Development of Simpliﬁed Building Energy Prediction Model to Support Policymaking in South Korea—Case Study for Ofﬁce Buildings

: This study aims to support building energy policymaking for ofﬁce buildings in South Korea through regression models by considering the global temperature rise. The key variables representing building energy standards and codes are selected, and their impact on the annual energy consumption is simulated using EnergyPlus reference models. Then, simpliﬁed regression models are built on the basis of the annual energy consumption using the selected variables. The prediction performance of the developed model for forecasting the annual energy consumption of each reference building is good, and the prediction error is negligible. An additional global coefﬁcient is estimated to address the impact of increased outdoor air temperature in the future. The ﬁnal model shows fair prediction performance with global coefﬁcients of 1.27 and 0.9 for cooling and heating, respectively. It is expected that the proposed simpliﬁed model can be leveraged by non-expert policymakers to predict building energy consumption and corresponding greenhouse gas emissions for the target year.


Introduction
Globally, efforts are being made to mitigate the impact of greenhouse gases (GHGs) on the environment and daily life.Since the universal agreement on climate change, known as the Conference of the Parties (COP21) in 2015 [1], many developed and developing countries have endeavored to lower GHGs by establishing long-term goals and implementing measures such as the nationally determined contribution (NDC) [2].International corporations are also endeavoring to drive the industry toward environmentally friendly directions to limit the global temperature increase to 2 • C.
The Green New Deal was established by the United States in 2006, followed by acceptance from several other developed countries, including Canada and the European Union (EU), in 2019 [3].The South Korean government also launched the Green New Deal policy in 2020 as a benchmark precedent [4].The national building energy policy is a part of the Green New Deal and vitally includes building-related policies owing to the high CO 2 emissions of buildings; the energy-related CO 2 emissions of the building sector account for about 10% of emissions among all the sectors, including transportation and industry [5].Thus, reducing building energy consumption is one of the critical tasks in mitigating GHGs.
Decision making for the policies and standards regarding building energy performance is significant from the perspective of existing and new buildings.The stricter the policy enacted, the more improved the building performance realized, thereby reducing energy consumption [6].Most buildings benefit from retrofits and renovations of existing buildings to new policies and standards [7][8][9].Further, the impacts for new buildings are not small, owing to the long life cycles of buildings.The effects of building energy performance can last until the demolition or retrofit phase of the building.
However, building energy policies cannot be made without robust energy predictions for different building categories.Detailed prediction models using simulation models, such as the grey-box model structure with state-space formulation, were used for model-based predictive control [10].These are regarded as control-oriented building models that retain a simple structure with constant model parameters.The other approach is that with a blackbox model, for which classical system identification methods are used [11].More recently, machine-learning methods, which are a kind of black-box model, have been applied to predict the cooling/heating loads of buildings using artificial neural networks [12] and multiple linear regression [13].Only a few studies have used machine-learning methods to predict the annual energy consumption and corresponding CO 2 emissions compared to data gathered from actual buildings [14].These two methods, including grey-and black-box models, have been consequentially used in building energy management applications and for control purposes, such as model-based predictive control.However, these approaches involve heavy computations to calculate the thermal dynamics of the building, and large engineering costs are required in the modeling phase.This is because of the nature of these models, which need to be estimated against data from either experiments or simulations of specific target buildings.Therefore, such models are not adequate and overengineered for predicting the annual energy consumption to support decision making for the national building energy policy.
The other approach is to leverage the developed reference building models in building energy simulation tools, such as EnergyPlus or TRNSYS.These reference models represent the typical thermal characteristics of each building category so that the representative energy consumptions can be predicted and forecasted with respect to weather, thermal performance of the envelope, operation, as well as heating, ventilation, and air-conditioning (HVAC) efficiency [15,16].Separate models were created with respect to age/vintage as the performances of the building envelopes and HVAC systems evolve with time based on revisions to the energy policies and function degradations over the life cycles.Prototype building models suited to the South Korean infrastructure have been developed on the basis of mass building data, including their surveys and measurements.For example, flexible research and flexible modeling approaches were developed with a focus on nonresidential buildings, such as offices, sales, accommodation, educational, and cultural structures [17].Moreover, the impact and effectiveness of building energy policies on GHGs were investigated with the developed reference building models targeting office buildings in South Korea [18].A new type of reference building model was developed with the proposed methodology targeting religious buildings in the US [19].The reference model for residential building envelope in Europe was leveraged to optimize the thermal performance of the building [20].Further, the reference building models were used to support decision making for building energy code development by focusing on nonresidential structures [21] in Europe.
Nevertheless, the use of simulation tools is limited only to experts who are familiar with thermal phenomena in buildings and HVAC systems.The key stakeholders, such as policymakers, are not able to easily test and analyze the inputs and outputs of the simulation tools.Even when such tools are systematically integrated to evaluate potential building energy performances upon policy modifications, the computation times for energy simulations are long and hinder usage for the non-experts to manipulate the tools easily and straightforwardly.Therefore, a simplified but robust and straightforward measure is needed for scientific decision making regarding the national building energy standards and policies.This research direction was suggested in a recent and extensive review [22]; in the study, the pros and cons of physics-based, data-driven, and hybrid models integrating the two were analyzed.The overall recommendation was to develop fast and accurate models to support decision making for building energy policies.
As the global climate changes are rapidly increasing, building energy performances from the viewpoint of the long-term future will be influenced subtly.Therefore, using typical or newly measured weather data may provide biased energy consumption, especially for long-term predictions over several decades.As reported in a previous review [23], building energy consumption depends on global environmental changes and the resulting outdoor air temperatures predicted with CO 2 emission scenarios, such as the representative concentration pathway (RCP).Therefore, the global impact needs to be considered during the decision making for enacting policies and standards.This research direction was also highlighted in the recent review [22], where the authors concluded that climate change, along with occupants' behaviors, needs to be introduced as uncertainties.
The present study leverages newly developed reference building models suited to South Korea.Simplified regression models were built on the basis of generated building energy data from the EnergyPlus reference building models.In contrast to recent studies predicting a more granular time scale, our study forecasts the annual energy consumption with respect to changes in key variables, where the simplified model structure is applicable.The weather data containing time differences for the target region were used to consider the impact of global temperature increase for energy prediction.This is to consider more realistic scenarios for global warming, as proposed in a recent review [22].Building energy policymakers can leverage these developed regression models to evaluate the national building energy impact on GHGs.Effective decision making for establishing key policies and revisions for long-term impacts, such as the next 30 years, can thus be achieved based on scientific analyses.

Research Flow
In this study, we leveraged previously developed reference building models [24].Figure 1 represents the schematic of this study.Two types of weather data were used to evaluate the impact of global warming on building energy consumption.Multiple EnergyPlus input files (IDF) were generated for the key variables impacting building energy performances.These were simulated in a group, and the inputs (key variables) and outputs (annual heating and cooling energy consumption) were generated.Then, using the input/output data along with 1982-1997 Typical Meteorological Year Version 3 (TMY3) data, linear regressions were performed with linear and quadratic terms for the variables in the Python environment.Finally, an additional coefficient that can be multiplied with the previously regressed model was estimated against the input/output from 2004-2018 TMY3 data.
standards and policies.This research direction was suggested in a recent and extensive review [22]; in the study, the pros and cons of physics-based, data-driven, and hybrid models integrating the two were analyzed.The overall recommendation was to develop fast and accurate models to support decision making for building energy policies.
As the global climate changes are rapidly increasing, building energy performances from the viewpoint of the long-term future will be influenced subtly.Therefore, using typical or newly measured weather data may provide biased energy consumption, espe cially for long-term predictions over several decades.As reported in a previous review [23], building energy consumption depends on global environmental changes and the re sulting outdoor air temperatures predicted with CO2 emission scenarios, such as the rep resentative concentration pathway (RCP).Therefore, the global impact needs to be con sidered during the decision making for enacting policies and standards.This research di rection was also highlighted in the recent review [22], where the authors concluded tha climate change, along with occupants' behaviors, needs to be introduced as uncertainties The present study leverages newly developed reference building models suited to South Korea.Simplified regression models were built on the basis of generated building energy data from the EnergyPlus reference building models.In contrast to recent studies predicting a more granular time scale, our study forecasts the annual energy consumption with respect to changes in key variables, where the simplified model structure is applica ble.The weather data containing time differences for the target region were used to con sider the impact of global temperature increase for energy prediction.This is to consider more realistic scenarios for global warming, as proposed in a recent review [22].Building energy policymakers can leverage these developed regression models to evaluate the na tional building energy impact on GHGs.Effective decision making for establishing key policies and revisions for long-term impacts, such as the next 30 years, can thus be achieved based on scientific analyses.

Research Flow
In this study, we leveraged previously developed reference building models [24] Figure 1 represents the schematic of this study.Two types of weather data were used to evaluate the impact of global warming on building energy consumption.Multiple Ener gyPlus input files (IDF) were generated for the key variables impacting building energy performances.These were simulated in a group, and the inputs (key variables) and out puts (annual heating and cooling energy consumption) were generated.Then, using the input/output data along with 1982-1997 Typical Meteorological Year Version 3 (TMY3 data, linear regressions were performed with linear and quadratic terms for the variables in the Python environment.Finally, an additional coefficient that can be multiplied with the previously regressed model was estimated against the input/output from 2004-2018 TMY3 data.

Reference Building Models
Previously developed reference building models in EnergyPlus [25] were used in this work and consist of three building types that are categorized as follows: The models were developed on the basis of available information as follows: (1) legal system of building classification, (2) national building area statistics, and (3) national building energy statistics.More detailed information regarding the designs, shapes, and dimensions can be found in a previous study [24].For HVAC systems, instead of modeling the individual components in detail, the efficiencies of the heating and cooling systems for the entire building were applied as variables.The default values of the design variables for these models were set using parameter estimations.The parameter estimations were performed using the gradient descent method (algorithm: L-BFGS-B [26]).The parameter estimations were carried out by combining the EnergyPlus execution program (energyplus.exe)and Python script (used library: Scipy) written for optimization.

Weather Profile
This study utilizes representative weather files for specific regions in South Korea to predict future building energy consumption.Thus, TMY3 weather data [27] were used, which is based on long-term real measurements.The data for each month are excerpted from the measurements to select the most representative profiles over 13 years.
The maximum, minimum, and median values were set by considering the potential range that can be imposed and implemented in the building standards and codes in the future [28,29].These values were summarized according to the building types, as noted in Tables A1-A3 in Appendix A. The same ranges of variables were applied to the three types of residential buildings (Table A1), while the commercial and public buildings have different ranges, as indicated in the last column.

Model Structure and Regression Method
The simplified regression model consists of nine variables and 54 coefficients multiplied with the variables (linear and quadratic terms), as shown in Equation ( 1).This polynomial model is of the 2nd order and incorporates the impact of correlation of two variables and quadratic impact of single variables.The annual heating or cooling energy consumptions are denoted as E. The coefficients used for estimations are denoted as c 1 -c 54 .The heating and cooling models were respectively regressed using the annual heating and cooling energy consumptions with the same model structure.
For the nine key variables, the maximum, minimum, and median values were set to estimate the coefficients of the polynomial model.The first case involved the baseline with medium values for all the variables.For the single term, two cases (max and min) were set for the nine key variables so that 18 cases were generated.For the correlation term, only the impact of paired variables was considered.Thirty-six combinations of paired variables were set, and each combination had four cases; thus, 144 cases were generated.In total, 163 cases were generated, and each case was treated as data to estimate the coefficients (c 1 -c 54 ).Based on the tabular data, the multiple EnergyPlus IDFs were modified manually from the baseline case and simulated in a group.
Based on the simulation results, the inputs (set of key variables) and outputs (annual heating/cooling energy consumptions) were tabulated and vectorized from Equation (1), as shown in Equation ( 2).Here, E, V, and C represent the annual heating/cooling demands (kWh) of the 163 cases, input variable set of the 163 cases, and coefficients (c 1 -c 54 ) that are to be estimated.The dimension of E is 1 × 163, while that of V is 54 × 163.Multivariate linear regression was performed with pseudoinverses (denoted by †).

Preliminary Results with Reference Buildings
Prior to model development, we investigated the methodology with a simpler model structure that does not consider the impact of variable correlations.Specifically, only the single terms in Equation (1) were considered.All building cases among the prototype reference building models were used with the weather profiles of Seoul from 2016, except for residential buildings that applied a more recent weather file from 2018.This is not a long-term weather profile such as the TMY, but the measured data are for specific regions and are more realistic as they may not be generalized.The simulation results for the baseline case were used for comparisons with actual measured massive building data from other research projects.The building energy consumption data gathered from actual building clusters were from different years, which was why two different weather profiles were used.

Regression Results and Sensitivity
As expected, the prediction performance of the regressed model was good, and the errors were negligible.The maximum absolute error for 19 cases, including the baseline case, was 4.69 × 10 −7 ; this means that the simple model structure is sufficient for forecasting the annual energy consumption of all simulated reference building models.
Instead, we evaluated the impact of each variable individually.The deviation of each case from the baseline was calculated to investigate the impact of the variable on energy consumption.S i represents the relative sensitivity of case i (%).E i and E baseline represent the annual heating/cooling energy consumptions of case i with the ith variable and baseline (case 1).
Figures 2 and 3 show the sensitivity of each variable to the annual heating and cooling energy consumption.In the heating case, infiltration has the largest impact on energy consumption in all building types.The energy consumption of residential buildings is sensitive to envelope performance, such as insulation (walls and windows) and SHGC, compared to the other types of buildings.This is mainly attributed to the different ranges of the variables between the residential and other buildings.
In the cooling season, the impact of insulation of the envelope is reduced in all buildings, while that of the thermal performance of the windows (insulation and SHGC) is high in residential buildings.Moreover, the impact of the internal heat gain, especially that of the occupants, is relatively high compared to that in the heating case, and the efficiency of the chiller has the largest impact among all variables.In the cooling season, the impact of insulation of the envelope is reduced in al ings, while that of the thermal performance of the windows (insulation and SHGC) in residential buildings.Moreover, the impact of the internal heat gain, especially the occupants, is relatively high compared to that in the heating case, and the eff of the chiller has the largest impact among all variables.

Multivariate Model Evaluation with Office Building in a Global Warming Sc
This study considered the global temperature increase for building energy pre with a simplified model.Figure 4 shows the average values of the global surface t ature changes from 1951-1980 [30].The Y axis shows the global surface tempera crease from the average value from 1951-1980.The recent annual surface temperat was around 0.5 °C over 20 years, and this trend is similarly seen in the target regi Incheon in South Korea.The hourly outdoor air temperature with two sets of TM from 1982 to 1997 and 2004 to 2018 was compared, as shown in Figure 5.The ann jectories between these two weather profiles are similar, but the average tempera crease was about 0.66 °C.In the cooling season, the impact of insulation of the envelope is reduced in al ings, while that of the thermal performance of the windows (insulation and SHGC in residential buildings.Moreover, the impact of the internal heat gain, especially the occupants, is relatively high compared to that in the heating case, and the ef of the chiller has the largest impact among all variables.

Multivariate Model Evaluation with Office Building in a Global Warming Sc
This study considered the global temperature increase for building energy pre with a simplified model.Figure 4 shows the average values of the global surface t ature changes from 1951-1980 [30].The Y axis shows the global surface tempera crease from the average value from 1951-1980.The recent annual surface temperat was around 0.5 °C over 20 years, and this trend is similarly seen in the target reg Incheon in South Korea.The hourly outdoor air temperature with two sets of TM from 1982 to 1997 and 2004 to 2018 was compared, as shown in Figure 5.The ann jectories between these two weather profiles are similar, but the average tempera crease was about 0.66 °C.

Multivariate Model Evaluation with Office Building in a Global Warming Scenario
This study considered the global temperature increase for building energy prediction with a simplified model.Figure 4 shows the average values of the global surface temperature changes from 1951-1980 [30].The Y axis shows the global surface temperature increase from the average value from 1951-1980.The recent annual surface temperature rise was around 0.5 • C over 20 years, and this trend is similarly seen in the target region, i.e., Incheon in South Korea.The hourly outdoor air temperature with two sets of TMY3 data from 1982 to 1997 and 2004 to 2018 was compared, as shown in Figure 5.The annual trajectories between these two weather profiles are similar, but the average temperature increase was about 0.66 • C.
Herein, we evaluated the single and correlated impacts of the key variables on energy consumption and investigated the applicability of the global coefficient incorporating the impact of global temperature increase.The office building was selected from among the reference building models for the analysis.Unlike the preliminary results shown in Section 3, the correlation of key variables was considered in the model structure such that the number of coefficients to be estimated was 54, as discussed in Section 2 and Equation (1).With the two different sets of TMY3 weather data for 1982-1997 and 2004-2018, two different EnergyPlus simulation sets, including the inputs (key variables) and outputs (annual heating/cooling energy consumptions), were generated.The first weather data for 1980-2000 were used for model development with Equations ( 1) and ( 2).The modeling performance was good, similar to that of the preliminary study noted in Section 3.  Herein, we evaluated the single and correlated impacts of the key variables on energy consumption and investigated the applicability of the global coefficient incorporating the impact of global temperature increase.The office building was selected from among the reference building models for the analysis.Unlike the preliminary results shown in Section 3, the correlation of key variables was considered in the model structure such that the number of coefficients to be estimated was 54, as discussed in Section 2 and Equation (1).With the two different sets of TMY3 weather data for 1982-1997 and 2004-2018, two different EnergyPlus simulation sets, including the inputs (key variables) and outputs (annual heating/cooling energy consumptions), were generated.The first weather data for 1980-2000 were used for model development with Equations ( 1) and ( 2).The modeling performance was good, similar to that of the preliminary study noted in Section 3.
The additional coefficient was introduced and multiplied with the developed model, as shown in Equation ( 4).This coefficient was estimated from the input/output data for the 1982-1997 and 2004-2018 weather profiles.Specifically, the coefficient reflects the impact of temperature rise on heating/cooling energy consumption.We investigated how this temperature rise impacts energy increased/decreased in each case for variation of the key variables.Herein, we evaluated the single and correlated impacts of the key variables on energy consumption and investigated the applicability of the global coefficient incorporating the impact of global temperature increase.The office building was selected from among the reference building models for the analysis.Unlike the preliminary results shown in Section 3, the correlation of key variables was considered in the model structure such that the number of coefficients to be estimated was 54, as discussed in Section 2 and Equation (1).With the two different sets of TMY3 weather data for 1982-1997 and 2004-2018, two different EnergyPlus simulation sets, including the inputs (key variables) and outputs (annual heating/cooling energy consumptions), were generated.The first weather data for 1980-2000 were used for model development with Equations ( 1) and ( 2).The modeling performance was good, similar to that of the preliminary study noted in Section 3.
The additional coefficient was introduced and multiplied with the developed model, as shown in Equation ( 4).This coefficient was estimated from the input/output data for the 1982-1997 and 2004-2018 weather profiles.Specifically, the coefficient reflects the impact of temperature rise on heating/cooling energy consumption.We investigated how this temperature rise impacts energy increased/decreased in each case for variation of the key variables.The additional coefficient was introduced and multiplied with the developed model, as shown in Equation ( 4).This coefficient was estimated from the input/output data for the 1982-1997 and 2004-2018 weather profiles.Specifically, the coefficient reflects the impact of temperature rise on heating/cooling energy consumption.We investigated how this temperature rise impacts energy increased/decreased in each case for variation of the key variables.
Figure 6 shows the variation of the global coefficient for the 163 cases of heating and cooling energy consumption.The coefficient for the cooling case is higher than 1, meaning that more cooling energy is consumed with the increase in outdoor air temperatures.In most cases, this coefficient value ranged between 1.2 and 1.4, with an average value of 1.27.For the heating case, the coefficient was lower than 1, meaning less heating energy was consumed with an increase in outdoor air temperatures.In most cases, this value ranged between 0.85 and 0.95, with an average value of 0.90.
Figure 6 shows the variation of the global coefficient for the 163 cases of heating and cooling energy consumption.The coefficient for the cooling case is higher than 1, meaning that more cooling energy is consumed with the increase in outdoor air temperatures.In most cases, this coefficient value ranged between 1.2 and 1.4, with an average value of 1.27.For the heating case, the coefficient was lower than 1, meaning less heating energy was consumed with an increase in outdoor air temperatures.In most cases, this value ranged between 0.85 and 0.95, with an average value of 0.90.The averaged values for the cooling and heating cases were 1.27 and 0.9, respectively, as explained previously.These values are intended to predict the annual heating/cooling energy consumption in the future (e.g., 20 years later) based on the model developed with old weather data.Thus, we evaluated the prediction performance of the coefficient.The covariance of root-mean-squared error (cvRMSE) of the 163 cases were 4.3% and 5.5%, while the maximum relative errors were 26% and 16% for the heating and cooling cases, respectively, as shown in Figure 7.These are cases where only infiltration (minimum only) and people heat gain (minimum only) were considered for the heating and cooling cases, respectively.The reason for the bias can be considered to be the impact of the difference in the increase in outdoor air temperature for each case.The averaged values for the cooling and heating cases were 1.27 and 0.9, respectively, as explained previously.These values are intended to predict the annual heating/cooling energy consumption in the future (e.g., 20 years later) based on the model developed with old weather data.Thus, we evaluated the prediction performance of the coefficient.The covariance of root-mean-squared error (cvRMSE) of the 163 cases were 4.3% and 5.5%, while the maximum relative errors were 26% and 16% for the heating and cooling cases, respectively, as shown in Figure 7.These are cases where only infiltration (minimum only) and people heat gain (minimum only) were considered for the heating and cooling cases, respectively.The reason for the bias can be considered to be the impact of the difference in the increase in outdoor air temperature for each case.
cooling energy consumption.The coefficient for the cooling case is higher than 1, meaning that more cooling energy is consumed with the increase in outdoor air temperatures.In most cases, this coefficient value ranged between 1.2 and 1.4, with an average value of 1.27.For the heating case, the coefficient was lower than 1, meaning less heating energy was consumed with an increase in outdoor air temperatures.In most cases, this value ranged between 0.85 and 0.95, with an average value of 0.90.The averaged values for the cooling and heating cases were 1.27 and 0.9, respectively, as explained previously.These values are intended to predict the annual heating/cooling energy consumption in the future (e.g., 20 years later) based on the model developed with old weather data.Thus, we evaluated the prediction performance of the coefficient.The covariance of root-mean-squared error (cvRMSE) of the 163 cases were 4.3% and 5.5%, while the maximum relative errors were 26% and 16% for the heating and cooling cases, respectively, as shown in Figure 7.These are cases where only infiltration (minimum only) and people heat gain (minimum only) were considered for the heating and cooling cases, respectively.The reason for the bias can be considered to be the impact of the difference in the increase in outdoor air temperature for each case.The relative sensitivity between the baseline and other cases provides intuitive information for estimating the impact of the key variables.These values are shown in Figure 8, where the two bars represent the simulated and predicted sensitivities.The deviations of the two bars represent the relative prediction errors, as explained in Figure 7.The simulated sensitivity indicates the ratio of the baseline (Case 1) to other cases from EnergyPlus simulations with the newer weather profile (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018).The predicted sensitivity represents that from predictions applying the global coefficient multiplied with the regression model against the old weather profile (1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997).These show that the sensitivities with the global coefficients follow the same trends as the simulated sensitivities.

Conclusions
In this study, simplified regression models were developed using the EnergyPlus reference office building model in South Korea for utilization by non-expert policymakers to aid the formulation of national energy policies and decision making.Nine main variables were selected, which are related to the key building energy policies.Then, the maximum, minimum, and median values were set based on the potential range of values that are to be established as standards and codes in the future.A total of 163 simulation cases were set for the range of key variables (max, min, and med), considering single and correlated impacts on energy consumption.The EnergyPlus simulations were executed as a group, and the inputs (key variables) and outputs (annual heating/cooling energy consumptions) were tabulated.Then, regression was conducted with the least-squares method, and the fitting performance of the proposed model was good.
A global coefficient was introduced to consider the impact of outdoor air temperature increases when predicting future building energy consumption.This multiplier was estimated with two sets of EnergyPlus simulations using old (1982-1997) and recent (2004-2018) weather profile data.Then, evaluations were performed for the future building energy consumption predictions with the estimated regression model and multiplier.
The primary research outcomes are as follows: • The global coefficients considering global warming with increased outdoor air temperatures were estimated to be 1.27 and 0.9 for cooling and heating, respectively; this means 27% more and 10% less energy consumption in 20 years, according to predictions.

Conclusions
In this study, simplified regression models were developed using the EnergyPlus reference office building model in South Korea for utilization by non-expert policymakers to aid the formulation of national energy policies and decision making.Nine main variables were selected, which are related to the key building energy policies.Then, the maximum, minimum, and median values were set based on the potential range of values that are to be established as standards and codes in the future.A total of 163 simulation cases were set for the range of key variables (max, min, and med), considering single and correlated impacts on energy consumption.The EnergyPlus simulations were executed as a group, and the inputs (key variables) and outputs (annual heating/cooling energy consumptions) were tabulated.Then, regression was conducted with the least-squares method, and the fitting performance of the proposed model was good.
A global coefficient was introduced to consider the impact of outdoor air temperature increases when predicting future building energy consumption.This multiplier was estimated with two sets of EnergyPlus simulations using old (1982-1997) and recent (2004-2018) weather profile data.Then, evaluations were performed for the future building energy consumption predictions with the estimated regression model and multiplier.
The primary research outcomes are as follows: • The global coefficients considering global warming with increased outdoor air temperatures were estimated to be 1.27 and 0.9 for cooling and heating, respectively; this means 27% more and 10% less energy consumption in 20 years, according to predictions.

•
The prediction performance of the simplified regression model (163 cases) was generally good, with cvRMSE values of 4.3% and 5.5%, while the maximum absolute errors were 26% and 16% for the heating and cooling cases, respectively.
In this study, the global coefficient was estimated over a span of about 20 years.Accordingly, the yearly coefficient can be derived, i.e., the coefficient can be divided by 20.This finding can be leveraged to predict the heating/cooling energy consumption for specific target years.

Discussion
The regression models developed herein were based on a specific region and weather profile.Strictly, this cannot be generalized to other regions or weather conditions.Thus, separate models need to be developed specifically for combinations of region and weather conditions.This requires engineering costs, so automating with co-simulation using Matlab and EnergyPlus might be needed.Alternatively, the weather or region can be included in the model structure as a variable.For example, the average outdoor air temperature or altitude of the region can be included.Moreover, the climate type (e.g., Koppen climate type) can be applied to the variables.The corresponding reference building models need to be developed with more generalized features covering various regions.
In this study, the number of simulated cases was finite, and manual modification of the EnergyPlus IDFs was possible without excess effort.However, automation of the simulation with different tools would be required if more simulation cases are considered, such as more building cases with different weather and regional conditions, as noted previously.
The results of the current study can be published using web-based tools or applications based on simple programs, such as MS Excel.The polynomial model structure with the estimated coefficient can be uploaded and compiled to a program where the users can select the building type, ranges of key variables, and target years.As for the key variables, up to two values can be selected while the remaining are fixed to nominal values.Cautious selection of the key variables, such as range, is noted with some recommendations of the typical ranges.Moreover, the selection of some key variables (e.g., infiltration and people heat gain) with relatively high prediction errors might need caution.Alternatively, a different global coefficient may be applied with selection rules based on more detailed analyses of the simulation results to provide more precise predictions.

Figure 1 .
Figure 1.Schematic of the study.

Figure 1 .
Figure 1.Schematic of the study.

Figure 2 .
Figure 2. Sensitivity of each variable on heating energy.

Figure 3 .
Figure 3. Sensitivity of each variable on cooling energy.

Figure 2 .
Figure 2. Sensitivity of each variable on heating energy.

Figure 2 .
Figure 2. Sensitivity of each variable on heating energy.

Figure 3 .
Figure 3. Sensitivity of each variable on cooling energy.

Figure 3 .
Figure 3. Sensitivity of each variable on cooling energy.

Figure 4 .
Figure 4. Trend of global surface temperatures.

Figure 4 .
Figure 4. Trend of global surface temperatures.

Figure 4 .
Figure 4. Trend of global surface temperatures.

Figure 6 .
Figure 6.Global coefficient variation for all cases.

Figure 7 .
Figure 7. Relative prediction errors of the cases.

Figure 6 .
Figure 6.Global coefficient variation for all cases.

Figure 6 .
Figure 6.Global coefficient variation for all cases.

Figure 7 .
Figure 7. Relative prediction errors of the cases.Figure 7. Relative prediction errors of the cases.

Figure 7 .
Figure 7. Relative prediction errors of the cases.Figure 7. Relative prediction errors of the cases.

Figure 8 .
Figure 8. Sensitivity from baseline for the heating (top) and cooling (bottom) cases.

Figure 8 .
Figure 8. Sensitivity from baseline for the heating (top) and cooling (bottom) cases.

Table A2 .
Variable ranges for commercial buildings.

Table A3 .
Variable ranges for public buildings.