A method of probabilistic risk assessment for energy performance and cost using building energy simulation

Energy and Buildings 110 (2016) 1–12

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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild

A method of probabilistic risk assessment for energy performance and cost using building energy simulation Shang Sun, Karen Kensek ∗ , Douglas Noble, Marc Schiler University of Southern California, School of Architecture, United States

a r t i c l e

i n f o

Article history: Received 16 July 2015 Received in revised form 28 September 2015 Accepted 29 September 2015 Available online 8 October 2015 Keywords: Building energy modeling (BEM) Building information modeling (BIM) Energy efficiency Energy use intensity (EUI) Sensitivity analysis Risk assessment Monte Carlo method Latin hypercube sampling

a b s t r a c t Energy efficient buildings rely on simulation to predict energy performance. However, problems associated with simulation tools can lead to surprises when discrepancies are found between actual and predicted building energy performance; this frustrates building owners, investors, and designers. A probabilistic method of risk assessment for the calculation of energy use intensity and total utility cost in energy performance has been developed. Sensitive and uncertain parameters were selected and given a probability distribution instead of one fixed value for the simulations. Latin hypercube sampling was used to generate input combinations with parameter values picked stochastically from distributions based on the Monte Carlo method. With these input combinations, 10,000 simulations on seven distributed parameters were run using a cloud processing service. The output data, energy use intensity and energy cost, were analyzed using curve-fitting techniques to find a best-fit distribution, which could be used for risk analysis of energy performance and cost. The results illustrate the probability and reliability of prediction within a specific range. Instead of relying on a single value, these curves would help designers better evaluate design alternatives, and the probability distribution of energy performance and cost would be useful in making decisions about investments for energy efficient projects. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The rapidly growing global energy consumption by buildings has exceeded the other major sectors of industrial and transportation in the past 20 years, and the upward trend continues with growth in population, increasing demand for building services, and comfort levels [1]. As a necessity instead of a matter of choice or luxury, energy efficient buildings ushered in an era of development including the updating of technology, new materials, design ideas, and advanced equipment. Although there is a burst of growing popularity in energy efficient buildings, the growth of this industry does not seem as strong as expected. In the United States in 2008, non-residential energy efficient construction starts were only 10% [2]. Among multiple difficulties like financial feasibility and public awareness of environment and policy, the performance risk in energy efficient building projects is a significant issue hindering the development of this industry. Performance risk is the possibility of occurrence of discrepancy between expected energy performance during the design stage and

∗ Corresponding author. E-mail addresses: [email protected] (S. Sun), [email protected] (K. Kensek), [email protected] (D. Noble), [email protected] (M. Schiler). http://dx.doi.org/10.1016/j.enbuild.2015.09.070 0378-7788/© 2015 Elsevier B.V. All rights reserved.

real energy performance after project completion. In a major review of the US Energy Service Company (ESCO) market, 40% of projects had savings that deviated by more than 15% from projections, and in 30% of the cases, predicted savings were greater than actual [3]. Among 120 LEED certified projects, 25% of the buildings show savings in excess of 50%, well above any predicted outcomes, while 21% show unanticipated measured losses [4]. Other studies also show performance uncertainty in LEED certified buildings; in one study, the results show that although collectively, the LEED buildings use the same amount of source energy as do other NYC office buildings, LEED Gold buildings show a 20% reduction while Certified and Silver level actually use more energy [5]. ESCOs can also benefit from a financial risk analysis to assess the probability of the payback period of their investment for making a profit. An analysis of residential construction by Soratana and Marriott showed a likely payback period between 16 and 55 years (mean 35 years), which is longer than the typical contract lengths (7–20 years). The auditor’s experience (in the parameter “offered savings”) had a major impact. This study showed that overall the residential market is risky for ESCOs [6]. Risks in energy efficient building projects lie in uncertainties and volatilities of many aspects including conceptual design, engineering simulation, construction, operation, maintenance, and verification and other extrinsic factors like energy cost, policy, and

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so on. Computer simulation is the key step of predicting building energy performance; however, despite preconceptions that it is accurate and precise, it has many uncertainties that lead to an unreliable prediction since most of the inputs are estimates from experience or code requirements instead of real or measured data. Even if a very high quality simulation has been accomplished, risk is still introduced in the building construction [7,8] and operation phase. No construction can be done 100% as the design team expected [9]. In operation, occupants’ behaviors also have significant influence on energy performance, 4.2% in one study [10]. A 3 year study of a multifamily residential complex in Switzerland, had what was they thought to be a not unusual difference of 50% between expected and real thermal energy consumption that they attributed to conditions of occupancy use, performance of new energy technologies, and the weather [11]. Other researchers have determined that occupant behavior in setting the thermostat and ventilation flow rates over-rule building considerations such as window g and U values, wall conductivity, and orientation for heating loads, which are important parameters when their behavior is not taken into account [12]. Research in ongoing to create methods of predicting occupant behavior [13,14], but currently these methods are often not included in popular energy software, and they are difficult to include because of the paucity of experimental data or models that include simulated occupant behavior [15]. All these factors affect the energy performance of buildings and unfortunately are all difficult to predict. Mills and Weiss identified the risks associated with energy efficiency projects into two categories: intrinsic and extrinsic volatilities and the risk into five categories: economic, contextual, technology, operation, and measurement and verification [16]. Van Gelder et al. propose a methodology that includes pre-processing for selection of parameters, screening and updating, and then probabilistic design. The authors’ intent was to use effectiveness and robustness indicators that are used in the manufacturing industry to also enable evaluation of the results: “effectiveness is defined as the ability of the design option to optimize the performance, while robustness is defined as the ability to stabilize this performance for the entire range of input uncertainties” [17]. Uncertainty in building performance must be taken into account [18]. Less has been done for incorporating overall risk assessment into energy simulations that takes multiple factors into consideration. Macdonald and Strachan reviewed the sources of uncertainty in the predictions from simulation with techniques of differential sensitivity analysis and Monte Carlo analysis and then incorporated uncertainty analysis into ESP-r [19]. Hopfe and Hensen from investigated the potential design support by applying uncertainty analysis in building performance simulation [20]. Heo et el. also cast concern on certain assumptions in energy modeling even for building retrofits where more is known than for new construction, specifically that the values used to create the “good fit between monitored and computed energy consumption” does not mean that those values are actually the ones that represent reality and concludes that “the current methods are not capable to support retrofit decision-makings at large scale with adequate risk management” [21]. They propose their own probabilistic methodology based on Bayesian calibration of normative energy models. Tian provides an overall review of sensitivity analysis methods including how to deal with correlated inputs and the difference between global and local techniques [22]. Spitz et al. used three sensitivity analysis methods: local sensitivity, correlation, and global sensitivity. They used EnergyPlus for simulations and validated their results against measured values in an experimental house that is a full scale test facility. Their metric was indoor air temperature. Because they used both real data and simulations, they were able to evaluate the uncertainties of the sensor readings and simulation uncertainty and discuss

which type was most prevalent in different parts of their case study [23]. 2. Methodology In order to assess uncertainty and risk in energy efficient building projects, a probabilistic based simulation method has been proposed. This section documents the overall methodology and workflow used to pursue this goal and details each step of the research process (Fig. 2.1). 2.1. Risk analysis There are numerous possible sources of risk that can cause the variation in building energy performance. Risk analysis is the main step to transform risk in practice to simulations. Also this is the step to identify sources of risk and quantify their possibility of occurring. This step is based on the input parameters of a certain simulation program (EnergyPlus in this case) by identifying and generating possibility distributions. It is possible to derive the possibility distributions mathematically based on the range of values for the parameters or from specific information, manufacturer specifications for instance, directly from practice. Although it is better to include all uncertain parameters to get accurate results, this is difficult to realize due to the limitation of explicit data and time. Therefore a sensitivity analysis was performed to eliminate the less important parameters and keep the most uncertain and influential ones. Preliminary selection was conducted to eliminate some ignorable parameters by professional experience, followed by a differential sensitivity analysis (DSA) for a detailed selection of key parameters. After the identification of key parameters, probabilistic analysis of each parameter was performed to present small pieces of risk in practice situations. This step was completed by curve fitting techniques with historical data, standard and guidelines, and judgment from professionals. 2.1.1. Sensitivity analysis Before proceeding to sensitivity analysis, a preliminary selection of input parameters is necessary due to the limitation of time and software capability. Others have used sensitivity testing for a large range of parameters reduced to a smaller number (eight) of parameters that represent properties of the building’s thermal performance with good matching of results [24]. Considering the final target of assessing risk, the parameters selected should have two attributes: sensitive to energy performance and uncertainty in practice. After collecting all the input parameters from model, preliminary selection can be processed based on the parameters’ sensitivity and uncertainty. Program settings (such as output file format) and geometry related parameters (such as building footprint) were eliminated with the assumption that simulation will be run correctly, and there will be no discrepancy in building geometry. Then non-sensitive parameters were eliminated, and finally parameters without uncertainty were eliminated. This preliminary selection was done by literature review and interviews of experienced professionals in related areas. Differential sensitivity analysis is widely used because it enables to explore the sensitivity of the outputs to inputs directly [25,26]. In addition, sensitivity analysis is relatively easy to implement in energy simulation programs. DSA involves varying just one input for each simulation while the remaining inputs stay fixed at their most likely base-case values. The changes in the output are therefore a direct measure of the effect of the change made in the single input parameter. Repeating simulations with variation of one input parameter each time enable the individual effects of all input changes and allows users to understanding potential priorities (for example, in building design of geometry versus material) [27]. This

S. Sun et al. / Energy and Buildings 110 (2016) 1–12

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Fig. 2.1. Methodology of research.

is quite different from optimization whereas the goal is usual to find a single solution or range of solutions along a Pareto front [28]. The sensitivity analysis is confronting uncertainty by providing a list of key parameters that effect the solution; however, it does not provide any indication of the uncertainty of those parameters. To use differential sensitivity analysis, one assumption has to be made that each parameter is linear about the output. To achieve this, reasonably ranges and intervals of each parameter selected based on interviews of professionals and background research. Based on the ultimate target of assessing risks, these selected ranges should cover the two extreme scenarios (the best and worst possible scenarios) in practice to present actual situations. For example, the range of cooling COP should cover the highest theoretical value and the lowest possible value that has been found in practice which could be caused by inappropriate operation, poor conditions, etc. Also, the ranges selected were symmetrical about the base case, in order to test the non-linearity problem by comparing the sensitivity of two symmetrical perturbations. The intervals of each parameter should be narrow enough to support the assumption of linearity. Meanwhile they should reflect the situations in reality. To measure sensitivity of input parameters to output, influential coefficient (IC) was defined as percentage change in output divided by percentage change in input parameters. The advantage of using this calculation approach is that the IC is dimensionless, which enables the comparison among different input parameters. IC =

(OP − OPbc )/OPbc (IP − IPbc )/IPbc

where, IC: influential coefficient; OP: output; IP: input parameter and bc: base case. After this preparation, sensitivity analysis was conducted for each selected parameter using simulations. Each parameter required 8–10 simulations based on its interval and range, and output of each simulation (HVAC energy consumption) was collected to calculate the mean IC value and its SD%. SD% is the percentage of standard deviation divided by the mean value of all calculated IC values. It is used to test the linearity of study parameters. A larger SD% indicates non-linearity of parameters; in this study, 50% was defined as a threshold of whether the non-linearity problem could be neglected. Although 50% is a relatively large number, considering that the purpose of DSA is to eliminate the most sensitive parameters instead of calculating the exact IC value, 50% is acceptable.

In this process, EnergyPlus was used as the simulation engine, and jEPlus was used as a parametric manage tool. 134 simulations were identified and run on a computer with an Intel Core i7 processor.

2.1.2. Probability analysis Probability analysis is used to develop the probabilistic distribution function (PDF) for each of the identified parameters from sensitivity analysis. This is a critical step in this analysis as the PDF represents the variations of each parameter in practical situations. Those variations are bearing the small pieces of risk in energy efficient building projects. Each selected parameter was compared with its mention in the literature review and in discussion with professionals to decide which distribution should be used, either continuous distribution or discrete distribution. However, in the case study, due to the limitation of time and data availability, the PDFs were not created by curve-fitting; instead, each selected parameter was compared with its mention in previous research and in discussion with professionals to decide which distribution should be used. The uncertainty of weather condition is an important aspect that leads to the risk of energy performance, especially in the life-cycle analysis [29]. Current simulations use one single weather file to predict energy performance. To better present the weather condition in simulation, and take the weather related risk into consideration, the HadCM3 weather change model was adopted to explore the impact of climate change on building energy use. Three weather files were generated using the HadCM3 model to present three different weather condition scenarios of 2020 in Los Angeles, low, medium, and high. These three scenarios present the weather condition in 2020 with three different level of weather change from the HadCM3 model [30]. The three generated weather files, along with the initial weather that is commonly used in current energy simulation method, formed the weather file variation in the case study. Since no information of the probability of these four weather conditions was found, they were assigned values: no change (60%); little change (22.5%), moderate change (12.5%), and a high amount of change (5%). These are conservative assumptions compared with some climate change theories. However, the purpose here is to showing that the uncertainty of weather condition should be taken into consideration. Other appropriate assumptions could be made based on different view of climate change.

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2.1.3. Risk amalgamation Risk analysis identified risks in uncertain parameters and their possibility distribution. Risk amalgamation is the step to collect all small pieces of risks into whole risk. The Monte Carlo method was used to translate the uncertainty in inputs into uncertainty in outputs by determining probabilities of possible outcomes by running large amount of scenario analyses. After assigning probability distribution to selected input parameters, values from within their probability distribution are picked randomly and one simulation is undertaken. Simulations are repeated with new randomly selected values each time. Basically, values were picked from distributions of each parameter by possibility, which generated thousands of combinations. Those combinations are treated as possible cases might occur in practice, which causes the discrepancy between predicted and actual building performance. In addition to EnergyPlus as a simulation engine, jEPlus was used as a parametric manager to implement this step. After the generation of input parameter combinations, jEPlus managed to run those massive simulations one at a time in EnergyPlus. The result of each simulation run was collected for use. To instruct jEPlus to finish the job, several CVS-style text files containing thousands of values of selected parameters were made. Since the simulation iteration requires a high performance processor and a lot of time, in the case study, this task was divided into five sub-iterations. These five jobs were finished in EnergyPlus with cloud based processing service JESS (jEPlus Simulation Server). 2.2. Risk assessment After collecting all the results from Monte Carlo simulation, curve-fitting techniques was used to establish the probability distribution of result, which could be used to present the risk of the prediction as well as to derive a more reliable prediction of building energy performance. This possibility distribution is the combination of all possibility distributions of input parameters, so the risk should be related to the parameters identified in sensitivity analysis. The results of each simulation (energy performance and utility cost) were collected and grouped with input values by jEPlus automatically. These data was processed by curve-fitting technique among possible distribution 10–16 curves, for instance, Logistic, LogLogistic, Normal, Triangular, and Uniform. Then three fit-ofgoodness tests were conducted: chi-square, Anderson–Darling, and Kolmogorov–Smirnov. The results from these three tests were used to rank all curves in order to identify the best fitted match. The generated distribution curve, for both energy performance and utility cost, presents the possibility of different scenarios in reality, thus can be used for risk assessment. These curves have a wide range of usage. It could be used to calculate the expectation value, mean value, standard deviation of building energy performance metrics such as EUI, electricity, etc. Also, it could be used to get reliability of possible outcome, either energy performance or utility cost. A preliminary analysis of energy cost risks analysis was done after the analysis of energy performance risk. This was implemented by including energy cost calculations in each Monte Carlo simulation along with the change in selected input parameters. While it is true that utility bills are often directly related to monthly energy consumption, due to the elaborate regulatory environment and the changing value of the energy based on load factor, the calculations involved are often complicated. The energy charges, demand charges, and service charges are added together to form the basis. The basis, adjustments, and surcharges are added together to form the subtotal. The subtotal and taxes are added together to be the total. The total represents the total charges on that tariff for the energy source used.

Table 3.0 Basic information of case study building model. Program ASHRAE 90.1-2004 climate zone Location Fabric Exterior walls Construction type R-value (m2 K/W) Roof Construction type R-value attic floor (m2 K/W) Window U-factor (W/m2 K) SHGC Visible transmittance Foundation Foundation type R-value (m2 K/W) HVAC System type Heating type Cooling type Fan control

3B-CA Los Angeles

Mass wall 1.17 Attic 5.18 3.24 0.25 0.16 Mass floor 0.54 PSZ-AC Gas furnace Unitary DX Constant volume

The charges for electricity use are based on the demand of amount and power in different time during a day, as well as different seasons. Three tariffs, each represent a scenario of electric usage, has been used in the small office model, and EnergyPlus will selected a qualified one for cost calculation in each Monte Carlo simulation. Also, the gas price varies from each month, which has also been taken in to consideration. After collecting all the cost results (yearly cost) from all of the Monte Carlo simulations, a curve-fitting technique was used to generate most fitted distribution curve. Economics risk assessment was accomplished based on the generated distribution. 2.3. Difference between standard energy simulation and proposed method The two major differences in inputs and simulation (adding of Monte Carlo method) are the key points that enable the proposed method to assess risk in energy efficient building projects (Fig. 2.2). There are distributed inputs instead of fixed values conveying uncertainty and risk into the simulation. These distributions were developed with real data from previous research, standards, and professional judgment to represent possible scenarios occurring after buildings are occupied. Monte Carlo simulation combines distributed possibilities from each parameter and therefore generates a distributed result. This is a stochastic process of collecting risk that is widely used in other disciplines. In a sense, each combination represent one possible scenario might occur in practice, and the amount of repetition of each combination shows the possibility of that scenario. This step should be proceeded with a large number of parametric simulations, the more the better. 3. Case study results To test and demonstrate the feasibility and effectiveness of the proposed risk assessment method, the DOE commercial reference building model [31], small office (new construction) in Los Angeles, was used as a case study (Table 3.0; Fig. 3.0). 3.1. Sensitivity analysis Based on information from the literature review and professional interviews, 17 uncertainty and energy-sensitive parameters

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Fig. 2.2. Current versus proposed methods.

Fig. 3.0. Case study building. Full information is available at http://energy.gov/eere/buildings/new-construction-commercial-reference-buildings (RefBldgSmallOfficeNew2004 v1.3 5.0 SI.xlsx).

from four categories were selected, based on their characteristics of uncertainty and sensitivity (Table 3.1). Defining an appropriate interval is critical to the sensitivity analysis; it should large enough so that the range could cover two

Table 3.1 Parameters identified after preliminary selection. Category

Fabric

Program

Zone setting

Equipment

Parameter

Unit

Wall insulation conductivity Roof insulation conductivity Glass U-factor Glass SHGC

W/m-k

0.049

W/m-k

0.049

W/m -k N/A

People density Lighting density Equipment density

m2 /person W/m2 W/m2

18.580 10.760 10.760

Infiltration rate Design airflow Cooling SA temperature Heating SA temperature Cooling setpoint Heating setpoint

m3 /s-m2 m3 /person ◦ C

0.000302 0.010 14.000

◦

C

40.000

◦

C C

24.000 21.000

Fan efficiency Fan motor efficiency Coil cooling COP Coil heating efficiency

N/A N/A

0.53625 0.825

N/A N/A

3.667 0.800

Base value

2

◦

3.240 0.250

extreme scenarios within several intervals, as discussed earlier. Also, in order to keep the range narrow enough to support the assumption of linearity, intervals should be as small as possible. In addition, the intervals should reflect the situations in reality. For example, for the cooling setpoint, a 1 ◦ C interval might be too large as the range could be non-linear, which could cause a false evaluation of its sensitivity. However, a 1 ◦ C interval is the real situation in practice when using a thermostat, so it is most appropriate interval. With these premises in mind, the interval and range of each parameter was carefully considered. In addition to literature and historical data review, three experienced professionals from the building energy industry were interviewed [32]. Their rich experience in parameter deviation of actual projects provided valuable information for this process. Ranges and intervals were determined for all 17 parameters (Table 3.2). These selected ranges would cover the two extreme scenarios in record from relevant literature to present actual situations. A sensitivity analysis was conducted for each selected parameter with simulations. Each parameter required 8–10 simulations based on its interval and range. The output of each simulation, HVAC EUI and Total EUI, was collected and put into formula with original EUI to calculate IC value, then the mean IC value and its percentage standard deviation (SD%) was also calculated (Table 3.3). Due to time limitations and the restriction of feasibility, only six of the most uncertain and sensitive parameters were selected and used in the Monte Carlo simulation (Table 3.4). These 6 parameters were selected considering both IC ranking of total energy use intensity and HVAC energy use intensity (Table 3.3). Other than IC values, attention should be paid to SD%, as it tested the nonlinearity issue according to the assumption of each parameter is

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Table 3.2 Results of range and interval selection. Category

Fabric

Program

Zone settings

Equipment

Parameter

Unit

Min.

Base

Max.

Interval

No.

Wall insulation conductivity Roof insulation conductivity Glass U-factor Glass SHGC People density Lighting density Equipment density Infiltration rate Design airflow Cooling supply air temperature Heating SA temperature Cooling setpoint Heating setpoint Fan efficiency Fan motor efficiency Coil cooling cop Coil heating efficiency

W/m-k W/m-k W/m2 -k N/A m2 /person W/m2 W/m2 m3 /s-m2 m3 /person ◦ C ◦ C ◦ C ◦ C N/A N/A N/A N/A

0.041 0.041 2.540 0.100 12.580 6.760 6.760 0.00010 0.005 10.000 36.000 21.000 18.000 0.33625 0.745 3.267 0.720

0.049 0.049 3.240 0.250 18.580 10.760 10.760 0.00030 0.010 14.000 40.000 24.000 21.000 0.53625 0.825 3.667 0.800

0.057 0.057 3.940 0.400 24.580 14.760 14.760 0.00050 0.015 18.000 44.000 27.000 24.000 0.73625 0.905 4.067 0.880

0.002 0.002 0.140 0.050 1.500 1.000 1.000 0.00005 0.001 1.000 1.000 1.000 1.000 0.050 0.020 0.100 0.020

8 8 10 6 8 8 8 8 10 8 8 6 6 8 8 8 8

Note: Min: minimum; Max: maximum; No.: number of intervals. Table 3.3 Result of differential sensitivity analysis. Parameter

IC EUI

SD% 1

Rank 1

IC HVAC

SD% 2

Rank 2

Wall insulation conductivity Roof insulation conductivity Glass U-factor Glass SHGC People density Lighting density Equipment density Infiltration rate Design airflow Cooling supply air temperature Cooling setpoint Heating setpoint Fan efficiency Coil cooling COP Coil heating efficiency

0.0023 0.0002 0.0076 0.0292 0.0242 0.3108 0.4506 0.0012 0.0043 0.2228 1.6307 0.2411 0.1595 0.0589 0.0055

5.36% 71.96% 38.73% 19.16% 29.91% 0.65% 0.97% 28.49% 71.28% 32.77% 32.00% 107.67% 29.89% 8.02% 7.35%

13 15 10 8 9 3 2 14 12 5 1 4 6 7 11

0.0094 0.0010 0.0316 0.1209 0.1004 0.3011 0.3399 0.0050 0.0177 0.9240 6.7615 0.9995 0.6614 0.2442 0.0229

5.36% 71.96% 38.73% 19.16% 29.91% 2.77% 5.35% 28.49% 71.28% 32.77% 32.00% 107.67% 29.89% 8.02% 7.35%

13 15 10 8 9 6 5 14 12 3 1 2 4 7 11

linear to output. As discussed in Section 2.1.1, 50% is the threshold; all parameters that have a SD% higher than 50% need to be eliminated. Although the relationship between inputs and outputs will not be exactly linear, the purpose of sensitivity analysis here is to eliminate the non-important parameters instead of identifying the exact influential coefficient of each input parameter. In this sensitivity analysis, the heating set point was ranked in the top 6 in both Total and HVAC EUI IC values, however it was eliminated due to particular high SD% value (107.67%), which means it has an unacceptable non-linearity problem. Considering the purpose of study is to illustrate and test a proposed methodology with a case study model located in Los Angeles, a cooling dominated climate area, it is reasonable to eliminate the heating set point. It would be interesting to investigate the parameter and non-linearity problems in future studies.

Table 3.4 Parameters finally selected from sensitivity analysis. Selected parameter

IC 1

Rank 1

IC 2

Rank 2

Cooling setpoint Cooling supply air (◦ C) Equipment density Lighting density Fan overall efficiency Coil cooling COP

1.63 0.45 0.31 0.24 0.22 0.16

1 5 6 2 3 7

6.76 0.92 0.66 0.33 0.30 0.20

1 3 4 5 6 7

Note: IC 1: influential coefficient of total EUI; Rank 1: ranking of IC 1. IC 2: influential coefficient of HVAC EUI; Rank 2: ranking of IC 2.

3.2. Parameter distribution derivation The six identified parameters from the sensitivity analysis were studied to develop their probabilistic distribution function (PDF). Due to the limitation of data availability and time, the PDFs were not created by curve-fitting; instead, each selected parameter was compared with its mention in literature review and in discussion with professionals [32] to decide which distribution should be used, and the mean values or mode values were the base values from DOE model (Table 3.5).

3.3. Monte Carlo simulation Latin hypercube sampling (LHS) was processed on each of the input parameters to generate 10,000 values based on the probability distribution. The 60,000 parameter values were used to generate 10,000 input combinations for the Monte Carlo simulation. 10,000 simulations were run with the input combinations from above and the four weather files discussed previously. JEPlus was used to manage the simulation jobs by automatically substituting selected input parameters with new-value combinations from sampling, and EnergyPlus was used as the simulation engine. The simulations were run with cloud based processing service JESS. 10,000 sets of simulation results were collected from the Monte Carlo simulation, including the energy usage of cooling, heating, fan, water heating, interior lighting, exterior lighting, and interior equipment, as well as the utility cost of electric and gas. These data

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Table 3.5 Probabilistic distribution function of selected parameters. Parameter

Unit

Distribution type

Distribution definition

References

Cooling setpoint

◦

Normal

Rodríguez et al. [33]

Equipment density

w/m2

Normal

Lighting density

w/m3

Normal

Cooling SA temperature

◦

C

Triangular

Overall fan efficiency

N/A

Triangular

Coil cooling COP

N/A

Normal

Mean: 24 SD 0.7 Mean: 10.76 SD: 3.2 Mean: 10.76 SD: 2.4 Mode: 14 Max: 16 Min: 13 Mode: 0.54 Max: 0.7 Min: 0.38 Mean: 3.67 SD: 0.15

C

Hopfe and Hensen [20] Hopfe and Hensen [20]

Macdonald and Strachan [34]

Table 3.6 Summary of best fitted curves for 5 outputs.

Total EUI HVAC EUI Total cost Electric cost Gas cost

Unit

Best curve

Mean

Mode

Median

Std. dev.

kBtu/sq kBtu/sq $/yr $/yr $/yr

Normal Gamma Gamma Gamma Log-normal

42.04 10.92 8343 8242 101

42.04 9.82 8008 7896 95

42.04 10.56 8232 8127. 99

6.81 2.80 1458 1468 9

were sorted and fitted to generate the probability distribution of energy usage and cost (Table 3.6). A curve-fitting technique was used to identify the best-fit curve for each output, by performing five goodness-of-fit tests, namely Akaike (AIC), Bayesian (BIC), Chi-square, K–S, and A–D for the 18 different types of distribution curves. The best fitted curves of total EUI and total cost, and their goodness-of-fit tests results of the seven top ranked curves will be used to measure the risk and conduct other related analyses (Figs. 3.1 and 3.2; Table 3.7). As shown in Table 3.7 and Table 3.8, the best fitted curves (#1 ranking) for total EUI and total cost are normal distribution

and Gamma distribution. The goodness-of-fit results show that the curves are a good representation of the data collected.

4. Discussion The distribution values of the total EUI and total cost allow the identification of ranges of specific probability that show reliability/risk in metrics that are more understandable for risk management.

Table 3.7 Results of goodness-of-fit test for total EUI, seven sample curves. ChiSq

ExtValue

Logistic

LogLogistic

Normal

Weibull

Laplace

Rankings by fit statistic Akaike (AIC) Bayesian (BIC) Chi-sq Statistic K–S statistic A–D statistic

#5 #5 #5 #5 #5

#7 #7 #6 #7 #7

#4 #4 #4 #3 #3

#3 #3 #3 #2 #2

#1 #1 #1 #1 #1

#2 #2 #2 #4 #4

#6 #6 #7 #6 #6

Distribution statistics Mean Mode Median Std. deviation Skewness Kurtosis

42.10 40.10 41.43 7.35 0.54 3.44

42.47 38.68 41.09 8.42 1.14 5.40

41.96 41.96 41.96 7.05 – 4.20

42.07 41.65 41.88 7.07 0.26 4.37

42.05 42.05 42.05 6.81 – 3.00

42.02 42.51 42.13 6.97 (0.05) 2.73

41.93 41.93 41.93 7.67 – 6.00

Information criteria Akaike (AIC) Bayesian (BIC)

67,047.82 67,062.24

67,892.74 67,907.16

66,922.17 66,936.59

66,903.51 66,925.14

66,749.74 66,764.16

66,860.32 66,881.94

67,686.72 67,701.14

Chi-sq test Minimum Maximum Input Fit

15.10 28.49 183.00 135.14

Infinity 29.09 232.00 135.14

Infinity 25.27 49.00 135.14

(88.47) 26.23 81.00 135.14

Infinity 26.99 107.00 135.14

18.30 26.77 100.00 135.14

Infinity 22.34 8.00 135.14

Anderson–Darling test A–D statistic

25.90

86.54

8.47

7.48

2.18

10.26

48.51

0.05

0.02

0.02

0.01

0.02

0.05

Kolmogorov–Smirnov test 0.03 K–S statistic

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S. Sun et al. / Energy and Buildings 110 (2016) 1–12

Fig. 3.1. Best fitted curve of total EUI, normal distribution [42.046, 6.81].

Fig. 3.2. Best fitted curve of total cost, gamma distribution.

Table 3.8 Results of goodness-of-fit test for total cost, seven sample curves. Gamma

InvGauss

LogLogistic

Lognorm

Pearson5

Triang

Weibull

Rankings by fit statistic Akaike (AIC) Bayesian (BIC) Chi-sq statistic K–S statistic A–D statistic

#1 #1 #1 #1 #1

#4 #4 #5 #5 #4

#2 #2 #2 #2 #2

#3 #3 #4 #4 #3

#6 #6 #6 #6 #6

#7 #7 #7 #7 #7

#5 #5 #3 #3 #5

Distribution statistics Mean Mode Median Std. deviation Skewness Kurtosis

8343.96 8008.74 8232.58 1458.28 0.46 3.32

8343.96 7819.91 8167.29 1521.88 0.72 3.86

8425.19 8034.71 8245.94 1578.38 1.30 8.91

8351.30 7842.93 8177.11 1518.92 0.73 3.97

8368.37 7669.65 8116.66 1631.91 1.10 5.40

8401.14 8377.98 8395.37 2617.99 0.01 2.40

8318.95 8560.67 8387.40 1545.57 (0.20) 2.83

Information criteria Akaike (AIC) Bayesian (BIC)

173,726.1 173,740.5

174,137.2 174,151.6

173,828.50 173,842.92

174,062.3 174,076.7

174,682.52 174,696.94

179,558.15 179,572.57

174,272.56 174,286.98

Chi-sq test Minimum Maximum Input Fit

2000.00 5561.82 190.00 135.14

2000.00 5667.88 239.00 135.14

2000.00 5563.79 191.00 135.14

2000.00 5667.07 239.00 135.14

2000.00 5735.66 273.00 135.14

2000.00 3051.38 – 135.14

2000.00 4744.21 39.00 135.14

Anderson–Darling test A–D statistic

14.51

42.18

21.08

37.34

77.14

784.28

50.45

0.05

0.03

0.04

0.06

0.17

0.04

Kolmogorov–Smirnov test 0.03 K–S statistic

S. Sun et al. / Energy and Buildings 110 (2016) 1–12

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Table 4.1 Total EUI under specific probability. Probability

1%

Total EUI (kBtu/sq) Probability Total EUI (kBtu/sq) Probability Total EUI (kBtu/sq)

26.20 35% 39.42 70% 45.62

5% 30.84 40% 40.32 75% 46.64

10% 33.32 45% 41.19 80% 47.78

4.1. Results analysis of total EUI The total EUI is a key parameter to measure the energy performance of a building, so the probability distribution of EUI presents the risk of the energy performance of the case project. 4.1.1. Identifying the total EUI range of specific probability The fitted curve of total EUI is a normal distribution, with mean value at 42.046 kBtu/sq and standard deviation of 6.81 kBtu/sq. Total EUI can be identified given any probability. The probability here refers to the possibility of occurring of EUI ranging from minimum to certain value (x). For example, if a probability of 50% is given, the total EUI value (x) is calculated. Using this method, given any probability, the corresponding total EUI value could be identified through calculation (Table 4.1). This type of risk analysis is useful for gaining a sense of the overall risk and uncertainty of the predicted energy performance. A sharp-shaped distribution curve shows better reliability and less risk. In contrast, a gentle-shaped distribution curve express relatively higher risk. 4.1.2. Identifying the probability of a specific EUI range Identifying the probability of a specific EUI range is more frequently used. Given any EUI range, the corresponding probability could be identified through calculation. This is very useful when specific EUI or energy saving is targeted. The identified probability shows the reliability of hitting the target, or in other words, the risk of failing. Current engineering energy simulations use best estimations of parameters as simulation input. In the case study, the best estimations were identified as the mean value of input distributions. So, the mean value of total EUI distribution, 42.046 kBtu/sq in this case, is likely to be equal to the result from single simulation with best estimations inputs, which is the energy performance prediction without taking risk into account. Following this statement, based on the deviation rate (error rate) of mean value, 42.046 kBtu/sq, the reliability and risk can be identified. Reliability is the confidence level (possibility) that the real energy performance will match the prediction within a certain deviation rate; and on the other hand, risk is the possibility that real energy performance will not match the prediction within a certain deviation rate (Table 4.2). This analysis allows engineers to analyze the risk at different level of discrepancy and evaluate the predicted energy Table 4.2 Reliability and risk of different deviation rate of mean value. Range (kBtu/sq) Lower

Upper

41.6 39.9 37.8 35.7 33.6 31.5 29.4 27.3

42.4 44.1 46.2 48.3 50.4 52.5 54.6 56.7

Deviation rate

Reliability

Risk

±1% ±5% ±10% ±15% ±20% ±25% ±30% ±35%

4.9% 24.3% 46.3% 64.5% 78.3% 87.7% 93.6% 96.9%

95.1 75.7% 53.7% 35.5% 21.7% 12.3% 6.4% 3.1%

15% 34.99 50% 42.05 85% 49.10

20% 36.31 55% 42.90 90% 50.77

25% 37.45 60% 43.77 95% 53.25

30% 38.47 65% 44.67 99% 57.89

performance. This is the extremely useful in assessing the risk of energy performance shortfall and evaluating different design alternatives. For examples, if the client only allows a tolerance of 10% in deviation, using the third row in Table 4.2 the predicted energy performance (mean value) will lead to a risk of 53.7%, which means there is more than a half possibility that the prediction will be deviated more than 10% with real energy performance! 4.1.3. Application of method The total EUI distribution from the proposed method can be used for many analyses regarding risk and other aspects. If the proposed methodology is to be applied in practice, three major benefits could be expected: gaining the knowledge of risk, supporting the evaluation of design alternatives, and facilitating risk management. With the assistance of the proposed risk assessment method, engineers and designers will have a better understanding of the realistic energy performance. With the EUI probability curves, they can target the energy savings in a more reliable way, hence gain confidence in the project. In energy performance contracting, engineers could identify the possible energy savings with risk analysis instead of compromising a conservative energy saving, which results in lower profit or the loss of clients. On the other hand, the process of assessing risk is an encouragement of seeking for better energy solutions. Engineers will try to narrow down the EUI distribution curve, so that the future real energy performance as close as possible to the prediction. The proposed method also provides a new way of evaluating design alternatives. Currently, regardless of non-energy aspects, engineers evaluate design alternatives based on the simulated energy performance of different design schemes. With the assistance of the proposed method, engineers can take risk into account to evaluate the possible energy performance. Risk management is dependent on identifying the risk and understanding what causes it. With the risk information from the probability distribution, stakeholders could managing the risk in two ways, establishing plans for possible losses and working on decreasing the risk. Sensitivity analysis reveals the factors that may cause risk and how they affect the energy performance. This provides the direction and chance for investigation and mitigation of risks in these factors, which helps in gaining reliability. 4.2. Results analysis of total cost Directly associated with total EUI, the total utility cost is an aspect that is important to the investors and building owners. The fitted curve of total utility cost is a gamma distribution, with mean value at 8343.96 $/yr and standard deviation of 1458.28 $/yr. The probability distribution curve contains a lot of information about total utility cost. Two main types of probability analysis method are used, identifying the cost range of specific probability and identifying the probability of curtain cost range. 4.2.1. Identifying the total cost range of specific probability Using cumulative distribution function, total cost can be identified given any probability. The probability here refers to the possibility of occurring of total utility cost ranging from minimum

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S. Sun et al. / Energy and Buildings 110 (2016) 1–12

Table 4.3 Total cost under specific probability. Probability

1%

5%

10%

15%

Total cost ($/yr) Probability Total cost ($/yr) Probability Total cost ($/yr)

5449 35% 7692 70% 9020

6150 40% 7873 75% 9257

6561 45% 8052 80% 9527

6854 50% 8232 85% 9850

Table 4.4 Reliability and risk of different deviation rate of mean value. Range ($/yr) Lower 8260 7926 7509 7092 6675 6257 5840 5423 5009

7095 55% 8415 90% 10,269

25% 7309 60% 8605 95% 10,917

30% 7506 65% 8805 99% 12,219

utility cost (mean value) will lead to an extremely large risk of 77.5%.

Deviation rate

Reliability

Risk

±1% ±5% ±10% ±15% ±20% ±25% ±30% ±35% ±40%

4.5% 22.5% 43.3% 61.2% 75.3% 85.4% 91.9% 95.7% 97.7%

95.5% 77.5% 56.7% 38.8% 24.7% 14.6% 8.1% 4.3% 2.3%

Upper 8427 8761 9178 9595 10,012 10,429 10,847 11,264 11,681

20%

to certain value (x). The probability and corresponding total cost at an interval of 5% was identified and listed below (Table 4.3). Similar to the analysis of total EUI, this method can be used for obtain further information. For example, the corresponding cost of 10% and 50% are 6561.40 $/yr and 8232.47 $/yr respectively. (So the probability of utility cost ranging from 6561.40 to 8232.47 $/yr is 40% (50–10%.)) 4.2.2. Identifying the probability of a specific cost range Identifying the probability of cost ranges is more frequently used. This analysis uses the cumulative distribution function and specific integral upper and lower limits are given. Using this method, given any cost range, the corresponding probability could be identified. This is valuable when a specific utility cost budget is targeted. The identified probability shows the reliability of hitting the target, or in other words, the risk of failing (Table 4.4). As discussed earlier, take the mean value of total cost probability distribution (8343.96 $/yr) as the best estimation. This analysis allows economic related stakeholders to analyze the risk at different level of discrepancy, and evaluate the predicted total utility cost. This is useful in making investment decisions. For example, if the investor only allows a tolerance of 5% in deviation, using the information in second row of Table 4.4, the predicted

4.2.3. Application prospects This type of risk analysis could be helpful in investment decision making and developing the business of insurance in energy efficient building projects. As discussed previously, the uncertainty and risk of possible savings from energy efficient measures is one of the issues that hinder the development of energy efficient buildings. The discrepancy between expected and real energy savings can surprise investors, and what is worse, can discourage them. Investors are not afraid of reasonable risk; they are afraid of not knowing about the risk. With the cost probability distribution, investors, owners can obtain the knowledge of the risk about their project. Calculation could be processed regarding return on investment, utility cost savings, incentives, interests, and many other. This could be a definite improvement for investment decision making. If there is risk, then there is a need for insurance. With the assistance of risk analysis of energy cost, insurance could be developed in the energy efficiency industry, which could protect each side of the project, both the investors and the designers. With the rapid growth of energy efficiency projects and peoples’ awareness of sustainability, the insurance business in such industry could be a big opportunity.

4.3. Case study evaluation If the mean values (expectation value) of input parameter distributions are assigned with the best estimations of these parameters that are used in a standard simulation method, the mean value of output distribution should have an equal value with the single simulation result. In the case study, the mean values of input distributions were assigned with the values from initial DOE model; these are the best estimations according to how the DOE model was created. However, the mean value of total EUI distribution

Fig. 4.1. Deviation of initial EUI with mean value of total EUI distribution.

S. Sun et al. / Energy and Buildings 110 (2016) 1–12

(42.046 kBtu/sq) is not equal to the initial DOE model simulation result, which is 41.01 kBtu/sq (Fig. 4.1). This deviation might be caused by the use of multiple weather files in the Monte Carlo (MC) simulation. In MC simulation, all the six input parameters used the initial value from DOE model as the mean value of their probability distribution. However, for the four weather files used, one of them is the weather file used in DOE model, and the other three weather files were newly created using the “climate change hypothesis”, which are all presented worse weather conditions (warmer). Therefore, the weather conditions used in the simulations are not “symmetrical” about the initial weather condition, and this is what causes the deviation. Apart from the weather variation, the deviation also attributes to two asymmetrical input parameter distributions, cooling SA temperature and overall fan efficiency. These two parameters have triangular distributions, and the right side of the mean value has a higher probability, therefore the mean value of the total EUI distribution is slightly higher than the initial EUI. Similar to the total EUI, the total cost curve has same issue of a deviation between mean total cost ($8343.96) and the initial total cost ($8108.65). The asymmetrical distribution of weather condition, as well as two other input parameters cause the deviation. The case study follows the proposed methodology, using a probability based method that takes multi-factors into consideration, which yielded building energy performance distributions and related energy cost information with associated probabilities. Some deficiencies exist, including neglect of less-sensitive parameters and imperfect input distributions, but the methodology works.

5. Conclusion Large discrepancies between real and predicted building energy performance have been observed, which frustrates building owners, designers, and investors and can hinder the development of energy efficient buildings. The issue is mainly caused by the uncertainties in building construction and operation and in the use of estimated or unrealistic parameter values in simulation. Aimed at solving this problem, a probabilistically based method of risk assessment using energy performance simulation, which takes multiple factors into consideration, was created to yield expected building energy performance and related energy cost information with associated probabilities. To test the effectiveness of the proposed method, a small office building from a DOE model was used as a case study. The results from the case study were that the normal probability distribution curve of total EUI has a mean value of 42.046 kBtu/sq and a standard deviation of 6.81 kBtu/sq; the gamma probability distribution of total utility cost has a mean value of 8343.96 $/yr and a standard deviation of 1458.28 $/yr. These two probability curves could be used to identify the risk related to the project, both energy and cost wise. • Other risk information can be obtained through the analysis: • The probability of EUI ranging from 33.318 to 42.046 kBtu/sq is 40%. • The risk of a 10% deviation in predicted and real total EUI is 53.7%. • The probability of utility cost ranging from $6561.40 to $8232.47 per year is 40%. • The risk of a 5% deviation in predicted and real utility cost is 77.50%. These risk related information obtained from the results can assist the stakeholders of energy efficient building projects in many ways:

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• Understanding the risk of discrepancy of predicted and real energy performance. • Targeting the energy savings in a more reliable way. • Supporting the evaluation of design alternatives. • Facilitating risk management. • Assisting investment decision making. • Providing opportunities for energy efficiency related insurance. • Encouraging the development of energy efficient building. This methodology has the potential to advance the agenda of sustainable design by providing additional knowledge to building owners and investors.

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