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J. Wang, S. Huang, W. Zuo, D. Vrabie 2021. “Occupant Preference-Aware Load
Scheduling for Resilient Communities.” Energy and Buildings, 252, pp. 111399.
Occupant Preference-Aware Load Scheduling for Resilient Communities
Jing Wanga, Sen Huangb, Wangda Zuoa,c,
, Draguna Vrabieb
a University of Colorado Boulder, Department of Civil, Environmental and Architectural
Engineering, Boulder, CO 80309, United States
b Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, WA 99354, United States
c National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, CO 80401,
The load scheduling of resilient communities in the islanded mode is subject to many uncertainties
such as weather forecast errors and occupant behavior stochasticity. To date, it remains unclear
how occupant preferences affect the effectiveness of the load scheduling of resilient communities.
This paper proposes an occupant preference-aware load scheduler for resilient communities
operating in the islanded mode. The load scheduling framework is formulated as a model
predictive control problem. Based on this framework, a deterministic load scheduler is adopted as
the baseline. Then, a chance-constrained scheduler is proposed to address the occupant-induced
uncertainty in room temperature setpoints. Key resilience indicators are selected to quantify the
impacts of the uncertainties on community load scheduling. Finally, the proposed preference-
aware scheduler is compared with the deterministic scheduler on a virtual testbed based on a real-
world net-zero energy community in Florida, USA. Results show that the proposed scheduler
performs better in terms of serving the occupants’ thermal preference and reducing the required
Email address: firstname.lastname@example.org.
battery size, given the presence of the assumed stochastic occupant behavior. This work indicates
that it is necessary to consider the stochasticity of occupant behavior when designing optimal load
schedulers for resilient communities.
Keywords: Microgrid; Optimal load scheduling; Uncertainty; Occupant behavior; Resilient
community; Model predictive control.
intercept coefficient for the logistic
battery charging power
slope coefficient for the logistic regression
scheduled critical loads
upper limit of battery energy
curtailed PV power
battery discharging power
MPC prediction horizon
HVAC system (heat pump) total power
total scheduled loads
number of critical loads in each building
scheduled modulatable loads
number of modulatable loads in each
scheduled sheddable loads
number of sheddable loads in each building
scheduled shiftable loads
number of shiftable loads in each building
average cycle time of each shiftable load
speed ratio of the heat pump
upper limit of battery power
indoor air temperature
critical load data
starting operation time of shiftable loads
HVAC system (heat pump) nominal power
internal heat gain
predicted loads upper bound
modulatable load data
binary decision variable for sheddable load
sheddable load data
binary variable for shiftable load starting
average nominal power of each shiftable
probability of setpoint-changing actions
building agent layer
scheduling matrix for each shiftable load
cumulative distribution function
ambient outdoor temperature
community operator layer
lower room temperature bound
distributed energy resource
upper room temperature bound
heating, ventilation, and air-conditioning
key resilience indicator
model predictive control
maximum constraint violation probability
battery charging efficiency
Root Mean Square Error
battery discharging efficiency
state of charge
mean of room temperature error distribution
probability density function
standard deviation of room temperature
proportional integral derivative
Due to the increasing frequency of extreme weather events such as the 2021 Texas Power Crisis
, there is an emerging need for community resilience studies. Resilient communities refer to
those that can sustain disruptions and adapt to them quickly by continuing to operate without
sacrificing the occupants’ essential needs [2, 3]. Enabling technologies for resilient communities
often involve distributed energy resources (DERs) such as photovoltaics (PV) and electrical energy
storage (EES) systems. When disconnected from the main grid, the adoption of advanced control
techniques can help enhance community resilience.
As an advanced control technique, optimal load scheduling determines the operation schedules of
controllable devices in the community to achieve optimization objectives. For a resilient
community, typical controllable assets include the EES, PV, and thermostatically controllable
devices in buildings such as the heating, ventilation, and air-conditioning (HVAC) system.
Building plug loads that are sheddable, shiftable, or modulatable can also be considered flexible
loads in islanded circumstances . The objectives of the load scheduling for resilient
communities often involve maximizing the self-consumption rate of locally generated PV energy,
minimizing PV curtailment, and minimizing the unserved ratio to critical loads.
It is important to account for uncertainties when designing a load scheduler for resilient
communities. Moreover, due to the limited amount of available PV generation during off-grid
scenarios, the uncertainties need to be more carefully dealt with to ensure a satisfying control
performance. Sources of uncertainties for a community load scheduling problem mainly lie in two
aspects: power generation and consumption. For renewable energy generation, weather forecast
errors play a prominent role in the cause of uncertainty. Whereas, for energy consumption,
occupant behavior stochasticity is a major source of uncertainty.
Much of existing load scheduling research has considered the uncertainty of weather forecasts [5–
13]. Kou  proposed a comprehensive scheduling framework for residential building demand
response (DR) considering both day-ahead and real-time electricity markets. The results
demonstrated the effectiveness of the proposed approach for large-scale residential DR
applications under weather and consumer uncertainties. Garifi  adopted stochastic
optimization in a model predictive control (MPC)-based home energy management system. The
indoor thermal comfort is ensured at a high probability with uncertainty in the outdoor temperature
and solar irradiance forecasts. Faraji  proposed a hybrid learning-based method using an
artificial neural network to precisely predict the weather data, which eliminated the impact of
weather forecast uncertainties on the scheduling of microgrids. Similarly, in the authors’ previous
publication , normally distributed outdoor temperature and solar irradiance forecast errors were
introduced into the community control framework, which accounted for the uncertainties in the
However, the uncertainties from the power consumption perspective, especially the occupant
behavior uncertainty, is rarely accounted for in load scheduling research [14–18]. Some efforts to
integrate occupant behavior modeling can be found in studies of building optimal control [19–22].
Aftab  used video-processing and machine-learning techniques to enable real-time building
occupancy recognition and prediction. This further facilitated the HVAC system operation control
to achieve building energy savings. Lim  solved a joint occupancy scheduling and occupancy-
based HVAC control problem for the optimal room-booking (i.e., meeting scheduling) in
commercial and educational buildings. Both the occupancy status of each meeting room and the
HVAC control variables were decision variables. Mixed-integer linear programming was adopted
to optimally solve the optimization problem.
Notably, all of the preceding control work considered the stochasticity of building occupancy
schedules, but the integration of other types of occupant behavior into building optimal control is
not well studied in existing literature. Some researchers integrate the occupant thermal sensation
feedback into the MPC for buildings [23, 24]. For instance, Chen  integrated a dynamic thermal
sensation model into the MPC to help achieve energy savings using the HVAC control. For the
occupant sensation model, the predictive performance of certainty-equivalence MPC and chance-
constrained MPC were compared.
To summarize, the literature review shows that current research mainly focuses on the load
scheduling of single buildings under grid-connected scenarios. There is a lack of research on the
optimal load scheduling of resilient communities informed by occupant behavior uncertainties in
the islanded mode. Given this gap, this paper proposes an occupant preference-aware load
scheduling framework for resilient communities in the islanded mode. The occupants’ thermal
preference for indoor air temperature will be reflected in the integration of thermostat adjustment
probabilistic models. The optimal load scheduling is formulated as an MPC problem, so the
stochastic thermostat-changing behavior will be regarded as the uncertainty in the MPC problem.
Different methods, such as the offset-free method and robust method, can be used to handle the
uncertainties in MPC problems . The chance-constraint method, also known as the stochastic
MPC, was selected to deal with the uncertainty in occupant preference in our study. It allows the
violation of certain constraints at a predetermined probability. It thus enables a systematic trade-
off between the control performance and the constraint violations . The advantage of
addressing occupant preference uncertainty by using the chance-constraint method lies in the a
priori handling of the uncertainty, which does not require the extra error-prediction models needed
by other methods (i.e., offset free method), and thus simplifies the control problem . Therefore,
less computational effort is required after the control design phase. Though it requires the
controller to know the estimated uncertainty distribution beforehand, the development of occupant
behavior probabilistic modeling will make knowing this less challenging.
In this work, we consider the load scheduling of a resilient community in islanded mode during
power outages. The goal is to study the impact of occupants’ thermal preference on the operation
of an islanded community. The load scheduling problem of the community will be solved using
an optimization-based hierarchical control framework. Occupant thermal preference will be
integrated through thermostat changing behavioral models to inform the development of the load
scheduler. The major contributions of this work include (1) a proposed new preference-aware load
scheduler for resilient communities, which assures better control performance related to satisfying
occupants’ thermal preferences and reducing the battery size; (2) the quantification of the impact
of occupant thermostat-changing behavior on resilient community optimal scheduling using
selected key resilience indicators (KRIs); and (3) the testing of the proposed scheduler on a high-
fidelity virtual testbed for resilient communities.
The remainder of this paper is organized as follows: Section 2 details the research methodology.
Section 3 describes the controllable device models used in this work involving the building HVAC
models, load models, and battery models. Section 4 then discusses the deterministic versus
stochastic scheduler formulations and proposes a chance-constrained controller for preference-
aware load scheduling of resilient communities. Section 5 applies the theoretical work to a case
study community and quantifies the impact of occupant preference uncertainty. Simulation results
and discussions are presented in this section. Finally, Section 6 concludes the paper by identifying
In this section, we first introduce a hierarchical optimal control structure for resilient community
load scheduling. Based on the structure, a deterministic scheduler will be implemented as the
baseline. Further, we propose a research workflow to implement a stochastic preference-aware
scheduler for addressing uncertainties in occupant thermostat-changing behavior. KRIs are
proposed at the end of this section.
2.1 Hierarchical Optimal Control for Resilient Communities
In this study, we assume that the only energy resource accessible to the islanded community is on-
site PV generation and the batteries for an extended period of more than 24 hours. In this problem
setting, in order to make full use of the limited amount of PV generation and satisfy the occupants’
essential needs, the building loads need to be shifted or modulated. The battery works as a temporal
arbitrage for meeting the demand at night. In addition, the occupant thermal preference will affect
the energy consumption of the HVAC system through the stochastic thermostat-changing behavior.
To optimally control such a community, considering the above factors, we adopted a hierarchical
As illustrated in Figure 1, two layers of control are formulated: a community operator layer (COL)
and a building agent layer (BAL). The COL optimally allocates the limited amount of the on-site
PV generation based on the load flexibility provided by each building. The calculated allowable
load for each building is then passed down to the BAL, where each building optimally schedules
its controllable devices (i.e., HVAC, battery, and controllable loads) to achieve its local
optimization goals. Both layers are formulated as MPC-based optimization problems.
Figure 1 The hierarchical optimal control structure for community operation.
The input of the hierarchical control involves the predicted PV generation data, outdoor air dry-
bulb temperature, and solar irradiance. The PV generation data are used by the COL to determine
the optimal allocation among buildings. The temperature and irradiance data are used by the
HVAC models for updating the indoor room temperature predictions. The occupant behavior
affects the two layers differently. The COL uses building occupancy schedules to decide the
weights of different buildings during the PV allocation (details can be found in ). The BAL
considers occupant thermal preference to be the uncertainty in the indoor room temperature
2.2 Proposed Workflow
Figure 2 depicts the workflow of this paper. A deterministic optimal load scheduler without the
occupant thermal preference uncertainty is implemented in the hierarchical control structure.
Further, to account for the uncertainties, we propose a chance-constrained controller. It is
developed based on the deterministic controller and involves an alteration of the room temperature
constraints, which accounts for the uncertainties in room temperature prediction errors caused by
the occupants’ thermostat-changing behavior. The Monte Carlo simulation method was adopted
to cover a wide range of simulation results.
Figure 2 Diagram of the proposed workflow.
Further, to reflect various styles of occupant behavior, three types of occupant thermostat-changing
models were adopted: low, medium, and high, which represent three levels of frequencies of the
thermostat-changing activities. Here, we assume that when the occupant decides to change the
indoor air temperature setpoint according to their preference, the predetermined optimal HVAC
equipment control setting at the current timestep will be overridden. Instead, a new control setting
will be calculated to achieve the occupants’ setpoint at the current timestep. At the next timestep,
the predetermined optimal setting will still be used if the occupant is not changing the setpoint
Finally, the optimal schedules determined by the chance-constrained controller and the
deterministic controller are tested on a high-fidelity virtual testbed  with respect to their
individual performances. KRIs such as the unserved load ratio, the required battery size, and the
unmet thermal preference hours were adopted to quantify the results.
The unserved load ratio in this paper is defined as the relative discrepancy between the served
and the originally predicted load
where is the MPC simulation horizon of 48 hours. The required battery size is obtained by
subtracting the minimum battery SOC from the maximum SOC. This gives us a sense of how much
of the battery capacity has been used under different scenarios. Finally, we define the unmet
thermal preference hours metric for the cumulative absolute difference between the actual and the
preferred room temperature over the optimization horizon:
It quantifies how well the controller performs to satisfy the occupants’ thermal preference and has
the unit of ºC·h (degree hours).
3 Models for Controllable Devices
3.1 HVAC Models
This study assumes that heating and cooling is provided by heat pumps and the heat pump energy
consumption represents the HVAC system energy consumption. We adopted linear regression
models for the HVAC system to predict room temperatures at each timestep. To precisely model
the building thermal reactions, two types of parameters that contribute to the heat gain of the
building space are considered. The first type is environmental parameters such as the outdoor air
dry-bulb temperature and solar irradiance. The second type represents the internal heat gain due to
the presence of the occupants and the operation of appliances. We assumed that the simulated
buildings are well sealed and thus the interference from the infiltration can be omitted. Therefore,
the HVAC model updates the indoor room temperature based on the room temperature at the last
timestep, the abovementioned heat gains, and the heating/cooling provided by the heat pump
system at every timestep. The control variable is the heat pump speed ratio, which ranges from 0
to 1 continuously. The resulting HVAC power is equal to the speed ratio multiplied by the nominal
heat pump power. Additionally, to better account for the effect of building thermal mass, for each
heat gain parameter, two past terms are adopted, respectively . The equations for the HVAC
model are as follows:
represent the room temperature, ambient dry-bulb temperature,
solar irradiance, and internal heat gain at timestep , respectively. The
and are the
heat pump speed ratio and the nominal HVAC system power. The linear regression coefficients
are represented by . For , a negative value means cooling and positive means heating.
In the model,
are related to the occupant presence and the operation of the
building appliances. When the building is occupied, 70% of the total heat rate of a person (i.e.,
100 W) is dissipated as sensible heat into the space and the rest 30% is latent heat . The heat
gain from appliances is calculated by the power of the appliance multiplied by its heat gain
coefficient, which reflects how much of the consumed electric power is dissipated into the space
as heat. Table A-1 in Appendix A lists the heat gain coefficients adopted from literature [31–33].
Note that the controllable loads are optimization variables of the scheduling problem, which will
be iteratively calculated at each optimization timestep. Therefore, to speed up the optimization, we
reduced the coupling between the thermal models and the electric demand models. This was done
by calculating the weighted average heat gain coefficients for each building based on the capacity
of each appliance (Table A-1).
3.2 Load and Battery Models
The building load models in this work are categorized into four types according to their power
flexibility characteristics: sheddable, modulatable, shiftable, and critical (Figure 3). We did the
categorization from the perspective of the building owners during power outages. The sheddable
loads are those that can be disconnected without affecting the occupants’ essential needs. For
instance, the microwave in a bakery is categorized as sheddable during an outage. The modulatable
loads are the systems that have varying power shapes such as an HVAC system with a variable
frequency drive. The shiftable loads are the appliances that have flexible operation schedules such
as washers and dryers. Lastly, the critical loads refer to appliances and systems related to the
occupants’ essential needs. In this work, we consider only loads used for lighting and food
preservation as critical loads, which aligns with the two bottom levels of Maslow’s Hierarchy of
Needs (i.e., physiological and safety needs) . The critical loads account for about 20% to 90%
of the total building loads depending on building type and time of day.
Figure 3 Power flexibility characteristics of the four load types .
The mathematical formulation of the sheddable load is shown in Equation (6):
is a binary optimization variable,
is the original sheddable load time series
data, and is the number of sheddable loads in the building. The actual sheddable load after
is determined by the ON/OFF status represented by the binary variable. The
is formulated as a continuous optimization variable, which ranges
between zero and its original power demand
. Equation (7) sets the lower and upper bound
of the modulatable load.
The shiftable loads are scheduled through scheduling matrices . First, using the power data
, we extracted the average cycle time and the average power demand of each
shiftable load. The starting operation timestep of each shiftable load is optimized over the
MPC horizon. At the scheduled starting timestep, the binary variable
equals 1 and is 0
is the MPC prediction horizon. Once the starting time of a shiftable load is selected, the power
demand of the load is then fixed at its average power until it finishes its cycle. The appliance must
finish its cycle before the horizon ends (). Here, we assume that each
shiftable load operates once and only once during each horizon, which is enforced by:
Next, a scheduling matrix of shape is generated for each shiftable
load. The actual power shape of the load, denoted
, is thus calculated by:
Finally, the actual critical load
must be exactly equal to the critical power demand
as enforced by:
Summing up the four types of loads in each building, we obtain the optimization variable
The linear battery model adopted in this work is represented by Equation (13). The battery state of
is predicted based on the SOC of the previous timestep
, the battery
or discharging power
at each step, and the battery charging/discharging
efficiencies and . The inequality constraints in Equations (14) and (15) enforce the
acceptable limits for the battery charging/discharging power and SOC, where and are
the maximum values for battery power and capacity:
4 Optimal Load Scheduling
This section first presents the mathematical formulation of the deterministic load scheduler. After
that, we will introduce the formulation of the occupant preference-aware stochastic scheduler
containing three parts: the thermostat-changing model, the uncertainty introduction mechanism,
and the method to address the uncertainty.
4.1 Deterministic Scheduler
As introduced in Section 2.1, the deterministic scheduler adopts a two-layer structure with COL
and BAL. The objective of the COL is to minimize the community-level PV curtailment to
facilitate better use of the limited PV power during the outage. The main constraints are the load
flexibility of each building, building occupancy, and building priority, etc. No detailed building
assets are simulated at the community layer. This ensures that the COL is computationally tractable,
especially when the problem scales up and the number of controllable building assets scales up.
The detailed mathematical formulation of the COL can be found in reference .
The objective of the BAL is to minimize the unserved load ratio of each building within the
allowable load range allocated by the COL. This is achieved through MPC-based optimal
scheduling of the building-owned HVAC system, controllable loads, and battery. The optimization
is a mixed-integer linear programming problem, because the sheddable and shiftable load models
contain binary variables. Next, the mathematical formulation of the optimization problem is
presented. Note that the formulation applies for every individual building in the community.
The cost function to minimize the unserved load ratio is formulated as:
is the predicted load upper bound from data. The difference between this upper bound
and the actual operated loads
is minimized to achieve a maximum served load to the building.
To avoid simultaneous battery charging and discharging as well as PV curtailment, the objective
function also includes small penalizations of charging
and are the penalization coefficients. The power balance of each building that must be satisfied
at each timestep is given by:
where PV curtailment
is limited by how much PV generation
The left-hand side of Equation (18) represents power generation, whereas the right-hand side
represents consumption. The
stand for the battery charging and discharging power as
in Equation (13). The
are the total building loads and the HVAC power calculated
in Equations (12) and (5), respectively. To assure thermal comfort of the indoor environment, a
temperature constraint is given by:
where and are the lower and upper room temperature bounds implemented as hard
constraints. The optimization variables in each building agent are collected in vector :
4.2 Stochastic Preference-aware Scheduler
To address the uncertainties of occupant thermal preference in the scheduling problem of resilient
communities, this section introduces the stochastic preference-aware scheduler. First, we discuss
the modeling of the occupant behavior uncertainties as a probability function. Then we show the
mechanism by which this uncertainty might affect the optimal control of the HVAC system. After
that, we propose using the chance-constraint method to address the uncertainty.
4.2.1 Stochastic Thermostat-Changing Model
The stochastic occupant thermostat-changing model adopted in this paper was proposed by Gunay
et al. . Through continuous observation of the occupants’ thermostat keypress actions in
private office spaces, the relationship between the thermostat-changing behavior and the
concurrent occupancy, temperature, and relative humidity was analyzed. It was noted that the
frequency of thermostat interactions (i.e., increasing or decreasing) can be approximated as a
univariate logistic regression model with the indoor temperature as the independent predictor
variable. Though the original data set was obtained from two office buildings, Gunay et al.
generalized the study to understand occupants’ thermostat user behavior and temperature
preferences. Given the universality of their work, we have adapted their models based on our use
cases. Note that occupants might have varied (e.g., higher) tolerance of indoor temperature during
an emergency situation. The exact thresholds need further experimental study and validation,
which is out of the scope of this work.
The thermostat-changing behavior models determine whether the occupants will change the
setpoint temperature based on the concurrent indoor air temperature. The probability of increasing
and decreasing the temperature setpoint is predicted with a logistic regression model:
where is the probability of the changing action, is the indoor room temperature, and and
are coefficients. To investigate different uncertainty levels, we proposed three different active
levels by revising the coefficients of the model in Equation (22). As shown in Table 1, the low
active level adopts the original coefficients in . Then, we proposed the medium and high active
levels to represent various occupant thermal preference styles. The standard errors and p-values of
the low active level coefficients are also provided in the table. As for the medium and high levels,
we do not have measurement data for the statistical analysis since we adapted the coefficients from
the original reference .
Table 1 Coefficients in different active levels of the occupant thermostat-changing behavior
Note that the adaptation of the original logistic regression models was made under the following
assumptions to ensure the adapted models remained realistic. For the setpoint increasing scenario,
the slope coefficient of is varied linearly to reflect a higher frequency of the changing behavior.
The intercept coefficient is then calculated to make sure that all active levels have the same value
of probability at the temperature of 40ºC. For the setpoint decreasing scenario, a similar approach
is taken to make sure the same value of probability at 16ºC is shared by all active levels. At each
thermostat interaction, we assume that 1ºC of setpoint change would take place. Figure 4 depicts
the probabilities of the three active levels. Note that this figure contains a wider temperature range
than 16ºC ~ 40ºC to show a more comprehensive performance of the behavior models.
Figure 4 Probability of different thermostat-changing behavior.
Once the probability of the thermostat-changing behavior is determined using the above models,
the increasing or decreasing action is determined by comparing the probabilities with a randomly
generated number. At each optimization timestep, a random number between 0 and 1 is generated.
If the number is larger than , the action will be to increase. On the contrary, if
it is smaller than , the action will be to decrease. Because the sum of the increase
and decrease probabilities is smaller than 1 in our case, this algorithm assures at most one action
will be taken at each timestep.
4.2.2 Introducing Occupant Behavior Uncertainties in Scheduling
To introduce the occupant thermostat-changing uncertainties to the load scheduling problem, a
stochastic simulation model representing the behavior needs to be incorporated into the
optimization. Figure 5 shows the control signal flow for the typical indoor air temperature control,
which affects the HVAC system operational status and its power consumption. The occupant sets
the temperature setpoint according to his/her preference through the thermostat. Behind the
thermostat, a proportional integral derivative (PID) controller decides the next heat pump speed to
offset the difference between the measured room temperature and the setpoint. This heat pump
speed signal is then fed into the heat pump system to provide cooling for the conditioned space.
Due to the presence of the dynamic environmental and behavioral disturbances, this process will
need to be repeated until the measured room temperature reaches the setpoint.
Figure 5 Diagram showing the introduction of occupant thermostat-changing behavior to the
However, in the optimal control mechanism, the optimal scheduler takes over the control of the
heat pump speed from the PID controller. As a result, the occupants’ preference has thus been
“disabled” to allow an optimal control determined by the scheduler. To mimic the overriding of
the room temperature setpoint by the occupants, the following algorithm was implemented in the
MPC problem and the pseudo code is shown below. Before each round of the optimization starts
(Steps 1–2), if the occupant decided to change the setpoint (Step 3), the heat pump speed for the
current timestep should be calculated to reach the setpoint instead of achieving the optimization
objective (Steps 4–7). Otherwise, the optimization runs normally because no overriding happens
(Step 7). After each optimization timestep, the flag variables indicating the thermostat-changing
actions need to be updated according to the concurrent room temperature (Step 8). It should be
noted that in the optimization, no PID controller has been implemented, so we assumed that
and the setpoint changes were directly added to the room temperature
Step 1. Start
Step 2. Initialization of flag variables: ;
Step 3. If or :
Step 5 Calculate the corresponding
Step 6 Disable
from the optimization variables;
Step 7. Run MPC for timestep ;
Step 8. Update flag variables (i.e., and ) according to
Step 9. Repeat Steps 3–8 until the end of the MPC horizon of 48 hours;
Step 10. End
4.2.3 Chance-Constraint Method
As mentioned in Section 4.2.1, the uncertainties in the occupants’ thermostat-changing behavior
are a probability function. In the scheduling optimization problem, the constraint directly affected
by the occupants’ thermostat-changing behavior is the room temperature bounds. The uncertainties
related to the occupants’ adjusting the thermostat could lead to the violation of the temperature
bounds during the implementation of the developed control strategies. Furthermore, this could lead
to other control-related performances being affected, including higher building load unserved ratio
and larger required battery size. To address this, we adopted the chance-constraint method.
By definition, the chance constraint allows the violation of a certain constraint with a small
probability, which thus presents a systematic trade-off between control performance and
probability of constraint violations . It can be expressed in general by the following equation:
where is the inequivalent constraint and is the maximum violation probability.
Given the uncertainties in the occupants’ thermostat-changing behavior, we assume that the
temperature bounds can be satisfied with a probability of . For the lower temperature
bounds, the chance constraint can thus be written as:
Then, we rewrite it as:
Let the indoor temperature be rewritten in terms of the prediction
is the predicted indoor room temperature and
is the error caused by uncertainties. Similarly,
. For both
timesteps, the room temperature distribution error follows the same distribution. The hypothetical
error distributions can be in different forms and here we assume the distribution to be normal.
Hence, it can be represented by:
is also normally distributed with the following mean and standard deviation :
The chance constraint can thus be reformulated as:
where is the cumulative distribution function (CDF) of the standard normal distribution
. By taking the inverse CDF of both sides, we can get:
Rearrange the above equation and substitute and with Equations (27) and (28). Finally, we
obtain the chance constraint for ensuring the indoor temperature will not fall below the lower
bound of with the probability of as follows:
Substituting Equation (3) into (31) and rearranging, we have:
Similarly, we have Equation (33) for the upper bound,
Taking a similar derivation process as that in Equations (24) to (32), we can obtain the chance
constraint for the temperature upper bound:
The updated inequivalent constraints indicate that the temperature bounds for the optimization
should be narrower than the original temperature bounds to account for the setpoint behavioral
uncertainty, which is consistent with the expectations. Note that because the uncertainty-dealing
method is focused on the temperature constraints, one possible limitation is that the above method
might have limited effect on the controller design for buildings that have larger thermal masses,
because the building temperature is insensitive to temperature constraints. More discussion of this
point follows in Section 5.3.1.
5 Case Study
5.1 Studied Community
The case study community is a net-zero energy community located in Anna Maria Island, Florida,
USA, which is a cooling dominated region. The community buildings are installed with both roof-
top PV panels and solar carports, which harvest about 85 MWh annually for the whole community.
A centralized ground source heat pump system provides the HVAC needs of the whole community
with high efficiency. Other sustainable features include well-insulated building envelopes, solar
thermal water heating, and rainwater recycling. This community achieved net-zero energy in the
year of 2014. In the community, there are various building types such as residential, small office,
gift shop, etc. We would like to cover both residential and commercial buildings in the case study.
So, we selected one residential and two small commercial buildings based on the measurement
data quality. More specifically, the selected three buildings consist of a residential building (area:
93.8 m2), an ice cream shop (area: 160.5 m2), and a bakery (area: 410 m2). The building layout of
the community can be found in reference .
For the given community, a virtual testbed based on the object-oriented modeling language
Modelica  was built and validated . In the testbed, the Typical Meteorological Year 3 data
for a nearby city, Tampa, was adopted for this case study. The building thermal models are
resistance-capacitance (RC) network models. For the optimal control in this work, the HVAC
models were trained using one month (i.e., August) of the simulation data exported from the
testbed. Table 2 lists the coefficients for the linear regression HVAC models, the Root Mean
Square Error (RMSE) of the models, as well as the corresponding nominal heat pump power. The
N/A in the table represents a coefficient that is too small and thus has been neglected in the model.
Three effective decimal places are provided.
Table 2 Coefficients and nominal power of the HVAC models.
Nominal Power [kW]
Additionally, Table 3 lists the load categorization for the studied buildings following the principles
proposed in Section 3.2. A complete list of the building load capacities and their heat gains can be
found in Appendix A.
Table 3 Building loads categorized into four types.
Ice Cream Shop
Coffee maker, soda
Mixer, unspecific room
plug loads, HVAC
Ice Cream Shop
Lights, cooler, display
We designed three uncertainty levels (i.e., low, medium, high) as in Table 1 to evaluate the
deterministic and preference-aware schedulers in this paper. They are compared to the baseline
scenario, where the deterministic scheduler is applied without occupant behavior uncertainties.
The following results and discussion are all based on these scenarios. All scenarios were run in the
three buildings for 48 hours with a timestep of 1 hour in the islanded mode.
5.2 Settings of Chance-Constrained Controllers for Different Buildings
The preference-aware schedulers use chance-constrained controllers, whose settings depend on
individual building properties and uncertainty levels. Following the method proposed in Section
4.2.3, this section provides the details of the chance-constrained controller settings for three
individual buildings in the case study, which is based on the control outcome of the deterministic
schedulers under three uncertainty levels.
Considering the occupant-preference-driven actions as the source of “prediction errors” for the
room temperature, we extracted the distributions of the room temperature prediction errors. The
Monte Carlo simulation method  was adopted, where 100 repeated simulations were run using
the deterministic scheduler with three uncertainty levels. We used the room temperature of the
deterministic baseline scenario as the benchmark to calculate the errors caused by the occupant
setpoint-changing behavior. To describe the room temperature errors, three hypothetical
distributions are proposed (i.e., fit distribution in Table 4). The normal distribution is mentioned
in the derivation in Section 4.2.3. The half-normal distribution is a fold of a normal distribution at
its mean. For the residential building medium uncertainty level, a half-normal distribution was
adopted. This can be attributed to the fact that almost no temperature decrease action was observed
and thus the errors were all above zero. Constants were used for the residential building and the
bakery under the low uncertainty level because the frequency of the setpoint-changing is too low
(nearly zero) to follow any distributions.
Chi-square goodness of fit tests  at a rejection level of 1% were conducted to evaluate whether
the proposed hypothetical distributions fit well. The types of fitting distributions, p-values of the
tests, and the distribution parameters are reported in Table 4. In the table, µ is the mean and σ is
the standard deviation of the normal/half-normal distribution. The null hypothesis here is that the
room temperature prediction error follows the hypothetical distribution. The p-value is the
evidence against this null hypothesis. Since all p-values are greater than 99%, all error distributions
failed to reject the hypothesis at the level of 1%. This means they all follow the corresponding
Table 4 Chi-square goodness of fit test p-values and normal distribution parameters.
Ice Cream Shop
The frequency histogram and probability density functions (PDFs) of each building under various
uncertainty levels are plotted in Figure 6. In the figure, it can be seen that the higher the uncertainty,
the wider the room temperature range. This is because in scenarios with a higher uncertainty,
occupants change the thermostat more frequently, which expands the possible temperature ranges.
We also noticed that the temperature range in the ice cream shop is relatively concentrated
compared to the other two buildings. This can be attributed to the large thermal mass of the
Figure 6 Room temperature prediction error PDFs obtained from the Monte Carlo simulations.
For the scenario where the temperature prediction error follows the half-normal distribution, we
applied the chance constraint only to the upper bound because only increasing actions happen in
this scenario. For the two scenarios where the room temperature error is estimated to be a constant,
we adopted the original temperature bounds of [20ºC, 25ºC] because the estimated errors in both
scenarios are smaller than 0.01ºC. We choose the to ensure a 99% probability of
abidance of the temperature constraints (Equation (24)). Table 5 lists the updated room
temperature lower and upper bounds for each building under different scenarios.
Table 5 Room temperature bounds for chance-constrained optimizations.
5.3 Results and Discussions
This section first quantifies the impact of introducing occupant behavior uncertainties to the
optimal scheduling problem. Then, the deterministic and chance-constrained controllers are tested
on the community virtual testbed. Their control performance in terms of the unserved load ratio,
the required battery size, and the unmet thermal preference hours are then compared.
5.3.1 Impact of Uncertainty
Figures 7 to 9 depict the occupant thermal preference and the corresponding room temperatures.
In the figures, the upper plots show the simulated stochastic thermostat-changing actions at
different uncertainty levels, where increase means a setpoint increase action, and vice versa. The
lower plots show the resulting room temperatures with dashed lines.
The results of the low uncertainty scenario overlap with that of the baseline scenario (i.e., the
deterministic scheduler without uncertainty) mainly due to the low probability of setpoint-
changing actions in this scenario. With the increase in the probability, we see more frequent
setpoint-changing actions in all three buildings. Further, the increase action happens more
frequently than the decrease action. This is because between the temperature range of 20ºC and
24ºC, the probability of increase is much higher than that of decrease (see Figure 4). This also
implies that the occupants’ temperature preference is closer to 24ºC than 20ºC. Additionally, for
the residential building and the bakery, the temperature difference between scenarios is more
noticeable than for the ice cream shop; this is attributable to the different building thermal masses
of the three buildings.
Figure 7 Residential building occupant thermostat changing actions (upper) and resulting room
temperatures (lower) under three levels of uncertainty.
Figure 8 Ice cream shop occupant thermostat changing actions (upper) and resulting room
temperatures (lower) under three levels of uncertainty.
Figure 9 Bakery occupant thermostat changing actions (upper) and resulting room temperatures
(lower) under three levels of uncertainty.
Table 6 lists the values of the KRIs in correspondence with Figures 7 to 9. The HVAC energy and
average room temperature over the optimization horizon are also provided to facilitate the analysis
of the results.
Table 6 Key resilience indicators for studied buildings under different uncertainty levels.
Unserved Load Ratio
Battery Size [kWh]
Ice Cream Shop
From the table, we see that the unserved load ratio remains the same across all scenarios for each
building. This can be attributed to the fact that in the controller design phase, the optimization
objective is set to minimize the unserved load ratio. Hence, the unserved load ratios for each
building are already minimal and are not affected by the occupants’ thermostat-overriding
behavior uncertainties. Instead, the battery-charging/discharging behavior is affected, as reflected
by the different required battery sizes in the table. Note that the unserved load ratios are minimal,
but not zero, because of our assumption that each shiftable load operates once and only once per
For the rest of the metrics, note that the battery size, HVAC energy, and the average room
temperature remain the same for the baseline and low uncertainty scenarios in all buildings. This
is because no setpoint-changing actions happened due to the relatively low probabilities, as shown
in the figures above. As for the medium uncertainty scenarios, both the residential building and
the bakery show higher room temperatures and lower HVAC energy while the ice cream shop still
has the same results as the baseline, given its large thermal mass.
In terms of the high uncertainty scenarios, due to the prominent increase in room temperatures, we
noticed more HVAC energy savings in all buildings. Note that though the average room
temperature increase is insignificant, the HVAC energy savings is large due to the cumulative
effect over the many hours of setpoint increase. Overall, we see a positive correlation between the
HVAC energy and the required battery size. When the PV generation and the other building loads
remain the same, the more HVAC energy, the larger required battery size. However, one opposite
case was noted in the bakery high uncertainty scenario where the required battery size is slightly
larger in the high uncertainty scenario than in the medium uncertainty scenario. This was caused
by a setpoint decrease action at hour 28, which resulted in a battery discharging during the night
and thus a smaller minimum SOC of the battery.
To summarize, occupant thermostat-changing behavior uncertainty needs to be considered when
designing optimal schedulers for resilient buildings because it affects the indoor room temperature,
the HVAC power, and thus the sizing of batteries. For the whole community, when considering
the highest occupant behavior uncertainty, the consumed HVAC energy can be 57.2% less and the
battery 8.08% smaller. Whereas the aforementioned impact depends on the uncertainty level (i.e.,
how frequently the occupants change the setpoint), heating or cooling season, and the occupants’
actual preference for the indoor room temperature compared to the room temperature designed by
the scheduler. In our case, a preferred higher indoor room temperature saves HVAC energy.
During the heating season, the observations could be the reversed.
5.3.2 Controller Performance
To further evaluate the performance of the chance-constrained controller in comparison with the
deterministic controller, tests were run on the virtual testbed  in a stochastic manner. In each
of the studied buildings, both the deterministic controller and the chance-constrained controller
were tested for two days (i.e., August 4 and 5) with the three levels of uncertainties. The testing
method is similar to the method proposed in Section 4.2.2. Additionally, the precalculated optimal
battery charging/discharging, as well as the optimized loads, are also implemented in the testbed.
One hundred repeated Monte Carlo simulations were run for each scenario to better observe the
controller performance. The KRIs of the unserved load ratio, the required battery size, and the
unmet thermal preference hours are adopted for the performance evaluation.
The upper plot of Figure 10 depicts the predetermined optimal schedules of the heat pump speed
ratio as the inputs of the test. The lower plot then shows the corresponding room temperatures
predicted by the linear regression models in the optimization. The data for the residential building
is adopted here for the analysis. The plots for the ice cream shop and the bakery can be found in
Appendix A. From the figure, we see that the scheduled speed ratios in the low and medium
uncertainty scenarios overlap with that of the deterministic scheduler. Whereas the high
uncertainty scenario tends to have lower speed ratios over the whole optimization horizon. This
can be attributed to the controller settings shown in Table 5, where the temperature bounds set in
the low and medium uncertainty scenarios are closer to the original bounds of [20ºC–25ºC]. Hence,
the temperature constraints are not binding in these two scenarios. However, in the high
uncertainty scenario, the temperature constraint is binding, which leads to the speed ratio
reductions. As a result, a higher room temperature can be seen in the high uncertainty scenario.
Figure 10 Optimal schedules of the heat pump speed ratio and predicted room temperatures by
various schedulers (residential building).
Figures 11 to 13 depict the room temperature boxplots as the controller testing outputs. The lower
and upper borders of the boxes represent the 25th and 75th percentiles of the data, respectively.
The longer the box, the more scattered the room temperature. The lines inside the boxes represent
the median values. The lines beyond the boxes represent the minimum and maximum values except
for outliers, which are not shown in these figures. Note in the figures that the temperatures first
concentrate together (shown as black lines) and then spread out (shown as boxes). This is because
at the beginning of the simulations, no overriding behavior of the setpoints happens and the heat
pump operates following the scheduled speed ratio. Once the overriding happens at a certain
timestep in some simulations, the room temperature trends start to deviate and become boxes. The
occupant-preferred temperature lines are also shown as orange lines in these figures as a reference;
they are average setpoints adjusted by the occupants in all the Monte Carlo tests.
Figure 11 Residential building room temperature boxplots for control testing results.
Figure 12 Ice cream shop room temperature boxplots for control testing results.
Figure 13 Bakery room temperature boxplots for control testing results.
In the figures, we see a general trend of narrower room temperature ranges from the low
uncertainty scenarios to high uncertainty scenarios. This is due to the introduction of the occupant
setpoint-overriding mechanism, which tends to moderate the extreme room temperatures. Also,
there is a plant-model mismatch, which describes the parametric uncertainty of modeling that
originates from neglected dynamics of the plant . In our case, the mismatch exists as the
simulated room temperatures in the testbed are slightly higher than those predicted by the reduced-
order linear HVAC models. This is understandable because the physics-based testbed has a much
higher fidelity and simulates the non-linearity of the real mechanical systems.
Because the difference in the room temperature between the two controllers is not depicted in these
figures, Table 7 and Table 8 provide further quantitative evaluations of the room temperatures
along with other controller performance. Additionally, note that the optimal schedules of some
scenarios remain the same because of the unbinding temperature constraints, which led to the same
testing outputs. Here we only discuss the scenarios that have different inputs and outputs. A full
list of all testing results is available in Table A-2.
Table 7 Comparison of controller performance in the residential building high uncertainty
In Table 7, we see a larger value of unmet thermal preference hours in the deterministic controller
than the chance-constrained one. This can be attributed to the higher room temperatures regulated
by the chance constraints to better satisfy the occupants’ thermal preferences. Again, the same
unserved load ratio is observed in both controllers because it is already minimal, which is enforced
by the objective function. In terms of the battery size, the chance-constrained controller shows a
smaller required battery size than the deterministic controller. This results from the fact that a
higher room temperature has led to less consumed HVAC energy in the chance-constrained
scenario. Thus, less discharging from the battery was happening, which led to a smaller required
battery size. For the bakery results shown in Table 8, the same trends for the battery size and the
unserved load ratio as the residential building can be observed under each uncertainty level.
Namely, smaller batteries and the same unserved load ratios.
Table 8 Comparison of controller performances in the bakery medium and high uncertainty
As for the unmet thermal preference hours, different trends are witnessed in the medium and high
uncertainty levels. In the medium level, the deterministic controller shows fewer unmet preference
hours than the chance-constrained controller. Whereas in the high uncertainty level, an opposite
trend is seen. This is reasonable as we see a generally higher mean room temperature regulated by
the chance-constrained controller under different uncertainty levels. However, in the medium
scenario, a lower preference temperature line was obtained from the Monte Carlo testing, which is
closer to the actual room temperatures of the deterministic controller. When the preference
temperature rises in the high uncertainty scenario, the chance-constrained controller outperforms
the deterministic controller with a higher actual room temperature and thus smaller unmet thermal
When we compare different uncertainty levels in the bakery, we see that the mean room
temperature decreases with the increase in uncertainty. This is because the lower temperature
upper bounds shown in Table 5 have regulated the room temperature to sink when the uncertainty
gets higher. Additionally, as seen in Figure 4, in the temperature range of 20ºC to 24ºC, the
probability of increasing the temperature setpoint is much higher than that of decreasing it While
above 24ºC, the probability to increase and to decrease is almost the same. This has caused the
room temperatures to end up around 24ºC in the high uncertainty scenarios for all buildings (Table
A-2). This reveals that with the increase in the occupant thermostat-changing uncertainties, the
room temperatures tend to get closer to the occupants’ preferred room temperature.
Though some improvement was noticed in the chance-constrained controller compared to the
deterministic controller, the overall improvement was less than expected. This could be attributed
to the following three factors. First, the impact of the uncertainty level on the controller
performance improvement is prominent as we observe higher performance improvement in high
uncertainty scenarios. Second, the thermal property, especially thermal mass, of the building itself
also affects the results. Thermal mass serves as a thermal buffer to filter the impact of various
HVAC supply temperatures. Hence, buildings with a larger thermal mass tend to experience less
impact from the occupant thermal preference uncertainty. This can be demonstrated by the results
of the ice cream shop, where the two controllers perform the same. Third, the plant-model
mismatch also plays a significant role in the transition from the optimal scheduler design to its
implementation. In the design phase, a series of control-oriented linear regression building models
was used. However, the testing took place on a high-fidelity physics-based testbed, where the
complex system dynamics of the whole buildings and HVAC systems were modeled with shorter
simulation timesteps. This is a common source of uncertainty to be addressed for MPC design and
In our opinion, joint effort from building scientists, modelers, and engineers is needed to facilitate
implementing stochasticity in the building domain and ultimately better serve the occupants. For
example, an open-source database focused on building performance related stochasticity such as
the occupant behavior and weather forecast needs to be established. Further, readily available
stochastic simulation tools need to be developed (e.g., Occupancy Simulator ). Finally,
stochasticity needs to be incorporated into the whole process of building modeling and design in
the form of boundary conditions or internal components.
In this paper, we proposed a preference-aware scheduler for resilient communities. Stochastic
occupant thermostat-changing behavior models were introduced into a deterministic load
scheduling framework as a source of uncertainty. The impact of occupant behavior uncertainty on
community optimal scheduling strategies was discussed. KRIs such as the unserved load ratio, the
required battery size, and the unmet thermal preference hours were adopted to quantify the impacts
of uncertainties. Generally, the proposed controller performs better in terms of the unmet thermal
preference hours and the battery sizes compared to the deterministic controller. Though only tested
on three buildings of the studied community, the methodology of introducing occupant behavior
uncertainty into load scheduling and testing can be generalized and applied to other building and
More specifically, we determined that occupant thermostat-changing behavior uncertainty should
be considered when designing optimal schedulers for resilient communities. For the whole
community, when considering the highest occupant behavior uncertainty, the consumed HVAC
energy can be 57.2% less and the battery 8.08% smaller. During the controller testing phase, the
proposed chance-constrained controller proves its advantage over the deterministic controller by
better serving the occupants’ thermal needs and demonstrating a savings of 6.7 kWh of battery
capacity for the whole community. Additionally, we noticed that with the presence of occupant
thermostat-changing uncertainties, the room temperatures tend to get closer to the occupants’
preferred room temperature.
During the simulation experiments, we noticed some limitations of the proposed work. Because
the proposed uncertainty method mainly deals with the uncertainty through the temperature
constraints, it can be less effective for buildings of larger thermal mass due to the insensitivity to
temperature constraints. Also, plant-model mismatch was noticed in the controller testing phase,
which is a common parametric uncertainty that originates from neglected dynamics of the
plant . Finally, we used the thermostat changing models developed based on data from private
office spaces in different building types, which can be debatable. Future work for this research
includes extending the scope to heating scenarios to further generalize the findings. Additionally,
real-time MPC control techniques could be integrated into the framework to overcome the lack of
flexibility in a priori designed controllers.
This research is partially supported by the National Science Foundation under Awards No. IIS-
1802017. It is also partially supported by the U.S. Department of Energy, Energy Efficiency and
Renewable Energy, Building Technologies Office, under Contract No. DE-AC05-76RL01830.
This work also emerged from the IBPSA Project 1, an internationally collaborative project
conducted under the umbrella of the International Building Performance Simulation Association
(IBPSA). Project 1 aims to develop and demonstrate a BIM/GIS and Modelica Framework for
building and community energy system design and operation.
Table A-1 Complete list of building loads and heat gain coefficients [31–33].
Figure A-1 Optimal schedules of the heat pump speed ratio and predicted room temperatures by
various schedulers (ice cream shop).
Figure A-2 Optimal schedules of the heat pump speed ratio and predicted room temperatures by
various schedulers (bakery).
Table A-2 Full comparison of controller performances under different uncertainty levels in all
Ice Cream Shop
 The Texas Tribune. Winter Storm 2021. https://www.texastribune.org/series/winter-storm-
power-outage/ (accessed Apr 1, 2021).
 Wang, J.; Garifi, K.; Baker, K.; Zuo, W.; Zhang, Y. Optimal Operation for Resilient
Communities through a Hierarchical Load Scheduling Framework. In Proceedings of 2020
Building Performance Analysis Conference & SimBuild; Virtual Conference, 2020.
 Wang, J.; Zuo, W.; Rhode-Barbarigos, L.; Lu, X.; Wang, J.; Lin, Y. Literature Review on
Modeling and Simulation of Energy Infrastructures from a Resilience Perspective. Reliab.
Eng. Syst. Saf., 2019, 183, 360–373. https://doi.org/10.1016/j.ress.2018.11.029.
 Tang, H.; Wang, S.; Li, H. Flexibility Categorization, Sources, Capabilities and
Technologies for Energy-Flexible and Grid-Responsive Buildings: State-of-The-Art and
Future Perspective. Energy, 2020, 119598. https://doi.org/10.1016/j.energy.2020.119598.
 Kou, X.; Li, F.; Dong, J.; Olama, M.; Starke, M.; Chen, Y.; Zandi, H. A Comprehensive
Scheduling Framework Using SP-ADMM for Residential Demand Response with Weather
and Consumer Uncertainties. IEEE Trans. Power Syst., 2020.
 Faraji, J.; Ketabi, A.; Hashemi-Dezaki, H.; Shafie-Khah, M.; Catalão, J. P. S. Optimal Day-
Ahead Self-Scheduling and Operation of Prosumer Microgrids Using Hybrid Machine
Learning-Based Weather and Load Forecasting. IEEE Access, 2020, 8, 157284–157305.
 Wang, J.; Garifi, K.; Baker, K.; Zuo, W.; Zhang, Y.; Huang, S.; Vrabie, D. Optimal
Renewable Resource Allocation and Load Scheduling of Resilient Communities. Energies.
 Yu, M. G.; Pavlak, G. S. Assessing the Performance of Uncertainty-Aware Transactive
Controls for Building Thermal Energy Storage Systems. Appl. Energy, 2021, 282, 116103.
 Liang, Z.; Huang, C.; Su, W.; Duan, N.; Donde, V.; Wang, B.; Zhao, X. Safe Reinforcement
Learning-Based Resilient Proactive Scheduling for a Commercial Building Considering
Correlated Demand Response. IEEE Open Access J. Power Energy, 2021, 8, 85–96.
 Ahmad, A.; Khan, J. Y. Real-Time Load Scheduling, Energy Storage Control and Comfort
Management for Grid-Connected Solar Integrated Smart Buildings. Appl. Energy, 2020,
259, 114208. https://doi.org/10.1016/j.apenergy.2019.114208.
 E Silva, D. P.; Salles, J. L. F.; Fardin, J. F.; Pereira, M. M. R. Management of an Island and
Grid-Connected Microgrid Using Hybrid Economic Model Predictive Control with
Weather Data. Appl. Energy, 2020, 278, 115581.
 Yundra, E.; Surabaya, U. N.; Kartini, U.; Wardani, L.; Ardianto, D.; Surabaya, U. N.;
Surabaya, U. N.; Surabaya, U. N. Hybrid Model Combined Fuzzy Multi-Objective Decision
Making with Feed Forward Neural Network (F-MODMFFNN) For Very Short-Term Load
Forecasting Based on Weather Data. Int. J. Intell. Eng. Syst., 2020, 13 (4), 182–195.
 Garifi, K.; Baker, K.; Christensen, D.; Touri, B. Stochastic Home Energy Management
Systems with Varying Controllable Resources. In 2019 IEEE Power & Energy Society
General Meeting (PESGM); IEEE: Atlanta, GA, USA, 2019; pp 1–5.
 Lu, M.; Abedinia, O.; Bagheri, M.; Ghadimi, N.; Shafie‐khah, M.; Catalão, J. P. S. Smart
Load Scheduling Strategy Utilising Optimal Charging of Electric Vehicles in Power Grids
Based on an Optimisation Algorithm. IET Smart Grid, 2020, 3 (6), 914–923.
 Khalid, Z.; Abbas, G.; Awais, M.; Alquthami, T.; Rasheed, M. B. A Novel Load Scheduling
Mechanism Using Artificial Neural Network Based Customer Profiles in Smart Grid.
Energies, 2020, 13 (5), 1062. https://doi.org/10.3390/en13051062.
 Kerboua, A.; Boukli-Hacene, F.; Mourad, K. A. Particle Swarm Optimization for Micro-
Grid Power Management and Load Scheduling. Int. J. Energy Econ. Policy, 2020, 10 (2),
 Kaur, R.; Schaye, C.; Thompson, K.; Yee, D. C.; Zilz, R.; Sreenivas, R. S.; Sowers, R. B.
Machine Learning and Price-Based Load Scheduling for an Optimal IoT Control in the
Smart and Frugal Home. Energy AI, 2021, 3, 100042.
 Chung, H.-M.; Maharjan, S.; Zhang, Y.; Eliassen, F. Distributed Deep Reinforcement
Learning for Intelligent Load Scheduling in Residential Smart Grids. IEEE Trans. Ind.
Informatics, 2020, 17 (4), 2752–2763. https://doi.org/10.1109/TII.2020.3007167.
 Aftab, M.; Chen, C.; Chau, C.-K.; Rahwan, T. Automatic HVAC Control with Real-Time
Occupancy Recognition and Simulation-Guided Model Predictive Control in Low-Cost
Embedded System. Energy Build., 2017, 154, 141–156.
 Lim, B.; Van Den Briel, M.; Thiébaux, S.; Backhaus, S.; Bent, R. HVAC-Aware Occupancy
Scheduling. In Proceedings of the AAAI Conference on Artificial Intelligence; 2015; Vol.
 Jin, Y.; Yan, D.; Zhang, X.; An, J.; Han, M. A Data-Driven Model Predictive Control for
Lighting System Based on Historical Occupancy in an Office Building: Methodology
Development. In Building Simulation; Springer, 2020; pp 1–17.
 Wang, J.; Zuo, W.; Huang, S.; Vrabie, D. Data-Driven Prediction of Occupant Presence and
Lighting Power: A Case Study for Small Commercial Buildings. In American Modelica
 Chen, X.; Wang, Q.; Srebric, J. Model Predictive Control for Indoor Thermal Comfort and
Energy Optimization Using Occupant Feedback. Energy Build., 2015, 102, 357–369.
 West, S. R.; Ward, J. K.; Wall, J. Trial Results from a Model Predictive Control and
Optimisation System for Commercial Building HVAC. Energy Build., 2014, 72, 271–279.
 Drgoňa, J.; Arroyo, J.; Figueroa, I. C.; Blum, D.; Arendt, K.; Kim, D.; Ollé, E. P.; Oravec,
J.; Wetter, M.; Vrabie, D. L. All You Need to Know about Model Predictive Control for
Buildings. Annu. Rev. Control, 2020. https://doi.org/10.1016/j.arcontrol.2020.09.001.
 Garifi, K.; Baker, K.; Touri, B.; Christensen, D. Stochastic Model Predictive Control for
Demand Response in a Home Energy Management System. In 2018 IEEE Power & Energy
Society General Meeting (PESGM); Portland, OR, USA, 2018; pp 1–5.
 Zhang, X.; Schildbach, G.; Sturzenegger, D.; Morari, M. Scenario-Based MPC for Energy-
Efficient Building Climate Control under Weather and Occupancy Uncertainty. In 2013
European Control Conference (ECC); IEEE, 2013; pp 1029–1034.
 He, D.; Huang, S.; Zuo, W.; Kaiser, R. Towards to the Development of Virtual Testbed for
Net Zero Energy Communities. In SimBuild 2016: Building Performance Modeling
Conference; Salt Lake City, UT, USA, 2016; Vol. 6.
 Zakula, T.; Armstrong, P. R.; Norford, L. Modeling Environment for Model Predictive
Control of Buildings. Energy Build., 2014, 85, 549–559.
 The Engineering ToolBox. Metabolic Heat Gain from Persons.
https://www.engineeringtoolbox.com/metabolic-heat-persons-d_706.html (accessed Feb
 Hosni, M. H.; Beck, B. T. Updated Experimental Results for Heat Gain from Office
Equipment in Buildings. ASHRAE Trans., 2011, 117 (2).
 ASHRAE. ASHRAE Handbook — Fundamentals 2017; 2017.
 Lawrence Berkeley National Laboratory. Home Energy Saver & Score: Engineering
Documentation - Internal Gains. http://hes-documentation.lbl.gov/calculation-
calculation/internal-gains (accessed Feb 16, 2021).
 Maslow, A. H. Motivation and Personality; Harper & Brothers: New York City, USA, 1954.
 Roth, A.; Reyna, J.; Christensen, J.; Vrabie, D.; Adetola, V. GEB Technical Report Webinar
Series: Whole-Building Control, Sensing, Modeling & Analytics
 Zhao, Z.; Lee, W. C.; Shin, Y.; Song, K.-B. An Optimal Power Scheduling Method for
Demand Response in Home Energy Management System. IEEE Trans. Smart Grid, 2013,
4 (3), 1391–1400. https://doi.org/10.1109/TSG.2013.2251018.
 SiteSage. Historic Green Village Submetering Data.
https://sitesage.net/home/management/index.php (accessed Oct 7, 2020).
 Garifi, K.; Baker, K.; Christensen, D.; Touri, B. Control of home energy management
systems with energy storage: Nonsimultaneous charging and discharging guarantees
 Gunay, H. B.; O’Brien, W.; Beausoleil-Morrison, I.; Bursill, J. Development and
Implementation of a Thermostat Learning Algorithm. Sci. Technol. Built Environ., 2018,
24 (1), 43–56. https://doi.org/10.1080/23744731.2017.1328956.
 Heirung, T. A. N.; Paulson, J. A.; O’Leary, J.; Mesbah, A. Stochastic Model Predictive
Control—How Does It Work? Comput. Chem. Eng., 2018, 114, 158–170.
 The Modelica Association. Modelica. 2019.
 Huang, S.; Wang, J.; Fu, Y.; Zuo, W.; Hinkelman, K.; Kaiser, M. R.; He, D.; Vrabie, D. An
Open-Source Virtual Testbed for a Real Net-Zero Energy Community; 2021.
 Mooney, C. Z. Monte Carlo Simulation; Sage, 1997.
 Statistics Solutions. Chi-Square Goodness of Fit Test.
https://www.statisticssolutions.com/chi-square-goodness-of-fit-test/ (accessed Feb 25,
 Chen, Y.; Hong, T.; Luo, X. An Agent-Based Stochastic Occupancy Simulator. In Building
Simulation; Springer, 2018; Vol. 11, pp 37–49.