Electric Water Heater Modeling for Large-Scale Distribution Power Systems Studies with Energy Storage CTA-2045 Based VPP and CVR

Abstract

As the smart grid involves more new technologies such as electric vehicles (EVs) and distributed energy resources (DERs), more attention is needed in research to general energy storage (GES) based energy management systems (EMS) that account for all possible load shifting and control strategies, specifically with major appliances that are projected to continue electrification such as the electric water heater (EWH). In this work, a methodology for a modified single-node model of a resistive EWH is proposed with improved internal tank temperature for user comfort modeling and capabilities for conservation voltage reduction (CVR) simulations as well as Energy Star and Consumer Technology Association communications protocol (CTA-2045) compliant controls, including energy storage calculations for “energy take”. Daily and weekly simulations are performed on a representative IEEE test feeder distribution system with experimental load and hot water draw (HWD) profiles to consider user comfort. Sequential controls are developed to reduce power spikes from controls and lead to peak shavings. It is found that EWHs are suitable for virtual power plant (VPP) operation with sustainable tank temperatures, i.e., average water temperature is maintained at set-point or above at the end of the control period while shifting up to 78% of EWH energy out of shed windows per day and 75% over a week, which amounts to up to 23% of the total load shifted on the example power system. While CVR simulations reduced the peak power of individual EWHs, the aggregation effect at the distribution level negates this reduction in power for the community. The EWH is shown as an energy constant load without consistent benefit from CVR across the example community with low energy reductions of less than 0.1% and, in some cases, increased daily energy by 0.18%.

Full text

Citation: Alden, R.E.; Gong, H.;
Rooney, T.; Branecky, B.; Ionel, D.M.
Electric Water Heater Modeling for
Large-Scale Distribution Power
Systems Studies with Energy Storage
CTA-2045 Based VPP and CVR.
Energies 2023,16, 4747. https://
doi.org/10.3390/en16124747
Academic Editor: Javier Contreras
Received: 12 May 2023
Revised: 6 June 2023
Accepted: 8 June 2023
Published: 15 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://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Electric Water Heater Modeling for Large-Scale Distribution
Power Systems Studies with Energy Storage CTA-2045 Based
VPP and CVR
Rosemary E. Alden 1, Huangjie Gong 2, Tim Rooney 3, Brian Branecky 3and Dan M. Ionel 1,*
1SPARK Laboratory, ECE Department, University of Kentucky, Lexington, KY 40506, USA;
rosemary.alden@uky.edu
2ABB USRC, Raleigh, NC 27606, USA; huangjie.gong@us.abb.com
3A. O. Smith Corporation, Milwaukee, WI 53224, USA; trooney@aosmith.com (T.R.);
bbranecky@aosmith.com (B.B.)
*Correspondence: dan.ionel@ieee.org
Abstract:
As the smart grid involves more new technologies such as electric vehicles (EVs) and
distributed energy resources (DERs), more attention is needed in research to general energy stor-
age (GES) based energy management systems (EMS) that account for all possible load shifting and
control strategies, specifically with major appliances that are projected to continue electrification
such as the electric water heater (EWH). In this work, a methodology for a modified single-node
model of a resistive EWH is proposed with improved internal tank temperature for user comfort
modeling and capabilities for conservation voltage reduction (CVR) simulations as well as Energy
Star and Consumer Technology Association communications protocol (CTA-2045) compliant con-
trols, including energy storage calculations for “energy take”. Daily and weekly simulations are
performed on a representative IEEE test feeder distribution system with experimental load and hot
water draw (HWD) profiles to consider user comfort. Sequential controls are developed to reduce
power spikes from controls and lead to peak shavings. It is found that EWHs are suitable for virtual
power plant (VPP) operation with sustainable tank temperatures, i.e., average water temperature is
maintained at set-point or above at the end of the control period while shifting up to 78% of EWH
energy out of shed windows per day and 75% over a week, which amounts to up to 23% of the
total load shifted on the example power system. While CVR simulations reduced the peak power
of individual EWHs, the aggregation effect at the distribution level negates this reduction in power
for the community. The EWH is shown as an energy constant load without consistent benefit from
CVR across the example community with low energy reductions of less than 0.1% and, in some cases,
increased daily energy by 0.18%.
Keywords:
virtual power plant; electric water heater; conservation voltage reduction; CTA-2045
standards; general energy storage
1. Introduction
Electricity is the art of equilibrium as the supply and demand have to match each
other at any given moment. Failing to do so will lead to voltage violation, power outage, or
even the damage of user appliances and facilities of the power system. The power demand
in a utility’s service area depends on seasonal and timely factors. It is highly predictable at
feeder level as the aggregated user behavior offsets the randomness from individual users.
In recent years, renewables have been penetrating the power system in a steady
trend [
1
]. The intermittent nature of renewable generation requires the grid operators to
respond quickly to provide the right amount of power through curtailment or increased
generation. Curtailing surplus generation is straightforward, unlike when the renewable
generation suddenly drops, the grid operators are left with no choice but to run the
Energies 2023,16, 4747. https://doi.org/10.3390/en16124747 https://www.mdpi.com/journal/energies

Energies 2023,16, 4747 2 of 22
expensive backup generators. Doing so might still not be enough when the gap left by
renewable generation is too large.
One potential solution is from the demand side by grouping residences as a virtual
power plant (VPP). A VPP offers deeper integration of renewables and demand flexibility
than traditional approaches. Residences in a VPP can share any local power generation and
offset the peak demand within the subsystem through smart controls. These neighborhood-
based VPPs also have several challenges, for example, the residences are located in the
same area, and therefore, all the local renewable generators experience the same external
weather conditions. As a result, all the local renewable generators in a VPP will have the
generation peak at the same time. When the penetration of renewable generation is high,
the VPP will be unable to retain the surplus local generation. Secondly, it is more likely the
residences in the same neighborhood have similar power usage pattern. When houses with
similar user pattern are aggregated, the peak power is more likely to be amplified.
Energy storage systems (ESSs) are a potential solution to mitigate these aggregation
effects on residential VPPs. Another application of energy storage is the assessment of
melting of phase change in latent heat storage technology [
2
]. Residential ESSs have
been shown to store the surplus VPP power generation and supply the peak demand [
3
].
Battery systems are expensive for both initial investment and maintenance, thus, will not
be discussed in this paper.
Instead, focus is placed on the adoption of ubiquitous electrical water heaters (EWHs)
as energy storage. The water tank provides large thermal mass and, when controlled as
energy storage, there is more flexibility for the homeowners to better adjust to market
prices, such as time of use (T.O.U.), and for utilities to implement VPP. Alternative heating
element designs in EWHs have been considered to improve the thermal energy storage
and dispersion of heated water in the tank [
4
]. Detailed thermo-hydraulic studies have
also been conducted to quantify the natural convection patterns of water in the EWH
tank [
5
] and support regions of water remaining cooler underneath the heating element, as
accounted for in this paper through the proposed modified single node model.
Through smart controls, such as Consumer Technology Association protocol 2045
(CTA-2045) for demand response (DR) [
6
], water heaters can avoid being turned ON during
the peak hours by preheating or postponing the heating process. When local renewable
generation is available, water can be preheated and the water heater can perform as
thermal ESS. When the heating process is postponed, the standby loss reduces because
the water in the tank has less thermal energy to lose, and—in the case of heat pump water
heaters—recovery efficiency increases by sending colder water to the compressor unit [
7
]. A
second method for energy storage controls considered in this paper is conservation voltage
reduction (CVR) for EWH, where the supply voltage to the appliance is reduced in an effort
to mitigate load and provide grid services, such as load shifting and energy savings.
A research gap remains as some previous studies did not consider that some homes
might not be able to participate in the DR due to the tank temperature and hot water draw
(HWD) of that home, i.e., that if tank temperatures dropped below a comfort limit to ensure
hot water, the home would remove itself from the controls. Additionally, the grid impacts
are different even for the same homes when they are connected to different nodes in the
distribution system. Previous studies usually left the temperature inside the water tank
different from its original status after control [
8
]. Such control is not sustainable as the water
temperature might be too low in the beginning of the next day. User behavior typically
has a week-long cyclical pattern. Previous studies for EWH control usually focused on the
daily performance and did not consider long-term controls.
The problems addressed by this paper are within the smart grid transition specifically,
the development of VPP controls to improve grid resilience and reliability. A main difficulty
with VPP controls is the security for data transfer and interoperability of residential ESS
devices. This paper aims to solve this problem with the development of industry communi-
cation protocol compatible VPP controls for one of the major residential appliances and
ESSs, the EWH. To do so, another problem must be solved, the development of an ultra-fast

Energies 2023,16, 4747 3 of 22
and satisfactorily accurate EWH model methodology that is scalable to large numbers of
homes on a residential electric power distribution system, which also has realistic load, hot
water draw (HWD) profiles, and user comfort limits.
This paper includes the following contributions, such as a modified ultra-fast single-
node EWH model suitable for large-scale power system studies with improved thermal
flexibility estimation while considering user comfort; a methodology for evaluating CVR
for resistive EWHs; daily CVR simulations on the IEEE 123 bus benchmark distribution
system [
9
] with experimental residential load and HWD profiles; development of a VPP
control framework compatible with short-term and long-term simulations, which considers
water temperature for user comfort; two case studies for daily and weekly CTA-2045 based
VPP on the benchmark distribution system; and the development of sequential controls
for peak mitigation using CTA-2045 standards. The structure of this paper is as follows.
A technology review of smart controls and previous studies in Section 2, methodology
formulation in Section 3, description of benchmark system used in all simulations in
Section 4, and CVR and CTA-2045 smart control daily and weekly simulation results in
Sections 5–7. Furthermore, included is a discussion for sequential control development in
Section 8followed by our conclusions.
2. Technology Review
The EWH is an important component in the achievement of effective home energy
management [
10
,
11
]. The storage capacity of water heaters is determined by the volume
of the water tank, and the the total electricity used by EWHs is determined by the user
behavior, i.e., the thermal energy reduction from hot water leaving the tank should be
almost equal to the electricity used for heating, given a near 100% insulation. The large
thermal mass of storage tanks in water heaters enables flexibility in the timing of heating
processes. An accurate and ultra-fast model is needed to understand the impact on the
hot water storage temperature when the controls are modified. The modeling of these
water heaters needs to consider climates zones, conditioned and unconditioned spaces, hot
water usage profiles, and water heater types, such as gas storage, gas tankless, condensing
storage, electric storage, heat pump, and solar water heaters [12].
The model should also be flexible to represent water heaters with different properties,
i.e., tank volume and rated power. When adopted in a transactive and large-scale systems,
the trade-off between accuracy and computational complexity of a EWH model must be
considered. Specifically, Mukherjee et al. considered a partial differential equations (PDE)
model, which could be, in principle, more accurate [
13
]. They also reach the conclusion that
the model is infeasible for large-scale evaluation studies, such as the IEEE 123 bus system
due to excessively long computational times. They recommended that much faster one-
node models could be employed as an alternative because they exhibit similar consumption.
For this reason, a modified single-node EWH model is proposed in this paper for large-scale
simulations of EWH smart controls.
Previous studies into smart controls for EWHs show that two concerns should be kept
in mind when implementing water heater controls for a community. The first concern is
also the bottom line for field deployment—the domestic hot water temperature should
never be too low [
14
]. Secondly, the limited access to real-time data—due to either hardware
limit or privacy concerns—is a significant obstacle [
15
]. Additionally, a control method
for large water tanks might not work properly for small water tanks—the temperature for
water inside the small tank might drop or increase too fast before the goals of control are
achieved [16].
Successful studies into EWH smart controls include a centrally adapted control model
which avoided the peak power by scheduling each EWH, thereby reducing the peak load
of 1.05 kW/EWH to 0.4 kW/EWH [
17
] and a deep Q-networks algorithm for water heaters
under T.O.U pricing that showed electricity cost savings up to 35% [
18
]. Other recent
examples of EWH controls to reduce grid impact from electric vehicles (EV) show that

Energies 2023,16, 4747 4 of 22
thermal energy storage is viable to improve grid operation, given the smart technology to
control them is in place [19,20].
Furthermore, planning the temperature inside the water tank could reduce the en-
ergy usage by up to 11% without compromising the user comfort [
21
]. In practice, the
temperature in the water tank is stratified and therefore, hard to measure. This is miti-
gated by viewing the EWH as general energy storage (GES) capable of following Energy
Star and ESS calculations, such as equivalent state-of-charge (SOC) and “energy take” as
proposed in this work. An advantage of this modeling approach is that the EWH may
be integrated into unified ESS controls through the CTA-2045 protocol. Previous reports,
including field deployment in [
15
,
22
], show that industry has interest in developing further
the CTA-2045 communication protocol and there is support for widespread adoption. A
preliminary case study by this same group of authors using CTA-2045 for GES-based
controls of a large group of EWHs in a modified IEEE-123 bus system [
23
] is detailed in
this paper to address the bouncing effect of spikes in power following control periods with
sequential implementation.
As for the second type of EWH controls considered in this paper, traditional imple-
mentation of CVR was to reduce the voltage across an entire distribution feeder, thus,
lowering the power to the entire residential load [
24
–
26
]. In these works, CVR is evaluated
using comparison-based, regression-based, synthesis-based, and simulation-based meth-
ods. Stochastic evaluations are employed to analyze the impact on feeders and select ones
for the highest benefit. Another study suggests that heavily loaded and higher voltage
feeders should be targeted for the deployment of CVR as it had the most benefits [
27
] and
recent capacitor placement and optimization techniques are underdevelopment to support
these CVR efforts [
28
]. A detailed review is provided for CVR modeling approaches; the
potential for use with low-income communities; and the steps to complete CVR studies,
building or updating circuit modeling, calibrating water heater models, simulating with
and without controls, and comparing for savings [29].
With the increasing penetration of DERs, one approach has been to adapt CVR studies
to include Volt/Var controls and assess the influence of sudden changes in power [
30
,
31
].
Another approach has been to apply CVR to select appliances or loads for maximum impact.
In these studies, it is important to consider the category of load because constant current
and resistance loads show the best results and constant power or energy loads have with
very little response to CVR in terms of energy reduction [
32
]. While EWH’s are constant
energy loads, there has been interest in CVR for them as they make up a significant portion
of residential load. An example of research into CVR at the appliance level demonstrated
reduced power from switching between 220 V to 110 V supply for EWHs in partnership
with PNNL [33] across an entire day.
Another previous case study of 1000 EWH shows a 14% reduction in ZIP load, when
the voltage was changed from 124 V to 116 V [
34
]. One issue with this study and other ZIP-
model-based simulations for CVR is that it is common for the ZIP modeling to stop heating
before tank temperature is reached as the same stop time is maintained with reduced
power, which does not ensure the same amount of energy is transformed from electricity to
thermal energy [
35
]. Within this paper, in addition to smart control development based
on communication standards, benchmark CVR simulations are completed with a physics-
based EWH model validated against experimental results to show that EWH load is energy
constant and will not have significant reduction in energy and why.
3. Ultra-Fast Model for EWH and Energy Storage Employing CBECC-Res Typical
Water Draw Profiles
While detailed studies into complex EWH thermal modeling focuses on the number of
thermal nodes accounted for [
36
] and thermal accuracy comparisons have been made [
37
]
for single EWHs, benchmark satisfactory models for large-scale simulations are still needed.
Mukherjee et al. found that advanced physics-based EWH models, such as partial differ-
ential equations (PDE), are complex and require significant computational power, which

Energies 2023,16, 4747 5 of 22
makes them unfit for smart grid community modeling with hundreds of homes in co-
simulation or with real-time purposes [
13
]. They assert that thermally stratified, two-node,
and single-node models serve as ultra-fast alternatives for estimations of power and grid
impact with small variance in the consumption results from the more advanced methods at
the community level. Therefore, a modified single-node model has been selected with the
lowest number of parameters for large-scale simulations to estimate the impact of smart
controls on the electric distribution system, while considering natural water convection
patterns.
The single-node model, in the form of a gray-box RC thermal model, has been vali-
dated against experimental resistive EWH results from smart control testing Of CTA-2045
based controls conducted by EPRI and NREL [
38
]. A modification for improved thermal
flexibility estimation is proposed in this work. Satisfactory simulation of smart controls
based on CTA-2045 communication standard and energy take limits for heating element
operation employing the proposed model are visualized in Figure 1, specifically “normal
operation” without controls and “load-up” cases. During load-up periods additional en-
ergy is accepted from the grid and stored—as opposed to “shed” cases where reduced
energy is drawn from the grid and stored energy used to meet the HWD.
(a) (b)
Figure 1.
Normal (
a
) and “load-up” (
b
) numerical simulation of an EWH satisfactorily modeled
based on hot water draw profiles from the CTA-2045 experimental testing by EPRI and NREL [
38
].
The proposed modified single node model is employed with Energy Star-based heating element
controls through the “energy take”.
The water tank volume,
V
(m
3
); density of water constant,
ρ
(993
kg
m3
); specific heat
capacity of water,
cp
(4179
J
kg◦C
); the average temperature in the water tank at time
t
with
time steps of one minute,
θT
(
◦C
); and a thermal region coefficient,
η
(0.9), are used to
calculate the thermal energy stored in the EWH, EW(t), following:
EW(t) = V·ρ·η·cp·θT(t). (1)
The thermal region coefficient has been proposed to account for typical heating ther-
modynamics of the water tank. The tank volume underneath the heating element does
not warm up or store a significant amount of energy and may be neglected in the energy
calculations to improve the modeling of the thermal flexibility and internal tank tempera-
ture with a single node model. The individual internal tank temperature and EWH power
are calculated considering affects from input electric power, standby heat loss, outlet flow
mixing with cold water, and hot water draw (HWD) activities.
4. Benchmark Distributions System with Representative HWD and Load
To unify the CTA-2045 smart controls of the EWH with GES so that a single energy
management system for thermal and electric energy storage may be employed, Energy
Star calculations are required for the energy a storage system may accept before reaching
capacity at a given time, i.e., “energy take”. For the EWH, the maximum capacity is

Energies 2023,16, 4747 6 of 22
determined based on the temperature in reference to the maximum temperature of hot
water allowed per user settings. It is proposed to use the initial tank temperature as
the reference point for large studies to avoid challenges associated with user input data
collection and allow for the adaption of the maximum tank temperature as part of the
control development. The energy take, ET,W(t), is calculated as
ET,W(t) = EW,i(0)−EW(t), (2)
where the
EW,i(
0
)
is the thermal energy stored per EWH at the start of the simulation.
The energy take per EWH calculated in this manner may be compared to control limits,
QT,min (t
,
HWD)
,
QT,max (t
,
HWD)
to determine the status of the heating element as follows:
S(t) = 




1, if S(t−1) = 0 & ET,W(t)≥QT,max(t,HWD)
0, if S(t−1) = 1 & ET,W(t)≤QT,min (t,HWD)
S(t−1), otherwise,
(3)
where
S(t)
is the status of the EWH, either ON at binary one or OFF at binary 0, and
HWD
is the hot water draw at that time,
t
. Using these controls, the CTA-2045 controls may be
applied by associating QT,min (t,HW D),QT,max (t,HWD)limits to DR operations.
The single-node model has also been expanded to include behind-the-meter (BTM)
voltage adjustments to the EWH as part of community-wide CVR testing. The power draw
of the EWHs is reduced through reduction in voltage supplied to the device. The adjusted
EWH power, PEW H (t), is calculated following these voltage changes as
PEWH (t) =
Ir
z}|{
Pr
Vr
·
VH(t)
z }| {
CVRj(t)·Vr, (4)
where
Pr
,
Vr
, and
Ir
are the rated power, voltage, and current;
CVRj(t)
is a coefficient to
adjust the voltage based on percent reduction,
j
; and
VEWH(t)
is the voltage experience by
the EWH. CVRj(t)is defined by:
CVRi(t) = (1−j
100 ). (5)
The gray-box RC model incorporates the
PEWH (t)
to calculate the change in tank
temperature as follows:
CdθT(t)
dt=S(t)·Pr(t)·CVRi−1
R[θT(t)−θA]−ρcpW(t)[θT(t)−θW,C], (6)
where
θT(t)
is the tank temperature,
θA
is the temperature of the ambient air;
θW,C
is
the temperature of cold inlet water; and
R
,
C
are the equivalent thermal resistance and
capacitance of the EWH tank. In this formulation, both the impact of the CTA-2045 and
CVR controls on the tank temperature and energy storage are considered. This proposed
single node model has been integrated into a co-simulation framework for VPP operation of
hundreds of homes through CTA-2045 and CVR control case studies in this paper (Figure 2).

Energies 2023,16, 4747 7 of 22
Figure 2.
The proposed single node EWH model for large-sale simulation with electric power
distribution systems has been integrated into a testbed framework for the CVR and CTA-2045 based
VPP simulations.
Within this paper, the proposed methodology has been applied to a benchmark distri-
bution system (Figure 3a), the IEEE 123 bus [
9
], in OpenDSS using the Python plug-in to
establish sustainable EWH controls based on industry standards for DR. In a previous paper
by the authors [
23
], including preliminary CTA-2045 controls case studies, the original
load across all nodes was replaced with a total of 353 residential load profiles, each with a
maximum power usage of 10 kW or less from the SET project [
39
], a large experimental
dataset of more than 5000 homes. Only profiles with typical residential daily usage of 20 to
40 kWh and no missing data points are selected. This work has been expanded to include
the described modifications to the single-node model for improved characterization of the
thermal energy flexibility and CVR controls. The simulation length has also been increased
to include week-long studies, each day with a unique profile from the SET homes for both
weekday and weekend types.
For the control simulations, each home is equipped with a 5.5 kW smart EWH with a
rated power, a tank size of 50 gal., and the initial water temperatures in the tanks are evenly
distributed between 46 and 57
◦
C. The equivalent thermal resistance of the water heaters
was assumed to be 1400
◦
C/kW. These parameters were selected to emulate a physical
A.O. Smith resistive EWH used in studies by NREL and EPRI for preliminary testing of
CTA-2045 Standard commands, as described in Section 3.
Realistic HWD profiles are assigned to each home from the 2019 CBECC-Res large
dataset [
40
]. Profiles from homes with different numbers of bedrooms (1–5) and occupancy,
as well as day of the week, are used to build a representative community for testing. An
example HWD profile with subsequent EWH power and temperature are visualized in
Figure 3b. The
QT,min (t
,
HWD)
,
QT,max (t
,
HWD)
limits for controlling the heating element
in each EWH per CTA-2045 case are described in Table 1. The energy take limits were
calculated to ensure a heating or cooling time around five minutes for the realistic load-up
and 15 min for the maximum load-up case using the the proposed single node model that
was validated against a physical EWH. Further evaluation of these limits for alternate
VPP peak power reduction performance over larger or shorter time periods is discussed in
Section 8.

Energies 2023,16, 4747 8 of 22
(a)(b)
Figure 3.
Modified IEEE 123 bus testfeeder populated with filed measured residential loads from
the SET project and EWH power from model-in-the-loop objects, (a). Example 1R1C thermal model
results for EWH power based on CBECC Res Project hot water draw (HWD) profile is illustrated. The
proposed heated tank volume assumption of an
η
of 0.9 based on typical thermal areas with respect
to the heating element, (b).
Table 1.
The three cases considered in this study for load shifting using CTA-2045 commands and
Energy Star energy storage calculations.
Cases Event Energy Take [Wh] Max Cap. [Wh]
(Thermal)
Min Max
Baseline Normal (Water
draw dependent) 0
300: >= 1 GPM 300
600: >=0.3 GPM 600
900: <0.3 GPM 900
No load-up Shed 1000 1500 1500
Realistic load-up load-up −300 * 0 1800
Shed 1000 1500
Max load-up load-up −1000 * 0 2500
Shed 1000 1500
* Temperatures higher than the set-point are represented by a negative sign, specifically for a set-point of 125
◦
F,
energy take values of −300 and −1000 correspond to internal tank temperatures of 128 and 133 ◦F.
5. Conservation Voltage Reduction (CVR) EWH Simulations
CVR simulations have been conducted to assess power shifting and energy savings
capabilities by reducing the per unit (p.u.) voltage to the EWH at each home in the
residential benchmark system. Normal operation controls based on the energy take of each
EWH for GES modeling is employed to determine the status of the EWH heating elements,
and the EWH voltages are reduced through CVR during DR periods. Voltages were varied
from 0.90 to 1.05 p.u. by increments of 0.05 p.u. All cases are compared to rated voltage
of 1.0 p.u. or 120 V. The representative synthetic community was used with profiles from
a Wednesday and were assumed able to receive a CVR command signal from the utility.
CVR periods of 7 to 10 and 17 to 20 military time were selected to reduce common work
week peak time load. This is especially important as these times may become frequent EV
charging windows as people prepare to leave for work, and utilities would benefit from
reduced loads from other appliances.
During the CVR simulations, the status of operation (ON/OFF), tank temperature,
and energy take were considered for the individual homes. An example of individual home
EWH power temperature and energy intake are illustrated in Figure 4during the CVR
morning time window.

Energies 2023,16, 4747 9 of 22
(a)(b)
Figure 4.
Individual home’s power, energy take (
a
), and temperature (
b
) in each case. The power
magnitude and speed the energy take changes with the voltage. The EWH remains on for longer time
the lower the power drops because the same amount of energy is required to heat the water to the set
temperature.
The magnitude of the power changes and the rate at which the energy take and
temperature adjusts is also affected by the voltage change, i.e., the EWH remains ON for
longer as the power decreases to make up for the slower change in tank temperature. This
demonstrates that the energy, visibly seen as the area under the power curve, remains
constant to physically heat the water to the desired temperature and energy usage range for
human comfort. In previous CVR case studies, this effect was not captured as a modeling
insufficiency with ZIP parameters and power is shown to stop at the same time regardless
of supplied voltage and decreased power [
35
]. This is indicative that the requirements
of the tank to meet the set comfort temperature point were not adequately considered in
previous studies. The controls proposed in this CVR simulation are based on the individual
energy usage of the EWHs and address this research gap.
The aggregate total power as simulated at the main feeder and calculated community
EWH power is illustrated in Figure 5with the 0.95 p.u. case in green to represent the lowest
allowed voltage per USA grid operation standards. The CVR periods are visualized by grey
shading and since the change in power is so small, zoomed in plots of EWH power during
the CVR time windows are provided in Figure 6. Peak load from the EWH is reduced from
the 1.0 p.u. case during portions of the time window, while at other times the power is
increased. The peak power demand for the EWH actually increased in the 0.95 Vp.u. case
by 0.47%. This indicates that CVR for EWH may not be successful at reducing aggregate
peak power for the EWHs across a community consistently. The peak power was not
reduced due to longer heating times as more EWHs are heating during spikes in demand as
compared to the baseline case (Figure 7). In summary, CVR may only be successful to shift
peak across an hour or more time window, if the human behavior-based HWD profiles are
spread out enough that the CVR does not cause additional overlap between EWH heating
times in response to comfort limits.
Other factors that may influence the impact of the CVR are the rated power of the
water heaters and their individual thermal resistivity. To test the effects of these factors, the
CVR simulations were repeated with 4.5 kW rated power and increased thermal resistivity
at 1500
◦
C/kW (Figure 8). In this scenario, the CVR successfully reduces the peak load
in the morning at 9:30 for all cases from 1.05 down to 0.90 p.u.; though in line with the
previous scenario, the power over the entire window is inconsistent for reductions. The
number of additional houses requiring heating was still affected if the CVR was able to
reduce the aggregate power, as seen in Figure 9.

Energies 2023,16, 4747 10 of 22
(a)(b)
Figure 5.
Aggregate active power on the IEEE 123 bus test-feeder at the main feeder (
a
) and total
EWH power from the community (
b
) has little affect in three CVR cases, where the BTM voltage of
the EWHs was changed to 1.05, 0.95, or 0.90 p.u. All DR periods in this paper are visualized by grey
shading and green color was assigned to Vp.u.0.95 case as this is the lowest voltage within typical
allowed range in the U.S.
(a) (b)
Figure 6.
Enlarged CVR periods in the morning (
a
) and afternoon (
b
) shows that the CVR completed
on individual EWH does not always translate to power reduction at an aggregate level as longer
heating times at lower powers may cause more EWH to be on at a time.
(a) (b)
Figure 7.
The hour surrounding the peak power in the morning (
a
) and evening (
b
). The percentage of
additional houses operating in comparison to the Vp.u.1.0 case shown by discrete points corresponds
to times when the aggregate power does not reduce. An example time when CVR does reduce the
power occurs at 9:15 a.m. when the number of houses operating is not increased.
In both cases, the energy across the community was shown to be minimally affected
by the CVR, and this is further explained by the individual EWHs remaining in the ON
operation for longer as the voltage p.u. decreases (Figure 10).

Energies 2023,16, 4747 11 of 22
(a) (b)
Figure 8.
Morning (
a
) and afternoon (
b
) CVR simulation repeated with higher thermal resistivity,
1500
◦
C/kW, and lower rated power, 4.5 kW, to show that many parameters affect the success of
CVR at the aggregate level. EWH peak load changes of
−
9.99,
−
5.00, and 3.98% in the 0.90, 0.95, and
1.05 V p.u. cases. Overall, power reductions are not consistent across the DR period like the previous
scenario.
(a) (b)
Figure 9.
A closer look at the hour surrounding the peak in the morning (
a
) and evening (
b
) shows
that while a reduction happens at 9:20 a.m. when the load is the highest, it is not consistent across
the time window. It also is affected an increased percentage of EWHs heating per minute, thus,
mitigating the affects of CVR at the community level.
Additionally, the EWHs heat for approximately 11 min longer in the 4.5 kW case than
the 5.5 kW case. The timing of the EWH’s switching ON and OFF affects how the peak
is shifted and not all combinations lead to peak shifting success at the community level.
Overall, adjusting the rate of power and thermal resistivity to represent smaller, more
thermally efficient EWHs did not lead to more effective power sifting or energy savings.
From our simulations, further CVR studies BTM would be more impactful on loads where
the amount of energy required to satisfy the consumer’s comfort limits does not remain
constant, such as cases with dimmer lights where the energy does not have to be recovered.
The impact on the total energy used by the EWH is not indicative that energy will be
reduced as all fluctuations in energy use are less than 0.02%. Additionally, more energy is
required when the voltage to each EWH is the lowest (Table 2). The CVR factors, a metric
commonly used to evaluate the effects of the voltage controls, is very low. As a result,
the authors can not conclude that the total energy required by the utility is significantly
changed by CVR on EWHs in this benchmark study. Since EWH’s require a constant
amount of thermal energy to heat and maintain the hot water in the tanks across the
community, reducing instantaneous active power does not change the amount of demand
for electrical energy.

Energies 2023,16, 4747 12 of 22
Figure 10.
The number of minutes the EWHs spend heating across the day reduces between p.u.
cases as the voltage increases as expected. On average, it is also lower for the 5.5 kW simulation (
top
)
than the 4.5 kW simulation (
bottom
). For example, in the Vp.u.0.95 case heating for 51 and 62 min,
respectively, as visualized by the green lines.
Table 2.
Energy over the simulation day for the EWHs shows minimal reduction in energy, i.e., less
than the anticipated 1–4% of energy reductions from CVR [29].
CVR Case Aggregate EWH
Energy [MWh]
Average
Individual
EWH Energy
[kWh]
Daily Energy
Reduction [%] CVR Factor [-]
V p.u. 1.05 1.639 1.139 0.04 −0.008
V p.u. 1.00 1.640 1.138 - * - *
V p.u. 0.95 1.638 1.137 0.07 0.014
V p.u. 0.90 1.643 1.140 −0.18 −0.018
* Base case that others are compared to for energy reduction.
6. Daily VPP for a Full Day Schedule
Virtual Power Plant (VPP) applications of EWHs have potential for load shifting when
considering CTA-2045 commands and the ability to preheat the water stored. Three case
studies were conducted on the same time period of 24 h as the CVR simulations, i.e., a
Wednesday during the summer as described in Section 4. Control windows for “load-up”
were selected to pre-heat the water before the “shed” commands, specifically from 3 to 4 at
night and 15–16 during the afternoon. Shed windows were selected from 7 to 10 a.m. and
17–20 to alleviate peak time stress from before work and return home activities.
The operation of the heating elements in the community are controlled by the energy
usage limits described in Table 1. These values were selected based on the length of time
it takes to heat the water from the initial value to the temperature corresponding to the
energy take limit, i.e., approximately five minutes to heat to
−
300 Wh and 15 min to
heat to
−
1000 Wh. The water temperatures are 128 and 133
◦
F, both of which are well
below the maximum temperature of 165
◦
F that was considered in previous studies with
a mixing valve in a residential setting [
22
]. The higher the maximum setpoint selected,
the more thermal energy is stored in the tank and the longer the EWHs will need to
operate. This leads to higher spikes during the day and less chance of mitigation through
sequential controls.
During the load-up period, a CTA-2045 standard command is sent to each EWH in the
community to decrease the energy take limit,
QT,min (t
,
HWD)
, and increase the thermal
energy stored. This will cause all the EWH to start at once to raise the equivalent SOC of the
VPP across the community. In Figure 11, the aggregate power spikes to more than double

Energies 2023,16, 4747 13 of 22
the original base load in the distribution system at the start of the load-up period. The
EWH load is subsequently decreased during the shed period as the water was pre-heated
to decrease the energy take of the equivalent VPP thermal battery. At the end of the shed
control period, the power spikes again as the EWHs turn ON to return the energy take and
temperature to the normal operation range.
(a)(b)
(c)(d)
Figure 11.
The CTA-2045 “load-up” case resulted in large spikes of power of more than twice the
typical peak load at the main feeder and in total EWH power, (
a
,
b
), respectively. Large spikes are also
present the following shed periods. The average energy take, (
c
), and internal tank temperature, (
d
),
of the load-up and max load-up cases returns within 4
◦
C, and the temperature of the water tanks do
not violate comfort limits.
While the power is mitigated during the shed time period, the large spikes from the
load-up and following the end of the shed are not suitable for deployment and may cause
issues to the utility for meeting the sudden brief spike in demand. Sequential controls are
proposed to accomplish the same shed in power incrementally. A systematic search was
completed to select a batch size of 24 houses, each deployed every 4 min to phase in for all
homes in an hour. Other combinations of batch size and phase-in time are feasible with
drawbacks such as slower reaction time to shed commands and longer load-up periods.
Further discussion is provided in Section 8.
Throughout the simulation, the state of each individual EWH’s energy usage and
subsequent internal water temperature is considered (Figure 12). The order of the cases in
the subplots is as follows, baseline, realistic load-up, no load-up, and maximum load-up.
The sequential controls are visible in Figure 12a, and the temperatures across the community
are seen increasing during the load-up and falling during the shed. The number of houses
with average temperatures below 35
◦
C increase in all three cases as compared to the
baseline. This is acceptable in the controls as the EWHs are set to kick on during shed if the
energy take limits are violated to reduce the disruption to hot water availability as much as
possible, and the users are assumed to be compensated for more relaxed service during
shed times.

Energies 2023,16, 4747 14 of 22
(a)(b)
(c)(d)
Figure 12. The sequential controls reduce power spikes by three times at the main feeder and in the
total EWH power, (
a
,
b
), respectively. They do not affect the temperature, (
c
), or energy usage, (
d
).
During shed times, the EWH power is curtailed and the sequential controls stop swing back spikes
following the event.
One of the contributions of this study is that the CTA-2045 commands are evaluated
and simulated at each individual EWH in the community through object-oriented program-
ming and class variables. The sequential operation of the EWHs across the community
as well as their internal tank temperatures are visualized in Figure 13. The red dots are
outliers in the distribution of temperatures that are beyond the quartile range at that time
(t), and should not be read as comfort violations. In this approach, each tank evaluates its
internal energy tank level and opts into the community DR events as possible per comfort
standards for realistic community impact analysis and individual home status assessments.
The energy take distributions and the limit,
QT,min (t
,
HWD)
, for EWH heating operation
to turn ON are visualized by the boxplot with blue lines in Figure 14. The outliers above
the maximum limit are the EWHs that still require heating during the shed. Through this
method, human comfort expectations to have hot water on demand are ensured. Additional
analysis of temperature and energy usage selection in the controls is described in Section 8.
The voltage across the system is unaffected by the controls as seen close up in Figure 15
with no voltage violations. The developed sequential controls reduced the spike caused
by the load-up to below the original base peak in the morning, making it more feasible
from a grid impact perspective. The EWH power demand was successfully shifted from
peak times to the load-up times selected at night and mid-afternoon. The temperature and
energy usage levels were returned to normal operation ranges at the end of the period. The
maximum load-up case serves as a test of the ability of the EWH to shift the load from
additional pre-heating. In comparison to the no load-up case where 21 MWh, 48.3%, of
demand is shed, the maximum case reduces the load during shed periods by 34 MWh,
78.9%, while the realistic load-up reduces it by 28.6 MWh, 65.5%. This indicates that the
pre-heating of water is conducive to further load shifting grid services, and, thus, in future
simulations, the no load-up case will not be considered.

Energies 2023,16, 4747 15 of 22
(a)(b)
Figure 13.
The status of the individual EWHs are visualized, (
a
), and the individual temperatures
in the tanks are depicted in a boxplot form based on the distribution with outliers shown as red
stars, (
b
). All EWH operated during the load-up periods and operation was postponed during shed
events. Following the shed, the EWH turn ON with the same spacing as the load-up, successfully
mitigating a bounce back spike.
(a)(b)
Figure 14.
The energy take per EWH (
a
) and bus voltages (
b
) across the community are visual-
ized as boxplots based on the distribution at that 30 min increments. The maximum energy take,
QT,max (t
,
HWD)
, per Table 1is depicted the solid blue line, this indicates that outliers above the
limit in shed periods required heating. No voltage violations were found across the buses in the
distribution system.

Energies 2023,16, 4747 16 of 22
Figure 15.
An enlarged visualization of the voltages during the CTA-2045 controls. No violations
found as a result of the controls.
7. Long-Term EWH VPP Feasibility Case Study
To assess the capability of the controls across a long-term period, the IEEE 123 bus
system was modified to co-simulate five distinct work-day and two weekend-day time
series profiles for residential load and HWD from experimental datasets, as described in
Section 4. The simulation starts on a Wednesday to encompass the affects of the weekend
in the middle of the week. Within this setup, a representative synthetic community is
employed with randomness from human behavior included.
The no load-up case was dropped and replaced with a maximum load-up every two
days to represent a program where users have agreed to more comfort violations in return
for an incentive. The control window times were kept constant from the daily case at time
windows of 3–4, 15–16 and 7–10, 17–20 for load-up and shed, respectively. Aggregate
power, EWH power, temperature, and energy take are visualized in Figure 16. Sequential
controls were used for each DR window to prevent large spikes in power. Through out the
simulation week, 194.2, 172.8, and 167.6 MWh of energy were shed during times of high
congestion and strain on the distribution system in the max load-up, max load-up every
two days, and realistic load-up cases, respectively. This represented 75, 66, and 64% of the
EWH load and 23, 21, and 20% of the total load during shed windows.
The realistic load-up case returns the temperature to be equal to the baseline case,
representing sustainability of the controls in terms of comfort and ability to meet the HWD
demand while providing grid services (Figure 17). The maximum load-up and maximum
load-up every two days cases leave the average temperature higher than the baseline but
within 2
◦
C. The total energy used to heat the water increases with the controls by 0.4, 1.3,
and 1.6%, which is a low amount justified by grid operation improvements from substantial
load shifting. The load-up periods that drive this energy increase could be aligned with
times of renewable energy generation as well.
Employing energy take to determine the heating element status of the EWH is success-
ful at maintaining acceptable tank temperatures and providing grid services. Using the
benchmark system and procedure within this work, further development of the timing of
controls is possible, including formal optimization of load-up and shed times to reduce cost
to the utility or increase renewable energy generation. The framework allows for long-term
control studies for smart controls while EWH modules opt into the shed period based on
internal tank temperature calculations.

Energies 2023,16, 4747 17 of 22
(a)
(b)
Figure 16.
The CTA-2045 controls applied to a week long case simulation period starting on a
Wednesday in the summer. The aggregate total (
a
) and EWH power (
b
) is consistent across days of
the work week, and load is successfully reduced during shed times.
(a)
(b)
Figure 17.
The VPP average temperature (
a
) in the tank recovers following the controls over the
course of the week and average energy take is visualized (
b
). Little variation occurs between weekend
and work-day effects.

Energies 2023,16, 4747 18 of 22
8. Discussion
Two scenarios of CVR across the VPP, including three cases each, were simulated from
with 1.05 to 0.90 p.u. voltages levels. The potential for power shifting at the aggregated
level and energy savings were not found in these studies on a representative distribution
system due to constant thermal energy requirements to maintain temperature comfort
limits. The aggregate power was also not reduced as the diversity in heating times across
the community was reduced as individual EWHs took longer durations to heat with lower
voltage. Further studies with CVR for particular appliances would be more impactful with
loads that do not require constant energy to maintain comfort limits and user expectations.
8.1. Sequential Control Development
The sequential controls proposed in this paper required a management system be in
place to coordinate the controls. The assumption in this work is that each home is equipped
with a smart EWH to receive signals for the controls. The energy management system
would need to select homes to be placed into a batch and select the order of the batches to
be deployed. Both of these decisions could be decided through optimization to minimize
impact on the distribution system.
Additionally, the size of batches and the energy usage limits could be optimized to
improve the controls. In this section, the effects of adjusting the batch size, spacing, and
energy take limits are assessed for their impacts on the benefits of sequential controls. In
Figure 18a, three cases with varied energy usage limits are compared. The batch size of
24 houses and 4 min deployment time is maintained from the VPP scenarios in previous
sections. The more thermal energy stored in the tank during load-up, the higher the spike
in power and strain on the distribution system from the controls could be. For example, the
Lim.
−
4000 Wh case is close to the true maximum allowed energy usage corresponding to
165
◦
F, results in significantly higher load-up spikes over 1500 kW even with the sequential
controls. To reach this high energy take limit,
QT,max (t
,
HWD)
, the EWHs must remain ON
for over an hour, which means no EWH turn OFF before the one hour load-up period is
complete and longer control periods would be necessary to spread out the additional spike.
This control pattern with more extreme controls may be useful with low batch size across
an entire night and utilities would have to gauge consumer adoption and incentive rates.
In Figure 18b, the energy usage limits were returned to Table 1maximum load-up
case, and the load-up period in the morning was increased from one hour to six hours. The
batch size and deployment time are varied in three cases, 1 min 1 house, 8 min 40 houses,
and 70 min 70 houses. Overall, the smaller the batch size, the lower and more constant the
increase in demand during load-up periods would be. The batch size needs to be balanced
with the length of the load-up period and the deployment time. For example, in the 1 min
1 house case, where a signal is sent to a house every minute, a low constant power draw
is seen in the load-up period. This would be an ideal case except the response speed in
this case was too slow to reduce the power during shed, so two sets of batch sizes and
deployment spacing may be necessary for load-up and shed periods.
For the second case with 40 houses deployed every 8 min, all houses are phased-in
within a shorter period of 3 h. The load-up power was higher than the baseline peak load
and was inconsistent as houses finished heating in
∼
5 min before others were deployed. In
a community with different EWH types, it would be more difficult to select a deployment
speed with out this effect. The 70 houses per 70 min case was included to show a deploy-
ment time and batch size that were not aligned as all houses finish before the next fleet,
resulting in evenly spaced spikes every hour, which would be more difficult for the utility
to meet. Further investigation of the controls per utilization purpose would be needed with
targeted objectives and constraints for distribution system and utility. The concept behind
the sequential smart controls has been demonstrated to highlight the potential for future
development.

Energies 2023,16, 4747 19 of 22
(a) (b)
Figure 18.
Three load-up cases are compared to show that the energy take limits directly affect the
magnitude of the power spikes (
a
). Three more examples are shown (
b
) to compare effects of the
batch size and spacing period of signals, and a longer control window is required for more spaced
out controls.
8.2. Large-Scale Energy Storage and Global Applications
The CTA-2045 based VPP simulations in this paper indicated that a common appliance
in homes across the globe, the EWH, may be used to improve resiliency of the grid system
without affecting comfort standards. Across the globe, EWH are projected to increase from a
global market value of USD 23 to 38 billion with growth drivers in North and Latin America,
Europe, Asia Pacific, and MEA [
41
], and, thus, are an excellent candidate for global VPP
control development for use of thermal storage. By design, the CTA-2045 Standard was
selected for the simulations because it is intended to facilitate interoperable VPP controls
in large-scale deployment across appliances from different manufacturers as found in
the U.S. and around the world. As part of the CTA-2045 industry standard, a modular
communications interface is defined to streamline communication methods and formatting
so that any demand response system may connect to any type of residential appliance.
The widely compatible RS-485 serial communication method is specified in a physical
communications module that attaches to the appliance itself, and serial opcodes are also
defined for the VPP commands to “load-up” the energy and “shed” to decrease the energy
stored. Then, per the protocol, common methods, such as Wi-Fi, ZigBee, etc., may be used
for secure data transport to and from any energy management system. In this paper, the
VPP simulations follow these protocol definitions and serve to represent the benefits of the
interoperable communications in communities with high user participation to motivate
further large-scale physical adoption.
For example, in the case studies on the IEEE 123 bus system, the peak power was
reduced by up to 23% at the power system level when the EWHs participated in the VPP
operation. The proposed sequential deployment prevented many EWHs from being turned
ON at the same time during pre-heating or after the controls. Up to 78% of EWH energy
in shed periods was shifted while maintaining the water temperature on this benchmark
distribution system. The co-simulation framework developed to simulate the CTA-2045
controls, EWH responses, and residential load on the distribution system is compatible with
other larger systems, such as the IEEE 8500 node test feeder. The testbed is object oriented
and the initialization of different distribution systems in OpenDSS in the U.S. or globally
could be used to assess the benefits of the VPP from the EWH energy storage formulation
and controls before infrastructure investment on the CTA-2045 physical modules and
energy management system.
9. Conclusions
The modified single node model of an electric water heater (EWH) proposed in the
paper provides ultra-fast results for the water temperature and energy storage estimates
supporting large-scale simulations. Based on the model, a methodology for conservation

Energies 2023,16, 4747 20 of 22
voltage reduction (CVR) and smart controls was applied to a community of EWHs operating
as a virtual power plant (VPP), and the impacts on the power system level were evaluated.
The capability of the VPP to shift peak demand while considering user comfort was
quantified on the benchmark IEEE 123 bus feeder, which was modified with experimental
residential load from a large field demonstration and hot water draw profiles from CBECC-
RES national survey. The CVR was tested in EWHs from 1.05 p.u. to 0.90 p.u. and results
show that reduced power, which was caused by reduced voltage, prolonged the heating
process of individual EWHs, leaving more EWHs operating during peak times. As a
consequence, the CVR did not reduce the aggregate power consistently throughout the
duration of the controlled event, nor did it reduce the daily energy demand.
Author Contributions:
Conceptualization, R.E.A., H.G., T.R., B.B. and D.M.I.; methodology, R.E.A.
and H.G.; software, R.E.A. and H.G.; validation, R.E.A., H.G., T.R., B.B. and D.M.I.; formal analysis,
R.E.A.; resources, H.G., T.R. and B.B.; writing—original draft preparation, R.E.A. and H.G.; writing—
review and editing, H.G., T.R., B.B. and D.M.I.; visualization, R.E.A.; supervision, D.M.I. All authors
have read and agreed to the published version of the manuscript.
Funding:
This material is based upon work supported by the National Science Foundation Grad-
uate Research Fellowship under Grant No. #1839289. Any opinion, findings, and conclusions or
recommendations expressed in this material are those of the authors and do not necessarily reflect
the views of the National Science Foundation.
Acknowledgments:
The support received by Rosemary E. Alden through a National Science Foun-
dation (NSF) Graduate Research Fellowship under Award No. #1839289 is gratefully acknowledged.
The support of the A.O. Smith Corporation and of the University of Kentucky L. Stanley Pigman
Chair in Power endowment is also gratefully acknowledged.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. Electricity in the United States Is Produced (Generated) with Diverse Energy Sources and Technologies. Technical Report, USA
Energy Information Administration (EIA). Available online: https://www.eia.gov/energyexplained/electricity/electricity-in-
the-us.php#:~:text=Most%20electricity%20is%20generated%20with%20steam%20turbines%20using,largest%20source%E2%8
0%94about%2038%25%E2%80%94of%20U.S.%20electricity%20generation%20in%202021 (accessed on 6 June 2023).
2.
Du, Z.; Liu, G.; Huang, X.; Xiao, T.; Yang, X.; He, Y.L. Numerical Studies on a Fin-foam Composite Structure Towards Improving
Melting Phase Change. Int. J. Heat Mass Transf. 2023,208, 124076. [CrossRef]
3.
Gong, H.; Rallabandi, V.; McIntyre, M.L.; Hossain, E.; Ionel, D.M. Peak Reduction and Long Term Load Forecasting for Large
Residential Communities Including Smart Homes With Energy Storage. IEEE Access 2021,9, 19345–19355. [CrossRef]
4.
Gómez, M.; Collazo, J.; Porteiro, J.; Míguez, J. Numerical Study of the Thermal Behaviour of a Water Heater Tank with a
Corrugated Coil. Int. J. Heat Mass Transf. 2018,122, 574–586. [CrossRef]
5.
Han, F.; Feng, D.; Xin, P.; Wang, W. Thermo-hydraulic Characteristics of Thermal Interface Induced by Natural Convection in
Water Tank with Internal Heat Source. Int. J. Heat Mass Transf. 2023,211, 124212. [CrossRef]
6.
CTA. CTA Standard: Modular Communications Interface for Energy Management; Technical Report; Consumer Technology Association
(CTA): Arlington, VA, USA, 2020.
7.
Larson, B.; Kvaltine, N. Laboratory Assessment of Demand Response Characteristics of Two CO
2
Heat Pump Water Heaters; Ecotope Inc.:
Seattle, WA, USA, 2015.
8.
Liu, Q.; Bao, Y. Scheduling and Control of Massive Electric Water Heaters Based on Equivalent Energy Storage Model. In
Proceedings of the 2021 IEEE 5th Conference on Energy Internet and Energy System Integration (EI2), Taiyuan, China, 22–24
October 2021; pp. 1928–1933. [CrossRef]
9.
IEEE PES Test Feeder: 123-BUS Feeder. Available online: https://cmte.ieee.org/pes-testfeeders/resources/ (accessed on
6 June 2023).
10.
Bandyopadhyay, A.; Conger, J.P.; Webber, M.E. Energetic Potential for Demand Response in Detached Single Family Homes in
Austin, TX. In Proceedings of the 2019 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, USA, 7–8 February
2019; pp. 1–6. [CrossRef]
11.
Abbas, A.O.; Chowdhury, B.H. A Stochastic Optimization Framework for Realizing Combined Value Streams From Customer-Side
Resources. IEEE Trans. Smart Grid 2022,13, 1139–1150. [CrossRef]
12.
Maguire, J.; Fang, X.; Wilson, E. Comparison of Advanced Residential Water Heating Technologies in the United States; Technical Report;
National Renewable Energy Lab. (NREL): Golden, CO, USA, 2013.

Energies 2023,16, 4747 21 of 22
13.
Mukherjee, M.; Bhattarai, B.; Hanif, S.; Pratt, R. Electric Water Heaters for Transactive Systems: Model Evaluations and
Performance Quantification. IEEE Trans. Ind. Inform. 2022,18, 5783–5794. [CrossRef]
14.
Porteiro, R.; Chavat, J.; Nesmachnow, S. A Thermal Discomfort Index for Demand Response Control in Residential Water Heaters.
Appl. Sci. 2021,11, 48. [CrossRef]
15.
Obi, M.; Metzger, C.; Mayhorn, E.; Ashley, T.; Hunt, W. Nontargeted vs. Targeted vs. Smart Load Shifting Using Heat Pump
Water Heaters. Energies 2021,14, 7574. [CrossRef]
16.
Maguire, J.; Roberts, D. Deriving Simulation Parameters for Storage-Type Water Heaters Using Ratings Data Produced from the Uniform
Energy Factor Test Procedure; Technical Report; National Renewable Energy Lab. (NREL): Golden, CO, USA, 2021.
17.
Ritchie, M.J.; Engelbrecht, J.A.A.; Booysen, M.J. Centrally Adapted Optimal Control of Multiple Electric Water Heaters. Energies
2022,15, 1521. [CrossRef]
18.
Amasyali, K.; Munk, J.; Kurte, K.; Kuruganti, T.; Zandi, H. Deep Reinforcement Learning for Autonomous Water Heater Control.
Buildings 2021,11, 548. [CrossRef]
19.
Moradzadeh, M.; Abdelaziz, M. Optimal Demand Control of Electric Water Heaters to Accommodate the Integration of Plug-in
Electric Vehicles in Residential Distribution Networks. In Proceedings of the 2020 IEEE Canadian Conference on Electrical and
Computer Engineering (CCECE), London, ON, Canada, 30 August–2 September 2020; pp. 1–6. [CrossRef]
20.
Moradzadeh, M.; Abdelaziz, M. Reducing the Loss of Life of Distribution Transformers Affected by Plug-In Electric Vehicles
Using Electric Water Heaters. In Proceedings of the 2019 IEEE Canadian Conference of Electrical and Computer Engineering
(CCECE), Edmonton, AB, Canada, 5–8 May 2019; pp. 1–5. [CrossRef]
21.
Ritchie, M.J.; Engelbrecht, J.A.; Booysen, M.J. Practically-Achievable Energy Savings with the Optimal Control of Stratified Water
Heaters with Predicted Usage. Energies 2021,14, 1963. [CrossRef]
22.
CTA-2045 Water Heater Demonstration Report including a Business Case for CTA-2045 Market Transformation; Technical Report; BPA
Technology Innovation Project 336; Northwest Energy Efficiency Alliance: Portland, OR, USA, 2018.
23.
Gong, H.; Jones, E.S.; Jakaria, A.H.M.; Huque, A.; Renjit, A.; Ionel, D.M. Large-Scale Modeling and DR Control of Electric Water
Heaters With Energy Star and CTA-2045 Control Types in Distribution Power Systems. IEEE Trans. Ind. Appl.
2022
,58, 5136–5147.
[CrossRef]
24.
Wang, Z.; Begovic, M.; Wang, J. Analysis of Conservation Voltage Reduction Effects Based on Multistage SVR and Stochastic
Process. In Proceedings of the 2014 IEEE PES General Meeting Conference & Exposition, National Harbor, MD, USA, 27–31 July
2014; p. 1. [CrossRef]
25.
Wang, Z.; Wang, J. Time-Varying Stochastic Assessment of Conservation Voltage Reduction Based on Load Modeling. IEEE Trans.
Power Syst. 2014,29, 2321–2328. [CrossRef]
26.
Wang, Z.; Wang, J. Review on Implementation and Assessment of Conservation Voltage Reduction. IEEE Trans. Power Syst.
2014
,
29, 1306–1315. [CrossRef]
27.
Schneider, K.P.; Fuller, J.C.; Tuffner, F.K.; Singh, R. Evaluation of Conservation Voltage Reduction (CVR) on a National Level; Technical
Report; Pacific Northwest National Lab. (PNNL): Richland, WA, USA, 2010.
28.
Jones, E.S.; Jewell, N.; Liao, Y.; Ionel, D.M. Optimal Capacitor Placement and Rating for Large-Scale Utility Power Distribution
Systems Employing Load-Tap-Changing Transformer Control. IEEE Access 2023,11, 19324–19338. [CrossRef]
29.
McNamara, M.; Feng, D.; Pettit, T.; Lawlor, D. Conservation Voltage Reduction/Volt Var Optimization EM&V Practices; Technical
Report; Climate Protection Partnerships Division in EPA’s Office of Atmospheric Programs, DNV GL, The Cadmus Group:
Waltham, MA, USA, 2017.
30.
Zhao, J.; Wang, Z.; Wang, J. Robust Time-Varying Load Modeling for Conservation Voltage Reduction Assessment. IEEE Trans.
Smart Grid 2018,9, 3304–3312. [CrossRef]
31.
Singh, S.; Babu, P.; Singh, S.P. Impact of Combined Operation of CVR and Energy Storage System in Distribution Grid. In
Proceedings of the 2018 20th National Power Systems Conference (NPSC), Tiruchirappalli, India, 14–16 December 2018; pp. 1–6.
[CrossRef]
32.
Ellens, W.; Berry, A.; West, S. A Quantification of the Energy Savings by Conservation Voltage Reduction. In Proceedings of
the 2012 IEEE International Conference on Power System Technology (POWERCON), Auckland, New Zealand, 30 October–2
November 2012; pp. 1–6. [CrossRef]
33.
Jia, R.; Nehrir, M.H.; Pierre, D.A. Voltage Control of Aggregate Electric Water Heater Load for Distribution System Peak Load
Shaving Using Field Data. In Proceedings of the 2007 39th North American Power Symposium, Las Cruces, NM, USA, 30
September–2 October 2007; pp. 492–497. [CrossRef]
34.
Pinney, D. Costs and Benefits of Conservation Voltage Reduction; National Rural Cooperative Association: Arlington, VA, USA, 2013.
35.
Lovas, T.; Pinney, D.; Miller, C. Costs and Benefits of Conservation Voltage Reduction. CVR Warrants Careful Examination; Technical
Report DE-0E0000222; Cooperative Research Network, National Rural Electric Cooperative Association (NERCA), Department of
Energy (DOE): Washington, DC, USA, 2014.
36.
Ritchie, M.; Engelbrecht, J.; Booysen, M. Impact of Node Count on Energy-optimal Control of Stratified Vertical Water Heaters in
Smart Grid Applications. In Proceedings of the 2022 IEEE PES/IAS PowerAfrica, Kigali, Rwanda, 22–26 August 2022; pp. 1–5.
[CrossRef]
37.
Xu, Z.; Diao, R.; Lu, S.; Lian, J.; Zhang, Y. Modeling of Electric Water Heaters for Demand Response: A Baseline PDE Model.
IEEE Trans. Smart Grid 2014,5, 2203–2210. [CrossRef]

Energies 2023,16, 4747 22 of 22
38.
Thomas, C. Performance Test Results: CTA-2045 Water Heater; Technical Report 3002011760; Electric Power Research Institute
(EPRI): Palo Alto, CA, USA, 2017.
39.
TVA Smart Community. Available online: https://www.tva.com/environment/environmental-stewardship/epa-mitigation-
projects/smart-communities (accessed on 6 June 2023).
40.
CBECC-Res Compliance Software Project. Available online: http://www.bwilcox.com/BEES/cbecc2019.html (accessed on 6
June 2023).
41.
GMI. Electric Water Heater Market Size, by Product (Instant, Storage), by Application (Residential, Commercial [College/University, Office,
Government/Military]), by Capacity, COVID-19 Impact Analysis & Global Forecast, 2022–2030; Technical Report GMI680; Global
Market Insights (GMI): Selbyville, DA, USA, 2022.
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