Available via license: CC BY
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Citation: Jones, E.S.; Alden, R.E.;
Gong, H.; Ionel, D.M. Co-Simulation
of Electric Power Distribution
Systems and Buildings Including
Ultra-Fast HVAC Models and
Optimal DER Control. Sustainability
2023,15, 9433. https://doi.org/
10.3390/su15129433
Academic Editor: Mohamed A.
Mohamed
Received: 24 March 2023
Revised: 1 June 2023
Accepted: 7 June 2023
Published: 12 June 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
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4.0/).
sustainability
Article
Co-Simulation of Electric Power Distribution Systems and
Buildings Including Ultra-Fast HVAC Models and Optimal
DER Control
Evan S. Jones 1, Rosemary E. Alden 1, Huangjie Gong 2and Dan M. Ionel 1,*
1SPARK Laboratory, ECE Department, University of Kentucky, Lexington, KY 40506, USA
2ABB USRC, 1021 Main Campus Dr, Raleigh, NC 27606, USA; huangjie.gong@ieee.org
*Correspondence: dan.ionel@ieee.org
Abstract:
Smart homes and virtual power plant (VPP) controls are growing fields of research with
potential for improved electric power grid operation. A novel testbed for the co-simulation of electric
power distribution systems and distributed energy resources (DERs) is employed to evaluate VPP
scenarios and propose an optimization procedure. DERs of specific interest include behind-the-
meter (BTM) solar photovoltaic (PV) systems as well as heating, ventilation, and air-conditioning
(HVAC) systems. The simulation of HVAC systems is enabled by a machine learning procedure
that produces ultra-fast models for electric power and indoor temperature of associated buildings
that are up to
133 times
faster than typical white-box implementations. Hundreds of these models,
each with different properties, are randomly populated into a modified IEEE 123-bus test system to
represent a typical U.S. community. Advanced VPP controls are developed based on the Consumer
Technology Association (CTA) 2045 standard to leverage HVAC systems as generalized energy
storage (GES) such that BTM solar PV is better utilized locally and occurrences of distribution system
power peaks are reduced, while also maintaining occupant thermal comfort. An optimization is
performed to determine the best control settings for targeted peak power and total daily energy
increase minimization with example peak load reductions of 25+%.
Keywords:
power distribution system; building energy model (BEM) ; HVAC systems; CTA-2045;
control; distributed energy resources (DERs); co-simulation; machine learning (ML); generalized
energy storage (GES); OpenDSS; optimization; smart grid; smart home
1. Introduction
Residential loads constituted 21% of the U.S. total annual energy in 2021 as com-
pared to commercial at 18% [
1
]. Within these communities, heating, ventilation, and air-
conditioning (HVAC) systems are the dominant load at around 50% of total typical building
loads. There is significant opportunity in leveraging distributed energy resources (DERs),
such as HVAC systems, as energy storage solutions to shift or shape load over time through
virtual power plant (VPP) controls [2,3].
Early studies from Sandia National Laboratory in 2017 defined the VPP concept as the
coordinated control of decentralized DERs, which include renewable energy generation and
energy storage. VPPs may be implemented in microgrids and in conventional electric power
distribution system networks such that they behave as a single entity with dispatchable and
responsive resources [
4
]. Sandia National Laboratory also investigated object-oriented VPP
implementation through full state feedback and concluded that accurate physics-based
modeling and the accurate estimation of dynamic states in real time is integral. Additionally,
they asserted that VPP will replace ancillary services, such as frequency regulation and
grid disturbance responses, that are required by electric power utilities, ISOs, and RTOs.
This assertion is due to faster response times compared to large fossil fuel power plants [5].
Sustainability 2023,15, 9433. https://doi.org/10.3390/su15129433 https://www.mdpi.com/journal/sustainability
Sustainability 2023,15, 9433 2 of 20
The VPP research field has grown significantly, and widespread efforts to summa-
rize the development and previous control studies, including optimization, have been
undertaken in review papers. Naval et al. summarized the types of optimization problems,
heuristic methods, and mathematical approaches that researchers have proposed for VPP
coordinated controls. Market schemes that employ mixed-integer linear programming and
branch-and-bound-methods were found to be the most common from among more than
100 references [
6
]. VPP optimization studies that incorporate economic objectives were
typically formulated for day-ahead market predictions to minimize costs and operational
risk while maximizing profit.
State-of-the-art resources considered part of the VPP include gas turbines, wind power,
solar photovoltaic (PV) systems, pumped storage and hydro electric systems, combined
heat and power plants, boilers, energy storage systems, flexible loads, and electric vehicles.
An identified limitation of the studies is that they were rarely applied to real cases, where
industrial processes, such as the management of energy consumption and generation, must
be monitored and modeled, indicating future work in the field. The methodology proposed
in this work is distinct from previous methods because realistic and representative modeling
of HVAC systems as flexible loads is employed, and the optimization objective function is
integrated with OpenDSS power system software to consider the physical modeling of the
distribution system, which is nonlinear to select optimal control start and end times.
The REV Demonstration for Clean VPP was an early initiative to implement these
types of controls in the field, by Con Edison in New York. It included a platform for
aggregated control of residential solar PV and energy storage to alleviate strain on night
peaking distribution systems [
7
]. Unfortunately, due to difficulty with obtaining approvals
with government agencies for the installation of batteries, the project was not able to be
carried out [
8
]. This highlights an important challenge for VPP implementation that may
be alleviated with use of standardized energy control protocols and reduced additional
equipment as implemented in this paper.
Another field demonstration that launched in 2022 to the public is the Shelter Valley
VPP conducted by the SDGE Utility and EPRI in San Diego, USA. It includes initiatives
to control thermostats, batteries, water heaters, and blinds in a vulnerable grid region
to reduce outages [
9
]. Additionally, a very recent industry report conducted for Google
found that VPP could perform as reliably as conventional resources at a similar scale [
10
]
if key barriers are addressed as well as program limitations, such as how often and when
programs may be called. Considering societal benefits, the potential of VPP was estimated
to have negative net cost to the utility and be approximately USD 15–35 billion dollars
cheaper than alternatives for 60 GW of power over the next decade.
Overall, controls for load manipulation are invaluable tools for utilities to manage the
emerging smart grid and optimally utilize increasingly more prevalent and intermittent
demand-side generators, such as behind-the-meter (BTM) PV systems [
11
–
13
]. As a promis-
ing DER type, battery energy storage systems (BESSs) are effective for utility grid energy
management, although the challenge of increased cost still needs to be addressed [
13
–
16
].
They also require planning and coordination strategies through simulation to ensure ad-
equate sizing for other DERs that may generate power intermittently [
17
]. Such DERs
can benefit greatly by the co-location of BESSs in terms of grid interconnection and cost
effectiveness [18].
As an alternative to BESSs, HVAC and water heating systems that are already widely
available offer similar functionality when operated as generalized energy storage (GES)
with additional appliance-specific constraints that are typically associated with occupant
comfort and weather effects. Control strategies can be developed and tested through
co-simulation [
12
,
19
]. They are an integral part of the smart grid, especially those that
coordinate multiple types of DERs, such as solar PV and GES. The simulation testbeds
themselves enable the development of VPP control schemes and in the planning of DER
deployment through large-scale studies [20,21].
Sustainability 2023,15, 9433 3 of 20
There are four main original contributions included in this paper. First, a methodology
to synthesize representative communities of hundreds of ultra-fast and distinct models for
residential buildings employing EnergyPlus, machine learning, and minimal experimental
data is proposed. This methodology is used in the second original contribution—a novel co-
simulation framework between OpenDSS and Python for real-time, time-series modeling
and controls of individual models for building and HVAC load as well as PV generation
per node of electric power distribution system selected. An additional contribution is
the demonstration of the benefits of gradual sequential controls and incremental HVAC
temperature set point adjustments in simulations of the VPP through the co-simulation
framework. Finally, the last main contribution is the development of an optimization
procedure for industry-standard-based controls to select time windows for VPP operation
while accounting for consumer comfort and physical behavior of the distribution system.
Further details of the main contributions include that the novel testbed for co-simulation
and holistic framework for control strategy development employs numerous GES systems,
namely HVAC systems, and DERs based on the Consumer Technology Association (CTA)
2045 standard [
22
,
23
]. This industry standard specifies a modular communications interface
to streamline communications so that any residential device may connect to any type of
demand response system. A physical communications module is specified to use the widely
compatible RS-485 serial communication method with the appliance and then a secure
transport protocol, such as Wi-Fi, ZigBee, etc., to any energy management system. Serial
opcodes are also specified for demand response commands ”load-up” to increase the energy
use and ”shed” to decrease the energy use. These commands are suitable for interoperable
VPPs across communities with different device manufacturers. The development of CTA-
2045-based controls with “load-up” and “shed” commands conducted in this paper at both
the power system and individual building levels is enabled by the proposed framework,
which is facilitated by a physics-informed machine learning modeling procedure that is
must faster than conventional white-box implementations.
The advanced control methodologies utilized incorporate HVAC system sequential
phasing in batches of houses throughout the community and more gradual changes in
setpoint temperatures. Additionally, the multi-objective control optimization proposed has
the objectives to minimize targeted power peaks and the possible resultant increases in
total energy use. Independent variables for the optimization include “shed” and “load-up”
control times for the HVAC systems, which are command types based on the CTA-2045
standard and made possible by GES characterization that inherently considers occupant
thermal comfort.
In Section 2, the models for DER, including generators and energy storage, are estab-
lished. Section 3provides the operation of the DERs in aggregate at the power system
level, considering different control and distribution-side generation scenarios. Section 4
formulates the optimization of HVAC system GES control settings. The results of the
optimization and preceding central composite and full factorial simulation experiments are
discussed in Section 5. Having determined a “best compromise” set of optimal settings,
Section 6further explores the effects of the control on individual buildings and occupants,
and conclusions are provided in Section 7.
2. Models for PV Generation and Energy Storage
A novel framework for co-simulation of DERs and distribution systems is utilized
as a testbed for control schemes, GES, and DER deployment (Figure 1). The building
models employed in the co-simulation framework consist of four components: residential
rooftop solar PV systems, thermal building envelopes, HVAC systems, and base loads
(i.e., other human-behavior-tied electric loads). As a basis for the HVAC and building
components, three houses ranging from conventional to near-net-zero energy (NNZE)
performance, were modeled and calibrated in EnergyPlus [
24
,
25
] to represent a spectrum of
energy efficiencies as seen in experimental residential communities. EnergyPlus is the U.S.
Department of Energy’s flagship physics-based, white-box simulator for whole-building
Sustainability 2023,15, 9433 4 of 20
modeling, including the effects of building construction and weather on HVAC system
energy calculations.
Figure 1.
Visual depiction of the novel co-simulation testbed, including hundreds of CTA-2045
control compatible HVAC and building modules. Smart homes with physics-informed machine
learning HVAC system models and distinct energy profiles for typical base load from human behavior
are employed. Through the proposed testbed, individually unique house models for both electric
power and indoor temperature may be simulated at the building and power system levels for a
representative community. Other DER types with controls, such as solar PV and battery energy
storage (BES) systems, may be incorporated.
Through the new EnergyPlus Python plugin, the novel co-simulation framework and
testbed were developed to synthesize hundreds of different house models by varying the
input parameters of the base conventional EnergyPlus building model, such as internal
HVAC and building construction characteristics. A normal distribution of key building
characteristics spanning from the lower efficiency conventional house to highly efficiency
NNZE house was used to ensure adequate and representative randomness between houses.
Heating and cooling thermal energy capacities, air flow rates, and coefficients of perfor-
mance (COP) are examples of the varied HVAC internal parameters to create the distinct
synthetic community of houses. Additionally, examples of input building characteristics
that are unique between individual houses in the study include the specific heat, conductiv-
ity, density, and thickness of such construction materials as studs; insulation; associated air
cavities for walls and roofing as well as for attic trusses and additional ceiling insulation;
solar heat gain coefficients (SHGCs); and window U-factors.
The next step in the proposed novel framework is to simulate the newly synthesized
EnergyPlus models for an example location, time period, and subsequent weather; as a
result, synthetic data of HVAC power and energy and indoor building temperature for an
entire community of individual houses are produced, and the training of ultra-fast models
is enabled. With these synthesized data, machine learning (ML) procedures may be applied
to develop physics-informed new black and grey box versions that emulate the EnergyPlus
and experimental data. Example methods used in the simulations throughout this paper
include a hybrid ML model of k-means clustering to identify weather groupings, multiple
linear regression (MLR), and specific heat conversions through thermodynamic equations
as visualized in Figure 2[
26
]. These methods may be updated in the object-oriented co-
simulation framework as further improved methods are proposed. Furthermore, various
sizes of communities may be synthesized following the ML procedure, and the individual
models produced are satisfactorily accurate in estimating the heating and cooling thermal
energy and electric power of the HVAC system, as well as the indoor temperature in the
house based on the external weather. Ultra-fast simulation that is up to approximately
Sustainability 2023,15, 9433 5 of 20
133 times faster than EnergyPlus is enabled through the proposed framework as well as
co-simulation with other software and each timestep over time-series simulations of various
lengths: daily, monthly, yearly, etc.
Figure 2.
Visual depiction of the time-dependent HVAC and building simulator. Explicit CTA-2045
commands are issued, and Energy Star GES performance metrics, such as energy take, equivalent
SOC, and electric energy capacity, may be estimated through the building simulator.
The ML models capture the thermal properties of the building and the HVAC system
and their relationship with weather from the EnergyPlus training data. As a result, given
a long enough training period with a wide range of weather combinations throughout
a year, the ultra-fast ML models may not be exclusive to the location of the original
experimental data and EnergyPlus models. If the operation of the HVAC system from
heating to cooling demand is provided to the ML model in training, then the “V-curve”,
a method for correlating weather to HVAC power [
27
,
28
], and the typical performance
is captured.
An example V-curve is illustrated in Figure 3from a building in the co-simulation
framework. It shows the spectrum of behavior and trends for heating and cooling annually
for the heat-pump system. The physical relationship shown in the V-curve along with other
weather parameters, such as humidity and irradiance, may then, in principle, be used by
the ML model for estimations of power and indoor temperature with weather from other
locations of similar annual climate. It is promising that the advanced ML may be able to
apply the physical trends per HVAC system outside the range of temperature, relative
humidity, and irradiance in the training set, as the performance is fairly linear.
Figure 3.
Example HVAC ”V-curve” and physical relationship between weather parameters and
power captured by the ML model. In principle, the ML model may be applied with weather at
different locations and employ the approximately linear trends to estimate the power demand.
It is important to calculate the building indoor temperature for the tracking and pre-
diction of occupant thermal comfort, as this is integral for proper, representative HVAC
control across different locations. The proposed framework is intentionally designed for
VPP studies and comparisons between locations because the only inputs to the HVAC
and building simulators are from human behavior/preference, weather, and the indoor
Sustainability 2023,15, 9433 6 of 20
temperature. Future work is recommended to conduct an in-depth VPP study at differ-
ent locations, where the benefit and improved grid resiliency from the controls may be
quantified to determine optimal areas for infrastructure investment, such as [
29
] for EVs.
Additional future work recommendations are described at the end of Section 4.
As part of the testbed, an HVAC and building simulator is custom developed to
utilize the ML models for co-simulation with a power distribution system and are assigned
to appropriate circuit nodes (Figure 2). Simulation processes and control logic for the
HVAC and building simulator are provided in Figure 4, where
td
is the indoor temperature
deviation;
ts
, the setpoint temperature;
ti
, the indoor temperature;
hm
, the HVAC mode
of operation;
hs
, the HVAC on or off status;
tdb
, the thermostat temperature dead-band;
ttol
, the thermostat temperature tolerance;
ph,kW
, the HVAC electric active power [kW],
tin
,
the indoor temperature of the next timestep;
p fh
, the power factor of the HVAC system;
ph,kvar
, the HVAC electric reactive power [kvar];
pvr
, the rated power of the solar PV system
[kW];
ppv
, the electric active power generated from the solar PV system;
pt,kW
, the total
electric active power of the building [kW];
pt,kvar
, the total electric reactive power of the
building [kvar];
pb,kW
, the electric active power of the base load [kW];
pb,kvar
, the electric
reactive power of the base load [kvar].
Figure 4.
Flowchart for the HVAC and building simulator that employs ML HVAC models as well as
the PV simulator.
Residential solar PV system modules may be assigned to the individual houses in
the framework and simulated through physical equations based on input weather data
(
Figure 1)
. This PV simulator portion of the framework determines the generated solar PV
power (pg,pv) as follows:
pg,pv =h γ
1000 pr,pvi1−kp
100 (tc−25 ◦C)∗ηpv, (1)
where
γ
is the solar irradiance [W/m
2
];
pr,pv
, the PV array rated power [W];
kp
, the tempera-
ture coefficient of maximum power [%
/◦
C];
ηpv
, the efficiency considering losses due to the
inverter, interconnection of modules with nonidentical properties, and dirt accumulation;
tc, the temperature of the PV cells [◦C], which is calculated by
tc=to+tn−20 ◦C
0.8 γ
1000 , (2)
where
to
is the outdoor ambient temperature [
◦
C] and
tn
is the nominal operating cell
temperature [◦C].
Typical household appliances and plug-loads, unlike HVAC and PV systems, are not
dominantly weather dependent and have more random behavior due to human choices.
Sustainability 2023,15, 9433 7 of 20
Therefore, random daily energy profiles of typical house loads, including electronics, water
heaters, and lights, may be assigned to each individual house. Minutely, household data
sourced from the EPRI SHINES project were employed as daily schedules for the following
studies [30].
3. Power System and DER Operation
To represent a large subdivision in the U.S., the IEEE 123 bus system was co-simulated
with the proposed novel framework with representative building simulators based on
the methodology described in Section 2. The testbed framework employs time-series co-
simulation of OpenDSS, a widely used open-source power system simulation software,
and Python to enable geographical information system (GIS) power system modeling
of the test system with the proposed optimized controls. To populate the IEEE 123 bus
system with synthetic residential load and PV generation, an initialization procedure in the
framework was performed to assign a building simulator with HVAC and PV modules to
each bus node per 10 kW of original peak load (Figure 5a) [31].
(a)(b)
Figure 5.
The circuit diagram for (
a
) the modified IEEE 123-bus test system. The original circuit has a
peak load of 3.6 MW, 1.3 MVAr, and is to be representative of a very large residential subdivision
in the U.S. Distribution system total active power for the (
b
) baseline and control cases. This is an
aggregation of all building loads minus the power losses across the distribution system without
considering any contributions from PV generation.
Through this initialization, 351 distinct buildings, 52 (15%) of which have a BTM
solar PV system with typical power ratings randomly selected between 3 and 7.5 kW,
are co-simulated with the IEEE 123 bus system. The houses with BTM PV generation
capability were distributed throughout the power system to represent gradual adoption
patterns of the technology. The proposed methodology to synthesize hundreds of distinct
representative homes into building simulators using EnergyPlus and ML was applied
using three experimental smart homes from the Tennessee Valley Authority (TVA) with
parameters ranging from conventional to NNZE as described in Section 2. These buildings
are then used in the initialization procedure to populate the distribution system.
Following the initialization of the framework, OpenDSS python API commands edit
the load at each bus based on building simulator results at each time step before the
power flow calculations are solved. In this formulation, the effects of the controls on the
residential HVAC load and available PV generation per house are considered individually
across the distribution system and at the aggregate level at the main feeder. This is an
important contribution of the proposed co-simulation framework because it enables in
control development and optimization of the assessment and feedback of physical behavior
across the distribution system, such as load tap changer, voltage regulator, capacitor,
and transformer operation; active power demand across lines and buses; and transformer
and line power losses.
Sustainability 2023,15, 9433 8 of 20
For the simulated example day, minutely solar irradiance and outdoor temperature
data collected in the southeast U.S. are employed as input to the models (Figure 6a).
The baseline simulation case does not include any VPP control, and the HVAC systems
operated as they normally would in accordance with their indoor temperature setpoints and
associated building thermal properties. At the power distribution system level, the total
power ramped up in the morning as both the solar irradiance and outdoor temperature
increased (Figure 5b). HVAC systems constitute almost half of the energy used by typical
residences and use more energy as the indoor temperature changes [
1
]. As this change in
temperature is reduced during midday, the HVAC systems settle into normal operation
and maintain an indoor temperature near the setpoint.
(a)(b)
Figure 6.
Results for the (
a
) distribution system total solar PV power generation and (
b
) total net
power for the simulated 15% and estimated solar PV penetration cases of up to 100%. The variability
in solar PV power generation is caused by variability in irradiance.
The total system power is ramped down as the sun sets, with a subsequent peak likely
due to occupant arrival in the evening. This secondary evening peak is of particular interest,
as electric-vehicle (EV) charging in scenarios of higher penetration may cause a significant
system-wide power increase at this time [
32
]. Additionally, the longer midday peak may
invert as distributed solar PV becomes more prevalent, which further contributes to the
concern of the secondary evening peak (Figure 6). The reshaping of the residential load
profile from higher DER penetration levels, including contributions from solar PV and EVs,
may be alleviated by VPP control of other residential loads, such as HVAC systems.
In conventional HVAC control, accounting for occupant thermal comfort is a significant
challenge due to the complex relationship between the weather, HVAC power, and indoor
temperature, which is unique for every building. Incorporating indoor temperature into
VPP control schemes that leverage HVAC systems as DER is necessary to abide by occupant
thermal comfort preferences. Improved control methods, for example, those utilizing the
CTA-2045 protocol for DER demand response and GES operation through Energy Star
definitions address the comfort issue by adopting energy storage capacity and equivalent
state-of-charge (SOC) calculations [
33
,
34
]. The equivalent HVAC energy storage capacity
and SOC at time tmay be calculated following
soch(t) = θmax −θi(t)
θmax −θmin
, (3)
ec,h(t) = eh,c·(1−soch(t)), (4)
where the
θmax
and
θmin
are the maximum and minimum indoor temperatures, respectively;
θi(t)
, the indoor temperature at time
t
;
eh,c
, the input electric energy required for the HVAC
system to reduce indoor temperature from θmax to θmin .
Sustainability 2023,15, 9433 9 of 20
During simulation, the HVAC system and building models, that are generally illus-
trated in Figure 2, determine their corresponding
ec,h(t)
internally upon initialization based
on their thermal properties and ability to maintain indoor temperature over time. The
recalculation of
ec,h(t)
at multiple timesteps throughout simulation captures the effects
of weather on the systems, which is similar to self-discharge and changes in capacity of
conventional electric BESSs.
When a CTA-2045 command is issued, such as a “shed” or “load-up”, the controller
adjusts individual building indoor temperature setpoints based upon their
ec,h(t)
, which
are determined by considering building thermal properties and typical ASHRAE standard
occupant thermal comfort limits [
34
]. Individual building characteristics are considered
when re-calculating HVAC setpoints per house and timestep, thereby improving the pre-
diction of the maximal available energy BTM while abiding by indoor temperature comfort
settings. By incorporating the consideration of occupant thermal comfort directly into the
controls, the degree to which occupant comfort is violated now correlates with the accuracy
of the building ec,h(t)estimations and the θmax and θmin settings.
4. Optimal VPP Control of HVAC Systems
A VPP control scenario is proposed that employs the CTA-2045 command types to
reduce the evening peak power. A “load-up” is planned before the evening to pre-cool the
houses while they are the least occupied to provide a more sustained “shed” that will turn
the HVAC systems off during the evening peak time window. In previous studies of HVAC
controls, it was established that large spikes in aggregate power occur if VPP signals are
sent at the same time to hundreds of homes and that using phased deployment of a selected
number of houses mitigates the spikes by spacing out the operational periods to not overlap
within the control time window [
34
]. With multi-speed HVAC systems as used in this
paper, spacing out the setpoint temperature changes in time to gradually reduce from,
for example 26
◦
C to 22
◦
C, further reduces the power spikes, as lower speeds operate for a
longer period, resulting in less power draw per house at a given time. For these reasons, in
the case studies throughout this paper, the indoor temperature setpoint adjustments are
issued incrementally over the first thirty minutes of the control period to provide a gradual
change in power over time.
Additionally, these advanced controls employ phasing before and after active periods,
by which batches of randomly selected HVAC systems are sequentially engaged and
disengaged from the control as illustrated in Figure 7a.
(a)(b)
Figure 7.
Simulation results for (
a
) individual on/off statuses for HVACs to show control phasing in
the baseline case (
top
) and in case P6 (
bottom
) as well as (
b
) hourly average bus voltages for both the
baseline and P6 cases. The “load-up” and “shed” event windows are shaded in light gray and purple,
respectively. This format is replicated in the following figures.
Sustainability 2023,15, 9433 10 of 20
The box-and-whisker format employed throughout is such that the box extends from
the first quartile to the third quartile with a green line at the median. Whiskers extend
from the box by 1.5
×
the inter-quartile range, and flier points are those past the end of
the whiskers.
The improved control functionality prevents power spikes that would have occurred
otherwise as illustrated with example case NP in Figure 5b. In such a case, all of the HVAC
systems engaged and disengaged simultaneously as soon as the “load-up” and “shed”
controls were issued, thereby causing a large spike and steep drop in the total distribution
system power. Another power spike occurred in the evening after the “shed” control ended,
as the HVAC systems resumed cooling all at once (Figure 8a).
(a) (b)
Figure 8.
Hourly average (
a
) indoor temperatures and (
b
) equivalent SOC, which is inversely related
to indoor temperature, of all buildings for the baseline and P6 cases. Blue dots represent outliers in
the box plot distributions.
To ensure the best performance, the controls are formulated as a multi-objective
optimization to minimize both the total distribution system peak power during the evening
time period (
pa,t=tep
) and possible resulting increase in total system energy use (
ed
) over
the example day, which are formally defined as
min "pa,t=tep =
nl
∑
i=1
(wa,l,i)+
nx
∑
j=1wa,x,j+
nd
∑
k=1
(pa,d,k)#, (5)
min "ed=
nt
∑
i=1
(pa,t=i)#, (6)
where
nl
is the total number of lines;
wa,l,i
, the active power losses over line number
i
;
nx
,
the total number of transformers;
wa,x,j
, the active power losses at transformer number
j
;
nd
,
the total number of loads;
pa,d,i
, the active power demand at load number
i
;
tep
, the moment
of maximum power in the evening peak time window of 5:30 to 9:00;
nt
, the total number
of timesteps (minutes) in the day.
The aggregate peak power during the evening time between 5:30 and 9 p.m. was
selected as the first optimization objective,
pa,t=tep
because this is the time during the day
where typically utilities are most vulnerable to strain and congestion on the distribution
system as it corresponds to increased amounts of human-behavior-driven load following
the return from work during the business week, including EV charging. The optimization
of VPP controls is considered passed for this metric if the peak power in the evening is
reduced by more than five percent to outperform estimates from conservation voltage
reduction (CVR) [
35
], another proposed method for power shifting, benefiting the utility
and grid resiliency.
A second objective, the daily total energy demand,
ed
, is included to prevent large
increases in total energy use for marginal improvements in peak power reduction. For ex-
Sustainability 2023,15, 9433 11 of 20
ample, a positive
ed
value indicates that the energy used during the “load-up” command to
pre-cool the homes through the HVAC systems is greater than that of the avoided energy
use during the “shed” command. Such a scenario presents a trade-off between
pa,t=tep
and
ed
, as both are to be minimized and have importance in the usefulness of the controls
to improve overall grid resiliency without environmental impact from large increases in
total daily load demand that would be more difficult to offset with increased DER penetra-
tion. In this case, a Pareto set of best control design candidates is beneficial as part of the
optimization to determine the optimal solution.
The independent variables of the control optimization include the “load-up” start time,
the control transition time, and the “shed” end time. To establish independent variable
bounds, a central composite and full factorial designs of experiments (DOE) with response
surfaces were performed (Figures 9and 10). The response surfaces for both the central
composite and full factorial suggest that the minimums for
ed
and
pa,t=tep
are achieved
with “load-up” start, control transition, and “shed” end times of 8:00, 15:00, and 22:00,
respectively. Based on the DOEs,
pa,t=tep
is significantly less dependent upon the “load-up”
start time than the other independent variables.
Figure 9.
Resulting evaluation of optimization objectives for both the central composite (CC) and full
factorial (FF) design of experiments (DOEs) with respect to the baseline case.The VPP controls are
capable of reducing the maximum peak power as shown by the CC and FF results to the left of the
baseline case, indicating that an optimization to select the control windows is justified and would
be beneficial.
With HVAC systems having been characterized as GES, they may be employed as
battery energy storage systems from the perspective of the power distributions system
with special availability constraints. Availability for HVAC systems is associated with the
thermal comfort of occupants and the assurance of service quality by the utility. Therefore,
constraints on indoor temperature are incorporated into each individual building implicitly
and are not explicitly applied by the optimization by having included an automatic thermo-
stat control mechanism that disengages the HVAC system from the control command when
an equivalent SOC bound is met. The equivalent energy capacities and SOC bounds are
determined by the minimum and maximum allowed temperatures, which are based on the
ASHRAE standards in this work, and they may be further customized by user application
in real-world implementations.
Sustainability 2023,15, 9433 12 of 20
Figure 10.
Response surfaces for the CC (
left
) and FF (
right
) DOEs serve as a sanity check for the
optimization by indicating the relationship between the independent variables and the optimization
objectives. In the application of the optimization on different distribution circuits, the CC and FF may
be run quickly first to estimate the benefit of the VPP controls.
The non-dominated sorting genetic algorithm (NSGA) III is utilized for the full opti-
mization [
36
]. Based on the CC and FF DOE, bounds were selected for each independent
variable: 6:00–8:00 for the “load-up” start time, 15:00–17:00 for the control transition period,
and 22:00–24:00 for the “shed” end time, respectively. Increments of five (5) min were
allowed within these independent variable bonds for design candidates. Comprised of over
750 simulation cases, the optimization confirms the relationships established by the central
composite and full factorial DOEs (Figure 11). The dependency of
pa,t=tep
on “load-up”
start time is more evident in the full optimization and opposes the objective to minimize
ed
.
Therefore, a Pareto front of eleven (11) best control settings is determined that showcases
the inverse relationship between the max power during the evening peak (
pa,t=tep
) and
total day energy use (ed) (Figures 11 and 12a,b).
The approach taken in this work assumed that all home owners in the distribution
system would enroll in the VPP program and all were equipped with the CTA-2045 com-
munication module on their HVAC systems. It also assumed that a financial system existed
in the market to compensate the home owner for their increased air conditioning flexibility
and potentially higher total daily energy usage. Further work could develop estimates for
user participation rates and expectations for compensation. Additionally, the optimization
enabled by the co-simulation framework with ML-based load modeling could be expanded
to include higher diversity of building types, consumer preferences, and locations in dif-
ferent climate regions for comparative VPP studies. In the future, modules for EVs, BESS,
and water heaters, second largest appliance, could be also be added for the optimization
of GES.
Sustainability 2023,15, 9433 13 of 20
Figure 11.
Relationships between the two (2) objectives and the three (3) independent variables of
control times for all simulated cases during the optimization.
Sustainability 2023,15, 9433 14 of 20
(a)(b)
Figure 12.
Resulting (
a
) objective evaluations and (
b
) a cropped view of all cases simulated during
the NSGA-III optimization with respect to the baseline case and with the Pareto front of the eleven
(11) best cases indicated.
5. Case Study and Discussion of Optimal Control Settings
The Pareto set of optimal control settings provides designs that reduce
pa,t=tep
within
a range of 24.45% and 28.75% by enacting the “shed” command (Tables 1and 2). Such
significant reduction in
pa,t=tep
is in part enabled by the pre-cooling of buildings through the
“load-up” command, which, in this case, increased
ed
by 7.98% to 10.73%. Of the considered
optimal control designs, P1 yielded the most reduction in
pa,t=tep
at 1.03 MW (28.75%) and
experienced the largest increase in
ed
of 2.07 MWh (10.73%) during the “load-up” with
respect to the baseline case. P10 represents the other extreme with a
pa,t=tep
reduction and
ed
increase of 0.29 MW (24.45%) and 1.54 MWh (7.98%), respectively. The “best compromise”
case of P6 achieved a
pa,t=tep
reduction of 0.32 MW (26.83%) with a
ed
increase of 1.63 MWh
(8.42%). The results of the two most extreme cases, P1 and P10, are emboldened, and the
“best compromise” case, P6, is both emboldened and italicized in Tables 1–3.
Table 1.
Results of optimal designs from the Pareto set and the baseline cases, including the maximum
power during the evening peak (on-peak) as well as total energy for the full day, the on-peak time
window, and off-peak time window.
Case Base P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
On-peak max power [MW] 1.20 0.86 0.86 0.87 0.88 0.88 0.88 0.89 0.90 0.90 0.91 0.91
Tot. day energy [MWh] 19.29 21.36 21.22 21.16 21.09 21.07 20.92 20.90 20.88 20.85 20.83 20.85
Tot. on-peak energy [MWh] 2.97 2.19 2.19 2.19 2.20 2.19 2.20 2.20 2.20 2.20 2.20 2.21
Tot. off-peak energy [MWh] 16.32 19.17 19.03 18.97 18.90 18.88 18.72 18.70 18.68 18.65 18.63 18.64
Table 2.
The control time settings and resulting percent change with respect to the baseline case for
all simulated cases in terms of maximum power during the evening peak (on-peak) as well as total
energy for the full day, the on-peak time window, and off-peak time window.
Case P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
Load-up start time 6:05 6:30 6:45 7:00 7:05 7:40 7:45 7:50 7:55 8:00 8:00
Control transition time 15:00 15:00 15:00 15:00 15:00 15:00 15:00 15:00 15:00 15:00 15:00
Shed end time 22:00 22:00 22:00 22:00 22:00 22:00 22:00 22:00 22:00 22:00 22:05
On-peak max power [%] −28.75 −28.60 −27.91 −27.10 −27.10 −26.83 −25.70 −25.01 −24.93 −24.45 −24.55
Tot. day energy [%] 10.73 9.99 9.65 9.32 9.21 8.42 8.31 8.20 8.07 7.98 8.06
Tot. on-peak energy [%] 24.75 23.70 23.27 22.88 22.82 22.06 21.98 21.86 21.73 21.68 21.68
Tot. off-peak energy [%] −4.40 −4.32 −4.21 −3.96 −3.95 −3.45 −3.42 −3.33 −3.27 −3.21 −2.93
Sustainability 2023,15, 9433 15 of 20
Table 3.
Total energy during the “load-up” and “shed” time windows, which are different for each
case based on the input time settings, with and without the controls active.
Case P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
Load-up w/ctrl [MWh] 11.78 11.44 11.22 10.95 10.86 10.15 10.05 9.95 9.84 9.73 9.73
Load-up w/o ctrl [MWh] 9.44 9.24 9.10 8.91 8.84 8.32 8.24 8.16 8.08 8.00 8.00
Shed w/ctrl [MWh] 5.82 5.83 5.83 5.85 5.85 5.88 5.88 5.89 5.89 5.89 5.95
Shed w/o ctrl [MWh] 6.09 6.09 6.09 6.09 6.09 6.09 6.09 6.09 6.09 6.09 6.13
If residential energy storage systems (RESSs) were to be utilized instead to realize
the results of P6, each house would require an approximate RESS capacity of 5.2 kWh,
or 1.83 MWh in total, based on the additional energy used in P6 during the “load-up”
control window provided in Table 3. With a typical Tesla Powerwall as a currently available
example RESS, which is rated at 13.5 kWh in capacity [
37
], around 136 out of the 351 sim-
ulated houses would need to adopt the technology in order to achieve the same effect.
Assuming a typical RESS round-trip efficiency of 86%, the RESSs would expend around
0.26 MWh in total
ed
as losses [
38
]. The
ed
increase of 1.63 MWh for P6 may be recuperated
over the following day(s) through specific controls, such as extended and more gradual
“shed” commands.
From the utility perspective, the “load up” during midday is timed such that the
energy generated by solar PV may be better utilized locally. Considering distribution
system configurations with high penetration levels of solar PV and utility-scale renewable
generation, improved BTM PV utilization by loading-up midday would also reduce total
associated carbon emissions even with increased ed, as it would essentially replace higher
carbon-emitting generation during the eliminated evening peak.
For the control and baseline cases at different levels of penetration, Table 4provides
the BTM PV utilization factor, which represents the percentage of solar PV generation
used BTM and not fed back to the utility. The generated energy begins to exceed the load
demand and is fed back onto the transmission system once solar PV adoption surpasses
45% of the distribution system. Each of the control cases improved BTM solar PV utilization
by approximately 3% to 8% across penetration levels. To further elaborate upon the features
of the co-simulation framework as well as the effects of the optimal VPP controls at both
the power system and individual occupant levels, P6, the ”best compromise”, is considered
the primary control case and discussed in further detail in the next section.
Table 4.
The BTM solar PV utilization for the baseline and control cases at different levels of penetration.
Pen./
Case Base NP P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
15% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
30% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
45% 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
60% 99.86 99.93 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
75% 91.36 98.30 99.05 99.05 99.05 99.18 99.12 98.98 98.91 98.98 99.05 99.05 99.05
90% 85.96 92.20 93.12 93.12 93.18 93.25 93.25 92.86 92.80 92.80 92.94 92.94 92.94
100% 84.27 88.96 89.57 89.71 89.58 89.38 89.45 89.22 89.22 89.29 89.09 89.10 89.10
6. Individual Building and Occupant Effects
As the individual buildings experience large changes in indoor temperature due to
quickly increasing outdoor ambient temperature and solar irradiance as the sun rises in the
morning, HVAC systems will use more energy to maintain indoor temperature setpoints
(Figures 6a, 8a and 13b). Once the transition into daytime is complete, the HVAC systems
enter normal operation to maintain the indoor temperature, which requires less energy,
as the change in outdoor temperature is significantly lower. As shown in Figure 6b, BTM
solar PV generation exacerbates the additional peak in the evening.
Sustainability 2023,15, 9433 16 of 20
The “load-up” and “shed” command types enact energy shifting rather than saving.
They are useful for reducing total system power peaks and shifting energy in time such
that the BTM renewable energy may be better utilized. HVAC systems will increase energy
use as the “load up” event decreases the setpoint temperature. This pre-cooling creates a
larger range for temperature to increase during “shed”, which allows for a more sustained
and significant drop in total system power during the on-peak time window (Figure 8a).
Upon control issuance, HVAC systems respond independently to newly assigned
indoor temperature setpoints that are based upon their own unique electric energy capaci-
ties and equivalent SOCs, which innately considers occupant comfort limits according to
ASHRAE standards [
34
]. Indoor temperatures change at different rates between houses due
to differing thermal properties and construction until equivalent SOC reaches a maximum
bound (Figure 8a,b). Since the equivalent SOC of the individual buildings is dependent
upon their estimated energy capacities, indoor temperatures may deviate from thermal
comfort bounds for a short time. Such violations may be mitigated by improving the energy
capacity estimation or by implementing tighter minimum and maximum SOC bounds.
(a) (b)
Figure 13.
Results for individual building. (
a
) Total energy use and (
b
) HVAC energy use only of the
baseline and P6 cases. Blue dots represent outliers in the box plot distributions.
7. Conclusions
A novel co-simulation framework is employed to optimize virtual power plant (VPP)
controls that leverage heating, ventilation, and air-conditioning (HVAC) systems as general-
ized energy storage (GES) to reduce a targeted distribution system power peak, while better
utilizing behind-the-meter (BTM) solar PV locally. The incorporation of HVAC system
phasing and gradual setpoint change functions effectively prevents power system peaking
or dropping from the start or completion of the controls. The minimization of on-peak
maximum power reduction (
pa,t=tep
) and possible resulting total day energy use increase
(ed) can compete in certain scenarios. Therefore, the optimization produces a Pareto set of
best designs with control settings that achieve a
pa,t=tep
of 24.45% to 28.75% and experience
an increase in
ed
of 7.98% to 10.73%. Each design yields improved BTM solar PV utilization
by approximately 3% to 8% because of the “load-up” timing.
From among the best control designs, P6 offers a “best compromise” with a
pa,t=tep
reduction of 0.32 MW (26.83%) and an
ed
increase of 1.63 MWh (8.42%). If residential
energy storage systems (RESSs) were to be utilized instead to realize the same results
as P6 with the HVAC system control only, they would require a combined capacity of
approximately 1.83 MWh. Assuming a typical RESS round-trip efficiency of 86%, the RESS
would expend around 0.26 MWh in
ed
as losses. In contrast, the 1.63 MWh increase in
ed
in P6 to achieve a more significant
pa,t=tep
may be recuperated over the following day(s)
through specific controls. For the P6 optimal control case, the individual building and
occupant effects are observed, including indoor temperature and equivalent state-of-charge
(SOC), which is made possible by the individual modeling of HVAC and building systems
Sustainability 2023,15, 9433 17 of 20
within the co-simulation framework. The ability to simulate individual effects in this
way, which enables their incorporation into distributed energy resource (DER) control
methodologies, is integral for the consideration of occupant thermal comfort during HVAC
system control events.
Author Contributions:
Conceptualization, E.S.J. and D.M.I.; Methodology, E.S.J. and R.E.A.; Software,
E.S.J. and R.E.A.; Validation, E.S.J. and R.E.A.; Formal analysis, E.S.J.; Investigation, E.S.J.; Resources,
D.M.I.; Writing—original draft, E.S.J.; Writing—review & editing, E.S.J., R.E.A., H.G. and D.M.I.;
Visualization, E.S.J.; Supervision, H.G. and D.M.I.; Project administration, D.M.I.; Funding acquisition,
D.M.I. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded in part by the Department of Energy (DOE) through the project
DEEE0009021 led by the Electric Power Research Institute (EPRI); Department of Education (DoEd)
through a GAANN Fellowship for Mr. Evan S. Jones; and by the National Science Foundation (NSF)
through a Graduate Research Fellowship under Grant No. 1839289 for Miss Rosemary E. Alden.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments:
The support of the Department of Energy (DOE) through the project DEEE0009021
led by the Electric Power Research Institute (EPRI) is gratefully acknowledged. The support received
by Evan S. Jones through a Department of Education (DoEd) GAANN Fellowship and by Rosemary
E. Alden through an NSF Graduate Research Fellowship (NSF) under Grant No. 1839289 is also
gratefully acknowledged. Any opinions, findings, and conclusions, or recommendations expressed in
this material are those of the authors and do not necessarily reflect the views of DOE, DoEd, and NSF.
Conflicts of Interest: The authors declare no conflicts of interest.
Nomenclature
The following main symbols and abbreviations are employed in this manuscript:
DERs Distributed energy resources
VPP Virtual power plant
BTM Behind-the-meter
PV Solar photovoltaic
HVAC Heating, ventilation, and air-conditioning
CTA Consumer Technology Association
CAPEX Capital expenditures
GES General energy storage
NNZE Near-net-zero energy
COP Coefficients of performance
SHGCs Solar heat gain coefficients
ML Machine learning
MLR Multiple linear regression
EPRI Electric Power Research Institute
SOC State-of-charge
U.S. United States of America
EV Electric vehicle
RESS Residential energy storage systems
ASHRAE American Society of Heating, Refrigerating and Air-Conditioning Engineers
NSGA-III Non-dominant sorting genetic algorithm
CC and FF DOE Central composite and full factorial design of experiments
tdIndoor temperature deviation
tsSetpoint temperature
tior θi(t)Indoor temperature
Sustainability 2023,15, 9433 18 of 20
hmHVAC mode of operation
hsHVAC on or off status
tdb Thermostat temperature dead-band
ttol Thermostat temperature tolerance
ph,kW HVAC electric active power
tin Indoor temperature of the next timestep
p fhPower factor of the HVAC system
ph,kvar HVAC electric reactive power
pvrRated power of the solar PV system
ppv Electric active power generated by the PV system
pt,kW and pt,kvar Total electric active and reactive power of the building
pb,kW and pb,kvar Electric active and reactive power of the baseload
γSolar irradiance
kpTemperature coefficient of maximum power
ηpv Efficiency considering losses due to numerous factors
tcTemperature of the PV cells
toOutdoor ambient temperature
tnNominal operating cell temperature
SOCh(t)Equivalent HVAC SOC
ec,h(t)Equivalent HVAC energy storage capacity
θmin,ma x Minimum and maximum indoor temperatures for user comfort
eh,cHVAC input electric energy required to reduce from θmax to θmin
pa,t=tep Total distribution peak power during evening period
edDaily increase in total energy use
nl,nx, and ndTotal number of distribution system lines, transformers, and loads
wa,l,iActive power losses over line number i
wa,x,jActive power losses at transformer number j
pa,d,iActive power demand at load number i
tep Moment of maximum power in the evening peak window
ntTotal number of time steps
P1–P11 Pareto front eleven points
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