Multiple regression models for energy consumption of office buildings in different climates in China

Abstract

The energy consumption of office buildings in China has been growing significantly in recent years. Obviously, there are significant relationships between building envelope and the energy consumption of office buildings. The 8 key building envelope influencing factors were found in this paper to evaluate their effects on the energy consumption of the air-conditioning system. The typical combinations of the key influencing factors were performed in Trnsy simulation. Then on the basis of the simulated results, the multiple regression models were developed respectively for the four climates of China—hot summer and warm winter, hot summer and cold winter, cold, and severely cold. According to the analysis of regression coefficients, the appropriate building envelope design schemes were discussed in different climates. At last, the regression model evaluations consisting of the simulation evaluations and the actual case evaluations were performed to verify the feasibility and accuracy of the regression models. The error rates are within±5% in the simulation evaluations and within±15% in the actual case evaluations. It is believed that the regression models developed in this paper can be used to estimate the energy consumption of office buildings in different climates when various building envelope designs are considered.

Keywords

regression model / energy consumption / building envelope / office building / different climates

Introduction

Except the energy consumption of urban centralized heating, public buildings consumed 0.141 billion tce in China where approximately 22% of the building energy consumption was used for the operation of public buildings in 2008 [1-4]. With economic development, more office buildings have been constructed and used compared with other types of public buildings in China [5-8]. Thus the energy performance of office buildings has a great influence on the total national building energy consumption.

A lot of researches have been conducted to evaluate the influencing factors of building energy consumption by multiple regression analysis. By the establishment of linear regression equations, Carlo and Lamberts [9] analyzed the effects of different building envelope influencing factors on the electricity consumption in commercial buildings of Brazil. The building volume indicator, the roof heat transfer coefficient (U-value), the solar heat gain coefficient (SHGC) and the area ratio of window to wall were considered in regression equations. Lam et al. [10] developed the regression models from DOE-2 simulation results to analyze the influences of 12 key building design variables on the energy consumption in the five major climates of China. After the evaluation of the regression models, it was convinced that they could also be used to estimate the energy savings when different building schemes were considered.

In addition to analyzing the relationships between building energy consumption and their influencing factors, regression models can also be used for the prediction of energy load and energy consumption. Catalina et al. [11] developed regression models to estimate the monthly heating load in residential buildings in France. The inputs for regression models contain the building envelope U-values, the area ratio of window to wall, the building time constant and the building shape factor. Li et al. [12] developed linear and non-linear regression models from EnergyPlus simulation to predict the energy consumption index of office buildings in Hongkong. The statistical results indicate that these regression models could be used to evaluate the energy performance of different building envelope designs with daylighting controls.

However, previous researches seldom focused on the relationships between the energy consumption of office buildings and the variations of building envelope influencing factors in different climates in China [13-16]. In this paper, the multiple regression models of energy consumption based on Trnsys simulation results were established. Then the appropriate energy-saving applications of building envelope were discussed in different climates.

Establishment of office building model

Selection of representative cities

There are five major climates in China: temperate, hot summer and warm winter, hot summer and cold winter, cold, and severely cold [17,18]. As the air-conditioning system is seldom considered, the potential of building energy efficiency is rather small in the temperate region. So only the representative cities of the other four regions were discussed in this paper. The main meteorological parameters of the four representative cities are listed in Table 1.

Office building model

A base case with the representative office building design was developed in this study. The base case has 8 floors with the construction area of 9600 m². The aspect ratio is 3.0 and the shape coefficient is 0.16. The base case operates 12 hours(from 8:00 to 20:00)every day except weekends. The area ratio of window to wall for each orientation is 0.4 in the north and south, 0.3 in the east and west. 4 mm single clear glazing is used in the base case. And the flexible internal and external shading devices are applied in June, July and August every year. The configurations and U-values of different building envelopes are summarized in Table 2. Besides, some other important parameters of the base case are presented in Table 3.

Air-conditioning system

The air-conditioning system with actual equipment in the base case was established in Trnsys Stutio. The air-conditioning system consists of electricity-driven refrigerating units, gas boilers, circulating pumps and cooling towers, etc. The energy consumption of the air-conditioning system in the base case should be simulated by Trnsys.

Energy simulation and multiple regression analysis

The building energy consumption varies a lot with different building envelope designs [19,20]. In order to analyze the energy consumption of office buildings, 8 key building envelope influencing factors were found. Then the different combinations of influencing factors were simulated in Trnsys. By the analysis of energy simulation results, regression models describing the relationships between the energy consumption index of air-conditioning system and the key building envelope influence factors were developed respectively in different climates.

Key building envelope influence factors

According to previous researches, the building envelope in relation to building energy consumption contains exterior wall, roof, exterior window, and shading device [21-23]. The thermal performance of exterior wall, roof, glazing and window frame can be evaluated by the corresponding U-value—U_wall, U_roof, U_glazing and U_frame. However, the glazing optical performance is also related to building energy consumption. Therefore it is necessary to evaluate the relationships between the glazing optical performance and building energy consumption by introducing the solar heat gain coefficient (SHGC) and the solar reflectivity rate (SRR). SHGC is defined as the ratio of the solar radiation through glazing and the solar radiation distributed at glazing. SHGC shows the transmitivity performance of glazing while the reflectivity performance can be evaluated by SRR. Besides, the applications of internal and external shading devices can be evaluated by the internal shading coefficient (ISC) and the external shading coefficient (ESC). Here the shading coefficient is defined as the ratio of the opaque glazing area caused by shading devices and the total glazing area. Overall, U_wall, U_roof, U_glazing, U_frame, SHGC, SRR, ISC and ESC would be used to evaluate the effects of building envelope on the energy consumption of the air-conditioning system.

Energy simulation

The typical meteorological year data [24] which contains 8760 hourly records of dry-bulb temperature, relative humidity and solar radiation was developed for each city. When the building model and air-conditioning system were completed in Trnsys, the various simulation results with different levels of building envelope influencing factors would be achieved in each climate. Table 4 shows the different levels of the 8 key influence factors. Once the glazing is selected, the combination of U_glazing, SHGC and SRR is fixed. So there is a total of 2×4³ combinations of building envelope influencing factors for each climate, and 2×4⁴ simulation runs would be conducted in the four climates in China. The number of simulation runs should be decreased to make the analysis manageable. So the above 8 building envelope influencing factors were divided into two parts. The first part consists of U_wall, U_roof, U_glazing, U_frame, SHGC, SRR and the second part contains ISC, ESC. As a result, there were 128 simulation runs in the first part and 16 simulation runs in the second part for each climate. A total of 144 simulation runs would be performed to analyze the energy consumption variations of the air-conditioning system with different levels of building envelope influence factors in each climate.

Multiple regression analysis

The energy consumption data per unit area obtained from Trnsys simulation should be multiple regression analyzed according to the 8 key building envelope influencing factors as follows:

(1)E=k_{\mathrm{1}}{U}_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}}+k_{\mathrm{2}}{U}_{\mathrm{r}\mathrm{o}\mathrm{o}\mathrm{f}}+k_{\mathrm{3}}{U}_{\mathrm{g}\mathrm{l}\mathrm{a}\mathrm{z}\mathrm{i}\mathrm{n}\mathrm{g}}+k_{\mathrm{4}}{U}_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}}+k_{\mathrm{5}}\mathrm{S}\mathrm{H}\mathrm{G}\mathrm{C}+k_{\mathrm{6}}\mathrm{S}\mathrm{R}\mathrm{R}+k_{\mathrm{7}}\mathrm{I}\mathrm{S}\mathrm{C}+k_{\mathrm{8}}\mathrm{E}\mathrm{S}\mathrm{C}+C,

where E is the energy consumption of the air-conditioning system per unit area (kW·h/m²), k_i is the regression coefficient of building envelope influencing factors, C is the constant term of regression models. The natural gas consumed by the boilers in the air-conditioning system was converted into power with a conversion coefficient of 3.01 [25] in Eq. (1). The regression coefficients of Eq. (1) were summarized in Table 5. It can be seen from Table 5 that the determined coefficient (R²) varies from 0.894 in Shenzhen to 0.962 in Shenyang. This means 89.4%-96.2% of the energy consumption changes in the air-conditioning system can be explained by the variations of the 8 key building envelope influencing factors. The relationships between energy consumption and building envelope influencing factors are getting stronger and stronger from the south to the north. This can be explained by the fact that the main part of the air-conditioning system energy consumption in northern China is caused by the heat transfer of building envelope. The energy consumption caused by heat transfer has linear relationships with the building envelope U-values. So the linear regression models can reflect the linear relationships between energy consumption and the building envelope U-values in northern China. However, the glazing optical performance contributes a lot to the energy consumption while the building envelope U-values have limited influence on the energy consumption in the hot summer and warm winter region. As a result, the no-linear relationships between the building envelope influencing factors and energy consumption cannot be described perfectly by the linear regression models. The negative coefficients in Table 5 mean that there is an inverse relationship between the influencing factor and the energy consumption per unit area. The symbol “-” indicates the building envelope influencing factor is statistically insignificant (P>0.05) which should be removed from the linear regression model. A detailed analysis of building envelope influencing factors in the four climates is performed in the following subsections.

Shenzhen

It can be seen from Table 5 that the k₁ and k₂ in Shenzhen are negative. This means significant energy-saving effects would not be achieved and the energy consumption may increase by the thermal performance improvement of exterior wall and glazing in the hot summer and warm winter region. On the other hand, the energy consumption of the air-conditioning system would decrease when U_wall and U_glazing increase within a limited range. Besides, U_roof and U_frame are not statistically significant in the regression model. So it is not necessary to improve the thermal performance of building envelope in the hot summer and warm winter region.

The k₅ is positive while k₆ in Shenzhen is negative. The changing trends of SHGC and SRR match well with the actual situations in the hot summer and warm winter region. The cooling energy consumption is dominant in the total energy consumption of the air-conditioning system in this climate. When SHGC decreases and SRR increases, the solar radiation through glazing reduces and most of the solar radiation would be reflected to the outdoor environment in the cooling season. As a result, the cooling load and energy consumption of the air-conditioning system would reduce. Obviously, the glazing with low SHGC and high SRR should be used to achieve building energy efficiency in the office buildings of the hot summer and warm winter region.

The k₇ and k₈ in Shenzhen are both negative in the regression model of Shenzhen. This means the shading device should be made full used of under the premise that the adequate natural light is ensured in this climate.

Shanghai

The k₁, k₂ and k₃ in Shanghai are positive while U_frame is insignificant. Limited energy-saving effects can be achieved by the thermal performance improvement of exterior wall, roof and glazing. There is no need to develop an energy-saving retrofit on window frame in the hot summer and cold winter region.

The k₅ and k₆ in Shanghai are both positive. It can be explained that the solar radiation reflected to the outdoor environment gets larger with the increase of SRR. Therefore the cooling energy consumption decreases while the heating energy consumption increases. The cooling and heating energy consumption are approximative in the hot summer and cold winter region. So the influences of SHGC and SRR on the total energy consumption are uncertain. Overall, U_glazing should be the most important consideration during the glazing selection in the hot summer and cold winter region.

The absolute values of k₇ and k₈ in Shanghai are significantly smaller than those in Shenzhen. This indicates that the energy savings achieved in the hot summer and cold winter region are less than those in the hot summer and warm winter region with the same shading measures.

Beijing

The k₁, k₂ and k₃ in Beijing are greater than those in Shanghai. It can, therefore, be concluded that more energy-saving effects in the cold region can be achieved by the same thermal performance improvement of exterior wall, roof and glazing. Besides, the window frame has little influence on the annual energy consumption.

In contrast to the hot summer and warm winter region, the k₅ in Beijing is negative while k₆ is positive. The heating energy consumption is significantly greater than the cooling energy consumption in cold region. As a result, the increment of cooling energy consumption is smaller than the reduction of heating energy consumption when SHGC increases and SRR decreases. So it is a good idea to apply the glazing with high SHGC and low SRR in the office buildings of cold region.

Compared with southern China (the hot summer and warm winter region, and the hot summer and cold winter region), the absolute value of k₇ and k₈ gets smaller in the cold region. With the consideration of the initial investment, the economic analysis may need to be performed to evaluate the suitability of shading devices in the cold region.

Shenyang

The k₁, k₂ and k₃ in Shenyang are greatest of the four climates and k₄ passes the significance test in the first time. Obviously, the best energy-saving effects would be achieved with the same thermal performance improvement of building envelope in the severely cold region.

The absolute values of the k₅ and k₆ in Shenyang are bigger than those in Beijing, which means there are more energy-saving potentials about the glazing optical performance in the severely cold region than in the cold region. So it is extremely important to take the SHGC and SRR of glazing into account during the design of building envelope.

k₇ and k₈ were removed from the regression model due to the statistical insignificance. The conclusion can be drawn that the shading measures have little influence on the total annual energy consumption of the air-conditioning system in the severely cold region. As a result, it is useless to apply shading devices in the office buildings in the severely cold region from the view of building energy efficiency.

Regression model evaluations

Regression models can not only analyze the influences of building envelope design on energy consumption, but also predict the actual energy consumption indexes of office buildings in different climates. However, the feasibility and accuracy of regression models are still uncertain in actual applications. So it is necessary to evaluate the regression models in different climates. The regression model evaluations can be divided into simulation evaluations and actual case evaluations. Simulation evaluations aim at evaluating the relationships between the regression models and Trnsys simulation. Actual case evaluations are performed to evaluate the differences between the regression models and actual research cases in different climates.

Simulation evaluations

The simulation results with different random inputs should be used for the simulation evaluations. Ten combinations of the key building envelope influencing factors were generated randomly as the input parameters of Trnsys simulation. The 10 sets of random inputs present the 8 key building envelope influencing factors discussed in the establishment of regression models. Besides, the 10 sets of random inputs should be within the reasonable range and not the same as the simulation runs in the regression models.

Figure 1 illustrates the differences between the Trnsys-simulated energy consumption indexes and the calculated results from the regression models. The comparisons indicate that the Trnsys-simulated energy consumption indexes are underestimated and overestimated in the four climates. The maximum error rate is -4.61% in Shenzhen, 2.34% in Shanghai, 3.65% in Beijing and -1.66% in Shenyang. Generally speaking, the energy consumption indexes obtained from the regression models and the simulated results are in good agreement. This indicates that the regression models can be used to estimate the energy consumption from Trnsys simulation.

Actual case evaluations

The actual office building with the typical building envelope design was selected for the actual case evaluation in each climate. In order to make the evaluations feasible and persuasive, the construction area, operating schedule, energy type of the actual office buildings should be similar to the base case. Beside, the selected office buildings should have the same type of air-conditioning system and cooling & heating source as the base case. The actual values of the 8 key building envelope influencing factors in the research cases are summarized in Table 6. The influencing factors should be brought into the regression model for each climate to estimate the energy consumption index. And the actual energy consumption of the air-conditioning system was recorded by the energy consumption sub-metering system in the office building of each climate in 2010. The differences between the results from the regression models and the actual energy consumption indexes are demonstrated in Table 7. It is observed that the actual energy consumption indexes were overestimated and underestimated by the regression models in the four cities. The error rates always remain within±15%. The error rates in actual case evaluations seem to be larger than those in simulation evaluations. This can be explained by the fact that the regression models were established on the basis of the typical meteorological year data while the actual energy consumption was recorded in a specific year. The differences of meteorological data cause the deviations between the regression results and the actual energy consumption indexes. In general, the calculated results obtained from the regression models match well with the actual energy consumption. As a result, it is appropriate to use the regression models to estimate the actual energy consumption in different climates.

Overall, the regression models were proved to be feasible and accurate to estimate the Trnsys simulation results and the actual energy consumption of office buildings in different climates through simulation evaluations and actual case evaluations.

Conclusions

Key building envelope influencing factors were selected to evaluate their effects on the energy consumption of office building in this paper. Different combinations of the 8 key influencing factors were simulated in Trnsys. Besides, the multiple regression models were established respectively in the four climates in China based on the simulated results. The determining coefficient varies from 0.894 in Shenzhen to 0.962 in Shenyang. This means 89.4%-96.2% of the energy consumption changes in the air-conditioning system can be explained by the variations of the 8 key building envelope influencing factors. Then the appropriate building envelope design schemes were discussed in different climates according to the analysis of regression coefficients. Finally, simulation evaluations and actual case evaluations were conducted to verify the feasibility and accuracy of the regression models. The following conclusions are reached concerning office buildings in the four climates of China.

1) There is no need to improve the thermal performance of building envelope in the hot summer and warm winter region. Besides, shading devices and the glazing with low SHGC and high SRR should be used to achieve building energy efficiency in this climate.

2) Limited energy-saving effects can be achieved by the thermal performance improvement of exterior wall, roof and glazing in the hot summer and cold winter region. And U_glazing should always be the most important consideration during the selection of glazing. With suitable shading measures, considerable energy savings can be achieved in the hot summer and cold winter region.

3) More energy-saving effects can be achieved in cold region than in southern China by the same thermal performance improvement of exterior wall, roof and glazing. The window frame has little influence on annual energy consumption. And the glazing with high SHGC and low SRR should be applied in office buildings. The application of shading devices should undergo economic analysis in the cold region.

4) Thermal performance improvement of building envelope can bring the best energy-saving effects in the severe cold region. The glazing with high SHGC and low SRR is proposed. In addition, it is unnecessary to apply shading devices in office buildings in the severely cold region.

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