Sensitivity analysis of building energy performance

Sensitivity analysis of building energy performance: A new simulation-based approach by means of the variance-based global sensitivity analysis

Abstract
This paper proposes a new and efficient methodology for the simulation-based sensitivity analysis of building energy performance, which facilitates decision making in the early phases of the building design stages. In this research, variance-based global sensitivity analysis algorithm is implemented in MATLAB and coupled with EnergyPlus building energy simulation program to clarify predominant variables affecting the building energy efficiency. To investigate the potential and effectiveness of the developed method, it is applied to a single room model; and the impacts of the building design parameters including the building orientation, the window size, the shading overhang specifications, and the wall and glazing material properties on the energy consumption are studied in four major climatic regions of Iran. In the result section, the local and global sensitivity analysis of the annual cooling, heating, lighting and total building electricity consumption is carried out to understand the trend of building energy demands due to the variations of input factors and rank the parameters based on the strength of their influence on the output variables. The results of the sensitivity analysis illustrate that for our typical model, in all climates; the window size is the prevailing parameter on the annual cooling, heating and total building energy demands, while the glazing visible transmittance has the most influence on the annual lighting one. The proposed simulation-based sensitivity analysis method shows a powerful and useful tool that aid architects and building designers to concentrate on the most important parameters in the initial stages of building design in order to enhance the building energy efficiency.

Keywords: Building energy performance, EnergyPlus, jEPlus, Sensitivity analysis, Variance-based method, Total effect index, Parameter prioritization
1. Introduction
Energy is one of the most important resources used by the modern society and is the core of the economic and social activities in the industrialized countries. In this vein, buildings are widely recognized as the largest energy consumer sectors, accounting about 40% of the total energy consumption and 36% of the carbon dioxide emission in the world [1-5]. Accordingly, energy efficiency of buildings has a great potential to decrease energy demands in comparison to the other sectors such as transportation, industry and agriculture.
Nowadays, improvement of buildings energy efficiency has become a major issue for building designers and engineers. One of the main obstacles for obtaining the aim of considerably improving energy efficiency of buildings is the lack of engineering knowledge about the influential and sensitive parameters on the building energy use. Thus, if the relationships and relative importance of envelope design parameters are well understood, it can be possible to obtain the optimum building energy consumption through proper selection of design variables [6].
Study of the factors affecting the energy consumption of building systems is one of the most essential measures for a better understanding of energy conserving design principles and operational strategies. In this regards, sensitivity analysis methods can identify the dominant and key variables influencing the building energy performance and present valuable perspective in prioritizing energy efficiency measures [2, 7]. Generally, sensitivity analysis is the study of how the uncertainty in the output of a system can be apportioned to different sources of uncertainty in its inputs [8]. In other words, sensitivity analysis refers to understanding how the design variables of a simulink model influence the model outputs. The techniques for sensitivity analysis applied in the domain of building energy performance can be broadly categorized into local and global approaches [7, 9].
Local sensitivity analysis belongs to the class of the one-factor-at-a-time (OFAT) methods [7]. The major objective of the OFAT sensitivity analysis approach is to study the changes in output model with the changes in input model in order to understand the effect of each parameter on the output variables. According to this method, the input of each decision variable is changed while all other building parameters are held fixed. This technique can be repeated iteratively with other variables [9].
Hoffman and Gardner [10] presented a preliminary method to determine the sensitivity index of each design parameter by calculating the output % difference for the extreme values of the design parameter. The relation to evaluate the sensitivity index (SI) is:

SI=(Y_max-Y_min)/Y_max ”100 (1)

where Y_max and Y_min represent the maximum and minimum output values, respectively, resulting from changing the design variable over its whole range. If the sensitivity index reaches a defined critical value, the design variable is considered to be important and it is included in a further analysis [10, 11]. Although OFAT sensitivity analysis methods are very straightforward to establish parameter dependencies of the solutions, and useful for studying models with a few uncertain parameters, these methods only explores the variations of energy performance around a single point or a base case, and the interactions of other design parameters are not considered [7, 9, 12]. In addition, the fatal limitation of local sensitivity analysis methods is that it is unwarranted when the model input is uncertain and when the model is of unknown linearity [13, 14]. In this respect, local sensitivity analysis methods give quite misleading results for the non-linear models.
In global sensitivity methods, output variability due to one design parameter is evaluated by varying all the other parameters at the same time, while also taking account of the effect of the other design parameters interactions over the whole input space [15]. Global sensitivity analysis approach uses a representative set of samples to explore the design space, which provides robust sensitivity measures in the presence of nonlinearity and interactions among the parameters compared to the local sensitivity analysis. As a result, the global methods are considered as a more reliable and more precise techniques [7]. However, the main drawback of the global sensitivity analysis methods is their high computational costs as complexity and numbers of design parameters increase in comparison with the local one.
There are several methods of global sensitivity analysis in building energy performance analysis such as screening-based method, variance-based, meta-model based method and regression methods. Among various global methods, variance-based sensitivity analysis methods have gained popularity [16].
In addition, some Whole building energy analysis and thermal load simulation programs such as DOE-2, EnergyPlus, ESP-r, TRNSYS can be used in the study of sensitivity analysis of the buildings performance [7]. It should be underlined that the careful selection of the prevailing building design factors is often a difficult task that requires good engineering knowledge of the simulation model. Therefore, combining an appropriate global sensitivity analysis procedure with a whole building energy simulation software makes it possible to achieve a powerful and worthy way to rank the design parameters based on their importance on the energy consumption in the shortest possible time.
Over the past years, simulation-based sensitivity analyses have been widely studied by many researchers to recognize the most influential parameters affecting the building energy performance. Tian [7] presented an admirable review on the application of sensitivity analysis in building thermal performance analysis to provide the practical advice on how to effectively use sensitivity analysis in different settings, and make recommendations for applying sensitivity analysis in building performance in the future. In another research, Tian et al. [1] used regression sensitivity analysis to understand the relationship between input parameters and building energy performance for creation a reliable energy model to estimate building energy consumption. Yu et al. [6] performed a sensitivity analysis of energy performance to assess the impacts of building envelope design parameters and identify the important characteristics four cities of China. Ruiz [17] coupled TRNSYS thermal simulation engine and MATLAB to identify the most influential parameters affecting the final energy consumption in office buildings. Furthermore, Tian and de Wilde [18] explored the uncertainties and sensitivities in the prediction of the thermal performance of buildings to assess the adaptability and resilience of buildings to changing climate conditions. de Wilde et al. [19] presented the application of two-dimensional Monte Carlo analysis to an office building to identify the key factors for uncertainty in the prediction of overheating and energy use. Capozzoli et al. [20] carried out a sensitivity analysis based on an extensive study of the linear thermal transmittance value of many types of thermal bridge using ANOVA-FAST method. Moreover, Lam and Hui [21] examined the sensitivity of energy performance of office buildings in Hong Kong to identify important input design parameters from points on the annual building energy consumption, peak design loads and building load profiles. In a similar work, Tavares and Martins [22] carried out a sensitivity analysis of some public building parameters at the center region of Portugal, relating to wall types, roofing, glazing and window frames, external shading devices, infiltration rates, air changes due to mechanical ventilation, equipment power density, HVAC systems, thermostat setting and tolerance range. Recently, Sun [23] performed a local sensitivity analysis method on a constructed dynamic simulation platform to study the impacts of each macro-parameter on the sizes of key net zero energy building (NZEB) systems to optimize the initial investment cost of systems in a NZEB. Additionally, De Wit and Augenbroe [24] applied uncertainty and sensitivity analysis with building energy simulation tools to demonstrate the effect of model uncertainties; and their potential impact on design decisions in order to addresses uncertainties in building performance evaluations. Burhenne et al. [25] analyzed the uncertainty associated with model parameters of a building using a solar thermal collector for heating and domestic hot water using Monte Carlo simulations. Besides, Dowd and Mourshed [26] investigated the sensitivity of building envelope construction comprising multi-layered wall construction and varying sizes of glazing on energy demand in a typical commercial building through dynamic thermal simulation. Basinska et al. [27] applied the global costs calculation method with regard to the energy assessment for the technical equipment of buildings by means of the net present value method in accordance with the cost-optimal draft regulation. Mainini et al. [28] assessed the sensitivity analysis of different locations, the orientation and window to wall ratio (WWR) value to evaluate primary energy use for heating, lighting and cooling energy demand for conventional Italian single office units equipped with static metal mesh shading devices with different geometries and openness factor values. Wang et al. [29] investigated uncertainties in energy consumption due to actual weather and building operational practices using a simulation-based analysis of a medium-size office building. Daly et al. [30] examined the sensitivity of total predicted building energy consumption to hard-to-measure simulation inputs for two template Australian office buildings. Wang et al. [31] analyzed the influences of the initial parameters including the technical, economic and environmental parameters, the building loads and the optimization setting parameters on the optimal decision variables and the performances of building cooling, heating and power system. Hemsath et al. [32] presented a methodology to evaluate building form to compare energy consumption of geometric variations and material considerations through two types of sensitivity analyses including the linear screening local sensitivity index and a Morris global sensitivity. Rasouli et al. [33] used local sensitivity analysis to evaluate the impact of uncertainty of building and HVAC system parameters on the energy savings potential and economics of energy recovery ventilators (ERVs) for an office building located in Chicago using TRNSYS simulations. Hygh et al. [34] used EnergyPlus program and a Monte Carlo framework in order to develop a multivariate linear regression model to quantify building energy performance in early design stages. Mauro et al. [35] employed simulation-based uncertainty analysis to identify the optimal representative building sample (RBS) size, followed by simulation-based sensitivity analysis to identify proper retrofit actions via the coupling between EnergyPlus and MATLAB. In the similar work, Delgarm et al. [36] integrated EnergyPlus with MATLAB program using jEPlus to study the effect of building design parameters, including the building orientation, shading overhang specifications, window size, glazing and the wall material properties on the building energy consumption in four major climatic regions of Iran. Mechri et al. [37] applied analysis of variance (ANOVA) method to determine the most effective design parameters affecting building energy performance for a typical office building in Italy. Spitz et al. [38] used the Sobol method to determine influential parameters in the building’s energy performance and to identify the influence of parameter uncertainty on the building performance for an experimental house in France. de Wilde and Tian [39] used rank regression and multivariate adaptive regression splines (MARS) global sensitivity analysis methods to analyze the impact of climate change on the thermal performance of a theoretical office in the UK in terms of annual carbon emissions, overheating risk, and work performance using Latin Hypercube sampling in SimLab and EnergyPlus. Eisenhower et al. [40] applied a meta-model method for sensitivity analysis of an EnergyPlus model with a large number of uncertain parameters to illustrate which parameter type influences the uncertainty in the two outputs of a building model including the district hot water consumption in winter and the facility electricity in summer. Lam et al. [41] used the analysis of variances (ANOVA) approach to quantify the impact of nine curtain wall design parameters on the energy consumption of an office space in the perimeter zone of a typical office building in Montreal. Shen and Tzempelikos [42] presented a global uncertainty and sensitivity analysis of daylighting and energy performance by means of the extended Fourier amplitude sensitivity testing (FAST) module in SimLab for private offices with automated interior roller shades.
In this research work, variance-based global sensitivity analysis algorithm implemented in MATLAB couples with EnergyPlus building energy simulation software using jEPlus as an interface environment to prioritize input design parameters according to their impact and importance on the building energy consumption, and to determine which parameters should be included in depth-examination. After presentation of the coupling strategy, the purposed method is applied to a single test case and the effects of building design parameters such as the room orientation, the window size, the shading overhang properties, and the wall and glazing material characteristics on the building energy consumption are entirely given for four major climate regions of Iran.

2. Methodology
2.1. Variance-based sensitivity analysis method
Variance-based method is a form of global sensitivity analysis, which was first employed by chemists in the early 1970s [13, 14]. The variance-based method is to decompose the uncertainty of outputs for the corresponding inputs [7, 43]. Two main sensitivity measures used in this approach are the first-order effect index (S_i) and total effect index (S_Ti).
Let us consider a given model in the form of Y=f(X), where Y is the model output and X=[x_1,x_1,x_1,’,x_n] is a vector of n input parameter. In the variance-based method, total unconditional variance, V(Y), can be decomposed into partial variances as follows [43-46]:

V(Y)=’_i^n’V_i +’_i^n”_(j>i)^n’V_ij +’+V_(1,2,3,’,n) (2)
Where,

V_i=V_(x_i ) [E_(X~i) (Y’X_i=’x_i’^* )]
(3)
V_ij=V_(x_i ) [E_(X~i) (Y’X_i=’x_i’^*,X_j=’x_j’^* )]-V_i-V_j (4)

and so on for the higher order terms. In the above equation, the X~i notation indicates the set of all variables except X_i. In addition, ‘_i^n’V_i is the sum of partial variances that include main effects of each input parameters and ‘_i^n”_(j>i)^n’V_ij includes all the partial variances main effects of interaction of two input parameters and so on. The above variance decomposition shows how the variance of the model output can be decomposed into terms attributable to each input, as well as the interaction effects between them. Together, all terms sum to the total variance of the model output.
A direct variance-based measure of sensitivity ‘(S’_i), called the “first-order sensitivity index”, or “main effect index” is stated as follows:

S_i=V_i/(V(Y))=(V_(x_i ) [E_(X~i) (Y’X_i)])/(V(Y)) (5)

where V_(x_i ) [E_(X~i) (Y’X_i)] is the expected reduction in variance that would be obtained if X_i could be fixed. The first-order sensitivity index ‘(S’_i) measures how the ith factor contributes to V(Y) without taking into account the interactions among factors. In other words, it represents the main effect contribution of each input factor to the variance of the output.
Another popular variance-based measure is the “total-effect index” or “total-order index”, which defined as follows:
S_Ti=(E_(X~i) [V_(x_i ) (Y’X_(~i))])/(V(Y))=1-(V_(X~i) [E_(x_i ) (Y’X_(~i))])/(V(Y)) (6)
where E_(X~i) [V_(x_i ) (Y’X_(~i))] is the expected variance that would be left if all factors but X_i could be fixed. This holds since V_(X~i) [E_(x_i ) (Y’X_(~i))] is the expected reduction in variance that would be obtained if all factors but X_i could be fixed. The total effects index ‘(S’_Ti) accounts the total contributions to the output variance due to the corresponding input, which includes both first order and higher-order effects because of interactions among inputs. As a result, S_Ti-S_i indicates the effects of interactions between variables. By definition, S_Ti is greater than S_i, or equal to S_i in the case that X_i is not involved in any interaction with other input factors. Moreover, it should be noted that S_Ti=0 implies that X_i is noninfluential and can be fixed anywhere in its distribution without affecting the variance of the output. Additionally, for additive models S_i =S_Ti, while for non-additive models S_Ti > S_i [43-46].
The variance-based method is an appropriate sensitivity analysis method for complex nonlinear and non-additive models [7, 43-46]. However, the disadvantage of this approach is its more computational cost in comparison to the other global sensitivity analysis methods.
There are a number of possible Monte Carlo estimators available to obtain the values of V(Y), S_i and S_Ti. In this study, the unconditional variance and the total order index are estimated by quasi-Monte Carlo estimators [8]:

V(Y)=(1/N) ‘_(n=1)^N'(‘y_A’^((n)) )^2 -((1/N) ‘_(n=1)^N”y_A’^((n) ) )^2
(7)
V_(x_i ) [E_(X~i) (Y’X_i )]=V(Y)-(1/2N) ‘_(n=1)^N””(y’_B’^((n) )-‘y_(C_i )’^((n) ))’^2
(8)
E_(X~i) [V_(x_i ) (Y’X_(~i) )]=(1/2N) ‘_(n=1)^N””(y’_A’^((n) )-‘y_(C_i )’^((n) ))’^2 (9)

Where N is sample size and ‘y_A’^((n) ), ‘y_B’^((n) ) and ‘y_(C_i )’^((n) ) are model outputs. Sobol quasi-random sequences are used to generate two sets of data, that is, matrix A and B corresponding to model outputs of ‘y_A’^((n) ) and ‘y_B’^((n) ). From A and B Matrices, matrix C_i is created such that all the dimensions in the matrix C_i are taken from matrix A, except ith column, which is taken from matrix B. The quasi-random sampling method is the most popular Monte Carlo method because the number of model executions needed for Sobol sensitivity analysis is significantly reduced in comparison with conventional Monte Carlo methods. Moreover, the quasi-random sequence helps to distribute the sampling points as uniformly as possible in the parameter space and avoid clustering, and to increase the convergence rate [8, 9, 44].
Because there are n factors, the cost of this approach is N +N runs of the model for matrices A,B, plus n times N to estimate n times the output vector corresponding to matrix C_i. The total computational cost is hence N(n+2). A higher N value would result in better estimation of sensitivity indices. In this study, we have N=3000 and n=11 columns, to solve Equations (7), (8) and (9).

2.2. Building energy simulation applications
2.2.1. EnergyPlus
EnergyPlus is a robust whole-building performance simulation program that combines the best capabilities and features from BLAST and DOE-2 along with new functionality [47]. EnergyPlus evaluates the heating and cooling loads necessary to maintain thermal control set points, conditions throughout a secondary HVAC system and coil loads, and the energy use of primary plant equipment of buildings by the heat balance method. This method considers all heat balances on outdoor and indoor surfaces and transient heat conduction through the building [48]. The simulation results of EnergyPlus have been validated through numerous analytical, comparative, and empirical tests. In the present study, EnergyPlus software is used to assess the building energy demands.

2.2.2. jEPlus
jEPlus is a building energy simulation manager tool which has been developed by Yi Zhang in 2009 [49, 50] with the purpose of managing complex parametric analysis on multiple design parameters using EnergyPlus and Transys. jEPlus tool has been designed to assist setting up parametric runs with models. In this way, building designers can quickly set up large amount of building simulation runs to explore the design options in order to select the most appropriate building design alternatives.

2.3. Setup of EnergyPlus and variance-based method
In order to accomplish the simulation-based sensitivity analysis of the building energy performance, variance-based sensitivity analysis algorithm has been written in MATLAB environment. It should be underlined that the evaluation of the simulation outputs are retrieved from EnergyPlus output files directly. In other words, MATLAB deals with EnergyPlus as a generator of hidden functions. Therefore, it is necessary to make a communication between EnergyPlus and MATLAB programs. Through an initiative, coupling functions have been created in MATLAB environment to launch jEPlus tool, which plays as an interface between MATLAB and EnergyPlus simulation software to identify and translate the building design parameters and output variables into EnergyPlus building model file. Afterwards, EnergyPlus is used to simulate the annual building energy consumptions. Finally, variance-based global sensitivity analysis is used to read the EnergyPlus simulation results to evaluate the sensitivity of the building energy demands to each input design variables. In this way, the communication between EnergyPlus and MATLAB programs will be obtained and therefore EnergyPlus will be fully controlled by MATLAB environment. With the proposed methodology, a powerful and efficient way for sensitivity analysis of building energy performance can be achieved without any restriction in choosing their sensitivity analysis algorithms; input building decision factors and output variables. Fig. 1 shows the coupling framework of the suggested simulation-based sensitivity analysis method.

Fig. 1. Flowchart of the purposed simulation-based sensitivity analysis approach
3. A Case Study
3.1. Description of the studied building model
In order to evaluate the capability and effectiveness of the proposed optimization approach, the developed method is applied to a single thermal zone test case room in a multi-story building to investigate the effect of architectural design parameters on the room energy performance at different climatic regions of Iran.
Firstly, SketchUp [51] 3D modeling software package has been used to define the building geometry and the thermal zone. Then EnergyPlus [52] building energy simulation program is used for modeling the thermo-physical properties of the building envelope, shading overhang system, artificial lighting and its room controller daylight sensor, for the assignment of the schedule of the artificial lighting and for modeling of the HVAC system and its zone thermostat controller. Fig. 2 shows the architectural schematic view of the baseline room. It should be noted that, in the initial building model, only the southern wall of the room is exposed to the sunlight and the outside air. The model orientation is in degrees with counter clockwise direction.
Fig. 2. Schematic view of the EnergyPlus building model

The length, width, and height of the room are 3 m. It has a double-layer clear glazing window with 13 mm air space equipped with an overhang. The overhang height above the window and its left and right extensions are fixed at zero. No blind is considered for the window. It is assumed that the building is equipped with a packaged terminal heat pump (PTHP) air conditioning system with a COP of 3 in heating mode and a COP of 2.75 in cooling operation. The heating and cooling set point temperatures are 20’C and 27’C, respectively, for operating strategy of the zone thermostat control. The room is equipped with 90 W compact fluorescent lamp (CFL) lighting system. The schedule of the artificial lighting system has been set to work twenty-four hours a day. Moreover, the model has a daylighting controller sensor to continually dim the lighting automatically with the threshold of 500 lux. When illuminance is higher than 500 lux, it is considered high enough not to require artificial lighting, and the lighting system is turned off. To focus on the thermal load due to the room exterior wall, other loads such as occupants and infiltration, does not take into account in this research. Table 1 summarizes the physical characteristics of the baseline case room, which are common in Iran.

Table 1. Physical characteristics of the examined case study
Component Property Value
Wall Conductivity (W/mK) 0.57
Thickness (m) 0.2
Specific heat (J/kgK) 790
Density (kg/m3) 1120
Floor / Roof Conductivity (W/mK) 1.11
Thickness (m) 0.1
Specific heat (J/kgK) 920
Density (kg/m3) 800

3.2. Climatic regions of Iran
Iran is located in the Middle East with an area of about 1,648,000 square kilometers; lies between latitudes 24” and 40” N, and longitudes 44” and 64” E. Iran has an arid or semiarid climate characterized by long, hot, dry summers and short, cool winters. Iran can be divided into four major climate zones, including mild, warm-dry, warm-humid and cold climates, as shown in Fig. 3 [53]. In the present paper, Tehran, Kerman, Bandar Abbas and Tabriz have been considered as representative cities for these climatic regions, respectively. According to the national center of climatology of Iran, the geographical locations of the representative cities are presented in Table 2.
Fig. 3. Climatic regions of Iran [53].

Table 2. Geographical location of the representative cities
City Latitude Longitude Elevation
Bandar Abass 27.20 ”N 56.15 ”E 10.00 m
Kerman 30.25 ”N 56.97 ”E 1754 m
Tehran 35.68 ”N 51.30 ”E 1191 m
Tabriz 37.80 ”N 46.25 ”E 1361 m

3.3. Input and output variables
Table 3 illustrates the list of input design parameters including the building orientation, the window size, the shading overhang specifications, and the wall and glazing material features as well as their range of variability to study their impacts on the building energy consumption. Additionally, to investigate the sensitivity analysis of the building energy performance, four important indicators related to the energy efficiency level of buildings are assigned in terms of the annual cooling, heating, lighting and the total building energy consumption.
Table 3 Description and range of the input design variables.
Variable name Symbol Unit Initial value Range
Building orientation BO ‘ 0 [0,360)
Window size WS m2 4 (0,9)
Glazing solar transmittance GST – 0.775 [0,1)
Glazing visible transmittance GVT – 0.881 [0,1)
Glazing conductivity GC W/mK 0.9 [0.1,1]
Wall thermal absorptance WTA – 0.9 [0,1)
Wall solar absorptance WSA – 0.7 [0,1]
Wall visible absorptance WVA – 0.7 [0,1]
Wall conductivity WC W/mK 0.57 [0.1,1]
Overhang tilt angle OTA ‘ 90 [0,180]
Overhang depth OD m 0.3 (0,0.5]

4. Results and discussion
In this section, the results of the purposed simulation-based sensitivity analysis of the building energy performance are provided based on two approaches. The first approach concerns with the one-factor-at-a-time (OFAT) method to understand how different design factors may influence on the building energy performance and to study the trend of the annual cooling, heating, lighting and total building electricity consumption with the design parameters changes at Tehran located in the mild climate region of Iran. At the second approach, the variance-based global sensitivity analysis method is conducted to determine the total effect index for each input design parameter and to clarify the most influential factors affecting the building energy performance at four different weather conditions of Iran.

Local sensitivity analysis
In this part, the results of local sensitivity analysis method are presented at Tehran located in the mild climate zone. Therefore, each time one factor is selected from the input building decision parameters, e.g. the room orientation, the window size, the shading overhang specifications, and the wall and glazing material features. Then, each parameter is changed over its entire range, but all the other input variables are considered to be fixed at their baseline mode.

4.1.1. Impacts of building orientation
Fig. 4 depicts the effect of the building orientation changes on the annual cooling, heating, lighting and total building electricity consumption, assuming that the rest of the input design variables are unchanged. As can be seen in Fig. 4, the building orientation has different and strong effects on the building energy demands. Moreover, it can be clearly deduced that the building energy performance has a fully nonlinear and complex behavior with the room orientation variations. In this case, the use of local sensitivity analysis may be thoroughly incorrect and misleading. Nevertheless, the impact of building orientation demonstrated that in order to have the minimum annual heating energy demand, the facing of the building model should be to the south to get the most thermal energy from the sun to reduce the room heating load as much as possible. On the other hand, to have the minimum annual lighting electricity, it should be to the east or west to achieve the most lighting energy from the sun to bring down the lighting energy demand to the lowest possible amount. Besides, in order to have the minimum annual cooling electricity consumption, the facing of the building model should be to the north with a rotation of 180” not to let the solar energy come in the room through the window to lessen the cooling electricity as far as possible. While in this case, the heating and lighting systems consume a lot of electricity. It is worth mentioning that for our typical model, the building model has the lowest energy demand, when its facing is to the south, regardless of considering the interaction effects of input parameters on each other.
Overall, in the analysis of the impacts of building orientation on the building energy use, the one-factor-at-a-time (OFAT) method was incapable to identify that which one of the building output variables is more sensitive to the building orientation, mainly due to nonlinearity of the process.
Fig. 4. Effect of building orientation on the annual cooling, heating, lighting and total building energy consumption at Tehran
4.1.2. Impacts of window size
Fig. 5 shows the trend of the annual cooling, heating, lighting and total building electricity with the window size changes over its allowable range, supposing that all the other design parameters are constant. It can be seen in Fig. 5, with the increase of window size value, the annual cooling energy use linearly increased about 58% compared to the initial model due to the excessive rise of the solar energy into the room model, which led to decline the annual heating energy demand linearly nearly 0.1%. Besides, the lighting energy demands exponentially decreased close to 32% in comparison to the basic test case, because of the increment of the lighting energy from the outside into the building model. Nevertheless, the impact of the window size on the total annual building energy use was completely different. As it is observed in Fig. 5, firstly, the total building energy use decreases, but after an area of 1.62 m2, it increases largely. The reason is that a larger window allows more solar gains to come into the room, which leads to diminish the heating and lighting electricity consumption. However, with the enormous increase in solar gains with the further enhance of the window to wall ratio (WWR), the annual cooling energy demand enhances dramatically, so that it leads to increase the total building electricity use greatly.
As an overall result, for our typical model, with the window size variations, the annual cooling energy use varied a lot, while there was a little change in the annual heating and lighting electricity consumption. In other words, the impact of window size on the annual cooling energy is far greater than that on the annual heating and lighting ones.
Fig. 5. Effect of window size on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.3. Impacts of glazing visible transmittance
Fig. 6 demonstrates the impact of glazing visible transmittance changes on the annual cooling, heating, lighting and total building electricity consumption. As is depicted in Fig. 6, with the increase of glazing visible transmittance value, the annual cooling, lighting and total building energy use decreased exponentially about 3.2, 34 and 10.3%, respectively, compared to the initial room model, whereas the annual heating one exponentially enhanced a little close to 1%. Thus, it can be concluded that the glazing visible transmittance has the most impact on the annual lighting, total, cooling and heating energy demand, respectively.

Fig. 6. Effect of glazing visible transmittance on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.4. Impacts of glazing solar transmittance
Fig. 7 indicates the influence of glazing solar transmittance on the annual cooling, heating, lighting and total building electricity consumption. As it can be seen in Fig. 7, with the increase of glazing solar transmittance value, the annual cooling energy demand linearly increased about 21% compared to the baseline model. However, the annual heating one linearly decreased close to 12%, due to the increase of thermal energy from the sun in to the building model and it had no effect on the annual lighting energy use. Moreover, the total annual building electricity consumption decreased exponentially almost 2.3% in comparison with the basic model. Therefore, it may be inferred that the glazing solar transmittance has the most influence on the annual cooling, heating and total building loads, respectively. However, it is an ineffectual parameter on the annual lighting one.

Fig. 7. Effect of glazing solar transmittance on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.5. Impacts of glazing Conductivity
In Fig. 8, the impact of glazing conductivity factor on the annual cooling, heating, lighting and total building electricity consumption is illustrated. As Fig. 8 shows, with the increase of glazing conductivity value, the annual cooling energy demand exponentially decreased about 0.51%, while the annual heating and total building energy demand exponentially enhanced close to 1 and 0.03%, respectively. Nevertheless, it had no effect on the lighting one.
In this respect, it can be concluded that the glazing conductivity parameter has the most influence on the annual heating, cooling, and total energy consumption, respectively. However, it is an inoperative and inconsequential variable on the annual lighting one.
Fig. 8. Effect of glazing conductivity on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.6. Impacts of wall thermal absorptance
Fig. 9 depicts the trend of the annual cooling, heating, lighting and total building electricity use with the variations of the wall thermal absorptance value, assuming that the other design parameters are unchanged at their initial value.
As it is can be noticed from Fig. 9, as the wall thermal absorptance value enhanced from its minimum to maximum value, the annual cooling energy demand almost linearly decreased about 8.5% compared to the basic model, whereas the annual heating one increased close to 10%. On the other hand, the wall thermal absorptance had no effect on the lighting energy use and the total building energy demand exponentially reduced almost 0.45%, in comparison to the initial room model. Therefore, it may be inferred that the wall thermal absorptance has the most influence on the annual heating, cooling and total annual building electricity consumption, respectively. However, it is an inoperative and inconsequential variable on the annual lighting energy demand.
Fig. 9. Effect of wall thermal absorptance on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.7. Impacts of wall solar absorptance
Fig. 10 shows the effect of the wall solar absorptance on the annual cooling, heating, lighting and total building electricity consumption.
As it is observed in Fig. 10, with the increase of wall solar absorptance amount, although it had no effect on the lighting energy demand, the annual cooling energy consumption linearly increased 11.4%, which led to bring down the annual heating energy demand linearly about 9.6%. However, its impact on the total annual building energy consumption was quite different. As Fig. 10 indicates, firstly, the total annual building energy consumption decreased, but after a value of 0.38, it increased. The reason is that a larger wall solar absorptance allows more solar energy to be absorbed by the wall, which leads to diminish the heating energy demand of the room. However, with the enormous increase in the solar heating gains, the cooling energy demands increases dramatically, which leads to a sharp rise in the total energy consumption. As an overall result, it might be inferred that the wall solar absorptance parameter has the most impact on the annual cooling and heating electricity consumption, respectively. However, it is an ineffective factor on the annual lighting one.

Fig. 10. Effect of wall solar absorptance on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.8. Impacts of wall visible absorptance
Fig. 11 illustrates the effect of the wall visible absorptance changes on the annual cooling, heating, lighting and total building electricity consumption.
As it is shown in Fig. 11, with the increase of wall solar absorptance value over its entire range, it had no effect on the annual cooling and heating energy demands. In addition, the lighting energy use linearly increased approximately 0.08% in comparison with the initial model, which led to enhance the total building energy consumption linearly close to 0.004%.
Therefore, it may be understood that the wall visible absorptance factor has the most influence on the lighting and total building energy use, respectively. However, it is an ineffectual element on the annual cooling and heating one. Furthermore, it can be clearly concluded that the wall visible absorptance has too small impact on the energy consumption due to a slight changes of building energy demands with the changes of wall visible absorptance.

Fig. 11. Effect of wall visible absorptance on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.9. Impacts of wall conductivity
Fig. 12 presents the impact of wall conductivity variable on the annual cooling, heating, lighting and total building electricity consumption. As it is observed in Fig. 12, with the increase of wall conductivity amount, the annual cooling, heating and total building electricity consumption almost nearly linearly increased about 4.6, 3.3 and 3.1% respectively, while the lighting one had no change with the changes of the wall conductivity value. In other words, the wall conductivity has the most influence on the annual cooling, heating and total energy use, respectively. However, it is an unimportant and insignificant variable on the annual lighting energy demand.
Fig. 12. Effect of wall conductivity on the annual cooling, heating, lighting and total building energy consumption at Tehran

4.1.10. Impacts of overhang tilt angle
Figs. 13 shows the effect of overhang tilt angle on the annual cooling, heating, lighting and total building electricity consumption, supposing that the other design parameters are considered fixed at their initial amount. As given in Fig. 13, it can be clearly concluded that the building energy performance has a nonlinear behavior with the overhang tilt angle changes. Therefore, the use of local sensitivity analysis can be entirely misleading. Nevertheless, by increasing the angle from the minimum to maximum value in its allowable range, firstly, the annual cooling electricity consumption decreased and then in the angel of 127”, it increased sharply. The reason for such behavior is due to the lack of permission the solar lighting energy to come into the room after the angle of 127”, and therefore the embedded electric lamp in the room lights up to provide room lighting. As a result, the heat from the electric lamp increases in the room and thus the cooling system turns on. In contrast to the annual cooling electricity consumption behavior, the heating one first increased and then in the angel of 152”, it reduced. However, with the increase of overhang tilt angle, the lighting energy demand increased continuously about 0.4% in order to supply the room lighting. Moreover, it is should be noted that for our typical model, the building has the lowest total energy demand in the angel of 120”, regardless of considering the interaction of input building design parameters on each other.
As an Overall result, in the analysis of the impacts of overhang tilt angle on the building energy consumption, the one-factor-at-a-time (OFAT) method was unable to determine that which one of the building output variables is more sensitive to the overhang tilt angle, mainly due to nonlinearity of the process.
Fig. 13. Effect of overhang tilt angle on the annual cooling, heating, lighting and total building energy consumption at Tehran

Source: Essay UK - http://www.essay.uk.com/essays/engineering/sensitivity-analysis-building-energy-performance/


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