how the WWR affected the cooling and heating load for buildings in hot summer and cold winter areas. Mehlika [17] analyzed the impact of the building's form coefficient and the size of the south-facing window on the heating and cooling load. Zhen [18] investigated how the cooling demand of office buildings was affected by various orientations and WWRs. Feng [19] examined the impact of various orientations' WWRs using one typical almost zero energy structure in Shenyang as a model by EnergyPlus software. Huang [20] analyzed the relationship between the WWR of four directions and the heating and cooling load by DeST-C software. With the office building as the object, Li [21] researched the lighting influence of different WWRs on all cloudy days by Ecotect software. The current research focuses on the effect of the change in WWR on the buildings' energy demand in a single area [19,22,23], while there is little research on the variation in energy demand in different areas with the same trend in the WWR of the same building. Additionally, the effect of the change of WWR on building energy demand is mainly analyzed by software and it is complex to learn the software.

In this paper, the energy equation is utilized to analyze how the WWR affects the building's energy demand in different climates through Excel. This method extricates itself from the dependence on energy consumption software, such as EnergyPlus and DeST. Moreover, the temperature variation equation in the building is obtained., and the effect of changing the same amount of the WWR on the energy demand in three representative cities in China is studied.

2. Methodology

The study's main focus is a four-story residential structure [Fig. 1(a and b)]. The standard floor area of this building is 180 m², and the total construction area is 720 m². According to energy conservation [[24], [25], [26]], the heat transfer in the house is described as:

$$\rho cV\frac{dt}{d\tau }=Q_{body}+Q_{glass}+Q_p+Q_a+Q_e+Q_s-Q_x\pm Q_o$$ (1)

Fig. 1.

Building model diagram.

Under steady-state conditions, Q_body can be written as:

$$Q_{body}=\sum K_i\left(t_{si}-t\right)F_i$$ (2)

Q_glass, Q_P, Q_air, Q_s, and Q_x, can be expressed as:

$$Q_{glass}=\sum F_{Gi}I\left({\eta }_i+\frac{{\alpha }_i}{{\alpha }_o}{\rho }_G\right)C_i$$ (3)

$$Q_p=knq$$ (4)

$$Q_a=n_{k}Vc{\rho }_{out}\left(t_{out}-t\right)/3600$$ (5)

$$Q_x=k_1\sum \sqrt{2\pi {\rho }_i{c}_i{\lambda }_i/T{F}_i}dt$$ (6)

Eq. (1) when substituted with Eqs. (2), (3), (4), (5), (6) results in:

$$\frac{dt}{d\tau }=\frac{\sum K_i{F}_i{t}_{si}+\sum F_{i}I\left({\eta }_i+\frac{{\alpha }_i}{{\alpha }_0}{\rho }_G\right)C_i+knq+\frac{n_k}{3600}Vc\rho t_{out}+Q_e+Q_s\pm Q_0}{\rho cV+k_1\sum F_i\sqrt{2\pi {\rho }_i{c}_i{\lambda }_i/T}}-\frac{\sum K_i{F}_i+\frac{n_k}{3600}\rho cV}{\rho cV+k_1\sum F_i\sqrt{2\pi {\rho }_i{c}_i{\lambda }_i/T}}t$$ (7)

Eq. (7) can be solved to obtain Eq. (8).

$$t=\frac{A}{B}-\left(\frac{A}{B}-t_0\right)e^{-B\tau }$$ (8)

A and B in Eq. (8) can be expressed by Eqs. (9) and (10).

$$A=\frac{\sum K_i{F}_i{t}_{si}+\sum F_{i}I\left({\eta }_i+\frac{{\alpha }_i}{{\alpha }_0}{\rho }_G\right)C_i+knq+\frac{n_k}{3600}Vc\rho t_{out}+Q_e+Q_s\pm Q_0}{\rho cV+k_1\sum F_i\sqrt{2\pi {\rho }_i{c}_i{\lambda }_i/T}}$$ (9)

$$B=\frac{\sum K_i{F}_i+\frac{n_k}{3600}\rho cV}{\rho cV+k_1\sum F_i\sqrt{2\pi {\rho }_i{c}_i{\lambda }_i/T}}$$ (10)

Thus, the temperature of the room changes according to Eq. (8) under the effect of various external and internal factors. Following the change in room temperature, the cooling and heating load of the room can be obtained.

In a room using artificial energy dissipation equipment for temperature control, the internal air is under the interaction of several disturbances. The air temperature in the room eventually tends to be a constant temperature when the time is long enough. The steady temperature is called the room's characteristic temperature. Based on the meteorological data of three cities (Harbin, Beijing, and Chengdu) provided by the meteorological database, the characteristic temperature method is used for theoretical calculation. The effects of the WWR on the cooling and heating demand and the change in energy-saving rate under different WWRs are investigated when the same improvement measures are taken for the building. Therefore, the remaining setting parameters remain unchanged; the indoor air-conditioning temperature and heating temperature are set to 27 °C and 18 °C, respectively; the external wall heat transfer coefficient and the heat transfer coefficient of outer window are set to be 1.1 W/(m²·K) and 2 W/(m²·K), respectively [27]; the window shade coefficient is 0.9, and the glass input coefficient is 0.8, the absorption rate is 0.05; the ventilation frequency is 0.5 times per hour, and the lighting power is 2 W/m²; each room has 3 people, 1 computer and 1 TV. Additionally, the variation of the average WWR from 0.14 to 0.56 is analyzed for air-conditioning and heating load.

3. Results and discussion

3.1. 1 Influence of WWR on cooling and heating load

• (1)Severe cold climate region

Harbin (45 N, 127.5E) is in a cold area, with long and chilly winter and brief and hot summer. Fig. 2 (a - d) illustrates the annual energy demand distribution of heating and air-conditioning in Harbin where the WWR of residential buildings rises from 0.14 to 0.56. As suggested in the figure, with a rise in WWR, Harbin's energy needs for heating and cooling increase. Under the same WWR, the heating load is higher than that of air-conditioning for the whole year. The highest heating load is in January, whereas the highest air-conditioning load is in July. The share of the heating and air-conditioning loads change with WWR in Harbin, as shown in Fig. 3. As the WWR rises from 0.14 to 0.56, the proportion of air-conditioning energy demand in Harbin increases from 18.7% to 39.8%, and the heating energy demand decreases from 81.29% to 60.19%. Fig. 4 (a, b) exhibits the energy-saving rate distribution of heating and air-conditioning in Harbin with WWR decreasing from 0.28 to 0.14. It is demonstrated that the energy-saving moments for cooling in Harbin are mainly concentrated at 5:00–17:00, and there are 1264 energy-saving moments for air-conditioning in one whole year.

Fig. 2.

Distribution of energy demand for heating and air-conditioning in Harbin.

Fig. 3.

Energy demand ratio of heating and air-conditioning in Harbin with WWR (WWR is 0.14, 0.28, 0.42 and 0.56, respectively).

Fig. 4.

Energy-saving rate of heating and air-conditioning in Harbin.

• (2)
  Cold climate region

Fig. 5 (a - d) displays the energy demand for heating and air-conditioning in Beijing (39.9 N, 116.4E) where the WWR of the residential building rises from 0.14 to 0.56. As observed in the figure, the energy demand for heating and air-conditioning in Beijing increases with a rise in WWR. The highest heating load is in January, whereas the highest air-conditioning load is in June. Fig. 6 depicts the proportion of heating and cooling loads in Beijing for one whole year with WWR. The results imply that as the WWR increases from 0.14 to 0.56, the cooling load in Beijing has increased from 51.8% to 71.9%, and the energy demand for heating has decreased from 48.2% to 28.1%. Fig. 7 (a, b) indicates the hourly heating and air-conditioning energy-saving rates when the residential building in Beijing adopts the same energy-saving measures to reduce the WWR from 0.28 to 0.14. The figure reveals 2077 air-conditioning energy-saving moments in Beijing throughout the year. There are 3040 heating energy-saving moments throughout the year, which are concentrated at 6:00–18:00. The energy-saving moments are mainly concentrated at 17:00–6:00 the next day.

Fig. 5.

Distribution of energy demand for heating and air-conditioning in Beijing.

Fig. 6.

Energy demand ratio of heating and air-conditioning in Beijing with WWR.

Fig. 7.

Energy-saving rate of heating and air-conditioning in Beijing.

• (3)
  Hot Summer and Cold Winter climate region

Fig. 8 (a - d) illustrates the annual energy demand distribution for heating and air-conditioning in Chengdu (30.7 N, 104.1E) where the WWR of the residential building rises from 0.14 to 0.56. It demonstrates that the heating and cooling loads in Chengdu increase with a rise in WWR. Under the same WWR, more energy is needed for air conditioning than for heating throughout the entire year. The highest heating load is in January, whereas the highest cooling load is in August. Fig. 9 exhibits the change in the proportion of air-conditioning and heating loads with WWR. The figure unveils that as the WWR increases from 0.14 to 0.56, the proportion of air-conditioning energy demand in Chengdu increases from 65.7% to 81.2%, and the heating energy demand decreases from 34.3% to 18.8%. The distribution of Chengdu's energy-saving rate for cooling and heating is shown in Fig. 10(a and b), with WWR falling from 0.28 to 0.14. The figure indicates 1899 air-conditioning energy-saving moments in Chengdu throughout the year, which are concentrated at 7:00–19:00. Furthermore, there are 2676 heating energy-saving moments throughout the year, and the energy-saving moments are mainly concentrated at 18:00–8:00 the next day.

Fig. 8.

Distribution of energy demand of heating and air-conditioning in Chengdu.

Fig. 9.

Energy demand ratio of heating and air-conditioning in Chengdu with WWR (WWR is 0.14, 0.28, 0.42, and 0.56, respectively).

Fig. 10.

Energy-saving rate of heating and air-conditioning in Chengdu.

3.2. Comparison of the three regions

Fig. 11 depicts the comparison of the energy-saving rate in the three cities when the same energy-saving measures are adopted to reduce from 0.28 to 0.14. The figure shows that the building adopts measures to reduce the WWR, and the heating and cooling loads throughout one year decrease, reflecting that the heating and cooling loads can be significantly lowered by changing the WWR. Moreover, with the same energy-saving measures, the energy conservation rate is similar under different weather conditions, the energy conservation rate is similar. Heating energy consevation rates range from 9.4% to 13.3%, and air-conditioning saves 34.3%–44.2% of its energy, confirming the commonness of energy conservation in buildings.

Fig. 11.

Average energy efficiency of the same measures in three cities.

Fig. 12 exhibits the trend of energy demand with WWR in the 3 cities throughout the year. The figure indicates the need for air-conditioning energy rises as WWR increases under different weather conditions. The cooling load rises more quickly and the heating load changes more slowly as the WWR increases. The annual energy demand for heating and air conditioning in three cities varies linearly with WWR.

Fig. 12.

Trend line of the energy demand of heating and air conditioning with WWR in three cities.

The WWR of a building plays crucial role in determining how much energy it uses. Under different meteorological conditions, the energy consumption for heating and cooling the same building varies dramatically. The order of air-conditioning energy demand from large to small is Beijing, Chengdu, and Harbin, and the order of heating energy demand from large to small is Harbin, Beijing, and Chengdu. This reflects the individuality of building energy demand. The WWR of the same building changes by the same amount. Additionally, despite the varying meteorological conditions, the building's rate of energy savings is near.

3.3. Comparison with software

The comparison of this study's method and the DeST building energy demand simulation software under the same conditions is presented in Fig. 13 (a, b). They are the cooling and heating loads of Chengdu when the WWR is 0.14. According to the graph, the outcomes of the strategy suggested in this research resemble those predicted by DeST software. Meanwhile, the results are consistent with the situation as it stands, that is, the heating load is the largest in November and December, and the cooling load is the largest in July and August. The cooling and heating loads of each month are close to the values calculated by DeST software. The errors between the total annual energy demand of cooling load and heating load calculated by the method proposed and the values calculated by DeST software are 8.4% and 12.1%, respectively.

Fig. 13.

Comparison of different methods.

Further, the mean absolute error (MAE) method is used to calculate the absolute deviation between the calculated value of the method proposed and the calculated value obtained by DeST software. The formula is shown in Equation (11). The results for the cooling load and heating load are listed in Table 1, which implied that every blunder was within the acceptable, reasonable bounds.

$$\text{MAE}=\frac{1}{N}\sum _{i=1}^N\left|y_{sim,i}-y_{dest,i}\right|$$ (11)

Table 1.

Statistics of MAE.

Parameter	MAE
Cooling load	967.3 kW
Heating load	444.8 kW

4. Conclusions

Without using any software, a theoretical approach was put forth to examine how the WWR affected the energy requirements of buildings. For performance analysis, a mathematical model of a building's energy balance was created. This theoretical analysis method was compared with DeST software to verify its accuracy. The following findings are reached by examining the cooling and heating loads of various climate zones at various WWRs.

• ●The temperature of the room changes according to the equation $t=\frac{A}{B}-\left(\frac{A}{B}-t_0\right)e^{-B\tau }$ under various disturbances. This equation can be adopted to calculate the temperature change in the room. The results demonstrate that under different meteorological conditions, the WWR of one building changes the same, and the absolute reduction of air-conditioning and heating energy demand significantly varies in different cities. When the WWR is 0.28, the annual maximum cooling load in the three cities is 1.7 times the minimum, and the maximum energy requirement for heating annually is 5.2 times the minimum.
• ●The absolute reduction of energy demand is closely associated with local climatic conditions, while the pace of change in heating and cooling loads varies little between cities. The WWR is decreased from 0.28 to 0.14, and the energy-saving rate of heating and cooling is 9.4%–13.3% and 34.3%–44.2%, respectively. With the same energy-saving measures, the higher the WWR, the bigger the annual cooling and heating loads. Cooling load is growing faster than heating load. The annual cooling energy requirement is more significantly impacted by the change in the WWR.
• ●WWR causes a linear change in the annual energy consumption for heating and cooling. The WWR is the inherent geometric feature of the building itself. This theoretical approach can be utilized to precisely assess how the WWR affects building energy demand.

Decarations

Author contribution statement

Ruihua Ma: Performed the experiments; Analyzed and interpreted the data; Wrote the paper. Ruijiang Ma: Performed the experiments; Contributed reagents, materials, analysis tools or data. Enshen Long: Conceived and designed the experiments; Analyzed and interpreted the data.

Funding statement

This work was supported by the Program of Sichuan Science and Technology (2021JDRC0122) , the programme of Sichuan Province Key Laboratory of Higher Education Institutions for Solar Energy Technology Integration and Application (TYN2015-08) and the scientific research project of Panzhihua college (2022PY04)

Data availability statement

Data will be made available on request.

Declaration of interest's statement

The authors declare no competing interests.

Additional information

No additional information is available for this paper.