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Energy efficient buildings: a method of probabilistic risk assessment using building energy simulation

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Energy efficient buildings: a method of probabilistic risk assessment using building energy simulation

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Content 1

ENERGY EFFICIENT BUILDINGS:
A Method of Probabilistic Risk Assessment Using Building
Energy Simulation

By

Shang Sun

Committee Members:
Karen M. Kensek
Douglas Noble, Marc Schiler

A Thesis Presented to the
FACULTY OF THE USC SCHOOL OF ARCHITECTURE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial fulfillment of the
Requirements for the Degree
MASTER OF BUILDING SCIENCE

May 2015

Copyright 2015 Shang Sun

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To my dear Dad and Mom, I couldn’t have done this without you.
Thank you for all of your support along the way.
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ACKNOWLEDGEMENTS
First and foremost, I would like to express my deepest gratitude to my committee chair,
Professor Karen Kensek, who has offered excellent advisory on this project. She provided
great ideas and help in ensuring the research direction in the right way. Her positive
attitude towards work, dedication in teaching, creative way of thinking, and paying
attention to details, will always benefit my life.
I would also like to express my special appreciation and thanks to my committee
members, Professor Douglas Noble, and Professor Marc Schiler. They provided great
support and encouragement. I really appreciate their valuable advice on improving the
project and my writing skills.
Last but not least, thank you, the lovely MBS family. It is you that make my life here
enjoyable. I had a really great time with you all. Without the support from MBS, I would
not complete this thesis project while enjoying such wonderful time.

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ABSTRACT
Even though the design of energy efficient buildings provides an excellent opportunity to
achieve large scale energy reductions, the process of achieving this still has difficulties.
As an essential and heavily relied upon tool in the design process, software simulation is
used to predict building energy performance. However, there are problems associated
with simulation tools including the following: estimated data is usually used instead of
real data, a lack of accurate occupant schedule and behavior models, inaccurate weather
data, and unrealistic performance expectations for mechanical equipment. Simulations
may not even be used for accurate predictions of energy performance, but instead just for
comparison of alternatives and payback periods, compliance with energy code protocols,
and perhaps just general estimates of energy usage. All these problems can lead to
surprises when discrepancies are found between actual and predicted building energy
performance, which frustrates the building owners, designers, and investors. Research
about energy model calibration and the uncertainty of single parameters (e.g. weather
data and occupancy), has been done before. Less has been done for incorporating overall
risk assessment into energy simulations that takes multiple factors into consideration.
A probabilistic method of risk assessment in energy performance simulations has been
proposed and tested. Literature review and discussion with professionals were conducted
to decide the parameters that produce most uncertainties in simulations, followed by
Differential Sensitivity Analysis (DSA) to identify the most influential parameters among
them. Each selected parameter was given a range of values and probability. These were
used in simulations in a distribution instead of one fixed value, either a continuous
distribution or discrete distribution. Latin Hypercube Sampling (LHS) was used to
generate input combinations with parameter values picked stochastically from
distributions based on the Monte Carlo method. With these input combinations,
thousands of simulations were run using a cloud processing service. Output data was
collected and analyzed using a curve-fitting technique to find a best fitted distribution,
which could be used for risk and uncertainty analysis of both energy performance and
cost information.
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A DOE reference building has been used to test this methodology. Among 17 uncertain
parameters, seven more influential ones were identified by DSA. 10,000 simulations were
run with these seven distributed parameters (weather file, cooling set-point, cooling
supply air temperature, equipment density, lighting density, fan overall efficiency, and
coil cooling COP). The output data, energy usage intensity (EUI) and energy cost, were
fitted into distribution for risk analysis. The results shows the probability and reliability
of prediction within a certain range, and both EUI and energy cost could possibly deviate
from original prediction in a large percentage.
This methodology has shown that a tool can be developed that expresses the EUI and
energy cost of a building simulation as a distribution of likely values rather than a single
value. The intent is that a finalized tool would help designers to better evaluate design
alternatives and that the results, probability distribution of energy performance and cost,
would be useful in making decisions about investments in building energy efficient
projects, both new and retrofits.

Keywords: Building energy simulation, uncertainty, risk assessment, sensitivity analysis,
probability analysis, Monte Carlo method, energy use intensity (EUI)
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CONTENTS

ACKNOWLEDGEMENTS ................................................................................................ 3
ABSTRACT ........................................................................................................................ 4
LIST OF TABLES ............................................................................................................ 10
LIST OF FIGURES .......................................................................................................... 12
1. Introduction ................................................................................................................... 14
1.1 Risk in energy efficient building projects .......................................................... 15
1.2 Uncertainty in energy performance simulation .................................................. 18
1.3 Hypothesis statement.......................................................................................... 21
1.3.1 Hypothesis ........................................................................................................ 21
1.3.2 Objectives ......................................................................................................... 21
1.4 Significance of study .......................................................................................... 22
1.4.1 Knowledge of risk ............................................................................................ 22
1.4.2 Risk management ............................................................................................. 22
1.4.3 Industry benefits ............................................................................................... 22
1.5 Study statement .................................................................................................. 23
1.5.1 Workflow overview .......................................................................................... 23
1.5.2 Thesis outline .................................................................................................... 24
1.6 Important Terminology ...................................................................................... 25
2. Background of risk and uncertainty analysis ................................................................ 27
2.1 Understanding the risk ....................................................................................... 27
2.1.1 Introduction ................................................................................................. 27
2.1.2 Sources of risk............................................................................................. 27
2.1.3 Energy simulation uncertainty .................................................................... 29
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2.2 Characterizing parameter uncertainty ................................................................ 30
2.2.1 Introduction ................................................................................................. 31
2.2.2 Probability Distributions ............................................................................. 32
2.2.3 Relevant research ........................................................................................ 34
2.3 Risk analysis techniques..................................................................................... 35
2.3.1 Introduction ................................................................................................. 35
2.3.2 Sensitivity analysis...................................................................................... 36
2.3.3 Monte Carlo method ................................................................................... 38
2.3.4 Relevant research ........................................................................................ 39
3. Methodology ................................................................................................................. 41
3.1 Workflow overview............................................................................................ 41
3.1.1 Methodology development ......................................................................... 41
3.1.2 Overall workflow ........................................................................................ 42
3.1.3 Implication of proposed method ................................................................. 45
3.2 Professional interviews ...................................................................................... 47
3.2.1 Introduction ................................................................................................. 47
3.2.2 Interview outline ......................................................................................... 47
3.2.3 Interview content ........................................................................................ 48
3.3 Sensitivity analysis ............................................................................................. 50
3.3.1 Theoretical basis of DSA ............................................................................ 51
3.3.2 Preliminary parameter selection ................................................................. 52
3.3.3 Selection of range and interval ................................................................... 54
3.3.4 Influential coefficient calculation ............................................................... 55
3.4 Probability analysis ............................................................................................ 55
3.4.1 Techniques of distribution derivation ......................................................... 56
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3.4.2 Weather file variation ................................................................................. 56
3.5 Monte Carlo simulation ...................................................................................... 58
3.5.1 Introduction of the Monte Carlo method .................................................... 58
3.5.2 Simulation iteration ..................................................................................... 59
3.5.3 Results analysis ........................................................................................... 60
4. Case study ..................................................................................................................... 61
4.1 Overview ............................................................................................................ 61
4.2 Introduction of the case model ........................................................................... 61
4.3 Results from sensitivity analysis ........................................................................ 63
4.3.1 Preliminary selection of parameters............................................................ 63
4.3.2 Perturbations ............................................................................................... 64
4.3.3 Differential sensitivity analysis................................................................... 65
4.4 Parameter distribution derivation ....................................................................... 66
4.5 Results from Monte Carlo simulation ................................................................ 68
4.5.1 Latin Hypercube Sampling ......................................................................... 68
4.5.2 Simulation iteration ..................................................................................... 70
4.5.3 Output probability distribution curves ........................................................ 71
4.6 Conclusion ............................................................................................................... 74
5. Evaluation and analysis of case study results ............................................................... 75
5.1 Common method of probability analysis ........................................................... 76
5.1.1 Probability distribution curve basics ........................................................... 76
5.1.2 Probability calculation ................................................................................ 77
5.1.3 Other probability distribution curves .......................................................... 78
5.2 Results analysis of total EUI .............................................................................. 80
5.2.1 Risk analysis ............................................................................................... 80
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5.2.2 Comparison with initial total EUI ............................................................... 83
5.2.3 Application prospects.................................................................................. 84
5.3 Results analysis of total cost .............................................................................. 86
5.3.1 Risk analysis ............................................................................................... 87
5.3.2 Comparison with initial total cost ............................................................... 89
5.3.3 Application prospects.................................................................................. 90
5.4 Other output results ............................................................................................ 91
5.5 Limitations of the current study ......................................................................... 92
5.6 Summary ............................................................................................................ 93
6. Conclusions and future work ........................................................................................ 94
6.1 Methodology developed ..................................................................................... 94
6.2 Future Work ....................................................................................................... 96
6.3 Concluding remarks ........................................................................................... 98
References ......................................................................................................................... 99
Bibliography ................................................................................................................... 102
Appendix A – Parameter identification of sensitivity analysis ....................................... 103
A-1 Parameter identification from document.............................................................. 103
A-2 Parameter identification from IDF file................................................................. 104
Appendix B Other output distribution ............................................................................ 106
B-1 Fitted probability distribution of HVAC EUI ...................................................... 106
B-2 Fitted probability distribution of Electric Cost .................................................... 107
B-3 Fitted probability distribution of Gas Cost ........................................................... 108

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LIST OF TABLES
Table 1-1 Typical risks in energy efficient building projects ........................................... 17
Table 3-1 Tariffs used in energy cost calculation ............................................................. 45
Table 3-2 Energy model input categories (Deru et al. 2011) ............................................ 53
Table 3-3 Parameters identified after Preliminary Selection ............................................ 54
Table 4-1 Brief description of major model thermal properties ....................................... 62
Table 4-2 Parameters identified after preliminary selection ............................................. 63
Table 4-3 Results of range and interval selection ............................................................. 64
Table 4-4 Result of differential sensitivity analysis ......................................................... 65
Table 4-5 Parameters finally selected from sensitivity analysis ....................................... 66
Table 4-6 Probabilistic distribution function of selected parameters ............................... 67
Table 4-7 Sample of 30 input combination from LHS ..................................................... 69
Table 4-8 Sample of 30 sets of results from Monte Carlo simulation .............................. 70
Table 4-9 Summary of best fitted curves for 5 outputs .................................................... 71
Table 4-10 Results of goodness-of-fit test for total EUI, 7 sample curves ....................... 72
Table 4-11 Results of goodness-of-fit test for total cost, 7 sample curves ....................... 73
Table 5-1 Initial simulation results and baseline information .......................................... 75
Table 5-2 Key parameters of normal distribution of total EUI ......................................... 76
Table 5-3 Total EUI under specific probability ................................................................ 81
Table 5-4 Reliability and risk of different deviation rate of mean value .......................... 82
Table 5-5 Total cost under specific probability ................................................................ 88
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Table 5-6 Reliability and risk of different deviation rate of mean value .......................... 88
Table A-1 Parameters identified from document ............................................................ 104
Table A-2 Parameters identified from IDF file ............................................................... 104
Table B-1 Results of goodness-of-fit test for HVAC EUI, 7 sample curves .................. 104
Table B-2 Results of goodness-of-fit test for Electric Cost, 7 sample curves ................ 104
Table B-3 Results of goodness-of-fit test for Gas Cost, 7 sample curves ...................... 104

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LIST OF FIGURES
Figure 1-1 Measured versus designed EUIs .................................................................... 19
Figure 1-2 Comparison of predicted EUI from seven programs of one building ............ 20
Figure 2-1 Matrix of risk in energy-efficiency projects .................................................... 29
Figure 2-2 Diagram of discrete distribution ...................................................................... 32
Figure 2-3 Curve of normal distribution ........................................................................... 33
Figure 2-4 Curve of log-normal distribution .................................................................... 33
Figure 2-5 Diagram of triangular distribution .................................................................. 34
Figure 2-6 Monte Carlo analysis in building energy efficient project .............................. 39
Figure 3-1 Overall workflow of proposed method ........................................................... 42
Figure 3-2 Energy cost calculation method in EnergyPlus ............................................... 44
Figure 3-3 Comparison between current method (top) and proposed method (bottom) .. 46
Figure 3-4 Process of sensitivity analysis using simulations ............................................ 55
Figure 3-5 Assumed probability of different climate change scenarios ........................... 58
Figure 3-6 Workflow of Monte Carlo simulation ............................................................. 58
Figure 3-7 Latin hypercube sampling ............................................................................... 59
Figure 3-8 Interface of jEPlus and EnergyPlus................................................................. 60
Figure 4-1 Index of results presented in Chapter 4 ........................................................... 61
Figure 4-2 Axonometric view of case model---small office in Los Angeles ................... 62
Figure 4-3 Probability density distribution curves of 6 selected parameters .................... 68
Figure 5-1 Standard normal distribution reference table .................................................. 79
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Figure 5-2 Best fitted curve of Total EUI, normal distribution ........................................ 80
Figure 5-3 Deviation of initial EUI with mean value of total EUI distribution ................ 83
Figure 5-4 Deviation of initial EUI with mean value of total EUI distribution ................ 84
Figure 5-5 Best fitted curve of total cost, gamma distribution ......................................... 86
Figure 5-6 Deviation of initial cost with mean value of cost distribution ........................ 89
Figure 5-7 Deviation of initial cost with mean value of cost distribution ........................ 90
Figure 6-1 Workflow of proposed risk assessment methodology .................................... 94
Figure 6-2 Distributions of output EUI and Cost from case study ................................... 95
Figure B-1 Best fitted curve of HVAC EUI, Gamma distribution ................................. 106
Figure B-2 Best fitted curve of Electric Cost, Gamma distribution ............................... 107
Figure B-3 Best fitted curve of Gas Cost, Log-normal distribution ............................... 108

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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 (Pérez-Lombard, Ortiz, and Pout 2008). In the United States, 41% of
primary energy was consumed by the building sector, compared to 30% by the industrial
sector, and 29% by the transportation sector (DOE, Building Energy Data Book, 2011).
Growth in population, increasing demand for building services and comfort levels,
together with the rise in time spent inside buildings, assure the upward trend in energy
demand will continue in the future. In the face of huge challenges, there is also an
excellent opportunity to achieve large scale energy reductions with the construction of
energy efficient buildings.
As a necessity instead of a matter of choice or luxury, energy efficient buildings ushered
in an era of development with the updating of technology, new materials, design
technique, and advanced equipment. Stakeholders have begun to take energy
performance into consideration from the very beginning of design to operation,
incorporating passive strategies, high-performance envelope materials, and efficient
systems into new constructions. Also owners are seeking to improve existing buildings
by replacing outdated systems, improving façades, and using renewable energy facing the
increasing cost of operation. Although there is a burst of growing popularity in energy
efficient buildings, the growth of this industry does not seem as good as expected. In the
United States, non-residential energy efficient construction starts were at 10% of totals
using 2008 numbers (Alev Durmus-Pedini, 2010). This is obviously not enough growth
to reach environmental targets of reducing carbon emission, despite the fact that energy
efficient building was introduced to the industry more than a decade ago. Among
multiple difficulties like financial feasibility, public awareness of environment and policy,
the performance risk in energy efficient building projects is a significant issue hindering
the development of this industry.
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1.1 Risk in energy efficient building projects
The performance risk affects the development of energy efficient buildings in both
techniques and practice. Performance risk is the possibility of occurrence of discrepancy
between expected energy performance during design stage and real energy performance
after project completion.
The case of energy performance contracting (EPC) is a good example of this issue. EPC
is a turnkey service in the area of building retrofit. EPC companies guarantee the energy
savings produced by an energy efficient building project will be sufficient to finance the
full cost of the project. In a major review of historic experience in 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
(Goldman et al., 2002). ESCOs have been extremely careful when signing the contract
and balance the risk of multiple factors in such projects versus their potential profit. Their
strategy, by compromise, is to promise a conservative energy saving, which results in
lower profit or the loss of clients(Mills and Weiss, n.d.). At the same time, building
owners are disappointed by the shortfall of energy savings that lead to a lower return of
investment or even abandon energy efficient building strategies after seeing the
conservative numbers provided by the ESCO.
EPC projects are relatively less vulnerable to risk since most of them are retrofit. In
retrofit projects, energy engineers have more access to accurate data, and they are able to
calibrate the energy model by site measurement and analysis of real data. This is
extremely important in energy performance prediction since some of the most
contributing parameters, occupancy for instance, can be accurately presented in energy
modeling. Also, most of the retrofit projects are the replacement of façade elements or
mechanical system, which has less uncertainty since these building components are
mature in industry thus more certain properties and data are available. For new
construction projects, many influential parameters used for energy performance
prediction are estimated instead of measured, either by code or professional judgment.
There are also more uncertainties faced by new construction projects, such as operations
and occupant behavior. All these make new construction projects more vulnerable than
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retrofit. So, the lack of risk assessment could be considered a major obstacle in the way
towards green innovation of building industry.
Performance risks in energy efficient building projects lie in uncertainties and volatilities
of many aspects, from conceptual design, to simulation, construction, operation,
maintenance and verification and other extrinsic factors like energy cost, policy, and so
on. Energy performance simulation is the main method of prediction; however most of
the inputs are estimates from experience or code requirements instead of real or measured
data. Sometimes simulated energy performance of new construction is not even
considered predictions, but instead compliance with energy code protocol that give
general estimates of energy usage; this leads to the discrepancy between predicted and
actual energy performance, for example, study has shown that there is a large energy
performance discrepancy of LEED certified projects (Frankel and Turner, 2008).
Even if a very high quality simulation has been accomplished, risk is still introduced in
the construction and operation phase of a building. No construction can be done 100% as
the design team expected; a tiny gap between window and wall may result in huge heat
loss. In operation, occupants’ behaviors also have significant influence on energy
performance, such as failed natural ventilation because of closed window by occupants’
preference or ignorance (Azar and Menassa 2012). Occupants never live the way
engineers expected. Other uncertainties also contribute to the risk, for example, a new tall
building in front blocking most of the solar gain, the fluctuating price of electricity and
gas, the transformation of the use of rooms. All these factors more or less affect the
energy performance of buildings and unfortunately are all hard to predict. There are many
potential risk factors in energy efficient building projects including computer simulation,
construction, operation procedures, occupancy, and others. Some major risk sources has
been included in the following table, which is compiled based on professional interviews
and literature review (Table.1-1).

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Table 1-1 Typical risks in energy efficient building projects
Potential risks
sources of EEB
Simulation
Tool restrict
Algorithm
Neighborhood
HVAC efficiency
Weather data
Inaccurate inputs
Schedule
Set point
Geometry
Other
Other
Mistake
Idealization
Unknown N/A
Construction
Quality
Properly
Compliance
Materials
Price
Performance
Unknown N/A
Operation
Control
Compliance
Schedule
Maintenance
Compliance
Replacement
Cost Price change
Unknown N/A
Occupancy
Behavior
Schedule
Difference
Needs
Preference
Control
Change(Owner) Room Function
Unknown N/A
Other
Owner Requirements
Budget
Preference
Project Type
Size
Usage
Designer Capacity N/A
Neighborhood Change
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1.2 Uncertainty in energy performance simulation
With the rapid development of energy efficient buildings, many new technologies and
materials have been developed and applied in practice. Among these new technologies,
energy simulation programs, eQuest, Green Building Studio, and IES for instance, are
heavily relied on by engineers because of their ability to evaluate building energy
performance at both the design stage and for optimizing final design decisions. After
inputting the parameters that would affect the energy use of a building (e.g. climate,
envelope, equipment, schedules of occupants, and internal heat gain), typical energy
performance software will output building energy use predictions in typical end-use
categories: heating, cooling, lighting, fan, plug, process, and etc.
Simulation is the key step of predicting building energy performance; however, it is also
the step that has most uncertainties that lead to an unreliable prediction, especially in new
construction. In practice designers often use empirical and idealistic data that are
unrepresentative of the actual situation because of the lack of measured data, such as
occupancy schedules, appliance power density, site weather conditions, etc. These data
are usually not accurate enough for a detailed model and sometimes could vary
significantly from actual data. The building may not be built exactly as drawn, which can
have an especially large effect on air leakage if that is a significant factor. The occupants
may use the building differently than predicted; they may use the building for more hours
or use less equipment. Or during extreme years, the climate may vary 20 to 30% from
that the weather files used in the software (Marc Rosenbaum, 2003). As a result, large
discrepancies are being observed between predicted and actual energy performance,
typically averaging around 30% and reaching as high as 100% in some cases (Energy
Performance of LEED® for New Construction Buildings, 2008).
Based on a study of 120 LEED certified buildings , the measured energy savings and
simulated savings vary (Frankel and Turner, 2008) (Fig. 1-1). Frankel and Turner
compared energy savings proposed in the energy simulation (horizontal axis) with actual
savings (vertical axis), all relative to the code baseline developed for each project.
Projects that fall on the diagonal line in the top half of the graph demonstrate actual
savings that align with predicted savings. Projects above this line save more energy than
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expected, while projects below save less. Projects which fall below this line are actually
using more energy than was predicted for the code baseline building. Fully 25% of the
buildings show savings in excess of 50%, well above any predicted outcomes, while 21%
show unanticipated measured losses, i.e., measured energy use exceeding the modeled
code baseline. The projects with more aggressive energy performance goals seem to
generate overly optimistic predictions of actual energy use, while projects anticipated to
be higher energy users seem more likely to overestimate actual energy use. This would
lead to the risk of project failure, either for designers or clients.

Figure 1-1 Measured versus designed EUIs (Frankel and Turner, 2008)
Although simulation tools are getting increasingly sophisticated and even ignoring for
now the entry of erroneous data, accurate results can still be difficult to achieve. Data
must not only be accurate but also complete. With HVAC systems, for example, in most
simulation programs, users can only set the equipment type, efficiency, and other basic
parameters. However, the performance of HVAC system is a synthetic result of many
factors, and it may change dramatically based on different loads and operation schedules.
Some design strategy or techniques are hard to simulate though they are important
contributor of saving energy, for example, the thermal benefits of green roof are
sometimes missing in energy models. Although workarounds might exist to compensate
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for lack of software features for specific items, the results may not be precise. Another
problem is that different simulation programs have different types and levels of detail for
inputs although some of them share the same simulation engine, DOE-2 and EnergyPlus
for example.
To investigate the results variation among different simulation programs, 11 case
buildings were used to run energy simulations using seven prevalent simulation programs,
with settings as close as possible (Fig. 1-2). Each series in this chart presents the
simulation results (EUI) from different programs. It is clearly shown that even though
there is a similar trend among these 11 series, the variation of simulated EUIs from
different programs is significant. The problem discussed in previous paragraph are the
main reason for this, although it could be also attribute to different uses of these programs,
for instance, performance simulation, code compliance, LEED points.

Figure 1-2 Comparison of predicted EUI from seven programs of one building
(Series 1-11 present the simulation results of 11 buildings, the connected lines are used to show the variation)
There is clearly a need of simulation support for risk analysis that allows the user to
assess uncertainty and to present predictions with their associated uncertainties. There are
many sources of uncertainty when using modeling to assess the thermal performance of a
proposed building or retrofit project. Sensitivity analysis is an important technique for
determining the effect that uncertainties or model variations have on the model
predictions. It is important to evaluate the risks that result from these uncertainties. There
are several problems to be overcome including an understanding of all the factors that
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causes uncertainty, together with an estimate of the degree of uncertainty in model input
parameters. Then there is the need to develop the structure to automate the process of
undertaking sensitivity analysis and presenting the results. Designers should understand
these issues in understanding and applying results of energy software programs.
1.3 Hypothesis statement
1.3.1 Hypothesis
A probabilistically based method of risk assessment using energy performance simulation
that takes multiple factors into consideration can be achieved to yield expected building
energy performance and related energy cost information with associated probabilities.
The hypothesis takes into account four aspects:
1. The lack of risk assessment features hinders understanding of the reliability and
deviation in energy savings from virtual to real buildings.
2. A probabilistically based simulation can be used to realize risk assessment in energy
efficient building design.
3. This method will assist the project to gain reliability with possibility of predicted
energy performance.
4. This method could yield project energy cost information with reliable probabilities,
which could help investment decisions.
1.3.2 Objectives
Based on the hypothesis and the goal, four objectives have been set:
 Investigate performance risks in energy efficient building projects;
 Identify the most uncertain parameters in simulation through sensitivity analysis and
derive their probability value distribution;
 Develop and test the proposed method of risk assessment for EUI in an energy efficient
building project.
 Analyze the results from proposed method to prove the effectiveness in both energy
and cost wise.
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1.4 Significance of study
A tool for risk assessment of predicting energy use can be developed that provides better
reliability for both EUI calculations and utility cost.
1.4.1 Knowledge of risk
The simulation results will provide the distribution of possible energy performance
instead of one value. This will give both engineers and building owners a better
knowledge of the risk related to their projects.
 For engineers, they will have more confidence in their design with the knowledge that
the possibility of the match of actual and predicted building energy performance, as well
as the possible deviation of predicted energy savings.
 For building owners, the knowledge of risk helps them with decision-making. They are
clearer of the possible energy savings and consumption of the building that match their
expectations and requirements.
1.4.2 Risk management
Risk assessment provides the premise of risk management.
 Sensitivity analysis reveals the parameters that cause risk and how it may affect the
result. This provides a chance and direction for investigation and mitigation of risks in
these parameters so that reduce the risk of the energy efficient building project.
 The proposed method also provides a new way of design optimization. Currently
engineers optimize their design based on the simulated energy performance of different
design schemes. With the proposed method, engineers can take risk into account to
evaluate the possible energy performance. For example, a scheme with less energy saving
and low risk might be better that a scheme with more energy savings but high risk that
the building will not achieve those goals.
1.4.3 Industry benefits
Risk assessment is essential to correctly value energy-efficiency projects in the context of
investment decision-making in the building industry.
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 A risk management view of energy-efficiency essentially provides a shared framework
and language for the physical and financial realms, making it more accessible to financial
markets and decision-makers.
 Furthermore, it affords new opportunities for a whole range of financial risk
management products such as energy savings insurance or real options and derivatives
for energy efficiency.
1.5 Study statement
The main types of performance risks in energy efficient buildings will be investigated to
determine an overview of the problem. Building energy performance simulation is used
to analyze these risk sources. The uncertainty of simulation inputs will be detailed,
followed by a sensitivity analysis that identifies key uncertain and influential parameters.
The possible values of selected parameters will be presented as a distribution. A
probabilistic based method, based mainly on the Monte Carlo method, will be used for
risk assessment of these parameters in simulation. How to appropriately incorporate this
method with a simulation software program will be the key task for this study. At the
same time, investigation of current situation of risk assessment in industry will conducted
with field trip and by interviews, which helps in understanding the problem in practice
and verify the effectiveness of the proposed method from professionals’ perspective.
1.5.1 Workflow overview
The workflow mainly consists of five parts: sensitivity analysis, parameter possibility
analysis, Monte Carlo simulation, results processing, and result analysis.
1. Conduct sensitivity analysis to identify the most influential parameters affecting
energy performance of selected case building, with applicable sensitivity analysis
techniques.
2. Develop possibility distributions of selected parameters from sensitivity analysis
based on historical data, previous research, and professional judgment.
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3. Run Monte Carlo simulations with the possibility distribution of selected parameters
in a detailed energy simulation program. Due to the number of simulations to be run, an
automated method will be developed.
4. Collect and analyze the results from Monte Carlo simulation and conduct curve-fitting
technique to generate most fitted distribution curves of both energy performance
measures and energy cost.
5. Analyze the results with characteristics of generated curves to obtain risk assessment
results in both energy performance and energy cost aspects.
(See Chapter 4 for further explanation)
1.5.2 Thesis outline
Chapter 1 Introduction. Introduce what is meant by risk assessment for predicting energy
use through software simulation.
Chapter 2 Background. Provides a detailed description of risk assessment and uncertainty
in simulation. Introduces the methods and tools. Previous related research is
examined.
Chapter 3 Methodology. States the workflow of sensitivity analysis, distribution
derivation, risk assessment in simulation, as well as the interviews of professionals in
energy efficient building projects.
Chapter 4 Case Study. Shows the findings and results from sensitivity analysis, Monte
Carlo simulation, results analysis, and other work.
Chapter 5 Evaluation. Further presentation of findings, discusses the findings according
to hypothesis and industrial effectiveness, both energy and cost wise. Benefits and
deficiencies are also discussed.
Chapter 6 Conclusions and Future work. Summarize the whole research, state
conclusions from methodology and results analysis. Discuss what should be done to
improve the proposed method as future work.
25

1.6 Important Terminology
 Energy efficient building
An energy efficient building (both new construction and renovated existing buildings)
provides a significant reduction of energy consumption, compared with baseline models
or previous condition, used for heating, cooling, air quality by incorporating passive
strategies, and high-tech equipment in design.
 Building energy simulation
Also called building energy modeling, it is the use of software to predict the energy
performance of buildings using all the parameters that would affect the energy use of a
building, including building environment, geometry, materials property, system,
occupancy.
 Uncertainty
Uncertainty is the lack of certainty. “A state of having limited knowledge where it is
impossible to exactly describe the existing state, a future outcome, or more than one
possible outcome.(“Uncertainty” 2014)
 Risk assessment
Risk assessment is the determination of quantitative or qualitative value of risk related to
a concrete situation and a recognized threat (“Risk Assessment” 2014) Risk refers to the
uncertainty in energy efficient building projects.
 Sensitivity analysis
It is an important technique for determining the effect that uncertainties or model
variations have on the model predictions, and can be used to address the following
issues(I. Macdonald and Strachan 2001);
 Energy performance contracting (EPC)
EPC is a turnkey service, sometimes compared to design/build construction contracting
that provides customers with a comprehensive set of energy efficiency, renewable energy,
and distributed generation measures and often is accompanied with guarantees that the
26

savings produced by a project will be sufficient to finance the full cost of the project.
(NAESC, 2007)
 Energy use intensity
Energy use intensity (EUI) is expressed as energy usage per square foot per year. It is
calculated by dividing the total energy consumed by the building in one year (measured
in kBtu or GJ) by the total gross floor area of the building (citation?).

27

2. Background of risk and uncertainty analysis
Investigation of the risk in energy efficient building projects demands a high level of
understanding of the physical aspects of energy efficiency and their volatilities, as well as
the techniques to quantify risk. This chapter introduces related background and previous
research, including sources of risk, characteristics of input parameters, and risk analysis
techniques.
2.1 Understanding the risk
2.1.1 Introduction
Due to its volatile factors, building energy performance estimation contains uncertainty.
However, most building energy-related projects are carried out without a clear
understanding of their risk and uncertainties, which can cause concern to sophisticated
investors that are accustomed to evaluating investments on a value, risk basis. This is the
one reason that slowed the progress of energy efficient building projects, although large
potential energy savings is well established.
Several reasons lead to the deficiency of risk assessment, such as lack knowledge about
this issue, inadequate methodology or time, difficulties in prediction of physical factors
and behavioral or operation changes, and volatility in future energy rates. Under such
circumstances, energy engineers tend to avoid metrics that show evidence of uncertainty
rather than attempt to assess these risk. They use the strategy of stipulating a discounted
energy savings to deal with the potential downsides, but with no reflection of the
potential upsides. To some extent, energy companies avoided failure in business, but they
also lost the opportunity of achieving better energy savings and profit and even making
projects no longer attractive to clients. As illustrated in the definition of Enterprise Risk
Management: “risk is not simply a potential liability; it is also a potential
opportunity.”(Casualty Actuarial Society 2001)
2.1.2 Sources of risk
To shift from the current situation to a more sophisticated approach of risk assessment,
the identification and allocation of risks is clearly an essential step. Risks of energy
28

efficient building project can be grouped into two categories, intrinsic volatilities and
extrinsic volatilities (Mills and Weiss, 2004). Intrinsic volatilities includes elements that
directly affect the energy consumption by changes within the facility, they are
measurable, verifiable, and controllable. Extrinsic volatilities represent the factors that
affect the energy consumption risks that outside the facility, such as energy price, labor
cost, interest rate.
Evan Mills identified the risks associated with energy efficiency projects and classified
them into five categories, namely economic, contextual, technology, operation, and
measurement and verification risks (Mills and Weiss, 2004). Each of these contains both
intrinsic and extrinsic dimensions. Evan Mill’s method of identification and classification
is more from a financial perspective; it concerns the evaluation of risk for investment
purpose.
29

Figure 2-1 Matrix of risk in energy-efficiency projects (Mills and Weiss, 2004)
2.1.3 Energy simulation uncertainty
The sources of risk discussed above are at an economic level; they focus on the cost and
payback of projects investment. Considering that cost is a direct result from energy
consumption, at the technical level, engineers are more eager to know how to manage the
risk of the prediction of energy performance. The work of engineers is more about the
intrinsic factors that are controllable for them instead of the uncontrollable extrinsic
dimensions. To make an effective plan of risk management in energy-related projects, it
is crucial to carry out risk assessment from design or research phase when engineers step
on the stage, since this is the step to decide the energy consumption its risk and
uncertainty.
30

Energy simulation has been the most popular and accurate method of prediction and has
been heavily relied on by engineers since it was developed. Although simulation
programs might also generate risk from modeling error and inappropriate algorithms, it is
still the best tool for engineers to model the risk. In this case, risk sources from Fig. 2-1
that modeled or reflected in energy simulation programs can be tested for uncertainty in
simulations. In other words, the uncertainty in simulation is carrying the risk in energy
efficient building projects. Transformation from intrinsic and extrinsic risk to uncertainty
in simulation parameters is actually a way of transforming the concept of risk from
abstract to practical situations.
Building energy performance simulation is a complex process with thousands of input
parameters. These parameters (excluding software settings) can be roughly grouped into
four categories, considering the case model which is going to be used -- DOE reference
building.
 Program: Includes the activity, location, occupancy, plug and process loads, service
water heating demand, and schedules.
 Form: Includes geometrical measures of walls, roof, floors and windows, as well as
internal mass and infiltration.
 Fabric: Includes the construction types and thermal properties of the walls, roofs,
floors, and windows.
 Equipment: Includes interior and exterior lighting, HVAC, SWH equipment, and
refrigeration systems (Deru et al. 2011).
These parameters contain uncertainty due to the inaccurate estimation in design phase
and volatility in practice situation. Uncertainty in simulations has been briefly discussed
in Chapter 1.2 and more details of uncertainty in inputs parameters will be discussed in
Chapter 2.2 and Chapter 3.
2.2 Characterizing parameter uncertainty
As uncertainty in simulation parameters conveys the risk in energy efficient building
projects, the understanding of their volatility and variation is necessary and important for
31

the study of risk assessment. Characteristics of parameter uncertainties, applicable
probability distribution models, and some examples and related research are useful issues
for understanding risk assessment.
2.2.1 Introduction
Uncertainty in simulation occurs when values of volatile parameters are predicted and
might have variation or differences in value in real buildings. This is a problem of using
predicted values due to unavailability of necessary information during simulation. This
issue can be treated as an error of measurement, though sometimes it might actually uses
engineers’ experience or code instead real measuring tools. So the universal error types in
measurement can be used in simulation uncertainties: systematic error and random error.
 “Systematic errors
1
: biases in measurement that lead to the situation where the mean
of many separate measurements differs significantly from the actual value of the
measured attribute.
 Random errors
2
: errors in measurement that lead to measurable values being
inconsistent when repeated measures of a constant attribute or quantity are taken. ”
For convenience, uncertainty in simulation uses the definition of these two types of errors
above, called systematic uncertainty and random uncertainty. These definitions help in
the derivation of parameter probability distributions. Systematic uncertainty cannot be
removed from simulation or results correction, This kind of error can occur in building
energy simulations in cases related to deficiency in simulation, such as using incorrect
data for the given parameter, and employing the wrong or incomplete model of the
physical process (Macdonald 2002). This type of uncertainty happens when inappropriate
data is given or a wrong choice is made in simulation, such as wrong choice of not
calculating the heat transfer of thermal mass of exterior walls. Random uncertainty
cannot be attributed to a certain cause, but can be removed. For example, although the
simulation model is well-defined, the input parameters could still be uncertain due to
some measuring errors.

1
http://en.wikipedia.org/wiki/Systematic_error
2
http://en.wikipedia.org/wiki/Random_error
32

2.2.2 Probability Distributions
Techniques such as curve fitting using historical data, detailed modeling, and formula
derivation can be used for probabilistic analysis in order to generate probability
distributions of uncertain parameters (Macdonald 2002) . These distributions represent
the uncertainty of the parameter, which can be perceived as small pieces of risk that
compounding the whole risk of energy efficient building projects.
Among several types of probability distribution, discrete distribution and continuous
distribution are most used in practical risk assessment. These distributions are likely to be
assigned to each uncertain parameter to describe the uncertainty. Four applicable
distribution forms are discreet distribution, normal distribution, log-normal distribution,
and triangular distribution, based on to data availability, characteristics of energy
modeling, and requirements of simulation programs.
1. Discrete distribution (Fig. 2-2)
The discrete distribution requires that each possible value is given a probability of
occurrence, and the sum of the total possibility be equal to one. Parameters in energy
simulation like sky condition and water heater operating schedule (on/off) could be a
discrete distribution (I. A. Macdonald 2002).

Figure 2-2 Diagram of discrete distribution

33

2. Normal distribution (Fig. 2-3)
The normal distribution is an unbounded distribution that requires the mean value and
standard deviation of the parameter (I. A. Macdonald 2002). Parameters like cooling/
heating COP and wall insulation conductivity could be a normal distribution.

Figure 2-3 Curve of normal distribution
3. Log-normal distribution (Fig. 2-4)
The log-normal distribution is the combination of two or more variables that are normally
distributed. The human metabolic rate and infiltration rate are typical parameters that are
log-normal distributions. d(I. A. Macdonald 2002).

Figure 2-4 Curve of log-normal distribution
34

4. Triangular distribution (Fig. 2-5)
The triangular distribution is a bounded continuous distribution. It is can be used to
describe the uncertainty of parameters with limited historical data (I. A. Macdonald 2002).
For example, the occupancy rate in a space can be a triangular distribution by defining
the maximum and minimum occupancy, if not much data is available for curve-fitting.

Figure 2-5 Diagram of triangular distribution
2.2.3 Relevant research
Relevant research has been found about the variation of building energy related
parameters, as well as their influence on energy consumption. Some of these research
uses data-based methodology, and some use theoretical analysis methods. Three are
especially applicable.
Iain Macdonald from University of Strathclyde researched the derivation of parameter
possibility distribution (Macdonald 2002). He attributed the uncertainty to random error
and systematic errors, then developed the distribution for thermophysical parameters and
casual gains with historical data. To overcome a lake of data, he discussed the method of
developing distribution by using detailed modeling. He demonstrated this method by
using an air flow network to calculate the variation in air change rate. This is an
important article that helps the theoretical and methodology of distribution derivation for
the new proposed method.
35

Wei Tian and Pieter de Wilde from the University of Plymouth researched uncertainty
and sensitivity analysis of building performance using probabilistic climate projections
(Tian and de Wilde 2011). Their study presented a comprehensive overview of the key
methodological steps needed for a probabilistic prediction of building performance in the
long-term future. They made a sensitivity analysis and uncertainty analysis due to climate
changes, including climate condition change and climate and interventions in buildings.
They proved their methodology in a case study of an air-conditioned university building.
Their simulation results indicated that annual heating energy will decrease and annual
cooling and carbon emissions will increase as the climate warms. This article helped
build the risk model of weather inputs that was used in the new proposed method.
Elie Azar and Carol C. Menassa from University of Wisconsin-Madison studied the
impact of occupancy parameters in energy simulation of office buildings (Azar and
Menassa 2012). They studied the parameters related to the energy consumption behavior
of occupants. They did sensitivity analysis on building energy consumption using
simulations of typical office buildings of different size and in different weather zones and
found that occupancy behaviors significantly influence energy use, and related parameter
inputs are rarely considered in modeling process. Also, they found that the influence of
the different occupancy behavioral parameters varies according to building size and
weather conditions. They support the hypothesis that uncertainty in energy efficient
buildings has great impact in performance.
2.3 Risk analysis techniques
There are many methods of assessing risk. One needs to determine what methods are
available and discover which technique is applicable for a specific methodology.
Sensitivity analysis and the Monte Carlo method may be useful in the risk assessment for
energy prediction.
2.3.1 Introduction
Risk analysis techniques have been well developed and are widely used in business
models. These techniques can be grouped into three groups: quantitative, qualitative, and
mixed qualitative-quantitative (Modarres 2006). These techniques can be applied to
36

building energy efficient projects with appropriate modification, considering the uniform
nature of risk, and quantitative risk analysis are most favored by practitioners. Facing the
problem of uncertainty in energy performance prediction, several techniques such as
uncertainty analysis and sensitivity analysis, have been studied and developed to perform
risk assessment in the context of building energy efficient projects.
Uncertainty analysis assesses the risk by taking into account uncertainties in simulations
due to deficiency in modeling or the lack of information with regard to input parameters.
Such analysis usually use a deterministic model with assignment of probability
distributions to uncertain input parameters (Calleja Rodríguez et al. 2013). Capozzoli et
al. used uncertainty analysis to assess the uncertainty of a set of variables identified
during building conceptual design stage (Corrado, Capozzoli, and H.E 2009). Hyun et al.
assessed the uncertainty of natural airflow rate of high-rise apartment buildings using
uncertainty analysis (Hyun, Park, and Augenbroe 2008). In addition, other methods have
also been studied in this area. Rickard et al. used a technique of coefficient of variation to
compare uncertainties in different energy efficiency measures (Rickard et al. 1998).
This method is an alternative to that developed.
2.3.2 Sensitivity analysis
Sensitivity analysis is an important technique that can be useful for a range of purposes in
many sectors. It is a process of measuring the magnitude of the effects on model outputs
by modifying model inputs. It enables both the parametric studies to determine the
influence of inputs variations on outcome and the error analysis to assess the
consequences of errors or uncertainties on predictions(Lomas and Eppel 1992). In the
context of building energy efficiency, sensitivity analysis plays an important role in
understanding the modeling. Two types of sensitivity, individual sensitivity of each
parameter and total sensitivity due to variations in all inputs, can be evaluated through
sensitivity analysis to help study the knowledge in building energy simulation as
following:
 Identify the most influential input parameters by calculating the sensitivity of input
parameters on output. This helps to identify which parameters have to be chosen for
37

certain purpose of study. For example, sensitivity analysis has been used in the proposed
method to identify the most influential and uncertain parameters.
 Identify important characteristics of the input and output variables and hence study
responses of building systems to perturbations (Lam and Hui 1996).
 Identify the features of building to one particular output is particularly sensitive. This
can guide the designers and fabricator towards an improved work.
 Identify the probability distribution of the results in order to learn the likelihood that
the energy use will not exceed a particular value (Lomas and Eppel 1992).
There are three common used sensitivity analysis techniques , differential sensitivity
analysis (DSA), random sensitivity analysis (RSA), and stochastic sensitivity analysis
(SSA) (Lomas and Eppel 1992).
1. Differential sensitivity analysis
Differential sensitivity analysis is the most used technique because of its ability of
exploring the sensitivity of output to input directly. It is a structured method based on the
behavior of the model for a base-case scenario and is theoretically based on partial
differentiation of the aggregated model. DSA often assumes that each input is distributed
normally about the base case value, and the relationship between inputs and output is
linear. So, an average value for the sensitivity, over the likely range of input parameter
change, is usually the most relevant measure (Lomas and Eppel 1992). Differential
sensitivity analysis was applied in the proposed method to eliminate non-important
parameters and identify most influential and uncertain parameters.
2. Random sensitivity analysis
In random sensitivity analysis (RSA), all uncertain inputs are assigned a definite
probability distribution. Simulations take place by selecting one value from each
distribution each time randomly. So a large amount of simulations will be performed to
obtain the total uncertainty. RSA can be used to study total sensitivity. This technique
also takes into account non-linearity relationships.

38

3. Stochastic sensitivity analysis
Compared with the other two techniques, stochastic sensitivity analysis (SSA) is
mathematically and computationally far more complex. It seeks to generate the
sensitivity of prediction to individual parameters. Also, SSA is different from the other
two methods since it is a process of varying input parameters simultaneously as the
simulation progress (Lomas and Eppel 1992). However, this method has rarely been used
in simulation due to its complexity and constraints of software.
2.3.3 Monte Carlo method
The Monte Carlo (MC) method, naming after a famous casino, is a well-known non-
structured risk analysis technique. It has been widely applied in many sectors, including
random sensitivity analysis discussed in Chapter 2.3.2. This technique seeks to represent
reality through a mathematical risk model, with a method of assigning values randomly to
the input parameters of the model. In the proposed method, the assigned values are from
possible scenarios that are obtained from empirical data collected from real practical
situations.
In operation, all input parameters or most influential parameters selected by sensitivity
analysis, are assigned a probability distribution. Then sampling is processed from those
distributions to generate inputs combinations, followed by a large number of simulation
iterations to get results. With the obtained results, a statistical study is usually performed
to extract conclusions with respect to the risk, such as mean, maximum and minimum
values, standard deviations, variances, and likehood of occurrence of the different
variables determined on which to measure the risk. Sufficient simulation iterations and
appropriate sampling are the fundamentals of a well-performed Monte Carlo simulation
(Hopfe and Hensen 2011).
The main difficulty in employing this method is in identifying the appropriate
distributions of input parameters ( Macdonald and Strachan 2001). In practice, basic
distribution, such as normal distribution, log-normal distribution, and triangular
distribution are assumed. The collecting of data from real situation are tough and time
consuming. However it is critical for accuracy. One major drawback of the Monte Carlo
39

method is that it can only measure the overall risk or uncertainty, and the simulation
iterations need high-performance computers and take a lot of time.
The Monte Carlo method has been favored by researchers in building energy related
studies, due to its advantage of the ability of showing a range of possible scenarios, and
simplicity for performing computer simulations. Jason has used Monte Carlo simulation
to study the energy cost variation of energy efficient building project, with three group of
distributed inputs: weather, performance, and energy price (Jackson 2010) (Fig. 2-6).

Figure 2-6 Monte Carlo analysis in building energy efficient project (Jackson 2010)
2.3.4 Relevant research
Research about sensitivity analysis, uncertainty analysis, and other related topics is more
common in other fields. There is less available about overall risk assessment of energy
efficient building projects. Three relevant studies provide clues as to future work.
Kevin J. Lomas and Herbert Eppel from De Montfort University explored sensitivity
analysis techniques for thermal simulation programs (Lomas and Eppel 1992). This is
almost the earliest research about sensitivity analysis in building science sector. In their
work, they studied the benefit of applying sensitivity and defined three applicable
techniques in building thermal simulation, differential sensitivity analysis, Monte Carlo
analysis, and stochastic sensitivity analysis. Then they compared these three techniques
by application in different simulation programs, measuring sensitivity in both hourly and
40

daily average prediction with 70 uncertain input parameters. They described advantages
and disadvantages of these three sensitivity analysis techniques. Kevin and Herbert’s
research gave a comprehensive introduction and comparison between different sensitivity
analysis techniques, as we as their application in energy simulations. This article helped
to make the decision of selecting differential sensitivity analysis as the appropriate and
feasible technique.
Iain Macdonald and Paul Strachan from University of Strathclyde studied the practical
application of uncertainty analysis in building energy simulation (Macdonald and
Strachan 2001). They 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. They tested this function of ESP-r
by an application on a refurbishment project in UK. It turned out that this helped the
owner to make an informed decision on plant size taking the possible energy savings and
the risk of potential under heating into consideration. Macdonald’s and Strachan’s
research helped in the development of initial methodology workflow. ESP-r is good tool
that has already capable of Monte Carlo simulation; however, it is not used in the test of
proposed method due to operability reasons.
Christina J. Hopfe and Jan L.M. Hensen from Cardiff University investigated the
potential design support by applying uncertainty analysis in building performance
simulation (Hopfe and Hensen 2011). They studied the uncertainty in physical parameters,
design parameters, and scenario parameters using Monte Carlo analysis and Latin
hypercube sampling in a realistic case. A conclusion was drawn that the uncertainty of
these three kind of parameters can lead to greater quality assurance of modeling and
better design decisions. This article is meaningful in demonstrate the effectiveness of the
proposed method, as well as the selection of uncertainty input parameters.
41

3. Methodology
In order to assess uncertainty and risk in energy efficient building projects, a probabilistic
based simulation method has been proposed. This chapter documents the overall
methodology and workflow used to pursue this goal, and details each step of the research
process, namely sensitivity analysis, probability analysis and Monte Carlo simulation. In
addition, the case model and interview of professionals and other related content are also
explained.
3.1 Workflow overview
3.1.1 Methodology development
Risk assessment has been used for many years in business applications, and there are
mature techniques in mathematics and statistics. However, those methods cannot be
directly used in energy efficient building projects unless appropriate modifications are
made due to the restriction of tools and lack of historical cases.
Literature review in mathematics, statistics, and energy simulations as well as discussions
with professionals in building energy industry provided the theoretical basis and the basic
idea of how to develop and design the methodology. The basic idea of the proposed
method is that one can use energy simulation program as a tool to assess risk by
incorporating applicable mathematic techniques with a few modifications and
assumptions to it. The risk in energy efficient building projects was presented as cases
varied from estimation or expectation in energy related building aspects, such as weather,
occupancy, construction and etc. Then these unexpected cases were presented and
collected in the inputs of simulation programs as uncertainties with an expression of
distributions. Finally, these small pieces of uncertainties were collected through
appropriate simulation processes to generate the overall risk of energy efficient building
projects.
The proposed method is relatively easy to realize considering the restriction of current
simulation programs and available data. The precision will be limited by assumptions and
simplification in order to create the prototype, but with good inputs for the probability
42

analysis and enough simulation, the proposed method is able to generate reasonably
reliable results.
3.1.2 Overall workflow
The workflow of proposed method can be divided into four steps: risk analysis, risk
combination, risk presentation, and economics analysis. (Fig.3-1).

Figure 3-1 Overall workflow of proposed method
1. Risk analysis
There are numerous possible sources of risk that can cause the variation in building
energy performance, such as the mistakes in installing insulation or change of cooling set
point. 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 for example)
by identifying and generating possibility distributions. It is possible to derive the
43

possibility distributions mathematically based on the range of values for the parameters
or from specific information (like manufacturer specifications) 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 done to eliminate some
parameters by professional experience, followed by a differential sensitivity analysis 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. Risk combination
Risk analysis identified risks in uncertain parameters and their possibility distribution.
Risk combination is the step to collect all small pieces of risks into whole risk. Monte
Carlo simulation was used here to implement this goal in a stochastic way. 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.
3. Risk presentation
After collecting all the results from previous step, a curve-fitting technique was processed
to get the possibility 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.
44

4. Economics analysis
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 (Fig. 3-2). The total represents the total charges on
that tariff for the energy source used (EnergyPlus Documentation, 2012).

Figure 3-2 Energy cost calculation method in EnergyPlus (EnergyPlus Documentation,
2012)
Actually the utility cost calculation is more sophisticated than the chart above. 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 (Table 3-1). 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.

45

Table 3-1 Tariffs used in energy cost calculation
Tariff
Qualify
(kW)
Energy use ($ / kWh) Demand ($ / kW)
Service
($/Mon)
Tax
On
Peak
Off
Peak
Mid
Peak
On
Peak
Off
Peak
Total
Electric
1
Summer
Demand
＞500
0.1676 0.1676 0.1676 8.84 0.76 n/a 246.33 8%
Winter/
Annual
0.1676 0.1676 0.1676 n/a n/a 6.35 246.33 8%
2
Summer
Demand
（20 ,
500 ）
0.0808 0.0808 0.0808 0 0 0 74.03 8%
Winter/
Annual
0.0351 0.0351 0.0351 0 0 0 74.03 8%
3
Summer
Demand
＜20
0.0189 0.0189 0.0189 7.04 7.04 n/a 15.25 8%
Winter/
Annual
0.0189 0.0189 0.0189 n/a n/a 5.44 15.25 8%
Gas 1 n/a n/a Different in each month 0 8%

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.
3.1.3 Implication of proposed method
To summarize, the main difference between the proposed method and the currently used
method are the inputs and simulation process. (Fig. 3-2). Those two differences are the
key points that enable the proposed method to assess risk in energy efficient building
projects.
46

Figure 3-3 Comparison between current method (top) and proposed method (bottom)
Two major differences between the current method and the proposed method are the
range of inputs and use of Monte Carlo simulation. There are distributed inputs instead of
fixed values conveying uncertainty and risk into simulation. These distributions were
developed with real data from previous research, standards, and professional judgment to
represent possible scenarios occurring after buildings get into use. This is the
fundamental process of the proposed method, should be processed in the right direction
(related with reality) and an appropriate way (accurate enough).
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 large amount of
parametric simulations, the more the better.

47

3.2 Professional interviews
Professionals can provide practical advice about real world reliable energy performance
prediction and methods of risk assessment.
3.2.1 Introduction
In order to gather first-hand information, four professionals from building energy related
companies in California were interviewed. California is the place that has the state-of-art
green building concept and technologies, as well as strict energy codes and standards.
These four professionals are experts in building energy analysis with years of practical
experience. The information and suggestions they provided were important and valuable
in this research.
One professional (James Rudd) is from a consulting company (Honeywell) which
provides Energy Performance Contracting (EPC) service. EPC is a turnkey service that
guarantees the energy savings produced by an energy efficient building project will be
sufficient to finance the full cost of the project. EPC projects focus on retrofit projects
that enable designers and engineers to calibrate energy model with real data, which is a
little different from the proposed method. Nonetheless, the information from EPC
professionals is still valuable since they have good knowledge of risk and risk
management. One professional is from a consulting firm, he is an energy analyst with
emphasis on energy modeling. The other two professionals are from energy consulting
companies that provide building energy simulation, integrated design, and
commissioning. They all have good knowledge and rich experience in simulation,
prediction discrepancy, and practical situations.
3.2.2 Interview outline
Each of these four professionals was interviewed several times through emails or face-to-
face meeting during different phase of the research process. The interview outline can be
summarized in the following three categories:
1. Risk in energy efficient building projects
This was the topic during interviews at the early stage of research, preparation, and
methodology development. These four professionals provided their experience in real
48

projects where they met problems like discrepancy between predicted and actual energy
performance. They agreed that a 15% accuracy rate is a widely accepted judgment of
good prediction and talked about how they usually deal with such problem in signing
contracts, doing code compliance, and remedying energy saving shortfall respectively.
Also, they provided ideas in how to manage risk in such projects and make more reliable
energy model. This information was valuable in identifying problems, setting objectives,
and developing methodology.
2. Experience and data in practice situations
During the stage of sensitivity analysis and parameter probabilistic analysis, professionals
shared their experience in real projects. They offered help in selecting important and
uncertain parameters. Also, they talked about possible scenarios in practice, like the
mistakes in installing wall insulation, HVAC operating, and etc. They provided the
parameter values of most likely and extremely scenarios. All these information helped in
preliminary parameter selection, derivation of probabilistic distribution by connecting the
proposed method with practice situations.
3. Information in energy simulation
Throughout the research, these professionals provided information in energy analysis
techniques. They shared their experience in how to collect data and information for
energy modeling, find reference (code or research) for modeling, and pros and cons of
different simulation programs. They also generously provided help and ideas in technical
problems.
3.2.3 Interview content
 James Rudd
Company: Honeywell
Position: Solution Development Engineer (ESPC)
James Rudd is an experienced engineer in the field of energy performance contracting,
which guarantee energy savings. The interview with him was mainly about how they
manage the risk in EPC projects. He stated that most of their projects were retrofit of
upgrading HVAC system, lighting, and building envelop. The main method he used in
49

managing the risk of discrepancy between real and predicted energy performance is to
well use the Measurements and Verification (M&V). He explained that there are four
M&V options for EPC, retrofit insolation with key parameter, retrofit insolation with all
parameter measurement, utility data analysis, and calibrated computer simulation. Among
these four options, the last one is most used. Since most of the EPC projects are retrofit,
the real data can be obtained by metering, measurement, and from utility bills. With these
information, engineers are able to well calibrate the energy simulation model, make sure
that the simulation input values are as close as possible to real data.
 Justin Di Palo
Company: Glumac
Position: Energy Analyst
Justin Di Palo is an experienced engineer in the field of energy modeling and analysis.
The interview with him was mainly about how he decides the simulation inputs values
and the associated uncertainty. He stated that most of value used are obtained from
guidelines, architect, and the owner. These values are all best estimations since no real
data is available, thus there is clear uncertainty and risk. They never guarantee the energy
performance, and usually give a conservative range of prediction. He stated that they
were always trying to make the simulation more accurate and decrease the risk. One
strategy is that, he keep in touch with clients or owners from the beginning to the end,
requiring most updated information for occupancy schedules and internal loads, which is
very helpful to calibrate the energy model. Glumac keeps track of its previous projects,
comparing the real and predicted energy performance. Justin showed a chart, which
indicates the discrepancy of different kind of buildings, commercial, residential,
education, and others. Because of the confidential reasons, he was not able to share the
information, but he stated that usually they take 15% accuracy rate as a criteria to
evaluate if the energy simulation is good enough.
 Jason Lorcher
Company: Green Dinosaur
Position: Principal
50

Jason Lorcher is an experienced engineer providing consultant in energy efficiency,
commissioning, and sustainability. The interview with him was mainly about possibility
of discrepancy between true value in reality and estimated value used in simulation. He
introduced many real cases he had met in practice regarding the uncertainty of parameters,
including the mistakes in construction of wall insulation, poor operation of HVAC
system, under-performed chiller, and many other. Based on his experience, he introduced
the parameters that has the most uncertainty, and more likely to deviate from estimation.
He said that the commissioning and metering are important steps that make sure the
system works as expected. Besides, he also mentioned the inaccuracy of weather files
used in simulation, the historical data is not enough to present the real weather conditions
any more due to the climate change. Jason agreed with Justin that, prediction within 15%
error rate is evaluated as a good simulation. He also suggested several guidelines and data
bases that could be used to develop parameter probability distribution.
 Jeffrey Landreth
Company: CTL-E
Position: Principal
Jeffrey Landreth is an experienced engineer providing consultant in energy efficiency,
and he has very a good skill and knowledge of using energy simulation softwares. The
interview with him was mainly about simulation programs, and the sensitivity of input
parameters. Based on his experience, Jeffrey talked about the feasibility of realize Monte
Carlo simulation in different simulation programs, he suggested that, EnergyPlus and
Grasshopper might be good choices. Also, he gave advices on how to automatically run a
large amount of simulations in a limited time. Jeffrey stated that, in the Los Angeles
climate zone, cooling related input parameters, such setpoint, chiller COP, and internal
cooling load could be very sensitive to the total energy performance.
3.3 Sensitivity analysis
Sensitivity analysis (SA) plays an important role in the understanding of complex models
like building energy performance simulation. This technique helps to understand the
influence of input parameters in relation to the outputs, hence identify the influential
51

parameters, and eliminate the non-important parameters as well. After comparing three
different kinds of sensitivity analysis techniques, differential sensitivity analysis (DSA)
was finally selected.
3.3.1 Theoretical basis of DSA
Differential sensitivity analysis is widely used because it enables to explore the
sensitivity of the outputs to inputs directly. In addition, sensitivity analysis is relatively
easy to implement in energy simulation programs. This is another reason that makes DSA
the best choice here. DSA involves varying just one input for each simulation whilst 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. Appropriate assumptions had been made to
accommodate sensitivity analysis in building energy simulation, considering the
characteristic of inputs and outputs. The theoretical basis of this step is shown below.
The output (OP) of building energy simulation is the result of many input parameters, so
the simulation process can be expressed in general by multi-variable function f with n
numbers of depending variables:
12
( , ,..., )
n
OP f x x x 
(3-1)
Based on the chain rule of partial differentiation, the differential is given by:
12
12
...
n
n
f f f
df dx dx dx
x x x
  
   
  
(3-2)
So, the gradient of the function for one parameter, take
1
x for example, can be expressed
as:
23
1 1 2 1 3 1 1
. . ...
n
n
df f f dx f dx f dx
dx x x dx x dx x dx
   
    
   
(3-3)
To make it possible to change one input parameter at one time and measure its sensitivity
of the output, two assumptions had been made:
52

 Assumption 1: All the input parameters are independent with each other.
So,
1
x is independent of
23
, ,..., ,
n
x x x then

23
1 1 1
... 0
n
dx dx dx
dx dx dx
   
(3-4)
Substituting equation (4) into (3), therefore, the partial derivatives of
1
x may be
approximated by the simple differential:

11
df f
dx x



(3-5)

 Assumption 2: Assume each parameter is linear about the output.

1 1 1
df f f
dx x x



(3-6)
After the theoretical deviation and assumptions, DSA is ready to be used in building
energy simulations. Although not all the input parameters are independent with each
other, also the relationship between of inputs and outputs won’t be exactly linear, the
purpose of sensitivity analysis here, however, is to eliminate the non-important
parameters instead of identifying the exact influential coefficient of each input parameter.
Also the changes made in input parameters were in a small scale around its mean value,
which the relationship can be approximately treated as linear.
3.3.2 Preliminary parameter selection
Before the sensitivity analysis, a preliminary selection of input parameters is necessary
due to the limitation of time and software capability. Building energy simulation is a
complex process of more than a thousand input parameters. It is unnecessary to do
sensitivity analysis of each parameter, since some of them can be eliminated easily by the
judgment of experienced energy modeler. Considering the final target of assessing risk in
energy efficient building projects, the parameters selected from sensitivity analysis
should have two attributes: sensitive to output and uncertain in practice. Besides their
53

sensitivity, these parameters should be uncertain which lead to value variations in real
situations. For example, the building orientation is of high sensitivity to building energy
consumption, it will be eliminated by preliminary selection because the orientation of the
building (once selected) is set fairly tightly in construction and hence that parameter’s
uncertainty is low.
The preliminary parameter selection was based on parameters from two sources: the
documentation for the reference building from DOE and the EnergyPlus file of the model.
In the DOE reference building document, energy model parameters are grouped into four
categories (Table 3-2).
Table 3-2 Energy model input categories (Deru et al. 2011)
Program Form Fabric Equipment
Location Number of floors Exterior walls Lighting
Total floor area Aspect ratio Roof HVAC system types
Plug and process loads Window fraction Floors Water heating equipment
Ventilation requirements Window
locations
Windows Refrigeration
Occupancy Shading Interior
partitions
Component efficiency
Space environmental
conditions
Floor height Internal mass Control settings
Service hot water demand Orientation Infiltration
Operating schedules

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.
Finally, 17 parameters in four categories were kept from the preliminary elimination
(Table 3-3).

54

Table 3-3 Parameters identified after Preliminary Selection
Category Parameter Unit Value
Fabric
Wall Insulation Conductivity
w/m-k 0.049
Roof Insulation Conductivity
w/m-k 0.049
Glass U-Factor
W/m
2
-k 3.240
Glass SHGC
N/A 0.250
Program
People Density
m
2
/person 18.580
Lighting Density
W/ m
2
10.760
Equipment Density W/ m
2
10.760
Zone Setting
Infiltration Rate
m
3
/s-m2 0.000302
Design Airflow
m³/person 0.010
Cooling SA Temperature ℃ 14.000
Heating SA Temperature
℃ 40.000
Cooling Setpoint
℃ 24.000
Heating Setpoint
℃ 21.000
Equipment
Fan Efficiency
N/A 0.53625
Fan Motor Efficiency
N/A 0.825
Coil Cooling COP
N/A 3.667
Coil Heating Efficiency
N/A 0.800

3.3.3 Selection of range and interval
One perturbation is enough to get the sensitivity of one parameter at a time based on the
theoretical derivation and assumptions. However, to minimize the impact of dependence
of parameters as well as non-linearity problems, several simulations with different
perturbations of each parameter were processed in order to get more accurate result. 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 in practice to present actual situations. 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. Take the Cooling Setpoint for example, the interval was decided
as 1 ℃ to represent the real situation in practice of using thermostat.
55

3.3.4 Influential coefficient calculation
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
enable the comparison among different input parameters. IP is input parameter from 17
parameters selected from preliminary selection, and OP is the total HVAC energy
consumption. All base cases (bc) are the inputs values or HVAC energy consumption
from initial DOE reference model. To test the non-linearity problem, SD% is defined as
the standard deviation (SD) of IC values divided by IC mean value.

bc bc
bc bc
OP OP IP IP
IC
OP IP


(3-7)
IC: Influential Coefficient; OP: Output; IP: Input Parameter; bc: Base Case

After this preparation, a sensitivity analysis was conducted for each selected parameter
using simulations. Each parameter required 8 to10 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%. In this process, EnergyPlus was used as the
simulation engine, and jEPlus was used as a parametric manage tool (Fig. 3-4). Finally,
134 simulations were identified and run on a computer with an Intel Core i7 processor.

Figure 3-4 Process of sensitivity analysis using simulations
3.4 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
56

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.
3.4.1 Techniques of distribution derivation
Based on attributes of selected parameters and the previous research of probability
analysis, two types of distribution were considered: discrete distribution and continuous
distribution. Four different forms of continuous distribution were considered: even
distribution, normal distribution, long-term distribution, and triangular distribution.
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 (See chapter 2.2 and 3.2). Then data was
collected from official empirical database and previous research to determine the
corresponding probabilistic distribution function (See chapter 2.2) Some adjustment was
made on choice of distribution forms based on the quantity of available data, and a
triangular distribution would be proposed to represent the PDF if the available data is
very limited. For parameters with enough empirical data, curve-fitting techniques will be
used to generate their PDF. To test and evaluate the reliability, three goodness-of-fit tests
were performed: Chi-square test, the Kolmogorov-Smirnov (K-S) test, and the Anderson-
Darling (A-D) test.
However, in the case study (see Chapter 4), 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.
3.4.2 Weather file variation
As the growing issue of global warming, the impact of weather change on building
energy performance cannot be ignored, especially when passive strategies are used,
natural ventilation for example. The uncertainty of weather condition is an important
aspect that leads to the risk of energy performance, especially in the life-cycle analysis.
Current simulations use one single weather file to predict energy performance. This
weather file is generated from the weather data collected in the past a period of time
57

instead of real time data, using the average values. This is clearly a flawed prediction of
real weather condition in the future.
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. The model is developed in Hadley
Centre in United Kingdom (Collins, Tett, and Cooper 2001). The model divides the
climate zone into small blocks by 96 longitudes and 73 latitudes, and in each block
formed by the grid lines, a specific local scenario is provided to accurately reflect the
climate change level in that specific region.
In the case study, 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 (Yiyu Chen, 2015).
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 probability of these four weather conditions was found, thus an
assumption was made regarding to the probability (Fig.3-5). This is a relatively
conservative assumption comparing 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.

58

Figure 3-5 Assumed probability of different climate change scenarios
3.5 Monte Carlo simulation
Using the probability distributions of selected input parameters, the Monte Carlo method
was used in the analysis to generate distributed simulation results that can be used for risk
analysis. As mentioned in previous chapters, the process of parameters’ probability
distribution derivation is to identify their risk and uncertainty in practice situations.
Respectively, Monte Carlo simulation served the purpose of collecting all these small
pieces of risk in a stochastic way (Fig. 3-5).

Figure 3-6 Workflow of Monte Carlo simulation
3.5.1 Introduction of the Monte Carlo method
The Monte Carlo method is one of the most used statistical sampling methods in solving
problems with uncertainty. It translates the uncertainty in inputs into uncertainty in
outputs by determining probabilities of possible outcomes by running large amount of
59

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.
Sampling, which is selecting value from distribution, is one important step in this
analysis. Among several sampling techniques, Latin Hypercube Sampling (LHS) was
finally selected due to its advantage of reflecting the shape of a defined distribution more
precisely with relative small sample size. In LHS, the probability distribution is first
divided into ranges of equal probability, and then one sample is taken from each range
(Lu, Huang, and Zhang 2013).

Figure 3-7 Latin hypercube sampling
3.5.2 Simulation iteration
The sampling of probability distributions generated thousands of combinations of
different values from each input parameter. These value combinations were used as
inputs for simulation iteration (Fig. 3-5). JEPlus was used to manage the parametric
simulation task by automatically substituting selected input parameters with new-value
combinations from sampling. To instruct jEPlus to finish the job, several CVS-style text
files containing thousands of values of selected parameters were made. Since the
60

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) and
Amazon EC2.

Figure 3-8 Interface of jEPlus and EnergyPlus
3.5.3 Results 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-of-goodness was
conducted, Chi-Square Test, Anderson-Darling Test, and Kolmogorov-Smirnov Test. The
results from these three tests was used to rank all curves in order to identify the best fitted
one.
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.

61

4. Case study
4.1 Overview
To test and demonstrate the feasibility and effectiveness of the proposed risk assessment
method, the DOE commercial reference building model, small office (new construction)
in Los Angeles, was used as a case study. Following proposed methodology, this chapter
gives a brief introduction of the case model and then shows the results from each major
step of the case study. For clarity and readability, this chapter follows the exact order of
chapter 3 (Fig.4-1).

Figure 4-1 Index of results presented in Chapter 4
4.2 Introduction of the case model
The reference models were created by the Department of Energy (DOE) to represent new
and existing buildings and therefore provide support for building energy efficiency
research. Some of the input parameters were determined from ASHRAE Standards 90.1-
2004, 62.1-2004, and 62-1999; others were determined from studies of data and standard
practices (Deru et al. 2011). The Los Angeles small office model was selected because
62

of its complete building description and representativeness of reasonably realistic
building characteristics and construction practices. The file is also publically available if
others would like to examine it more carefully both for the building specification and
simulation results (http://energy.gov/eere/buildings/new-construction-commercial-
reference-buildings).

Figure 4-2 Axonometric view of case model---small office in Los Angeles (Deru et al.
2011)
DOE has provided an EnergyPlus file (.idf) and a whole model description. This building
is a rectangular 1-floor

small office with a total floor area of 511 m
2
, one core thermal
zone, and four perimeter zones (Table 4-1).
Table 4-1 Brief description of major model thermal properties
Program
ASHRAE 90.1-2004 Climate Zone 3B-CA
Location Los Angeles
Fabric
Exterior walls
Construction Type Mass wall
R-value (m
2
·K / W) 1.17
Roof
Construction Type Attic
R-value attic floor (m
2
·K / W) 5.18
Window
U-Factor (W / m
2
·K) 3.24
SHGC 0.25
Visible transmittance 0.16
Foundation
Foundation Type Mass Floor
63

R-value (m
2
·K / W) 0.54
HVAC
System Type PSZ-AC
Heating Type Gas furnace
Cooling Type Unitary DX
Fan Control Constant volume
4.3 Results from sensitivity analysis
4.3.1 Preliminary selection of parameters
The preliminary parameter selection was conducted by first examining all parameters
used in the energy modeling. Two sources were used to extract these parameters: the
document from DOE and the EnergyPlus file (.idf) of the model. Excluding geometrical
parameters and other nonnumeric parameters, such as building type and material types,
46 parameters and their values from the document were listed in a spreadsheet (Appendix
A-1). Then, a careful check of the EnergyPlus file was done in EP-launch to uncover any
parameters not mentioned in the document (Appendix A-2).
Based on information from the literature review and professional interviews (see Chapter
3.3.2), 17 uncertainty and energy-sensitive parameters from four categories were selected,
based on their characteristics of uncertainty and sensitivity (Table 4-2).
Table 4-2 Parameters identified after preliminary selection
Category Parameter Unit Base Value
Fabric
Wall Insulation Conductivity
W/m-k 0.049
Roof Insulation Conductivity
W/m-k 0.049
Glass U-Factor
W/m
2
-k 3.240
Glass SHGC
N/A 0.250
Program
People Density
m
2
/person 18.580
Lighting Density
W/ m
2
10.760
Equipment Density W/ m
2
10.760
Zone Setting
Infiltration Rate
m
3
/s- m
2
0.000302
Design Airflow
m³/person 0.010
Cooling SA Temperature ℃
14.000
Heating SA Temperature ℃
40.000
Cooling Setpoint ℃
24.000
Heating Setpoint ℃
21.000
64

Equipment
Fan Efficiency
N/A 0.53625
Fan Motor Efficiency
N/A 0.825
Coil Cooling COP
N/A 3.667
Coil Heating Efficiency
N/A 0.800

4.3.2 Perturbations
To proceed with the differential sensitivity analysis, appropriate range and intervals were
determined for all 17 parameters (Table 4-3). These selected ranges would cover the two
extreme scenarios in record from relevant literature to present actual situations, and the
intervals of each parameter are narrow enough to support the assumption of linearity. The
column headers are shown in the following, more information can be found in Chapter
3.3:
 Parameter: Energy simulation inputs that were identified from preliminary selection
 Unit: Unit used in simulation program for selected parameters.
 Min. (Minimum): Minimum value defined for the range of parameter values
 Base: Value of base case, which is extracted from DOE reference model file.
 Max. (Maximum): Maximum value defined for the range of parameter values
 Interval No. : Numbers of intervals in sensitivity analysis.
Table 4-3 Results of range and interval selection
Category Parameter Unit Min. Base Max. Interval No.
Fabric
Wall insulation
conductivity
W/m-k 0.041 0.049 0.057 0.002 8
Roof insulation
conductivity
W/m-k 0.041 0.049 0.057 0.002 8
Glass u-factor W/m
2
-k 2.540 3.240 3.940 0.140 10
Glass SHGC N/A 0.100 0.250 0.400 0.050 6
Program
People density m
2
/person 12.580 18.580 24.580 1.500 8
Lighting density W/ m
2
6.760 10.760 14.760 1.000 8
Equipment density W/ m
2
6.760 10.760 14.760 1.000 8

Zone
Settings
Infiltration rate m
3
/s- m
2
0.00010 0.00030 0.00050 0.00005 8
Design airflow m³/person 0.005 0.010 0.015 0.001 10
Cooling supply air
temperature
℃
10.000 14.000 18.000 1.000 8
Heating SA
Temperature
℃
36.000 40.000 44.000 1.000 8
65

Cooling setpoint
℃
21.000 24.000 27.000 1.000 6
Heating setpoint
℃
18.000 21.000 24.000 1.000 6
Equipment
Fan efficiency N/A 0.33625 0.53625 0.73625 0.050 8
Fan motor
Efficiency
N/A 0.745 0.825 0.905 0.020 8
Coil cooling cop N/A 3.267 3.667 4.067 0.100 8
Coil heating
Efficiency
N/A 0.720 0.800 0.880 0.020 8

4.3.3 Differential sensitivity analysis
A sensitivity analysis was conducted for each selected parameter with simulations
(Chapter 1.3). Each parameter required 8 to10 simulations based on its interval and range.
The output of each simulation, HVAC EUI and Total EUI, was collected and put into
formula (Eq. 3-7) with original EUI to calculate IC value, then the mean IC value and its
percentage standard deviation was also calculated (see Chapter 1.3.4). Using EnergyPlus
and jEplus, 134 simulations were run on a computer with an Intel Core i7 processor. The
parameters were then ranked by the value of their influential coefficient, which could
reflect their sensitivity towards energy consumption (Table 4-4).
Table 4-4 Result of differential sensitivity analysis
Parameter IC_EUI SD%_1 Rank_1 IC_HVAC SD%_2 Rank_2
Wall insulation
Conductivity
0.0023 5.36% 13 0.0094 5.36% 13
Roof insulation
Conductivity
0.0002 71.96% 15 0.0010 71.96% 15
Glass u-factor 0.0076 38.73% 10 0.0316 38.73% 10
Glass SHGC 0.0292 19.16% 8 0.1209 19.16% 8
People density 0.0242 29.91% 9 0.1004 29.91% 9
Lighting density 0.3108 0.65% 3 0.3011 2.77% 6
Equipment density 0.4506 0.97% 2 0.3399 5.35% 5
Infiltration rate 0.0012 28.49% 14 0.0050 28.49% 14
Design airflow 0.0043 71.28% 12 0.0177 71.28% 12
Cooling Supply air
temperature
0.2228 32.77% 5 0.9240 32.77% 3
Cooling setpoint 1.6307 32.00% 1 6.7615 32.00% 1
Heating setpoint 0.2411 107.67% 4 0.9995 107.67% 2
Fan efficiency 0.1595 29.89% 6 0.6614 29.89% 4
66

Coil cooling COP 0.0589 8.02% 7 0.2442 8.02% 7
Coil heating
efficiency
0.0055 7.35% 11 0.0229 7.35% 11

Because of the limitation of time and the restriction of feasibility, only 6 of the most
uncertain and sensitive parameters were selected and used in the Monte Carlo simulation.
And these 6 parameters were selected with consideration of both IC ranking of total
energy use and HVAC (site) energy use, (Table 4-5). The energy usage here refers to site
energy instead of source energy. Although heating set point was ranked in the top 6 in
both total and HVAC EUI, it was eliminated due to high SD% (107.67%), which means it
has an unacceptable non-linearity problem.
Table 4-5 Parameters finally selected from sensitivity analysis
Ranking Selected Parameter IC Value
1 Cooling Setpoint
6.76
2
Cooling Supply Air ℃
0.92
3 Equipment Density
0.66
4 Lighting Density
0.33
5 Fan Overall Efficiency
0.30
6 Coil Cooling COP
0.20

4.4 Parameter distribution derivation
The 6 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
(Jason Lorcher, Justin Di Palo) to decide which distribution should be used, and the mean
values or mode values were the base values from DOE model (Table 4-6). Also, the
distribution curves of these 6 parameters are drawn and shown in the following (Fig. 4-3).
67

Table 4-6 Probabilistic distribution function of selected parameters
Parameter Unit
Distribution
Type
Distribution
Definition
Reference
Cooling
setpoint
℃
Normal
Mean: 24
SD 0.7
Calleja Rodríguez et al. 2013
Equipment
density
w/ m
2

Normal
Mean: 10.76
SD: 3.2
Hopfe and Hensen 2011
Lighting
density
w/m
3

Normal
Mean: 10.76
SD: 2.4
Hopfe and Hensen 2011
Cooling SA
temperature
℃
Triangular
Mode: 14
Max: 16 ; Min: 13
Griffith, Torcellini, and Ryan 2006
Overall fan
efficiency
N/A
Triangular
Mode: 0.54
Max: 0.7 ; Min: 0.38
Griffith, Torcellini, and Ryan 2006
Coil cooling
COP
N/A
Normal
Mean: 3.67
SD: 0.15
Macdonald and Strachan 2001

68

Figure 4-3 Probability density distribution curves of 6 selected parameters
4.5 Results from Monte Carlo simulation
4.5.1 Latin Hypercube Sampling
Latin Hypercube Sampling (LHS) was processed on each of the input parameters to
generate 10,000 values based on the probability distribution (Chapter 1.5.1). The 60000
parameter values were used to generate 10,000 input combinations for the following
Monte Carlo simulation, and 30 combination samples containing 6 parameters (Table 4-
7).

69

Table 4-7 Sample of 30 input combination from LHS
No.
Setpoint
temp.
Equipment
density
Lighting
density
Supply air temp. Fan efficiency
Cooling coil
COP
℃
w/m2 w/m2
℃
n/a n/a
Normal
SD 0.7
Normal
SD 3.2
Normal
SD 2.4
Triangular,
[13,16]
Triangular,
[0.38,0.7]
Normal, SD
0.15
Mean: 24 Mean:10.76 Mean:10.76 Mean:14 Mean:0.54 Mean:3.67
1 24.67296 9.9503918 11.763 13.84616 0.560317 3.440733
2 24.35416 10.707837 14.30104 14.83692 0.53325 3.698975
3 24.76326 18.425129 11.71732 14.57484 0.591622 3.714942
4 23.82464 11.955161 8.894792 14.60949 0.483517 3.82577
5 24.3247 6.5979074 11.57998 15.14405 0.540727 3.572842
6 24.38604 6.6639197 10.06762 14.0969 0.523765 3.711221
7 22.969 7.3411172 12.14319 14.78626 0.558879 3.642757
8 22.67872 12.797181 7.975455 13.97622 0.491321 3.82755
9 23.42283 13.232338 11.34249 15.60463 0.51824 3.73415
10 23.47914 6.9393704 8.91311 15.19717 0.469113 3.362048
11 22.77363 11.968905 6.152076 15.14126 0.460252 3.529421
12 25.77233 15.114562 12.41705 13.66953 0.628301 3.655337
13 23.56684 9.1707246 12.84222 15.73827 0.631557 3.706816
14 24.32071 8.288703 11.84382 14.61757 0.594489 3.762572
15 22.73532 14.972064 11.98395 15.41809 0.48434 3.726819
16 24.41288 10.406915 13.33968 13.99554 0.541426 3.493018
17 24.51417 6.2714968 7.602504 14.56905 0.55734 3.684019
18 24.40312 5.8781105 9.06787 14.64643 0.496286 3.552825
19 22.92286 13.008615 11.28505 13.57275 0.468961 3.882045
20 22.59641 10.626845 11.3385 13.81332 0.453507 3.498717
21 24.92688 4.6572587 10.66411 13.85358 0.43045 3.686262
22 24.56999 9.2324746 11.84577 14.19055 0.575264 3.864471
23 24.2053 11.010112 13.23397 14.2835 0.478071 3.576925
24 21.96151 14.756145 13.27433 14.76432 0.601578 3.458834
25 23.40492 5.9692698 11.49821 14.92717 0.401551 3.684834
26 23.84899 9.9566543 7.040868 14.096 0.444048 3.827113
27 23.87609 7.2467392 13.19492 14.18917 0.505246 3.535643
28 23.85047 8.9834304 10.30133 14.86755 0.589377 3.497686
29 23.32815 10.773879 6.389826 14.60836 0.490998 3.626263
... ... ... ... ... ... ...
10,000
24.44677 15.9303120 11.5552100 14.74832374 0.556027961 3.5937986

70

4.5.2 Simulation iteration
10,000 simulations were run with the input combinations from above and the 4 weather
files discussed in Chapter 3.4.2. 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 (jEPlus Simulation Server). In one sample of
results from 30 simulation jobs, containing both energy performance and cost information.
These 10,000 outputs were used to generate the probability distribution (Table 4-8),
which is shown in the next chapter.
Table 4-8 Sample of 30 sets of results from Monte Carlo simulation

Cooling
(Electric)
Heating
(Gas)
Fan
(Electric)
Water
(Gas)
Interior
lighting
Exterior
lighting
Interior
Equipment
EUI
(Total)
EUI
(HVAC)
Electric Gas Total
GJ GJ GJ GJ GJ GJ GJ kBtu/ Sq kBtu/ Sq $ $ $
1 14.40 0.77 24.20 10.90 62.00 36.20 81.10 39.56 8.66 7744 98 7842
2 19.20 0.51 34.20 10.90 75.30 36.20 87.30 45.43 11.17 8934 96 9030
3 22.00 0.37 30.80 10.90 61.70 36.20 150.00 53.76 11.04 10613 95 10708
4 15.40 1.04 38.00 10.90 46.90 36.20 97.50 42.38 11.26 8287 101 8387
5 9.23 2.40 28.10 10.90 61.00 36.20 53.80 34.74 8.72 6704 113 6817
6 14.90 0.84 24.10 10.90 53.00 36.20 54.30 33.47 8.74 6538 99 6637
7 39.40 0.21 41.70 10.90 64.00 36.20 59.90 43.48 15.89 8607 93 8700
8 24.70 0.70 48.50 10.90 42.00 36.20 104.00 46.01 14.61 9056 98 9154
9 23.30 0.60 50.20 10.90 59.80 36.20 108.00 49.80 14.65 9799 97 9895
10 14.80 1.97 39.10 10.90 47.00 36.20 56.60 35.60 11.51 6908 109 7017
11 31.70 0.32 54.20 10.90 32.40 36.20 97.60 45.38 16.74 8954 94 9049
12 8.38 1.07 18.40 10.90 65.40 36.20 123.00 45.38 6.68 8874 101 8975
13 22.50 0.55 37.40 10.90 67.70 36.20 74.80 43.09 12.30 8470 96 8566
14 18.10 0.58 26.10 10.90 62.40 36.20 67.60 38.23 9.60 7497 97 7593
15 34.20 0.29 67.80 10.90 63.10 36.20 122.00 57.64 19.50 12230 94 12324
16 13.30 1.28 29.30 10.90 70.30 36.20 84.80 42.40 9.44 8285 103 8388
17 5.42 4.31 19.90 10.90 40.10 36.20 51.10 28.94 6.98 5459 130 5588
18 6.91 3.52 24.70 10.90 47.80 36.20 47.90 30.66 7.93 5839 123 5962
19 25.40 0.57 50.10 10.90 59.50 36.20 106.00 49.74 14.99 9795 97 9892
20 35.90 0.28 54.50 10.90 59.70 36.20 86.60 48.95 17.50 9679 94 9773
21 4.61 4.06 22.30 10.90 56.20 36.20 38.00 29.69 7.22 5610 128 5738
22 12.80 0.82 24.60 10.90 62.40 36.20 75.30 38.43 8.46 7509 99 7608
23 15.80 0.99 36.90 10.90 69.70 36.20 89.80 44.85 11.13 8788 100 8888
24 58.40 0.04 63.40 10.90 69.90 36.20 120.00 61.83 22.87 13120 92 13212
25 26.60 0.45 48.30 10.90 60.60 36.20 48.70 39.94 14.86 7865 95 7961
26 16.40 0.71 34.30 10.90 37.10 36.20 81.20 37.36 10.74 7311 98 7409
27 13.80 1.68 34.00 10.90 69.50 36.20 59.10 38.80 10.40 7553 106 7659
28 30.70 0.29 30.30 10.90 54.30 36.20 73.20 40.65 12.44 8029 94 8123
29 16.70 1.33 38.90 10.90 33.70 36.20 87.80 38.86 11.69 7581 103 7685
… … … … … … … … … … … … …
10000 22.70 0.38 34.00 10.90 60.88 36.19 129.88 50.82 11.71 10022 95 10117
Utility Cost Energy Performance
Job
No.
71

4.5.3 Output probability distribution curves
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 were sorted and fitted to generate the probability distribution of energy usage
and cost (Table 4-9).
Table 4-9 Summary of best fitted curves for 5 outputs
Unit Best Curve Mean Mode Median Std. Dev.
Total EUI kBtu/sq Normal 42.04 42.04 42.04 6.81
HVAC EUI kBtu/sq Gamma 10.92 9.82 10.56 2.80
Total Cost $/yr Gamma 8343 8008 8232 1458
Electric Cost $/yr Gamma 8242 7896 8127. 1468
Gas Cost $/yr Log-Normal 101 95 99 9

A curve-fitting technique was used to identify the best-fit curve for each output, by
performing 5 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 7 top ranked curves
will be used to measure the risk and conduct other related analyses (Fig. 4-4, Fig. 4-5,
Table 4-10, and Table 4-11). The results for the other 3 outputs (HVAC EUI, electric
cost, and gas cost) can be found in Appendix B.

72

Figure 4-4 Best fitted curve of total EUI, Normal distribution [42.046, 6.81]
Table 4-10 Results of goodness-of-fit test for total EUI, 7 sample curves
ChiSq ExtValue Logistic LogLogistic Normal Weibull Laplace
Rankings By Fit Statistic
Akaike (AIC) #5 #7 #4 #3 #1 #2 #6
Bayesian
(BIC)
#5 #7 #4 #3 #1 #2 #6
Chi-Sq
Statistic
#5 #6 #4 #3 #1 #2 #7
K-S Statistic #5 #7 #3 #2 #1 #4 #6
A-D Statistic #5 #7 #3 #2 #1 #4 #6
Distribution Statistics
Mean 42.10 42.47 41.96 42.07 42.05 42.02 41.93
Mode 40.10 38.68 41.96 41.65 42.05 42.51 41.93
Median 41.43 41.09 41.96 41.88 42.05 42.13 41.93
Std. Deviation 7.35 8.42 7.05 7.07 6.81 6.97 7.67
Skewness 0.54 1.14 - 0.26 - (0.05) -
Kurtosis 3.44 5.40 4.20 4.37 3.00 2.73 6.00
Information Criteria
Akaike (AIC) 67,047.82 67,892.74 66,922.17 66,903.51 66,749.74 66,860.32 67,686.72
Bayesian(BIC) 67,062.24 67,907.16 66,936.59 66,925.14 66,764.16 66,881.94 67,701.14
Chi-Sq Test
Minimum 15.10 -Infinity -Infinity (88.47) -Infinity 18.30 -Infinity
Maximum 28.49 29.09 25.27 26.23 26.99 26.77 22.34
Input 183.00 232.00 49.00 81.00 107.00 100.00 8.00
73

Fit 135.14 135.14 135.14 135.14 135.14 135.14 135.14
Anderson-Darling Test
A-D Statistic 25.90 86.54 8.47 7.48 2.18 10.26 48.51
Kolmogorov-Smirnov Test
K-S Statistic 0.03 0.05 0.02 0.02 0.01 0.02 0.05

Figure 4-5 Best fitted curve of total cost, Gamma distribution
Table 4-11 Results of goodness-of-fit test for total cost, 7 sample curves
Gamma InvGauss LogLogistic Lognorm Pearson5 Triang Weibull
Rankings By Fit Statistic
Akaike
(AIC)
#1 #4 #2 #3 #6 #7 #5
Bayesian
(BIC)
#1 #4 #2 #3 #6 #7 #5
Chi-Sq
Statistic
#1 #5 #2 #4 #6 #7 #3
K-S
Statistic
#1 #5 #2 #4 #6 #7 #3
A-D
Statistic
#1 #4 #2 #3 #6 #7 #5
Distribution Statistics
Mean 8,343.96 8,343.96 8,425.19 8,351.30 8,368.37 8,401.14 8,318.95
Mode 8,008.74 7,819.91 8,034.71 7,842.93 7,669.65 8,377.98 8,560.67
Median 8,232.58 8,167.29 8,245.94 8,177.11 8,116.66 8,395.37 8,387.40
Std. 1,458.28 1,521.88 1,578.38 1,518.92 1,631.91 2,617.99 1,545.57
74

Deviation
Skewness 0.46 0.72 1.30 0.73 1.10 0.01 (0.20)
Kurtosis 3.32 3.86 8.91 3.97 5.40 2.40 2.83
Information Criteria
Akaike
(AIC)
173,726.1 174,137.2 173,828.50 174,062.3 174,682.52 179,558.15 174,272.56
Bayesian
(BIC)
173,740.5 174,151.6 173,842.92 174,076.7 174,696.94 179,572.57 174,286.98
Chi-Sq Test
Minimum 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00
Maximum 5,561.82 5,667.88 5,563.79 5,667.07 5,735.66 3,051.38 4,744.21
Input 190.00 239.00 191.00 239.00 273.00 - 39.00
Fit 135.14 135.14 135.14 135.14 135.14 135.14 135.14
Anderson-Darling Test
A-D
Statistic
14.51 42.18 21.08 37.34 77.14 784.28 50.45
Kolmogorov-Smirnov Test
K-S
Statistic
0.03 0.05 0.03 0.04 0.06 0.17 0.04

4.6 Conclusion
Results from the case study are as expected. The generated distribution curves, for both
energy consumption and utility cost, present the possibility of different scenarios in
reality, and thus can be used for risk assessment. The outputted probability distribution
curves have a wide range of usage. For example, they could be useful in making
decisions about investments in building energy efficient projects and also help designers
to better evaluate design alternatives. These results will be further analyzed in the next
chapter.
75

5. Evaluation and analysis of case study results
The proposed methodology aims at analyzing the risk associated with uncertainties of
EUI calculations and utility cost for energy efficient building projects, and this analysis
relies on the developed probability distributions of energy performance (EUI for instance)
and/or utility cost. The probability distributions contain a large amount of useful
information in terms of risk, uncertainty, expectation value, and many others. Based on
the results from the case study risk analysis was conducted, in order to show examples of
how to utilize the obtained results for risk analysis and to provide proof of the
effectiveness of the proposed method. The analyses and conclusions here are totally
based on the case study (DOE small office building in Los Angeles) with a specific
building, climate, and other data. The conclusions cannot be directly applied to any other
building or project. However, the proposed method can be applied to any project or
building at any location to analyze the risk, if used appropriately.
To conduct the results and risk analyses, some important information should be identified
first. This information includes the baseline condition from initial simulation results
regarding both energy performance and utility cost information (Table 5-1).
This baseline condition refers to the initial simulation results from the DOE reference
building model, not the benchmark baselines from relevant codes or standards. This is
appropriate given the fact that the goal of the proposed method is to assess the risk that is
directly relative to the initial predicted energy performance or cost. In addition, the DOE
reference models were created based on the data collected from the majority of buildings,
which presents the most likely real scenario.
Table 5-1 Initial simulation results and baseline information
Energy Performance Utility Cost
Total EUI HVAC EUI Total Cost Electric Cost Gas Cost
kBtu/sq kBtu/sq $/yr $/yr $/yr
41.01 9.89 8108 8005 103

76

5.1 Common method of probability analysis
The probability distribution curve is the main information source to process the risk
analysis. These curves are the final product of the proposed methodology, and they were
generated from curve-fitting of 10,000 simulation results in the case study. The goodness-
of-fit tests have supported a high level of reliability of these curves (see Chapter 4.5.3),
so the fitted curves can be used to express the results from the 10,000 simulations. As the
main idea of the proposed method, this probability distribution curve is formed by
thousands of possible energy performance or utility cost, and each of them represents a
real scenario in practice; thus the curves can be used to assess the risk. To conduct risk
analysis a good understanding of the basics of curves are necessary, and then appropriate
mathematical methods should be used to assess the risk.
A brief introduction of common probability analysis methods, using the example of the
probability distribution of total EUI in the case study, is useful to understand this part of
the methodology.
5.1.1 Probability distribution curve basics
The best fitted curve of total EUI is a normal distribution (Chapter 4.5.3). The normal
distribution is also called Gaussian distribution; it is a very commonly occurring
continuous probability distribution. The curve is symmetric around its mean value, which
is at the same time the mode, the median, and the mean of the distribution. There are six
key parameters that define the normal distribution: mean, mode, median, standard
deviation, skewness, and kurtosis. The values of these parameters of total EUI probability
distribution were obtained from the curve-fitting, which has been detailed discussed in
Chapter 4.5.3 (Table 5-2).
Table 5-2 Key parameters of normal distribution of total EUI
Mean Mode Median Std. Dev. Skewness Kurtosis
42.046 42.046 42.046 6.81 0 3

77

5.1.2 Probability calculation
The use of probability distribution curves is to find out the probability of any scenario, in
other words, any point on x axis. This requires the probability density function (PDF).
For the normal distribution it is dependent on the mean value and the standard deviation
(Eq. 5-1).
2
2
(x )
2
1
(x, , )
2
fe






 (Eq. 5-1)
 - Mean value;  - Standard deviation; e - Mathematical constant

Put the mean value (42.046) and standard deviation (6.81) into Eq. 5-1, the PDF of the
distribution will be calculated (Eq. 5-2).
2
(x 42.046)
92.752
(x,42.046,6.81) 0.059 fe



(Eq. 5-2)
The integral F of f (Eq. 5-3) will calculates the probability of the range from minimum
to the assigned x (Eq. 5-3).
2
(x 42.046)
92.752
(x) 0.059
x
F e dt






(Eq. 5-3)
For example, if x=45 kBtu/sq, the integral F will calculates the probability of the total
less than 45 kBtu/sq. The probability of any range, 40 to 45 kBtu/sq for instance, can also
be calculated.
Since the function is difficult to integrate, reference tables are used to calculate
probabilities in a standard format (Fig. 5-1); then the standard probabilities are converted
to the actual required variable, also many convenient tools are available for this use
(http://stattrek.com/online-calculator/normal.aspx). This method is based on the standard
normal distribution (  =0;  =1). The relation between the standard variable ( z ) and a
typical problem variable (x) is shown in Eq. 5-3.
(x )
z



 (Eq. 5-3)
78

5.1.3 Other probability distribution curves
Besides normal distribution, there are another two types of curves has been used for
output distribution, gamma distribution and log-normal distribution (Chapter 4.5.3, Table
4-9).
Gamma:
(x )
z



 (Eq. 5-4)
Log-Normal:
(x )
z



 (Eq. 5-5)
Although the distribution of other outputs have different curves and corresponding
equations, the probability calculations share the same methodology and thus it will not be
further discussed here, and abundant reference can be found in the literature.
79

Figure 5-1 Standard normal distribution reference table(“Standard Normal Table” 2014)
80

5.2 Results analysis of total EUI
The total EUI is the 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.
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 (Fig. 5-2).

Figure 5-2 Best fitted curve of Total EUI, normal distribution
5.2.1 Risk analysis
The probability distribution curve contains a lot of information about total EUI. Based on
the specific purpose, different analysis could be done. There are two main types of
probability analysis: identifying the EUI range of specific probability and identifying the
probability of curtain EUI range. All of the analyses are based on one of the two types of
analyses or the combination of them. Based on this distribution curve of total EUI, both
have been calculated.
 Identifying the total EUI range of specific probability
Using the method discussed in Chapter 5.1.2, total EUI can be identified given any
probability using Eq. 5-3. The probability here refers to the possibility of occurring of
81

EUI ranging from minimum to certain value ( x ). So, using Eq. 5-3, and F ( x ) equals
the specific probability, the x value can be calculated. For example, if a probability of 50%
is given, the total EUI value ( x ) is calculated (Eq. 5-6).
2
(x 42.046)
92.752
(x) 50% 0.059
42.046 /
x
F e dt
x kBtu sq






(Eq. 5-6)
Using this method, given any probability, the corresponding total EUI value could be
identified through calculation, or the standard normal distribution table (Fig. 5-2). The
probability and corresponding total EUI at an interval of 5% was identified (Table 5-3).
Table 5-3 Total EUI under specific probability
Probability 1% 5% 10% 15% 20% 25% 30%
Total EUI
(kBtu/sq)
26.20 30.84 33.32 34.99 36.31 37.45 38.47
Probability 35% 40% 45% 50% 55% 60% 65%
Total EUI
(kBtu/sq)
39.42 40.32 41.19 42.05 42.90 43.77 44.67
Probability 70% 75% 80% 85% 90% 95% 99%
Total EUI
(kBtu/sq)
45.62 46.64 47.78 49.10 50.77 53.25 57.89

 This method can be used for obtain further information. For example, in Table 5-3, the
corresponding EUI of 10% and 50% are 33.318 kBtu/sq and 42.046 kBtu/sq respectively.
So the probability of EUI ranging from 33.318 to 42.046 kBtu/sq is 40% (50% -10%).
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.
 Identifying the probability of curtain EUI range
Identifying the probability of the curtain EUI range is more frequently used. This analysis
also uses Eq. 5-3, and specific integral upper and lower limits are given. For example, the
probability of EUI ranging from 40 kBtu/sq to 44 kBtu/sq can be calculated (Eq. 5-7).
82

(x 42.046)
44
92.752
40
(44) F(40) 0.059
61.3% 38.2% 23.1%
P F e dt
P


  
   

(Eq. 5-7)
Using this method, given any EUI range, the corresponding probability could be
identified through calculation or the standard normal distribution table (Fig. 5-2). 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 (Table 5-4). 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 5-4 Reliability and risk of different deviation rate of mean value
Range (kBtu/sq) Deviation
Rate
Reliability Risk
Lower Upper
41.6 42.4 ±1% 4.9% 95.1%
39.9 44.1 ±5% 24.3% 75.7%
37.8 46.2 ±10% 46.3% 53.7%
35.7 48.3 ±15% 64.5% 35.5%
33.6 50.4 ±20% 78.3% 21.7%
31.5 52.5 ±25% 87.7% 12.3%
29.4 54.6 ±30% 93.6% 6.4%
27.3 56.7 ±35% 96.9% 3.1%

This analysis allows engineers to analyze the risk at different level of discrepancy and
evaluate the predicted energy performance. This is the extremely useful in assessing the
risk of energy performance shortfall and evaluating different design alternatives. For
83

examples, if the client only allows a tolerance of 10% in deviation, using the third row in
Table 5-4, 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!
5.2.2 Comparison with initial total EUI
If the mean values (expectation value) of input parameter distributions are assigned with
the best estimations of these parameters that are used in a normal 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 (42.046 kBtu/sq) is
not equal to the initial DOE model simulation result, which is 41.01 kBtu/sq (Fig. 5-3).

Figure 5-3 Deviation of initial EUI with mean value of total EUI distribution
This deviation might be caused by the use of multiple weather files (Chapter 3.4.2) 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
84

weather conditions used in the simulations are not “symmetrical” about the initial
weather condition, and this is what causes the deviation shown in Fig. 5-3.
To demonstrate this conclusion, 2,000 simulations were run using the same six input
parameter distributions, but without weather file variation, which means only one
weather file (initial weather file) was used in these simulations. Results show that the
total EUI distribution is still a normal distribution (Fig. 5-4).

Figure 5-4 Deviation of initial EUI with mean value of total EUI distribution (uniform
weather)
The results in Fig. 5-4 demonstrate that the weather file variations are one reason for the
deviation. The mean value of total EUI with the uniform weather file is 41.56 kBtu/sq,
which is much closer to the initial EUI, 41.01 kBtu/sq. However, there is still a minor
deviation; it is caused by the asymmetry of two input parameter distributions, cooling SA
temperature and overall fan efficiency. These two parameters have triangular
distributions (see Chapter 4.4), 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.
5.2.3 Application prospects
The total EUI distribution from the proposed method can be used for many analyses
regarding risk and other aspects. Chapter 5.2.1 and 5.2.2 have shown some examples of
85

the usefulness, and more valuable information can be obtained with further analysis. If
the proposed methodology is to be applied in practice, many benefits could be expected
including gaining the knowledge of risk, supporting the evaluation of design alternatives,
and facilitating risk management.
 Gaining the knowledge of risk
As discussed in Chapter 1 and Chapter 2, there is a significant problem regarding the
discrepancy between predicted and real building energy performance. The uncertainty of
various energy related factors and the neglect of including them into simulation have led
to many failures of energy efficient projects.
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. This is extremely useful in the case of 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. This
process itself informs engineers a better knowledge of what factors affect the energy
efficiency most, what causes the uncertainty. The proposed method, to some extent, make
industrial practitioners think more about the reality, instead of merely relying on
positively estimated numbers on the screen.
 Supporting the evaluation of design alternatives
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. For example, when two design alternatives share the same mean value of
EUI, 40 kBtu/sq, the one with lower standard deviation, which means the energy
performance is more certain, will be the preferable option. In another case, a scheme
86

with less energy saving and low risk might be better that a scheme with more energy
savings but high risk that the building will not achieve those goals.
 Facilitating risk management
Identifying the risk and understanding what causes risk are the premise of risk
management. 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.
5.3 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 (Fig.
5-5).

Figure 5-5 Best fitted curve of total cost, gamma distribution
The gamma distribution is a two-parameter family of continuous probability distributions,
the shape of the curve is defined by two parameters, the shape parameter k , and the scale
87

parameter  . The value of them are 18.93 and 335.21 respectively. The other key
parameters of the total cost probability distribution are shown in Table 5-5.
Table 5-5 Key parameters of gamma distribution of total cost
Mean Mode Median Std. Dev. Skewness Kurtosis
8343.96 8008.74 8232.58 1458.28 0.46 3.32

The equations for the probability density function (Eq. 5-7) and cumulative distribution
function (Eq. 5-8) are different from that of the normal distribution.
1
( ; ; )
()
x
k
k
xe
f x k
k






(Eq. 5-7)
0
( , )
F( ; ;
(
) ( ; ; )
)
x
x
k
x k f x k du
k



 




(Eq. 5-8)
k - Shape parameter;  - Scale parameter; e - Mathematical constant
Since the methodology of probability calculation and risk analysis have been thoroughly
discussed in chapter 5.1 and chapter 5.2, only the analysis and results are shown.
5.3.1 Risk analysis
The probability distribution curve contains a lot of information about total utility cost.
Following the methodology in chapter 5.2.1, two main types of probability analysis
method are used, identifying the cost range of specific probability and identifying the
probability of curtain cost range. Other analyses could be done using either one or the
combination of these two methods.
 Identifying the total cost range of specific probability
Using cumulative distribution function in Eq. 5-8, total cost can be identified given any
probability. The probability here refers to the possibility of occurring of total utility cost
ranging from minimum to certain value ( x ). The probability and corresponding total
cost at an interval of 5% was identified and listed below (Table 5-6).
88

Table 5-5 Total cost under specific probability
Probability 1% 5% 10% 15% 20% 25% 30%
Total cost
($/yr)
5449 6150 6561 6854 7095 7309 7506
Probability 35% 40% 45% 50% 55% 60% 65%
Total cost
($/yr)
7692 7873 8052 8232 8415 8605 8805
Probability 70% 75% 80% 85% 90% 95% 99%
Total cost
($/yr)
9020 9257 9527 9850 10269 10917 12219

Similar with 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 (Table 5-6). So the probability of utility cost ranging from
6561.40 to 8232.47 $/yr is 40% (50% -10%).
 Identifying the probability of curtain cost range
Identifying the probability of cost ranges is more frequently used. This analysis uses the
cumulative distribution function in Eq. 5-8, and specific integral upper and lower limits
are given. Using this method, given any cost range, the corresponding probability could
be identified. This is very useful when specific utility cost budget is targeted. The
identified probability shows the reliability of hitting the target, or in other words, the risk
of failing.
As discussed in Chapter 5.2.2, take the mean value of total cost probability distribution
(8343.96 $/yr) as the best estimation. A cost deviation (error rate) analysis can be
processed to identify the corresponding reliability and risk (Table 5-7).
Table 5-6 Reliability and risk of different deviation rate of mean value
Range ($/yr) Deviation
Rate
Reliability Risk
Lower Upper
8260 8427 ±1% 4.5% 95.5%
7926 8761 ±5% 22.5% 77.5%
7509 9178 ±10% 43.3% 56.7%
7092 9595 ±15% 61.2% 38.8%
6675 10012 ±20% 75.3% 24.7%
89

6257 10429 ±25% 85.4% 14.6%
5840 10847 ±30% 91.9% 8.1%
5423 11264 ±35% 95.7% 4.3%
5009 11681 ±40% 97.7% 2.3%

This analysis allows economic related stakeholders to analyze the risk at different level of
discrepancy, and evaluate the predicted total utility cost. This is the extremely 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 5-7, the predicted utility cost
(mean value) will lead to an extremely large risk of 77.5%.
5.3.2 Comparison with initial total cost
Similar to the total EUI, the total cost curve has same issue of a deviation between mean
total cost and the initial total cost (Fig. 5-6).

Figure 5-6 Deviation of initial cost with mean value of cost distribution
Using the same hypothesis that multiple weather files (Chapter 3.4.2) caused this
deviation, 2,000 simulations were run using the same six input parameter distributions,
but without the weather file variation, which means only one weather file (initial weather
90

file) was used in these simulations. Results show that the total cost distribution is still a
gamma distribution (Fig. 5-7).

Figure 5-7 Deviation of initial cost with mean value of cost distribution (uniform weather)

The results show that the weather file variations are the main reason for the deviation,
even more so than the results for the total EUI. The mean value of total cost with uniform
weather file is 8107.9 $/yr, which is almost the same as initial cost, 8108.65 $/yr.
5.3.3 Application prospects
The probability distribution of total cost using the proposed method is a valuable resource
for economic analysis. Chapters 5.3.1 and 5.3.2 have shown some examples of the
usefulness, and more valuable information can be obtained through further analysis. If
applied, this risk analysis could be helpful in investment decision making, as well as
developing the business of insurance in energy efficient building projects.
 Assisting investment decision making
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
91

buildings. The discrepancy between expected and real energy savings surprises the
investors, and what’s worse, can discourage them. Investor 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. The risk analysis could also help the engineers and designers; they can make
better design decisions compromising the possible cost and budget. For energy
performance contracting projects, this would be more valuable, because energy service
companies (See chapter 1.1) would be able to develop better business opportunities. All
of these aspects will potentially positively affect the development of energy efficient
buildings.
 Providing opportunities for insurance
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.
5.4 Other output results
In addition to the total EUI and total cost probability distributions, there is other useful
information available from the results, including cooling electricity usage, fan electricity
usage, water system gas usage, interior/exterior lighting electricity usage, interior
equipment electricity usage, and many other calculated outputs, such as HVAC EUI,
electricity cost, and gas cost.
The same methodology used in the analysis above could be applied to all other outputs
for the analyses of different research or practical purposes. For example, the distribution
of lighting electricity usage can be analyzed for lighting upgrade projects; the study of
fan energy usage and HVAC EUI is helpful to analyze the correlation between them, and
test the performance of fan-driven air conditioning systems.
92

However, these studies are not the main topic here, and the analysis methodology has
been introduced. So these analyses are not further discussed, and more information is
available in Appendix B.
5.5 Limitations of the current study
There are current limitations in the study that may cause inaccuracy or error in the results
including potential issues with the input parameter selection, parameter distribution,
insufficient simulation iteration, and any information inadvertently overlooked, although
great care has been taken.
 Input parameter selection
There are a vast number of parameters in energy simulations, and many of them are
uncertain and may lead to risk. However, due to the limitation of feasibility and time,
only six of the most sensitive and uncertain parameters and weather files were identified
and used in the analysis. Many other parameters, for example, occupancy schedules, have
an influence on energy consumption and relative uncertain. This issue can cause
significant inaccuracy in the results.
 Parameter distribution
The input parameter distributions are critical in deciding the shape of output distribution
and hence the risk. In the case study, the input parameter distributions were decided by
literature review and professional judgment. This might be insufficient when high level
precision is required, in which the distribution should be identified by curve-fitting of
abundant historical real data at a specific location, Los Angeles for example. This
information may not be available and requires a great deal of effort to create.
 Insufficient simulation iteration
One key point of getting accurate results with the Monte Carlo method is having an
abundance of simulation iterations. In the case study, 10,000 simulations were processed.
Better results that are more accurate to present the real risk can be achieved if even more
simulation iterations are conducted. The use of cloud-based processing service has made
this possible and saves a lot of time.
93

 Some information inadvertently overlooked
The proposed methodology requires a broad range of knowledge, statistics, probability,
data processing, and many other areas. So the limitation of the grasp of this knowledge
may also cause inaccuracy in results and insufficient analysis.
5.6 Summary
Results from the case study of the DOE reference building, a small office in Los Angeles,
are analyzed. The common methodology of probability analysis is introduced in the
beginning. Following the methodology, risk analysis are conducted through two
probability distribution curves, Total EUI and Total Cost. Also, prospects of these risk
analysis are also discussed. Limitations of the study were also clarified.
94

6. Conclusions and future work
Large discrepancies between real and predicted building energy performance have been
observed, which frustrates the building owners, designers, and investors, and can hinder
the development of energy efficient buildings. The issue is mainly caused by the
uncertainties in such projects and use of estimated and unrealistic parameter values in
simulation. Research about energy model calibration and the uncertainty of single
parameters has been done before. Less research has been done for incorporating overall
risk assessment into energy simulations that take multiple factors into consideration.
6.1 Methodology developed
Aimed at solving this problem, the hypothesis has been proposed: a probabilistically
based method of risk assessment using energy performance simulation that takes multiple
factors into consideration can be achieved to yield expected building energy performance
and related energy cost information with associated probabilities. Following the
hypothesis, the methodology of risk assessment was studied and developed (Fig.6-1).
Figure 6-1 Workflow of proposed risk assessment methodology

95

To test the effectiveness of the proposed method, the small office building from a DOE
model (Los Angeles) was used as a case study. First, literature review and discussion
with professionals were conducted to decide the parameters that produce most
uncertainties in simulations, then the differential sensitivity analysis identified six
energy-sensitive parameters (cooling set-point, cooling supply air temperature, equipment
density, lighting density, fan overall efficiency, and coil cooling COP). Then each
selected parameter was assigned with a probability distribution developed from curve-
fitting of historical real data. These six distributions, along with for weather files that
convey the uncertainty of climate change, were used as simulation inputs. Latin
Hypercube sampling generated input combinations based on the Monte Carlo method;
then 10,000 simulation iterations were completed using a cloud processing service.
Output data, EUI and cost, was collected and fitted into probability distributions (Fig. 6-
2), which was used for risk and analysis of both energy performance and utility cost.

Figure 6-2 Distributions of output EUI and Cost from 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, some examples are:
 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%
96

 The probability of utility cost ranging from 6561.40 to 8232.47 $/yr 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 aspects:
 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
In summary, 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. Although some deficiencies exist, including neglect of less-sensitive
parameters, imperfect input distributions, and insufficient of knowledge broadness; the
case study supports the hypothesis and the proposed methodology well. This does not
preclude the designer using those additional factors in any given design. It merely gives
probabilities for the most sensitive parameters.
6.2 Future Work
There are aspects where the methodology could be improved with further research and
work, including evaluating the proposed method by professionals, establishing a
parameter based historical database, improving the economic analysis, developing a risk
assessment tool, and developing a risk management plan.
 Evaluating the proposed method by professionals
The proposed method is difficult to verify since its concern of risk assessment needs a
large number of cases to test it thoroughly. One way to test its effectiveness is to ask
professionals to evaluate the proposed method with their rich experience and judgment in
97

energy efficient building projects. Their opinions could be collected through
questionnaires. Professionals could make judgment in aspects like feasibility,
applicability, accuracy, sophistication and so on. Advice and comments on how to
improve the proposed method from professionals are valuable, since this tool aims at
provides assistance in engineering practice.
 Establishing a parameter based historical database
In the proposed method, the input parameter distributions are essential to obtain accurate
output distribution curves and are important for improving the risk assessment
confidential level. The parameter distributions are developed from historical data
collected from real cases, so establishing the database for historical is valuable. This
could be a challenging and long-term task, since there is a vast amount of parameters
related with building energy efficiency. In addition, the database needs to take many
factors into consideration, such as location, culture, material manufacturer, and even
different contractors.
 Improving the economic analysis
To better assist the investment decision making process, the economic analysis should be
improved. The price variation of energy is one important factor that generates significant
uncertainty and risk. Some capital factors, rate of interest for instance, also needs to be
considered. Because of the growing financial incentives for sustainable design that are
offered by the government (including local, state, and federal) these should be integrated
into economic analysis. In addition, the analysis of cost or profit should be conducted in a
life-cycle basis.
 Developing a risk assessment tool
The application of the proposed risk assessment method requires a lot of effort and time.
It is unrealistic for engineers in industry to utilize within a limited time, so the
development of an easy-to-use tool is necessary. This tool is expected to be highly
automated and have the capability of sensitivity analysis, Monte Carlo simulation, and
have access to parameter database. Also, cloud based processing service should be
considered since a large amount of simulations need to be run.
98

 Developing a risk management plan
Risk assessment is only the first step, the management of risk is truly the ultimate goal.
The information from the sensitivity analysis and output probability distribution could
provide the direction and chance for investigation and mitigation of risks. A risk
management plan should be developed with regards to factors that generates uncertainty,
and it could help achieving better energy efficiency and profit.
6.3 Concluding remarks
The issue of discrepancies between real and predicted building energy performance has
been investigated and discussed. Regarding this problem, a probabilistic based
methodology that take multi-factors into consideration has been developed. To test the
effectiveness of the proposed method, a case study of DOE reference model was
conducted. The results showed that risk related information of both energy performance
and utility cost can be obtained and analyzed. Based on the case study, the application of
proposed method were discussed and expected. The possible improvements of the
limitation of current study, as well as future work regarding this topic was also discussed.
In summary, the proposed methodology is solid and shows promising prospects of
application in a broad range of fields.

99

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103

Appendix A – Parameter identification of sensitivity analysis
A-1 Parameter identification from document
Table A-1 Parameters identified from document
Sector Subsector Value Source
Program
Occupancy Rate 200 ft
2
/ person ADEG study
Ventilation 20 cfm/person ASHRAE 1999
Plug and Process Loads
Lights 1.0 W/ft
2

Engineer
judgment
Elec. Process 1.0 W/ft
2

Gas Process 0.00
Infiltration
Core: 0 ACH; ZN1 & ZN3:
0.62 ACH ; ZN2 & ZN4: 0.66
ACH; Attic: 1 ACH;
Service Hot Water Demand T=110 F 3.0 Gal/h (Core only) ASHRAE 2007
Schedules
ASHRAE 1989 &
Modification
Fabric
Exterior walls
Construction Type Mass wall
CBECS &
ASHRAE 90.1
R-value (m
2
·K / W) 1.17
Roof
Construction Type Attic
R-value 5.18
Window
U-Factor (W / m
2
·K) 3.24
SHGC 0.25
Visible transmittance 0.16
Skylights/TDD
U-Factor (W / m
2
·K) n/a
SHGC n/a
Visible transmittance n/a
Foundation
Foundation Type Mass Floor
Construction 4in slab w/carpet
R-value (m
2
·K / W) 0.54
Equipment
Air Conditioning
Type PSZ-AC, Unitary DX
2003 CBECS
COP 3.67
Heating
Type Gas furnace
Efficiency 0.80
DWH
Type Gas furnace
Standard 90.1-
2004
Efficiency 0.80
Temperature Setpoint 60.00
Fan Table 36
Lighting
Interior 1.0 w/m2
Exterior Table 27
Form
Total Floor Area (ft
2
) 5500.36
Jarnagin et al.
2006, EIA 2005
Building Shape Rectangle
Aspect Ratio 1.50
Number of Floors 1.00
Window Fraction (Window
to Wall Ratio)
South 0.24
East 0.20
North 0.20
West 0.20
Total 0.21
Skylight/TDD Percentage
Shading Geometry None
Azimuth 0.00
Thermal Zoning
core zone with four perimeter
zones
Floor to Ceiling Height (ft) 10.17
Roof type Attic
104

A-2 Parameter identification from IDF file
Table A-1 Parameters identified from IDF file
Type
Obj.
No
Parameter Notes
Simulation Parameters
1 Version
1 Simulation Control
1 Building
1 Shadow Calculation
1 Surface Convection Algorithm: Inside
1 Surface Convection Algorithm: Outside
1 Heat Balance Algorithm
1 Zone Air Heat Balance Algorithm
1 Time Step
1 Convergence Limits
Location and Climate
1 Site Location
2 Sizing Period: Design Day
1 Run Period
10 Run Period: Special days
1 Run period: Day light Saving Time
1 Site: Ground Temperature: Building Surface
1 Site: Water Mains Temperature
Annual dry outdoor air
temp, for calculation of
ground temp.
Schedules 24 Schedule Compact
Surface Construction
Elements
14 Material
2 Material: No Mass
1 Window Material: Simple Glazing System
9 Construction
Thermal zones and
surfaces
1 Global Geometry Rules
6 Zone Definition of each zone
and its construction type 43 Building Surface: Detailed
21 Fenestration Surface: Detailed
Definition of each glazing
and its construction type
5 Internal Mass
Seems to describe internal
partitions?
Internal Gains
5 People
5 Lights
5 Electric Equipment
Zone Airflow
Zone Infiltration: Design Flow Rate
Only for infiltration,
design airflow is under
HVAC outdoor air
Exterior Equipment 1 Exterior: Lights
HVAC Design Objects
5 Design Specification: Outdoor Air
Design Flowrate/ per
person
1 Sizing: Parameters
5 Sizing: Zone
Supply air temperature
and humidity ratio
5 Sizing: System
Preheat, precool, central
cooling/heating supply air
temperature and humidity.
And system types
1 Sizing: Plant
Zone HVAC controls
and Thermostats
5 Zone Control: Thermostat
set control type, "4"
means-Dual setpoint
(Heating and Cooling)
105

with dead band
5 Thermostat Setpoint: Dual Setpoint set control temperature
Zone HVAC Air Loop
Terminal Units
5 Air terminal: Single Duct: Uncontrolled
Zone HVAC
Connections
5 Zone HVAC: Equipment list
5 Zone HVAC: Equipment Connections
Fans
5 Fan: Constant Volume
Schedule; Fan Efficiency;
Motor Efficiency
Coils
5 Coil: Cooling: DX: Single Speed Rated COP;
5 Coil: Heating: Gas Gas burner efficiency
5 Coil System: Cooling: DX
Controller
5 Controller: Outdoor Air
5 Air Loop HVAC: Controller list
Air Distribution
5 Air Loop HVAC
5
Air Loop HVAC: Outdoor system: Equipment
list

5 Air Loop HVAC: Outdoor system
5 Outdoor Air: Mixer
5 Air Loop HVAC: Zoon Splitter
5 Air Loop HVAC: Supply Path
5 Air Loop HVAC: Zoon Mixer
5 Air Loop HVAC: Return Path
Pump 1 Pump: Constant Speed Motor Efficiency
Water Heater 1 Water Heater: Mixer Heater Efficiency
Plant-Condenser Loop
1 Plant Loop
Max & Min Loop
Temperature
1 Plant Equipment Operation: Heating Load
1 Plant Equipment Operation Schemes
Setpoint Managers
1 Setpoint Manager: Scheduled
5 Setpoint Manager: Single Zone: Reheat
Min & Max Supply Air
Temperature
15 Setpoint Manager: Mixer Air
Water System
1 Water Use: Equipment
1 Water Use: Connections
Performance Curve
1 Curve: Quadratic
1 Curve: Cubic
2 Curve: Biquadratic
Economics
4 Utility Cost: Tariff
4 Utility Cost: Qualify
23 Utility Cost: Charge: Simple
1 Utility Cost: Charge: Block
1 Utility Cost: Variable
Output Reporting
1 Output: Table: Summary Report
1 Output Control: Table Style
1 Output Control: Reporting Tolerances
17 Output: Meter
1 Output: SQLite
1 Environmental Impact Factors
2 Fuel Factors

106

Appendix B Other output distribution
B-1 Fitted probability distribution of HVAC EUI

Figure B-1 Best fitted curve of HVAC EUI, Gamma distribution
Table B-1 Results of goodness-of-fit test for HVAC EUI, 7 sample curves
ExtValue Gamma InvGauss LogLogistic Lognorm Pearson5 Weibull
Rankings By Fit Statistic
Akaike (AIC) #5 #1 #2 #7 #3 #4 #6
Bayesian (BIC) #5 #1 #2 #7 #3 #4 #6
Chi-Sq Statistic #5 #2 #1 #7 #4 #3 #6
K-S Statistic #5 #1 #2 #6 #3 #4 #7
A-D Statistic #5 #1 #2 #6 #3 #4 #7
Distribution Statistics
Minimum -Infinity 3.70 0.67 1.62 0.77 (2.56) 4.47
Mean 10.95 10.92 10.92 11.00 10.92 10.92 10.93
Mode 9.62 9.83 9.83 10.03 9.85 9.88 10.34
Median 10.47 10.56 10.55 10.55 10.55 10.56 10.74
Std. Deviation 2.98 2.81 2.82 3.13 2.82 2.83 2.82
Skewness 1.14 0.78 0.82 1.93 0.86 0.88 0.39
Kurtosis 5.40 3.91 4.13 16.43 4.33 4.50 2.88
Chi-Squared Test
Chi-Sq Statistic 133.55 68.77 59.56 272.53 71.44 70.28 260.60
Chi-Sq Test
Bin #1 : Minimum -Infinity 3.70 0.67 1.62 0.77 (2.56) 4.47
Bin #1 : Maximum 6.23 6.16 6.14 5.88 6.12 6.09 5.73
Bin #1 : Input 156.00 141.00 136.00 71.00 129.00 117.00 46.00
Bin #1 : Fit 135.14 135.14 135.14 135.14 135.14 135.14 135.14
Anderson-Darling Test
A-D Statistic 8.41 0.77 1.50 13.23 1.91 2.38 20.36
Kolmogorov-Smirnov Test
K-S Statistic 0.02 0.01 0.01 0.02 0.01 0.01 0.02
107

B-2 Fitted probability distribution of Electric Cost
`
Figure B-2 Best fitted curve of Electric Cost, Gamma distribution
Table B-2 Results of goodness-of-fit test for Electric Cost, 7 sample curves
Gamma InvGauss LogLogistic Lognorm Pearson5 Triang Weibull
Rankings By Fit Statistic
Akaike (AIC) #1 #5 #2 #3 #6 #7 #4
Bayesian (BIC) #1 #5 #2 #3 #6 #7 #4
Chi-Sq Statistic #1 #5 #3 #4 #6 #7 #2
K-S Statistic #1 #5 #2 #4 #6 #7 #3
A-D Statistic #1 #4 #2 #3 #6 #7 #5
Distribution Statistics
Minimum 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00 2,000.00
Maximum +Infinity +Infinity +Infinity +Infinity +Infinity 14,734.08 +Infinity
Mean 8,242.22 8,242.22 8,328.17 8,250.66 8,270.36 8,571.40 8,218.54
Mode 7,896.54 7,698.67 7,926.11 7,724.75 7,543.09 8,980.11 8,450.07
Median 8,127.38 8,058.84 8,143.46 8,070.20 8,007.15 8,666.53 8,283.49
Std. Deviation 1,468.94 1,539.42 1,593.13 1,535.46 1,661.43 2,603.35 1,545.97
Skewness 0.47 0.74 1.34 0.75 1.14 (0.09) (0.19)
Kurtosis 3.33 3.91 9.24 4.02 5.60 2.40 2.82
Information Criteria
Akaike (AIC) 173,854.30 174,327.69 173,951.80 174,234.20 174,933.90 179,907.45 174,322.63
Bayesian (BIC) 173,868.72 174,342.11 173,966.22 174,248.62 174,948.32 179,921.87 174,337.05
Chi-Squared Test
108

Chi-Sq Statistic 303.29 549.37 424.44 514.73 910.87 5,516.04 412.78
Anderson-Darling Test
A-D Statistic 16.38 47.35 22.53 41.48 85.43 909.07 47.39
Kolmogorov-Smirnov Test
K-S Statistic 0.03 0.05 0.03 0.04 0.06 0.20 0.04

B-3 Fitted probability distribution of Gas Cost

Figure B-3 Best fitted curve of Gas Cost, Log-normal distribution
Table B-3 Results of goodness-of-fit test for Gas Cost, 7 sample curves
ExtValue Gamma InvGauss LogLogistic Lognorm Pearson5 Weibull
Rankings By Fit Statistic
Akaike (AIC) #7 #5 #2 #4 #1 #3 #6
Bayesian (BIC) #7 #5 #2 #4 #1 #3 #6
Chi-Sq Statistic #7 #5 #1 #4 #2 #3 #6
K-S Statistic #7 #5 #1 #4 #2 #3 #6
A-D Statistic #7 #5 #1 #4 #2 #3 #6
Distribution Statistics
Minimum -Infinity 91.66 90.70 91.58 91.17 89.14 91.65
Maximum +Infinity +Infinity +Infinity +Infinity +Infinity +Infinity +Infinity
Mean 101.34 101.74 101.74 102.54 101.76 101.92 101.82
Mode 98.35 96.03 95.62 96.47 95.85 96.15 95.21
109

Median 100.25 99.91 99.26 99.19 99.24 99.15 99.95
Std. Deviation 6.64 7.59 8.55 21.22 9.00 10.69 7.89
Skewness 1.14 1.51 2.32 +Infinity 3.17 11.13 1.35
Kurtosis 5.40 6.40 11.99 +Infinity 24.98 +Infinity 5.44
Information Criteria
Akaike (AIC) 65,996.30 64,593.29 64,055.59 64,266.07 64,049.98 64,142.70 65,115.49
Bayesian (BIC) 66,010.72 64,614.92 64,077.21 64,287.70 64,071.61 64,164.33 65,137.12
Chi-Squared Test
Chi-Sq Statistic 1,657.84 514.62 114.72 309.12 128.99 197.47 842.94
Anderson-Darling Test
A-D Statistic 117.45 38.12 1.79 13.72 2.67 9.46 76.18
Kolmogorov-Smirnov Test
K-S Statistic 0.07 0.04 0.01 0.02 0.01 0.02 0.05

Abstract (if available)

Abstract Even though the design of energy efficient buildings provides an excellent opportunity to achieve large scale energy reductions, the process of achieving this still has difficulties. As an essential and heavily relied upon tool in the design process, software simulation is used to predict building energy performance. However, there are problems associated with simulation tools including the following: estimated data is usually used instead of real data, a lack of accurate occupant schedule and behavior models, inaccurate weather data, and unrealistic performance expectations for mechanical equipment. Simulations may not even be used for accurate predictions of energy performance, but instead just for comparison of alternatives and payback periods, compliance with energy code protocols, and perhaps just general estimates of energy usage. All these problems can lead to surprises when discrepancies are found between actual and predicted building energy performance, which frustrates the building owners, designers, and investors. Research about energy model calibration and the uncertainty of single parameters (e.g. weather data and occupancy), has been done before. Less has been done for incorporating overall risk assessment into energy simulations that takes multiple factors into consideration. ❧ A probabilistic method of risk assessment in energy performance simulations has been proposed and tested. Literature review and discussion with professionals were conducted to decide the parameters that produce most uncertainties in simulations, followed by Differential Sensitivity Analysis (DSA) to identify the most influential parameters among them. Each selected parameter was given a range of values and probability. These were used in simulations in a distribution instead of one fixed value, either a continuous distribution or discrete distribution. Latin Hypercube Sampling (LHS) was used to generate input combinations with parameter values picked stochastically from distributions based on the Monte Carlo method. With these input combinations, thousands of simulations were run using a cloud processing service. Output data was collected and analyzed using a curve-fitting technique to find a best fitted distribution, which could be used for risk and uncertainty analysis of both energy performance and cost information. ❧ A DOE reference building has been used to test this methodology. Among 17 uncertain parameters, seven more influential ones were identified by DSA. 10,000 simulations were run with these seven distributed parameters (weather file, cooling set-point, cooling supply air temperature, equipment density, lighting density, fan overall efficiency, and coil cooling COP). The output data, energy usage intensity (EUI) and energy cost, were fitted into distribution for risk analysis. The results shows the probability and reliability of prediction within a certain range, and both EUI and energy cost could possibly deviate from original prediction in a large percentage. ❧ This methodology has shown that a tool can be developed that expresses the EUI and energy cost of a building simulation as a distribution of likely values rather than a single value. The intent is that a finalized tool would help designers to better evaluate design alternatives and that the results, probability distribution of energy performance and cost, would be useful in making decisions about investments in building energy efficient projects, both new and retrofits.

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Asset Metadata

Creator Sun, Shang (author)

Core Title Energy efficient buildings: a method of probabilistic risk assessment using building energy simulation

School School of Architecture

Degree Master of Building Science

Degree Program Building Science

Publication Date 04/08/2015

Defense Date 03/23/2015

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag building energy simulation,energy use intensity,EUI,Monte Carlo method,OAI-PMH Harvest,probability analysis,risk assessment,sensitivity analysis,uncertainty

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kensek, Karen M. (committee chair), Noble, Douglas (committee member), Schiler, Marc (committee member)

Creator Email shangsun@usc.edu,shangsun100@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-543429

Unique identifier UC11298274

Identifier etd-SunShang-3256.pdf (filename),usctheses-c3-543429 (legacy record id)

Legacy Identifier etd-SunShang-3256.pdf

Dmrecord 543429

Document Type Thesis

Format application/pdf (imt)

Rights Sun, Shang

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA