20210318Avista to Staff PR 39 Attachment A.PDF

Report Number: 1608_01
REDUCED ORDER WHOLE BUILDING ENERGY
SIMULATION FOR VIRTUAL COMMISSIONING
PROJECT REPORT PREPARED FOR AVISTA UTILITIES
August 31, 2017
Prepared for:
Avista Utilities
Authors:
Sean Rosin
Damon Woods
Elizabeth Cooper
Jinchao Yuan
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Prepared by:
University of Idaho Integrated Design Lab | Boise
306 S 6th St. Boise, ID 83702 USA
www.uidaho.edu/idl

IDL Director:
Elizabeth Cooper

Authors:
Sean Rosin
Damon Woods
Elizabeth Cooper
Jinchao Yuan

Prepared for:
Avista Utilities

Contract Number: R-39872

Please cite this report as follows: Rosin S., Wood, D., Cooper, E.,
and Yuan, J. (2017). Using reduced-order models for simulation
based commissioning of buildings. (1608_01). University of Idaho
Integrated Design Lab, Boise, ID.
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DISCLAIMER
While the recommendations in this report have been reviewed for
technical accuracy and are believed to be reasonably accurate,
the findings are estimates and actual results may vary. All energy
savings and cost estimates included in the report are for
informational purposes only and are not to be construed as
design documents or as guarantees of energy or cost savings. The
user of this report, or any information contained in this report,
should independently evaluate any information, advice, or
direction provided in this report.
THE UNIVERSITY OF IDAHO MAKES NO REPRESENTATIONS,
EXTENDS NO WARRANTIES OF ANY KIND, EITHER EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF
MERCHANTABILITY, AND FITNESS FOR A PARTICULAR PURPOSE
WITH RESPECT TO THE INFORMATION, INCLUDING BUT NOT
LIMITED TO ANY RECOMMENDATIONS OR FINDINGS, CONTAINED
IN THIS REPORT. THE UNIVERSITY ADDITIONALLY DISCLAIMS ALL
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SPECIAL AND CONSEQUENTIAL DAMAGES, ATTORNEYS’ AND
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INCLUDING BUT NOT LIMITED TO DAMAGES OF ANY KIND IN
CONNECTION WITH THIS REPORT OR THE INSTALLATION OF
RECOMMENDED MEASURES CONTAINED HEREIN.

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TABLE OF CONTENTS
1. Acknowledgements .................................................................................................................... 3
2. Executive Summary .................................................................................................................... 4
3. Research Motivation .................................................................................................................. 5
4. Project Background .................................................................................................................... 7
4.1 Whole Building Energy Simulation ....................................................................................... 8
4.2 Reduced Order Thermal Models (Grey Box Models) ............................................................ 9
4.3 Prior Research Using Reduced Order Models to Describe the Dynamic Behavior of
Buildings ................................................................................................................................... 12
4.4 Simplified HVAC Model ....................................................................................................... 17
4.4.1 Economizer Controls Model ......................................................................................... 19
4.4.2 AHU Preheat Coil and Cooling Coil Model ................................................................... 21
4.4.3 Terminal Reheat Model ............................................................................................... 22
4.4.4 Supply Air Flow Rate .................................................................................................... 24
5. Results ...................................................................................................................................... 26
5.1 Virtual Commissioning ........................................................................................................ 31
6. Discussion and Future Work ..................................................................................................... 34
7. Budget Summary ...................................................................................................................... 36
8. References ................................................................................................................................ 37

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ACRONYMS AND ABBREVIATIONS
AHU Air Handling Unit
BACnet Building Automation Controls Networking Protocol
BCVTB Building Controls Virtual Test Bed
COBE College of Business and Economics
EMS Energy Management Control System
HVAC Heating, Ventilation and Air Conditioning
IDL Integrated Design Lab
ROM Reduced Order Model
SASP Supply Air Set Point
TOT Terminal Outlet Temperature
UI University of Idaho
VAV Variable Air Volume
VFD Variable Frequency Drive

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1. ACKNOWLEDGEMENTS
This research was made possible through funding support from Avista Utilities via Idaho PUC Case Number
AVU-E-13-08. The research team expresses gratitude to Avista staff and project managers for their
support of this project. This project could not have happened without the coordination and help received
from the University of Idaho’s facilities team for the access they provided. Particular thanks is due to
Keven Hattenburg who went out of his way to help with our research.

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2. EXECUTIVE SUMMARY
The University of Idaho – Integrated Design Lab (UI-IDL) modeled an existing building using reduced
order modeling techniques as a tool for virtual commissioning. The research focused on the
Albertson’s College of Business and Economics building at the University of Idaho Moscow Campus.
The reduced order model was composed of sets of differential equations with system parameters
which describe the dynamic nature of heat transfer though a building. These parameters were
determined through software optimization in order for the model to best predict the zone
temperature of the building when compared to the zone temperature as predicted by EnergyPlus. The
reduced order model was coupled with an HVAC model to predict the total annual energy
consumption of the building which was then used to determined potential energy savings measures.
It was found that the COBE building lacked thermostat setbacks during periods of unoccupancy, and
the ROM model was used to predict the energy savings associated with updating the controller. It was
found that approximately 104,000 kWh of potential energy savings could be realized if the thermostat
had properly programed temperature setbacks during times the building is unoccupied.

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3. RESEARCH MOTIVATION
While new buildings increasingly rely on automated controls for their Energy Management
Systems (EMS), commissioning of these controls in new buildings and verification of existing sequences in
existing buildings are a time intensive process. They could run the risk of suboptimal occupant comfort,
and expose the building owners to unnecessary liability and higher energy costs during the time period
before commissioning is accomplished. The building commissioning process encompasses a wide range
of stages, starting with design development and ending at least one year after the building is occupied [1].
New building control commissioning typically takes one full year of building operation, so that all weather
conditions and all modes of operation are experienced, and often takes two full years before the system
is operating nearest to its potential. In addition, it is often difficult to set up, or is time consuming to wait
for, specific space or outdoor conditions to occur for all aspects of an EMS control logic to be tested and
addressed, leaving large gaps in the verification process for some modes of operation. Older buildings can
also suffer from poor controls that are out of tune with the current building occupancy patterns or not up
to date with current best practices control techniques. In current practice, suboptimum and incorrect
control programming can take months or years to detect, if they are ever detected [2]. When controls
issues arise, they can also be difficult to reproduce and take weeks or months to rectify [3]. Operational
issues can often go undetected, especially if they do not directly affect human comfort. Simulation-based
commissioning holds promise as a way to reduce or avoid these hazards.
The previous research the Integrated Design Lab (IDL), Boise, conducted energy simulations as a tool
to virtually commission buildings. This research focused on using an EnergyPlus model and connecting it
to a duplicate of the Alerton Building controller that is used at the University of Idaho Albertson’s College
of Business and Economics (COBE) building in Moscow, Idaho. This was accomplished by enabling
communications from the EnergyPlus simulation to the building controller, which was done using the
Building Controls Virtual Test Bed (BCTVB). BCVTB is “middle-ware” which translates the outputs from the
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EnergyPlus simulation to either a voltage or digital input that the building controller can understand [4].
The variables that were chosen for the study included outdoor air temperature, outdoor air damper
position, mixed air temperature, and return air temperature. The Alterton controller requires inputs from
other equipment and feedbacks from each of the thermal zones, which was not practical to model in
EnergyPlus due to computational limitations. These inputs were bypassed by adjusting the logic to allow
the controller to continue to function without each individual feedback loop. This method of simulation-
based commissioning is less time intensive than traditional commissioning approaches, but developing an
accurate energy model takes time and knowledge that most practitioners do not possess. Although the
cost of commissioning a building is prohibitive for many owners, the research demonstrated that virtually
commissioning a building is a viable alternative. The current phase of the research explored ways to
reduce the time and monetary expenditures of virtual commissioning still further.
The current research aims to simplify the modeling process to allow practitioners a means of virtually
commissioning a building without the steep learning curve associated with modeling in EnergyPlus. This
approach reduces the modeling time, allows for innovative control strategies to be investigated quickly,
and can be used by practitioners to quickly diagnose an operational or control issues. There are still
limitations with reduced order energy modeling that need to be addressed before the methods of virtual
commissioning can be fully utilized.

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4. PROJECT BACKGROUND
The team selected the COBE building, on the University of Idaho campus in Moscow, ID for study.
The 50,000-square-foot facility was constructed in 2001 and is a mix of classroom spaces and faculty
offices. It also has a unique simulation room with over twenty computer stations and a terminal for real-
time market analysis and trading, requiring a high electric load. The building is equipped with a Variable
Air Volume (VAV) system and relies on district heating and cooling from campus water lines that serve
two air-handling units (AHUs) in the building. The smaller of these two AHUs conditions the basement,
while the larger AHU provides air to the upper three floors. Non-fan powered VAV boxes are located in
each zone. Some of the building’s geometry can be seen in Figure 1.

Figure 1. COBE Building photo (left) model geometry (right)
The COBE Building was chosen for the previous research because the building’s controllers communicate
through a standard building automation and control network protocol: BACnet. This communication
protocol was essential for the research so that the energy model could interact with the controllers in a
standard way. The team continued using this building for the reduced order model (ROM) virtual
commissioning reseach to so that the new method could be compared against the calibrated baseline
EnergyPlus model from the previous research. Reduced Order Modeling Background
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4.1 Whole Building Energy Simulation
There are several different types of modeling approaches used in whole building simulation. Black
box modeling is a data driven modeling approach which uses actual building time series data to statistically
fit a model to determine building parameters. Black box modeling does not provide insightful information
about the mechanism or the behavior of the building [5]. Rather, it is solely a statistical representation of
a building’s data correlations. Black box models only focus on finding relationships between the model’s
inputs and outputs [6], which is not very useful for virtual commissioning.
Another practice of whole building energy simulation is through white box modeling, or models
that are developed through physics and first principles [6]. One of the best known white box modeling
techniques for whole building energy simulation is EnergyPlus. EnergyPlus was developed by the
Department of Energy for engineers and architects to model energy and water usage of buildings. This
method is an exhaustive process which can take several months to build accurately. All the building’s
geometry, construction, zone characteristics, heating ventilation and air-condition (HVAC) controls and
layouts must be defined properly for EnergyPlus to accurately predict the energy consumption of the
building. When the building ages, there is no way to account for the degradation of equipment and
insulation in the modeling process. Therefore, after the building has been virtually constructed, the model
must undergo calibration using actual building energy data. Due to this lengthy process, whole building
energy modeling with EnergyPlus is often neglected, and as a result many energy savings opportunities
go undetected.
A third modeling technique that has been underutilized is grey box modeling. Grey box modeling
is still built on the foundation of first principles, but it uses real run-time data to optimize model
parameters [6]. For thermal systems, grey box modeling uses a set of differential equations to model the
dynamic nature of heat transfer throughout the structure. There is no limit to the order of the system,
but as the complexity of the model increases so does the computational expense. Each model order is an
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additional differential equation, and each additional order equates to an additional set of model dynamics
that must be accounted for. The time constant of a building is related to time of thermal energy decay
and it is composed of thermal resistance and thermal capacitance of the building. These parameters are
then optimized using actual data from the physical structure to obtain the best fit of the model. This
modeling technique is less computationally expensive than white box modeling, and takes much less time
to develop a predictive model for the thermal performance of buildings.
4.2 Reduced Order Thermal Models (Grey Box Models)
There are two parameters that are used to describe the dynamics of thermal systems using ROMs:
the thermal capacitance and thermal resistance. The thermal capacitance of a substance is a function of
known material properties and is defined in Equation 1 as:
𝐶 = 𝜌𝐶$𝑉 (1)
Where r is the density of the material [kg/m3], Cp is the specific heat [J/kgK], and V is the volume [m3].
When a building has a large cumulative thermal capacitance, otherwise known as massive building
construction, the rate at which the building’s temperature can change due to environmental and internal
effects is low. The thermal capacitance is an important parameter to estimate the transient behavior of a
building [7], but is oftentimes hard to calculate even when the material properties of a building are known.
Another parameter used to describe thermal systems is the thermal resistance of a material. The thermal
resistance describes the material’s natural tendency to resist the flow of heat. There are several different
forms of thermal resistance, but they all have the units of [W/K] and all describe resistance to heat
transfer. The thermal capacitance and the thermal resistance are the basis of ROMs.
Reduced order thermal models are commonly referred to as a lumped RC model and are
represented using thermal circuits which are similar to electrical circuits, an example is shown below in
Figure 2.
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Figure 2. 2nd Order Lumped RC Thermal Network
To model a building using reduced order techniques there are several assumptions that have to be made:
1. The zone air is well mixed and at a consistent temperature
2. Heat transfer is one directional
3. There is no temperature gradient in the wall making the heat flux a constant value for
the entire surface
4. There is a homogenous temperature throughout each ‘lump’
Theoretically, a material can be broken into an infinite number of lumps. However, each lump increases
the order of the system which increases the computational complexity and slows down the runtime of
the simulation. Reduced order modeling is one of the most powerful methods of modeling dynamic
systems due to the simplicity when compared to other approaches. For these types of models there exists
a minimum number of variables, i.e. states, that when known can completely describe the system [8].
These states are well known and measurable, and for thermal systems they are the temperatures of nodes
distributed throughout the system. These state variables can be described using a vector and the
linearized state space representation of the thermal circuit illustrated above is shown in Equation 3.
𝑇= 𝐴𝑇+ 𝐵𝑈 (3)
Where 𝑇 is a vector of all nodal temperatures, and 𝑈 is a vector of all system inputs. A and B are coefficient
matrices containing the thermal parameters that describe the relationship between the inputs and the
desired outputs. Equation 3 can be expanded and expressed in matrix form to represent the thermal
circuit shown above in Figure 2.
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𝑇+
𝑇,
=
−1
𝐶+
1
𝑅+
+1
𝑅,
1
𝑅,𝐶+1
𝐶,𝑅,
−1
𝐶,𝑅,
+
𝑇0
𝑅+
𝑄23456
(4)

Where:
Table 1. 2R2C Variable Definitions
Variable Description Units
𝑇0 The outside ambient temperature [°C]
𝑇+ The wall temperature [°C]
𝑇, The zone temperature [°C]
𝑅+ The effective thermal resistance of the wall [W/°C]
𝑅, The effective thermal resistance between the wall and the zone [W/°C]
𝐶+ The effective thermal capacitance of the wall [J/°C]
𝐶, The effective thermal capacitance of the zone [J/°C]
𝑄23456 The heat load of the system (solar, internal, infiltration, HVAC) [W]

The inputs for this system are the ambient temperature and all heat gains (i.e. plug loads, solar gains, and
fenestration gains), which are all applied at zonal node. A simplified diagram illustrating the locations of
the Rs and Cs is shown below in Figure 3.

Figure 3. 2R2C Thermal Parameter Diagram
C2 is the thermal capacitance of the zone, which includes the air and all the interior mass, i.e. furniture,
carpet, etc. C1 is the effective thermal capacitance of the building constructions. The location of C1 is
arbitrary and the only known information about its location is that it falls somewhere in between the
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building’s wall construction. The wall is not partitioned in any symmetrical manner; it is divided such that
the temperature at each node is uniform throughout the entire lump of material. R1 is the effective
thermal resistance in between the ambient temperature and T1, and R2 is the effective thermal resistance
in between T1 and the center of the zone. This model structure was utilized in a simplified case study to
investigate the effects of the thermal parameters before modeling the COBE Building. The model of the
COBE building is more intricate than the 2R2C model shown above due to the complexity of the building’s
dynamics.
4.3 Prior Research Using Reduced Order Models to Describe the Dynamic Behavior of
Buildings
The simplest way to represent the construction of a building is by a 1R1C model, which only has
a single thermal resistance and a single thermal capacitance. This representation of a building is unrealistic
because it lumps the mass of the wall and the mass of the interior together [9]. This forces the
temperatures of these two masses to be equal at all times by not identifying them as two separate thermal
capacitances. Additionally, most of the thermal capacitance of a building is contained in the wall of the
structure, and there is a thermal barrier between the wall construction and the interior zone, which this
model ignores. It has been concluded that if you add an additional resistance between the zone
temperature and the external temperature it greatly reduces the peak instantaneous loads during
warmups [9] which helps the model’s overall fidelity.
Bacher et al. [10] investigated which models offer the best performance for the least complexity
to fully describe the dynamic of the building. The process starts with determining the simplest model that
describes all the information embedded in the data, being the 1R1C thermal network. The model’s order
was increased to see how the higher order model statistically compares the previous model. This was
done using a likelihood tests which compares the predicted results with the previous model to determine
the likelihood there exists a higher order model that statistically predicts the zone temperature more
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accurately. This method was applied to an experiment facility in Denmark where all the construction
materials were known. It was determined that a 3R3C model describes the building’s dynamics adequately
enough and a higher order model is not worth the extra computational expense. The three thermal
capacitances were associated with the heater, the interior space, and the construction of the building.
Based on the findings of Bacher et al. [10], the model structure that was chosen to describe the
dynamics of the building was a 3R3C model, which was coupled with a 2R1C model to describe the
dynamics of the ground and foundation. A diagram showing the model’s thermal circuit superimposed on
a simple building diagram illustrating the relative location of the model parameters can be seen in Figure
4.

Figure 4. Diagram of Thermal Network used in Modeling COBE Building

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Where:
Variable Description Units
𝑇0 The outside ambient temperature [°C]
𝑇8 The temperature of the ground [°C]
𝑅+ The effective thermal resistance of the wall [°C]
𝑅, The effective thermal resistance of the wall [°C]
𝑅9 The effective thermal resistance between the
interior of the wall and the zone
[°C]
𝑅: The effective thermal resistance of the windows [W/°C]
𝑅; The effective thermal resistance between the
center of the foundation and the central interior
zone
[W/°C]
𝑅8 The effective thermal resistance of the ground and
the midsection of the building’s foundation
[J/°C]
𝐶+ The effective thermal capacitance of the wall [J/°C]
𝐶, The effective thermal capacitance of the zone [J/°C]
𝐶; The effective thermal capacitance of the
foundation
[J/°C]
𝑄23456 The heating and cooling loads of the system (solar,
internal, infiltration, HVAC)
[W]

This thermal circuit can be expressed using a set of linear differential equations to describe the states of
the structure. The selected states used to fully describe the system are the temperature of the foundation
(Tf), the internal zone temperature (Tz), and the wall temperatures in between the interior and the façade
(T1), and (T2). It should be noted that states are the effective temperatures of the modeled capacitances
and they represent the overall average temperature for each lump. An expanded matrix showing the full
set of Equations can be seen below.

𝑇+
𝑇,
𝑇<
𝑇;
=
−𝑅++ 𝑅,
𝑅+𝑅,𝐶+
1
𝑅,𝐶+
0 0
1
𝑅,𝐶,
−𝑅,+ 𝑅9
𝑅,𝑅9𝐶,
1
𝑅9𝐶,
0
0 1
𝑅9𝐶<−𝑅9𝑅;+ 𝑅:𝑅;+ 𝑅:𝑅9
𝑅9𝑅:𝑅;𝐶<
1
𝑅;𝐶<
0 0 1
𝑅;𝐶;−𝑅;+ 𝑅8
𝑅;𝑅8𝐶;
∙
𝑇+𝑇,𝑇<𝑇;
+
𝑇0
𝑅+0𝑇0
𝑅:
+ 𝑄23456
𝑇8
𝑅8
(5)

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The loads included in the model were the internal loads, and the solar gains which were outputted
from EnergyPlus and used as an input into the ROM. These values can be determined computationally
using ASHRAE standards in the EnergyPlus mode. In this study, equivalent values used in EnergyPlus was
again used to avoid any additional errors. All of these loads were applied at the center of the zone which
is an oversimplification of the system. It is known that the solar loads will be distributed throughout the
interior of the structure, and the distribution pattern is determined by the geometry, reflectance, and
many other parameters of the building. As well, the conditioned air will be distributed throughout the
entire space and not just supplied to the center of the zone, without knowing the exact distribution
pattern, the loads have to be applied at the center. Additionally, the solar gains do not only come from
the radiation directly admitted into the space via the window, the also come from the thermal storage
properties of the exterior wall construction. As the day progresses the building materials store energy and
their internal temperature increases, thus causing conductive heat transfer to increase throughout the
entire surface of the exterior wall. These gains are happening simultaneously over the entire exterior wall,
not just at the center of the zone.
The model parameters were estimated using a Simulink® Optimization package that iterates
through different parameter values until the model best predicts values when compared to a user
inputted time series, the estimated parameter values are shown in Table 2.
Table 2. Optimized Model Parameter Values
Thermal Resistance Thermal Capacitance
R1 6.617 E2 C1 7.029 E8
R2 1.272 E-1 C2 2.583 E12
R3 3.021 E-4 Cz 4.520 E7
Rw 3.768 E-4 Cf 1.296 E9
Rf 2.909 E-5
Rg 2.968 E-4

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The model parameters shown in Table 2 best predicted the ROM’s zone temperature when compared to
the results of EnergyPlus. The zone temperatures from EnergyPlus have been plotted against those from
the ROM in Figure 5. The left-top and left-bottom figures show the hourly zone temperature for the first
week of February and the first week of August respectively.

Figure 5. (Left – Top) EnergyPlus vs Simulink Zone Temperature for first week of February. (Left – Bottom)
EnergyPlus vs Simulink Zone Temperature for first week of August. (Right) Daily Average Temperature
Residual Distribution
During February the EnergyPlus zone temperature settles to the set point whereas the lumped RC model
does not accurately predict this behavior. This is believed to be from the nature of ROMs, which are
typically utilized to model dynamic systems. The ROM has better fidelity when there are instabilities in
the zone temperature and it does not settle to a set point, which is illustrated in the August zone
temperature figure. The daily average temperature difference between EnergyPlus and the ROM have
been plotted in a histogram which shows the frequency and the magnitude of the temperature. Figure 5
(Right) shows a right skewed histogram centered around an average of 0.039°C. This is an indication that
the ROM over-predicts the zone temperature by an average of 0.039°C. This should translate into a higher
magnitude of cooling needed to compensate for the over-prediction of the zone temperature when
compared to EnergyPlus. While the reduced order thermal model predicts the indoor zone temperature,
indoor zone temperature is not a direct indication of energy consumption. In order to “convert” these
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temperature predications to energy, an HVAC model and controller are needed. To use this model as a
tool of virtual commissioning, the HVAC model needs to describe the mechanical systems as accurately
and simply as possible, a diagram illustrating the flow of the fully integrated model can be seen below in
Figure 6.

Figure 6. Integrated Reduced Order Thermal Model Flow Diagram
The thermal model will predict the zone temperature of the buildings, which will be passed through to a
controller to inform the simplified HVAC model how to condition the space. The HVAC model will predict
the magnitude and duration of zone conditioning which will be relayed back to the thermal model and
applied at the center of the zone like the other zone loads, which completes the feedback loop.
4.4 Simplified HVAC Model
As discussed earlier, the COBE Building is a mixed use educational facility. It has over fifty zones
that have varying occupancy, internal loads and thermostat set points. The HVAC equipment that the
COBE building uses is a district heating/cooling variable VAV system with non-fan powered terminal
reheat. There is a district chiller and boiler that provide each building with chilled water and hot water,
which is utilized as the working fluid in the main AHUs. The COBE building has two AHUs, one that services
only the basement, and the other that services the three above ground floors. For simplicity, the HVAC
model was altered to only have one AHU to service the entire building. Figure 7 shows a diagram of a
typical air handler unit.
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Figure 7. AHU Diagram [11]
There are four main parts of a typical HVAC system used at the COBE building: the supply and
return air fans, air dampers, heating and cooling coils, and the terminal reheat box (not illustrated above).
The supply air fan provides the necessary air flow to meet the minimum outdoor air standard and to
condition the zone to the required thermostat set point. The supply air fan is connected to a variable
frequency drive (VFD) which controls the speed of the fan, which is the most efficient way of controlling
the air flow. The next elements of the HVAC system are the AHU dampers, which are used to vary the
amount of outside air and return air vented into the mixing chamber. The dampers optimize their position
to meet the mixed air temperature set point, which is done through modulating the flow of the two
streams entering the mixing chamber. After the air passes through the mixing chamber it is conditioned
to the supply air temperature set point, which oftentimes is the same as the mixed air set point. The
heating and cooling coils in the AHU are only used when the dampers cannot meet the mixed air set point.
The last components of these systems are the terminal units which are located at each individual zone
and are used to reheat the air before it enters the space. These boxes have their own hot water heating
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coils, which are also supplied from the district boiler. Each component of the VAV district heating/cooling
HVAC system needs to be modeled individually to have an accurate representation of the entire system.
4.4.1 Economizer Controls Model
The HVAC system used in the COBE building relies on an economizer to capture free cooling during
times when the ambient conditions permit. Economizers have four different operational modes: heating,
modulating, integrating, and mechanical cooling mode [12]. When the outdoor temperature is less than
1°C (heating mode) the economizer only allows in the minimum required outdoor air for ventilation. The
outdoor air is mixed in with the return air in the mixing chamber and is then heated to the necessary
temperature to meet the heating demand. During mild outdoor temperatures (1°C to 13°C) the full
cooling demand of the building can be met by modulating the fraction of outdoor air that is mixed with
the return air (i.e., modulated economizer mode). This operational mode allows the economizer to
provide the most amount of free cooling to the building. The next operational mode is integrated
economizer mode which occurs when the outdoor temperature is too high for to meet the full load by
solely using outdoor air (13°C to 24°C), during this temperature band some mechanical cooling must take
place to meet the cooling demand of the building. The last operational mode occurs when the outdoor air
temperature is above the economizer’s high limit shut off. During this mode the economizer only allows
the minimum required outdoor air to meet ventilation requirements and the space conditioning is
accomplished through mechanical cooling. Figure 8 illustrates of all economizer operational modes
throughout the year.
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Figure 8. Typical Economizer Operation [12]
The above operational modes are the basis for the economizer controls utilized in the HVAC model. They
have been transformed into block diagram logic, which can be seen below in Figure 9.

Figure 9. Economizer Simulink Model
The economizer model has several subsystems which all carry out essential functions that allow the model
to accurately calculate the percent outside air. The percent outside air is a function of the air’s physical
properties, which have to be determined before the economizer positioned can be calculated.
4●Trane Engineers Newsletter volume 35–2 providing insights for today’s HVAC system designer
to 100% and the return-air damper closes completely. The system enters integrated economizer mode, where 100% outdoor airflow provides part of the required cooling capacity and mechanical cooling provides the balance, modulating or cycling as necessary to maintain the required space (or supply-air) temperature. The red area in Figure 4a represents the mechanical cooling energy that’s saved during integrated economizer operation.The system stays in integrated economizer mode until the outdoor-air condition reaches the high-limit shutoff setting. At this point, the controls disable economizer operation and the system enters the mechanical cooling mode, where a water valve modulates or a compressor cycles to provide all cooling capacity needed to maintain space (or supply-air) temperature. In this mode, the outdoor-air damper closes to allow only minimum intake airflow. In some locations, direct expansion (DX) systems may be designed to enter the mechanical cooling mode directly from the modulated economizer mode. If 100% outdoor air
is unable to provide the required
cooling capacity, then the outdoor-air
damper closes to its minimum position
and mechanical cooling modulates to
provide all of the needed cooling
capacity. This “non-integrated
economizer” approach avoids unstable
refrigerant system operation and coil
frosting, which can occur when a DX
system cycles at low loads. But it also
reduces the potential savings in
mechanical cooling energy represented
by the red-shaded area in Figure 4a.
Figure 4b: Variable-volume
systems.Consider a single-duct,
chilled water VAV system with reheat
terminals: In heating mode, minimum
outdoor airflow enters the system and
recirculated return air provides the
balance of supply airflow. Supply
airflow usually decreases as the
heating load diminishes because the
reheat terminals need less airflow when cooling than when heating. When the cooling load starts to rise, the modulated economizer mode begins. Supply airflow increases (that is, intake airflow increases while return airflow decreases) to maintain the required supply-air temperature without mechanical cooling. In the integrated economizer mode, the outdoor-air damper stays wide open
to provide some cooling capacity
while the mechanical system
modulates to provide the balance.
The system enters mechanical cooling mode when outdoor air reaches the high-limit shutoff condition. Intake airflow drops to the minimum requirement, and supply and return airflows increase while the cooling coil provides the required cooling capacity.Both constant-volume and VAV systems use linked outdoor- and return-air dampers, which are operated
by a single actuator or by multiple
coordinated actuators. However, as
mentioned in the Standard 90 user’s
Figure 4b. Typical economizer control sequence for variable-volume (VAV) systems
Figure 4a. Typical economizer control sequence for constant-volume systems
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4.4.2 AHU Preheat Coil and Cooling Coil Model
Once the air has been mixed in the mixing chamber, it passes through the supply air fan and is
blown over the AHU heating/cooling coils, where the air is conditioned to the supply air set point (SASP)
temperature. When the AHU is operating in modulated economizer mode, the temperature differential
between the mixed air set point and the supply air set point is minimal, reducing the energy required to
condition the supply air. During the other modes of operation, the main AHU heating/cooling coils will
have to condition the supply air to the correct set point.
The driving force in moving air around the building is the pressure differential between the supply
air and the zone air, which is supplied by the supply air fan. This process is non-adiabatic and the air
stream collects a small amount of residual energy as it passes though the blower, which increases the
overall temperature of the air stream. This rise in temperature can be determined through computational
methods, but for simplicity and accuracy the temperature rise was outputted from the EnergyPlus model
and included in the Simulink model.
The AHU heating/cooling model compares the supply air set point temperature to the current
mixed air temperature to determine the amount of heating or cooling that needs to be added. To avoid
issues of simultaneous heating and cooling, a dead-band was modeled which represents the realistic
characteristics of actual systems, and the dead band temperature range was set at ±1°C. If the differential
between the mixed air and the supply air set point is more than one degrees Celsius, the conditioning is
turned on until the temperature falls within the dead band of the controller. The amount of
heating/cooling required is determined through Equation 6, which was developed using first principles of
heat transfer.
𝑄?@A = 𝜌B?𝐶$𝑉B?𝑇B?BC − 𝑇D? (6)
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Where 𝜌B? is the density of the supply air [kg/m3], 𝐶$ is the specific heat of air [J/kgK], 𝑉B? is the volumetric
supply air flow [m3/s], TSASP is the supply air set point temperature [°C], and TMA is the mixed air
temperature [°C]. The relay in Figure 10 corresponds to the dead band discussed above. When the
absolute value of the difference between the mixed air temperature and the supply air set point is more
than unity, the relay outputs a zero which forces the heating/cooling to go to zero.

Figure 10. AHU Coil Heating/Cooling Block Diagram
The energy calculated in the AHU model is not a direct feedback loop for the thermal model but it does
contribute to the overall energy consumption of the building.
4.4.3 Terminal Reheat Model
Once the air stream has been conditioned to the supply air set point temperature, it is distributed
throughout the building. The supply air set point for the COBE Building is 12.78°C, meaning during the
winter and shoulder seasons the air is going to need reheat before entering the zone. This is accomplished
through the terminal reheat boxes located at each zone. The terminal boxes at the COBE Building are
known as single-duct VAV pressure-independent terminal boxes with reheat. The terminal reheat unit
only has a hot coil which is supplied from the same central plant as the main AHU heating coil in. Along
with the hot water coil there is a terminal box damper, and a flow sensor. As the zone temperature
changes the controller modulates the damper position to vary the amount of air delivered into the zone.
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The flow sensor serves as a failsafe to insure the flow does not fall below the minimum requirements for
ventilation. If the heating load of the building is not being met by modulating the damper, the controller
opens a valve allowing more water to flow through the coils which increases the temperature of the air
supplied to the zone [13]. A typical terminal box control loop diagram can be seen below in Figure 11.

Figure 11. Typical Terminal Box Feedback Diagram [13]
These dampers are an essential component to multi-zone VAV HVAC systems. Our model was simplified
to a single zone building so the terminal damper feedback loop was not modeled directly, but its main
function was captured and utilized elsewhere in the model. In multi-zone system, the terminal box
dampers modulate the flow supplied to the zone. When the dampers are at their minimum allowed
flowrate, and all the zone are being adequately conditioned, the main air handler reduces the supply flow
rate using the VFD. In the simplified COBE model there is only a single zone, so when the zone is meeting
the temperature set point there is a feedback loop, acting similarly to the VFD signal, to reduce the supply
air flow rate. The modulation happens at the main air handler instead of the terminal box damper so there
is no need for an additional damper in the reduced order system.
When modeling the terminal reheat there were two separate perspectives that had to be
accounted for: the amount of energy supplied to the zone, and the amount of energy consumed by
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conditioning the air. The air entering the terminal reheat box is at the supply air set point temperature,
which is below cooling thermostat set point, so even if the terminal reheat unit is not being utilized, it is
still cooling the zone which is a feedback loop for the thermal model. Even though the terminal reheat
unit is only capable of supplying heat to the air stream, all the energy contained in the air stream needs
to be accounted for when coupling the HVAC model with the reduced order thermal model. The amount
of energy being supplied to the zone from the terminal unit can be seen below in Equations 7 and 8.
𝑄EFGHIJ4K LFMF4N O3JF @F4N = {𝜌B?BC𝐶$𝑉B?𝑇EQ − 𝑇<3JF ,𝑖𝑓 𝑇EQ > 𝑇<3JF} (7)
𝑄EFGHIJ4K LFMF4N O3JF W33K = {𝜌B?BC𝐶$𝑉B?𝑇EQ − 𝑇<3JF ,𝑖𝑓 𝑇EQ < 𝑇<3JF} (8)
Where 𝜌B? is the density of the supply air [kg/m3], 𝐶$ is the specific heat of air [J/kgK], 𝑉B? is the volumetric
supply air flow [m3/s], TTO is the terminal outlet temperature [°C], and Tzone is the zone temperature [°C].
The amount of energy supplied to the zone is proportional to the temperature differential between the
terminal outlet temperature and the zone temperature. It should be noted that the cooling energy
supplied to the zone is negative which keeps the HVAC model compatible with the thermal model. When
the terminal outlet temperature is less than the current zone temperature, the zone is currently being
cooled, but due to the operational modes of the terminal reheat boxes, the air may still need be reheated
even though the room is being cooled. During cooling mode, the terminal outlet temperature will be
modulated between the range of the supply air set point (12.78°C) and approximately 18°C, and during
heating mode, the terminal outlet temperature will be modulated from 18°C up to 33°C.
4.4.4 Supply Air Flow Rate
The supply air flow rate is modeled the same way as the terminal outlet temperature; for both
heating and cooling, the flow rate is controlled by applying a linear gain to the temperature differential
between the zone temperature and the current set point, which can be seen in Equation 7. The supply air
flow rate modulation is turned on and off through a ‘VFD’ signal that originates in the terminal outlet
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temperature model. When the cooling or heating demand cannot be met by controlling the terminal
outlet temperature, the VFD signal is turned on which allows the flow rate to be modulated, if the signal
is off, the flow rate vented into the space is set at the minimum required for ventilation.
SA Flow =𝑇<3JF − 𝑇6N4N ⋅ 1.1 +𝑀𝑖𝑛 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒 (9)
The linear gain used in the controller was determined using an iterative process. The minimum and
maximum flow rate of the system was determined by surveying at the EnergyPlus’ flow rate. Once again,
the actual COBE Building may achieve a higher or lower flow rate, but since the ROM’s effectiveness is
based off a comparison with EnergyPlus, the values predicted by the EnergyPlus are more critical. Once
the flow rate of the system is accurately calculated, the amount of heat or cooling entering the space can
be determined. The energy flow entering the space is a feedback for the thermal model and is applied at
the center of the zone. The HVAC system was integrated with the thermal model and energy consumption
could be compared between the reduced order and EnergyPlus model.

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5. RESULTS
The ROM was compared to both the single zone and the fully zoned EnergyPlus model of the COBE
building. The single zone EnergyPlus model was used to compare individual output parameters such as
zone heating and cooling loads, supply air flow rate, etc., whereas the fully zoned EnergyPlus model was
compared to the ROM for the virtual commission recommendations. This comparison method was chosen
due to the simplifications that were made earlier in the modeling process. The ROM was optimized to
thermally perform close to the single zone EnergyPlus model. The parameters were optimized to match
the response of the single zone EnergyPlus model, and as such the individual output parameters should
represent the single zone model more accurately. The commissioning recommendations are going to be
compared against the fully zone model of the COBE building. The fully zoned COBE building has been
calibrated according to ASHRAE’s standards and is a more accurate representation of the actual building
than the single zone model.
Common energy consumption metrics between the two models were chosen for comparison with
the parameters being the zone heating and cooling loads and the AHU coil energy consumptions. It should
be noted that the heating a cooling loads do not account for system efficiency, it is the ideal load that will
keep the space conditioned at the given set point, given all ambient and internal effects. The zone heating
and cooling load was chosen to improve errors caused by the VAV box system efficiency. The ROM did not
include any measure of efficiency, making the modeled value more representative of a load, and not a
consumption. If this parameter was not chosen for comparison, it would have to be assumed that VAV
box system efficiency is independent of the heating or cooling load, which is typically not the case. The
losses in the terminal box are from the heat exchanger, where the efficiency of the unit being dependent
of both fluid flows (supply air cross flow and hot water flow). The inlet and outlet temperature of the heat
exchanger water was not modeled directly, so determining the VAV system efficiency of the ROM was not
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feasible. This made it necessary to compare the ROM predicted terminal reheat energy usage to the
EnergyPlus model’s predicted heating and cooling load of the zone.
ASHRAE has designated a comparison method for energy modeling and according to ASHRAE
Guideline 14, the two recommend modes of comparison are the coefficient of variation of the root mean
square error (CVRMSE) and the normalized mean bias error (NMBE). ASHRAE Guideline 14 considers a
building model calibrated with hourly data to have a CVRMSE within the range of ±30%, and NMBE in the
range of ±10% [14]. The CVRMSE and the NMBE error are shown below in Equations 8 and 9 respectively.
CVRMSE =
ΣIp+
qr 𝑦I − 𝑦I ,
𝑛 − 𝑝
𝑦 (8)
NMBE = ΣIp+
qr 𝑦I − 𝑦I
(𝑛 − 𝑝)𝑦 (9)

Where 𝑦I and 𝑦I are the ROM and EnergyPlus predicted value respectively, n is the number of sample
data points, p is the number of parameters in the baseline model used in comparison (in this case one),
and 𝑦 is the arithmetic mean of the EnergyPlus observations. The CVRMSE value is representative of how
well the two parameter values trend together throughout the year. Whereas the NMBE is an indication
of how accurate the overall magnitudes compare to one another. Both values must fall within the range
set by ASHRAE to be considered ‘calibrated’. Typically, this standard is used to compare the energy
consumption predicted by an energy model and the actual building energy consumption, as reported on
the energy bills, but this method should still serve valid when comparing one energy model to another.
The amount of heating or cooling supplied to the zone is, in part, a function of the supply air flow
rate. This parameter was compared by looking at the difference between the daily average values
between the ROM and the single zone EnergyPlus model, otherwise known as the residuals. A histogram
of the daily average residual values is shown below in Figure 12.
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Figure 12. Daily Average Supply Air Flow Rate Residual
The daily average difference between EnergyPlus and the ROM is -0.095 𝑚9 𝑠. The CVRMSE and the
NMBE for the supply air flow rate were 6.057% and -0.561% respectively. These results are an indication
that the flow rate was modeled correctly and the linear gain factor, as discussed earlier, are similar
between the two models.
The next parameter compared was the energy supplied to the zone. As discussed earlier, EnergyPlus
does not decouple this parameter from the VAV energy consumption, making the comparison only
possible if the HVAC heat and cooling zone loads are used from EnergyPlus. These heating and cooling
loads are going to be compared to the ROM predicted value of energy supplied to the zone, as seen in
Equations 7 and 8. These two parameters are comparable due to the fact that the heating and cooling
supplied to the zone, disregarding efficiency, should be the amount of energy required to maintain the
space at the thermostat set point, otherwise known as a ‘load’. If the thermal parameters have been
estimated correctly, the zone load and the supplied energy should be equivalent, which indicates both
models have the same effective overall heat transfer coefficient. A histogram of the residuals can be seen
below in Figure 13.
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Figure 13. Daily Average Zone Demand Residual
The CVRMSE and the NMBE for the Zone Demand was 63.7% and 2.38% respectively. The zone demand
showed poor performance for the CVRMSE, but that should be expected. ROMs lump masses together
and assume each mass has an equivalent temperature, varying the magnitude of heat transfer at any
given time when compared to EnergyPlus. The NMBE shows the two models use similar overall
magnitudes of energy throughout the year which indicates the model is performing as expected. The
average daily residual was approximately -1,336 watts, meaning the ROM is predicting a zone energy
demand of 1,336 watts less than EnergyPlus. This is what should be expected after the ROM zone
temperature was over predicted, as seen in the previous chapter. This over prediction of zone
temperature equates to the HVAC system having to add less thermal energy to condition the zone and
match the thermostat set points.
The last parameter compared was the total energy consumption of conditioning the building,
which includes the energy supplied to preconditioning the air stream after the mixing chamber and at the
terminal boxes. The total energy consumption does not include any mechanical energy consumed by the
supply or return fans, this parameter is just the thermal energy supplied to the air stream. The first method
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of comparison was with an energy signature of the COBE building as predicted by both models. An energy
signature is a plot of the energy consumption vs. the average ambient temperature, typically tabulated
daily [15]. Characterizing building using an energy signature offers a quick comparison to determine how
the building is performing and is a way to graphically illustrate the amount of heating or cooling required
for any given outdoor temperature conditions. The energy signature of the COBE building, as predicted
by the ROM, was compared against the EnergyPlus energy signature, which is shown in Figure 14.

Figure 14. EnergyPlus and Reduced Order Model Energy Signature of COBE Building. (Left – Cooling Energy
Signature, Right – Heating Energy Signature)
The balance temperature of the building is the ambient temperature at which the building does not
require heating or cooling after adjusting for internal loads was determined to be approximately 2.5°C for
both the EnergyPlus and the reduced order model. Both heating and cooling energy signatures from the
reduced order model are similar to the predicted signatures from EnergyPlus. This is an indication that
both model have similar thermal properties. However, the cooling energy signature for the reduced order
model mirrors that of the EnergyPlus’ model better than the heating energy signature. This is thought to
originate from the terminal reheat VAV box sub model. The daily average residuals were also calculated
and a histogram of the results can be seen below in Figure 15.
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Figure 15. Daily Average Total Energy Demand Residual Histogram
The total energy demand residual had an average of approximately -1,401 watts. The overall CVRMSE and
the NMBE for the total energy demand when compared to EnergyPlus was 42.4% and 1.7% respectively.
This is indicating that the ROM is using, on average, 1,401 watts less energy per hour than the EnergyPlus
model. This error originates from the same over estimation of the ROMs zone temperature, as discussed
above. The ROM accurately predicted the magnitude of total energy consumption when comparing the
results to the previous EnergyPlus model. The CVRMSE value was greater than allowed by the ASHRAE
standard, but due to how the model lumps various thermal masses together this variance is to be
expected. The ROM is verified to be an accurate representation of the COBE building and the next step is
using this model as a tool for virtual commissioning by looking for recommendations that can yield realized
energy saving at the COBE building in Moscow.
5.1 Virtual Commissioning
The team was allowed remote access to the EMS for the COBE building at the University of Idaho, and
while logging into the system we noticed that the building was operating in “occupied” mode at a time
when the building should have been unoccupied. While running in occupied mode the HVAC conditions
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the building to different temperature set points and uses more electricity than when operating in
unoccupied mode. We logged in several times and the problem persisted which points to the discrepancy
not being by chance, but on overall operational and control issue. This was confirmed in a follow-up
meeting with the facilities team at the end of the project. The reduced order model was used to determine
the energy savings associated with having thermostat setbacks. Table 3 shows the current and
recommend thermostat settings, which were the values used in the study.
Table 3. Current and Recommended Thermostat Set Points
Occupancy Status Heating Set Point
[°C]
Cooling Set Point
[°C]
Current Thermostat Set Points
Occupied/Unoccupied 20.0 22.78
Recommended Thermostat Set
Points

Occupied 21.0 24.0
Unoccupied 15.6 26.7

The values for the current set points were determined by examining the trend logs of zone temperatures
from the COBE’s EMS system. The values represent an average of the zones. The recommended
thermostat set points were determined using ASHRAE’s Standard 90.1 [16]. We found by having
thermostat setbacks during unoccupied times, it would save approximately 9.6% of HVAC energy
consumption. This study was also conducted using the fully calibrated COBE EnergyPlus model that was
developed during the previous Avista Research Grant. With the full EnergyPlus model, it is predicted to
save approximately 9.97% of heating and cooling energy by adjusting the thermostat set points. This
energy savings does not include pump of fan power savings; the reported value is only the amount of
energy consumed while conditioning the space. The 9.6% energy savings equates to approximately
104,000 kWh annually.
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The access to live data provided two other insights that could lead to significant energy savings at
the site. The economizer was unable to run in integrated mode and would lock out the cooling coil any
time it was engaged. The outdoor air sensor was also located in a concrete well and was not providing
accurate readings of the outdoor air intake. In the words of one of the facilities managers: “it’s whacked.”
Our team was able to coordinate a meeting with several facilities and HVAC managers at the University of
Idaho as well as several representatives from Avista to discuss the findings and follow up on these issues.
The discussion served to make several connections and spur action on correcting these issues. The
controls contractor is sending out a service engineer on Tuesday September 5th to specifically address the
outdoor air sensor, setback scheduling, and correcting of the air handler/economizer operation at the
COBE building.

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6. DISCUSSION AND FUTURE WORK
This research has shown that using ROM for virtual building commission is a viable option for whole
building commissioning. This approach lessens the time and money constraints that are prohibitive for
many building owners. The difference between the results of the fully-zoned EnergyPlus model and the
reduced order model was insignificant when predicting the amount of energy savings from thermostat
setbacks. Approximately 104,000 kWh annually can be saved with temperature setbacks during
unoccupied periods.
Without access to accurate data from the COBE building, outputs from the previously developed
EnergyPlus model had to be used to find the thermal parameters of the ROM. Ideally, this method of
building modeling would be a standalone process and would not rely on an EnergyPlus model; all the ROM
inputs would be calculated, or measured, or estimated using ASHRAE standard 90.1 [16]. For ROM virtually
commissioning to progress, there needs to be research done in calculating the thermal parameters of the
building without using software optimization. Promising results were achieved at determining the
parameters using the buildings response for the BESTEST case study. It was shown that the thermal
parameters could be determined both ways, through optimization and through numerically fitting the
parameters to best fit the building’s thermal decay of energy. The differences between the time constants
of the two models were insignificant and would have minimal effects on the overall building energy
consumption. The method of using the buildings temperature decay needs to be further investigated, and
eventually needs to be used with an actual building to see if the parameters can be found from a large
temperature setback similar to the process used in the BESTEST case study.
The facilities team were open to learning about the results and have blocked out a day to address
each of the commissioning issues found during this research. Data will continue to be collected at the site
so that the savings might be verified and used as an example for future commissioning projects and
applications for incentives. A group meeting between University of Idaho facilities, Avista, and IDL on
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August 29th served to enhance understanding between parties and build stronger partnerships for future
efficiency projects.

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7. BUDGET SUMMARY
These hours reflect only Avista’s contribution to this project and are not reflective of total project
investment by the research team, industry sponsors, or other university staff.
Personnel Hours estimate Description
Elizabeth Cooper 56 Provide overall management of the project
Jinchao Yuan, Ph.D., P.E. 75 Provide technical support in supervising the
student intern(s)
Damon Woods, P.E. 504 Provide technical support and execute daily
tasks of this project
Sean Rosin 820 Execute daily tasks of this project

FY16/FY17
Personnel (All Hourly Rates are averages over FY16 and FY17)
Salary: Support Requested for Elizabeth Cooper at 57 hours ($51.28/hr), Dr. Jinchao Yuan at 75 hours
($40.15/hr), Damon Woods at 504 hours ($21.00/hr) and Sean Rosin at 820 hours ($16.00/hr). Total
Salary amount requested for project period is $29,596.

Fringe Benefits: Total Fringe requested for project period $2,422.

Other Direct Costs
Travel: Estimated travel cost for project period $2,250
Operating Expenses: Estimated research supply cost for project period is $1,500
Tuition: Estimated tuition costs for one graduate student for Fall of 2016 and Spring of 2017 $3,080

Indirect Costs
For this contract, UI-IDL was considered an on-campus unit of the University of Idaho with a federally
negotiated rate of 50.3%.

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8. REFERENCES
[1] ASHRAE. (2005). ASHRAE Guideline 0-2005: "The Commissioning Process". Atlanta: American
Society of Heating, Refrigerating, and Air-Conditioning Engineers.
[2] Nouidui, T., Wetter, M., Li, Z., Pang, X., Bhattacharya, P., & Haves, P. (2011). BacNet and
Analog/Digital Interfaces of the Building Controls Virtual Testbed. Conference of International
Building Performance Simulation Association, (pp. 294-301). Sydney.
[3] Haves, P., & Xu, P. (2007). The Building Controls Virtual Test Bed - A Simulation Environment for
Developing and Testing Control Algorithms Strategies and Systems. International Building
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Staff_PR_39 Attachment A
Integrated Design Lab | Boise 38
Using reduced-order models for simulation based commissioning of buildings (Report 1608_01)

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Staff_PR_39 Attachment A